# Do Proxies for Informed Trading Measure Informed Trading? Evidence from Illegal Insider Trades

Do Proxies for Informed Trading Measure Informed Trading? Evidence from Illegal Insider Trades
Ahern, Kenneth, R
2020-06-15 00:00:00
Abstract This paper exploits hand-collected data on illegal insider trades to provide new evidence on the ability of a host of standard measures of illiquidity to detect informed trading. Controlling for unobserved cross-sectional and time-series variation, sampling bias, and strategic timing of insider trades, I find that when information is short-lived, only absolute order imbalance and effective spread are statistically and economically robust predictors of illegal insider trading. However, when information is long-lasting, insiders strategically time their trades to avoid illiquidity, and none of the standard measures considered are reliable predictors, including bid-ask spreads, order imbalance, Kyle’s λ, and Amihud illiquidity. (JEL D53D82G12G14K42) Received: March 14, 2019; Editorial decision: February 18, 2020 by Editor Thierry Foucault. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. Identifying reliable proxies for information asymmetry from observable market data “ranks as one of the most important goals of empirical microstructure research” (Hasbrouck, 2007, p. 53). To achieve this goal, finance scholars have developed a battery of proxies for information asymmetry based on measures of illiquidity, such as bid-ask spread decompositions (Madhavan, Richardson, and Roomans 1997), order imbalance (Easley et al. 1996), and price impact (Glosten and Harris 1988). Though the theory is compelling and these proxies are widely used, there is little credible empirical evidence that the proxies are valid. This is because validating the proxies requires the rare opportunity to directly observe informed trading. Given the importance of information asymmetry in finance, empirically assessing which proxies of informed trading are valid and under what circumstances is crucial. This paper provides new evidence on the validity of a host of proxies for informed trading in a unique setting: illegal insider trades. Though illegal insider trading does not represent all informed trading, it does represent trading that is of great importance to regulators and market participants. Moreover, data on illegal insider trading help to overcome a number of empirical obstacles. First, the legal documents in insider trading cases provide direct observations of the timing of information flows and trades. Second, the trades documented in illegal insider trading cases are, by definition, based on material nonpublic information, not speculation or public information. Third, the data include observations of informed trading in a wide range of firms and events. Finally, the longevity of information varies in the data, allowing a comparison of short-lived versus long-lasting information. The observations of insider trading are hand-collected from all insider trading cases filed by the Securities and Exchange Commission (SEC) and the Department of Justice (DOJ) between 2009 and 2013, as collected in Ahern (2017). The sample includes 312 different firms in 410 different insider trading events over the period 1996 to 2013. Mergers and acquisitions are the most common events in the sample, followed by earnings announcements, news about drug regulation, and other announcements about operations, security issuance, and financial distress. The median sample firm is comparable to the median firm on the NYSE, though firms range from recently public firms to the largest firms in the economy, including Microsoft, Procter & Gamble, and Berkshire Hathaway. Using intraday data from the NYSE Trades and Quotes (TAQ) database, I calculate the following widely used measures of illiquidity: quoted and effective spreads, price impact, absolute order imbalance, Kyle’s λ, and parameters from the spread decomposition of Madhavan, Richardson, and Roomans (1997) (MRR). Using daily data, I calculate the illiquidity measure of Amihud (2002). I then test whether these measures can predict the presence of illegal insider trading. There are two primary obstacles to using illegal insider trading data to test illiquidity measures: omitted variables and sampling bias. First, informed trading does not occur in a random set of firms and dates. This means that omitted variables could cause a spurious relationship between illiquidity and informed trading. For example, high-tech firms might have higher illiquidity for reasons unrelated to information asymmetry and at the same time, high-tech firms might also have greater insider trading. Similarly, omitted variables could drive both the time-series pattern of illiquidity and insider trading. To address these concerns, I use event fixed effects, event-day fixed effects, and time-varying firm-level noise trading to absorb omitted variables. The event fixed effects control for all time-invariant properties of the firm and event, such as the type of event, the firm’s industry, financial policies, and geographic location. The event-day fixed effects control for the average runup of informed trading and illiquidity before the public announcement of the event. Daily noise trading controls for fluctuations in uninformed trading volume. A related concern is strategic timing by informed traders. The theoretical model of Collin-Dufresne and Fos (2016) predicts that insiders with long-lived information will strategically trade on days with high levels of noise trading volume, generating a negative relationship between insider trading and illiquidity. To address this concern, I exploit the variation of inside traders’ lead time before their private information becomes public. Given a limited number of trading opportunities, as lead times become shorter, inside traders have less freedom to strategically time their trades to coincide with noise trades. Thus, relative to strategically timed trades, the relationship between illiquidity measures and insider trading will be more positive when lead times are shorter. The second obstacle to using illegal insider trading data is sampling bias. If regulators detect illegal insider trading using only the same measures of illiquidity that I study, then my results may not generalize to a wider population. To address this concern, I first show that regulators detect insider trading using many methods, of which abnormal market data is just one. Second, I use empirical proxies to measure the likelihood that the SEC used market data to detect insider trading in a particular case. The proxies are based on the network structure of inside traders and the involvement in a case by regulatory agencies that monitor the stock market for abnormal patterns. My first results show that in tests that do not control for strategic timing or sampling bias, none of the measures of illiquidity are statistically correlated with insider trading. This result is consistent with endogenous trading by rational inside traders. When I control for strategic timing, the results are strikingly different. I find that the greater is the urgency of trading, the stronger is the positive correlation between measures of illiquidity and insider trading, as predicted. When urgency is high, a 1-standard-deviation increase in the quoted bid-ask spread is associated with an increase in the volume of insider trading by 35% of the average volume, compared to a 2.5% increase when the urgency of trading is at its mean. Other measures, including the effective spread and Kyle’s λ, have similar economic magnitudes. I also verify that when urgency is higher, the volume of insider trading is less correlated with the volume of noise trading. However, controlling for sampling bias nullifies the predictive power of most standard measures of illiquidity. Only the effective spread and order imbalance remain significantly correlated with insider trading, controlling for the urgency of trading. Additionally, because the effective spread has significantly greater predictive power in cases that were likely detected by abnormal market patterns, it suggests that regulators use a detection mechanism correlated with bid-ask spreads, but not with order imbalance. These results may help regulators improve their detection methods. Finally, to provide a ranking of the predictive power of illiquidity measures, I run a horse race in a multivariate regression that includes all measures simultaneously. Controlling for the correlation across measures, effective spread and order imbalance are the only significant predictors of insider trading. These results are statistically significant even using higher thresholds from Bonferroni corrections to account for the multiple comparisons problem in this type of study. Had I found none of the measures were reliable predictors of insider trading, it would be easy to argue that the tests were underpowered. Because I find strong results for some of the measures and not others, it suggests that the tests have sufficient power to detect meaningful relationships. These results are robust to a number of potential concerns. Effective spread and order imbalance remain reliable predictors of insider trading after controlling for prescheduled events, positive events, events occurring in the second half of my sample period, firm size, and trader sophistication. Order imbalance tends to be unaffected by these controls, while effective spread is more sensitive. This paper’s results have a number of important implications. First, though some illiquidity measures have the power to predict insider trading, they are only predictive when information is short-lived and traders cannot strategically time their trades to avoid illiquid markets. This means that in real time, these measures have limited usefulness for other traders to detect informed trades. At the same time, the results indicate that market makers have some ability to adjust quotes on a daily basis in response to informed trading, consistent with the finding that order imbalance is a reliable predictor of insider trading. Second, though the urgency of trading is not typically known in real time, with the benefit of hindsight, these measures can help regulators identify instances of illegal insider trading. Finally, for academics who want to measure informed trading, this paper shows that some proxies are more useful than others, but only in certain contexts. 1. Prior Literature This paper follows a diverse literature that investigates the validity of measures of informed trading using indirect observations of informed trades, rather than direct observations, as used in this paper. These include institutional holdings and R&D expenses (Van Ness, Van Ness, and Warr 2001), analyst coverage (Kelly and Ljungqvist 2012), family-firms (Anderson, Reeb, and Zhao 2012), geographic proximity (Coval and Moskowitz 2001), and retail short-sellers (Kelley and Tetlock 2017). Some papers have used direct observations of informed trading for single trading events (Cornell and Sirri 1992; Chakravarty and McConnell 1999) or one class of events (Petchey, Wee, and Yang 2016), but typically do not control for strategic timing or sampling bias. A few recent papers use direct observations of informed trading, while accounting for strategic timing. Collin-Dufresne and Fos (2015) show that Schedule 13d filers who privately increase their ownership in target firms before publicly disclosing their ownership positions, strategically time their purchases to avoid illiquidity. Thus, they find a negative correlation between measures of illiquidity and informed trading when activists do not face time constraints. Consistent with my hypothesis, the correlations become more positive when activists have shorter horizons. Finally, similar to this paper, Kacperczyk and Pagnotta (2019b) (KP) use data on illegal insider trading to test measures of informed trading. Though KP study a similar question and use similar data as this paper, our two papers come to different conclusions. Without conditioning on urgency, KP finds a strong negative correlation between insider trading and measures of illiquidity. They conclude that illiquidity measures are predictive of insider trading, albeit with the opposite sign than expected. Instead, this paper shows that without conditioning on urgency, illiquidity measures are uncorrelated with insider trading. In addition, this paper shows that only some variables are reliable predictors under certain circumstances, whereas KP argue that nearly all liquidity variables are predictive. The difference in results between this paper and KP is likely caused by differences in research designs. KP use firm-level fixed effects and a control period of 15 days per event to establish normal liquidity values. I use event-level fixed effects (which subsume firm fixed effects), and I use a longer control period of over 100 days per event. Thus KP’s design permits more omitted variables and uses control samples with artificially low variance which could cause the significant results in KP. Both papers consider urgency and sampling bias, but KP runs tests in subsamples and hints at minor differences in outcomes, while I run unified tests on the entire sample with interaction terms and provide statistical tests of significant differences. In addition, I account for the multiple comparisons problem with Bonferroni corrections, whereas KP do not. KP use a slightly longer sample period than I do, and they study illiquidity in options markets. I explicitly do not study options in this paper to avoid additional endogenity problems caused by traders who strategically avoid options to reduce detection by regulators. Finally, KP do not formally rank the usefulness of illiquidity measures, whereas I run a horse race to test which illiquidity measures are the most reliable indicators of insider trading. The Internet Appendix discusses the differences between this paper and KP’s in more detail. 2. Research Design In an ideal research setting, informed trading is directly observable by the researcher and occurs randomly across firms and time. In this setting, if illiquidity is consistently higher or lower on firm-days with informed trading than firm-days without informed trading, we could conclude that informed trading causes illiquidity to change. In reality, informed trading is not randomly assigned to firms or days and is not directly observable. Below, I discuss how I address these two limitations. 2.1 Nonrandom selection of firms and dates The firms in which informed traders invest are not randomly assigned in the real world. First, informed trading requires private valuable information. The existence of valuable information varies across firms in nonrandom ways. For instance, information that a firm is a takeover target is valuable, but firms are not randomly assigned to be takeover targets. Second, the spread of information is not random. For instance, some firms might more heavily rely on outside contractors who are more likely to spread private information. Because informed trading is not randomly assigned to firms, an omitted variable could cause both illiquidity and informed trading. For example, high-tech firms might have a high likelihood of informed trading because they are more likely to be takeover targets. At the same time, high-tech firms also might be more illiquid for reasons unrelated to informed trading, such as a lack of institutional investors. Thus, omitted variables could generate a spurious relationship between illiquidity and informed trading. To control for omitted variables, I use event fixed effects, where an event is a specific piece of information, such as a takeover or earnings announcement. The event window includes the period from 120 days to 2 days before the public announcement of the information. Any characteristic that does not change over the 119 days in the event window is absorbed in the fixed effects. Such characteristics include the type of information and time-invariant characteristics of the firm, such as industry, firm policies, or location. Thus, event fixed effects subsume firm fixed effects. Event fixed effects also normalize time-varying liquidity measures by their average values to produce abnormal liquidity. Second, in reality, the timing of informed trading is not random. For example, private information about an upcoming earnings announcement might spread faster as the announcement date approaches, leading to increased informed trading. At the same time, illiquidity might increase as investors respond to earnings announcements of peer firms. Therefore, both illiquidity and informed trading could increase as an announcement date approaches, creating a spurious relationship. To control for nonrandom timing of informed trading, I use event-day fixed effects. The event-day fixed effects are dummy variables for each event day from –120 to –2. These event-day fixed effects normalize each event’s time-series pattern by the average time-series pattern across all events.1 The final concern with nonrandom assignment is the strategic timing of informed trading. Collin-Dufresne and Fos (2016) show that if private information is long-lived and noise trading is time varying, informed investors will choose to trade when liquidity is high to limit the price impact of their trades. This will cause a negative relationship between illiquidity and insider trading and a positive relationship between insider trading and noise trading. Therefore, in all of my tests, I control for time-varying daily noise trading volume. Altogether, event fixed effects, event-day fixed effects, and time-varying factors absorb a wide range of potential omitted variables. To further control for the strategic timing of insider trading, I create two variables to measure the urgency of trading. When urgency is high, informed investors have less freedom to strategically time their trades to coincide with noise traders and the timing of trades is closer to the idealized experiment of random assignment of trading days. The first measure, Daily urgency, is a daily measure of the time remaining before the private information is publicly announced. In particular, Daily urgencyτ=−1τ for event dates τ=-120,…,-2. Daily urgency increases as the public announcement date gets closer to the current date. Because Daily urgency is identical across all events, it is perfectly correlated with the event-day fixed effects, though an interaction with daily illiquidity is not. However, unlike fixed effects, Daily urgency can be interpreted with an economic meaning. Therefore, the first econometric model I estimate is as follows: Insider tradingιτ=α+β·Illiquidityιτ+ϕ·Daily urgencyτ+ψ·Illiquidityιτ×Daily urgencyτ+γ1Noiseιτ+γ2Noiseιτ×Daily urgencyτ+κι+ειτ, ∀ι∈I and τ=-120,…,-2,(1) where κι are event fixed effects and Noiseιτ is the logged volume of noise trading in event-firm ι on day τ, defined below. A positive estimate of ψ indicates that illiquidity is more positively related to insider trading when trading is more likely to occur randomly in time. A negative estimate of γ2 indicates that when the lead time to the public announcement is shorter, insiders are less likely to time their trades to coincide with noise traders. A drawback to Daily urgency is that it does not account for the lead time from the day of the original information leak to the day of the public announcement. For example, Daily urgency at τ=−4 is the same whether the original leak happened at τ=−5 or τ=−20 . However, when the original leak occurs with a long lead time, strategic traders may have already timed their trades to reduce their price impact. To overcome this limitation, I also use a stricter measure of urgency, Event urgency, that is the inverse of the lead time between the original leak and the public announcement. This is stricter because it is measured for the entire event, rather than at a daily level. If we let τ¯ι be the event-date of the original leak in event ι, then Event urgencyι=−1τ¯ι. Because Event urgency is constant across all event-dates for a given event, it is perfectly correlated with the event fixed effects. However, the interaction with daily illiquidity and noise trading is not. Therefore, I estimate the following econometric model, Insider tradingιτ=α+β·Illiquidityιτ+ϕ·Illiquidityιτ×Event urgencyι+γ1Noiseιτ+γ2Noiseιτ×Event urgencyι+κι+δτ+ειτ, ∀ι∈I and τ=-120,…,-2,(2) where δτ are event-day fixed effects. As above, the coefficient ϕ in Equation (2) measures the difference-in-differences marginal effect of illiquidity on insider trading when the real-world setting is closer to the ideal randomized setting, where insiders have less ability to endogenously time their trades. 2.2 Nonrandom selection of observations The second major deviation of my setting from the ideal setting is that I cannot directly observe informed trading. Instead, I must rely on illegal insider trading cases filed by regulators. While these data provide exceptional detail on individual trading behavior, sampling bias could limit the generalizability of my results. To better understand how sampling bias could affect my results, consider two different firm-days, one with illegal insider trading and one without. Regulators’ initial detection methods could (1) correctly identify the firm-day with insider trading (true positive), (2) incorrectly identify the firm-day with insider trading (false negative), (3) correctly identify the firm-day without insider trading (true negative), and (4) incorrectly identify the firm-day without insider trading (false positive). The negative firm-days (both true and false) will not be investigated further by regulators. The positive firm-days will be investigated further to build legal cases, but the false positives will be subsequently rejected for lack of evidence. Therefore, only true positive firm-days in which the regulators detect actual insider trading will be made publicly available. Though only true positive firm-days are identified by regulators, I also need to identify true negative firm-days to serve as a comparison group. Because regulators do not specifically identify true negative firm-days, I make the following assumption: for a given corporate event, firm-days not identified by regulators as insider trading days are true negative firm-days in which no insider trading occurred. This is a weak assumption for two reasons. First, regulators have an incentive to fully investigate all firm-days before an event if they find any evidence of illegal insider trading. Finding other trades by the same individual or connected traders will increase the importance and credibility of the case. It is also easier for regulators to find other traders through social connections, once one trader has been identified (Ahern 2017). Second, this is a weak assumption because if undetected insider trading occurs in my sample, the difference in illiquidity between identified insider trading days and control days will be be smaller, causing lower statistical significance of my results. This attenuation will occur regardless of the sign of the coefficient, assuming that the misclassification is random. If the misclassified observations are systematically different than the correctly classified observations, the estimates will be biased. I address this concern next. Though I can use noninsider trading days within each of the sample event’s time-series as a benchmark, the sample of events provided by regulator case files may not be representative of all events with insider trading. This concern is larger if the detection method used by regulators only detects a certain type of stock market behavior. Thus, insiders who choose a strategy to avoid this behavior would be omitted from the sample. To address this concern, it is important to understand how regulators detect illegal insider trading. If regulators use a variety of methods to detect insider trading, the resultant sample is more likely to be representative of all insider trading. For brevity, I provide a short summary of the regulatory process below. For a longer description, see (Ahern, 2017, internet appendix). Illegal insider trading is detected by a number of different entities, including the SEC, the DOJ, the Financial Industry Regulatory Authority (FINRA), and the Federal Bureau of Investigation (FBI). Each entity relies on various detection methods including computerized monitoring of trading behavior, tips submitted by the public, and traditional investigation methods. FINRA has the primary responsibility for monitoring abnormal market behaviors. In 2009, FINRA created the Office of Fraud Detection and Market Intelligence (OFDMI), and began using a computer program called Securities Observation News Analysis and Regulation (SONAR) that monitors news feeds, SEC filings, and market data to identify suspicious trades. If SONAR flags an event as suspicious, human investigators at FINRA collect additional information from trading records. If the investigations produce sufficient evidence, FINRA refers the case to the SEC.2 In addition to referrals from FINRA, the SEC initiates its own investigations and commonly receives information from other sources, including the DOJ, the FBI, and sometimes tips submitted directly from individuals. If the SEC’s investigation identifies evidence of insider trading in a particular event by a particular individual, it expands its investigation to other trades by the same individual in different events and to other traders in the same event. The SEC, DOJ, and FBI identify other potential traders through phone and email records, in-person interrogations, and in some cases, wire taps (see Hurtado (2011) for details). Therefore, the detection of a single episode of insider trading can lead regulators to identify other insider trading events and other inside traders.3 Even if FINRA’s algorithm detects one event based on abnormal market patterns, the regulators subsequent investigations might detect other events that FINRA missed. Therefore, many cases in the data are likely to be detected by methods other than abnormal illiquidity. The wide range of detection techniques used by the various regulators reduces the concern that my sample is unrepresentative of all insider trading. However, it is useful to understand whether my results are mechanically related to a detection method that is correlated with the measures of illiquidity I study. In particular, it would be useful to identify a subsample of inside traders that successfully avoided the illiquidity-based detection mechanism, but were caught for unrelated reasons, such as informants. I can then test whether a statistical relationship between insider trading and illiquidity generalizes to the subsample of my data in which I have greater confidence that the detection mechanism was not related to illiquidity. I use three proxies to measure the likelihood that insider trading is detected by market data. The first two proxies rely on the argument that different regulators use different detection methods. If FINRA is involved in an investigation, the trades are more likely to have been detected by abnormal market data. In contrast, if the FBI is involved in the investigation, the trades are more likely to have been detected by traditional investigation techniques rather than abnormal market data. I record dummy variables for events that are investigated by FINRA and the FBI, using data from SEC press releases that acknowledge the assistance of other organizations in their investigations. Out of the 410 events in the sample, 47% of the events involve FINRA’s support and 17% involve the FBI’s support. The FINRA and FBI dummy variables are negatively correlated (–14%). The third proxy relies on the argument that illegal inside traders in larger networks are more likely to have been detected through traditional investigations than through abnormal market data. Following Ahern (2017), to calculate the size of insider trading networks, I first count the number of inside traders involved in an event. I then calculate the total number of people in the traders’ complete network, including people who traded in other events. I use a dummy variable for networks with less than three people. Of the 410 events, this dummy variable is equal to one in 65% of the events. The small network dummy has a correlation of 14% with the FINRA dummy, and –16% with the FBI dummy, consistent with the assumption that large insider trading networks are more likely detected by traditional investigation methods used by the FBI, and less likely detected by monitoring stock markets for abnormal patterns, as FINRA does. Internet Appendix Figure 2 presents the overlap of these three detection mechanisms for the events in the sample. Using the detection proxies, I estimate the following triple interaction regression: Insider tradingιτ=α+β·Illiquidityιτ+ϕ·Illiquidityιτ×Event urgencyι+π·Illiquidityιτ×Detectionι+ω·Illiquidityιτ×Event urgencyι×Detectionι+γ1ln(1+Noiseιτ)+γ2ln(1+Noiseιτ)×Event urgencyι+κι+δτ+ειτ, ∀ι∈I and τ=−120,…,−2.(3) The coefficient ω measures whether the central results of Equation (2) are significantly different when the insider trading case is more likely detected by abnormal market data or traditional investigations. As discussed above, Kacperczyk and Pagnotta (2019b) (KP) also address sampling bias, but use different methods than I do. First, to exploit variation in detection mechanisms, KP use cases referred to the SEC through the Whistleblower Reward Program established in 2010. I do not use this approach for a few reasons. For one, it is not clear where the whistleblower data that KP use are published. Though KP state that 55 of 102 insider trading cases from 2011 to 2015 were investigated through the whistleblower program, the 2015 annual report on the program states otherwise. In particular, across all forms of fraud covered by the whistleblower program, the report states that “since the beginning of the whistleblower program, awards have been made to 22 individuals in connection with 16 covered actions” (U.S. SEC 2015). Given that only about 7% of all whistleblower tips submitted through the program are related to insider trading, the number of valid insider trading whistleblower tips is likely about one or two (U.S. SEC 2015). Second, KP also use FINRA to capture variation in detection methods, as I do in this study, though it is important to note that this approach was originated in my paper and KP used it afterward. Finally, KP test for generalizability by running separate regressions in subsamples delineated by detection method, but do not test whether the regression coefficients are statistically equal. KP’s approach allows for more degrees of freedom, because all of the other regression coefficients can shift in each subsample. For these reasons, I believe that my approach provides more robust tests of generalizability. The Internet Appendix offers more details on this issue. 3. Theoretical Framework of Measures of Informed Trading I study three main types of illiquidity measures: price impact of order flow, bid-ask spreads, and order imbalance. In this section, I first provide the general theoretical underpinnings of these measures. Then I explain the limitations of the theoretical measures for empirical use. Finally, I provide predictions, given my specific research design. 3.1 Price impact of order flow The first class of theoretical models of illiquidity was initiated by the seminal work of Kyle (1985). Kyle assumes that a risk-neutral market maker receives orders from a single, risk-neutral informed trader combined with orders from uninformed, nonstrategic noise traders. Kyle generates a measure of illiquidity, denoted λ, which is the equilibrium price impact of order flow. In a continuous-time setting, Kyle shows that the optimal strategy for insiders is to continually trade such that their inside information is gradually incorporated into prices and λ remains constant over the trading window. Subsequent research shows that Kyle’s prediction of a constant λ is sensitive to key assumptions. First, Holden and Subrahmanyam (1992) show that if there are multiple informed traders with identical information, informed investors trade more aggressively early and λ falls monotonically over the trading window. Foster and Viswanathan (1996) and Back, Cao, and Willard (2000) show similar nonconstant patterns of λ with multiple informed traders. Second, if informed traders are risk averse, then λ is not constant. In discrete time, Holden and Subrahmanyam (1994) show that risk-averse informed investors trade sooner and more aggressively than a risk-neutral trader. Baruch (2002) finds the same result in a continuous-time model. Third, if uninformed traders act with discretion, then λ is not constant. In a model with short-lived information and a myopic, risk-neutral informed trader, Admati and Pfleiderer (1988) show that λ varies over trading periods as informed traders decide to enter or exit the market. Collin-Dufresne and Fos (2016) extend Admati and Pfleiderer (1988) by studying a single informed trader with long-lived information and stochastic noise trading. They find that informed traders strategically trade when noise trading volume is high. Collin-Dufresne and Fos (2016) show that depending on the initial level of noise trading and future regime switches in noise trading, the time series of λ could be increasing or decreasing over the trading window. 3.2 Bid-ask spreads The second class of theoretical models, starting with Glosten and Milgrom (1985), assumes that nonstrategic, risk-neutral informed traders and uninformed liquidity traders arrive to the market in sequence, following known probabilities. The risk-neutral, competitive market maker quotes bid and ask prices such that the bid price is the expectation of the true value given that a sell order is received and the ask price is the expectation given that a buy order is received. In a static equilibrium, the bid-ask spread is wider if the proportion of informed traders in the population is larger. In a dynamic setting, a greater fraction of informed traders leads to faster information revelation, causing the bid-ask spread to narrow more quickly. Easley and O’Hara (1992) extend Glosten and Milgrom to allow information events to occur stochastically each day. In this model, in addition to buys and sells, the market maker also observes when traders do not trade, which implies a lower likelihood that an information event has occurred. This model predicts that a longer time lag between trades causes spreads to narrow, as market makers update their beliefs. As in Glosten and Milgrom, with enough trading rounds, the bid-ask spread disappears and the quoted price equals its true value. Subsequent research decomposes the bid-ask spread to separate the adverse selection component of the spread from other trading frictions. Madhavan, Richardson, and Roomans (1997) (MRR) extend the Glosten and Milgrom model to include public information, market maker inventory and transaction costs, and trades executed within the bid-ask spread. Rather than independent draws of informed and uninformed traders, as in earlier models, MRR assume that trade initiations follow a Markov process with potentially positive autocorrelation in trade direction. This model can be estimated as a system of equations to identify the variable, θ, that represents the price impact of the order flow caused by information asymmetry. 3.3 Absolute order imbalance Finally, sequential trade models also form the basis for absolute order imbalance as a measure of informed trading. Easley et al. (1996) use the underlying primitive assumptions of the Glosten-Milgrom models to generate the ‘probability of informed trading’ (PIN). Traders arrive at the market probabilistically, following a continuous Poisson arrival processes, then choose either to buy or sell one unit, or not to trade. With these assumptions, the paper calculates PIN as the unconditional probability that a random trader on a random day is informed. Thus, PIN is determined solely by the order arrival process, without any notion of an equilibrium that satisfies the market maker’s objective function, as in earlier sequential trade models. As detailed below, under certain conditions, PIN can be measured at a high frequency as the absolute order imbalance in trades. 3.4 Theoretical assumptions and empirical reality The standard theoretical models make six major assumptions that deviate from my empirical setting in important ways. First, all of the models assume that the only way to exploit inside information is to trade on it. In reality, Ahern (2017) shows that insiders share information for monetary benefit or to win favor with others. Introducing information sharing into the Kyle models would likely change the traders’ strategies. For instance, an information monopolist might trade more aggressively before she shares the information and gives up her information advantage. In contrast, in the Glosten-Milgrom models, informed traders would be willing to share information because they are perfectly competitive price-takers (Walden 2019). Second, the models assume that market makers know when an information event has occurred and the distributions of noise trades and inside information. In reality, it is not obvious if market makers know these underlying parameters, or can recognize in real-time if the parameters change. Thus, spreads and λ may not respond to insider trading in real time, though the absolute order imbalance does not depend on market makers knowing the underlying arrival process. Third, strategic trader models assume that the number of informed traders is known by all participants. In reality, it is unlikely that an informed trader knows how many other informed traders exist. Schnitzlein (2002) shows in an experimental setting that strategic informed traders are less aggressive when they do not know how many other inside traders exist. Fourth, Kyle models with multiple informed traders assume that insiders receive the information at the same time. In reality, Ahern (2017) reports that information spreads from one inside trader to another with a delay of about five to ten days, on average. Therefore, the number of informed traders increases as the date of public disclosure approaches, decreasing informed traders’ information advantage, which could lead informed traders to trade earlier (Foster and Viswanathan 1990). The Glosten-Milgrom models do not model how informed traders receive information. Thus, the model parameter that reflects the fraction of informed trading could already incorporate information sharing, or alternatively, the parameter could increase as information is shared. Fifth, time is an abstract concept in both classes of models. In the strategic trader model, the time horizon is fixed, though it could be any length of time. In the Glosten-Milgrom models, time is equally arbitrary. In reality, trading speed for the average trader is limited and the number of trading opportunities will vary with the lead time before the public announcement. Finally, informed traders in Kyle models strategically trade to avoid detection by the market maker in real time. In practice, illegal inside traders also try to avoid detection by regulators who conduct investigations in hindsight. For instance, anecdotal evidence and theory models predict insiders use a variety of strategies not captured in Kyle models to avoid detection by regulators (Packer 2011; Kacperczyk and Pagnotta 2019a). In the Glosten-Milgrom models, though traders are not strategic in trading, legal risk could influence the parameters of the arrival process. 3.5 Theoretical predictions of empirical measures of illiquidity Given the theoretical background, I next describe how measures of liquidity are predicted to behave in my specific regression setting. In particular, the use of event fixed effects imposes time-series predictions; the event-day fixed effects imposes cross-sectional predictions; and conditioning on urgency imposes time-varying predictions. 3.5.1 Event fixed effects Using event fixed effects isolates the time-series patterns of illiquidity measures, including the period before an insider receives private information. Though the theory models do not explicitly model the period before information is endowed, Kyle models imply that with no informed traders, λ would equal zero. At the moment an insider receives information, the insider begins to trade and λ will increase from zero to a positive value. Similarly, in the long-run equilibrium of the Glosten-Milgrom models, the price equals the true value and the bid-ask spread is zero. When a new information event occurs, bid-ask spreads widen. Therefore, assuming market makers know when a new information event occurs, the theoretical models predict positive correlations between measures of illiquidity and insider trading. Following the initial positive correlation between insider trading and measures of illiquidity, the predicted time-series pattern of illiquidity and insider trading depends on the underlying assumptions of the model. Though the original Kyle model predicts that λ is constant over time, with more realistic assumptions, such as multiple informed traders or risk-averse traders, λ declines over the trading window. Similarly, in the Glosten-Milgrom models, after the initial jump, bid-ask spreads converge to zero as insider trading reveals information. Nevertheless, spreads and λ still would be greater than zero until the information is revealed publicly. Therefore, within a long time series of observations, in which most observations occur before information is endowed, and assuming that noise trading is not stochastic, we would still expect a positive correlation between insider trading and measures of illiquidity within an event’s time series.4 3.5.2 Event-day fixed effects Controlling for event-day fixed effects isolates cross-sectional correlations between insider trading and illiquidity on a particular day in the time series. In Kyle models, for a given lead time to the public release of the information, λ and the intensity of insider trading are negatively correlated. However, as discussed above, before information is endowed, λ and insider trading intensity are both zero. In addition, the same lead time before the public announcement could be prior to the endowment of private information in one event, but the mid-point of the trading window for a different event. Thus, on a given event date, according to theory, the data would include both negatively correlated observations of λ and insider trading, plus observations before insider trading begins where λ is predicted to be zero. Depending on the number of observations where λ is zero, the overall correlation could be positive or negative. 3.5.3 Conditioning on urgency As mentioned above, time is abstract in the theoretical models. In the real world, some insiders will enjoy longer lead times before the public announcement, which provide more discrete trading periods. At the same time, as mentioned above, in the real world, market makers are unlikely to know that an event is imminent and trading is urgent. If noise trading is stochastic, strategic traders with more opportunity to conceal their trades will cause insider trading to be negatively correlated with illiquidity measures, and positively correlated with noise trading, as in Collin-Dufresne and Fos (2015). If lead times are shorter, and trading is more urgent, then insider trading is predicted to be positively related to measures of illiquidity, as discussed above. Though market makers do not know that trading is urgent, because insiders cannot camouflage their trades in urgent events, market makers may be better able to recognize informed trades in urgent events, and respond accordingly. The Glosten-Milgrom models do not allow for variation in the urgency of trading because the arrival process is fixed and traders are not strategic. Therefore, the predictions of these models are unrelated to the lead time to the public release of the information. 3.6 Summary of theoretical framework for empirical tests This discussion highlights that the predictions of the theoretical models depend on a host of underlying assumptions. Moreover, although the measures of illiquidity are based in theory, my results are not tests of the theories. All of the theories make assumptions that are not plausible in my empirical setting. This is not because my empirical setting is unusual, but rather because the models make strong assumptions for analytical tractability. Therefore, if a measure of illiquidity does not behave as predicted, I cannot claim the theory is incorrect. Instead, the tests cast light on which measures are reliable predictors of insider trading in a common real-world setting. 4. Data 4.1 Measures of informed trading Data on illegal insider trading comes from the data used in Ahern (2017). These data are collected from legal filings by the Securities and Exchange Commission and the Department of Justice in connection with civil and criminal complaints of illegal insider trading. The data are from cases filed between 2009 and 2013, but include insider trading dates from 1996 to 2013. The data set includes the nature of the inside information, the date on which the original source leaked the inside information, the dates on which the information was shared with others, with whom the information was shared, and the days on which insiders traded. For a full description of the data, see Ahern (2017). The advantage of using illegal insider trading data is that they provide direct observations of informed trading. Moreover, though the data come from filings that are allegations brought by the SEC and DOJ, they are most likely to be accurate. Most cases are not challenged by the defendants. In the cases that are challenged, the defense is usually based on a technicality of the legal definition of insider trading, not a dispute about the information or trading. A second advantage is that the data include the dates and the number of shares that the insiders traded. In a minority of cases, the filings only provide a range of trading dates, not specific trading dates. In these cases, I assign an equal fraction of the total number of shares to each of the days in the range. This limitation will weaken the ability of measures of informed trading to correctly identify days with increased informed trading.5 I use two measures of informed trading. The first measure, Trade dummy, is a dummy variable that equals one if any insider trading occurred on a particular date. The second measure is ln(1+Number of shares traded), which measures the total number of shares traded by all inside traders on a particular date. Though this variable is measured in levels, the fixed effects in the regressions convert them into deviations from the event’s average. Prior research shows that the urgency of informed trading can influence the use of limit orders versus market orders. Kaniel and Liu (2006) presents a theory model to show that longer-lived private information allows for the use of limit orders, but greater mispricing leads to the use of market orders. Baruch, Panayides, and Venkataraman (2017) extends the model to include short sale constraints and tests the predictions using data on all orders submitted to the Euronext-Paris stock exchange, though without direct observation of informed trades. Their evidence is consistent with the theory’s predictions. It would be informative to test the same theory using data on illegal insider trading, but the SEC filings do not provide complete data on order type. Given the data limitations, I do not investigate order type in this paper. 4.2 Measures of illiquidity One of the challenges to this sort of study is the multiple comparisons problem. Given enough measures of illiquidity, some of the measures will be statistically related to insider trading by random chance alone. Therefore, increasing the number of potential indicators of insider trading reduces the power of my tests. To address this problem, I limit my investigation to popular measures of illiquidity, though I recognize many others exist. In robustness tests, I consider different calculations of these measures and alternative illiquidity measures. Between all of the alternatives, I test 26 variables (seven main measures, 4 placebo variables, 4 alternative measures, and 11 alternative calculations, all discussed below). The most conservative way to address multiple comparisons problem is the Bonferroni correction which rejects the null hypothesis for p-values less than or equal to α/m , where α is the significance level and m is the number of hypotheses. The Bonferroni correction is conservative because it treats all tests as independent. Setting m = 26, the Bonferroni correction would make the conventional significance levels of 0.10, 0.05, and 0.01 equal to 0.004, 0.002, and 0.0004. Because many of my measures are correlated, both the main variables, and especially the alternative calculations of the main variables, the true correction is less severe. As a point of reference, assuming all seven of the main variables are statistically independent but their alternative calculations are dependent, the Bonferroni correction for seven tests produces significance levels of 0.014, 0.007, and 0.0014, which I denote as Bonferroni significance levels. In the tables, I indicate statistical significance following the conventional levels used in the literature, but in the text, I will also discuss significance relative to these Bonferroni significance levels. I calculate measures of illiquidity based on both intraday and daily data. To calculate intraday measures of illiquidity, I use the NYSE Monthly Trades and Quotes (TAQ) database. Holden and Jacobsen (2014) show that compared to the more accurate Daily TAQ database, the monthly database produces biased estimates of illiquidity measures. Therefore, I follow Holden and Jacobsen’s three recommendations designed to reduce errors in the monthly TAQ database: (1) set withdrawn quotes to missing, rather than omitting the quotes altogether, (2) estimate time stamps within the second using interpolated times based on the ordering of trades and quotes in the database, and (3) omit quotes and trades that occur when quotes are crossed or locked (where the national best bid is equal to or greater than the national best offer). In particular, I follow the programming code provided in (Holden and Jacobsen, 2014, internet appendix) to generate National Best Bid and Offer (NBBO) quotes and matched trades. Daily data come from the Center for Research in Security Prices (CRSP). 4.2.1 Quoted bid-ask spread The percentage quoted bid-ask spread is At−BtMt , where At is the National Best Ask quoted at time t, Bt is the National Best Bid quoted at time t, and Mt is the midpoint of At and Bt. Following Holden and Jacobsen (2014), I aggregate the spread to the daily level by taking the weighted average of the intraday quoted spreads, where the weights on each observed intraday spread is the amount of time the spread is in force. In robustness checks, I also use the dollar quoted spread, which is the time-weighted dollar spread, At−Bt . 4.2.2 Effective spread The quoted bid-ask spread implicitly assumes that trades occur at the ask or bid price. The effective spread accounts for trades that occur within the quoted spread. The effective spread subtracts the midpoint of the NBBO quotes from the trading price to estimate the difference between the proxy for the true price (the midpoint) and what the trader actually pays. This difference is multiplied by two to give a full spread. In particular, the percentage effective spread is calculated per trade, k, as 2Dk(Pk−Mk)Mk . Dk is a trade indicator that equals + 1 if the trade is a buy and –1 if it is a sell. Pk is the trade price of trade k, and Mk is the midpoint of the NBBO quotes prevailing when trade k occurs. Following Holden and Jacobsen (2014), I aggregate the effective spread to the daily level by taking the dollar-volume weighted average of the effective spread across all trades per day. In robustness checks, I also use the dollar effective spread, which is not normalized by Mk. 4.2.3 Price impact The price impact is a quote-based estimate of the permanent change in a stock price following a trade, as in the Glosten-Milgrom models. It is calculated as the change in the current quoted midpoint to the quoted midpoint 5 minutes in the future. In particular, the percentage price impact per trade k is 2Dk(Mk+5−Mk)Mk . Mk+5 is the midpoint of the NBBO quotes prevailing 5 minutes after trade k. Again following Holden and Jacobsen (2014), I aggregate the price impact to the daily level by taking the dollar-volume weighted price impact across all trades per day. As above, I also calculate a dollar price impact that does not normalize by Mk. 4.2.4 Absolute order imbalance Following Holden and Jacobsen (2014), I calculate absolute order imbalance as |Buys−SellsBuys+Sells| , where Buys and Sells are the number of buys and sells per day, and buys and sells are identified using the algorithm of Lee and Ready (1991). Assuming the probability of an information event is constant across days, Aktas et al. (2007) show that the expected absolute order imbalance of trades per day is theoretically equivalent to the PIN measure in Easley, Hvidkjaer, and O’Hara (2002). Thus, daily absolute order imbalance can be used as a daily estimate of PIN. 4.2.5 Kyle’s lambda I estimate Kyle’s (1985) lambda as the coefficient λ in the following regression, Δpk=λ·Sk+uk, where Δpk is the change in the transaction price, Sk=DkDollarVolumek is the signed dollar volume of the trade, and uk is an unobserved error term. Observations include all price changes per day and I require at least ten price changes to estimate λ. The Internet Appendix discusses alternative estimators of Kyle’s lambda. 4.2.6 MRR bid-ask spread decomposition Madhavan, Richardson, and Roomans (1997) (MRR) presents a structural model to decompose the bid-ask spread into transaction costs and adverse selection costs of informed trading. Following MRR, I estimate five parameters using five moment conditions. The parameter of interest is θ, which measures the degree of information asymmetry between the market maker and investors. A higher value of θ is predicted to lead to a larger change in beliefs about the true stock price for a given change in order flow. 4.2.7 Amihud illiquidity I calculate a daily measure of Amihud Illiquidity, following Amihud (2002). This measure is popularly used in the literature because it does not rely on intraday data. In particular, Amihud illiquidity is calculated as the daily absolute value of the stock return divided by the dollar volume of trading in the stock, using data from CRSP. 4.2.8 Noise trading Finally, I include ln(1+noise trading), denoted Noise trading, as a control variable in all of the regressions. Separating total observed volume into noise trading and informed trading is difficult because informed trading is not observable. Other papers use various proxies to identify informed traders, though few measures exist at the daily level (Peress and Schmidt 2018). However, one of the novel features of this paper is the daily observation of an important component of informed trading: insider trades. Therefore, a good estimate of daily noise trading is calculated as the total observed trading volume on CRSP minus the insider trading volume in my sample. Because the dependent variable in my regressions is a transformation of insider trading volume, this calculation of noise trading means that the same variable will influence both the dependent and explanatory variables. In the Internet Appendix, I show that this could cause the estimated coefficients on the illiquidity measures and noise trading to be attenuated. The smaller is the fraction of the true noise trading volume captured in my calculation, the greater is the attenuation. In addition, the attenuation is smaller when urgency is high. However, using transformed trading volumes (logged values and a dummy variable for insider trading) mitigates the attenuation bias considerably. In untabulated simulations, the attenuation bias is reduced from 66% to 9% using transformed variables. 4.3 Summary statistics Table 1 presents summary statistics of the sample by event. The table also provides average characteristics separately for events with low urgency and high urgency, where high urgency is defined as event urgency greater than the median event urgency of nine days. The sample comprises 410 events over the period 1996 to 2013. The average time from the original leak of the information to the public announcement of the event is 22.9 days. In low urgency events, the average is 43 days, and in high urgency events, the average is four days. I assign an event to be positive if the inside traders took long positions before the public announcement. In the entire sample, 75% of events are positive events. Positive events are significantly more common when urgency is low (82%) compared to when urgency is high (67%). Panel B provides the fraction of events by the nature of the news. The most common type of event is a merger or acquisition, at 52% of the sample. Earnings news is the next most common type of event, with 28% of the sample. The remaining types of events are much less common: drug regulation news (9%), sale of securities (7.5%), and operations (2.4%). Financial distress, fund liquidation, and events with various news each account for less than 1% of the total. Mergers are significantly more likely to be low urgency events, whereas earnings news are significantly more likely to be high urgency events. Table 1 Summary statistics by event . All events . Urgency . . . . Mean . Median . Low . High . Difference . p-value . A: Event timing Information leak to event lag (days) 22.88 9.00 42.59 3.73 38.86*** <0.001 Positive event (%) 74.51 100.00 82.18 66.99 15.19*** <0.001 B: Event type (% of total) Mergers & acquisitions 51.71 100.00 64.36 39.42 24.93*** <0.001 Earnings 28.05 0.00 19.31 36.54 −17.23*** <0.001 Drug regulation 9.02 0.00 7.43 10.58 −3.15 0.266 Sale of securities 7.56 0.00 6.44 8.65 −2.22 0.396 Operations 2.44 0.00 0.99 3.85 −2.86* 0.059 Financial distress 0.49 0.00 0.99 0.00 0.99 0.158 Fund liquidation 0.24 0.00 0.00 0.48 −0.48 0.318 Various 0.49 0.00 0.50 0.48 0.01 0.984 C: Firm characteristics Market equity ($billions) 10.09 1.01 3.45 16.58 −13.13*** <0.001 Tobin’s q 2.54 1.87 2.46 2.61 −0.14 0.560 R&D/assets (%) 10.54 1.24 12.32 8.80 3.53 0.147 Intangibles/assets (%) 17.88 9.90 19.56 16.31 3.25 0.102 D: Industry (% of total) NAICS 21: Mining, oil, and gas 3.17 0.00 1.49 4.81 −3.32* 0.053 NAICS 22: Utilities 0.49 0.00 0.99 0.00 0.99 0.158 NAICS 23: Construction 0.49 0.00 0.50 0.48 0.01 0.984 NAICS 31: Manufacturing (food, apparel, leather) 9.76 0.00 5.45 13.94 −8.50*** 0.004 NAICS 32: Manufacturing (chemical) 21.95 0.00 21.29 22.60 −1.31 0.750 NAICS 33: Manufacturing (computers and electronics) 22.20 0.00 23.76 20.67 3.09 0.453 NAICS 42: Wholesale 4.39 0.00 4.95 3.85 1.10 0.587 NAICS 44: Retail (electronics, food, clothing) 2.93 0.00 1.49 4.33 −2.84* 0.086 NAICS 45: Retail (sports, books, and general) 1.46 0.00 0.50 2.40 −1.91 0.105 NAICS 48: Transportation 0.98 0.00 1.49 0.48 1.00 0.306 NAICS 51: Publishing 9.51 0.00 11.88 7.21 4.67 0.109 NAICS 52: Finance and insurance 6.59 0.00 5.94 7.21 −1.27 0.605 NAICS 53: Real estate 1.95 0.00 3.47 0.48 2.98** 0.031 NAICS 54: Professional, scientific services 4.88 0.00 6.93 2.88 4.05* 0.059 NAICS 56: Administrative and support services 1.95 0.00 1.49 2.40 −0.92 0.501 NAICS 61: Educational services 0.24 0.00 0.50 0.00 0.50 0.319 NAICS 62: Health care 1.95 0.00 2.97 0.96 2.01 0.145 NAICS 72: Accomodation and food service 0.98 0.00 0.99 0.96 0.03 0.977 NAICS 99: Unknown 0.24 0.00 0.00 0.48 −0.48 0.318 . All events . Urgency . . . . Mean . Median . Low . High . Difference . p-value . A: Event timing Information leak to event lag (days) 22.88 9.00 42.59 3.73 38.86*** <0.001 Positive event (%) 74.51 100.00 82.18 66.99 15.19*** <0.001 B: Event type (% of total) Mergers & acquisitions 51.71 100.00 64.36 39.42 24.93*** <0.001 Earnings 28.05 0.00 19.31 36.54 −17.23*** <0.001 Drug regulation 9.02 0.00 7.43 10.58 −3.15 0.266 Sale of securities 7.56 0.00 6.44 8.65 −2.22 0.396 Operations 2.44 0.00 0.99 3.85 −2.86* 0.059 Financial distress 0.49 0.00 0.99 0.00 0.99 0.158 Fund liquidation 0.24 0.00 0.00 0.48 −0.48 0.318 Various 0.49 0.00 0.50 0.48 0.01 0.984 C: Firm characteristics Market equity ($billions) 10.09 1.01 3.45 16.58 −13.13*** <0.001 Tobin’s q 2.54 1.87 2.46 2.61 −0.14 0.560 R&D/assets (%) 10.54 1.24 12.32 8.80 3.53 0.147 Intangibles/assets (%) 17.88 9.90 19.56 16.31 3.25 0.102 D: Industry (% of total) NAICS 21: Mining, oil, and gas 3.17 0.00 1.49 4.81 −3.32* 0.053 NAICS 22: Utilities 0.49 0.00 0.99 0.00 0.99 0.158 NAICS 23: Construction 0.49 0.00 0.50 0.48 0.01 0.984 NAICS 31: Manufacturing (food, apparel, leather) 9.76 0.00 5.45 13.94 −8.50*** 0.004 NAICS 32: Manufacturing (chemical) 21.95 0.00 21.29 22.60 −1.31 0.750 NAICS 33: Manufacturing (computers and electronics) 22.20 0.00 23.76 20.67 3.09 0.453 NAICS 42: Wholesale 4.39 0.00 4.95 3.85 1.10 0.587 NAICS 44: Retail (electronics, food, clothing) 2.93 0.00 1.49 4.33 −2.84* 0.086 NAICS 45: Retail (sports, books, and general) 1.46 0.00 0.50 2.40 −1.91 0.105 NAICS 48: Transportation 0.98 0.00 1.49 0.48 1.00 0.306 NAICS 51: Publishing 9.51 0.00 11.88 7.21 4.67 0.109 NAICS 52: Finance and insurance 6.59 0.00 5.94 7.21 −1.27 0.605 NAICS 53: Real estate 1.95 0.00 3.47 0.48 2.98** 0.031 NAICS 54: Professional, scientific services 4.88 0.00 6.93 2.88 4.05* 0.059 NAICS 56: Administrative and support services 1.95 0.00 1.49 2.40 −0.92 0.501 NAICS 61: Educational services 0.24 0.00 0.50 0.00 0.50 0.319 NAICS 62: Health care 1.95 0.00 2.97 0.96 2.01 0.145 NAICS 72: Accomodation and food service 0.98 0.00 0.99 0.96 0.03 0.977 NAICS 99: Unknown 0.24 0.00 0.00 0.48 −0.48 0.318 Observations include 410 events over the period 1996–2013. High urgency events have lead times from the original leak to the public announcement of the event greater than the median of nine days. The last column presents the p-value of a t-test of the equality of the means of the low and high urgency subsamples. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Table 1 Summary statistics by event . All events . Urgency . . . . Mean . Median . Low . High . Difference . p-value . A: Event timing Information leak to event lag (days) 22.88 9.00 42.59 3.73 38.86*** <0.001 Positive event (%) 74.51 100.00 82.18 66.99 15.19*** <0.001 B: Event type (% of total) Mergers & acquisitions 51.71 100.00 64.36 39.42 24.93*** <0.001 Earnings 28.05 0.00 19.31 36.54 −17.23*** <0.001 Drug regulation 9.02 0.00 7.43 10.58 −3.15 0.266 Sale of securities 7.56 0.00 6.44 8.65 −2.22 0.396 Operations 2.44 0.00 0.99 3.85 −2.86* 0.059 Financial distress 0.49 0.00 0.99 0.00 0.99 0.158 Fund liquidation 0.24 0.00 0.00 0.48 −0.48 0.318 Various 0.49 0.00 0.50 0.48 0.01 0.984 C: Firm characteristics Market equity ($billions) 10.09 1.01 3.45 16.58 −13.13*** <0.001 Tobin’s q 2.54 1.87 2.46 2.61 −0.14 0.560 R&D/assets (%) 10.54 1.24 12.32 8.80 3.53 0.147 Intangibles/assets (%) 17.88 9.90 19.56 16.31 3.25 0.102 D: Industry (% of total) NAICS 21: Mining, oil, and gas 3.17 0.00 1.49 4.81 −3.32* 0.053 NAICS 22: Utilities 0.49 0.00 0.99 0.00 0.99 0.158 NAICS 23: Construction 0.49 0.00 0.50 0.48 0.01 0.984 NAICS 31: Manufacturing (food, apparel, leather) 9.76 0.00 5.45 13.94 −8.50*** 0.004 NAICS 32: Manufacturing (chemical) 21.95 0.00 21.29 22.60 −1.31 0.750 NAICS 33: Manufacturing (computers and electronics) 22.20 0.00 23.76 20.67 3.09 0.453 NAICS 42: Wholesale 4.39 0.00 4.95 3.85 1.10 0.587 NAICS 44: Retail (electronics, food, clothing) 2.93 0.00 1.49 4.33 −2.84* 0.086 NAICS 45: Retail (sports, books, and general) 1.46 0.00 0.50 2.40 −1.91 0.105 NAICS 48: Transportation 0.98 0.00 1.49 0.48 1.00 0.306 NAICS 51: Publishing 9.51 0.00 11.88 7.21 4.67 0.109 NAICS 52: Finance and insurance 6.59 0.00 5.94 7.21 −1.27 0.605 NAICS 53: Real estate 1.95 0.00 3.47 0.48 2.98** 0.031 NAICS 54: Professional, scientific services 4.88 0.00 6.93 2.88 4.05* 0.059 NAICS 56: Administrative and support services 1.95 0.00 1.49 2.40 −0.92 0.501 NAICS 61: Educational services 0.24 0.00 0.50 0.00 0.50 0.319 NAICS 62: Health care 1.95 0.00 2.97 0.96 2.01 0.145 NAICS 72: Accomodation and food service 0.98 0.00 0.99 0.96 0.03 0.977 NAICS 99: Unknown 0.24 0.00 0.00 0.48 −0.48 0.318 . All events . Urgency . . . . Mean . Median . Low . High . Difference . p-value . A: Event timing Information leak to event lag (days) 22.88 9.00 42.59 3.73 38.86*** <0.001 Positive event (%) 74.51 100.00 82.18 66.99 15.19*** <0.001 B: Event type (% of total) Mergers & acquisitions 51.71 100.00 64.36 39.42 24.93*** <0.001 Earnings 28.05 0.00 19.31 36.54 −17.23*** <0.001 Drug regulation 9.02 0.00 7.43 10.58 −3.15 0.266 Sale of securities 7.56 0.00 6.44 8.65 −2.22 0.396 Operations 2.44 0.00 0.99 3.85 −2.86* 0.059 Financial distress 0.49 0.00 0.99 0.00 0.99 0.158 Fund liquidation 0.24 0.00 0.00 0.48 −0.48 0.318 Various 0.49 0.00 0.50 0.48 0.01 0.984 C: Firm characteristics Market equity ($billions) 10.09 1.01 3.45 16.58 −13.13*** <0.001 Tobin’s q 2.54 1.87 2.46 2.61 −0.14 0.560 R&D/assets (%) 10.54 1.24 12.32 8.80 3.53 0.147 Intangibles/assets (%) 17.88 9.90 19.56 16.31 3.25 0.102 D: Industry (% of total) NAICS 21: Mining, oil, and gas 3.17 0.00 1.49 4.81 −3.32* 0.053 NAICS 22: Utilities 0.49 0.00 0.99 0.00 0.99 0.158 NAICS 23: Construction 0.49 0.00 0.50 0.48 0.01 0.984 NAICS 31: Manufacturing (food, apparel, leather) 9.76 0.00 5.45 13.94 −8.50*** 0.004 NAICS 32: Manufacturing (chemical) 21.95 0.00 21.29 22.60 −1.31 0.750 NAICS 33: Manufacturing (computers and electronics) 22.20 0.00 23.76 20.67 3.09 0.453 NAICS 42: Wholesale 4.39 0.00 4.95 3.85 1.10 0.587 NAICS 44: Retail (electronics, food, clothing) 2.93 0.00 1.49 4.33 −2.84* 0.086 NAICS 45: Retail (sports, books, and general) 1.46 0.00 0.50 2.40 −1.91 0.105 NAICS 48: Transportation 0.98 0.00 1.49 0.48 1.00 0.306 NAICS 51: Publishing 9.51 0.00 11.88 7.21 4.67 0.109 NAICS 52: Finance and insurance 6.59 0.00 5.94 7.21 −1.27 0.605 NAICS 53: Real estate 1.95 0.00 3.47 0.48 2.98** 0.031 NAICS 54: Professional, scientific services 4.88 0.00 6.93 2.88 4.05* 0.059 NAICS 56: Administrative and support services 1.95 0.00 1.49 2.40 −0.92 0.501 NAICS 61: Educational services 0.24 0.00 0.50 0.00 0.50 0.319 NAICS 62: Health care 1.95 0.00 2.97 0.96 2.01 0.145 NAICS 72: Accomodation and food service 0.98 0.00 0.99 0.96 0.03 0.977 NAICS 99: Unknown 0.24 0.00 0.00 0.48 −0.48 0.318 Observations include 410 events over the period 1996–2013. High urgency events have lead times from the original leak to the public announcement of the event greater than the median of nine days. The last column presents the p-value of a t-test of the equality of the means of the low and high urgency subsamples. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Panel C shows that the median target firm is large, with market equity of about $1 billion, though the sample includes a wide range of firm sizes. Firms with urgent events tend to be larger firms, with an average market equity of $16.6 billion, compared to an average market equity of $3.5 billion for low urgency firms. The other firm characteristics reported in the table, namely, Tobin’s q, R&D, and intangible assets, are not significantly different in high urgency events compared with low urgency events. Panel D provides the industry breakdown of the firm-events in the sample. The most common industries are chemical manufacturing and computers and electronics manufacturing. Ahern (2017) shows that the sample is biased toward high-tech industries relative to the industry distribution of all public listings and also targets in acquisitions. However, neither chemicals or computers and electronics manufacturing firms exhibits a prevalence for high or low urgency events. Table 2 presents summary statistics using roughly 48,000 observations of daily data from τ=−120 to τ=−2 over the 410 events in the sample. These statistics can be used to interpret the coefficients in the regressions presented below. All illiquidity measures and stock returns are winsorized at the 1st and 99th percentiles. Insider trading occurred in 4% of all days in the sample. The quoted spread is 0.31%, on average, and 0.13% at the median. The effective spread is 0.31%, on average, and 0.12% at the median. The average price impact is 0.15%, and the median is 0.06%. The spreads are slightly higher than those reported in the random sample of Holden and Jacobsen (2014), though the price impact is less. Absolute order imbalance is 11%, slightly less than reported in Holden and Jacobsen (2014). Kyle’s λ is 8.5 on average, with a median of 6.3. At the median, this implies that a $10,000 order will lead to a price change of 0.0063. At the median stock price of $19.39 in the sample, this is equivalent to 3.25 basis points. MRR θ is 0.224% at the average, and 0.080% at the median. Amihud illiquidity is 0.05% on average and 0.001% at the median. These compare similarly to statistics in Harris and Amato (2019). The average log volume of noise trading is –0.618, which equates to 524,451 shares. The median is slightly less at 511,722 shares. Table 2 Summary statistics by trading day . Mean . SD . 25th . Median . 75th . Observations . A: Informed trading measures Trade dummy 0.040 0.195 0.000 0.000 0.000 47,737 ln(1+Number of shares traded) 0.312 1.582 0.000 0.000 0.000 47,737 B: Trading window measures Daily urgency 0.037 0.063 0.011 0.016 0.032 47,737 Event urgency 0.183 0.255 0.032 0.091 0.200 42,620 C: Illiquidity measures Quoted spread (%) 0.314 0.521 0.071 0.131 0.298 44,389 Effective spread (%) 0.307 0.526 0.067 0.121 0.285 46,424 Price impact (%) 0.148 0.287 0.022 0.064 0.155 46,424 Order imbalance 0.110 0.115 0.032 0.074 0.146 42,548 Kyle’s λ 8.508 7.874 3.679 6.275 10.273 43,778 MRR θ 0.224 0.516 0.012 0.080 0.235 46,165 Amihud illiquidity 0.049 0.195 0.000 0.001 0.008 47,693 D: Noise trading ln(1+Noise) −0.618 2.003 −1.855 −0.603 0.689 47,737 . Mean . SD . 25th . Median . 75th . Observations . A: Informed trading measures Trade dummy 0.040 0.195 0.000 0.000 0.000 47,737 ln(1+Number of shares traded) 0.312 1.582 0.000 0.000 0.000 47,737 B: Trading window measures Daily urgency 0.037 0.063 0.011 0.016 0.032 47,737 Event urgency 0.183 0.255 0.032 0.091 0.200 42,620 C: Illiquidity measures Quoted spread (%) 0.314 0.521 0.071 0.131 0.298 44,389 Effective spread (%) 0.307 0.526 0.067 0.121 0.285 46,424 Price impact (%) 0.148 0.287 0.022 0.064 0.155 46,424 Order imbalance 0.110 0.115 0.032 0.074 0.146 42,548 Kyle’s λ 8.508 7.874 3.679 6.275 10.273 43,778 MRR θ 0.224 0.516 0.012 0.080 0.235 46,165 Amihud illiquidity 0.049 0.195 0.000 0.001 0.008 47,693 D: Noise trading ln(1+Noise) −0.618 2.003 −1.855 −0.603 0.689 47,737 Statistics are calculated using daily observations over days t=−120,…,−2 , relative to the public announcement date (t = 0), across 410 firm-events. Trade dummy equals one if there is any insider trading on a given day. ln(1+Number of shares traded) is based on inside trades. Daily Urgency is the inverse of the number of days to t = 0. Event Urgency is the inverse of the number of days from the original information leak to t = 0. Noise is the daily trading volume minus the daily insider trading volume in my sample, in millions of shares. Open in new tab Table 2 Summary statistics by trading day . Mean . SD . 25th . Median . 75th . Observations . A: Informed trading measures Trade dummy 0.040 0.195 0.000 0.000 0.000 47,737 ln(1+Number of shares traded) 0.312 1.582 0.000 0.000 0.000 47,737 B: Trading window measures Daily urgency 0.037 0.063 0.011 0.016 0.032 47,737 Event urgency 0.183 0.255 0.032 0.091 0.200 42,620 C: Illiquidity measures Quoted spread (%) 0.314 0.521 0.071 0.131 0.298 44,389 Effective spread (%) 0.307 0.526 0.067 0.121 0.285 46,424 Price impact (%) 0.148 0.287 0.022 0.064 0.155 46,424 Order imbalance 0.110 0.115 0.032 0.074 0.146 42,548 Kyle’s λ 8.508 7.874 3.679 6.275 10.273 43,778 MRR θ 0.224 0.516 0.012 0.080 0.235 46,165 Amihud illiquidity 0.049 0.195 0.000 0.001 0.008 47,693 D: Noise trading ln(1+Noise) −0.618 2.003 −1.855 −0.603 0.689 47,737 . Mean . SD . 25th . Median . 75th . Observations . A: Informed trading measures Trade dummy 0.040 0.195 0.000 0.000 0.000 47,737 ln(1+Number of shares traded) 0.312 1.582 0.000 0.000 0.000 47,737 B: Trading window measures Daily urgency 0.037 0.063 0.011 0.016 0.032 47,737 Event urgency 0.183 0.255 0.032 0.091 0.200 42,620 C: Illiquidity measures Quoted spread (%) 0.314 0.521 0.071 0.131 0.298 44,389 Effective spread (%) 0.307 0.526 0.067 0.121 0.285 46,424 Price impact (%) 0.148 0.287 0.022 0.064 0.155 46,424 Order imbalance 0.110 0.115 0.032 0.074 0.146 42,548 Kyle’s λ 8.508 7.874 3.679 6.275 10.273 43,778 MRR θ 0.224 0.516 0.012 0.080 0.235 46,165 Amihud illiquidity 0.049 0.195 0.000 0.001 0.008 47,693 D: Noise trading ln(1+Noise) −0.618 2.003 −1.855 −0.603 0.689 47,737 Statistics are calculated using daily observations over days t=−120,…,−2 , relative to the public announcement date (t = 0), across 410 firm-events. Trade dummy equals one if there is any insider trading on a given day. ln(1+Number of shares traded) is based on inside trades. Daily Urgency is the inverse of the number of days to t = 0. Event Urgency is the inverse of the number of days from the original information leak to t = 0. Noise is the daily trading volume minus the daily insider trading volume in my sample, in millions of shares. Open in new tab 5. Empirical Results This section of the paper first presents time-series patterns of returns, volume, measures of illiquidity, and insider trading, then it presents estimates of the empirical models described above. 5.1 Time-series evidence of illiquidity and insider trading Panel (A) of Figure 1 presents the time series of insider trading activity in event time from τ=−40 to τ=−1 . The solid line represents the fraction of positive events in the sample in which insider trading occurs, per event day. The dashed line represents the same concept for negative events. The figure shows that insider trading occurs in 5% of events as far back as 40 days before the announcement. As the public announcement date draws closer, the fraction of events with insider trading increases steadily to around 30% in the few days before the announcement. For negative events, insider trading is less common overall, but increases substantially in the last 15 days before the announcement. Thus, insider trading activity ramps up close to the public announcement date, but positive events have wide variation in the timing of trades. Figure 1 Open in new tabDownload slide Event-time series of insider trading, returns, and volume These panels present the time series of daily insider trading, abnormal returns, and total volume in event time relative to the public announcement of the event at t = 0. The sample comprises 410 events over the period 1996 to 2013. Positive (negative) events are events in which inside traders took long (short) positions. Panel A presents the fraction of events per day in which insider trading occurred. Panel B presents cumulative abnormal returns, where abnormal returns are a firm’s daily return minus the firm’s average return over the period t = – 120 to t = – 41. Panel C presents the cumulative abnormal trading volume. Abnormal volume is a firm’s daily ln(1+volume) minus the firm’s average ln(1+volume) over the period t = – 120 to t = – 41. Figure 1 Open in new tabDownload slide Event-time series of insider trading, returns, and volume These panels present the time series of daily insider trading, abnormal returns, and total volume in event time relative to the public announcement of the event at t = 0. The sample comprises 410 events over the period 1996 to 2013. Positive (negative) events are events in which inside traders took long (short) positions. Panel A presents the fraction of events per day in which insider trading occurred. Panel B presents cumulative abnormal returns, where abnormal returns are a firm’s daily return minus the firm’s average return over the period t = – 120 to t = – 41. Panel C presents the cumulative abnormal trading volume. Abnormal volume is a firm’s daily ln(1+volume) minus the firm’s average ln(1+volume) over the period t = – 120 to t = – 41. Panel (B) of Figure 1 presents cumulative abnormal returns of event firms in the period τ=−40 to τ=+10 . Abnormal returns are calculated as the difference between a firm’s daily return and the firm’s average return in the period τ=−120 to τ=−41 . This figure shows that insider trading is moving prices to their full-information value, as positive events have runups of roughly 8% over the period τ=−40 to τ=−1 , while negative events have declines of about –2.5%. The asymmetry reflects that negative events in the sample tend to be less extreme earnings events, compared to the large positive gains in merger events. Short-selling constraints might also contribute to the asymmetry. On the announcement day, stock prices jump considerably and are constant afterward. This shows that though insider trading moves prices toward their full information value, it only moves prices to a fraction of their full information value. For this study, the most relevant fact is that stock prices are moving considerably before the public announcement. Panel (C) of Figure 1 shows that abnormal volume substantially increases during the period before the public announcement. Starting on the announcement day, there is a large increase in trading volume that continues in the 10 days after the announcement. Taken together, these figures show prior to the public announcement, insiders are trading, stock prices are moving toward their full information value, and volume is increasing. Figure 2 presents the time series of abnormal illiquidity for the seven illiquidity variables, plus noise trading. Abnormal illiquidity is calculated as the daily illiquidity measure minus the firm’s average illiquidity measure during the period from τ=−120 to the day before the information was originally leaked. Gray areas represent the 95th percentile confidence interval. Figure 2 Open in new tabDownload slide Event-time series of abnormal illiquidity These figures present the time-series from t = – 40 to t=+10 , relative to the public announcement of the event at t = 0. Abnormal illiquidity and ln(1+noise trading) is calculated as the daily value minus the average value of the variable over the period from t = – 120 to the day before the original insider leak of the information. The gray bands represent the 95th percentile confidence interval. Figure 2 Open in new tabDownload slide Event-time series of abnormal illiquidity These figures present the time-series from t = – 40 to t=+10 , relative to the public announcement of the event at t = 0. Abnormal illiquidity and ln(1+noise trading) is calculated as the daily value minus the average value of the variable over the period from t = – 120 to the day before the original insider leak of the information. The gray bands represent the 95th percentile confidence interval. The patterns in these figures are in stark contrast to the steep runup in insider trading, volume, and prices. Instead of increasing, the measures of abnormal illiquidity are nearly flat, or slightly decreasing before the announcement date. For example, quoted spread and effective spread are significantly less than average for a number of days in the period τ=−10 to τ=−1 and never significantly positive. Likewise, order imbalance and Kyle’s λ become significantly more negative as the event gets closer. Noise trading is roughly constant, but increases in the few days before the announcement. These figures suggest that illiquidity decreases slightly at the same time that insider trading increases greatly. At the announcement, all of the illiquidity measures decline significantly, except absolute order imbalance, which rises significantly. The decrease in illiquidity at the public announcement is consistent with a sharp reduction in information asymmetry. The increase in order imbalance at the public announcement reflects investors responding to unambiguously positive or negative news. 5.2 Naïve tests Table 3 presents the relationship between insider trading and illiquidity without controlling for the strategic timing of trades. The dependent variable in panel A is an indicator for insider trading. In panel B, it is the volume of insider trading. Each panel presents tests that have no fixed effects, event fixed effects only, and event and event-day fixed effects. The qualitative results are similar when using either a dummy variable or a continuous measures of insider trading as the dependent variable. All regressions in the paper cluster standard errors at the event level.6 Table 3 Naïve relationship between illiquidity and insider trading Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy No fixed effects Illiquidity 0.021* 0.019* 0.018* 0.008 0.001* −0.011** 0.030 (0.092) (0.078) (0.065) (0.760) (0.088) (0.013) (0.302) Noise trading −0.007*** −0.008*** −0.009*** −0.010*** −0.008*** −0.011*** −0.008*** (0.006) (0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Event fixed effects Illiquidity −0.008 0.003 0.000 −0.022* −0.001** −0.007 −0.010 (0.586) (0.773) (0.999) (0.069) (0.014) (0.178) (0.569) Noise trading 0.008** 0.010*** 0.010*** 0.010*** 0.007* 0.009*** 0.009*** (0.020) (0.004) (0.004) (0.006) (0.053) (0.009) (0.008) Event and event-day fixed effects Illiquidity 0.003 0.011 0.005 −0.007 0.000 −0.001 0.000 (0.816) (0.229) (0.360) (0.520) (0.221) (0.801) (0.985) Noise trading 0.003 0.004 0.003 0.003 0.002 0.003 0.003 (0.288) (0.205) (0.245) (0.261) (0.564) (0.353) (0.237) B. Dependent variable: ln(1+informed trading volume) No fixed effects Illiquidity 0.184** 0.175** 0.197** 0.081 0.003 −0.100*** 0.265 (0.033) (0.025) (0.015) (0.662) (0.342) (<0.001) (0.186) Noise trading −0.036* −0.043** −0.055*** −0.066*** −0.059*** −0.074*** −0.048*** (0.060) (0.017) (0.002) (<0.001) (<0.001) (<0.001) (0.005) Event fixed effects Illiquidity −0.050 0.044 0.016 −0.186* −0.009*** −0.052 −0.072 (0.699) (0.626) (0.755) (0.051) (0.005) (0.140) (0.638) Noise trading 0.073** 0.083*** 0.082*** 0.083*** 0.063** 0.078*** 0.074*** (0.014) (0.003) (0.003) (0.005) (0.043) (0.008) (0.005) Event and event-day fixed effects Illiquidity 0.041 0.108 0.057 −0.065 −0.004 −0.004 0.008 (0.697) (0.154) (0.198) (0.452) (0.141) (0.907) (0.947) Noise trading 0.031 0.032 0.030 0.031 0.018 0.026 0.031 (0.212) (0.164) (0.210) (0.219) (0.501) (0.299) (0.174) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy No fixed effects Illiquidity 0.021* 0.019* 0.018* 0.008 0.001* −0.011** 0.030 (0.092) (0.078) (0.065) (0.760) (0.088) (0.013) (0.302) Noise trading −0.007*** −0.008*** −0.009*** −0.010*** −0.008*** −0.011*** −0.008*** (0.006) (0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Event fixed effects Illiquidity −0.008 0.003 0.000 −0.022* −0.001** −0.007 −0.010 (0.586) (0.773) (0.999) (0.069) (0.014) (0.178) (0.569) Noise trading 0.008** 0.010*** 0.010*** 0.010*** 0.007* 0.009*** 0.009*** (0.020) (0.004) (0.004) (0.006) (0.053) (0.009) (0.008) Event and event-day fixed effects Illiquidity 0.003 0.011 0.005 −0.007 0.000 −0.001 0.000 (0.816) (0.229) (0.360) (0.520) (0.221) (0.801) (0.985) Noise trading 0.003 0.004 0.003 0.003 0.002 0.003 0.003 (0.288) (0.205) (0.245) (0.261) (0.564) (0.353) (0.237) B. Dependent variable: ln(1+informed trading volume) No fixed effects Illiquidity 0.184** 0.175** 0.197** 0.081 0.003 −0.100*** 0.265 (0.033) (0.025) (0.015) (0.662) (0.342) (<0.001) (0.186) Noise trading −0.036* −0.043** −0.055*** −0.066*** −0.059*** −0.074*** −0.048*** (0.060) (0.017) (0.002) (<0.001) (<0.001) (<0.001) (0.005) Event fixed effects Illiquidity −0.050 0.044 0.016 −0.186* −0.009*** −0.052 −0.072 (0.699) (0.626) (0.755) (0.051) (0.005) (0.140) (0.638) Noise trading 0.073** 0.083*** 0.082*** 0.083*** 0.063** 0.078*** 0.074*** (0.014) (0.003) (0.003) (0.005) (0.043) (0.008) (0.005) Event and event-day fixed effects Illiquidity 0.041 0.108 0.057 −0.065 −0.004 −0.004 0.008 (0.697) (0.154) (0.198) (0.452) (0.141) (0.907) (0.947) Noise trading 0.031 0.032 0.030 0.031 0.018 0.026 0.031 (0.212) (0.164) (0.210) (0.219) (0.501) (0.299) (0.174) This table presents ordinary least squares (OLS) regression coefficients where the dependent variable in panel A is a dummy equal to one if any insider trading occurred on a given day, and in panel B is the logged volume of shares traded by insiders on a given day. Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. Each regression specification includes a measure of illiquidity, which is listed at the top of the column. For each panel and each column, I estimate three distinct regressions that differ by the fixed effects included in the regression (event fixed effects, event-day fixed effects, or both). Constant terms are not reported. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Table 3 Naïve relationship between illiquidity and insider trading Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy No fixed effects Illiquidity 0.021* 0.019* 0.018* 0.008 0.001* −0.011** 0.030 (0.092) (0.078) (0.065) (0.760) (0.088) (0.013) (0.302) Noise trading −0.007*** −0.008*** −0.009*** −0.010*** −0.008*** −0.011*** −0.008*** (0.006) (0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Event fixed effects Illiquidity −0.008 0.003 0.000 −0.022* −0.001** −0.007 −0.010 (0.586) (0.773) (0.999) (0.069) (0.014) (0.178) (0.569) Noise trading 0.008** 0.010*** 0.010*** 0.010*** 0.007* 0.009*** 0.009*** (0.020) (0.004) (0.004) (0.006) (0.053) (0.009) (0.008) Event and event-day fixed effects Illiquidity 0.003 0.011 0.005 −0.007 0.000 −0.001 0.000 (0.816) (0.229) (0.360) (0.520) (0.221) (0.801) (0.985) Noise trading 0.003 0.004 0.003 0.003 0.002 0.003 0.003 (0.288) (0.205) (0.245) (0.261) (0.564) (0.353) (0.237) B. Dependent variable: ln(1+informed trading volume) No fixed effects Illiquidity 0.184** 0.175** 0.197** 0.081 0.003 −0.100*** 0.265 (0.033) (0.025) (0.015) (0.662) (0.342) (<0.001) (0.186) Noise trading −0.036* −0.043** −0.055*** −0.066*** −0.059*** −0.074*** −0.048*** (0.060) (0.017) (0.002) (<0.001) (<0.001) (<0.001) (0.005) Event fixed effects Illiquidity −0.050 0.044 0.016 −0.186* −0.009*** −0.052 −0.072 (0.699) (0.626) (0.755) (0.051) (0.005) (0.140) (0.638) Noise trading 0.073** 0.083*** 0.082*** 0.083*** 0.063** 0.078*** 0.074*** (0.014) (0.003) (0.003) (0.005) (0.043) (0.008) (0.005) Event and event-day fixed effects Illiquidity 0.041 0.108 0.057 −0.065 −0.004 −0.004 0.008 (0.697) (0.154) (0.198) (0.452) (0.141) (0.907) (0.947) Noise trading 0.031 0.032 0.030 0.031 0.018 0.026 0.031 (0.212) (0.164) (0.210) (0.219) (0.501) (0.299) (0.174) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy No fixed effects Illiquidity 0.021* 0.019* 0.018* 0.008 0.001* −0.011** 0.030 (0.092) (0.078) (0.065) (0.760) (0.088) (0.013) (0.302) Noise trading −0.007*** −0.008*** −0.009*** −0.010*** −0.008*** −0.011*** −0.008*** (0.006) (0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Event fixed effects Illiquidity −0.008 0.003 0.000 −0.022* −0.001** −0.007 −0.010 (0.586) (0.773) (0.999) (0.069) (0.014) (0.178) (0.569) Noise trading 0.008** 0.010*** 0.010*** 0.010*** 0.007* 0.009*** 0.009*** (0.020) (0.004) (0.004) (0.006) (0.053) (0.009) (0.008) Event and event-day fixed effects Illiquidity 0.003 0.011 0.005 −0.007 0.000 −0.001 0.000 (0.816) (0.229) (0.360) (0.520) (0.221) (0.801) (0.985) Noise trading 0.003 0.004 0.003 0.003 0.002 0.003 0.003 (0.288) (0.205) (0.245) (0.261) (0.564) (0.353) (0.237) B. Dependent variable: ln(1+informed trading volume) No fixed effects Illiquidity 0.184** 0.175** 0.197** 0.081 0.003 −0.100*** 0.265 (0.033) (0.025) (0.015) (0.662) (0.342) (<0.001) (0.186) Noise trading −0.036* −0.043** −0.055*** −0.066*** −0.059*** −0.074*** −0.048*** (0.060) (0.017) (0.002) (<0.001) (<0.001) (<0.001) (0.005) Event fixed effects Illiquidity −0.050 0.044 0.016 −0.186* −0.009*** −0.052 −0.072 (0.699) (0.626) (0.755) (0.051) (0.005) (0.140) (0.638) Noise trading 0.073** 0.083*** 0.082*** 0.083*** 0.063** 0.078*** 0.074*** (0.014) (0.003) (0.003) (0.005) (0.043) (0.008) (0.005) Event and event-day fixed effects Illiquidity 0.041 0.108 0.057 −0.065 −0.004 −0.004 0.008 (0.697) (0.154) (0.198) (0.452) (0.141) (0.907) (0.947) Noise trading 0.031 0.032 0.030 0.031 0.018 0.026 0.031 (0.212) (0.164) (0.210) (0.219) (0.501) (0.299) (0.174) This table presents ordinary least squares (OLS) regression coefficients where the dependent variable in panel A is a dummy equal to one if any insider trading occurred on a given day, and in panel B is the logged volume of shares traded by insiders on a given day. Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. Each regression specification includes a measure of illiquidity, which is listed at the top of the column. For each panel and each column, I estimate three distinct regressions that differ by the fixed effects included in the regression (event fixed effects, event-day fixed effects, or both). Constant terms are not reported. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab With no fixed effects, Kyle’s λ and the spread-based illiquidity measures are positively related to insider trading, MRR θ is negatively related, and order imbalance and Amihud illiquidity are unrelated. Once event fixed effects are included, only order imbalance and λ are significantly negatively related to insider trading, while all other variables are insignificant. Adding event-day fixed effects makes all of the illiquidity measures statistically unrelated to insider trading. Likewise, with no fixed effects, noise trading is negatively related to insider trading, positively related after controlling for event fixed effects, and statistically unrelated after controlling for event and event-day fixed effects. In sum, these results show that time-invariant cross-sectional heterogeneity across event firms and a common daily factor explain a substantial portion of the variation in illiquidity and noise trading. These results differ markedly from those in Kacperczyk and Pagnotta (2019b) who find very strong statistical relationships between insider trading and measures of illiquidity; many of their coefficients have t-statistics of six or greater. Given that we use very similar data, the differences are likely to be caused by different specifications. In particular, if I shorten the number of days in the control period, following their method, my estimated coefficients become statistically significant. The Internet Appendix provides more details. 5.3 Tests that control for strategic timing Table 4 presents estimates of Equation (1), in which the measures of illiquidity are interacted with Daily urgency. In panel A, where the dependent variable is a dummy variable for insider trading, all illiquidity variables are unrelated to insider trading, either in the main effect, or in the interaction with urgency, except that Kyle’s λ is negative when urgency is low. This is consistent with insiders strategically trading on days with low levels of λ. In panel B, where the dependent variable is the level of insider trading, the interaction of urgency and the spread-based measures are significantly positively related to the level of insider trading at conventional significance levels. This implies that as the public announcement date approaches, spreads widen by larger amounts on days with insider trading than when the public announcement date is further away. In contrast, the other measures of insider trading do not display similar results. Second, Table 4 shows that noise trading is positively related to insider trading, but the relationship is mitigated as urgency increases. This result is consistent with the prediction that insiders try to conceal their information by strategically trading when noise trading volume is high. However, as the public announcement date approaches, insiders are less likely to time their trades to coincide with noise traders, consistent with the prediction that shorter lead times allow less strategic timing. Table 4 Daily urgency and the relationship between illiquidity and insider trading Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.008 0.002 −0.005 −0.007 −0.001** 0.004 −0.011 (0.490) (0.819) (0.566) (0.703) (0.042) (0.465) (0.588) Daily urgency 0.824*** 0.831*** 0.850*** 0.906*** 0.831*** 0.912*** 0.876*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 0.231 0.207 0.256 0.026 0.010 0.010 0.449 (0.228) (0.233) (0.248) (0.957) (0.291) (0.291) (0.471) Noise trading 0.007** 0.008*** 0.008*** 0.009*** 0.007** 0.010*** 0.008*** (0.014) (0.005) (0.003) (0.003) (0.038) (0.002) (0.004) Noise trading×Daily urgency −0.102** −0.111*** −0.124*** −0.143*** −0.122*** −0.160*** −0.113*** (0.010) (0.004) (<0.001) (<0.001) (0.002) (<0.001) (0.002) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.101 −0.013 −0.073 −0.184 −0.007* 0.049 −0.175 (0.316) (0.857) (0.297) (0.212) (0.067) (0.137) (0.312) Daily urgency 6.845*** 6.891*** 7.186*** 7.509*** 7.530*** 7.931*** 7.473*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 3.130** 2.964** 3.455* 3.460 0.029 −1.825*** 6.616 (0.046) (0.042) (0.075) (0.398) (0.672) (0.005) (0.212) Noise trading 0.041* 0.049** 0.056** 0.063** 0.050* 0.069*** 0.057** (0.079) (0.033) (0.017) (0.012) (0.060) (0.007) (0.013) Noise trading×Daily urgency −0.329 −0.411 −0.602** −0.737** −0.773** −0.979*** −0.506* (0.336) (0.204) (0.044) (0.019) (0.031) (0.002) (0.096) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.008 0.002 −0.005 −0.007 −0.001** 0.004 −0.011 (0.490) (0.819) (0.566) (0.703) (0.042) (0.465) (0.588) Daily urgency 0.824*** 0.831*** 0.850*** 0.906*** 0.831*** 0.912*** 0.876*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 0.231 0.207 0.256 0.026 0.010 0.010 0.449 (0.228) (0.233) (0.248) (0.957) (0.291) (0.291) (0.471) Noise trading 0.007** 0.008*** 0.008*** 0.009*** 0.007** 0.010*** 0.008*** (0.014) (0.005) (0.003) (0.003) (0.038) (0.002) (0.004) Noise trading×Daily urgency −0.102** −0.111*** −0.124*** −0.143*** −0.122*** −0.160*** −0.113*** (0.010) (0.004) (<0.001) (<0.001) (0.002) (<0.001) (0.002) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.101 −0.013 −0.073 −0.184 −0.007* 0.049 −0.175 (0.316) (0.857) (0.297) (0.212) (0.067) (0.137) (0.312) Daily urgency 6.845*** 6.891*** 7.186*** 7.509*** 7.530*** 7.931*** 7.473*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 3.130** 2.964** 3.455* 3.460 0.029 −1.825*** 6.616 (0.046) (0.042) (0.075) (0.398) (0.672) (0.005) (0.212) Noise trading 0.041* 0.049** 0.056** 0.063** 0.050* 0.069*** 0.057** (0.079) (0.033) (0.017) (0.012) (0.060) (0.007) (0.013) Noise trading×Daily urgency −0.329 −0.411 −0.602** −0.737** −0.773** −0.979*** −0.506* (0.336) (0.204) (0.044) (0.019) (0.031) (0.002) (0.096) This table presents OLS regression coefficients where the dependent variable is a dummy equal to one if any insider trading occurred on a given day (panel A) or the logged volume of shares traded by insiders on a given day (panel B). Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. Daily urgency is the inverse of the number of days from a given day to t = 0. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Table 4 Daily urgency and the relationship between illiquidity and insider trading Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.008 0.002 −0.005 −0.007 −0.001** 0.004 −0.011 (0.490) (0.819) (0.566) (0.703) (0.042) (0.465) (0.588) Daily urgency 0.824*** 0.831*** 0.850*** 0.906*** 0.831*** 0.912*** 0.876*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 0.231 0.207 0.256 0.026 0.010 0.010 0.449 (0.228) (0.233) (0.248) (0.957) (0.291) (0.291) (0.471) Noise trading 0.007** 0.008*** 0.008*** 0.009*** 0.007** 0.010*** 0.008*** (0.014) (0.005) (0.003) (0.003) (0.038) (0.002) (0.004) Noise trading×Daily urgency −0.102** −0.111*** −0.124*** −0.143*** −0.122*** −0.160*** −0.113*** (0.010) (0.004) (<0.001) (<0.001) (0.002) (<0.001) (0.002) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.101 −0.013 −0.073 −0.184 −0.007* 0.049 −0.175 (0.316) (0.857) (0.297) (0.212) (0.067) (0.137) (0.312) Daily urgency 6.845*** 6.891*** 7.186*** 7.509*** 7.530*** 7.931*** 7.473*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 3.130** 2.964** 3.455* 3.460 0.029 −1.825*** 6.616 (0.046) (0.042) (0.075) (0.398) (0.672) (0.005) (0.212) Noise trading 0.041* 0.049** 0.056** 0.063** 0.050* 0.069*** 0.057** (0.079) (0.033) (0.017) (0.012) (0.060) (0.007) (0.013) Noise trading×Daily urgency −0.329 −0.411 −0.602** −0.737** −0.773** −0.979*** −0.506* (0.336) (0.204) (0.044) (0.019) (0.031) (0.002) (0.096) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.008 0.002 −0.005 −0.007 −0.001** 0.004 −0.011 (0.490) (0.819) (0.566) (0.703) (0.042) (0.465) (0.588) Daily urgency 0.824*** 0.831*** 0.850*** 0.906*** 0.831*** 0.912*** 0.876*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 0.231 0.207 0.256 0.026 0.010 0.010 0.449 (0.228) (0.233) (0.248) (0.957) (0.291) (0.291) (0.471) Noise trading 0.007** 0.008*** 0.008*** 0.009*** 0.007** 0.010*** 0.008*** (0.014) (0.005) (0.003) (0.003) (0.038) (0.002) (0.004) Noise trading×Daily urgency −0.102** −0.111*** −0.124*** −0.143*** −0.122*** −0.160*** −0.113*** (0.010) (0.004) (<0.001) (<0.001) (0.002) (<0.001) (0.002) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.101 −0.013 −0.073 −0.184 −0.007* 0.049 −0.175 (0.316) (0.857) (0.297) (0.212) (0.067) (0.137) (0.312) Daily urgency 6.845*** 6.891*** 7.186*** 7.509*** 7.530*** 7.931*** 7.473*** (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) (<0.001) Illiquidity×Daily urgency 3.130** 2.964** 3.455* 3.460 0.029 −1.825*** 6.616 (0.046) (0.042) (0.075) (0.398) (0.672) (0.005) (0.212) Noise trading 0.041* 0.049** 0.056** 0.063** 0.050* 0.069*** 0.057** (0.079) (0.033) (0.017) (0.012) (0.060) (0.007) (0.013) Noise trading×Daily urgency −0.329 −0.411 −0.602** −0.737** −0.773** −0.979*** −0.506* (0.336) (0.204) (0.044) (0.019) (0.031) (0.002) (0.096) This table presents OLS regression coefficients where the dependent variable is a dummy equal to one if any insider trading occurred on a given day (panel A) or the logged volume of shares traded by insiders on a given day (panel B). Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. Daily urgency is the inverse of the number of days from a given day to t = 0. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab The magnitudes of the coefficients on spreads in panel B are economically meaningful. Given the average value of daily urgency (27 days before the announcement), a 1-standard-deviation increase in the quoted spread is associated with a 2.5% increase in insider trading volume, relative to the average insider trading volume. When Daily urgency is one-standard deviation higher (10 days before the announcement), a 1-standard-deviation increase in the quoted spread is associated with a 35% increase in insider trading volume, relative to the average. Thus, the quoted spread is a stronger predictor of insider trading when there is less lead time before the public announcement. Likewise, a 1-standard-deviation increase in noise trading is associated with an increase in insider trading volume of 18.5%, relative to the average, compared to just 5.2% when urgency is 1 standard deviation higher. Table 5 provides estimates of Equation (2) using Event urgency to provide a stricter test of the relationship between illiquidity and informed trading, controlling for both event fixed effects and event-day fixed effects. When event urgency is high, order imbalance and λ are positive and significantly related to both the incidence of informed trading (panel A) and the level of insider trading (panel B) at conventional levels of significance; at Bonferroni levels, none of the measures are statistically significant. As before, noise trading is positively correlated with insider trading when urgency is low, but the correlation diminishes as event urgency increases. These results provide evidence that when order imbalance and Kyle’s λ are higher, the likelihood of insider trading is higher, as long as insiders cannot strategically time their trades to mitigate price impact. In those cases, λ is negatively related to insider trading, as predicted. Table 5 Event urgency and the relationship between illiquidity and insider trading Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.005 0.006 0.000 −0.017 −0.001* −0.006 −0.003 (0.753) (0.599) (0.953) (0.252) (0.068) (0.413) (0.877) Illiquidity×Event urgency 0.039 0.026 0.026* 0.061** 0.002** 0.016 0.035 (0.134) (0.146) (0.061) (0.029) (0.047) (0.134) (0.302) Noise trading 0.006 0.008* 0.008* 0.008* 0.005 0.007 0.007* (0.151) (0.053) (0.053) (0.065) (0.282) (0.111) (0.055) Noise trading×Event urgency −0.016* −0.021*** −0.023*** −0.022*** −0.017* −0.021** −0.021*** (0.052) (0.008) (0.003) (0.006) (0.061) (0.014) (0.008) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.018 0.077 0.027 −0.150 −0.007** −0.038 −0.005 (0.894) (0.437) (0.641) (0.192) (0.031) (0.414) (0.972) Illiquidity×Event urgency 0.289 0.180 0.165 0.539** 0.018** 0.118 0.236 (0.181) (0.224) (0.135) (0.016) (0.040) (0.109) (0.403) Noise trading 0.055 0.066** 0.066** 0.065* 0.043 0.058* 0.066** (0.107) (0.043) (0.046) (0.054) (0.249) (0.096) (0.036) Noise trading×Event urgency −0.140** −0.170*** −0.186*** −0.178*** −0.141* −0.173** −0.175*** (0.043) (0.007) (0.004) (0.007) (0.059) (0.014) (0.006) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.005 0.006 0.000 −0.017 −0.001* −0.006 −0.003 (0.753) (0.599) (0.953) (0.252) (0.068) (0.413) (0.877) Illiquidity×Event urgency 0.039 0.026 0.026* 0.061** 0.002** 0.016 0.035 (0.134) (0.146) (0.061) (0.029) (0.047) (0.134) (0.302) Noise trading 0.006 0.008* 0.008* 0.008* 0.005 0.007 0.007* (0.151) (0.053) (0.053) (0.065) (0.282) (0.111) (0.055) Noise trading×Event urgency −0.016* −0.021*** −0.023*** −0.022*** −0.017* −0.021** −0.021*** (0.052) (0.008) (0.003) (0.006) (0.061) (0.014) (0.008) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.018 0.077 0.027 −0.150 −0.007** −0.038 −0.005 (0.894) (0.437) (0.641) (0.192) (0.031) (0.414) (0.972) Illiquidity×Event urgency 0.289 0.180 0.165 0.539** 0.018** 0.118 0.236 (0.181) (0.224) (0.135) (0.016) (0.040) (0.109) (0.403) Noise trading 0.055 0.066** 0.066** 0.065* 0.043 0.058* 0.066** (0.107) (0.043) (0.046) (0.054) (0.249) (0.096) (0.036) Noise trading×Event urgency −0.140** −0.170*** −0.186*** −0.178*** −0.141* −0.173** −0.175*** (0.043) (0.007) (0.004) (0.007) (0.059) (0.014) (0.006) This table presents OLS regression coefficients where the dependent variable in panel A is a dummy equal to one if any insider trading occurred on a given day, and in panel B is the logged volume of shares traded by insiders on a given day. Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. Event urgency is the inverse of the number of days between the day of the original leak of the information to t = 0. Each regression includes event and event-time fixed effects. These coefficients are not reported. Each regression specification includes a measure of illiquidity, which is listed at the top of the column. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Table 5 Event urgency and the relationship between illiquidity and insider trading Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.005 0.006 0.000 −0.017 −0.001* −0.006 −0.003 (0.753) (0.599) (0.953) (0.252) (0.068) (0.413) (0.877) Illiquidity×Event urgency 0.039 0.026 0.026* 0.061** 0.002** 0.016 0.035 (0.134) (0.146) (0.061) (0.029) (0.047) (0.134) (0.302) Noise trading 0.006 0.008* 0.008* 0.008* 0.005 0.007 0.007* (0.151) (0.053) (0.053) (0.065) (0.282) (0.111) (0.055) Noise trading×Event urgency −0.016* −0.021*** −0.023*** −0.022*** −0.017* −0.021** −0.021*** (0.052) (0.008) (0.003) (0.006) (0.061) (0.014) (0.008) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.018 0.077 0.027 −0.150 −0.007** −0.038 −0.005 (0.894) (0.437) (0.641) (0.192) (0.031) (0.414) (0.972) Illiquidity×Event urgency 0.289 0.180 0.165 0.539** 0.018** 0.118 0.236 (0.181) (0.224) (0.135) (0.016) (0.040) (0.109) (0.403) Noise trading 0.055 0.066** 0.066** 0.065* 0.043 0.058* 0.066** (0.107) (0.043) (0.046) (0.054) (0.249) (0.096) (0.036) Noise trading×Event urgency −0.140** −0.170*** −0.186*** −0.178*** −0.141* −0.173** −0.175*** (0.043) (0.007) (0.004) (0.007) (0.059) (0.014) (0.006) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Dependent variable: Informed trading dummy Illiquidity −0.005 0.006 0.000 −0.017 −0.001* −0.006 −0.003 (0.753) (0.599) (0.953) (0.252) (0.068) (0.413) (0.877) Illiquidity×Event urgency 0.039 0.026 0.026* 0.061** 0.002** 0.016 0.035 (0.134) (0.146) (0.061) (0.029) (0.047) (0.134) (0.302) Noise trading 0.006 0.008* 0.008* 0.008* 0.005 0.007 0.007* (0.151) (0.053) (0.053) (0.065) (0.282) (0.111) (0.055) Noise trading×Event urgency −0.016* −0.021*** −0.023*** −0.022*** −0.017* −0.021** −0.021*** (0.052) (0.008) (0.003) (0.006) (0.061) (0.014) (0.008) B. Dependent variable: ln(1+informed trading volume) Illiquidity −0.018 0.077 0.027 −0.150 −0.007** −0.038 −0.005 (0.894) (0.437) (0.641) (0.192) (0.031) (0.414) (0.972) Illiquidity×Event urgency 0.289 0.180 0.165 0.539** 0.018** 0.118 0.236 (0.181) (0.224) (0.135) (0.016) (0.040) (0.109) (0.403) Noise trading 0.055 0.066** 0.066** 0.065* 0.043 0.058* 0.066** (0.107) (0.043) (0.046) (0.054) (0.249) (0.096) (0.036) Noise trading×Event urgency −0.140** −0.170*** −0.186*** −0.178*** −0.141* −0.173** −0.175*** (0.043) (0.007) (0.004) (0.007) (0.059) (0.014) (0.006) This table presents OLS regression coefficients where the dependent variable in panel A is a dummy equal to one if any insider trading occurred on a given day, and in panel B is the logged volume of shares traded by insiders on a given day. Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. Event urgency is the inverse of the number of days between the day of the original leak of the information to t = 0. Each regression includes event and event-time fixed effects. These coefficients are not reported. Each regression specification includes a measure of illiquidity, which is listed at the top of the column. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab The economic magnitude of the statistically significant relationships are meaningful. In particular, in an event with average urgency, a 1-standard-deviation increase in λ is associated with a 9.4% decrease in insider trading volume, relative to the average, consistent with strategic timing. In contrast, in events with an urgency 1 standard deviation higher than average, a one-standard deviation increase in λ is associated with an increase in insider trading volume of 2.2%, consistent with the predictions outlined above. In terms of the likelihood of insider trading, when urgency is normal, an increase in λ is associated with a 12.5% decrease in the likelihood of insider trading. When urgency is high, an increase in λ is associated with a 2.4% decrease in the likelihood of insider trading. For absolute order imbalance, the magnitudes are smaller: an increase in order imbalance is associated with a decrease of 2% of insider trading volume when urgency is average, compared to an increase of 3% when urgency is high. 5.4 Tests that control for sampling bias Table 6 presents the estimates of Equation (3) that control for sampling bias based on regulators’ detection methods. Panel A includes the FINRA dummy; panel B includes the FBI dummy; panel C includes the network size dummy; and panel D includes all three variables simultaneously. All regressions include noise trading and its interaction with urgency, though the coefficients are not reported for brevity. Internet AppendixTable 2 provides analogous results using the volume of shares traded by insiders as the dependent variable. Table 6 Relationship between illiquidity and insider trading when controlling for sampling bias Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Investigation inclusion or not of FINRA participation Illiquidity 0.036 0.049*** 0.007 −0.035** 0.000 −0.003 0.027 (0.114) (0.003) (0.549) (0.043) (0.785) (0.865) (0.319) Illiquidity×Event urgency −0.021 −0.033 0.012 0.089*** 0.001 0.010 −0.004 (0.543) (0.164) (0.510) (0.001) (0.594) (0.612) (0.931) Illiquidity×FINRA −0.079*** −0.083*** −0.015 0.032 −0.002* −0.007 −0.061 (0.009) (<0.001) (0.330) (0.259) (0.099) (0.738) (0.109) Illiquidity×Urgency×FINRA 0.212** 0.282*** 0.082* −0.068 0.004 0.057 0.089 (0.030) (<0.001) (0.084) (0.394) (0.384) (0.386) (0.625) B. Investigations inclusion or not of FBI participation Illiquidity −0.003 0.007 0.001 −0.018 −0.001* −0.004 −0.002 (0.856) (0.566) (0.924) (0.211) (0.082) (0.625) (0.894) Illiquidity×Event urgency 0.039 0.026 0.026* 0.067** 0.002** 0.013 0.034 (0.135) (0.162) (0.060) (0.019) (0.030) (0.207) (0.311) Illiquidity×FBI −0.049 −0.051 −0.010 0.038 0.000 −0.042*** −1.476*** (0.393) (0.615) (0.910) (0.610) (0.848) (0.001) (0.002) Illiquidity×Urgency×FBI −0.004 0.058 0.003 −0.130 −0.003 0.058 −0.751 (0.961) (0.745) (0.977) (0.375) (0.695) (0.478) (0.898) C. Traders belong to small versus large network Illiquidity −0.032* −0.027 0.000 −0.033 −0.002** −0.017 −0.018 (0.055) (0.130) (0.997) (0.277) (0.045) (0.339) (0.151) Illiquidity×Event urgency 0.044 0.066** 0.021 0.104 0.002 0.027 0.034 (0.287) (0.048) (0.496) (0.102) (0.253) (0.378) (0.548) Illiquidity×Small network 0.034 0.040* 0.001 0.023 0.002 0.016 0.019 (0.171) (0.069) (0.974) (0.519) (0.135) (0.387) (0.426) Illiquidity×Urgency×Small nwk. −0.012 −0.049 0.005 −0.057 0.000 −0.017 −0.003 (0.811) (0.203) (0.892) (0.421) (0.834) (0.604) (0.956) D. Three detection methods Illiquidity 0.031 0.040 0.012 −0.059* −0.001 −0.013 0.049 (0.293) (0.106) (0.561) (0.060) (0.430) (0.564) (0.283) Illiquidity×Event urgency −0.010 −0.025 0.004 0.143** 0.001 0.013 −0.078 (0.839) (0.435) (0.909) (0.018) (0.768) (0.698) (0.712) Illiquidity×FINRA −0.080*** −0.080*** −0.016 0.033 −0.002* −0.007 −0.068 (0.010) (<0.001) (0.309) (0.259) (0.090) (0.738) (0.160) Illiquidity×Urgency×FINRA 0.213** 0.283*** 0.087* −0.053 0.008 0.097 0.129 (0.037) (<0.001) (0.076) (0.525) (0.124) (0.216) (0.650) Illiquidity×FBI −0.059 −0.023 −0.013 0.052 0.001 −0.040*** −1.449*** (0.318) (0.831) (0.893) (0.492) (0.635) (0.004) (0.002) Illiquidity×Urgency×FBI 0.010 −0.080 −0.009 −0.139 −0.009 −0.030 −0.781 (0.897) (0.676) (0.945) (0.360) (0.257) (0.776) (0.893) Illiquidity×Small network 0.010 0.009 −0.005 0.028 0.001 0.017 −0.022 (0.702) (0.654) (0.768) (0.433) (0.201) (0.362) (0.548) Illiquidity×Urgency×Small nwk. −0.014 −0.007 0.009 −0.064 0.000 −0.009 0.075 (0.762) (0.831) (0.802) (0.366) (0.982) (0.764) (0.717) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Investigation inclusion or not of FINRA participation Illiquidity 0.036 0.049*** 0.007 −0.035** 0.000 −0.003 0.027 (0.114) (0.003) (0.549) (0.043) (0.785) (0.865) (0.319) Illiquidity×Event urgency −0.021 −0.033 0.012 0.089*** 0.001 0.010 −0.004 (0.543) (0.164) (0.510) (0.001) (0.594) (0.612) (0.931) Illiquidity×FINRA −0.079*** −0.083*** −0.015 0.032 −0.002* −0.007 −0.061 (0.009) (<0.001) (0.330) (0.259) (0.099) (0.738) (0.109) Illiquidity×Urgency×FINRA 0.212** 0.282*** 0.082* −0.068 0.004 0.057 0.089 (0.030) (<0.001) (0.084) (0.394) (0.384) (0.386) (0.625) B. Investigations inclusion or not of FBI participation Illiquidity −0.003 0.007 0.001 −0.018 −0.001* −0.004 −0.002 (0.856) (0.566) (0.924) (0.211) (0.082) (0.625) (0.894) Illiquidity×Event urgency 0.039 0.026 0.026* 0.067** 0.002** 0.013 0.034 (0.135) (0.162) (0.060) (0.019) (0.030) (0.207) (0.311) Illiquidity×FBI −0.049 −0.051 −0.010 0.038 0.000 −0.042*** −1.476*** (0.393) (0.615) (0.910) (0.610) (0.848) (0.001) (0.002) Illiquidity×Urgency×FBI −0.004 0.058 0.003 −0.130 −0.003 0.058 −0.751 (0.961) (0.745) (0.977) (0.375) (0.695) (0.478) (0.898) C. Traders belong to small versus large network Illiquidity −0.032* −0.027 0.000 −0.033 −0.002** −0.017 −0.018 (0.055) (0.130) (0.997) (0.277) (0.045) (0.339) (0.151) Illiquidity×Event urgency 0.044 0.066** 0.021 0.104 0.002 0.027 0.034 (0.287) (0.048) (0.496) (0.102) (0.253) (0.378) (0.548) Illiquidity×Small network 0.034 0.040* 0.001 0.023 0.002 0.016 0.019 (0.171) (0.069) (0.974) (0.519) (0.135) (0.387) (0.426) Illiquidity×Urgency×Small nwk. −0.012 −0.049 0.005 −0.057 0.000 −0.017 −0.003 (0.811) (0.203) (0.892) (0.421) (0.834) (0.604) (0.956) D. Three detection methods Illiquidity 0.031 0.040 0.012 −0.059* −0.001 −0.013 0.049 (0.293) (0.106) (0.561) (0.060) (0.430) (0.564) (0.283) Illiquidity×Event urgency −0.010 −0.025 0.004 0.143** 0.001 0.013 −0.078 (0.839) (0.435) (0.909) (0.018) (0.768) (0.698) (0.712) Illiquidity×FINRA −0.080*** −0.080*** −0.016 0.033 −0.002* −0.007 −0.068 (0.010) (<0.001) (0.309) (0.259) (0.090) (0.738) (0.160) Illiquidity×Urgency×FINRA 0.213** 0.283*** 0.087* −0.053 0.008 0.097 0.129 (0.037) (<0.001) (0.076) (0.525) (0.124) (0.216) (0.650) Illiquidity×FBI −0.059 −0.023 −0.013 0.052 0.001 −0.040*** −1.449*** (0.318) (0.831) (0.893) (0.492) (0.635) (0.004) (0.002) Illiquidity×Urgency×FBI 0.010 −0.080 −0.009 −0.139 −0.009 −0.030 −0.781 (0.897) (0.676) (0.945) (0.360) (0.257) (0.776) (0.893) Illiquidity×Small network 0.010 0.009 −0.005 0.028 0.001 0.017 −0.022 (0.702) (0.654) (0.768) (0.433) (0.201) (0.362) (0.548) Illiquidity×Urgency×Small nwk. −0.014 −0.007 0.009 −0.064 0.000 −0.009 0.075 (0.762) (0.831) (0.802) (0.366) (0.982) (0.764) (0.717) This table presents results from specifications identical to those in panel A of Table 5, except for the inclusion of an interaction dummy variable to proxy for detection method by regulators. The dummy variables are FINRA (panel A), which is equal to one for events in which FINRA assisted in the investigation; FBI (panel B), which is equal to one for events in which the FBI assisted in the investigation; and Small network (panel C), which is equal to one for events in which the traders belong to a trading network with three or less members. Panel D includes all three proxies. FINRA and Small network interaction dummies indicate a higher likelihood that insider trading was detected by market-based patterns. Each regression includes event and event-time fixed effects and noise trading and its interaction with event urgency. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Table 6 Relationship between illiquidity and insider trading when controlling for sampling bias Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Investigation inclusion or not of FINRA participation Illiquidity 0.036 0.049*** 0.007 −0.035** 0.000 −0.003 0.027 (0.114) (0.003) (0.549) (0.043) (0.785) (0.865) (0.319) Illiquidity×Event urgency −0.021 −0.033 0.012 0.089*** 0.001 0.010 −0.004 (0.543) (0.164) (0.510) (0.001) (0.594) (0.612) (0.931) Illiquidity×FINRA −0.079*** −0.083*** −0.015 0.032 −0.002* −0.007 −0.061 (0.009) (<0.001) (0.330) (0.259) (0.099) (0.738) (0.109) Illiquidity×Urgency×FINRA 0.212** 0.282*** 0.082* −0.068 0.004 0.057 0.089 (0.030) (<0.001) (0.084) (0.394) (0.384) (0.386) (0.625) B. Investigations inclusion or not of FBI participation Illiquidity −0.003 0.007 0.001 −0.018 −0.001* −0.004 −0.002 (0.856) (0.566) (0.924) (0.211) (0.082) (0.625) (0.894) Illiquidity×Event urgency 0.039 0.026 0.026* 0.067** 0.002** 0.013 0.034 (0.135) (0.162) (0.060) (0.019) (0.030) (0.207) (0.311) Illiquidity×FBI −0.049 −0.051 −0.010 0.038 0.000 −0.042*** −1.476*** (0.393) (0.615) (0.910) (0.610) (0.848) (0.001) (0.002) Illiquidity×Urgency×FBI −0.004 0.058 0.003 −0.130 −0.003 0.058 −0.751 (0.961) (0.745) (0.977) (0.375) (0.695) (0.478) (0.898) C. Traders belong to small versus large network Illiquidity −0.032* −0.027 0.000 −0.033 −0.002** −0.017 −0.018 (0.055) (0.130) (0.997) (0.277) (0.045) (0.339) (0.151) Illiquidity×Event urgency 0.044 0.066** 0.021 0.104 0.002 0.027 0.034 (0.287) (0.048) (0.496) (0.102) (0.253) (0.378) (0.548) Illiquidity×Small network 0.034 0.040* 0.001 0.023 0.002 0.016 0.019 (0.171) (0.069) (0.974) (0.519) (0.135) (0.387) (0.426) Illiquidity×Urgency×Small nwk. −0.012 −0.049 0.005 −0.057 0.000 −0.017 −0.003 (0.811) (0.203) (0.892) (0.421) (0.834) (0.604) (0.956) D. Three detection methods Illiquidity 0.031 0.040 0.012 −0.059* −0.001 −0.013 0.049 (0.293) (0.106) (0.561) (0.060) (0.430) (0.564) (0.283) Illiquidity×Event urgency −0.010 −0.025 0.004 0.143** 0.001 0.013 −0.078 (0.839) (0.435) (0.909) (0.018) (0.768) (0.698) (0.712) Illiquidity×FINRA −0.080*** −0.080*** −0.016 0.033 −0.002* −0.007 −0.068 (0.010) (<0.001) (0.309) (0.259) (0.090) (0.738) (0.160) Illiquidity×Urgency×FINRA 0.213** 0.283*** 0.087* −0.053 0.008 0.097 0.129 (0.037) (<0.001) (0.076) (0.525) (0.124) (0.216) (0.650) Illiquidity×FBI −0.059 −0.023 −0.013 0.052 0.001 −0.040*** −1.449*** (0.318) (0.831) (0.893) (0.492) (0.635) (0.004) (0.002) Illiquidity×Urgency×FBI 0.010 −0.080 −0.009 −0.139 −0.009 −0.030 −0.781 (0.897) (0.676) (0.945) (0.360) (0.257) (0.776) (0.893) Illiquidity×Small network 0.010 0.009 −0.005 0.028 0.001 0.017 −0.022 (0.702) (0.654) (0.768) (0.433) (0.201) (0.362) (0.548) Illiquidity×Urgency×Small nwk. −0.014 −0.007 0.009 −0.064 0.000 −0.009 0.075 (0.762) (0.831) (0.802) (0.366) (0.982) (0.764) (0.717) Illiquidity measure: . Quoted spread . Effective spread . Price impact . Order imbalance . Kyle’s λ . MRR θ . Amihud illiquidity . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . A. Investigation inclusion or not of FINRA participation Illiquidity 0.036 0.049*** 0.007 −0.035** 0.000 −0.003 0.027 (0.114) (0.003) (0.549) (0.043) (0.785) (0.865) (0.319) Illiquidity×Event urgency −0.021 −0.033 0.012 0.089*** 0.001 0.010 −0.004 (0.543) (0.164) (0.510) (0.001) (0.594) (0.612) (0.931) Illiquidity×FINRA −0.079*** −0.083*** −0.015 0.032 −0.002* −0.007 −0.061 (0.009) (<0.001) (0.330) (0.259) (0.099) (0.738) (0.109) Illiquidity×Urgency×FINRA 0.212** 0.282*** 0.082* −0.068 0.004 0.057 0.089 (0.030) (<0.001) (0.084) (0.394) (0.384) (0.386) (0.625) B. Investigations inclusion or not of FBI participation Illiquidity −0.003 0.007 0.001 −0.018 −0.001* −0.004 −0.002 (0.856) (0.566) (0.924) (0.211) (0.082) (0.625) (0.894) Illiquidity×Event urgency 0.039 0.026 0.026* 0.067** 0.002** 0.013 0.034 (0.135) (0.162) (0.060) (0.019) (0.030) (0.207) (0.311) Illiquidity×FBI −0.049 −0.051 −0.010 0.038 0.000 −0.042*** −1.476*** (0.393) (0.615) (0.910) (0.610) (0.848) (0.001) (0.002) Illiquidity×Urgency×FBI −0.004 0.058 0.003 −0.130 −0.003 0.058 −0.751 (0.961) (0.745) (0.977) (0.375) (0.695) (0.478) (0.898) C. Traders belong to small versus large network Illiquidity −0.032* −0.027 0.000 −0.033 −0.002** −0.017 −0.018 (0.055) (0.130) (0.997) (0.277) (0.045) (0.339) (0.151) Illiquidity×Event urgency 0.044 0.066** 0.021 0.104 0.002 0.027 0.034 (0.287) (0.048) (0.496) (0.102) (0.253) (0.378) (0.548) Illiquidity×Small network 0.034 0.040* 0.001 0.023 0.002 0.016 0.019 (0.171) (0.069) (0.974) (0.519) (0.135) (0.387) (0.426) Illiquidity×Urgency×Small nwk. −0.012 −0.049 0.005 −0.057 0.000 −0.017 −0.003 (0.811) (0.203) (0.892) (0.421) (0.834) (0.604) (0.956) D. Three detection methods Illiquidity 0.031 0.040 0.012 −0.059* −0.001 −0.013 0.049 (0.293) (0.106) (0.561) (0.060) (0.430) (0.564) (0.283) Illiquidity×Event urgency −0.010 −0.025 0.004 0.143** 0.001 0.013 −0.078 (0.839) (0.435) (0.909) (0.018) (0.768) (0.698) (0.712) Illiquidity×FINRA −0.080*** −0.080*** −0.016 0.033 −0.002* −0.007 −0.068 (0.010) (<0.001) (0.309) (0.259) (0.090) (0.738) (0.160) Illiquidity×Urgency×FINRA 0.213** 0.283*** 0.087* −0.053 0.008 0.097 0.129 (0.037) (<0.001) (0.076) (0.525) (0.124) (0.216) (0.650) Illiquidity×FBI −0.059 −0.023 −0.013 0.052 0.001 −0.040*** −1.449*** (0.318) (0.831) (0.893) (0.492) (0.635) (0.004) (0.002) Illiquidity×Urgency×FBI 0.010 −0.080 −0.009 −0.139 −0.009 −0.030 −0.781 (0.897) (0.676) (0.945) (0.360) (0.257) (0.776) (0.893) Illiquidity×Small network 0.010 0.009 −0.005 0.028 0.001 0.017 −0.022 (0.702) (0.654) (0.768) (0.433) (0.201) (0.362) (0.548) Illiquidity×Urgency×Small nwk. −0.014 −0.007 0.009 −0.064 0.000 −0.009 0.075 (0.762) (0.831) (0.802) (0.366) (0.982) (0.764) (0.717) This table presents results from specifications identical to those in panel A of Table 5, except for the inclusion of an interaction dummy variable to proxy for detection method by regulators. The dummy variables are FINRA (panel A), which is equal to one for events in which FINRA assisted in the investigation; FBI (panel B), which is equal to one for events in which the FBI assisted in the investigation; and Small network (panel C), which is equal to one for events in which the traders belong to a trading network with three or less members. Panel D includes all three proxies. FINRA and Small network interaction dummies indicate a higher likelihood that insider trading was detected by market-based patterns. Each regression includes event and event-time fixed effects and noise trading and its interaction with event urgency. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab In panel A, the interaction with FINRA is designed to control for algorithmic detection methods used by FINRA. The results shows that quoted and effective spreads are reliable predictors of insider trading in cases in which FINRA is involved. When FINRA is involved and urgency is low, quoted and effective spread are negatively related to insider trading, consistent with strategic timing. As urgency increases for FINRA cases, quoted and effective spread become more positively related to insider trading. The coefficients are highly significant, even at Bonferroni significance levels. In contrast, when FINRA is not involved, these measures have little predictive power. These results imply that FINRA’s detection algorithm uses a measure correlated with spreads to detect insider trading. In cases not detected by algorithmic detection software, spreads did not reveal insider trading. In contrast, Table 6 shows that order imbalance is a good predictor of insider trading, regardless of FINRA’s involvement. When urgency is low, order imbalance is significantly negatively related to insider trading. However, as urgency increases, the relationship between order imbalance and insider trading becomes more positive. The coefficients indicate that for average urgency, a 1-standard-deviation increase in order imbalance is associated with a 5.4% decrease in the likelihood of insider trading. When urgency is 1 standard deviation above its average, a 1-standard-deviation increase in order imbalance is associated with a 1.1% increase in the likelihood of insider trading. These results show that order imbalance is a reliable indicator of informed trading in all samples, and that FINRA’s detection method is unlikely to incorporate order imbalance. The other illiquidity measures display little predictive power. Using FBI participation to identify nonalgorithmically detected insider trading, panel B of Table 6 shows that order imbalance and Kyle’s λ are negatively related to insider trading when urgency is low, but positively related when urgency is high, consistent with the predictions. None of the spread-based measures, order imbalance, or λ are influenced by FBI investigations. MRR θ and Amihud illiquidity are lower in FBI cases that are not urgent. In panel C, effective spreads are higher when traders belong to smaller networks, consistent with the SEC detecting small networks using algorithmic detection methods. Finally, panel D includes all three detection mechanisms. As before, the spread-based measures are correlated only with FINRA, while order imbalance has predictive power that is unrelated to any of the detection mechanisms. Kyle’s λ, MRR θ, and Amihud illiquidity have little statistical power. These results likely reflect that the FINRA dummy is the best test of sampling bias. The findings in these tests have important implications. First, effective spread and order imbalance are the most robust predictors of insider trading after all controls. These measures correctly identify insider trading in cases detected by abnormal market behavior as well as cases detected by traditional investigative techniques. In contrast, the other measures lose their predictive power after controlling for detection methods. Second, the algorithm used by FINRA to detect insider trading appears to use inputs related to spreads, but not the other illiquidity measures I study. These results differ from those in Kacperczyk and Pagnotta (2019b) which argues that all of their stock-based measures of illiquidity are robust to sampling bias. As stated above, methodological choices likely causes these differences. In particular, my triple interaction framework controls for both urgency and sample bias simultaneously and provides statistical tests of the equality of coefficients, while forcing control variables to be constant across subsamples. 5.5 Factor analysis To better understand how the seven measures of illiquidity are related to each other, panel A of Table 7 presents the results of a factor analysis of the variables’ correlations. The first factor explains 91.7% of the variance common to all measures. This suggests that there is an unobserved latent variable that determines almost all of the variability across measures. The second factor explains 17.2% of the common variance. The rest of the factors have very small or negative eigenvalues.7 Table 7 Latent factor model of illiquidity measures A: Factor analysis . Factor . Eigenvalue . Proportion of variance . Cumulative proportion . Factor 1 3.239 0.917 0.917 Factor 2 0.607 0.172 1.089 Factor 3 0.083 0.024 1.112 Factor 4 −0.019 −0.005 1.107 Factor 5 −0.073 −0.021 1.086 Factor 6 −0.091 −0.026 1.061 Factor 7 −0.214 −0.061 1.000 B: Factor loadings Illiquidity measure Factor 1 Factor 2 Uniqueness Quoted spread 0.929 −0.084 0.126 Effective spread 0.922 −0.152 0.120 Price impact 0.670 −0.095 0.499 Order imbalance 0.455 0.009 0.785 Kyle’s λ 0.544 0.484 0.470 MRR θ 0.243 0.553 0.634 Amihud 0.718 −0.166 0.436 A: Factor analysis . Factor . Eigenvalue . Proportion of variance . Cumulative proportion . Factor 1 3.239 0.917 0.917 Factor 2 0.607 0.172 1.089 Factor 3 0.083 0.024 1.112 Factor 4 −0.019 −0.005 1.107 Factor 5 −0.073 −0.021 1.086 Factor 6 −0.091 −0.026 1.061 Factor 7 −0.214 −0.061 1.000 B: Factor loadings Illiquidity measure Factor 1 Factor 2 Uniqueness Quoted spread 0.929 −0.084 0.126 Effective spread 0.922 −0.152 0.120 Price impact 0.670 −0.095 0.499 Order imbalance 0.455 0.009 0.785 Kyle’s λ 0.544 0.484 0.470 MRR θ 0.243 0.553 0.634 Amihud 0.718 −0.166 0.436 This table presents a factor analysis of seven measures of illiquidity. Panel A presents the eigenvalues of each latent factor, which represents the variance of the factor. Proportion is the proportion of total variance accounted for by the factor. Cumulative is the cumulative proportion of variance. Panel B presents the factor loadings of each of the illiquidity measures on the first two factors. The loadings represent the correlations between the variable and the latent factors. Uniqueness represents the proportion of the variance of the measures of illiquidity not associated with the two factors. Open in new tab Table 7 Latent factor model of illiquidity measures A: Factor analysis . Factor . Eigenvalue . Proportion of variance . Cumulative proportion . Factor 1 3.239 0.917 0.917 Factor 2 0.607 0.172 1.089 Factor 3 0.083 0.024 1.112 Factor 4 −0.019 −0.005 1.107 Factor 5 −0.073 −0.021 1.086 Factor 6 −0.091 −0.026 1.061 Factor 7 −0.214 −0.061 1.000 B: Factor loadings Illiquidity measure Factor 1 Factor 2 Uniqueness Quoted spread 0.929 −0.084 0.126 Effective spread 0.922 −0.152 0.120 Price impact 0.670 −0.095 0.499 Order imbalance 0.455 0.009 0.785 Kyle’s λ 0.544 0.484 0.470 MRR θ 0.243 0.553 0.634 Amihud 0.718 −0.166 0.436 A: Factor analysis . Factor . Eigenvalue . Proportion of variance . Cumulative proportion . Factor 1 3.239 0.917 0.917 Factor 2 0.607 0.172 1.089 Factor 3 0.083 0.024 1.112 Factor 4 −0.019 −0.005 1.107 Factor 5 −0.073 −0.021 1.086 Factor 6 −0.091 −0.026 1.061 Factor 7 −0.214 −0.061 1.000 B: Factor loadings Illiquidity measure Factor 1 Factor 2 Uniqueness Quoted spread 0.929 −0.084 0.126 Effective spread 0.922 −0.152 0.120 Price impact 0.670 −0.095 0.499 Order imbalance 0.455 0.009 0.785 Kyle’s λ 0.544 0.484 0.470 MRR θ 0.243 0.553 0.634 Amihud 0.718 −0.166 0.436 This table presents a factor analysis of seven measures of illiquidity. Panel A presents the eigenvalues of each latent factor, which represents the variance of the factor. Proportion is the proportion of total variance accounted for by the factor. Cumulative is the cumulative proportion of variance. Panel B presents the factor loadings of each of the illiquidity measures on the first two factors. The loadings represent the correlations between the variable and the latent factors. Uniqueness represents the proportion of the variance of the measures of illiquidity not associated with the two factors. Open in new tab Panel B of Table 7 presents the factor loadings of the seven illiquidity measures on the first two latent factors. These loading suggest that the dominant factor explains quoted and effective spreads, price impact, and Amihud illiquidity. The second factor has greater explanatory power for Kyle’s λ and MRR θ. Order imbalance has the lowest factor loadings overall, with a high degree of unique variance that is unexplained by the factors. Pairwise correlations of the illiquidity measures, noise trading, and the two factors are presented in the Internet Appendix, after normalizing the variables by event and event day fixed effects. The spread-based measures and Amihud illiquidity are highly positively correlated with the first factor and slightly negatively correlated with the second. Kyle’s λ and MRR θ are more heavily correlated with the second factor. Order imbalance has lower correlations with both factors and all other variables, consistent with its high level of unique variance. These correlations emphasize that two latent factors, plus absolute order imbalance explain most of the variance in illiquidity. These correlations also provide evidence that the strictest version of the Bonferroni correction would be overly conservative since the variables are not independent. 5.6 Horse race between measures of illiquidity Given the latent factor structure underlying illiquidity measures, in this section, I run a horse race to determine which measures have the most explanatory power, including the factors, controlling for other measures. Table 8 presents coefficient estimates from the same regressions as before, but including the measures simultaneously in the same specification. In the first three columns, to avoid multicollinearity problems, I only include 1 of the 3 spread-based measures at a time. The coefficients in Table 8 reflect the marginal effect of each variable on the likelihood of insider trading, while partialing out variation that is correlated with the other measures of illiquidity. Table 8 Multivariate regressions . (1) . (2) . (3) . (4) . (5) . Factor 1 0.024** 0.025** (0.036) (0.030) Factor 1×Urgency −0.012 −0.014 (0.538) (0.470) Factor 1×FINRA −0.051*** −0.052*** (0.002) (0.002) Factor 1×Urgency×FINRA 0.189*** 0.194*** (0.001) (0.001) Factor 2 −0.016 −0.016 (0.115) (0.107) Factor 2×Urgency 0.020 0.020 (0.130) (0.128) Factor 2×FINRA 0.015 0.015 (0.177) (0.167) Factor 2×Urgency×FINRA −0.032 −0.033 (0.496) (0.480) Order imbalance −0.044** −0.034* −0.034* −0.049*** (0.025) (0.067) (0.067) (0.010) Order imbalance×Urgency 0.104*** 0.089*** 0.090*** 0.107*** (0.002) (0.003) (0.002) (0.001) Order imbalance×FINRA 0.043 0.032 0.031 0.060* (0.206) (0.312) (0.332) (0.086) Order imbalance×Urgency×FINRA −0.095 −0.073 −0.054 −0.171* (0.295) (0.404) (0.531) (0.086) Quoted spread 0.037 (0.116) Quoted spread×Urgency −0.028 (0.426) Quoted spread×FINRA −0.075** (0.012) Quoted spread×Urgency×FINRA 0.209** (0.030) Effective spread 0.046** (0.011) Effective spread×Urgency −0.032 (0.193) Effective spread×FINRA −0.077*** (<0.001) Effective spread×Urgency×FINRA 0.326*** (<0.001) Price impact 0.003 (0.815) Price impact×Urgency 0.015 (0.448) Price impact×FINRA −0.013 (0.450) Price impact×Urgency×FINRA 0.097** (0.043) Kyle’s λ 0.000 −0.001 0.000 (0.876) (0.520) (0.967) Kyle’s λ×Urgency 0.000 0.001 0.001 (0.873) (0.399) (0.587) Kyle’s λ×FINRA −0.001 0.000 −0.001 (0.620) (0.706) (0.224) Kyle’s λ×Urgency×FINRA 0.003 0.000 0.004 (0.606) (0.948) (0.439) MRR θ −0.018 −0.001 −0.001 (0.308) (0.959) (0.962) MRR θ×Urgency 0.030 0.005 0.005 (0.162) (0.815) (0.825) MRR θ×FINRA 0.018 0.000 0.000 (0.362) (0.999) (0.981) MRR θ×Urgency×FINRA −0.006 0.029 0.021 (0.921) (0.617) (0.713) Amihud 0.008 0.014 0.030 (0.780) (0.597) (0.373) Amihud×Urgency 0.025 0.007 −0.005 (0.614) (0.877) (0.927) Amihud×FINRA −0.007 −0.018 −0.042 (0.859) (0.656) (0.360) Amihud×Urgency×FINRA −0.125 −0.143 −0.039 (0.635) (0.560) (0.878) Noise trading 0.004 0.004 0.005 0.004 0.004 (0.452) (0.376) (0.282) (0.406) (0.433) Noise trading×Urgency −0.011 −0.014 −0.016* −0.013 −0.012 (0.250) (0.122) (0.095) (0.175) (0.201) Event fixed effects Yes Yes Yes Yes Yes Event-day fixed effects Yes Yes Yes Yes Yes Observations 37,786 38,869 38,869 37,786 37,786 Adjusted R2 0.288 0.294 0.292 0.288 0.288 . (1) . (2) . (3) . (4) . (5) . Factor 1 0.024** 0.025** (0.036) (0.030) Factor 1×Urgency −0.012 −0.014 (0.538) (0.470) Factor 1×FINRA −0.051*** −0.052*** (0.002) (0.002) Factor 1×Urgency×FINRA 0.189*** 0.194*** (0.001) (0.001) Factor 2 −0.016 −0.016 (0.115) (0.107) Factor 2×Urgency 0.020 0.020 (0.130) (0.128) Factor 2×FINRA 0.015 0.015 (0.177) (0.167) Factor 2×Urgency×FINRA −0.032 −0.033 (0.496) (0.480) Order imbalance −0.044** −0.034* −0.034* −0.049*** (0.025) (0.067) (0.067) (0.010) Order imbalance×Urgency 0.104*** 0.089*** 0.090*** 0.107*** (0.002) (0.003) (0.002) (0.001) Order imbalance×FINRA 0.043 0.032 0.031 0.060* (0.206) (0.312) (0.332) (0.086) Order imbalance×Urgency×FINRA −0.095 −0.073 −0.054 −0.171* (0.295) (0.404) (0.531) (0.086) Quoted spread 0.037 (0.116) Quoted spread×Urgency −0.028 (0.426) Quoted spread×FINRA −0.075** (0.012) Quoted spread×Urgency×FINRA 0.209** (0.030) Effective spread 0.046** (0.011) Effective spread×Urgency −0.032 (0.193) Effective spread×FINRA −0.077*** (<0.001) Effective spread×Urgency×FINRA 0.326*** (<0.001) Price impact 0.003 (0.815) Price impact×Urgency 0.015 (0.448) Price impact×FINRA −0.013 (0.450) Price impact×Urgency×FINRA 0.097** (0.043) Kyle’s λ 0.000 −0.001 0.000 (0.876) (0.520) (0.967) Kyle’s λ×Urgency 0.000 0.001 0.001 (0.873) (0.399) (0.587) Kyle’s λ×FINRA −0.001 0.000 −0.001 (0.620) (0.706) (0.224) Kyle’s λ×Urgency×FINRA 0.003 0.000 0.004 (0.606) (0.948) (0.439) MRR θ −0.018 −0.001 −0.001 (0.308) (0.959) (0.962) MRR θ×Urgency 0.030 0.005 0.005 (0.162) (0.815) (0.825) MRR θ×FINRA 0.018 0.000 0.000 (0.362) (0.999) (0.981) MRR θ×Urgency×FINRA −0.006 0.029 0.021 (0.921) (0.617) (0.713) Amihud 0.008 0.014 0.030 (0.780) (0.597) (0.373) Amihud×Urgency 0.025 0.007 −0.005 (0.614) (0.877) (0.927) Amihud×FINRA −0.007 −0.018 −0.042 (0.859) (0.656) (0.360) Amihud×Urgency×FINRA −0.125 −0.143 −0.039 (0.635) (0.560) (0.878) Noise trading 0.004 0.004 0.005 0.004 0.004 (0.452) (0.376) (0.282) (0.406) (0.433) Noise trading×Urgency −0.011 −0.014 −0.016* −0.013 −0.012 (0.250) (0.122) (0.095) (0.175) (0.201) Event fixed effects Yes Yes Yes Yes Yes Event-day fixed effects Yes Yes Yes Yes Yes Observations 37,786 38,869 38,869 37,786 37,786 Adjusted R2 0.288 0.294 0.292 0.288 0.288 This table presents OLS regression coefficients where the dependent variable is a dummy equal to one if any insider trading occurred on a given day. Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Table 8 Multivariate regressions . (1) . (2) . (3) . (4) . (5) . Factor 1 0.024** 0.025** (0.036) (0.030) Factor 1×Urgency −0.012 −0.014 (0.538) (0.470) Factor 1×FINRA −0.051*** −0.052*** (0.002) (0.002) Factor 1×Urgency×FINRA 0.189*** 0.194*** (0.001) (0.001) Factor 2 −0.016 −0.016 (0.115) (0.107) Factor 2×Urgency 0.020 0.020 (0.130) (0.128) Factor 2×FINRA 0.015 0.015 (0.177) (0.167) Factor 2×Urgency×FINRA −0.032 −0.033 (0.496) (0.480) Order imbalance −0.044** −0.034* −0.034* −0.049*** (0.025) (0.067) (0.067) (0.010) Order imbalance×Urgency 0.104*** 0.089*** 0.090*** 0.107*** (0.002) (0.003) (0.002) (0.001) Order imbalance×FINRA 0.043 0.032 0.031 0.060* (0.206) (0.312) (0.332) (0.086) Order imbalance×Urgency×FINRA −0.095 −0.073 −0.054 −0.171* (0.295) (0.404) (0.531) (0.086) Quoted spread 0.037 (0.116) Quoted spread×Urgency −0.028 (0.426) Quoted spread×FINRA −0.075** (0.012) Quoted spread×Urgency×FINRA 0.209** (0.030) Effective spread 0.046** (0.011) Effective spread×Urgency −0.032 (0.193) Effective spread×FINRA −0.077*** (<0.001) Effective spread×Urgency×FINRA 0.326*** (<0.001) Price impact 0.003 (0.815) Price impact×Urgency 0.015 (0.448) Price impact×FINRA −0.013 (0.450) Price impact×Urgency×FINRA 0.097** (0.043) Kyle’s λ 0.000 −0.001 0.000 (0.876) (0.520) (0.967) Kyle’s λ×Urgency 0.000 0.001 0.001 (0.873) (0.399) (0.587) Kyle’s λ×FINRA −0.001 0.000 −0.001 (0.620) (0.706) (0.224) Kyle’s λ×Urgency×FINRA 0.003 0.000 0.004 (0.606) (0.948) (0.439) MRR θ −0.018 −0.001 −0.001 (0.308) (0.959) (0.962) MRR θ×Urgency 0.030 0.005 0.005 (0.162) (0.815) (0.825) MRR θ×FINRA 0.018 0.000 0.000 (0.362) (0.999) (0.981) MRR θ×Urgency×FINRA −0.006 0.029 0.021 (0.921) (0.617) (0.713) Amihud 0.008 0.014 0.030 (0.780) (0.597) (0.373) Amihud×Urgency 0.025 0.007 −0.005 (0.614) (0.877) (0.927) Amihud×FINRA −0.007 −0.018 −0.042 (0.859) (0.656) (0.360) Amihud×Urgency×FINRA −0.125 −0.143 −0.039 (0.635) (0.560) (0.878) Noise trading 0.004 0.004 0.005 0.004 0.004 (0.452) (0.376) (0.282) (0.406) (0.433) Noise trading×Urgency −0.011 −0.014 −0.016* −0.013 −0.012 (0.250) (0.122) (0.095) (0.175) (0.201) Event fixed effects Yes Yes Yes Yes Yes Event-day fixed effects Yes Yes Yes Yes Yes Observations 37,786 38,869 38,869 37,786 37,786 Adjusted R2 0.288 0.294 0.292 0.288 0.288 . (1) . (2) . (3) . (4) . (5) . Factor 1 0.024** 0.025** (0.036) (0.030) Factor 1×Urgency −0.012 −0.014 (0.538) (0.470) Factor 1×FINRA −0.051*** −0.052*** (0.002) (0.002) Factor 1×Urgency×FINRA 0.189*** 0.194*** (0.001) (0.001) Factor 2 −0.016 −0.016 (0.115) (0.107) Factor 2×Urgency 0.020 0.020 (0.130) (0.128) Factor 2×FINRA 0.015 0.015 (0.177) (0.167) Factor 2×Urgency×FINRA −0.032 −0.033 (0.496) (0.480) Order imbalance −0.044** −0.034* −0.034* −0.049*** (0.025) (0.067) (0.067) (0.010) Order imbalance×Urgency 0.104*** 0.089*** 0.090*** 0.107*** (0.002) (0.003) (0.002) (0.001) Order imbalance×FINRA 0.043 0.032 0.031 0.060* (0.206) (0.312) (0.332) (0.086) Order imbalance×Urgency×FINRA −0.095 −0.073 −0.054 −0.171* (0.295) (0.404) (0.531) (0.086) Quoted spread 0.037 (0.116) Quoted spread×Urgency −0.028 (0.426) Quoted spread×FINRA −0.075** (0.012) Quoted spread×Urgency×FINRA 0.209** (0.030) Effective spread 0.046** (0.011) Effective spread×Urgency −0.032 (0.193) Effective spread×FINRA −0.077*** (<0.001) Effective spread×Urgency×FINRA 0.326*** (<0.001) Price impact 0.003 (0.815) Price impact×Urgency 0.015 (0.448) Price impact×FINRA −0.013 (0.450) Price impact×Urgency×FINRA 0.097** (0.043) Kyle’s λ 0.000 −0.001 0.000 (0.876) (0.520) (0.967) Kyle’s λ×Urgency 0.000 0.001 0.001 (0.873) (0.399) (0.587) Kyle’s λ×FINRA −0.001 0.000 −0.001 (0.620) (0.706) (0.224) Kyle’s λ×Urgency×FINRA 0.003 0.000 0.004 (0.606) (0.948) (0.439) MRR θ −0.018 −0.001 −0.001 (0.308) (0.959) (0.962) MRR θ×Urgency 0.030 0.005 0.005 (0.162) (0.815) (0.825) MRR θ×FINRA 0.018 0.000 0.000 (0.362) (0.999) (0.981) MRR θ×Urgency×FINRA −0.006 0.029 0.021 (0.921) (0.617) (0.713) Amihud 0.008 0.014 0.030 (0.780) (0.597) (0.373) Amihud×Urgency 0.025 0.007 −0.005 (0.614) (0.877) (0.927) Amihud×FINRA −0.007 −0.018 −0.042 (0.859) (0.656) (0.360) Amihud×Urgency×FINRA −0.125 −0.143 −0.039 (0.635) (0.560) (0.878) Noise trading 0.004 0.004 0.005 0.004 0.004 (0.452) (0.376) (0.282) (0.406) (0.433) Noise trading×Urgency −0.011 −0.014 −0.016* −0.013 −0.012 (0.250) (0.122) (0.095) (0.175) (0.201) Event fixed effects Yes Yes Yes Yes Yes Event-day fixed effects Yes Yes Yes Yes Yes Observations 37,786 38,869 38,869 37,786 37,786 Adjusted R2 0.288 0.294 0.292 0.288 0.288 This table presents OLS regression coefficients where the dependent variable is a dummy equal to one if any insider trading occurred on a given day. Observations come from a panel of 410 events with trading days t = – 120 to t = – 2, relative to the announcement date of t = 0. p-values from standard errors are clustered at the event level and presented in parentheses. * p<0.1; ** p<0.05; *** p<0.01. Open in new tab Quoted spread, effective spread, and order imbalance have the strongest statistical predictive power for insider trading. All three are significant at conventional levels. However, only effective spread and order imbalance are statistical significant at Bonferroni levels. All of the other variables have no statistical relation to insider trading, after controlling for the explanatory power of these variables. As before, the results indicate that while effective spread is correlated with insider trading in non-FINRA-related cases, its predictive power is stronger when FINRA is involved. In contrast, the predictive ability of order imbalance is unaffected by FINRA participation. Columns 4 and 5 in Table 8 test the factors’ ability to identify insider trading. Column 4 only includes the two factors and noise trading controls. The results show that the first factor mirrors effective spread, while the second factor is not significantly related to insider trading. Column 5 adds absolute order imbalance to the regression as an additional predictor. Given that order imbalance has a low correlation with the factors, but explains a large fraction of variance not captured by the factors, it may serve as an independent source of variation. In this specification, the first factor and order imbalance are statistically significantly correlated with insider trading, whereas the second factor is not. These results show that combining the various measures of illiquidity into factors does not provide more reliable predictors. Instead, two separate measures, effective spread and absolute order imbalance, provide the best predictions of insider trading. 5.7 Discussion of the empirical results in the context of the theoretical predictions The empirical results show that quoted spread, effective spread, and order imbalance are the strongest predictors of daily changes in insider trading, controlling for the urgency of trading and sampling bias. Kyle’s λ and quote-based price impact have less predictive power. MRR θ and Amihud illiquidity have no predictive power. The results also show that insider trading is higher when noise trading is higher if the public release of information is not imminent. These results are consistent with theoretical predictions. First, consistent with the strategic traders models, insiders attempt to conceal their information by trading on days when noise trading is high. In addition, after controlling for the ability to conceal information, the spread-based measures generated by the nonstrategic, sequential trading models have more predictive power than the price impact measures generated by the strategic trader models. These results suggest that market makers can infer when adverse selection is higher and increase the bid-ask spread, but they cannot infer the direction of future price moves. Second, the fact that absolute order imbalance is a reliable predictor of insider trading may shed light on the assumptions of the theoretical models. In contrast to both the Kyle and Glosten-Milgrom models, the predictions of absolute order imbalance do not rely on the beliefs of the market maker, assumptions about competitive markets, or the risk neutrality of the traders. In contrast to MRR θ, which makes the most modeling assumptions and has little predictive power, absolute order imbalance makes the fewest assumptions, but has the strongest predictive power. Given that the theoretical models rely on many assumptions that are not valid in this real-world setting, as outlined above, absolute order imbalance may be a better predictor because it relies on fewer assumptions. 6. Robustness Tests In this section, I discuss alternative measures of illiquidity and different sample characteristics. The Internet Appendix presents all results. First, I consider three additional measures of illiquidity based on primary summary statistics. Following Kacperczyk and Pagnotta (2019b), I calculate Price range as the maximum national best offer minus the minimum best bid per day. Realized variance is the realized variance of all 5-minute window returns per day. I also calculate the realized spread as the effective spread minus price impact. This variable is designed to capture non-information-based gains to the market maker. Following Holden and Jacobsen (2014), I aggregate the realized spread to the daily level by taking the dollar-volume-weighted realized spread across all trades per day. All three measures are positively related to insider trading controlling for event urgency and FINRA. However, these variables become insignificant after controlling for the other measures of illiquidity, though order imbalance and effective spread remain significant. Second, I calculate Kyle’s λ using alternative formulations that use returns rather than price changes and observations of 5-minute windows of trades, rather than transaction level observations. The results show that the relationship between Kyle’s λ and insider trading depends on the way that λ is calculated. In particular, the relationship between λ and insider trading is stronger using 5-minute windows, rather than transactions. Nevertheless, all of the different calculations have marginal or no statistical significance. Third, I use dollar-based measures of the quoted spread, effective spread, realized spread, and price impact. The results show that the percentage spreads used in the main tests provide a stronger signal of insider trading than dollar spreads. Fourth, I run triple interaction regressions to tests whether the main results of the paper vary across different sorts of events. To test whether illiquidity measures react differently to insider trading before prescheduled events, I include a dummy variable for regular earnings announcements. Order imbalance remains statistically significant, but almost all other variables lose significance.8 Next, I find that most of the variables have larger responses in positive news events than negative news events. This could reflect short sale constraints. Events that occur in 2009 or later show significantly different outcomes based on FINRA-assisted cases for quoted and effective spread, while order imbalance remains unchanged. This could reflect the introduction of the SONAR detection software in 2009. Using a dummy for firms above the median market capitalization, I find very small differences in predictive power. Last, using a dummy for events in which buyside analysts and managers trade to proxy for sophisticated investors, I find that effective spread has greater predictive power in events with buyside traders, while order imbalance is not affected by trader identities. Fifth, though my results show that MRR θ is not a reliable predictor of insider trading, I test whether the other parameters in the structural model of MRR have predictive power to identify insider trading. Controlling for noise trading, none of the other parameters are significantly related to insider trading, as expected. Finally, to provide more detail on which insiders trade in urgent situations and which strategically time their trades, I study the relationship between insider trading and illiquidity by inside traders’ occupations. In urgent events, there is a strong positive relationship between illiquidity and informed trading of buy-side managers and analysts. In contrast, corporate executives and managers do not influence illiquidity, even when trading is urgent. This shows that buy-side traders drive the positive relationship in the full sample between illiquidity and informed trading. 7. Conclusion Foundational theories in finance predict that informed trading impacts stock prices and transaction costs. In turn, researchers have designed many empirical proxies based on observable price and quote data to capture the presence of informed trading. However, testing the efficacy of these proxies has been inhibited by the inability to observe the behavior of informed traders. This paper helps to overcome some of the limitations of prior work by using direct observations of insider trading as a laboratory to test whether standard measures of illiquidity detect insider trading. A key contribution of this paper is the research design that reduces confounding effects from cross-sectional and time-series variation unrelated to illiquidity. This allows me to isolate the connection between private information and illiquidity, while controlling for omitted factors. The results show that controlling for sampling bias and strategic timing, effective spread and absolute order imbalance are positively and significantly related to informed trading. In contrast, many of the popular measures of informed trading, including Kyle’s λ, Amihud illiquidity, price impact, and spread decompositions, do not predict insider trading, even ex post, controlling for a host of other confounding factors. These results provide some of the cleanest evidence to date on the theoretical predictions of models of adverse selection in financial markets. However, these results only hold when information is short-lived. When information is long-lived, none of the illiquidity measures correctly detect insider trading. These results show that though proxies for informed trading are ubiquitous in finance research, they may not be informative in many situations. It is important to note that these results may not generalize to all forms of informed trading. The behavior of informed traders that risk criminal charges may differ from informed traders who are not committing a crime. At the same time, illegal insider trading is an important component of informed trading because it represents trades based on valuable, nonpublic information. Future theoretical research on informed trading should consider informed investors’ ability to strategically time their trades to avoid price impact, as in Collin-Dufresne and Fos (2016), and to avoid detection by regulators. Addressing these concerns will shed light on information asymmetry in financial markets and may aid practitioners who bear the cost of adverse selection and regulators whose task it is to detect insider trading. For helpful comments, I thank an anonymous referee. I also thank Thierry Foucault (editor), Patrick Augustin, Snehal Banerjee, Peter Cziraki, Pierre Collin-Dufresne, Slava Fos, Craig Holden, Stacey Jacobsen, Chad Kendall, Maureen O’Hara, Gideon Saar, Jonathan Sokobin, Kumar Venkataraman, and Wenyu Wang and seminar participants at Bocconi University, Cornell University, Financial Industry Regulatory Authority (FINRA), Indiana University, Loyola Marymount University, Securities and Exchange Commission (SEC), Southern Methodist University, Swiss Finance Institute and HEC Lausanne, University of Hawaii, Texas A&M University, University of Southern California, and University of Toronto for useful feedback on this paper. Footnotes 1 The Internet Appendix presents tests that show that insider trading events are idiosyncratic and unrelated to market-wide forces. Thus, calendar-time fixed effects that control for market-wide variation are not useful. 2 The SEC also has its own computer program, called Advanced Relational Trading Enforcement Metrics Investigation System (ARTEMIS), to monitor trading. However, the SEC began using the program in 2016, after the end of my sample period. Whereas SONAR looks for patterns at the stock level, ARTEMIS looks for patterns at the trader level. Both algorithms are kept secret. 3 Because the SEC identifies tippees through records of social interaction, rather than trading similarities, tippees who trade in different patterns or time periods are still likely to be discovered. 4 Another consideration that could affect the time-series patterns is information sharing. If we regard each trader that receives a tip as a new information event, the Kyle models would predict a sequence of spikes in λ coinciding with new insider trading. 5 I requested specific trading dates from the SEC for the cases that didn’t provide specific dates, but the SEC denied my Freedom of Information Act requests. 6 Two-way clustering at the event level and event-time levels produce nearly identical results. Clustering by calendar time makes no difference, because the event dates are not correlated by calendar time. 7 Rencher (2002) explains that small, negative eigenvalues often occur in factor analysis. 8 Unfortunately, this is not a clean test because it confounds the event type (earnings) with whether an event is prescheduled. Bolandnazar et al. (2020) provide more cleanly identified tests of insider trading with random time horizons. References Admati A. R. , Pfleiderer P.. 1988 . A theory of intraday patterns: Volume and price variability . 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