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Approaches to learn about employer learning

Approaches to learn about employer learning IntroductionWhat employers believe about the skills of workers is bound to determine their labour market outcomes. How schooling affects these beliefs is thus crucial for determining the returns to an additional year of schooling. Thus, schooling might act as a signal to the job market and this function might distort decisions to acquire schooling from the social optimum (Spence 1973).Job market signalling is difficult to test because it is about objects that are inherently hard to observe: the latent skills of workers and how costs of schooling vary with these skills. As such, it is difficult to measure how much job market signalling contributes to the private returns to education and how much the social and the private returns diverge from each other due to job market signalling.This viewpoint describes one approach to quantify how large this gap might be, an approach that builds on the specification proposed of the common employer learning model proposed by Farber and Gibbons (1996) and further developed by Altonji and Pierret (2001). Central to this approach are the assumptions that: (i) individual productivity has a persistent, time‐invariant component, (ii) individual compensation equals expected productivity and (iii) employers learn about this persistent component as workers spend time in the labour market. To empirically operationalize these assumptions, the literature on common (or public) employer learning that grew out of Farber and Gibbons (1996) and Altonji and Pierret (2001) explicitly formulates both how potential employers learn about unobserved skills of workers and what information about underlying skills researchers have access to. These assumptions are leveraged to derive testable predictions of the employer learning model for how earnings vary with schooling and proxies of productivity across the life cycle.In this paper, we use a simplified version of the employer learning model to illustrate this approach to quantify how important job market signalling is. Two papers form the basis of this discussion. Lange (2007) follows Altonji and Pierret (2001) and assumes that the researcher has access to a correlate of productivity that employers do not use in wage setting.1The literature has used primarily cognitive test scores from surveys as such correlates. In particular, the main papers in this literature discussed below rely on the Armed Forces Qualification Test score collected as part of the National Longitudinal Survey of Youth. Other examples of productivity correlates that employers might not use are skill measures collected from siblings or other family members, assuming that skills are correlated within the family.That paper: (i) shows how functional form assumptions can be used to summarize the process of employer learning in a single parameter, the “speed of employer learning,” (ii) derives conditions under which we can identify this parameter and (iii) proceeds to estimate it. Lange (2007) goes on to impose additional structure on the schooling decision to bound the contribution of signalling to the economic returns from years of schooling.The second paper, Aryal et al. (2022), takes a different but related approach. Again, the analysis starts with the specification proposed by Farber and Gibbons (1996) and shows under what circumstances one can interpret instrumental variable estimates of the causal effect of schooling on earnings as representing either private or social returns to education.2A natural interpretation of the gap between social and private returns is the returns to job market signalling.The main insight is that how one interprets the IV estimates depends on whether or not potential employers know that the instrument induces the variation in schooling in the population. To the extend that employers do know about this variation, instrumental variable estimates of the returns to education represent social returns to education. To the extend that they do not, they represent private returns.As we discuss these approaches to bound or estimate the returns to signalling, we also reference empirical work that implements these approaches. In two online appendices, we provide additional evidence (appendix A) and review the existing empirical literature (appendix B). Our view is that the evidence in this field suggests that the returns to signalling make up at most 25% of the returns to education. However, we also find that the empirical basis for this conclusion is narrow and more work, using either of the approaches highlighted above, is necessary to firm up our confidence in this assessment. Ideally, new work will use the basic model following Lange (2007) to provide estimates of the learning process and the returns to signalling that can be compared with the existing estimates.We begin by first introducing in section 2 the basic model of wage setting and learning that we will rely on throughout the remainder of the article. It is based on but less general than the model analyzed by Farber and Gibbons (1996), Altonji and Pierret (2001) and Lange (2007). We then show in section 3 how access to a hidden correlate, that is a correlate of productivity not observed by employers, enables the researcher to test this model and estimate its parameters using the partial correlation of earnings with schooling and the hidden correlate across the life cycle. The section also briefly reviews the empirical work based on a hidden correlate and discusses how Lange (2007) proposes to bound the returns to signalling. The following section, section 4, explores how to interpret instrumental variable regressions in a model of employer learning. Again, we need to make assumptions on what employers observe, notably how much they know about the variation in schooling induced by the instrument. Instrumental variables have the advantage that rather than bound the returns to schooling, they allow, under suitable assumptions, to point‐identify the private and/or the social returns to schooling. Section 5concludes.A model of productivity, wages and informationAssume that log productivity yit$$ {y}_{it} $$ is additively separable into an individual heterogeneity Ai$$ {A}_i $$, an experience component H(t)$$ H(t) $$ common to all and an iid shock εit$$ {\varepsilon}_{it} $$,1yit=Ai+H(t)+εit.$$ {y}_{it}={A}_i+H(t)+{\varepsilon}_{it}.\kern0.5em $$Next, use δA|S$$ {\delta}^{A\mid S} $$ to define the causal effect of schooling on productivity and write2Ai=δA|SSi+Ai˜.$$ {A}_i={\delta}^{A\mid S}{S}_i+\tilde{A_i}.\kern0.5em $$Ai˜$$ \tilde{A_i} $$ then stands for unobserved components of ability that are not caused by schooling. Crucially, we do not restrict cov(Ai˜,Si)=0$$ \mathit{\operatorname{cov}}\left(\tilde{A_i},{S}_i\right)=0 $$ so that schooling can be correlated with productivity not caused by schooling. The coefficient δA|S$$ {\delta}^{A\mid S} $$ represents the social return to education because it captures the increase in productivity independent of whether it accrues to the worker.Combining, we obtain that log output yit$$ {y}_{it} $$ depends on (Si,Ai˜,t)$$ \left({S}_i,\tilde{A_i},t\right) $$ as follows:3yit=δA|SSi+Ai˜+H(t)+εit.$$ {y}_{it}={\delta}^{A\mid S}{S}_i+\tilde{A_i}+H(t)+{\varepsilon}_{it}.\kern0.5em $$Further, assume that (Ai˜,Si,εit)$$ \left(\tilde{A_i},{S}_i,{\varepsilon}_{it}\right) $$ are jointly normally distributed and {εit}$$ \left\{{\varepsilon}_{it}\right\} $$ is iid.Throughout, we maintain that compensation Wit$$ {W}_{it} $$ of individual i$$ i $$ with experience t$$ t $$ equals expected productivity conditional on the information employers at time t have access to. This information at experience level t is ℰit={Si,{yi,τ}τ<t,t}.$$ {\mathcal{E}}_{it}=\left\{{S}_i,{\left\{{y}_{i,\tau}\right\}}_{\tau <t},t\right\}. $$ This information set grows with experience t, which implies that employers learn about unobserved productivity Ai˜$$ \tilde{A_i} $$. The literature on employer learning hypothesizes that with time in the labour market more information is revealed and limt→∞Wit−E[exp(yit)|ℰit]=0.$$ {\lim}_{t\to \infty}\left({W}_{it}-E\Big[\mathit{\exp}\left({y}_{it}\right)|{\mathcal{E}}_{it}\Big]\right)=0. $$ This becomes useful for differentiating between human capital and signalling as we make additional functional form and substantive assumptions.Two brief remarks are in order. First, this is a model of common employer learning in the sense that any information is shared among a sufficient number of competing employers to ensure that compensation equals expected productivity. We also rule out long‐term contracts linking compensation to expected productivity over longer time periods. Common employer learning is a strong assumption, but models of private or asymmetric employer learning entail complex strategic interactions on the part of firms and workers that make them hard to use to model the life cycle of earnings.3Those interested in empirical models of asymmetric employer learning might want to consult, among others, Waldman (1984), Schönberg (2007) and Kahn (2013).Second, it is straightforward to incorporate additional observable controls in the analysis. Importantly, Farber and Gibbons (1996) and all authors following in their footsteps also allow for employers to observe productivity correlates Qi$$ {Q}_i $$ that researchers do not have access to. This implies that standard Mincer earnings equations will not identify the parameters of the learning model nor the private or the social returns to education because estimated returns to education will always be biased by the correlation between Qi$$ {Q}_i $$ and Si.$$ {S}_i. $$ This paper abstracts from both Qi$$ {Q}_i $$ and observable controls because this simplifies the expressions and because we believe we can still communicate the basic arguments without these.Yi,t$$ {Y}_{i,t} $$ is log normally distributed, and we can write4log(Wit)=log(𝔼[Yi,t|ℰit])=δA|SSi+H(t)+var(Ai˜+εi,t|ℰit)2+𝔼[Ai˜|ℰit].One of the features of updating expectations about normal variables using normal signals is that the posterior variance does not depend on the realization of the signal itself. This property of normal–normal learning applies here and we therefore have that var(Ai˜+εi,t|ℰit)=var(Ai˜+εi,t|t).$$ \mathit{\operatorname{var}}\left(\tilde{A_i}+{\varepsilon}_{i,t}|{\mathcal{E}}_{it}\right)=\mathit{\operatorname{var}}\left(\tilde{A_i}+{\varepsilon}_{i,t}|t\right). $$ Thus, we can control for H˜(t)=H(t)+var(Ai˜+εi,t|t)2$$ \tilde{H}(t)=H(t)+\frac{\mathit{\operatorname{var}}\left(\tilde{A_i}+{\varepsilon}_{i,t}|t\right)}{2} $$ in equation (4) with a set of experience controls. The interesting object is 𝔼[Ai˜|ℰit], and we can again draw on the properties of normal random variables to characterize this:5𝔼Ai˜|ℰit=θ(t,κ)ϕA|SSi⏟𝔼Ai˜|S+1−θ(t,κ)ξit‾,where ξ‾it=1t∑τ≤t{yiτ−δA|SSi−H(τ)}$$ {\overline{\xi}}_i^t=\frac{1}{t}{\Sigma}_{\tau \le t}\left\{{y}_{i\tau}-{\delta}^{A\mid S}{S}_i-H\left(\tau \right)\right\} $$. That is, at t$$ t $$, the observed output yit$$ {y}_{it} $$ net of the predictable component δW|SSi+H(t)$$ {\delta}^{W\mid S}{S}_i+H(t) $$ serves as a signal ξit$$ {\xi}_{it} $$ on unobserved ability Ai˜$$ \tilde{A_i} $$ with noise εit.$$ {\varepsilon}_{it}. $$ The average of these signals received up to period t is ξ‾it.$$ {\overline{\xi}}_i^t. $$ We discuss θ(t,κ)$$ \theta \left(t,\kappa \right) $$, the weight on the initial signal Si$$ {S}_i $$ in more detail below.Equations (4) and (5) together produce the experience t private return to an additional year of education. At t=0$$ t=0 $$, an additional year of education raises expected earnings because of the direct productivity effect δA|S$$ {\delta}^{A\mid S} $$ and because it raises the inferred Ãi$$ {\overset{\widetilde }{A}}_i $$ by ϕA|S.$$ {\phi}_{A\mid S}. $$ At experience t, the private return δtW|S$$ {\delta}_t^{W\mid S} $$ an individual can expect from an additional year of schooling is thus6δtW|S=δA|S+θ(t,κ)ϕA|S.$$ {\delta}_t^{W\mid S}={\delta}^{A\mid S}+\theta \left(t,\kappa \right){\phi}_{A\mid S}.\kern0.5em $$Equation (5) shows that the conditional expectation of ability Ai˜$$ \tilde{A_i} $$ at experience t is a weighted average of the conditional expectation of ability prior to entry to the labour market (at t=0$$ t=0 $$) and the average signal received up to t. The relative weights θ(t,κ)$$ \theta \left(t,\kappa \right) $$ depend only on the number of signals t received and one single parameter, κ$$ \kappa $$:7θ(t,κ)=1−κ1+t−1κwithκ=σ02σ02+σ2.ε$$ \theta \left(t,\kappa \right)=\frac{1-\kappa }{1+\left(t-1\right)\kappa}\kern.5em \mathrm{with}\kern.5em \kappa =\frac{\sigma_0^2}{\sigma_0^2+{\sigma}^2{.}_{\varepsilon }}\kern0.5em $$Here var(Ai˜)=σ02$$ \mathit{\operatorname{var}}\left(\tilde{A_i}\right)={\sigma}_0^2 $$ and var(εit)=σε2$$ \mathit{\operatorname{var}}\left({\varepsilon}_{it}\right)={\sigma}_{\varepsilon}^2 $$ and the parameter κ$$ \kappa $$ is the signal‐to‐noise ratio in the learning process, ie the ratio of the variance of the object to learn about (ie Ai˜$$ \tilde{A_i} $$) and the variance of the signal ξit=Ai˜+εit$$ {\xi}_{it}=\tilde{A_i}+{\varepsilon}_{it} $$.This model of wages developed so far forms the basis of the discussion that follows. We invoke stronger assumptions than strictly required, sometimes significantly so, but they allow uncovering in a fairly transparent way the reasoning behind the empirical employer learning literature.The hidden correlate approachPredictionsThe two foundational papers in this literature, Farber and Gibbons (1996) and Altonji and Pierret (2001), combine a wage‐setting model similar to the one developed in section 2 with the assumption that the researcher has access to a variable Z$$ Z $$ that employers do not have direct access to. We will refer to this variable as a hidden correlate. Farber and Gibbons (1996), Altonji and Pierret (2001) and Lange (2007) assume access to such a hidden correlate and derive predictions for the partial regression coefficients on S$$ S $$ and Z$$ Z $$ in log earnings regressions and how these evolve with experience.4Farber and Gibbons (1996) actually consider regressions in levels.A main reason for the popularity of this literature is that these predictions conform to simple intuitions about learning models.So, what do we predict for a regression of log wages on a hidden correlate Z$$ Z $$ as well as schooling S$$ S $$ at experience t? Substituting equation (5) into equation (4), we obtain the linear projection (denoted by 𝔼∗) of log wages at experience t on (Si,Zi)$$ \left({S}_i,{Z}_i\right) $$:8𝔼∗[log(Wit)|S,Z,t]=αt+δA|SSi+𝔼∗[𝔼[Ai˜|ℰit]]=αt+(δA|S+θ(t,κ)ϕA|S)Si+(1−θ(t,κ))𝔼∗[ξit‾|S,Z].We note that 𝔼∗[ξit‾|S,Z]=𝔼∗[Ai˜|Si,Zi] and use (β^AS,β^AZ)$$ \left({\hat{\beta}}_{AS},{\hat{\beta}}_{AZ}\right) $$ for the coefficients that project Ai$$ {A}_i $$ on (Si,Zi).$$ \left({S}_i,{Z}_i\right). $$ From this follow the coefficients projecting wages on (Si,Zi)$$ {S}_i,{Z}_i\Big) $$:9β^wS,t=δA|S+θ(t,κ)ϕA|S+(1−θ(t,κ))β^AS,$$ {\hat{\beta}}_{wS,t}\kern0.5em ={\delta}^{A\mid S}+\theta \left(t,\kappa \right){\phi}_{A\mid S}+\left(1-\theta \left(t,\kappa \right)\right){\hat{\beta}}_{AS}, $$10β^wZ,t=(1−θ(t,κ))β^AZ.$$ {\hat{\beta}}_{wZ,t}\kern0.5em =\left(1-\theta \left(t,\kappa \right)\right){\hat{\beta}}_{AZ}. $$These coefficients and their evolution over the life cycle are the primary empirical objects of interest in the literature following Farber and Gibbons (1996), especially in Altonji and Pierret (1997), Altonji and Pierret (2001) and Lange (2007). Each of these papers can be associated with a different set of predictions on these coefficients.First, Farber and Gibbons (1996) (in a level specification analogous to this log specification) show that {β^wZ,t}$$ \left\{{\hat{\beta}}_{wZ,t}\right\} $$ (equation (10)) increase in experience if Zi$$ {Z}_i $$ correlates positively with unobserved ability Ai˜.$$ \tilde{A_i}. $$ Second, Altonji and Pierret (2001) observe that when projecting log wages on Si$$ {S}_i $$ but not Zi$$ {Z}_i $$ the projection coefficient on Si$$ {S}_i $$ exceeds β^wS,t$$ {\hat{\beta}}_{wS,t} $$ by (1−θ(t,κ))β^AZcov(Z,S)/var(S).$$ \left(1-\theta \left(t,\kappa \right)\right){\hat{\beta}}_{AZ}\mathit{\operatorname{cov}}\left(Z,S\right)/\mathit{\operatorname{var}}(S). $$5To derive the latter, use the omitted variable formula.Thus, across experience, one can use the emerging differences between the projection coefficients on schooling in a projection of log wages on schooling alone and on schooling and Z$$ Z $$ jointly to test whether employers screen for unobserved ability using schooling. Third, Lange (2007) exploits the functional form restrictions implied by normal–normal learning on θ(t,κ)$$ \theta \left(t,\kappa \right) $$ (see equation (7)) to summarize the learning process with the single parameter κ$$ \kappa $$. This parameter can be estimated using the partial regression coefficients {β^wS,t,β^wZ,t}$$ \left\{{\hat{\beta}}_{wS,t},{\hat{\beta}}_{wZ,t}\right\} $$.The contrast between equation (9) and the private return to education defined in equation (6) also shows that the projection of log earnings on education will not directly deliver an estimate of the social returns to education even when controlling for the hidden correlate Zi$$ {Z}_i $$ as long as schooling correlates with the component of ability not caused by education.EvidenceEmpirically, the literature on employer learning has relied heavily on the NLSY 1979, the data used by Farber and Gibbons (1996), Altonji and Pierret (2001) and Lange (2007). The NLSY 1979 is a long panel of individuals during the early part of their careers with good earnings data as well as a cognitive skill measure that can serve as a hidden correlate.6Of course, the fact that the NLSY 1979 is US data is another major advantage in securing a prominent place for this data set in the literature.This measure, the Armed Forces Qualification Test (AFQT) score is based on a battery of tests administered to respondents to the NLSY 1979.In 1979, the NLSY 1979 started collecting data on a panel of US residents born between 1957 and 1964. From 1997 on, collection of data on a new cohort born between 1980 and 1984 commenced. This panel is known as the NLSY 1997. Figure 1 shows the partial regression coefficients on schooling and the AFQT in regressions by year of experience in both data. Each scatter point represents the coefficient estimate on either schooling or the AFQT (measured in standard deviations) up to experience 17.7Online appendix A contains information on the precise specification and data selection criteria.1FIGUREReturns to schooling and AFQT over the life cycle NOTES: The scatters display the estimated coefficients on schooling and the standardized Armed Forces Qualification Test (AFQT) score for each experience level. The line shows the predicted returns to schooling and AFQT score over the life cycle implied by the estimates in table 1. The estimation of these parameters is described in online appendix section A2.For both data sets, we obtain that the regression coefficients on Z$$ Z $$ increase and those on S$$ S $$ decrease with experience, as we expect in a learning model. Visual inspection suggests that the functional form implied by the normal–normal learning model developed above fits the data quite well. The line fitted to the experience profiles is obtained by estimating the parameter κ$$ \kappa $$ using the regression coefficients on S$$ S $$ or Z$$ Z $$ and the restrictions of the normal learning model. As described by Lange (2007), these regression coefficients at experience t are weighted averages of the regression coefficients at experience t=0$$ t=0 $$ and a limit value to which the coefficient converges as t→∞.$$ t\to \infty . $$ Thus, the projection coefficients at any experience level are a function of three parameters only (the initial and limit values of the projection coefficients and the parameter κ$$ \kappa $$), and we can estimate these by fitting the estimated coefficients using non‐linear least squares.8Our results differ from Castex and Kogan Dechter (2014) in that we find increasing returns to the AFQT and decreasing returns with experience for both males and females. The differences in the findings can be largely accounted for by the fact that we have access to a longer panel and estimate a non‐linear specification. Additional details are presented in online appendix C.1TABLESpeed of employer learning(1)(2)(3)(4)(5)(6)(7)NLSY 1979NLSY 1997Aryal et al. (2022)Years ofAFQTYears ofAFQTYears ofIQ testYears ofschoolingscoreschoolingscoreschoolingscoreschooling (IV)Speed of learning κ$$ \kappa $$0.2360.2530.0610.1140.4760.1260.550(0.002)(0.001)(0.001)(0.002)(0.069)(0.034)(0.126)Initial errors decline by 50% (years)3.2382.95315.4557.8081.1016.9360.818Initial value b0$$ {b}_0 $$0.109−$$ - $$0.0170.100−$$ - $$0.0040.1000.0110.195(0.007)(0.001)(0.000)(0.012)(0.007)(0.005)(0.012)Limit value b∞$$ {b}_{\infty } $$0.0550.1590.0340.1020.0230.0930.055(0.001)(0.000)(0.027)(0.042)(0.002)(0.006)(0.008)NOTES: The reported parameters are estimated by nonlinear least squares using the coefficient estimates on schooling and Armed Forces Qualification Test (AFQT) score at different experience levels. The reported initial errors decline is obtained using equation (7). The standard errors in columns (1) to (4) are obtained by bootstrapping with 5,000 repetitions. Columns (5) to (7) are from Aryal et al. (2022).Data generated by other learning processes would generate the basic features shown in figure 1 as well. The usefulness of the normal learning model is not in that it delivers a particularly good fit (even though it does), but that it allows summarizing the learning process in a simple manner whose main features can be summarized in a single parameter κ$$ \kappa $$.Table 1 shows the estimated speed of learning parameter κ$$ \kappa $$ for both data sets and both variables (Si,Zi).$$ {S}_i,{Z}_i\Big). $$ Columns (1) and (2) reproduce the main empirical results from Lange (2007) using data stemming from a longer time period and document identical findings as in Lange (2007). The estimated coefficient on κ$$ \kappa $$ for AFQT score (column (2)) implies that initial expectation errors by employers on average decline by 25% after workers spend around one year in the labour market. After three years, the initial error will have declined by around 50%. After workers spend around nine years in the labour market, initial expectation errors will on average have fallen by 75%, and after around 27 years, they will have declined by 90%. The point estimate of κ$$ \kappa $$, therefore, suggests that a worker's productivity is revealed to the employer mostly within the first few years of her labour market career.The point estimates in columns (3) and (4) on the other hand suggest that employer learning is relatively slow for the cohort entering the labour market in the early 2000s. Specifically, the estimate of κ$$ \kappa $$ from column (4) implies that initial expectation errors by employers on average decrease by around 11% during the first year a worker spends in the labour market. It takes about eight years for initial expectation errors to on average decline by 50%, 23 years to decline by 75% and a full 70 years to decline by 90%. This finding suggests that the speed of employer learning has slowed down between the 1980s and 2000s.Columns (5) and (6) report analogous estimates based on a sample of Norwegian males and their IQ test scores collected as part of military conscription procedures.9The same data is discussed in section 4. The data consists of administrative data on the population of Norwegian males born between 1950 and 1980 with earnings data between 1967 and 2014.The estimates from the Norwegian data bracket the estimates from the two NLSY cohorts. Those using schooling coefficients imply very rapid learning, while those using the IQ score imply learning similar to those from the NLSY 1979. Nevertheless, even the lower point estimate indicate that substantial learning about individual skills does take place in the first 10 years of an individual's career.10The NLSY cohorts have also been a rich source of data to explore heterogeneity and channels of learning. Arcidiacono et al. (2010), Mansour (2012) and Light and McGee (2015) explore the role of education, occupations and skill types in the employer learning framework. We review this literature in online appendix B.Unfortunately, the evidence from other countries and settings is not as abundant as desirable. And, unfortunately, few of these papers explicitly use the learning structure proposed by Lange (2007) to provide parameter estimates of the speed of learning that would allow comparing and synthesizing across sometimes quite different economic environments. We review this literature in online appendix B.Bounds on the returns to signallingLange (2007) takes the analysis one step further and uses the estimates of the speed of learning to quantify the contribution of the private returns to signalling in the total gains from schooling.11See Altonji and Pierret (1997) for a similar attempt to use estimates of how rapidly information is revealed to inform the question of how large signalling returns are.Two aspects of this approach bear particular mentioning. First, because the information available to employers Qi$$ {Q}_i $$ (which we abstracted from above) is not available to researchers, the estimate Lange (2007) arrives at is an upper bound for the contribution of signalling to the total return to education.Second, he relies on additional information in the form of an estimate of the cost of schooling. Lange (2007) here follows the tradition in the literature that views schooling primarily as an investment and assumes that the cost of schooling is determined largely by the opportunity costs and thus the discount rate on future earnings. His estimate of the bound on the returns to signalling thus depends on the assumption that schooling costs are due largely to discounting as well as the particular rate of discounting used. Both are strong assumptions are central to the bound he provides. For discount rates between 3% and 7% and using his preferred estimate of the speed of learning parameter of κ=0.26$$ \kappa =0.26 $$, he finds that the upper bound on the contribution of signalling to the overall private returns to schooling varies between 3% and 26%. The lower bound of the 95% confidence interval on the speed of learning parameter is κ=0.14.$$ \kappa =0.14. $$ If learning is this slow, then the upper bound varies between 6% and 47%.Instrumental variables and employer learningThe hidden correlate approach discussed above delivers testable predictions for employer learning and allows summarizing in a single, estimable parameter how rapidly firms learn about unobserved ability. And, with suitable assumptions, we can bound the contribution of signalling to the private returns to education. However, this approach does not produce a point estimate of the private or the social returns to education. And, the additional assumptions required to arrive at the bound on the signalling returns are strong.Aryal et al. (2022) show that instrumental variable estimates can provide useful information on the social and the private returns to education without having to invoke strong assumptions on the costs of schooling as required by Lange (2007). Rather, if the researcher is willing to take a stand on whether or not an instrument can be observed by employers, then the instrumental variable estimates can inform discussions about the productivity and signalling returns to education.We follow Aryal et al. (2022) and discuss a binary instrument for schooling.12Importantly, their argument extends beyond instrumental variables (binary or not) to all quasi‐experimental approaches.How to interpret the IV estimates depends on whether or not employers understand and price the variation induced by the instrument correctly. The usual reason offered to justify instrumenting is ability bias. Using our formulation in equation (2) the concern is that Ãi$$ {\overset{\widetilde }{A}}_i $$ correlates with schooling Si.$$ {S}_i. $$ Various instruments have been proposed claiming to increase schooling but to also be orthogonal to Ãi.$$ {\overset{\widetilde }{A}}_i. $$ We are not interested in re‐opening debates about these claims but posit that there indeed is an instrument Li∈{0,1}$$ {L}_i\in \left\{0,1\right\} $$ that satisfies both the rank and orthogonality condition. That is, we assume that11𝔼[Si|Li=1]≠𝔼[Si|Li=0],12𝔼[Ãi|Li]≡0.The IV coefficient for our binary instrument is (Wald 1940): bIV,t=𝔼[log(Wit)|Li=1]−𝔼[log(Wit)|Li=0]𝔼[Si|Li=1]−𝔼[Si|Li=0].And, using equation (4), we have that 𝔼[log(Wit)|Li=1]−𝔼[log(Wit)|Li=0]=δA|S∗(𝔼[Si|Li=1]−𝔼[Si|Li=0])+𝔼[𝔼[Ãi|ℰit]|Li=1]−𝔼[𝔼[Ãi|ℰit]|Li=0]. Thus, we have13bIV,t=δA|S+𝔼[𝔼[Ãi|ℰit]|Li=1]−𝔼[𝔼[Ãi|ℰit]|Li=0]𝔼[Si|Li=1]−𝔼[Si|Li=0].Equation (13) shows that interpreting bIV,t$$ {b}_{IV,t} $$ comes down to making assumptions about how the instrument Li$$ {L}_i $$ enters into the information ℰit$$ {\mathcal{E}}_{it} $$ held by employers. Aryal et al. (2022) focus on two polar cases. First, they consider “transparent instruments” that form part of the information held by firms so that ℰit={Si,ξit,Li}$$ {\mathcal{E}}_{it}=\left\{{S}_i,{\xi}_i^t,{L}_i\right\} $$. And, they contrast this with “hidden instruments” that are not observed by employers and thus do not form part of the firms information set. For these, Li∉ℰit.$$ {L}_i\notin {\mathcal{E}}_{it}. $$For transparent instruments, applying the LIE to equation (13) and using equation (12) implies that bIV,t=δA|S.$$ {b}_{IV,t}={\delta}^{A\mid S}. $$ Intuitively, when potential employers are aware of the instrument, they will not use the induced variation in schooling to infer Ãi.$$ {\overset{\widetilde }{A}}_i. $$ By assumption, we imposed that the instrument is orthogonal to the endogenous unobserved ability Ãi.$$ {\overset{\widetilde }{A}}_i. $$ Thus, transparent IVs identify the effect of schooling on productivity itself: δA|S.$$ {\delta}^{A\mid S}. $$For hidden instruments, we have from equation (5) that 𝔼[Ãi|ℰit]=θ(t,κ)ϕA|SSi⏟𝔼Ai˜|S+1−θ(t,κ)ξit‾ and thus 𝔼[𝔼[Ãi|ℰit]|Li]=θ(t,κ)ϕA|S𝔼[Si|Li] because 𝔼[ξit‾|Li]=0. Substituting in equation (13), we find that for a hidden instrument, the instrumental coefficient is bIV,t=δA|S+ϕA|Sθ(t,κ).$$ {b}_{IV,t}={\delta}^{A\mid S}+{\phi}_{A\mid S}\theta \left(t,\kappa \right). $$ Hidden instruments thus identify the private returns to additional schooling that consist of both the productivity return and the signalling return. Employers are unaware of the instrument and thus variation in schooling induced by the instrument induces them to update their conjectures of Ãi.$$ {\overset{\widetilde }{A}}_i. $$ Thus, hidden instruments identify the private returns to schooling.Causal estimation using instruments already requires a priori assumptions on the validity of the instrument that cannot be tested. As such, when researchers employ instruments they need to carefully argue based on contextual evidence that an instrument will in fact satisfy the exclusion restrictions. In such cases, researchers might also be able to determine whether or not an instrument is in fact plausibly hidden or transparent. As Aryal et al. (2022) show, being willing to make such a determination reaps rewards in being able to identify deep policy‐relevant parameters when the analysis is embedded in the employer learning framework.For instance, as argued above, with a transparent instrument one can recover immediately the policy‐relevant parameters δA|S$$ {\delta}^{A\mid S} $$ that describe the productivity effect of schooling. A hidden instrument delivers the private returns bIV,t=δA|S+ϕA|Sθ(t,κ).$$ {b}_{IV,t}={\delta}^{A\mid S}+{\phi}_{A\mid S}\theta \left(t,\kappa \right). $$ But, using data from repeated cross‐sections allows recovering δA|S$$ {\delta}^{A\mid S} $$ as the limit to which bIV,t$$ {b}_{IV,t} $$ converges as t→∞.$$ t\to \infty . $$ And, it also allows estimating κ$$ \kappa $$ using an approach analogous to that using a hidden correlate.Of course, all this does not come for free. The assumptions on whether employers are aware of the instrument will be debatable. And, the strong identification results described above derive partially from the functional form assumptions, in particular the assumption that δA|S$$ {\delta}^{A\mid S} $$ does not vary with experience. Aryal et al. (2022) and their companion working paper Aryal et al. (2019) however do show ways to relax some of these assumptions, especially if access to multiple instruments with different information assumptions is available.Aryal et al. (2022) illustrate how to use this approach using a compulsory schooling law lengthening the mandatory school length. The data draws on administrative records for Norwegian males that also includes IQ scores collected as part of the military draft.13Columns (5) and (6) in table 1 report estimates of the speed of learning measure based on these IQ scores and schooling measures using the hidden correlate approach discussed in section 3.The effect of the law was to extend minimum required schooling from seven to nine years across Norway, but the law was locally implemented at different times during the 1960–1975 period. The effect was to induce variation in the law across different jurisdictions that were often geographically very close. Frequently, small communities with a few thousand inhabitants would extend the compulsory schooling period at earlier or later dates than much larger jurisdictions within the same broad labour market. Empirically, this provides variation across locations and time that can be used to identify the causal impact of the law on wages. More important in the present context is that it allows dividing the sample in distinct populations that are separated by how plausible it is that the instrument is either hidden or transparent. As such, this setting provides an opportunity to illustrate and apply the ideas on transparent and hidden instruments.In particular, Aryal et al. (2022) argue that for the central communities in commuting zones in which the majority of the population of a given labour market lives, the variation induced by the instrument is plausibly understood by market participants. They interpret the estimates obtained from this sample as generated by a transparent instrument, and thus they identify the social (or productivity) returns to additional schooling. By contrast, employers are much less likely to be informed of variation in the time when the law was implemented across small localities forming part of a large labour market. The instrument can thus plausibly be argued to be hidden for the sample of individuals growing up in smaller communities surrounding the larger central community forming the core of a labour market. Thus, Aryal et al. (2022) construct two samples, one for which the instrument is plausibly hidden and one for which it is observed.The coefficients on years of schooling over the life cycle estimated using this instrument are shown in figure 2.2FIGUREReturns to Schooling estimated using a Hidden and a Transparent Instrument NOTES: This figure reproduces figure 3 in Aryal et al. (2022). It shows the returns to education estimated using the compulsory schooling reform discussed in the main text. The right panel shows the estimates on the sample that permits interpreting the instrument as transparent. The left panel shows the estimates on the sample for which the instrument is hidden.The right panel shows the estimates using the transparent instruments. These estimates do not display the typical decline in the returns to education associated with learning model, suggesting that the assumption that this instrument is transparent is indeed valid. We see that the returns to education are high and roughly stable across experience levels. By contrast, the estimates from the hidden sample (left panel) display the typical shape expected from a learning model when the instrument is not observed. The rapid decline in the estimated returns to education during the first few years in the labour market gives rise to the high estimated value for κ$$ \kappa $$ reported in column (7) of table 1.What does all this imply for the productivity and signalling returns to education? Aryal et al. (2022) report a total return to education of 7.9% per year of schooling. 70% of is accounted for by a causal effect of schooling on productivity with the remainder due to signalling effects. These estimates are local average treatment effects applying to an extension of required minimum schooling 50 years in the past and might therefore be of limited utility for current use. We hope that more current estimates will emerge from other settings that explicitly try to implement this approach to inform on the social and private returns to education.Aryal et al. (2022) are able to distinguish signalling and productivity effects of schooling because they are willing to take a stand on whether or not employers price the instrument correctly. This idea is related to a literature examining variation in education credentials induced by variation in test scores across a cut‐off required for graduation (see the review of the related literature in online appendix B).14An early related literature pointed to higher than usual returns to years of schooling required to complete a degree as evidence of information rents (Hungerford and Solon (1987),Layard and Psacharopoulos (1974)). However, those not completing degree years are likely to be negatively selected, casting doubts on these conclusions (Lange and Topel 2006). Hungerford and Solon (1987) themselves note that diploma effects cannot be understood without relying on screening.Clark and Martorell (2014) employ this approach to estimate the causal effect of a diploma by comparing individuals who just passed or failed high school exit exams. This approach is clearly related to the instrumental variable approach as discussed by Aryal et al. (2022) in that employers do not observe the variation in test scores around the discontinuity. Thus, this regression discontinuity approach sets up a contrast between the treated group (those with scores just above the discontinuity) and the control group (just below) that is analogous to the hidden instrument case. Graetz (2021) provides a useful discussion of how RD estimates of returns to degrees or diplomas should be interpreted in light of the employer learning model.ConclusionThis paper discussed how one approach to quantify the relative contributions of signalling versus human capital to the private return to education based on the assumption that firms learn over time about unobserved productive skills of individuals. In the process, we showed how to estimate the speed of employer learning. Our view of the literature is that the evidence on balance suggests that learning is rapid but not instantaneous. There is evidence from a variety of countries that supports the basic linear tests of employer learning following Altonji and Pierret (2001), but few papers estimate the speed of learning parameter (Lange 2007) or use this parameter to bound the returns to signalling. Those that do tend to find that signalling accounts at most for one quarter of the returns to education, but we argue that the empirical basis for these conclusions is narrow.The model of job market signalling emphasizes that incomplete information distorts the returns to invest into observable signals of productivity, such as schooling. Incomplete information however also lowers the returns to other investments into one's productivity as long as these investments are not directly observable. How large these distortions are will generally depend on the speed of employer learning. Kahn and Lange (2014) for instance show evidence of employer learning throughout individuals' careers. This evidence suggests a wedge between the social and private returns to on‐the‐job investments. Graetz (2022) explores how gradual employer learning affects the returns for unobserved investments through studying and effort while in school. Again, as in Kahn and Lange (2014), individuals will underinvest in their skills if their investments can not be directly observed. And, the degree to which they invest less than the first best depends on the speed of employer learning. Obtaining better estimates of the speed of employer learning and more generally of learning processes in the labour market should thus be high on the priority list of empirical labour economists.ReferencesAltonji, J.G., and C. Pierret (1997) “Employer learning and the signaling value of education.” In I. Ohashi and T. Tachibanaki, eds., Industrial Relations, Incentives, and Employment, pp. 159–95. London: Macmillan Press Ltd.Altonji, J.G., and C. R. Pierret (2001) “Employer learning and statistical discrimination,” Quarterly Journal of Economics 116(1), 313–50Arcidiacono, P., P. Bayer, and A. Hizmo (2010) “Beyond signaling and human capital: Education and the revelation of ability,” American Economic Journal: Applied Economics 2(4), 76–104Aryal, G., M. Bhuller, and F. Lange (2019) “Signaling and employer learning with instruments,” NBER working paper no. w25885Aryal, G., M. Bhuller, and F. Lange (2022) “Signaling and employer learning with instruments,” American Economic Review 112(5), 1669–702Castex, G., and E. Kogan Dechter (2014) “The changing roles of education and ability in wage determination,” Journal of Labor Economics 32(4), 685–710Clark, D., and P. Martorell (2014) “The signaling value of a high school diploma,” Journal of Political Economy 122(2), 282–318Farber, H.S., and R. Gibbons (1996) “Learning and wage dynamics,” Quarterly Journal of Economics 111(4), 1007–47Graetz, G. (2021) “On the interpretation of diploma wage effects estimated by regression discontinuity designs,” Canadian Journal of Economics 54(1), 228–58Graetz, G. (2022) “Imperfect signals,” working paperHungerford, T., and G. Solon (1987) “Sheepskin effects in the returns to education,” Review of Economics and Statistics 69(1), 175–77Kahn, L.B. (2013) “Asymmetric information between employers,” American Economic Journal: Applied Economics 5(4), 165–205Kahn, L.B., and F. Lange (2014) “Employer learning, productivity, and the earnings distribution: Evidence from performance measures,” Review of Economic Studies 81(4), 1575–613Lange, F. (2007) “The speed of employer learning,” Journal of Labor Economics 25(1), 1–35Lange, F., and R. Topel (2006) “The social value of education and human capita.,” In E. Hanushek and F. Welch, eds., Handbook of the Economics of Education. vol. 1, ch. 8, pp. 459–509Layard, R., and G. Psacharopoulos (1974) “The screening hypothesis and the returns to education,” Journal of Political Economy 82(5), 985–98Light, A., and A. McGee (2015) “Employer learning and the ‘importance’ of skills,” Journal of Human Resources 50(1), 72–107Mansour, H. (2012) “Does employer learning vary by occupation?,” Journal of Labor Economics 30(2), 415–44Schönberg, U. (2007) “Testing for asymmetric employer learning,” Journal of Labor Economics 25(4), 651–91Spence, M. (1973) “Job market signaling,” Quarterly Journal of Economics 87(3), 355–74Wald, A. (1940) “The fitting of straight lines if both variables are subject to error,” Annals of Mathematical Statistics 11(3), 284–300Waldman, M. (1984) “Job assignments, signalling, and efficiency,” RAND Journal of Economics 15(2), 255–67 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Canadian Journal of Economics/Revue canadienne d économique Wiley

Approaches to learn about employer learning

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Abstract

IntroductionWhat employers believe about the skills of workers is bound to determine their labour market outcomes. How schooling affects these beliefs is thus crucial for determining the returns to an additional year of schooling. Thus, schooling might act as a signal to the job market and this function might distort decisions to acquire schooling from the social optimum (Spence 1973).Job market signalling is difficult to test because it is about objects that are inherently hard to observe: the latent skills of workers and how costs of schooling vary with these skills. As such, it is difficult to measure how much job market signalling contributes to the private returns to education and how much the social and the private returns diverge from each other due to job market signalling.This viewpoint describes one approach to quantify how large this gap might be, an approach that builds on the specification proposed of the common employer learning model proposed by Farber and Gibbons (1996) and further developed by Altonji and Pierret (2001). Central to this approach are the assumptions that: (i) individual productivity has a persistent, time‐invariant component, (ii) individual compensation equals expected productivity and (iii) employers learn about this persistent component as workers spend time in the labour market. To empirically operationalize these assumptions, the literature on common (or public) employer learning that grew out of Farber and Gibbons (1996) and Altonji and Pierret (2001) explicitly formulates both how potential employers learn about unobserved skills of workers and what information about underlying skills researchers have access to. These assumptions are leveraged to derive testable predictions of the employer learning model for how earnings vary with schooling and proxies of productivity across the life cycle.In this paper, we use a simplified version of the employer learning model to illustrate this approach to quantify how important job market signalling is. Two papers form the basis of this discussion. Lange (2007) follows Altonji and Pierret (2001) and assumes that the researcher has access to a correlate of productivity that employers do not use in wage setting.1The literature has used primarily cognitive test scores from surveys as such correlates. In particular, the main papers in this literature discussed below rely on the Armed Forces Qualification Test score collected as part of the National Longitudinal Survey of Youth. Other examples of productivity correlates that employers might not use are skill measures collected from siblings or other family members, assuming that skills are correlated within the family.That paper: (i) shows how functional form assumptions can be used to summarize the process of employer learning in a single parameter, the “speed of employer learning,” (ii) derives conditions under which we can identify this parameter and (iii) proceeds to estimate it. Lange (2007) goes on to impose additional structure on the schooling decision to bound the contribution of signalling to the economic returns from years of schooling.The second paper, Aryal et al. (2022), takes a different but related approach. Again, the analysis starts with the specification proposed by Farber and Gibbons (1996) and shows under what circumstances one can interpret instrumental variable estimates of the causal effect of schooling on earnings as representing either private or social returns to education.2A natural interpretation of the gap between social and private returns is the returns to job market signalling.The main insight is that how one interprets the IV estimates depends on whether or not potential employers know that the instrument induces the variation in schooling in the population. To the extend that employers do know about this variation, instrumental variable estimates of the returns to education represent social returns to education. To the extend that they do not, they represent private returns.As we discuss these approaches to bound or estimate the returns to signalling, we also reference empirical work that implements these approaches. In two online appendices, we provide additional evidence (appendix A) and review the existing empirical literature (appendix B). Our view is that the evidence in this field suggests that the returns to signalling make up at most 25% of the returns to education. However, we also find that the empirical basis for this conclusion is narrow and more work, using either of the approaches highlighted above, is necessary to firm up our confidence in this assessment. Ideally, new work will use the basic model following Lange (2007) to provide estimates of the learning process and the returns to signalling that can be compared with the existing estimates.We begin by first introducing in section 2 the basic model of wage setting and learning that we will rely on throughout the remainder of the article. It is based on but less general than the model analyzed by Farber and Gibbons (1996), Altonji and Pierret (2001) and Lange (2007). We then show in section 3 how access to a hidden correlate, that is a correlate of productivity not observed by employers, enables the researcher to test this model and estimate its parameters using the partial correlation of earnings with schooling and the hidden correlate across the life cycle. The section also briefly reviews the empirical work based on a hidden correlate and discusses how Lange (2007) proposes to bound the returns to signalling. The following section, section 4, explores how to interpret instrumental variable regressions in a model of employer learning. Again, we need to make assumptions on what employers observe, notably how much they know about the variation in schooling induced by the instrument. Instrumental variables have the advantage that rather than bound the returns to schooling, they allow, under suitable assumptions, to point‐identify the private and/or the social returns to schooling. Section 5concludes.A model of productivity, wages and informationAssume that log productivity yit$$ {y}_{it} $$ is additively separable into an individual heterogeneity Ai$$ {A}_i $$, an experience component H(t)$$ H(t) $$ common to all and an iid shock εit$$ {\varepsilon}_{it} $$,1yit=Ai+H(t)+εit.$$ {y}_{it}={A}_i+H(t)+{\varepsilon}_{it}.\kern0.5em $$Next, use δA|S$$ {\delta}^{A\mid S} $$ to define the causal effect of schooling on productivity and write2Ai=δA|SSi+Ai˜.$$ {A}_i={\delta}^{A\mid S}{S}_i+\tilde{A_i}.\kern0.5em $$Ai˜$$ \tilde{A_i} $$ then stands for unobserved components of ability that are not caused by schooling. Crucially, we do not restrict cov(Ai˜,Si)=0$$ \mathit{\operatorname{cov}}\left(\tilde{A_i},{S}_i\right)=0 $$ so that schooling can be correlated with productivity not caused by schooling. The coefficient δA|S$$ {\delta}^{A\mid S} $$ represents the social return to education because it captures the increase in productivity independent of whether it accrues to the worker.Combining, we obtain that log output yit$$ {y}_{it} $$ depends on (Si,Ai˜,t)$$ \left({S}_i,\tilde{A_i},t\right) $$ as follows:3yit=δA|SSi+Ai˜+H(t)+εit.$$ {y}_{it}={\delta}^{A\mid S}{S}_i+\tilde{A_i}+H(t)+{\varepsilon}_{it}.\kern0.5em $$Further, assume that (Ai˜,Si,εit)$$ \left(\tilde{A_i},{S}_i,{\varepsilon}_{it}\right) $$ are jointly normally distributed and {εit}$$ \left\{{\varepsilon}_{it}\right\} $$ is iid.Throughout, we maintain that compensation Wit$$ {W}_{it} $$ of individual i$$ i $$ with experience t$$ t $$ equals expected productivity conditional on the information employers at time t have access to. This information at experience level t is ℰit={Si,{yi,τ}τ<t,t}.$$ {\mathcal{E}}_{it}=\left\{{S}_i,{\left\{{y}_{i,\tau}\right\}}_{\tau <t},t\right\}. $$ This information set grows with experience t, which implies that employers learn about unobserved productivity Ai˜$$ \tilde{A_i} $$. The literature on employer learning hypothesizes that with time in the labour market more information is revealed and limt→∞Wit−E[exp(yit)|ℰit]=0.$$ {\lim}_{t\to \infty}\left({W}_{it}-E\Big[\mathit{\exp}\left({y}_{it}\right)|{\mathcal{E}}_{it}\Big]\right)=0. $$ This becomes useful for differentiating between human capital and signalling as we make additional functional form and substantive assumptions.Two brief remarks are in order. First, this is a model of common employer learning in the sense that any information is shared among a sufficient number of competing employers to ensure that compensation equals expected productivity. We also rule out long‐term contracts linking compensation to expected productivity over longer time periods. Common employer learning is a strong assumption, but models of private or asymmetric employer learning entail complex strategic interactions on the part of firms and workers that make them hard to use to model the life cycle of earnings.3Those interested in empirical models of asymmetric employer learning might want to consult, among others, Waldman (1984), Schönberg (2007) and Kahn (2013).Second, it is straightforward to incorporate additional observable controls in the analysis. Importantly, Farber and Gibbons (1996) and all authors following in their footsteps also allow for employers to observe productivity correlates Qi$$ {Q}_i $$ that researchers do not have access to. This implies that standard Mincer earnings equations will not identify the parameters of the learning model nor the private or the social returns to education because estimated returns to education will always be biased by the correlation between Qi$$ {Q}_i $$ and Si.$$ {S}_i. $$ This paper abstracts from both Qi$$ {Q}_i $$ and observable controls because this simplifies the expressions and because we believe we can still communicate the basic arguments without these.Yi,t$$ {Y}_{i,t} $$ is log normally distributed, and we can write4log(Wit)=log(𝔼[Yi,t|ℰit])=δA|SSi+H(t)+var(Ai˜+εi,t|ℰit)2+𝔼[Ai˜|ℰit].One of the features of updating expectations about normal variables using normal signals is that the posterior variance does not depend on the realization of the signal itself. This property of normal–normal learning applies here and we therefore have that var(Ai˜+εi,t|ℰit)=var(Ai˜+εi,t|t).$$ \mathit{\operatorname{var}}\left(\tilde{A_i}+{\varepsilon}_{i,t}|{\mathcal{E}}_{it}\right)=\mathit{\operatorname{var}}\left(\tilde{A_i}+{\varepsilon}_{i,t}|t\right). $$ Thus, we can control for H˜(t)=H(t)+var(Ai˜+εi,t|t)2$$ \tilde{H}(t)=H(t)+\frac{\mathit{\operatorname{var}}\left(\tilde{A_i}+{\varepsilon}_{i,t}|t\right)}{2} $$ in equation (4) with a set of experience controls. The interesting object is 𝔼[Ai˜|ℰit], and we can again draw on the properties of normal random variables to characterize this:5𝔼Ai˜|ℰit=θ(t,κ)ϕA|SSi⏟𝔼Ai˜|S+1−θ(t,κ)ξit‾,where ξ‾it=1t∑τ≤t{yiτ−δA|SSi−H(τ)}$$ {\overline{\xi}}_i^t=\frac{1}{t}{\Sigma}_{\tau \le t}\left\{{y}_{i\tau}-{\delta}^{A\mid S}{S}_i-H\left(\tau \right)\right\} $$. That is, at t$$ t $$, the observed output yit$$ {y}_{it} $$ net of the predictable component δW|SSi+H(t)$$ {\delta}^{W\mid S}{S}_i+H(t) $$ serves as a signal ξit$$ {\xi}_{it} $$ on unobserved ability Ai˜$$ \tilde{A_i} $$ with noise εit.$$ {\varepsilon}_{it}. $$ The average of these signals received up to period t is ξ‾it.$$ {\overline{\xi}}_i^t. $$ We discuss θ(t,κ)$$ \theta \left(t,\kappa \right) $$, the weight on the initial signal Si$$ {S}_i $$ in more detail below.Equations (4) and (5) together produce the experience t private return to an additional year of education. At t=0$$ t=0 $$, an additional year of education raises expected earnings because of the direct productivity effect δA|S$$ {\delta}^{A\mid S} $$ and because it raises the inferred Ãi$$ {\overset{\widetilde }{A}}_i $$ by ϕA|S.$$ {\phi}_{A\mid S}. $$ At experience t, the private return δtW|S$$ {\delta}_t^{W\mid S} $$ an individual can expect from an additional year of schooling is thus6δtW|S=δA|S+θ(t,κ)ϕA|S.$$ {\delta}_t^{W\mid S}={\delta}^{A\mid S}+\theta \left(t,\kappa \right){\phi}_{A\mid S}.\kern0.5em $$Equation (5) shows that the conditional expectation of ability Ai˜$$ \tilde{A_i} $$ at experience t is a weighted average of the conditional expectation of ability prior to entry to the labour market (at t=0$$ t=0 $$) and the average signal received up to t. The relative weights θ(t,κ)$$ \theta \left(t,\kappa \right) $$ depend only on the number of signals t received and one single parameter, κ$$ \kappa $$:7θ(t,κ)=1−κ1+t−1κwithκ=σ02σ02+σ2.ε$$ \theta \left(t,\kappa \right)=\frac{1-\kappa }{1+\left(t-1\right)\kappa}\kern.5em \mathrm{with}\kern.5em \kappa =\frac{\sigma_0^2}{\sigma_0^2+{\sigma}^2{.}_{\varepsilon }}\kern0.5em $$Here var(Ai˜)=σ02$$ \mathit{\operatorname{var}}\left(\tilde{A_i}\right)={\sigma}_0^2 $$ and var(εit)=σε2$$ \mathit{\operatorname{var}}\left({\varepsilon}_{it}\right)={\sigma}_{\varepsilon}^2 $$ and the parameter κ$$ \kappa $$ is the signal‐to‐noise ratio in the learning process, ie the ratio of the variance of the object to learn about (ie Ai˜$$ \tilde{A_i} $$) and the variance of the signal ξit=Ai˜+εit$$ {\xi}_{it}=\tilde{A_i}+{\varepsilon}_{it} $$.This model of wages developed so far forms the basis of the discussion that follows. We invoke stronger assumptions than strictly required, sometimes significantly so, but they allow uncovering in a fairly transparent way the reasoning behind the empirical employer learning literature.The hidden correlate approachPredictionsThe two foundational papers in this literature, Farber and Gibbons (1996) and Altonji and Pierret (2001), combine a wage‐setting model similar to the one developed in section 2 with the assumption that the researcher has access to a variable Z$$ Z $$ that employers do not have direct access to. We will refer to this variable as a hidden correlate. Farber and Gibbons (1996), Altonji and Pierret (2001) and Lange (2007) assume access to such a hidden correlate and derive predictions for the partial regression coefficients on S$$ S $$ and Z$$ Z $$ in log earnings regressions and how these evolve with experience.4Farber and Gibbons (1996) actually consider regressions in levels.A main reason for the popularity of this literature is that these predictions conform to simple intuitions about learning models.So, what do we predict for a regression of log wages on a hidden correlate Z$$ Z $$ as well as schooling S$$ S $$ at experience t? Substituting equation (5) into equation (4), we obtain the linear projection (denoted by 𝔼∗) of log wages at experience t on (Si,Zi)$$ \left({S}_i,{Z}_i\right) $$:8𝔼∗[log(Wit)|S,Z,t]=αt+δA|SSi+𝔼∗[𝔼[Ai˜|ℰit]]=αt+(δA|S+θ(t,κ)ϕA|S)Si+(1−θ(t,κ))𝔼∗[ξit‾|S,Z].We note that 𝔼∗[ξit‾|S,Z]=𝔼∗[Ai˜|Si,Zi] and use (β^AS,β^AZ)$$ \left({\hat{\beta}}_{AS},{\hat{\beta}}_{AZ}\right) $$ for the coefficients that project Ai$$ {A}_i $$ on (Si,Zi).$$ \left({S}_i,{Z}_i\right). $$ From this follow the coefficients projecting wages on (Si,Zi)$$ {S}_i,{Z}_i\Big) $$:9β^wS,t=δA|S+θ(t,κ)ϕA|S+(1−θ(t,κ))β^AS,$$ {\hat{\beta}}_{wS,t}\kern0.5em ={\delta}^{A\mid S}+\theta \left(t,\kappa \right){\phi}_{A\mid S}+\left(1-\theta \left(t,\kappa \right)\right){\hat{\beta}}_{AS}, $$10β^wZ,t=(1−θ(t,κ))β^AZ.$$ {\hat{\beta}}_{wZ,t}\kern0.5em =\left(1-\theta \left(t,\kappa \right)\right){\hat{\beta}}_{AZ}. $$These coefficients and their evolution over the life cycle are the primary empirical objects of interest in the literature following Farber and Gibbons (1996), especially in Altonji and Pierret (1997), Altonji and Pierret (2001) and Lange (2007). Each of these papers can be associated with a different set of predictions on these coefficients.First, Farber and Gibbons (1996) (in a level specification analogous to this log specification) show that {β^wZ,t}$$ \left\{{\hat{\beta}}_{wZ,t}\right\} $$ (equation (10)) increase in experience if Zi$$ {Z}_i $$ correlates positively with unobserved ability Ai˜.$$ \tilde{A_i}. $$ Second, Altonji and Pierret (2001) observe that when projecting log wages on Si$$ {S}_i $$ but not Zi$$ {Z}_i $$ the projection coefficient on Si$$ {S}_i $$ exceeds β^wS,t$$ {\hat{\beta}}_{wS,t} $$ by (1−θ(t,κ))β^AZcov(Z,S)/var(S).$$ \left(1-\theta \left(t,\kappa \right)\right){\hat{\beta}}_{AZ}\mathit{\operatorname{cov}}\left(Z,S\right)/\mathit{\operatorname{var}}(S). $$5To derive the latter, use the omitted variable formula.Thus, across experience, one can use the emerging differences between the projection coefficients on schooling in a projection of log wages on schooling alone and on schooling and Z$$ Z $$ jointly to test whether employers screen for unobserved ability using schooling. Third, Lange (2007) exploits the functional form restrictions implied by normal–normal learning on θ(t,κ)$$ \theta \left(t,\kappa \right) $$ (see equation (7)) to summarize the learning process with the single parameter κ$$ \kappa $$. This parameter can be estimated using the partial regression coefficients {β^wS,t,β^wZ,t}$$ \left\{{\hat{\beta}}_{wS,t},{\hat{\beta}}_{wZ,t}\right\} $$.The contrast between equation (9) and the private return to education defined in equation (6) also shows that the projection of log earnings on education will not directly deliver an estimate of the social returns to education even when controlling for the hidden correlate Zi$$ {Z}_i $$ as long as schooling correlates with the component of ability not caused by education.EvidenceEmpirically, the literature on employer learning has relied heavily on the NLSY 1979, the data used by Farber and Gibbons (1996), Altonji and Pierret (2001) and Lange (2007). The NLSY 1979 is a long panel of individuals during the early part of their careers with good earnings data as well as a cognitive skill measure that can serve as a hidden correlate.6Of course, the fact that the NLSY 1979 is US data is another major advantage in securing a prominent place for this data set in the literature.This measure, the Armed Forces Qualification Test (AFQT) score is based on a battery of tests administered to respondents to the NLSY 1979.In 1979, the NLSY 1979 started collecting data on a panel of US residents born between 1957 and 1964. From 1997 on, collection of data on a new cohort born between 1980 and 1984 commenced. This panel is known as the NLSY 1997. Figure 1 shows the partial regression coefficients on schooling and the AFQT in regressions by year of experience in both data. Each scatter point represents the coefficient estimate on either schooling or the AFQT (measured in standard deviations) up to experience 17.7Online appendix A contains information on the precise specification and data selection criteria.1FIGUREReturns to schooling and AFQT over the life cycle NOTES: The scatters display the estimated coefficients on schooling and the standardized Armed Forces Qualification Test (AFQT) score for each experience level. The line shows the predicted returns to schooling and AFQT score over the life cycle implied by the estimates in table 1. The estimation of these parameters is described in online appendix section A2.For both data sets, we obtain that the regression coefficients on Z$$ Z $$ increase and those on S$$ S $$ decrease with experience, as we expect in a learning model. Visual inspection suggests that the functional form implied by the normal–normal learning model developed above fits the data quite well. The line fitted to the experience profiles is obtained by estimating the parameter κ$$ \kappa $$ using the regression coefficients on S$$ S $$ or Z$$ Z $$ and the restrictions of the normal learning model. As described by Lange (2007), these regression coefficients at experience t are weighted averages of the regression coefficients at experience t=0$$ t=0 $$ and a limit value to which the coefficient converges as t→∞.$$ t\to \infty . $$ Thus, the projection coefficients at any experience level are a function of three parameters only (the initial and limit values of the projection coefficients and the parameter κ$$ \kappa $$), and we can estimate these by fitting the estimated coefficients using non‐linear least squares.8Our results differ from Castex and Kogan Dechter (2014) in that we find increasing returns to the AFQT and decreasing returns with experience for both males and females. The differences in the findings can be largely accounted for by the fact that we have access to a longer panel and estimate a non‐linear specification. Additional details are presented in online appendix C.1TABLESpeed of employer learning(1)(2)(3)(4)(5)(6)(7)NLSY 1979NLSY 1997Aryal et al. (2022)Years ofAFQTYears ofAFQTYears ofIQ testYears ofschoolingscoreschoolingscoreschoolingscoreschooling (IV)Speed of learning κ$$ \kappa $$0.2360.2530.0610.1140.4760.1260.550(0.002)(0.001)(0.001)(0.002)(0.069)(0.034)(0.126)Initial errors decline by 50% (years)3.2382.95315.4557.8081.1016.9360.818Initial value b0$$ {b}_0 $$0.109−$$ - $$0.0170.100−$$ - $$0.0040.1000.0110.195(0.007)(0.001)(0.000)(0.012)(0.007)(0.005)(0.012)Limit value b∞$$ {b}_{\infty } $$0.0550.1590.0340.1020.0230.0930.055(0.001)(0.000)(0.027)(0.042)(0.002)(0.006)(0.008)NOTES: The reported parameters are estimated by nonlinear least squares using the coefficient estimates on schooling and Armed Forces Qualification Test (AFQT) score at different experience levels. The reported initial errors decline is obtained using equation (7). The standard errors in columns (1) to (4) are obtained by bootstrapping with 5,000 repetitions. Columns (5) to (7) are from Aryal et al. (2022).Data generated by other learning processes would generate the basic features shown in figure 1 as well. The usefulness of the normal learning model is not in that it delivers a particularly good fit (even though it does), but that it allows summarizing the learning process in a simple manner whose main features can be summarized in a single parameter κ$$ \kappa $$.Table 1 shows the estimated speed of learning parameter κ$$ \kappa $$ for both data sets and both variables (Si,Zi).$$ {S}_i,{Z}_i\Big). $$ Columns (1) and (2) reproduce the main empirical results from Lange (2007) using data stemming from a longer time period and document identical findings as in Lange (2007). The estimated coefficient on κ$$ \kappa $$ for AFQT score (column (2)) implies that initial expectation errors by employers on average decline by 25% after workers spend around one year in the labour market. After three years, the initial error will have declined by around 50%. After workers spend around nine years in the labour market, initial expectation errors will on average have fallen by 75%, and after around 27 years, they will have declined by 90%. The point estimate of κ$$ \kappa $$, therefore, suggests that a worker's productivity is revealed to the employer mostly within the first few years of her labour market career.The point estimates in columns (3) and (4) on the other hand suggest that employer learning is relatively slow for the cohort entering the labour market in the early 2000s. Specifically, the estimate of κ$$ \kappa $$ from column (4) implies that initial expectation errors by employers on average decrease by around 11% during the first year a worker spends in the labour market. It takes about eight years for initial expectation errors to on average decline by 50%, 23 years to decline by 75% and a full 70 years to decline by 90%. This finding suggests that the speed of employer learning has slowed down between the 1980s and 2000s.Columns (5) and (6) report analogous estimates based on a sample of Norwegian males and their IQ test scores collected as part of military conscription procedures.9The same data is discussed in section 4. The data consists of administrative data on the population of Norwegian males born between 1950 and 1980 with earnings data between 1967 and 2014.The estimates from the Norwegian data bracket the estimates from the two NLSY cohorts. Those using schooling coefficients imply very rapid learning, while those using the IQ score imply learning similar to those from the NLSY 1979. Nevertheless, even the lower point estimate indicate that substantial learning about individual skills does take place in the first 10 years of an individual's career.10The NLSY cohorts have also been a rich source of data to explore heterogeneity and channels of learning. Arcidiacono et al. (2010), Mansour (2012) and Light and McGee (2015) explore the role of education, occupations and skill types in the employer learning framework. We review this literature in online appendix B.Unfortunately, the evidence from other countries and settings is not as abundant as desirable. And, unfortunately, few of these papers explicitly use the learning structure proposed by Lange (2007) to provide parameter estimates of the speed of learning that would allow comparing and synthesizing across sometimes quite different economic environments. We review this literature in online appendix B.Bounds on the returns to signallingLange (2007) takes the analysis one step further and uses the estimates of the speed of learning to quantify the contribution of the private returns to signalling in the total gains from schooling.11See Altonji and Pierret (1997) for a similar attempt to use estimates of how rapidly information is revealed to inform the question of how large signalling returns are.Two aspects of this approach bear particular mentioning. First, because the information available to employers Qi$$ {Q}_i $$ (which we abstracted from above) is not available to researchers, the estimate Lange (2007) arrives at is an upper bound for the contribution of signalling to the total return to education.Second, he relies on additional information in the form of an estimate of the cost of schooling. Lange (2007) here follows the tradition in the literature that views schooling primarily as an investment and assumes that the cost of schooling is determined largely by the opportunity costs and thus the discount rate on future earnings. His estimate of the bound on the returns to signalling thus depends on the assumption that schooling costs are due largely to discounting as well as the particular rate of discounting used. Both are strong assumptions are central to the bound he provides. For discount rates between 3% and 7% and using his preferred estimate of the speed of learning parameter of κ=0.26$$ \kappa =0.26 $$, he finds that the upper bound on the contribution of signalling to the overall private returns to schooling varies between 3% and 26%. The lower bound of the 95% confidence interval on the speed of learning parameter is κ=0.14.$$ \kappa =0.14. $$ If learning is this slow, then the upper bound varies between 6% and 47%.Instrumental variables and employer learningThe hidden correlate approach discussed above delivers testable predictions for employer learning and allows summarizing in a single, estimable parameter how rapidly firms learn about unobserved ability. And, with suitable assumptions, we can bound the contribution of signalling to the private returns to education. However, this approach does not produce a point estimate of the private or the social returns to education. And, the additional assumptions required to arrive at the bound on the signalling returns are strong.Aryal et al. (2022) show that instrumental variable estimates can provide useful information on the social and the private returns to education without having to invoke strong assumptions on the costs of schooling as required by Lange (2007). Rather, if the researcher is willing to take a stand on whether or not an instrument can be observed by employers, then the instrumental variable estimates can inform discussions about the productivity and signalling returns to education.We follow Aryal et al. (2022) and discuss a binary instrument for schooling.12Importantly, their argument extends beyond instrumental variables (binary or not) to all quasi‐experimental approaches.How to interpret the IV estimates depends on whether or not employers understand and price the variation induced by the instrument correctly. The usual reason offered to justify instrumenting is ability bias. Using our formulation in equation (2) the concern is that Ãi$$ {\overset{\widetilde }{A}}_i $$ correlates with schooling Si.$$ {S}_i. $$ Various instruments have been proposed claiming to increase schooling but to also be orthogonal to Ãi.$$ {\overset{\widetilde }{A}}_i. $$ We are not interested in re‐opening debates about these claims but posit that there indeed is an instrument Li∈{0,1}$$ {L}_i\in \left\{0,1\right\} $$ that satisfies both the rank and orthogonality condition. That is, we assume that11𝔼[Si|Li=1]≠𝔼[Si|Li=0],12𝔼[Ãi|Li]≡0.The IV coefficient for our binary instrument is (Wald 1940): bIV,t=𝔼[log(Wit)|Li=1]−𝔼[log(Wit)|Li=0]𝔼[Si|Li=1]−𝔼[Si|Li=0].And, using equation (4), we have that 𝔼[log(Wit)|Li=1]−𝔼[log(Wit)|Li=0]=δA|S∗(𝔼[Si|Li=1]−𝔼[Si|Li=0])+𝔼[𝔼[Ãi|ℰit]|Li=1]−𝔼[𝔼[Ãi|ℰit]|Li=0]. Thus, we have13bIV,t=δA|S+𝔼[𝔼[Ãi|ℰit]|Li=1]−𝔼[𝔼[Ãi|ℰit]|Li=0]𝔼[Si|Li=1]−𝔼[Si|Li=0].Equation (13) shows that interpreting bIV,t$$ {b}_{IV,t} $$ comes down to making assumptions about how the instrument Li$$ {L}_i $$ enters into the information ℰit$$ {\mathcal{E}}_{it} $$ held by employers. Aryal et al. (2022) focus on two polar cases. First, they consider “transparent instruments” that form part of the information held by firms so that ℰit={Si,ξit,Li}$$ {\mathcal{E}}_{it}=\left\{{S}_i,{\xi}_i^t,{L}_i\right\} $$. And, they contrast this with “hidden instruments” that are not observed by employers and thus do not form part of the firms information set. For these, Li∉ℰit.$$ {L}_i\notin {\mathcal{E}}_{it}. $$For transparent instruments, applying the LIE to equation (13) and using equation (12) implies that bIV,t=δA|S.$$ {b}_{IV,t}={\delta}^{A\mid S}. $$ Intuitively, when potential employers are aware of the instrument, they will not use the induced variation in schooling to infer Ãi.$$ {\overset{\widetilde }{A}}_i. $$ By assumption, we imposed that the instrument is orthogonal to the endogenous unobserved ability Ãi.$$ {\overset{\widetilde }{A}}_i. $$ Thus, transparent IVs identify the effect of schooling on productivity itself: δA|S.$$ {\delta}^{A\mid S}. $$For hidden instruments, we have from equation (5) that 𝔼[Ãi|ℰit]=θ(t,κ)ϕA|SSi⏟𝔼Ai˜|S+1−θ(t,κ)ξit‾ and thus 𝔼[𝔼[Ãi|ℰit]|Li]=θ(t,κ)ϕA|S𝔼[Si|Li] because 𝔼[ξit‾|Li]=0. Substituting in equation (13), we find that for a hidden instrument, the instrumental coefficient is bIV,t=δA|S+ϕA|Sθ(t,κ).$$ {b}_{IV,t}={\delta}^{A\mid S}+{\phi}_{A\mid S}\theta \left(t,\kappa \right). $$ Hidden instruments thus identify the private returns to additional schooling that consist of both the productivity return and the signalling return. Employers are unaware of the instrument and thus variation in schooling induced by the instrument induces them to update their conjectures of Ãi.$$ {\overset{\widetilde }{A}}_i. $$ Thus, hidden instruments identify the private returns to schooling.Causal estimation using instruments already requires a priori assumptions on the validity of the instrument that cannot be tested. As such, when researchers employ instruments they need to carefully argue based on contextual evidence that an instrument will in fact satisfy the exclusion restrictions. In such cases, researchers might also be able to determine whether or not an instrument is in fact plausibly hidden or transparent. As Aryal et al. (2022) show, being willing to make such a determination reaps rewards in being able to identify deep policy‐relevant parameters when the analysis is embedded in the employer learning framework.For instance, as argued above, with a transparent instrument one can recover immediately the policy‐relevant parameters δA|S$$ {\delta}^{A\mid S} $$ that describe the productivity effect of schooling. A hidden instrument delivers the private returns bIV,t=δA|S+ϕA|Sθ(t,κ).$$ {b}_{IV,t}={\delta}^{A\mid S}+{\phi}_{A\mid S}\theta \left(t,\kappa \right). $$ But, using data from repeated cross‐sections allows recovering δA|S$$ {\delta}^{A\mid S} $$ as the limit to which bIV,t$$ {b}_{IV,t} $$ converges as t→∞.$$ t\to \infty . $$ And, it also allows estimating κ$$ \kappa $$ using an approach analogous to that using a hidden correlate.Of course, all this does not come for free. The assumptions on whether employers are aware of the instrument will be debatable. And, the strong identification results described above derive partially from the functional form assumptions, in particular the assumption that δA|S$$ {\delta}^{A\mid S} $$ does not vary with experience. Aryal et al. (2022) and their companion working paper Aryal et al. (2019) however do show ways to relax some of these assumptions, especially if access to multiple instruments with different information assumptions is available.Aryal et al. (2022) illustrate how to use this approach using a compulsory schooling law lengthening the mandatory school length. The data draws on administrative records for Norwegian males that also includes IQ scores collected as part of the military draft.13Columns (5) and (6) in table 1 report estimates of the speed of learning measure based on these IQ scores and schooling measures using the hidden correlate approach discussed in section 3.The effect of the law was to extend minimum required schooling from seven to nine years across Norway, but the law was locally implemented at different times during the 1960–1975 period. The effect was to induce variation in the law across different jurisdictions that were often geographically very close. Frequently, small communities with a few thousand inhabitants would extend the compulsory schooling period at earlier or later dates than much larger jurisdictions within the same broad labour market. Empirically, this provides variation across locations and time that can be used to identify the causal impact of the law on wages. More important in the present context is that it allows dividing the sample in distinct populations that are separated by how plausible it is that the instrument is either hidden or transparent. As such, this setting provides an opportunity to illustrate and apply the ideas on transparent and hidden instruments.In particular, Aryal et al. (2022) argue that for the central communities in commuting zones in which the majority of the population of a given labour market lives, the variation induced by the instrument is plausibly understood by market participants. They interpret the estimates obtained from this sample as generated by a transparent instrument, and thus they identify the social (or productivity) returns to additional schooling. By contrast, employers are much less likely to be informed of variation in the time when the law was implemented across small localities forming part of a large labour market. The instrument can thus plausibly be argued to be hidden for the sample of individuals growing up in smaller communities surrounding the larger central community forming the core of a labour market. Thus, Aryal et al. (2022) construct two samples, one for which the instrument is plausibly hidden and one for which it is observed.The coefficients on years of schooling over the life cycle estimated using this instrument are shown in figure 2.2FIGUREReturns to Schooling estimated using a Hidden and a Transparent Instrument NOTES: This figure reproduces figure 3 in Aryal et al. (2022). It shows the returns to education estimated using the compulsory schooling reform discussed in the main text. The right panel shows the estimates on the sample that permits interpreting the instrument as transparent. The left panel shows the estimates on the sample for which the instrument is hidden.The right panel shows the estimates using the transparent instruments. These estimates do not display the typical decline in the returns to education associated with learning model, suggesting that the assumption that this instrument is transparent is indeed valid. We see that the returns to education are high and roughly stable across experience levels. By contrast, the estimates from the hidden sample (left panel) display the typical shape expected from a learning model when the instrument is not observed. The rapid decline in the estimated returns to education during the first few years in the labour market gives rise to the high estimated value for κ$$ \kappa $$ reported in column (7) of table 1.What does all this imply for the productivity and signalling returns to education? Aryal et al. (2022) report a total return to education of 7.9% per year of schooling. 70% of is accounted for by a causal effect of schooling on productivity with the remainder due to signalling effects. These estimates are local average treatment effects applying to an extension of required minimum schooling 50 years in the past and might therefore be of limited utility for current use. We hope that more current estimates will emerge from other settings that explicitly try to implement this approach to inform on the social and private returns to education.Aryal et al. (2022) are able to distinguish signalling and productivity effects of schooling because they are willing to take a stand on whether or not employers price the instrument correctly. This idea is related to a literature examining variation in education credentials induced by variation in test scores across a cut‐off required for graduation (see the review of the related literature in online appendix B).14An early related literature pointed to higher than usual returns to years of schooling required to complete a degree as evidence of information rents (Hungerford and Solon (1987),Layard and Psacharopoulos (1974)). However, those not completing degree years are likely to be negatively selected, casting doubts on these conclusions (Lange and Topel 2006). Hungerford and Solon (1987) themselves note that diploma effects cannot be understood without relying on screening.Clark and Martorell (2014) employ this approach to estimate the causal effect of a diploma by comparing individuals who just passed or failed high school exit exams. This approach is clearly related to the instrumental variable approach as discussed by Aryal et al. (2022) in that employers do not observe the variation in test scores around the discontinuity. Thus, this regression discontinuity approach sets up a contrast between the treated group (those with scores just above the discontinuity) and the control group (just below) that is analogous to the hidden instrument case. Graetz (2021) provides a useful discussion of how RD estimates of returns to degrees or diplomas should be interpreted in light of the employer learning model.ConclusionThis paper discussed how one approach to quantify the relative contributions of signalling versus human capital to the private return to education based on the assumption that firms learn over time about unobserved productive skills of individuals. In the process, we showed how to estimate the speed of employer learning. Our view of the literature is that the evidence on balance suggests that learning is rapid but not instantaneous. There is evidence from a variety of countries that supports the basic linear tests of employer learning following Altonji and Pierret (2001), but few papers estimate the speed of learning parameter (Lange 2007) or use this parameter to bound the returns to signalling. Those that do tend to find that signalling accounts at most for one quarter of the returns to education, but we argue that the empirical basis for these conclusions is narrow.The model of job market signalling emphasizes that incomplete information distorts the returns to invest into observable signals of productivity, such as schooling. Incomplete information however also lowers the returns to other investments into one's productivity as long as these investments are not directly observable. How large these distortions are will generally depend on the speed of employer learning. Kahn and Lange (2014) for instance show evidence of employer learning throughout individuals' careers. This evidence suggests a wedge between the social and private returns to on‐the‐job investments. Graetz (2022) explores how gradual employer learning affects the returns for unobserved investments through studying and effort while in school. Again, as in Kahn and Lange (2014), individuals will underinvest in their skills if their investments can not be directly observed. And, the degree to which they invest less than the first best depends on the speed of employer learning. Obtaining better estimates of the speed of employer learning and more generally of learning processes in the labour market should thus be high on the priority list of empirical labour economists.ReferencesAltonji, J.G., and C. Pierret (1997) “Employer learning and the signaling value of education.” In I. Ohashi and T. Tachibanaki, eds., Industrial Relations, Incentives, and Employment, pp. 159–95. London: Macmillan Press Ltd.Altonji, J.G., and C. R. Pierret (2001) “Employer learning and statistical discrimination,” Quarterly Journal of Economics 116(1), 313–50Arcidiacono, P., P. Bayer, and A. Hizmo (2010) “Beyond signaling and human capital: Education and the revelation of ability,” American Economic Journal: Applied Economics 2(4), 76–104Aryal, G., M. Bhuller, and F. Lange (2019) “Signaling and employer learning with instruments,” NBER working paper no. w25885Aryal, G., M. Bhuller, and F. Lange (2022) “Signaling and employer learning with instruments,” American Economic Review 112(5), 1669–702Castex, G., and E. Kogan Dechter (2014) “The changing roles of education and ability in wage determination,” Journal of Labor Economics 32(4), 685–710Clark, D., and P. Martorell (2014) “The signaling value of a high school diploma,” Journal of Political Economy 122(2), 282–318Farber, H.S., and R. Gibbons (1996) “Learning and wage dynamics,” Quarterly Journal of Economics 111(4), 1007–47Graetz, G. (2021) “On the interpretation of diploma wage effects estimated by regression discontinuity designs,” Canadian Journal of Economics 54(1), 228–58Graetz, G. (2022) “Imperfect signals,” working paperHungerford, T., and G. Solon (1987) “Sheepskin effects in the returns to education,” Review of Economics and Statistics 69(1), 175–77Kahn, L.B. (2013) “Asymmetric information between employers,” American Economic Journal: Applied Economics 5(4), 165–205Kahn, L.B., and F. Lange (2014) “Employer learning, productivity, and the earnings distribution: Evidence from performance measures,” Review of Economic Studies 81(4), 1575–613Lange, F. (2007) “The speed of employer learning,” Journal of Labor Economics 25(1), 1–35Lange, F., and R. Topel (2006) “The social value of education and human capita.,” In E. Hanushek and F. Welch, eds., Handbook of the Economics of Education. vol. 1, ch. 8, pp. 459–509Layard, R., and G. Psacharopoulos (1974) “The screening hypothesis and the returns to education,” Journal of Political Economy 82(5), 985–98Light, A., and A. McGee (2015) “Employer learning and the ‘importance’ of skills,” Journal of Human Resources 50(1), 72–107Mansour, H. (2012) “Does employer learning vary by occupation?,” Journal of Labor Economics 30(2), 415–44Schönberg, U. (2007) “Testing for asymmetric employer learning,” Journal of Labor Economics 25(4), 651–91Spence, M. (1973) “Job market signaling,” Quarterly Journal of Economics 87(3), 355–74Wald, A. (1940) “The fitting of straight lines if both variables are subject to error,” Annals of Mathematical Statistics 11(3), 284–300Waldman, M. (1984) “Job assignments, signalling, and efficiency,” RAND Journal of Economics 15(2), 255–67

Journal

Canadian Journal of Economics/Revue canadienne d économique – Wiley

Published: May 1, 2023

References

  • Industrial Relations, Incentives, and Employment
    Altonji, J.G.; Pierret, C.
  • Employer learning and statistical discrimination
    Altonji, J.G.; Pierret, C. R.
  • Beyond signaling and human capital: Education and the revelation of ability
    Arcidiacono, P.; Bayer, P.; Hizmo, A.
  • Signaling and employer learning with instruments
    Aryal, G.; Bhuller, M.; Lange, F.
  • The changing roles of education and ability in wage determination
    Castex, G.; Kogan Dechter, E.
  • The signaling value of a high school diploma
    Clark, D.; Martorell, P.
  • Learning and wage dynamics
    Farber, H.S.; Gibbons, R.
  • On the interpretation of diploma wage effects estimated by regression discontinuity designs
    Graetz, G.
  • Sheepskin effects in the returns to education
    Hungerford, T.; Solon, G.
  • Asymmetric information between employers
    Kahn, L.B.
  • Employer learning, productivity, and the earnings distribution: Evidence from performance measures
    Kahn, L.B.; Lange, F.
  • The speed of employer learning
    Lange, F.
  • Handbook of the Economics of Education
    Lange, F.; Topel, R.
  • The screening hypothesis and the returns to education
    Layard, R.; Psacharopoulos, G.
  • Employer learning and the ‘importance’ of skills
    Light, A.; McGee, A.
  • Does employer learning vary by occupation?
    Mansour, H.
  • Testing for asymmetric employer learning
    Schönberg, U.
  • Job market signaling
    Spence, M.
  • The fitting of straight lines if both variables are subject to error
    Wald, A.
  • Job assignments, signalling, and efficiency
    Waldman, M.