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This paper explores the impact of product market competition on the positive relation be- tween labor mobility (LM ) and future returns. We develop a production-based model and formalize the intuition that low exposure to systematic risk in a concentrated industry lim- its LM 's amplifying eect on operating leverage. Therefore, the model predicts a stronger positive relation between LM and expected returns for rms in competitive industries. Con- sistent with the model's prediction, we empirically nd that LM predicts returns only among rms in competitive industries. This evidence suggests that the intensity of competition in rms' product market potentially drives the positive LM -return relation. (JEL G12, G14, J69) We are grateful to Hui Chen (the editor), an anonymous referee, Guofu Zhou, Erik Loualiche, Seok Young Hong, Seung Yeon Yoo, Zhou Zhang, and Di Luo for many useful comments and suggestions, as well as participants at the 57th Annual Eastern Finance Association Meeting, the 37th International Conference of the French Finance Association, and 2021 FMA Annual Meeting. Send correspondence to Xiaoxia Ye, X.Ye@exeter.ac.uk. © The Author(s) 2023. Published by Oxford University Press on behalf of The Society for Financial Studies. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Labor mobility (LM ) is the exibility of workers to enter and exit an industry in response to better opportunities. Recently, this has attracted much attention in the nance literature as Donangelo (2014) shows that rms in industries employing workers whose labor skills are more portable to other industries earn higher average stock returns than those in industries where workers have less portable skills. When the performance of an industry is relatively good, it tends to attract more mobile workers. But in times of adverse productivity shocks, mobile workers tend to leave this industry. The degree of dependency on mobile labor ampli es rms' existing exposure to productivity shocks, as out ows of mobile workers in bad times reduce cash ows. This is precisely the source of the LM premium shown in Donangelo (2014) and closely related to the risk ampli cation eect of labor leverage in Donangelo et al. (2019). This line of analysis, however, assumes optimistically a perfectly competitive product market environment. Congruently, product market competition is the other well-known industrial characteristic that aects rms' exposure to productivity shocks, but in an opposite way to the LM . For example, Dou, Ji, and Wu (2021), Hou and Robinson (2006), and Peress (2010) show that market power shields rms from nondiversi able aggregate shocks. In other words, the operating pro ts of rms in more concentrated (i.e., less competitive) industries are less sensitive to the productivity shocks thanks to the bene ts brought by the market power (stemming from tougher barriers to entry, low elasticity of substitution, etc.). In light of their connection with the productivity shocks, it is particularly interesting to study the juxtaposition of product market competition and LM as well as their joint asset pricing eect on the cross-section of stock returns. More concretely, in view of the market power to insulate rms from the productivity shocks, it is no longer clear whether the risk ampli cation from LM is still signi cant for rms in less competitive industries. In a concentrated industry, where the performance is less correlated with nondiversi able productivity shocks, from investors' point of view, the risk induced by in ow and out ow of mobile labor is more idiosyncratic and hedgeable. Therefore, it remains unanswered that whether LM in a concentrated industry still carries a premium in equilibrium. To the best of our knowledge, despite the rst-order importance of these questions, no prior studies have attempted to answer them. These questions motivate our research in this paper and are answered in our theoretical and empirical analyses. Guided by the work of Peress (2010), our model generalizes the mobility-production econ- omy of Donangelo (2014) and allows for a variable measure of the product market competition. Empirically, we nd that product market competition do not have a clear shielding eect on other shocks such the market excess return factor of the capital asset pricing model, the Fama and French (2015) ve factors, and the Hou, Xue, and Zhang (2015) q factors (see the factor loadings in Table IA2 of the Internet Appendix), but has a clear shielding eect on the systematic productivity shocks identi ed by the (high minus low) LM factor (see Table A2). This evidence further shows the unique bond in productivity shocks shared by the product market competition and LM , highlighting the importance in studying their juxtaposition. 1 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 This competition measure plays a key role in quantifying the combined sensitivity to the sys- tematic productivity shocks from the interplay between LM and product market competition. Speci cally, the imperfect elasticity of substitution combined with the market concentration, which measures (the inverse of ) the degree of product market competition, propagates to the demand for mobile labor, which further determines the operating pro ts, in the initial pro- duction stage through the price of the intermediate goods in the nal product market. By construction, the mobility-production model of Donangelo (2014) is nested as a special case assuming perfect competition within our model. The solution of our model allows to study the joint eect of LM and market competition on operating leverage, which acts as a systematic risk multiplier in the rm risk. Importantly, we show that when market power within an indus- try is large enough, LM can barely have any eect on rms' systematic risk. This means that the insulation induced by the market power can quickly overshadow the LM 's ampli cation on systematic productivity shocks. These results from our model indicate that the LM premium is more signi cant or exists only for rms in highly competitive industries. To verify this novel theoretical prediction, we develop a testable hypothesis that the positive LM -return relation strengthens with the intensity of product market competition. We test our hypothesis both by independently double sorting stocks on LM and product market competition and by Fama and MacBeth (1973) cross-sectional regressions. The results from the portfolio analyses show that the positive LM -return relation exists only in competitive industries. For example, the high-minus-low LM portfolio in competitive industries delivers an economically signi cant value-weighted average monthly return of 0.83% (t-statistic = 3.05). The value-weighted characteristic-adjusted return of 0.79% per month on this hedge portfolio is also statistically signi cant, with a t-statistic of 3.76. The LM premium in competitive industries persists even after adjusting for risk using premier asset pricing models. In particular, the value-weighted average monthly abnormal returns on the hedge portfolio relative to the (unconditional) capital asset pricing model of Sharpe (1964) and Lintner (1965), the Ferson and Schadt (1996) conditional capital asset pricing model, the Fama and French (1993) three- factor model, the Fama and French (1993) and Carhart (1997) four-factor model, the Fama and French (2015) ve-factor model, and the Hou, Xue, and Zhang (2015) q-factor model are 0.82%, 0.84%, 0.92%, 0.69%, 0.83%, and 0.69%, with t-statistics of 3.07, 2.96, 3.23, 2.44, 2.53, and 2.08, respectively. In contrast, the high-minus-low LM portfolio in concentrated industries generates a monthly return of 0.15% (t-statistic = 0.91). The value-weighted characteristic-adjusted return of 0.23% per month on the portfolio is also statistically insigni cant (t-statistic = 1.30). Furthermore, the average monthly abnormal returns on the portfolio relative to the 2 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 asset pricing models are all negative and statistically indistinguishable from zero at conventional levels. Speci cally, the capital asset pricing, the conditional capital asset pricing, the three- factor, the four-factor, the ve-factor, and the q-factor model alphas are, respectively, 0.09% (t-statistic = 0.58), 0.14% (t-statistic = 0.87), 0.02% (t-statistic = 0.12), 0.02% (t- statistic = 0.13), 0.02% (t-statistic = 0.14), and 0.08 (t-statistic = 0.42). We also empirically verify the key mechanism of our model, in which the market power overshadows LM 's risk amplifying eect, by showing the cross-sectional variation of factor loadings on the LM -based productivity risk factor is larger (smaller) in more (less) competitive industries. The empirical results, supporting our hypothesis, remain robust to using: the all-but- microcaps sample, which excludes stocks with a market value of equity below the 20th percentile of the NYSE market capitalization distribution; an extended sample period; unlevered returns; industry-level returns; independent double-sorted quartile or quintile portfolios; and a wide range of product market competition measures suggested in the recent literature. For example, we employ competition measures based on the data from the U.S. Census of Manufacturers (as in Bustamante and Donangelo, 2017), both private and public rms (as in Hoberg and Phillips, 2010), rm's product market uidity (as in Hoberg, Phillips, and Prabhala, 2014), total assets instead of net sales (as in Hou and Robinson, 2006), and price-cost margin (as in Peress, 2010). The model's prediction is also supported by the results from the cross-sectional regressions. After controlling for the potential eects of size, book-to-market equity, short-term reversal, momentum, and leverage, the results con rm that a signi cantly positive LM -return relation prevails only for rms in competitive industries. For example, the average slope estimates of returns on LM are 0.46 (t-statistic = 4.74) and 0.09 (t-statistic = 1.39), respectively, in compet- itive and concentrated industries. Importantly, the average spread between the slope estimates of returns on LM in competitive and concentrated industries is 0.37, which is statistically signif- icant with a t-statistic of 3.01. The results remain qualitatively similar, when we conduct cross- sectional regression analyses using: the all-but-microcaps sample; an extended sample period; and dierent measures of product market competition. In a separate cross-sectional regression analysis, we also create interaction terms involving market competition dummy variables. After controlling for rm-level attributes, such as size, book-to-market equity, short-term reversal, momentum, and leverage, the results remain robust and support our theoretical model's pre- diction of a stronger LM -return relation among rms in competitive industries. For example, we nd that, all else being equal, a one-standard deviation increase in LM is associated with 24 basis points higher future returns per month for rms in competitive industries relative to all other rms. A qualitatively similar nding emerges when we run panel data regressions. 3 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Our paper contributes to two strands of literature. First, our model belongs to the burgeon- ing literature discussing economic mechanisms that generate labor-induced operating leverage. The general equilibrium model by Danthine and Donaldson (2002) is one of the rst to artic- ulate a mechanism in which operating leverage induced by the priority status of wage claims magni es the risk properties of the residual payments to rm owners and justi es a substantial risk premium. Favilukis and Lin (2016) develop a general equilibrium model to examine the quantitative eect of sticky wages and labor leverage on the equity premium and the value premium. Along this line of research, Donangelo et al. (2019) provide theoretical support and empirical validation that rm-level labor share acts as a proxy for rm-level labor leverage. Our model is most close to Donangelo (2014), who shows that labor ows make bad times worse for shareholders through the LM -induced operating leverage. But dierent from Donangelo (2014), we focus on the more plausible case of imperfect competition. Second, our paper is related to the theoretical studies linking industrial organization to - nancial markets. Aguerrevere (2009) explores the opposing eects of market competition and industry growth on expected returns. Opp, Parlour, and Walden (2014) emphasize that market competition is linked with market eciency in a very complex way. Bustamante and Donan- gelo (2017) study the impact of market competition on systematic risk through the operating leverage, the entry threat, and the risk feedback channels with opposing eects. Our model is also closely related to Peress (2010), who investigates the interplay between competition in the product market and information asymmetries in the equity market. We adopt the two-sector (a nal and an intermediate goods sector) economy setup of Peress (2010) in our model. Other recent studies that are broadly related to our paper include Corhay, Kung, and Schmid (2020) and Loualiche (Forthcoming). By building general equilibrium models with endogenous rm entry, both these papers examine the interaction between product market competition and asset prices. Our paper is also related more generally to Chen et al. (2021) and Dou, Ji, and Wu (2021). Chen et al. (2021) study the dynamic interactions between endogenous strategic com- petition and nancial distress. Dou, Ji, and Wu (2021) develop an industry-equilibrium model with dynamic strategic competition to examine the joint uctuations in aggregate discount rates, pro tability, market competition intensity, and asset prices. The uniqueness of our contribution is from the fact that we contribute to the joint venue of these two important strands of literature. The novelty of our continuous-time model lies in the analytical resolution of asset pricing implications from the interplay between LM and product market competition. To the best of our knowledge, we are the rst to show, both theoretically and empirically, that market competition has a nontrivial eect on risk and return 4 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 pro les of rms in high-mobility industries. In other words, the intensity of competition in rms' product market drives a signi cant portion of the positive LM -return relation. This novel nding contributes to the growing subset of the asset pricing literature that investigates the interaction eect of rm characteristics on expected stock returns. Speci cally, some recent papers documenting the important role that product market competition plays in explaining other cross-sectional asset pricing anomalies include Deng (2019, pro tability), Dou, Ji, and Wu (2021, 2022, pro tability), Giroud and Mueller (2011, corporate governance), and Gu (2016, research and development investment). In this context, we provide robust evidence of another important role that competition plays in the riskiness among rms in low- and high-mobility industries. Our study also contributes to the strand of production-based asset pricing literature that links rm characteristics to expected stock returns (see, among others, Belo, Lin, and Bazdresch, 2014; Belo et al., 2017; Cochrane, 1991; Croce, 2014; Zhang, 2019, and the references therein). Taken together, our theoretical model and strong supporting evidence improve the understanding of the joint issues across the industrial organization, and the labor and nancial markets. 1. The Model In this section, we derive a partial equilibrium model characterizing the role of product market competition in the positive relation between LM and expected stock returns. Building on the work of Peress (2010), the model introduces the more plausible case of imperfect compe- tition to the mobility-production model developed by Donangelo (2014), which in fact assumes a perfectly competitive product market environment. Below, we outline the environment of our dynamic model and present the mechanism underlying the model's testable prediction. 1.1 Output integrating labor and competition We integrate LM and market competition by extending the mobility-production economy setup of Donangelo (2014) with the risk-less technology of nal good production in Peress (2010). Speci cally, we assume N rms produce g intermediate goods at time t, and the nal i;t good is produced by a competitive representative nal good producer (see, e.g., Corhay, Kung, Our model can be pitched as an industry-equilibrium model, with the labor mobility of the industry and the competitiveness within the industry as two primitive industry characteristics. Thus, the nal goods in the model should be regarded as industry-level composite goods. 5 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 and Schmid, 2020) according to a risk-less technology Y g ; i;t i 1 where g is the intermediate output from ith rm and Y is the nal output of the economy at i;t t time t, and 0 ! ⁄ 1. The lower !, the less the elasticity of substitution between any two goods and a less competitive input market (Peress, 2010). Therefore, it measures the degree of competition in the intermediate goods sector. Following the mobility-production economy of Donangelo (2014), we model each intermedi- ate good output as g A l ; (1) i;t t i;t where l is the industry-speci c labor skills employed by ith rm, 0 1 is the output i;t elasticity of labor, and A denotes total factor productivity (TFP), which follows the diusion process dA dZ : (2) A t 1.2 Operating pro ts Similar to Peress (2010), we use the price of the nal good as the numeraire in what follows. It is worth mentioning that introducing an intermediate goods market with imperfect competi- tion into the model economy is a convenient way to embrace imperfect competition at the whole industry level. When considering the operating pro ts for an average rm in the industry, we focus on the pro ts of each intermediate good producer. 1.2.1 Pro ts of the intermediate goods market. Total pro ts of the nal good producer are given by Y P g ; (3) 0;t t i;t i;t i 1 where P is the price of the ith intermediate good. The nal good producers set their demand i;t for inputs to maximize pro ts, . The resultant demand for each intermediate good input 0;t Here, ! is strictly positive in order to avoid a degenerated economy in which the production is constant without any inputs. 6 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 1 ! is g p ! {P q . This means that when the intermediate goods market clears, the price of i;t i;t the intermediate good is simply ! 1 P !g : (4) i;t i;t Given Equations (1) and (4), total revenue for each intermediate good producer is ! ! ! P g !g !A l : (5) i;t i;t i;t t i;t We follow Donangelo (2014) and assume the only cost for the intermediate good producers is wage. Therefore, the pro t of each intermediate good producer is given by S ! ! S P g W l !A l W l ; (6) i;t i;t i;t i;t i;t t t i;t t where W is the hourly wage of the labor with speci c skills (see Donangelo, 2014). Each intermediate good producer sets her demand for labor to maximize pro ts, taking the wage, W , as given. The rst-order condition yields the following: S 2 ! ! 1 W ! A l : (7) t t i;t From Equation (7), we can see that because of the identical technology and constant elasticity of substitution, the labor demand, l , is identical for all rms, that is, l l for i 1; : : : ; N , in i i;t t equilibrium. This further implies that we have g g and P P in equilibrium. Therefore, i;t t i;t t the equilibrium nal output can be simpli ed as Y Ng : Substituting (7) for W into Equation (6) yields ! ! p 1 ! q !A l : (8) t t 1.2.2 Wages and labor supply. Considering N intermediate good producers with identical labor demand l , the total demand for labor is L Nl . Therefore, the pro t of each intermediate good producer is connected to t t We relax this assumption in Appendix A, where we add a rm-speci c xed market entry cost and endogenize the number of intermediate good producers by linking their market entering decision to their optimal pro ts. 7 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 L and N as p 1 ! q !A : (9) Hourly wages per unit of general skills are exogenously given by the diusion process dW dZ : (10) Following Donangelo (2014), we derive the equilibrium supply of the labor with speci c skills. Specially, labor markets are composed of a continuum of workers with permanent occupations based on their endowed composition of labor skills. The occupations, labeled by the index j ¡ 0 in decreasing order of labor skill specialty, are modeled as l ; where 0 1: (11) The parameter determines the level of generality of labor skills required by the production technology. Thus, represents the level of LM in the industry (see Donangelo, 2014). Same as !, we treat as another exogenous parameter. Insigni cant correlations between empirical measures of these two parameters justify this exogeniety setting. We present the empirical observations in Appendix A. At time t, given an indierence marginal occupation j , labor markets are in equilibrium when all workers in occupations j j strictly prefer to remain inside the industry, and all workers in occupations j ¡ j strictly prefer to remain outside the industry; therefore, the equilibrium level of employable labor skills useful inside the industry is given by: » » j j t t L l d d : (12) 0 0 The equilibrium indierence marginal occupation j and the resultant equilibrium level of employable labor skills are derived and summarized in the following proposition. Proposition 1. Given the general skill wage, W , the TFP, A , the average level of competition, t t !, and the number of intermediate good producers, N , the supply of labor with speci c skills in equilibrium is pc 1q ! 1 ! p! q A N L ; (13) and 0 1. where c 1 ! 8 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Proof. See Appendix A. Now, the equilibrium operating pro t of each intermediate good producer, , can be expressed formally as ! 2 1 ! 1 p! q A pN q ! t p 1 ! q !A : (14) N W Several comments are in order before we move on. The market competition is captured primarily by !. A simple inspection of Equation (14) shows that together with !, LM partially 2 ! 1 ! p! q A pN q controls operating pro ts' sensitivity to , which Donangelo (2014) de nes as the relative productivity of the industry. Indeed, conditional on !, increases operating pro ts' sensitivity to systematic shocks. However, from Equation (14), we also see that more exten- sively than the LM , ! controls 's direct connection with A . This is consistent with Peress t t (2010), who nds that market power makes pro ts less sensitive to systematic shocks. More ! 1 concretely, ! aects through three channels: (1) p1 ! q !A re ecting the source of uncertainty when there is no LM , the general productivity level A is now scaled to be A ; (2) 2 1 ! p! q A pN q re ecting the relative productivity; and (3) c re ecting 's loading on the rel- ative productivity due to LM . Our results show that imperfect competition (small !) not only reduces the systematic risk in both absolute (channel 1) and relative (channel 2) productivity but also limits the loading on the systematic risk in the relative productivity due to the LM (channel 3). In sum, we generalize the Donangelo (2014) model to allow for imperfect market competition, and show that the in uence of LM on rms' systematic risk is much weakened when the product market is not perfectly competitive. These eects are more directly quanti ed via operating leverage in Section 2.3. The following proposition formalizes the dynamics of . Proposition 2. Given the dynamics of A and W , has the following dynamics t t t dt dZ ; (15) Also, we can easily show that in equilibrium the average intermediate good price is explicitly linked to A, !, N , and W as p1 ! q pc 1q p1 ! qr1 p1 ! qpc 1qs p! 1qr1 p1 cqs P !N A : p! q It is straightforward to see that P increases with W and decreases with A. This is consistent with the fact that both W and A determine the cost of intermediate goods but in opposite ways. Although not immediately straightforward, with reasonable parameter values (e.g., N 50, A 0:5, 0:5, 0:4, and W 1), it also can be shown numerically that P decreases with ! in a reasonable range, for example, [0.3, 0.9], meaning that the average price of the intermediate goods is lower when the market is more competitive. These results are consistent with common sense and serve as additional validation on the way we model the product market competition. 9 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 1 ! 1 2 2 where pc 1qc ! ! 2! and p 1 cq! c . A W A W 2 c A W Proof. See Appendix A. 1.3 Operating leverage as a systematic risk multiplier d dA dA t t t Donangelo (2014) derives Cov ; {Var 1, which the author denotes A A t t t as operating leverage, to quantify the systematic risk ampli cation. Note that in Donangelo d dA dA t t t (2014), Cov ; {Var is always larger than one and therefore one is subtracted A A t t t from the quantity to have representing the systematic risk ampli cation. In our case, d dA dA t t t Cov ; {Var can be less than one (but always positive, which is shown in Propo- A A t t t sition 3 and proven in Appendix A), we therefore de ne the operating leverage directly as d dA dA t t t Cov ; {Var 1. Note that measures the sensitivity of cash ow A A t t t growth to the fundamental source of risk in a multiplier sense as opposed to the Donangelo (2014) ampli cation sense. Given Equation (15), the equilibrium operating leverage is expressed as p 1 cq! c : (16) A A It is also important to note that Equation (13) in Donangelo (2014) is a special case of Equa- tion (16) when ! 1, which corresponds to a perfectly competitive intermediate goods market. is increasing in ! when ¡ , which is generally true as wages for general skills are typi- A W cally smoother than TFP (see Donangelo, 2014). This result is also consistent with Bustamante and Donangelo (2017, Proposition 1), where the authors show that the operating leverage is decreasing in concentration (which measures the inverse of market competition). However, dif- ferent from Donangelo (2014), with ! the relation between and is no longer always positive and depends on the value of !. We formalize these results in Proposition 3 below. Proposition 3. Given the dynamics of and A , the de nition of , and assuming ¡ , t t A W the following expressions are true: 1. B{B cp1 cq ! {; 2. B{B! p 1 cq 1 ¡ 0; and Although our operating leverage result is consistent with Bustamante and Donangelo (2017), their systematic risk loading is negatively related to market competition while ours is positive, same as for the operating leverage. The Bustamante and Donangelo (2017) modeling framework is not directly comparable to ours. They assume perfect elasticity of substitution among inputs (see the industry output production function in Equation (2) of their paper), that is, ! 1. As we show here, ! plays a crucial role in modeling a more realistic industrial organization environment. The fact that ! is missing in their model casts doubt on the robustness of their theoretical predictions on the relation between systematic risk loading and product market competition. 10 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 3. ¡ 0. Proof. See Appendix A. Proposition 3 quanti es the eects of LM and market competition on the systematic risk multiplier. Figure 1 illustrates the results. When ! 1, we reproduce the results of Donangelo (2014). The eect of LM on the systematic risk multiplier decreases mostly with the gradual decreasing of !. More importantly, when ! is small enough, can barely have any eect on the rms' systematic risk. In other words, rms' market power can shield their pro ts from sys- tematic shocks, and this insulation quickly overshadows LM 's ampli cation on systematic risk. These results of the systematic risk multiplier indicate that the asset pricing implications of LM (see, e.g., Donangelo, 2014) are likely to be strong or only exist in more competitive industries. Indeed, we nd empirically that, in the cross-sectional dimension, in competitive industries, shocks are ampli ed by LM , but in concentrated industries, they are not (see Table A1 in the Appendix). In the time-series dimension, using large tari cuts (LTC ) as a proxy of increasing market competition (see Chen et al., 2021), we nd that the sensitivity of rms' pro ts and stock returns to a TFP factor becomes higher after the LTC and is only positively correlated with LM conditional on LTC (see Table IA3 in the Internet Appendix). We show in the next section that the results in Proposition 3 are directly linked to the asset pricing implications. 1.4 Asset pricing implications To explore asset pricing implications, we derive the value of a representative unlevered rm whose operating pro ts are given by . Consistent with the literature (see, among others, Berk, Green, and Naik, 1999, 2004; Donangelo, 2014), we take the pricing kernel as exogenous. The dynamics of the pricing kernel, denoted by , are given by r dt dZ ; (17) f t where Z is a standard Wiener process representing the single source of systematic risk in the model, r ¡ 0 is the instantaneous risk-free rate, and ¡ 0 is the market price of risk in the economy. Then, the value of the rm is the sum of all expected future operating pro ts cp1 cq ! { is nonlinear (skewed U-shaped) in !, with a minimal point slightly dipping below zero when ! is small. But most of the curve is monotonic. Based on the coecient estimates from Table IA3, the sensitivity of pro ts to TFP shocks is 1:84 p 0:89 0:77LM qLTC and that of stock returns is p0:03 0:04LM qLTC , where LM is the Donangelo (2014) labor mobility measure and LTC is a dummy variable that equals one if an industry experiences a large tari cut in the last 2 years and is zero otherwise. The assumption of an exogenously given pricing kernel provides the analytical tractability needed to focus on the dynamics for the relative risks of individual rms (Berk, Green, and Naik, 1999). 11 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 (discounted properly): V E ds : (18) t t s dV dt t t Given V , the rm's instantaneous expected excess return is r E r . The asset t t t f V dt pricing implications of the interplay between LM and market competition can be revealed from Br {B, which is linearly linked to B{B. The proposition below formalizes the results. Proposition 4. Given the dynamics of and , and assuming ¡ , the following t t A W expressions are true: 1. V ; 2. r ; and 3. Br {B B{B. t A Proof. See Appendix A. Part (3) of Proposition 4 combined with Part (1) of Proposition 3 indicates that LM has a positive eect on the rm's expected excess return only when ! ¡ { , and the degree of W A the eect is positively related to ! since Bc{B! cp1 cq{! ¡ 0. The asset pricing implication of LM diminishes when ! is close to zero. Therefore, we develop a testable hypothesis that the positive relation between LM and expected stock returns for rms strengthens with the degree of product market competition. In other words, the LM premium is more signi cant or prevails only for rms in highly competitive industries. In the following sections, we test our hypothesis and show robust evidence consistent with our theoretical model's prediction. Although in the model we derive above we treat ! and N as independent parameters, we argue that ! can be correlated with N which captures the market concentration, for example, Her ndahl-Hirschman Index (HHI), in a more general setting. Indeed, in Appendix A, we show that in an extended version of the current model HHI is endogenously and negatively related to !. This result justi es the various competition measures we use in our empirical analyses. 2. Data and Summary Statistics This section describes the data used in the empirical analyses and the construction of product market competition and LM measures, and presents the summary statistics of relevant variables. 12 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 2.1 Data and measures of product market competition and LM In this paper, we resort to a variety of data sources to conduct the empirical analyses. Firms' monthly stock returns and all accounting information are sourced from the Center for Research in Security Prices (CRSP) and the Compustat Annual Industrial Files, respectively. Our preliminary sample includes all NYSE-, AMEX-, and NASDAQ-listed ordinary common stocks (CRSP share code SHRCD = 10 or 11). We lter the preliminary sample by excluding rms whose four-digit primary standard industrial classi cation (SIC) code is between 4900 and 4999 (regulated rms) or between 6000 and 6999 ( nancial rms), and rms with a nonpositive book value of equity. To account for delisting bias, we follow the approach of Shumway (1997) by imputing a return of 30% if the delisting return is missing and the delisting is performance related; however, this adjustment has no material eect on our empirical ndings. The data on delisting returns are sourced from the CRSP. Our sample is restricted to the period from January 1990 to December 2016. This is due to the unavailability of data on LM for a longer sample period in the public domain, described below, which are a key ingredient of our analyses. We focus on two samples constructed from the ltered preliminary sample, namely, the full sample and the all-but-microcaps sample. The full sample includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and LM estimates in a given year are obtainable. Conversely, the all-but-microcaps sample excludes stocks, from the full sample, with an end- of-June market value of equity below the 20th percentile of the NYSE market capitalization cross-sectional distribution. Excluding microcaps (i.e., very small stocks) helps mitigating their possible undue in uence on the empirical results obtained from the full sample. In an average month, the full sample comprises 2,891 rms, whereas 1,233 rms in the all-but-microcaps sample. We employ all accounting variables at the end of June of calendar year t by using accounting information available for the scal year ending in the calendar year t 1 from the Compustat annual database. This adjustment, suggested in Fama and French (1992), provides time long enough for accounting information to be incorporated into rms' stock prices. Consistent with the literature (see, e.g., Giroud and Mueller, 2011; Hoberg and Phillips, 2010; Hou and Robinson, 2006), product market competition (also known as market concentra- 13 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 tion) for an industry is measured by the HHI. Formally, the index is de ned as HHI s ; (19) j;t i;j;t i 1 where s is the market share of rm i in industry j in year t, N is the number of rms i;j;t j operating in industry j in year t, and HHI is the Her ndahl-Hirschman Index of industry j j;t in year t. For each industry, we rst aggregate the squared market shares of all rms in that industry in a given year t and then average the HHI values over the past 3 years. This adjustment prevents undue in uence of potential data errors in the estimation of market concentration. To further improve the accuracy of the product market competition measure, we follow Hou, Xue, and Zhang (2020) and exclude an industry if the market share data are available for fewer than ve rms or 80% of all rms in that industry. Throughout the main body of this paper, we compute the HHI using the market shares based on net sales (Compustat item SALE) and denote the resultant measure of product market competition by HSALE. We also resort to six alternative measures of market competition in order to establish the robustness of the empirical ndings. The rst of them, denoted by HSALE , is measured per HR Hou and Robinson (2006), where we abstain from excluding an industry for which the market share data are available for fewer than ve rms or 80% of all rms in that industry. The second of them, denoted by HAT , is the product market competition measured analogous to HSALE but using total assets (Compustat item AT) instead of net sales (Compustat item SALE). The third of them, denoted by HSALE , is obtained from Hoberg and Phillips HP (2010), which considers both privately held and public rms operating in a given industry by combining Compustat data with Her ndahl data from the U.S. Census Bureau and uses the tted HHI to capture competitiveness. The fourth of them, denoted by PMF , is obtained from Hoberg, Phillips, and Prabhala (2014), which is a rm-speci c competitive pressure measure (also known as rm's product market uidity) based on information from product descriptions contained in a rm's 10-Ks. This measure captures changes in rival rms' products relative to the rm's products, so a higher value implies greater competitive threats faced by a rm in its product market. The fth of them, denoted by HHI , is obtained from the U.S. Census of CM The elasticity of substitution in our theoretical model is not easy to measure. In the empirical study, we use HHI to measure the market competition captured by the elasticity of substitution. The numerical results in Appendix A.3 showing a clearly negative relation between HHI and ! justify the use of HHI as an empirical proxy for the elasticity of substitution. As in Grullon, Larkin, and Michaely (2019), Gu (2016), Hoberg and Phillips (2010), and Hou and Robinson (2006), we use three-digit SIC codes to de ne industry membership. Estimates of HSALE and PMF are sourced from the Hoberg-Phillips Data Library at http:// HP hobergphillips.usc.edu/industryconcen.htm. Details of the estimation of HSALE and PMF can be found HP in Hoberg and Phillips (2010) and Hoberg, Phillips, and Prabhala (2014), respectively. 14 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Manufacturers, per Bustamante and Donangelo (2017). The last of them, denoted by PCM , is the rm-level price-cost margin as in Peress (2010). With the exception of PMF , we multiply the estimates of HSALE, HSALE , HAT , HSALE , HHI , and PCM by minus one to HR HP CM simplify interpretation of the results. Hence, a higher value of these indexes/measures indicates a higher level of market competition. That is, the product market is shared by many competing rms. All competition measures are estimated and/or employed at the end of June of each year t. The measure of LM is based on Donangelo (2014), who captures the level of interindustry dispersion of workers across occupations. Speci cally, LM is constructed in two stages. In the rst stage, the interindustry concentration of workers assigned to each occupation is estimated. This serves as a proxy for (the inverse of ) workers' intrinsic exibility to switch industries. The second stage involves aggregating the occupation-level concentration measure by industry, weighted by the average annual wage expenditure corresponding to each occupation. Further details of estimating LM are provided in Donangelo (2014) and the standardized data (i.e., demeaned and rescaled to have standard deviation of one in each year) are sourced from Andr es Donangelo's website. Consistent with Donangelo (2014), LM is lagged 18 months in our empirical analyses. In the portfolio analyses, we utilize six prominent asset pricing models to compute average abnormal returns. These are the (unconditional) capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), the Ferson and Schadt (1996) conditional capital asset pricing (FS) model, the Fama and French (1993) three-factor (FF3) model, the Fama and French (1993) and Carhart (1997) four-factor (FFC) model, the Fama and French (2015) ve-factor (FF5) model, and the Hou, Xue, and Zhang (2015) q-factor (HXZ) model. Our motivation for using the FS model is to account for possible time variation in model betas and risk premiums. The time-series data on the pricing factors (i.e., market, size, value, momentum, pro tability, and investment) of the CAPM, FF3, FFC, and FF5 models, and monthly risk-free security returns are sourced from the Data Library maintained by Kenneth French. The time-series data on the HXZ model factors are sourced from Lu Zhang's website. To compute monthly average abnormal returns on portfolios relative to the FS model, we obtain data of a set of instruments Speci cally, we collect data on HHI directly from the U.S. Census of Manufacturers publications for CM the years 1992, 1997, 2002, 2007, and 2012. As in Bustamante and Donangelo (2017), we forward- ll missing observations and use 2-year lags in empirical exercises. The U.S. Census provided the index at the four-digit SIC level in 1992. Since 1997, the index has been published at the six-digit NAICS level. Following Ali, Klasa, and Yeung (2009), we use NAICS correspondence tables provided by the U.S. Census to convert the index to four-digit SIC levels. More details on HHI can be found in Bustamante and Donangelo (2017). CM Details of the computation of PCM at the rm-level can be found in Peress (2010). See https://faculty.mccombs.utexas.edu/donangelo/. See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html. See https://sites.google.com/site/theqfactormodel/?pli=1. 15 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 comprising the dividend yield of the Standard and Poor's 500 Index from Robert Shiller's website , and the term spread between 10-year and 3-month Treasury constant-maturity yields, the Treasury-bill rate, and the default spread between BAA and AAA-rated corporate bond yields from Amit Goyal's website. All of these instruments are demeaned before applying them in the time-series regressions for computing average abnormal returns on portfolios. We use several control variables in our cross-sectional regressions. These variables include rm-level attributes, such as past 1-month return, past 1-year return skipping the last month, book-to-market equity, size, and leverage ratio. Following Fama and French (1992, 1993), we compute the book-to-market ratio, denoted by BM , at the end of June of year t as the ratio of the book value of equity at the end of the scal year ending in the calendar year t 1 to the market value of equity at the end of December of the calendar year t 1. In the event of a missing book value of equity, we resort to the Davis, Fama, and French (2000) book value of equity from the Data Library maintained by Kenneth French. The market value of equity, denoted by ME, is computed as absolute price per share times number of equity shares outstanding at the end of June of each year t. We obtain data on stock prices and shares outstanding from the CRSP. As in Bustamante and Donangelo (2017) and Donangelo (2014), the leverage ratio, denoted by LEV , is computed as the ratio of the book value of debt to the book value of assets minus the book value of equity plus the market value of equity at the end of June of year t. 2.2 Summary statistics The empirical analyses begin by investigating nancial and accounting characteristics across LM -sorted portfolios to help understand the data. In doing so, we allocate stocks in the full sample into three portfolios at the end of June of each year t based on the NYSE breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of LM . The portfolios are rebalanced annually at the end of June. Panel A of Table 1 re- ports the time-series averages of the cross-sectional means of characteristics including HSALE, ME, BM , past 1-month return (R ), past 1-year return (R ) skipping the most re- 1;0 12; 2 cent month's return, and LEV . We see that the Low LM -sorted portfolio comprises stocks from the least competitive (or, equivalently, the most concentrated) industries, whereas the Medium LM -sorted portfolio comprises stocks from the most competitive (or, equivalently, the least concentrated) industries. Consistent with Donangelo (2014), we also nd that the High LM portfolio contains stocks smaller than those comprising the other portfolios. The average See http://www.econ.yale.edu/ shiller/data.htm. See http://www.hec.unil.ch/agoyal/. Details of the construction of the book value of equity can be found in Novy-Marx (2013). Internet Appendix Table IA1 provides summary statistics of portfolios based on the all-but-microcaps sample. 16 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 market capitalization of such stocks amounts to $2,740.02 million. It is worth mentioning that both HSALE and ME exhibit a nearly inverted U-shaped relation with LM . On the contrary, average BM ratios show a monotonically decreasing relation with LM . That is, stocks in the High LM portfolio tend to be a growth stock, while stocks in the Low LM portfolio tend to be a value stock. Furthermore, past 1-month and 1-year returns increase monotonically with LM , whereas LEV displays a nearly decreasing pattern for LM -sorted portfolios. We then proceed to examine whether one-way sorting on LM alone generates a pattern in average excess returns over the risk-free rate. Panel B of Table 1 reports the results from such an investigation where we construct three portfolios based on the NYSE breakpoints set to the bottom 30%, middle 40%, and top 30% of the ranked values of LM at the end of June of each year t. We nd that the value-weighted (equal-weighted) average monthly excess portfolio returns increase monotonically, from 0.61% (0.73%) for the Low LM portfolio to 0.88% (1.14%) for the High LM portfolio. The value-weighted (equal-weighted) average return of 0.27% (0.41%) per month for the high-minus-low LM is statistically indistinguishable (distinguishable) from zero, with a t-statistic of 1.59 (2.33). Although the value-weighted average monthly return on the high-minus-low portfolio appears to be statistically insigni cant at conventional levels, the portfolio generates an economically large and statistically signi cant average return of 0.83% (t-statistic = 3.05) per month for stocks in competitive industries (see Table 3). Panel C of Table 1 presents the results from the univariate portfolio analyses where stocks are sorted into quintile portfolios. By construction, the Low LM portfolio contains stocks below the 20th percentile of the NYSE cross-sectional distribution of LM , while the High LM portfolio contains stocks above the 80th percentile of the NYSE cross-sectional distribution of LM . We see that both the value-weighted and the equal-weighted average excess returns on portfolios generate neither a monotonically increasing nor a monotonically decreasing pattern. The high-minus-low LM portfolio delivers a value-weighted average return of 0.27% per month (t-statistic = 1.60). The corresponding equal-weighted average return amounts to 0.47% per month (t-statistic = 2.37). Note that the high-minus-low portfolio generates a value-weighted average return of 0.90% per month (t-statistic = 2.90) for stocks in competitive industries (see Table IA5). In contrast to the univariate sort results based on LM in Donangelo (2014, table V), the value-weighted average return on the high-minus-low LM portfolio is statistically insigni cant at the 10% level. A possible reason is that our sample composition is a bit dierent from Donangelo (2014) in that we require a sample of rms with both nonmissing product market competition and LM estimates. 17 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 3. Empirical Results This section tests our theoretical model, which predicts that the positive LM -return relation is stronger for rms in competitive industries. We follow two complementary methodologies: an independent double-sorted portfolio approach and a cross-sectional regression approach. 3.1 Portfolio-level analysis At the end of June of each year t, we assign stocks to three groups using the breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of HSALE in end-of-June. Independently, we also divide stocks into three groups according to the breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of LM , which is lagged 18 months, at the end of June of year t. The intersections of the three market competition and three LM groups result in nine portfolios, which are rebalanced annually at the end of June. Consequently, the transaction costs associated with implementing the trading strategy are expected to be low. Standard in the empirical asset pricing literature, we then obtain the value-weighted average excess returns for portfolios based on the full sample, while the equal-weighted average excess returns for portfolios based on the all- but-microcaps sample. These average excess returns allow us to provide a comprehensive picture of the relation between LM and future stock returns for rms in concentrated and competitive industries. To ensure that our results from both the full sample and the all-but-microcaps sample are robust to rm characteristics, we further compute characteristic-adjusted returns of portfolios. Speci cally, following the exact procedure in Daniel et al. (1997), characteristic- adjusted returns are computed as the dierence between individual stocks' returns and 125 (5 5 5) size/book-to-market/momentum benchmark portfolio returns. Table 2 summarizes the time-series averages of the cross-sectional mean characteristics of the independent double-sorted portfolios. The rst two rows in panels A and B show the sorting variables LM and HSALE. As expected, LM increases monotonically when moving from the Low LM portfolio, denoted by LM , to the High LM portfolio, denoted by LM , and this L H pattern is similar for both the Low competition and the High competition industries. It is also observable that rms in the High competition industries tend to have lower ME, lower BM , higher past returns, and lower LEV than rms in the Low competition industries. We report The results based on six alternative measures of product market competition, HSALE , HAT , HR HSALE , PMF , HHI , and PCM , are qualitatively similar to those based on HSALE. To conserve HP CM space, we report these robustness check results in the Internet Appendix Tables IA13 through IA20. To establish the robustness of our baseline empirical ndings, we further conduct 4 4 and 5 5 bivariate independent-sort portfolio analyses. These additional results provided in the Internet Appendix Tables IA4 and IA5 are very similar to those reported in this paper. 18 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 the main results from the bivariate independent-sort portfolio analyses in Table 3. In panel A, which makes use of the full sample and the NYSE breakpoints to sort variables, we nd that the value-weighted average monthly excess returns of LM -sorted portfolios in the High competition industries increase monotonically when moving from the Low LM portfolio, LM , to the High LM portfolio, LM . Importantly, the high-minus-low LM portfolio generates an economically large value-weighted average monthly return of 0.83%, which is highly statistically signi cant, with a Newey and West (1987)-adjusted t-statistic of 3.05. A monotonically increasing pattern also can be seen for the characteristic-adjusted returns when moving from the Low LM portfolio, LM , to the High LM portfolio, LM . The value-weighted characteristic-adjusted return of L H the high-minus-low LM portfolio is 0.79% per month, with a corresponding t-statistic of 3.76. The monthly average abnormal returns on this spread portfolio relative to the CAPM, FS, FF3, FFC, FF5, and HXZ models are also economically large and statistically distinguishable from zero; they are 0.82% (t-statistic = 3.07), 0.84% (t-statistic = 2.96), 0.92% (t-statistic = 3.23), 0.69% (t-statistic = 2.44), 0.83% (t-statistic = 2.53), and 0.69% (t-statistic = 2.08), respectively. Note that the economic magnitude of the conditional alpha (i.e., the FS model alpha) is similar to unconditional ones (i.e., the FF3, FFC, FF5, and HXZ model alphas). This suggests somewhat of a negligible time variation in the pricing model betas. However, we observe a completely dierent picture for LM -sorted portfolios in the Low competition industries (i.e., concentrated industries). For example, the value-weighted average monthly return of 0.15% on the high-minus-low LM portfolio is statistically insigni cant at conventional levels (t-statistic = 0.91). The value-weighted characteristic-adjusted return of 0.23% per month on this hedge portfolio is also statistically insigni cant (t-statistic = 1.30). Neither the average excess returns nor the average abnormal returns on portfolios displays a monotonically increasing pattern. For the high-minus-low LM portfolio, we also see that the value-weighted average abnormal returns relative to the six workhorse asset pricing models are all negative and statistically insigni cant at conventional levels. Speci cally, the CAPM, FS, FF3, FFC, FF5, and HXZ model alphas are 0.09%, 0.14%, 0.02%, 0.02%, 0.02%, and 0.08%, respectively, with t-statistics of 0.58, 0.87, 0.12, 0.13, 0.14, and 0.42. All these empirical results suggest that the positive LM -return relation exists only among rms in competitive industries. It is important to mention that the higher and statistically signi - cant return of the high-minus-low LM portfolio of stocks in competitive industries indicates a stronger LM -return relation rather than a larger variation in the LM estimates. In fact, the spread in the LM estimates among rms with a high HSALE value in the average cross-section is 2.07, whereas it is higher at 2.17 among low HSALE rms (see Table 2). 19 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Our empirical ndings on the relation between rms' LM and future stock returns in com- petitive industries are not sensitive to the all-but-microcaps sample analyzed in panel B of Table 3. For example, the equal-weighted average monthly return on the high-minus-low LM portfolio is 0.84%, which is statistically signi cant (t-statistic = 2.60). The equal-weighted characteristic-adjusted return on the portfolio is 0.79% per month, with a t-statistic of 3.11. Similar to that in panel A, the monthly average excess returns and the characteristic-adjusted returns of LM portfolios increase monotonically when moving from the Low LM portfolio, LM , to the High LM portfolio, LM . Moreover, the LM premium persists for rms in L H competitive industries even after adjusting for common risk factors using all ve asset pricing models. In fact, the CAPM, FS, FF3, FFC, FF5, and HXZ model alphas on the high-minus-low LM portfolio are 0.93%, 0.79%, 0.99%, 0.64%, 0.95%, and 0.70% per month, respectively, with t-statistics of 3.06, 2.23, 3.35, 2.17, 2.68, and 2.07. On the contrary, the equal-weighted average return and the characteristic-adjusted return are, respectively, 0.16% (t-statistic = 1.31) and 0.13% (t-statistic = 1.08) per month for the high-minus-low LM -sorted portfolio in the Low competition industries. Likewise, the CAPM, FS, FF3, FFC, FF5, and HXZ model alphas re- main small in magnitude and statistically insigni cant at conventional levels. Speci cally, they turn out to be 0.14% (t-statistic = 1.18), 0.11% (t-statistic = 0.90), 0.18% (t-statistic = 1.57), 0.12% (t-statistic = 0.96), 0.19% (t-statistic = 1.46), and 0.08% (t-statistic = 0.56), respectively. Overall, these results support our theoretical model's prediction leading to the hypothesis that the positive LM -return manifests itself for rms in competitive industries. We also nd that the results are qualitatively the same as those in Table 3 when we consider returns computed by rst forming industry portfolios and then equally weighting industry returns within each competition-mobility portfolio (see Table 4). Furthermore, the ndings in Tables 3 and 4 that the LM premium disappears, or even becomes negative, for rms in concentrated industries suggest that the positive LM -return relation identi ed in Donangelo (2014) is an average eect of rms from industries with dierent degrees of market competition. One important prediction from our theoretical model that leads to the hypothesis is Part (1) in Proposition 3, which shows that market power shields rms' pro ts from systematic shocks and such insulation over- shadows LM 's ampli cation on systematic risk. This means that the dierence in the loadings on the systematic risk between high LM and low LM portfolios should be much smaller in less competitive industries. As shown in Table A2, this prediction is veri ed empirically. We use the (high minus low) labor mobility factor of Donangelo (2014), denoted by LM , as a proxy H-L The Internet Appendix provides strong evidence that the empirical results are qualitatively similar to those in Tables 3 and 4 when we conduct 4 4 and 5 5 bivariate independent-sort portfolio analyses using industry-level returns (see Tables IA6 and IA7) and use unlevered stock returns (see Table IA8). 20 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 for the systematic risk. In Table A2, we report the factor loadings of eight double-sorted portfolios: low LM , medium LM , high LM , and high-low LM in the low competition and high competition groups. Take the full sample as an example (panel A in Table A2), the factor loadings increase monotonically with the LM in both groups, but the pattern is much stronger in the high competition group: the H-L factor loading is 1.08 (t-statistic = 12.84) in the high competition group as opposite to that being 0.38 (t-statistic = 6.17) in the low competition group. This pattern is fairly robust in the all-but-microcaps sample and to controlling for the market excess return factor of the CAPM. To evaluate the robustness of our preceding empirical ndings over time, we also plot the value-weighted and equal-weighted cumulative log returns on the high-minus-low LM portfolios for the Low and High market competition industries in Figure 2. We see that cumulative returns only on the high-minus-low LM portfolio of stocks in competitive industries steadily increase throughout the sample period between July 1992 and December 2016. This evidence suggests that the power of LM to predict future stock returns in the cross-section persists over time only for rms in competitive industries. Taken together, the empirical results in Tables 3 and 4 and Figure 2 provide signi cant evidence that the positive relation between the rm's LM and the future stock returns strengthens with the intensity of product market competition. 3.2 Cross-sectional regressions We also test our hypothesis by conducting the Fama and MacBeth (1973) cross-sectional regressions of monthly stock returns on lagged LM estimates and other lagged rm-level char- acteristics known to predict returns. Similar to that of the portfolio approach, we rst sort stocks into three market competition groups according to the breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of HSALE at the end of June of each year t. Then, in each month from July of year t to June of year t 1, we run the following cross-sectional regressions for the Low and High competition industries separately: R R R lnpBM q lnpME q LEV LM; (20) 0 1 1;0 2 12; 2 3 4 5 6 Per our model, if an empirical factor that well represents the model's single source of systematic risk, then we should observe the loadings on this risk factor exhibit stronger (weaker) increasing monotonic pattern with the LM in more (less) competitive industries. This is exactly what we see in Table A2 with the labor mobility factor, LM . Therefore, LM is a good proxy of the systematic risk in our model. We report the factor H-L H-L loadings on various other factors in Table IA2 of the Internet Appendix. We nd that neither the CAPM nor the other factors we consider can reproduce this pattern, indicating that none of the traditional factors empirically represents the systematic risk in our model. 21 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 where R is the monthly returns from July of year t to June of year t 1 on an individual stock, R is the past one-month return, R is the (cumulative average) return over the past 12 1;0 12; 2 months skipping the most recent month's return, ln(ME) is the natural logarithm of market value of equity, ln(BM ) is the natural logarithm of book-to-market ratio, and LEV is the leverage ratio. Labor mobility, LM , is lagged 18 months, at the end of June of year t. We include R , R , BM , ME, and LEV as control variables to simultaneously account 1;0 12; 2 for the potential eects of short-term reversal, medium-term price momentum, book-to-market ratio, size, and leverage ratio on the cross-section of future stock returns. With the exception of LM , we also winsorize all explanatory variables at the 2% level (1% in each tail of the distribution) on a monthly basis prior to running the cross-sectional regressions. This help reduce possible undue in uence of outlier observations on the empirical results. In Table 5, we present the time-series average slope and intercept coecient estimates, from the Fama and MacBeth (1973) cross-sectional regressions, along with their time-series t- statistics. To demonstrate that the LM premium increases with the level of market competition, we further report the time-series averages of the dierences in slope and intercept coecient estimates between the High and Low product market competition industries. In panel A, which utilizes the full sample and the NYSE breakpoints to sort on HSALE, we notice that the estimated average coecient of 0.46 (t-statistic = 4.74) on LM for stocks in the High competition industries is much larger (both economically and statistically) than that of 0.09 (t- statistic = 1.39) for stocks in the Low competition industries. The average spread between the estimated slope coecients for LM for stocks in the High competition and the Low competition industries is 0.37, which is also highly statistically signi cant, with a t-statistic of 3.01. When the all-but-microcaps sample is examined in panel B, we nd that the results are very similar to those based on the full sample in panel A. The average coecient estimates on LM are 0.07 (t-statistic = 1.28) and 0.37 (t-statistic = 2.82), respectively, for stocks in the Low and High product market competition industries. More importantly, the estimated average slope spread of 0.30 on LM is statistically signi cant, with a t-statistic of 2.61. In summary, our results from a series of monthly Fama and MacBeth (1973) cross-sectional regressions in Table 5 indicate that after controlling for the eects of rm characteristics, such as size, book- to-market ratio, momentum, short-term reversal, and leverage, the positive relation between LM and future stock returns is much stronger for rms in competitive industries. In fact, the existence of a signi cantly positive LM -return relation for rms only in competitive industries is consistent with our previous results from the independent double-sorted portfolio analyses. Internet Appendix Table IA9 shows that the results remain robust when stocks are sorted into ve groups based on the NYSE breakpoints set to the 20th, 40th, 60th, and 80th percentiles of the ranked values of HSALE. 22 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 3.3 Cross-sectional regressions with market competition dummies To further examine the relation between LM and future stock returns across rms with dierent levels of market competition, we run the Fama and MacBeth (1973) cross-sectional regressions augmented with product market competition dummy and interaction variables. In particular, two market competition dummy variables are created by sorting stocks into three groups based on the breakpoints set to the 30th and 70th percentiles of the ranked values of HSALE estimated at the end of June of each year t. We then estimate the following cross- sectional regressions in each month from July of year t to June of year t 1: R X; (21) R X LM HSALE HSALE ; (22) 0 7 L 8 L R X LM HSALE HSALE ; (23) 0 7 H 8 H R X LM HSALE LM HSALE HSALE HSALE ; (24) 0 7 H 8 L 9 H 10 L where X is a vector of explanatory variables including R , R , ln(BM ), ln(ME), LEV , 1;0 12; 2 and LM ; HSALE (HSALE ) is a dummy variable that is equal to one for stocks in the High H L (Low) competition industries at the end of June of each year and is zero otherwise. Analogous to Table 5, we winsorize all but LM and dummy variables, HSALE and HSALE , at the H L 1% and 99% levels on a monthly basis before running the cross-sectional regressions. We nd that the results in Table 6 are consistent with our earlier ndings based on indepen- dent double-sorted portfolio and cross-sectional regression approaches, respectively, in Sections 4.1 and 4.2. In panel A, for the full sample and the NYSE breakpoints, when we focus on the baseline monthly cross-sectional regressions given by Equation (21), we see that LM has a signi cantly positive relation with future stock returns. Moving to the cross-sectional regres- sions speci ed by Equation (22), we observe that the average coecient estimate of 0.17 on the interaction variable LM HSALE is marginally statistically signi cant, with a t-statistic of 1.66. The sum of the average coecient estimates on LM and LM HSALE is 0.07 (t-statistic = 1.14). This shows the absence of a signi cantly positive LM -return relation for rms in concentrated industries. Analyzing the cross-sectional regressions speci ed by Equa- tion (23), we nd an estimated average coecient for the interaction variable LM HSALE of 0.24, which is both economically and statistically signi cant at conventional levels (t-statistic = 2.65). Since LM is standardized, the magnitude of this coecient estimate implies that, all else being equal, a one-standard deviation increase in LM is associated with a future stock return per month for rms in the High competition industries that is 24 basis points higher than for 23 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 rms in all other groups. Also, the slope estimate of returns on LM for stocks in the High competition industries (i.e., the sum of the average coecients for LM and LM HSALE ) is 0.36, with a t-statistic of 3.96. For the cross-sectional regressions speci ed by Equation (24), we notice that the average coecient estimates on the interaction variables LM HSALE and LM HSALE are, respectively, 0.08 (t-statistic = 0.67) and 0.21 (t-statistic = 2.07). Col- lectively, these results based on the full sample provide evidence supportive to our hypothesis that the positive LM -return relation strengthens with the level of product market competition. Turning now to the monthly cross-sectional regressions using the all-but-microcaps sample in panel B of Table 6, we also nd that the results are qualitatively similar to those obtained using the full sample. For example, the average coecient estimate of 0.17 on LM from the baseline cross-sectional regressions (i.e., Equation (21)) is statistically signi cant (t-statistic = 3.04). For the cross-sectional regressions given by Equation (22), the average coecient for the interaction variable LM HSALE is 0.15 (t-statistic = 1.58). Moreover, the sum of coecient estimates on LM and LM HSALE is 0.08, which is economically small and statistically insigni cant, with a t-statistic of 1.43. All of these results suggest that LM has no signi cantly positive eect on future stock returns for rms in concentrated industries. In the case of cross-sectional regressions speci ed by Equation (23), we notice that the average coecient estimate of 0.26 on the interaction variable LM HSALE is statistically signi cant, with a t-statistic of 2.09. Economically this means that, all else being equal, a one-standard deviation increase in LM is associated with a future stock return per month for rms in the High competition industries that is 26 basis points higher than that for all rms in the Medium and Low competition industries. Notably, the sum of the average coecient estimates on LM and LM HSALE is 0.37, with a t-statistic of 2.77. Finally, for the monthly cross- sectional regressions given by Equation (24), we nd that the average coecient estimates on the interaction variables LM HSALE and LM HSALE are 0.05 (t-statistic = 0.52) L H and 0.24 (t-statistic = 1.99), respectively. Taken together, consistent with our hypothesis, the results in panels A and B of Table 6 clearly show that the power of LM to predict future stock returns is much stronger for the cross-section of rms in competitive industries. Furthermore, Table IA11 in the Internet Appendix shows that the results are qualitatively the same as those in Table 6 when we run panel data regressions instead of the periodic cross-sectional regressions. Internet Appendix Table IA10 shows that the results are qualitatively similar when HSALE (HSALE ) is H L equal to one for stocks in the top (bottom) 20% percentile of the ranked values of HSALE and is zero otherwise. 24 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 3.4 Evidence from an extended sample Because of the lack of availability of data on LM estimates for a longer period of time, our preceding empirical analyses are based on a restrictive sample that starts in January 1990 and ends in December 2016. Hence, one may argue that the ndings in this paper are speci c to the relatively short sample period under investigations. In this section, we address this concern by reporting the results from independent double-sorted portfolio analyses as in Section 4.1 but using a longer sample that covers the period from January 1973 to December 2016. Speci cally, we follow Donangelo (2014) in this regard and extend the baseline sample backward by setting the LM estimates in 1973 to 1989 equal to those estimated for 1990. Overall, the results in Table 7 suggest a signi cantly positive LM -return relation for rms only in competitive industries, which is supportive to our hypothesis. For example, in panel A for the full sample, the high-minus-low LM portfolio in the High competition industries generates a value-weighted average monthly return (value-weighted characteristic-adjusted return) of 0.39% (0.44%), which is statistically signi cant, with a t-statistic of 2.68 (2.82). The monthly average abnormal returns on this portfolio relative to the asset pricing models are also statistically distinguishable from zero. However, the high-minus-low LM portfolio in the Low competition industries generates statistically insigni cant value-weighted average monthly return and value- weighted characteristic-adjusted return of 0.20% (t-statistic = 1.48) and 0.14% (t-statistic = 1.05), respectively. A qualitatively similar picture emerges for the all-but-microcaps sample, in panel B, where the high-minus-low LM portfolios delivers a statistically signi cant LM premium only for rms in the High competition industries. To verify the robustness of these ndings, we further reestimate the Fama and MacBeth (1973) cross-sectional regressions in Table 5 using the extended sample that spans January 1973 to December 2016. The results reported in Table IA12 of the Internet Appendix strongly support our hypothesis. 4. Conclusion This paper investigates the role of product market competition in the relation between LM and expected stock returns. To do so, we construct a production-based model in which the imperfect elasticity of substitution combined with the market concentration propagates to the demand for mobile labor, which further determines the operating pro ts, in the initial production stage through the price of the intermediate goods in the nal product market. We show that LM can barely have any eect on the rms' systematic risk when the market power See table IA.XIII in the internet appendix of Donangelo (2014). To get an idea about labor mobility transition probabilities, see also table IA.XI of Donangelo (2014). 25 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 within an industry is substantial. This implies that the insulation induced by the market power can quickly overshadow the LM 's ampli cation on systematic risk. Hence, our model predicts that the LM premium is stronger or exists only in highly competitive industries. Consistent with our theoretical model's prediction, we nd robust evidence that the posi- tive LM -return relation exists only among rms in competitive industries. This novel nding suggests that the intensity of competition in rms' product market drives a signi cant portion of the positive LM -return relation. We hope that our paper enhances the understanding of the LM premium through the lens of product market competition and inspires future research combining other aspects of the industrial organization, and the labor and nancial markets. 26 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 References Aguerrevere, F. L. 2009. Real options, product market competition, and asset returns. Journal of Finance 64:957{83. Ali, A., S. Klasa, and E. Yeung. 2009. The limitations of industry concentration measures constructed with Compustat data: Implications for nance research. 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Markup cycles, dynamic misallocation, and ampli cation. Journal of Economic Theory 154:126{61. Peress, J. 2010. Product market competition, insider trading, and stock market eciency. Journal of Finance 65:1{43. Sharpe, W. F. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19:425{42. Shumway, T. 1997. The delisting bias in CRSP data. Journal of Finance 52:327{40. Zhang, M. B. 2019. Labor-technology substitution: Implications for asset pricing. Journal of Finance 74:1793{839. 29 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Figure 1 versus 1.8 1.4 1.6 1.2 1.4 1.2 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 -0.2 -0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 The left panel plots as a function of , and the right panel plots the rst-order partial derivatives of w.r.t. . Four lines for ! 1; 0:75; 0:5, and 0:25 are plotted. The numerical values for the plots are shown in the subtitles. 30 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Figure 2 Returns on high-minus-low labor mobility portfolios 3.0 High competition (value-weighted) Low competition (value-weighted) 2.5 High competition (equal-weighted) Low competition (equal-weighted) 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 The gure plots the value-weighted and equal-weighted cumulative log returns on the high-minus-low labor mobility portfolios in the Low and High product market competition industries. The value-weighted portfolio returns are computed based on the full sample, whereas the equal-weighted portfolio returns are computed based on the all-but-microcaps sample. The sample spans July 1992 to December 2016. See also the legends to Tables 1 and 3. Cumulative log return Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table 1 Summary statistics The sample includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. There are 2,891 rms in an average month. HSALE is the product market competition measured by the Her ndahl-Hirschman Index (HHI), where for each industry, we rst aggregate the squared net sales-based market shares of all rms in that industry in a given year and then average the HHI values over the past 3 years. We multiply HSALE by minus one so that a higher value indicates a higher level of product market competition. LM is the measure of labor mobility, which is computed in two stages, rst at the occupation-level and then at the industry level. ME is the market value of equity (in million $), which is computed as the number of shares outstanding times the absolute price of one share at the end of June of each year t. BM is the book-to-market ratio, which is computed in June of each year t as the ratio of the book value of equity at the end of the scal year ending in the calendar year t 1 to the market value of equity at the end of December of the calendar year t 1. R is the past 1-month return (in %). R is the past 1-year return (in %) skipping 1;0 12; 2 the most recent month. LEV is the leverage ratio calculated as the ratio of the book value of debt to the book value of assets minus the book value of equity plus the market value of equity at the end of June of year t. At the end of June of each year t, stocks are sorted into three portfolios based on the NYSE breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of LM , which is lagged 18 months, at the end of June of year t. Panel A reports the time-series averages of the cross-sectional mean characteristics of the portfolios of rms sorted by LM . Panel B (panel C) reports both the value-weighted (VW) and the equal-weighted (EW) average monthly excess returns (in %) for portfolios (quintile portfolios) sorted on LM . All portfolios are rebalanced annually at the end of June. H L denotes the high-minus-low portfolio, that is, long stocks in the High portfolio and short stocks in the Low portfolio. Numbers in parentheses are t-statistics adjusted following Newey and West (1987). The sample period is from January 1990 to December 2016. A. Characteristics of portfolios sorted on LM Portfolio HSALE ME BM R R LEV 1;0 12; 2 Low 0.213 2,946.152 1.059 1.014 11.301 0.411 Medium 0.178 3,421.161 0.746 1.225 12.150 0.313 High 0.206 2,740.021 0.739 1.411 16.102 0.320 B. Portfolio excess returns Low Medium High H L LM VW 0.61 0.66 0.88 0.27 (1.77) (2.28) (3.02) (1.59) EW 0.73 0.95 1.14 0.41 (1.75) (2.20) (2.71) (2.33) C. Excess returns of quintile portfolios Low 2 3 4 High H L LM VW 0.73 0.54 0.66 0.68 1.00 0.27 (2.01) (1.55) (2.19) (2.56) (3.46) (1.60) EW 0.72 0.68 1.11 0.92 1.19 0.47 (1.74) (1.58) (2.53) (2.28) (2.73) (2.37) 32 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table 2 Characteristics of portfolios double-sorted on product market competition and labor mobility The table reports the time-series averages of the cross-sectional mean characteristics of the portfolios of rms sorted on product market competition and labor mobility, LM . At the end of June of each year t, stocks are sorted into three groups based on the NYSE breakpoints for the bottom 30% (Low (L)), middle 40% (Medium (M)), and top 30% (High (H)) of the ranked values of product market competition at the end of June of year t. Product market competition for an industry is measured using net sales-based market shares of all rms in that industry. Independently, stocks are sorted into three groups based on the NYSE breakpoints for the bottom 30% (L), middle 40% (M), and top 30% (H) of the ranked values of labor mobility, which is lagged 18 months, at the end of June of year t. The intersections of the product market competition and labor mobility groups result in nine portfolios. All portfolios are rebalanced annually at the end of June. The full sample in panel A includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. The all-but-microcaps sample in panel B excludes stocks, from the full sample, with an end-of-June market value of equity below the 20th percentile of the NYSE market capitalization distribution and the remaining stocks are used to compute the breakpoints for product market competition and labor mobility separately. H L is the high-minus-low portfolio. The sample period is from January 1990 to December 2016. See also the legend to Table 1. Low competition High competition LM LM LM H L LM LM LM H L L M H L M H A. Full sample LM 0.92 0.15 1.25 2.17 0.93 0.17 1.13 2.07 HSALE 0.40 0.40 0.41 0.00 0.10 0.09 0.08 0.02 ME 3,577.30 2959.38 3284.64 292.66 2,983.62 2,941.98 2,238.16 745.46 BM 0.82 0.91 0.78 0.04 0.86 0.61 0.69 0.17 R 1.01 0.99 1.14 0.13 0.81 1.35 1.53 0.72 1;0 R 11.72 11.93 13.89 2.17 9.71 14.90 17.70 7.99 12; 2 LEV 0.38 0.39 0.37 0.01 0.37 0.23 0.26 0.10 B. All-but-microcaps sample LM 0.86 0.29 1.24 2.10 0.74 0.23 1.06 1.80 HSALE 0.36 0.35 0.36 0.00 0.08 0.09 0.07 0.01 ME 6,299.22 6,491.35 6,374.82 75.60 4,864.52 7,285.73 6,202.86 1,338.34 BM 0.61 0.55 0.49 0.12 0.51 0.36 0.34 0.17 R 0.96 1.08 1.18 0.22 0.78 1.25 1.65 0.87 1;0 R 11.13 12.40 13.37 2.24 8.69 15.09 19.29 10.61 12; 2 LEV 0.36 0.35 0.33 0.04 0.27 0.19 0.18 0.09 33 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table 3 Double sorts on product market competition and labor mobility The table reports monthly returns of portfolios sorted on product market competition and labor mobility, LM . At the end of June of each year t, stocks are sorted into three groups based on the NYSE breakpoints for the bottom 30% (Low (L)), middle 40% (Medium (M)), and top 30% (High (H)) of the ranked values of product market competition at the end of June of year t. Product market competition for an industry is measured using net sales-based market shares of all rms in that industry. Independently, stocks are sorted into three groups based on the NYSE breakpoints for the bottom 30% (L), middle 40% (M), and top 30% (H) of the ranked values of labor mobility, which is lagged 18 months, at the end of June of year t. The intersections of the product market competition and labor mobility groups result in nine portfolios. All portfolios are rebalanced annually at the end of June. The full sample includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. The all-but-microcaps sample excludes stocks, from the full sample, with an end-of-June market value of equity below the 20th percentile of the NYSE market capitalization distribution and the remaining stocks are used to compute the breakpoints for product market competition and labor mobility separately. Panel A (panel B) reports the value-weighted (equal-weighted) average monthly returns (in %) on portfolios. Excess return is the portfolio return in excess of the 1-month Treasury-bill rate. Characteristic-adjusted (Char-adj) returns are computed by adjusting returns using 125 (5 5 5) size/book-to-market/momentum benchmark portfolios (as in Daniel et al., 1997). The alphas (in %) are estimated from the time-series regressions of portfolio excess returns on various factor models including the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), the Ferson and Schadt (1996) conditional capital asset pricing (FS) model, the Fama and French (1993) three-factor (FF3) model, the Fama and French (1993) and Carhart (1997) four-factor (FFC) model, the Fama and French (2015) ve-factor (FF5) model, and the Hou, Xue, and Zhang (2015) q-factor (HXZ) model. H L is the high-minus-low portfolio. Numbers in parentheses are t-statistics adjusted following Newey and West (1987). The sample period is from January 1990 to December 2016. See also the legend to Table 1. Low competition High competition LM LM LM H L LM LM LM H L L M H L M H A. Full sample Excess return 0.95 0.76 0.80 0.15 0.19 0.77 1.02 0.83 (3.15) (2.66) (3.10) ( 0.91) (0.50) (2.34) (3.02) (3.05) Char-adj return 0.06 0.21 0.17 0.23 0.68 0.12 0.11 0.79 (0.38) ( 2.18) ( 1.53) ( 1.30) ( 3.97) ( 1.02) (0.96) (3.76) CAPM 0.33 0.14 0.24 0.09 0.54 0.06 0.28 0.82 (2.10) (1.12) (2.20) ( 0.58) ( 2.35) (0.27) (1.66) (3.07) FS 0.29 0.13 0.14 0.14 0.54 0.18 0.30 0.84 (2.01) (0.97) (1.29) ( 0.87) ( 2.32) (1.05) (1.85) (2.96) FF3 0.22 0.09 0.20 0.02 0.54 0.26 0.38 0.92 (1.67) (0.77) (1.91) ( 0.12) ( 2.18) (1.76) (2.47) (3.23) FFC 0.27 0.15 0.25 0.02 0.36 0.44 0.33 0.69 (1.91) (1.20) (2.53) ( 0.13) ( 1.48) (2.31) (2.07) (2.44) FF5 0.05 0.00 0.03 0.02 0.46 0.43 0.37 0.83 (0.37) (0.00) (0.25) ( 0.14) ( 1.79) (2.25) (2.15) (2.53) HXZ 0.17 0.07 0.09 0.08 0.30 0.58 0.39 0.69 (1.08) (0.50) (0.81) ( 0.42) ( 1.00) (2.88) (1.99) (2.08) B. All-but-microcaps sample Excess return 0.77 0.87 0.93 0.16 0.49 0.93 1.33 0.84 (2.21) (2.86) (2.74) (1.31) (1.07) (2.19) (3.33) (2.60) Char-adj return 0.29 0.27 0.16 0.13 0.54 0.07 0.26 0.79 ( 2.84) ( 2.45) ( 1.80) (1.08) ( 3.25) ( 0.49) (1.67) (3.11) CAPM 0.03 0.17 0.17 0.14 0.47 0.03 0.45 0.93 (0.14) (0.92) (1.17) (1.18) ( 2.17) (0.12) (1.77) (3.06) FS 0.04 0.12 0.15 0.11 0.28 0.21 0.51 0.79 (0.23) (0.61) (0.97) (0.90) ( 1.12) (0.86) (1.80) (2.23) FF3 0.15 0.01 0.03 0.18 0.46 0.15 0.53 0.99 ( 1.06) (0.07) (0.28) (1.57) ( 2.17) (0.88) (3.16) (3.35) FFC 0.10 0.19 0.22 0.12 0.15 0.37 0.49 0.64 (0.78) (1.33) (2.15) (0.96) ( 0.65) (1.86) (3.01) (2.17) FF5 0.22 0.15 0.03 0.19 0.33 0.50 0.62 0.95 ( 1.37) ( 0.95) ( 0.22) (1.46) ( 1.18) (2.45) (3.78) (2.68) HXZ 0.03 0.05 0.11 0.08 0.03 0.64 0.68 0.70 (0.13) (0.24) (0.73) (0.56) ( 0.09) (3.25) (3.05) (2.07) 34 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table 4 Double sorts on product market competition and labor mobility: Industry-level returns The table reports monthly returns of portfolios sorted on product market competition and labor mobility, LM . The setup is the same as in Table 3, except that the results are based on returns computed by rst forming (three-digit SIC code) industry portfolios, and then equally weighting industry returns within each competition-mobility portfolio. Product market competition for an industry is measured using net sales-based market shares of all rms in that industry. The full-sample includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. The all-but-microcaps sample excludes stocks with an end-of-June market value of equity below the 20th percentile of the NYSE market capitalization distribution and the remaining stocks are used to compute the breakpoints for product market competition and labor mobility separately. For each portfolio in panel A (panel B), individual stock excess and adjusted returns are rst value-weighted (equal-weighted) averaged within each industry comprising the portfolio, and then equal-weighted averaged across industries within the same portfolio. Excess return of a stock is the return in excess of the 1-month Treasury-bill rate. Characteristic-adjusted (Char-adj) returns of a stock are computed by adjusting returns using 125 (5 5 5) size/book-to-market/momentum benchmark portfolios (as in Daniel et al., 1997). The alphas (in %) are estimated from the time-series regressions of portfolio excess returns on various factor models including the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), the Ferson and Schadt (1996) conditional capital asset pricing (FS) model, the Fama and French (1993) three-factor (FF3) model, the Fama and French (1993) and Carhart (1997) four-factor (FFC) model, the Fama and French (2015) ve-factor (FF5) model, and the Hou, Xue, and Zhang (2015) q-factor (HXZ) model. H L is the high-minus-low portfolio. Numbers in parentheses are t-statistics adjusted following Newey and West (1987). The sample period is from January 1990 to December 2016. See the legends to Tables 1 and 3. Low competition High competition LM LM LM H L LM LM LM H L L M H L M H A. Full sample Excess return 0.67 0.84 0.70 0.03 0.34 0.86 1.06 0.72 (1.90) (2.44) (2.29) (0.14) (1.04) (2.63) (3.74) (4.18) Char-adj return 0.36 0.36 0.29 0.07 0.39 0.24 0.16 0.55 ( 1.74) ( 2.58) ( 2.23) (0.36) ( 3.29) ( 1.90) (1.44) (4.35) CAPM 0.05 0.14 0.07 0.02 0.32 0.20 0.44 0.76 (0.19) (0.79) (0.43) (0.09) ( 1.58) (1.10) (2.27) (4.04) FS 0.03 0.09 0.01 0.02 0.33 0.15 0.34 0.66 ( 0.11) (0.46) ( 0.08) (0.07) ( 1.90) (0.83) (1.76) (3.74) FF3 0.10 0.02 0.04 0.06 0.47 0.03 0.30 0.77 ( 0.43) ( 0.15) ( 0.27) (0.27) ( 3.17) (0.20) (1.99) (3.91) FFC 0.05 0.14 0.02 0.04 0.42 0.18 0.37 0.79 (0.26) (0.90) (0.12) ( 0.18) ( 2.74) (1.28) (2.57) (3.93) FF5 0.18 0.08 0.20 0.01 0.58 0.12 0.11 0.68 ( 0.76) ( 0.50) ( 1.29) ( 0.06) ( 3.71) ( 0.76) (0.72) (3.47) HXZ 0.01 0.11 0.12 0.13 0.48 0.04 0.24 0.72 (0.04) (0.63) ( 0.69) ( 0.55) ( 2.78) (0.17) (1.37) (3.37) B. All-but-microcaps sample Excess return 0.75 1.02 0.81 0.07 0.44 0.83 1.16 0.72 (2.31) (3.17) (2.64) (0.37) (1.30) (2.36) (3.50) (4.26) Char-adj return 0.23 0.15 0.22 0.01 0.45 0.28 0.09 0.54 ( 1.27) ( 1.27) ( 1.84) (0.04) ( 4.15) ( 2.21) (0.78) (3.90) CAPM 0.07 0.29 0.18 0.11 0.25 0.10 0.44 0.70 (0.29) (1.54) (0.97) (0.65) ( 1.22) (0.49) (2.12) (4.14) FS 0.00 0.31 0.12 0.12 0.25 0.04 0.38 0.63 (0.01) (1.48) (0.69) (0.65) ( 1.29) (0.18) (1.93) (3.80) FF3 0.11 0.14 0.03 0.14 0.44 0.11 0.26 0.71 ( 0.59) (0.90) (0.23) (0.80) ( 3.00) ( 0.74) (1.83) (4.39) FFC 0.06 0.26 0.08 0.02 0.33 0.09 0.38 0.72 (0.34) (1.76) (0.59) (0.12) ( 2.39) (0.71) (2.76) (3.89) FF5 0.24 0.02 0.19 0.05 0.56 0.27 0.05 0.61 ( 1.18) (0.14) ( 1.38) (0.28) ( 3.50) ( 1.81) (0.40) (3.57) HXZ 0.02 0.13 0.09 0.07 0.47 0.07 0.27 0.73 ( 0.08) (0.73) ( 0.59) ( 0.31) ( 2.45) ( 0.31) (1.70) (3.86) 35 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table 5 Cross-sectional regressions The table reports the time-series average slope and intercept coecient estimates from the Fama and MacBeth (1973) cross-sectional regressions. At the end of June of each year t, stocks are sorted into three groups based on the NYSE breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of product market competition at the end of June of year t. Product market competition for an industry is measured using net sales-based market shares of all rms in that industry. Then, in each month from July of year t to June of year t 1 for the Low (High) competition industries, we run a cross-sectional regression of monthly returns on lagged variables including past 1-month return (R ), past 1-year return skipping the 1;0 most recent month (R ), the natural logarithm of market value of equity (ln(ME)), the natural logarithm 12; 2 of book-to-market ratio (ln(BM )), leverage ratio (LEV ), and labor mobility (LM ), which is lagged 18 months. The full sample, in panel A, includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. The all-but-microcaps sample, in panel B, excludes stocks, from the full sample, with an end-of-June market value of equity below the 20th percentile of the NYSE market capitalization distribution and the remaining stocks are used to compute the breakpoints for product market competition. High Low is the time-series average of the dierence in slope or intercept coecient estimates between the High and Low competition industries. Numbers in parentheses are t-statistics adjusted following Newey and West (1987). All in- dependent variables (with the exception of LM ) are winsorized at the 1% and 99% levels on a monthly basis prior to running the regressions. The sample period is from January 1990 to December 2016. See the legend to Table 1. Intercept R R ln(BM ) ln(ME) LEV LM 1;0 12; 2 A. Full sample Low 1.05 0.42 0.24 0.45 0.01 0.24 0.09 (2.15) (0.74) (0.59) (5.61) (0.10) ( 0.55) (1.39) High 2.01 1.64 0.08 0.42 0.11 0.53 0.46 (2.64) ( 3.31) (0.26) (4.46) ( 1.41) ( 1.22) (4.74) High Low 0.95 2.06 0.16 0.03 0.11 0.29 0.37 (2.42) ( 3.57) ( 0.72) ( 0.40) ( 2.59) ( 0.71) (3.01) B. All-but-microcaps sample Low 0.87 0.25 0.25 0.19 0.02 0.23 0.07 (1.78) ( 0.32) (0.53) (1.74) ( 0.50) (0.54) (1.28) High 1.36 1.24 0.20 0.14 0.06 0.47 0.37 (2.02) ( 1.64) (0.56) (1.35) ( 0.95) (0.85) (2.82) High Low 0.49 0.99 0.05 0.05 0.04 0.24 0.30 (1.03) ( 1.30) ( 0.19) ( 0.48) ( 0.84) (0.44) (2.61) 36 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table 6 Cross-sectional regressions with product market competition dummies The table reports the time-series averages of the coecient estimates from the Fama and MacBeth (1973) cross-sectional regressions. At the end of June of each year t, dummy variables are created by sorting stocks into three groups based on the NYSE breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of product market competition at the end of June of year t. Product market competition for an industry is measured using net sales-based market shares of all rms in that industry. Then, in each month from July of year t to June of year t 1, we run a cross-sectional regression of monthly returns on lagged variables including past 1-month return (R ), past 1-year return skipping the most recent month (R ), the natural logarithm of market value of equity (ln(ME)), the natural logarithm 1;0 12; 2 of book-to-market ratio (ln(BM )), leverage ratio (LEV ), labor mobility (LM ), which is lagged 18 months, and product market competition dummy and interaction variables. HSALE (HSALE ) is a dummy variable equal to one for stocks in the High (Low) competition industries in a given month and is zero otherwise. The full sample, in panel H L A, includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. The all-but-microcaps sample, in panel B, excludes stocks, from the full sample, with an end-of-June market value of equity below the 20th percentile of the NYSE market capitalization distribution and the remaining stocks are used to compute the breakpoints for product market competition. Numbers in parentheses are t-statistics adjusted following Newey and West (1987). All continuous independent variables (with the exception of LM ) are winsorized at the 1% and 99% levels on a monthly basis prior to running the cross-sectional regressions. The sample period is from January 1990 to December 2016. See also the legend to Table 1. Intercept R R ln(BM ) ln(ME) LEV LM LM HSALE LM HSALE HSALE HSALE 1;0 12; 2 H L H L A. Full sample 1.59 0.55 0.04 0.40 0.07 0.28 0.19 (2.53) ( 1.22) (0.11) (4.68) ( 1.11) ( 0.71) (3.30) 1.59 0.55 0.03 0.40 0.07 0.21 0.24 0.17 0.18 (2.53) ( 1.24) (0.09) (4.77) ( 1.06) ( 0.56) (3.29) ( 1.66) ( 1.66) 1.40 0.58 0.04 0.42 0.06 0.14 0.12 0.24 0.27 (2.38) ( 1.31) (0.10) (5.20) ( 1.00) ( 0.37) (2.09) (2.65) (2.34) 1.37 0.58 0.03 0.42 0.06 0.11 0.15 0.21 0.08 0.27 0.03 (2.30) ( 1.34) (0.07) (5.22) ( 0.98) ( 0.29) (1.97) (2.07) ( 0.67) (2.30) ( 0.27) B. All-but-microcaps sample 1.17 0.55 0.14 0.16 0.05 0.21 0.17 (2.08) ( 0.84) (0.33) (1.71) ( 0.94) (0.52) (3.04) 1.18 0.56 0.14 0.17 0.04 0.27 0.23 0.15 0.12 (2.10) ( 0.86) (0.34) (1.78) ( 0.89) (0.69) (2.92) ( 1.58) ( 1.36) 1.05 0.59 0.14 0.18 0.04 0.32 0.11 0.26 0.18 (1.95) ( 0.92) (0.33) (1.95) ( 0.82) (0.84) (1.98) (2.09) (1.49) 1.07 0.60 0.13 0.18 0.04 0.33 0.13 0.24 0.05 0.16 0.06 (1.96) ( 0.95) (0.31) (2.00) ( 0.82) (0.87) (1.84) (1.99) ( 0.52) (1.25) ( 0.62) Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table 7 Double sorts on product market competition and labor mobility: 1973{2016 The table reports monthly returns of portfolios sorted on product market competition and labor mobility, LM . The setup is the same as in Table 3, except that the sample period is from January 1973 to December 2016. The labor mobility estimates in 1973 to 1989 are set equal to those estimated for 1990 (as in Donangelo, 2014). The full sample includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. The all-but-microcaps sample excludes stocks, from the full sample, with an end-of-June market value of equity below the 20th percentile of the NYSE market capitalization distri- bution and the remaining stocks are used to compute the breakpoints for product market competition and labor mobility separately. Panel A (panel B) reports the value-weighted (equal-weighted) average monthly returns (in %) on portfolios. Excess return is the portfolio return in excess of the 1-month Treasury-bill rate. Characteristic-adjusted (Char-adj) returns are computed by adjusting returns using 125 (5 5 5) size/book-to-market/momentum benchmark portfolios (as in Daniel et al., 1997). The alphas (in %) are estimated from the time-series regressions of portfolio excess returns on various factor models including the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), the Ferson and Schadt (1996) conditional capital asset pricing (FS) model, the Fama and French (1993) three-factor (FF3) model, the Fama and French (1993) and Carhart (1997) four-factor (FFC) model, the Fama and French (2015) ve-factor (FF5) model, and the Hou, Xue, and Zhang (2015) q-factor (HXZ) model. H L is the high-minus-low portfolio. Numbers in parentheses are t-statistics adjusted following Newey and West (1987). See also the legend to Table 3. Low competition High competition LM LM LM H L LM LM LM H L L M H L M H A. Full sample Excess return 0.80 0.67 0.59 0.20 0.38 0.73 0.77 0.39 (3.77) (2.85) (2.72) ( 1.48) (1.33) (3.24) (3.10) (2.68) Char-adj return 0.28 0.45 0.42 0.14 0.63 0.25 0.19 0.44 ( 2.29) ( 5.94) ( 5.08) ( 1.05) ( 4.99) ( 2.78) ( 2.04) (2.82) CAPM 0.26 0.02 0.00 0.25 0.29 0.14 0.09 0.39 (2.23) (0.25) (0.02) ( 1.79) ( 1.70) (1.03) (0.72) (2.92) FS 0.22 0.01 0.05 0.27 0.37 0.15 0.10 0.47 (2.16) ( 0.06) ( 0.49) ( 1.68) ( 2.17) (1.27) (0.79) (2.30) FF3 0.14 0.00 0.01 0.15 0.34 0.35 0.21 0.55 (1.38) ( 0.03) ( 0.13) ( 1.07) ( 1.90) (3.15) (1.81) (2.70) FFC 0.22 0.06 0.04 0.18 0.16 0.50 0.23 0.39 (2.09) (0.60) (0.49) ( 1.22) ( 0.88) (3.63) (1.98) (2.01) FF5 0.08 0.12 0.18 0.26 0.30 0.50 0.25 0.56 (0.81) ( 1.23) ( 1.89) ( 1.59) ( 1.55) (3.31) (1.82) (2.25) HXZ 0.21 0.05 0.01 0.20 0.11 0.54 0.46 0.58 (1.88) ( 0.47) (0.07) ( 1.27) ( 0.50) (2.99) (2.66) (1.97) B. All-but-microcaps sample Excess return 0.77 0.84 0.77 0.00 0.58 0.85 1.09 0.50 (3.01) (3.27) (2.91) ( 0.02) (1.90) (2.84) (3.61) (2.27) Char-adj return 0.43 0.40 0.41 0.02 0.56 0.26 0.10 0.45 ( 5.47) ( 5.07) ( 5.57) (0.26) ( 5.31) ( 2.61) ( 0.88) (2.57) CAPM 0.07 0.13 0.04 0.03 0.21 0.06 0.27 0.48 (0.61) (0.96) (0.36) ( 0.35) ( 1.42) (0.38) (1.54) (2.20) FS 0.04 0.07 0.01 0.03 0.20 0.12 0.31 0.51 (0.36) (0.54) (0.08) ( 0.35) ( 1.35) (0.75) (1.63) (2.28) FF3 0.12 0.04 0.10 0.02 0.25 0.15 0.32 0.57 ( 1.30) ( 0.34) ( 1.09) (0.26) ( 1.68) (1.18) (2.48) (2.68) FFC 0.07 0.09 0.06 0.01 0.03 0.35 0.34 0.31 (0.67) (0.80) (0.73) ( 0.07) (0.17) (2.55) (2.79) (1.97) FF5 0.20 0.21 0.20 0.00 0.08 0.45 0.43 0.52 ( 1.74) ( 1.82) ( 1.95) ( 0.00) ( 0.42) (3.05) (3.35) (1.98) HXZ 0.01 0.04 0.05 0.04 0.15 0.58 0.78 0.63 (0.07) ( 0.26) (0.36) (0.26) (0.66) (3.31) (4.17) (2.05) 38 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Appendix A. A.1 Proofs Proof of Proposition 1. We omit time subscripts in this proof for conciseness. Following Donangelo (2014), occupations are labeled by the index j ¡ 0 in decreasing order of their associated ratio of industry-speci c to general labor skills, which is de ned as l : (A1) The supply of labor with speci c skills is given by » » j j L l d d : (A2) 0 0 As stated in Equation (8) of Donangelo (2014), the indierence condition for a worker in occu- pation j to decide whether stay or leave is W l W . Therefore, given Equations (A1), (A2), and (7), we can solve for the marginal occupation j from the following: c 1 p! 1q 1 2 1 ! j j p! q A pN q 2 1 ! p! q A pN q W æ j ; (A3) where c is de ned in the main body of the paper. Then, the equilibrium level of labor supply, L , is given by pc 1q 2 1 ! j p! q A pN q L : This completes the proof of Proposition 1. Proof of Proposition 2. The following lemma is helpful for streamlining the proof. Lemma A1. Given the same Wiener process Z , for any two positive constants and , and two Geometric Brownian Motions A and W whose dynamics are given by t t dA A dt A dZ ; (A4) t A t A t t dW W dt W dZ ; (A5) t W t W t t respectively, the following conditions are true: 1. if Q A , then dQ Q dt Q dZ , where p 1q and . t t Q t Q t t Q A Q A 2 A 2. if Q A {W , then dQ Q dt Q dZ , where p q t t t t Q t Q t t Q A W W A and . Q A W 39 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Proof. 1. By It^ o's lemma, we have 1 2 dQ A dA p 1qA pdA q t t t t t A p p 1q qdt A p qdZ : A A t t A t 2. A and W can be solved analytically with A and W as t t 0 0 A A exp t Z ; t 0 A A t W W exp t Z : t 0 W W t Therefore, 2 2 A W Q A {W A {W exp t p qZ t t t 0 0 A W A W t p q A W Q exp p q t p qZ : 0 A W W A A W t ! pc 1q c 2 ! p 1 ! qc Now, we rewrite as A {W , where p 1 ! q! ! N . By t t t t Lemma A1, we formally have 1 ! 1 2 2 pc 1qc ! ! 2! ; A W A W 2 c ! pc 1q c : A W This completes the proof of Proposition 2. Proof of Proposition 3. At the outset, it is helpful to have Bc{B cp1 cq{ and Bc{B! cp1 cq{!. 1. B{B B c{B p! { q cp1 cqp! { q{; W A W A W 2 2. B{B! p 1 cqc p 1 cq p 1 cqc{! p 1 cq p1 { q: Since 0 1, W A and 0 { 1, we have B{B! ¡ 0; and W A 3. B{B! ¡ 0 æ p! q ¡ p0q 0. This completes the proof of Proposition 3. Proof of Proposition 4. 1. De ne ~ . By Lemma A1, we have t t t d ~ dt dZ ; ~ ~ t 40 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 where r and . Therefore, ~ f ~ V E ~ ds t t s " * » » 8 8 2 E ~ ds E exp s exp p Z q ds t s t ~ ~ s 0 0 2 2 V V t t ~ ~ æ1 2 2 t t t t æV : ~ f An alternative proof can be found in the Internet Appendix of Donangelo (2014). 2. dV V dt V dZ , therefore, t t t t dV dt t t t r E r r r : t ~ f f f V dt V t 3. Directly from Part (2) above and Equation (16). This completes the proof of Proposition 4. A.2 Evidence on Exogeneity between Market Competition and Labor Mobility In this appendix, we show empirically that the correlation between product market com- petition and labor mobility, LM , is negligible. Following Peress (2010), we use the rm-level price-cost margin, PCM , to construct an empirical proxy of ! for individual intermediate goods. Speci cally, ! normCDF p PCM q where normCDF is the standard normal distri- bution CDF. This transformation ensures that the constructed ! is inversely related to PCM and is always within (0, 1). Similarly, we construct as normCDF pLM q, where the mea- sure of individual LM is based on Donangelo (2014), which captures the level of interindustry dispersion of workers across occupations. The unconditional correlation between ! and is only 1.5%. We also calculate the corre- lations conditional on year and cross-industry: in each year we calculate two correlations, one from individual ! and , the other from ! and cross-industry, where ! normCDF PCM and PCM is the average PCM within an industry, and normCDF LM and LM is the average LM within an industry. These correlations are presented in Figure A1. Over the years, these conditional correlations between ! and are symmetrically dispersed around zero with small absolute values. This evidence serves as an indication of no systematic relation between product market competition and labor mobility. 41 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 A.3 Extending the Model with Endogenous N The model we drive in the main body of the paper is conditional on an exogenous number of intermediate good producers, N . In this Appendix, we endogenize N by linking the expected optimal pro t of each intermediate good producer, , to their market entry decision. Speci cally, the intermediate goods market is characterized by the average elasticity of substitution !. There is a mass of M potential producers whose xed entry costs are uniformly distributed across r ; s. So, the density of potential producers is . All three variables are functions 0 1 1 0 of !. It is sensible to expect M to be larger and to be smaller, therefore, to be larger in a more competitive market. We assume BM p! q{B! ¡ 0 and B p! q{B! 0. A potential producer only enters the market if the expected pro t is higher than her xed cost. Therefore, the equilibrium N solves the following equation p!;N q M p! q p!; N q d M p! q N; (A6) p! q p! q 1 0 1 0 where p!; N q as a function of ! and N is given in Equation (14). N p! q as a function of ! can be solved numerically. We use the following settings to numerically show the endogenous relation between N and !: A 0:3, 0:5, 0:4, W 1, 0:03, M p! q 10 120!, and p! q 1:1 !, and ! goes from 0.3 to 0.99. The HHI is de ned as the sum of the squared market shares. In our model, each intermediate good producer has an equal market share, therefore, HHI in our model is simply . The numerical illustrations are presented in Figure A2. We can see that N (HHI) increases (decreases) with !, while price and pro t decrease with !. The intuition is straightforward: the reduction of xed cost overweights the reduction of pro t in a higher ! (more competitive) market, making it appealing for more potential producers to enter the market. This pattern matches remarkably with empirical observations presented in Figure A3, where we show that an empirical measure of ! (constructed as the standard normal distribution CDF of the negative average price-cost margin, Peress 2010) is clearly negatively correlated with and HHI (computed using market shares based on net sales). Appendix B. Supplementary Data Supplementary results related to this article can be found in the Internet Appendix. 42 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Appendix Table and Figures Table A1 Labor mobility and sensitivities of pro ts and returns to industry shocks in subsamples split by product market competition The table reports the cross-sectional average slopes of univariate time-series regressions of percentage changes in industry-level pro tability and (percent) industry-level returns on percentage changes in total factor productivity (TFP). Data are sourced from the Manufacturing and Nonmanufacturing KLEMS/BLS and from the OES/BLS data sets. A list of the broad industry groups used in the KLEMS/BLS data set is provided in the Internet Appendix Table IA.I of Donangelo (2014). In the rst row of each panel, we assign industries into Low competition and High competition groups based on their average cross-sectional ranked values of product market competition. In the second and third rows of each panel, Low competition and High competition industry groups are further assigned to labor mobility subsamples based on their average cross-sectional ranking. Product market competition for an industry is measured using net sales-based market shares of all rms in that industry. Pro ts is growth in the ratio of payments to capital over productive capital stock. KLEMS TFP is multifactor productivity growth. Adjusted TFP is the residual of time-series regressions of KLEMS TFP growth on lagged employment and productive capital growth. Numbers in parentheses are t-statistics based on Huber-White robust standard errors. The sample period is from January 1990 to December 2016. De- tails on the estimation of the time-series regressions can be found in section II.D and table IV of Donangelo (2014). Low competition (28 industries) High competition (28 industries) Industries Dependent variable: Pro ts Industries Dependent variable: Pro ts High Low t t A. Sensitivities to KLEMS TFPt 28 0.76 28 3.89 3.13 (1.11) (17.30) (4.86) Low mobility 14 0.84 13 3.40 (0.54) (8.75) High mobility 14 0.72 15 4.38 (1.12) (19.08) High Low 0.12 0.98 ( 0.08) (2.18) B. Sensitivities to Adjusted TFP 28 0.95 28 3.84 2.89 (1.38) (17.14) (4.46) Low mobility 14 1.33 13 3.37 (1.66) (8.67) High mobility 14 0.76 15 4.31 (1.22) (19.01) High Low 0.56 0.93 ( 0.38) (2.08) Dependent variable: Returns Dependent variable: Returns C. Sensitivities to KLEMS TFP 28 0.05 28 0.27 0.22 (3.21) (5.81) (5.02) Low mobility 14 0.02 13 0.20 (1.83) (3.63) High mobility 14 0.08 15 0.41 (2.72) (4.69) High Low 0.06 0.21 (1.66) (2.14) D. Sensitivities to Adjusted TFP 28 0.08 28 0.28 0.20 (2.34) (5.44) (4.45) Low mobility 14 0.02 13 0.19 (1.77) (3.09) High mobility 14 0.15 15 0.43 (2.12) (4.02) High Low 0.13 0.24 (1.64) (2.03) 43 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Table A2 Labor mobility and market factor loadings of double-sorted portfolios The table reports risk factor loadings from the time-series regressions of portfolio excess returns (in Table 3) on: (1) a constant and the (high minus low) labor mobility factor of Donangelo (2014), denoted by LM ; and H-L (2) a constant, LM , and the value-weighted market excess return (MKT) factor. Details on LM can be H-L H-L found in Donangelo (2014). The full-sample includes all NYSE-, AMEX-, and NASDAQ-listed non nancial and nonregulated ordinary common stocks for which both nonmissing product market competition and labor mobility estimates in a given year t are available. The all-but-microcaps sample excludes stocks with an end-of-June market value of equity below the 20th percentile of the NYSE market capitalization distribution and the remaining stocks are used to compute the breakpoints for product market competition and labor mobility separately. H L is the high-minus-low portfolio. Numbers in parentheses are t-statistics adjusted following Newey and West (1987). The sample period is from January 1990 to December 2016. See also the legends to Tables 1 and 3. Low competition High competition LM LM LM H L LM LM LM H L L M H L M H A. Full sample LM factor H-L LM 0.35 0.16 0.03 0.38 0.65 0.09 0.42 1.08 H-L ( 2.72) ( 1.40) (0.27) (6.17) ( 3.47) ( 0.61) (2.32) (12.84) MKT and LM factors H-L MKT 0.94 0.94 0.87 0.07 1.11 1.10 1.15 0.04 (17.24) (20.92) (23.40) ( 1.43) (15.45) (10.94) (22.87) (0.54) LM 0.30 0.11 0.07 0.37 0.60 0.04 0.48 1.08 H-L ( 4.39) ( 2.00) (1.08) (6.42) ( 6.55) ( 0.31) (7.45) (13.10) B. All-but-microcaps sample LM factor H-L LM 0.40 0.21 0.17 0.23 0.39 0.10 0.48 0.87 H-L ( 2.42) ( 1.43) ( 1.14) (4.68) ( 1.79) (0.42) (1.83) (6.73) MKT and LM factors H-L MKT 1.13 1.07 1.16 0.03 1.47 1.38 1.36 0.11 (19.18) (32.72) (24.03) (0.94) (19.99) (13.99) (24.64) ( 1.34) LM 0.34 0.16 0.11 0.23 0.32 0.17 0.55 0.87 H-L ( 3.92) ( 2.13) ( 1.57) (4.63) ( 3.05) (1.35) (4.15) (6.39) 44 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Figure A1 Correlation coecients between ! and over time 0.4 0.3 0.2 0.1 -0.1 -0.2 -0.3 -0.4 1995 2000 2005 2010 2015 The gure plots yearly cross-industry correlations between the empirical measures of ! and (solid line) and those between ! and in each industry (dashed line). The empirical measure of ! () for an industry is de ned as the standard normal distribution CDF of PCM (LM ), where PCM (LM ) is the average value of PCM s (LM s) of all rms within the industry. Industries are identi ed at the three-digit SIC level. The sample period is from 1992 to 2016. 45 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Figure A2 Endogenous N as a function of ! alongside other key variables 2 0.15 1.8 0.1 1.6 1.4 0.05 1.2 1 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.25 12 0.2 10 0.15 8 0.1 6 0.05 4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 The numerical settings for the plots in this gure are A 0:3, 0:5, 0:4, W 1, 0:03, M p! q 10 120!, and p! q 1:1 !. The top two panels plot P and against !, respectively, and the bottom two panels plot HHI and N against !, respectively. 46 Downloaded from https://academic.oup.com/raps/advance-article/doi/10.1093/rapstu/raad001/6978206 by DeepDyve user on 11 January 2023 Figure A3 Correlation coecients between ! and HHI and 1{N over time 0.1 0.05 -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 -0.4 1995 2000 2005 2010 2015 The gure plots yearly cross-industry correlations between an empirical measure of ! and HHI (solid line), and those between the empirical measure of ! and the number of rms in each industry 1{N (dashed line). The empirical measure of ! for an industry is de ned as the standard normal distribution CDF of PCM , where PCM is the average value of PCM s of all rms within the industry. Industries are identi ed at the three-digit SIC level. The sample period is from 1992 to 2016.
The Review of Asset Pricing Studies – Oxford University Press
Published: Jan 9, 2023
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