What Drives Firms’ Hiring Decisions? An Asset Pricing Perspective

Abstract

We study the economic determinants of firms’ hiring decisions, a central variable in most theories of economic fluctuations, through the lens of asset pricing. We show that the aggregate hiring rate in the U.S. economy is high when the discount rate is low, and when expected short-term cash flow is high. In addition, we show that changes in discount rates and short-term expected cash flows explain most of the time-series variation in the aggregate hiring rate, each contributing to about 40|$\%$| and 60|$\%$| of the variation, respectively, while changes in long-term expected cash flows have no explanatory power.

To establish the theoretical link between hiring, discount rates, and expected cash flows, we consider a dynamic neoclassical model of the firm with labor market frictions. Hiring and firing (henceforth simply referred to as hiring) are costly, which is captured by an adjustment cost function. The presence of labor adjustment costs implies that labor hiring, similar to an investment, is a forward-looking decision. In particular, we show that when optimal labor hiring is higher than usual, expected stock returns (discount rates) must be lower than usual, expected long- or short-term cash flows must be higher than usual, or both. This link is the labor-analog of the findings in Shiller (1981) and Campbell and Shiller (1988) on the determinants of contemporaneous stock prices and price-to-dividend ratios, and implies that future stock returns, and short- and long-term cash flows, should be predictable from a firm’s current labor hiring rate.

Although the theory establishes that a firm’s hiring rate and future stock returns, or a firm’s hiring rate and future long- and short-term cash flows should be related, the sign of these relationships in predictability regressions is an empirical question. In particular, the sign depends on the relative strength of the opposing effects of discount rates and short- and long-term expected cash flows (which are all likely to be correlated in the data) on hiring decisions. Thus, analogous to the analysis of Campbell and Shiller (1988) on the price-to-dividend variation, we use our model to map the predictability results into a variance decomposition of a firm’s hiring rate to quantify the relative importance of the discount rate and short- and long-term cash flow channels for explaining the fluctuations in the hiring rate that we observe in the data.

We use the theoretical framework to guide our empirical analysis. Using aggregate-level data of publicly traded firms in the U.S. economy from |$1963$| to |$2019$|⁠, we run short- and long-horizon predictive regressions in which we use the aggregate hiring rate to predict future stock market returns, as well as future aggregate long- and short-term cash flows. Consistent with the model-implied variance decomposition, long-term cash flow is the aggregate dividend growth from year two onward, and short-term cash flow is the next year aggregate dividend-to-labor ratio.

We document three main empirical findings. First, the aggregate hiring rate of publicly-traded firms negatively predicts aggregate stock market excess returns at all investment horizons, both in-sample and out-of-sample. This predictability is stronger at longer horizons. At the 5-year horizon, we find that both the in-sample and out-of-sample |$R^{2\prime }s$| of the predictive regressions are around |$25\%$|⁠.

Second, the aggregate hiring rate of publicly traded firms positively predicts short-term cash flows with an in-sample |$R^{2}$| of about |$15\%$|⁠. In addition, hiring negatively predicts long-term cash flows, with an in- and out-of-sample |$R^{2}s$| of about |$20\%$| at the 5 year horizon.

Finally, interpreting the return and cash flow predictability slopes through the lens of the model-implied hiring rate variance decomposition, we find that changes in discount rates and short-term cash flows are the two main drivers of the time-series variation in the aggregate hiring rate, with contributions of |$42.1\%$| and |$61.5\%$|⁠, respectively. Perhaps surprisingly, the contribution of long-term expected cash flows to hiring rate variation is close to zero, |$-3.6\%$|⁠. Thus, in the data, the aggregate hiring rate is high when the discount rate is low, or expected short-term cash flow is high, but there is no systematic link to long-term expected cash flow.

To help understand the empirical findings, we estimate the parameters of the firm’s technology and stochastic processes in the model by the Simulated Method of Moments (SMM), and by targeting a large set of asset pricing and quantity moments. We specify the aggregate and firm-level stochastic productivity as AR(1) processes, a flexible stochastic discount factor (SDF) that allows for time-varying price of risk of the aggregate productivity shock, and we let firms choose their wage rate endogenously, by specifying a wage rate schedule that is a function of hours worked following the approach in Bloom (2009).

In addition, we reestimate alternative versions of the model in which we remove key model features, such as labor adjustment costs (labor market frictions) and time-varying price of risk, to evaluate the marginal importance of these features for the model fit. Finally, we also reestimate the baseline model ignoring asset pricing moments and targeting only quantity moments, to understand the information content of asset pricing moments for the identification of the structural parameters.

The estimation of the different specifications of the model provides three main insights. First, both labor adjustment costs and time-variation in the price of risk are important for the model to generate predictability of aggregate returns, as well as the significant weight of discount rates in the hiring rate variance decomposition. When we restrict the price of risk of aggregate productivity shocks in the SDF to be constant, the return predictability from the hiring rate and the variance of the hiring rate that is explained by discount rates drops by 40|$\%$| and 30|$\%$|⁠, respectively, when compared to the baseline model. This drop is even stronger when we shut down labor adjustment costs. This is because, in the model, labor adjustment costs are the main driver of time-variation in risk loadings (i.e., conditional betas). Turning off labor adjustment costs significantly lowers the variation in conditional beta, which in turn reduces the hiring rate variation driven by discount rates and lowers the return predictability from the hiring rate.

Second, labor adjustment costs are also important for the model to capture the cash flow predictability patterns, and the role of cash flows in the hiring rate variance decomposition, while variation in the price of risk does not play an important quantitative role here. Specifically, when labor can be freely adjusted, labor hiring positively predicts long-term cash flows, in contrast with the data; in addition, labor hiring only weakly predicts short-term cash flows. This happens because labor adjustment costs affect optimal hiring and hence optimal payout policies. Without labor adjustment costs, firms immediately hire workers to reach the optimal frictionless target level of labor and then they increase dividend payout afterward. This last effect leads to weak short-term cash flow predictability by hiring rates and positive long-term cash flow predictability. In addition, turning off labor adjustment costs also results in much more volatile hiring rates, which causes too high fractions of the hiring variation associated with changes in expected short-term and long-term cash flows. Adding labor adjustment costs makes it costly for a firm to reach the frictionless target labor level. Thus, firms gradually build up their labor stock, and therefore reduce dividend payout going forward after increases in hiring. As a result, hiring positively predicts the short-term cash flow and negatively predicts long-term cash flows, and the fraction of hiring rate variation explained by changes in expected short- and long-term cash flows is consistent with the data.

Lastly, we show that estimating the model using both asset pricing and quantity moments is important to learn about the size of labor adjustment costs (and hence the importance of labor market frictions) in the economy. Specifically, we find that when we only target quantity moments (as typically done in the labor demand literature) and ignore variation in asset prices, the labor adjustment costs are only half of those obtained when we target both quantity and asset pricing moments. This result has potential policy implications. Since adjustment costs are underestimated in models that only target quantity moments, policies aimed at mitigating the impact of labor market frictions (e.g., countercyclical subsidies) that are implemented based on estimates from models that ignore variation in asset prices, might not be sufficiently effective in stimulating labor demand.

Our work is related to a growing literature examining the link between the labor market and the financial market in production economies, both in the cross-section and in the time series.¹

Chen and Zhang (2011) document that variables that predict risk premiums also forecast aggregate employment growth but only find a mild predictive power of employment growth for stock market returns. As we will discuss in detail in Section 3.1, our return predictability results are stronger because we focus on the hiring rate of publicly traded firms only, whereas Chen and Zhang (2011) look at employment measures that include both publicly and privately traded firms.

Hall (2017) shows that the variation in discount rates helps explain the excess volatility in unemployment in a labor search model.² Following Merz and Yashiv (2007), Yashiv (2016) finds that the variation in future hiring (investment) returns, instead of future cash flows, drives most of the variation in labor (and capital) valuations. Liu (2019) finds a result similar to Yashiv (2016) using different empirical measures of labor valuations. Our paper complements these studies and also differs in an important dimension: We focus on the determinants of aggregate hiring rate through a variance decomposition both in the data and in the model, providing new insights on the different roles of discount rates, short-term and long-term cash flows in driving firms’ hiring decisions.

Our theoretical approach is related to Belo et al. (2014) (henceforth BLB) who also consider a dynamic model of the firm in which labor is costly to adjust. We depart from BLB in three important ways. First, BLB show that labor adjustment costs are important to account for the cross-sectional return predictability from firms’ hiring rates and the failure of the CAPM in asset pricing tests, while we focus on how labor adjustment costs affect the discount rate and dividend payout policies in determining hiring decisions. Second, empirically, BLB explore return predictability in the cross-section, whereas we explore both return and cash flow predictability in the time series to understand the fluctuations in the aggregate hiring rate through a variance decomposition. Third, BLB, as typically done in this literature, calibrates the model, while we estimate the model parameters, including the stochastic discount factor and labor adjustment costs, through SMM, which allows for a thorough analysis of the role of each model component in driving the quantitative results.

Lastly, this paper is also related to the large return and cash flow predictability literature in finance.³ We differ from this literature in that the goal of the predictability regressions is to understand firms’ labor hiring decisions, in particular, how discount rate, short-term and long-term cash flows effects drive fluctuations in hiring rates.

1. Model

In this section, we provide the theoretical framework to guide the empirical analysis. To establish the theoretical link between hiring, discount rates, and expected cash flows, we consider a simple neoclassical dynamic model of the firm with labor market frictions.

1.1 Model setup

Firms in the economy produce a homogeneous good. Here, we focus on the optimal production decision problem of a single firm in the economy. The firm is competitive and takes the price of the good, which is normalized to one, and the stochastic discount factor |$M$|⁠, as given.

1.2 Firm maximization problem

We refer to the cash flows |$D_{t}$| in Equation (5) simply as dividends. Negative dividends (i.e., |$D_{t}<0$|⁠) are interpreted as proceeds raised by the firm from equity holders.

This result is a direct implication of the standard Hayashi (1982) result applied here to labor, instead of physical capital (in the Internet Appendix we provide a formal proof of this result). Thus, the value of the firm is given by the labor’s marginal |$q$| (the shadow price of the labor force) times the size of the labor force.

1.3 Relation between hiring, discount rates, and cash flows

Equation (13) shows that, in the presence of labor adjustment costs, labor hiring, similar to an investment, is a forward-looking decision. All else equal, a firm hires more workers when discount rates are lower, and/or expected long- or short-term cash flows are higher. This link is the labor-analog of the findings in Shiller (1981) and Campbell and Shiller (1988) on the determinants of contemporaneous stock prices and price-to-dividend ratios, and implies that future stock returns, and/or short- and long-term cash flows, should be predictable from a firm’s current labor hiring rate.

The exact sign of the predictability relationship between a firm’s hiring rate and future stock returns or between a firm’s hiring rate and long- or short-term cash flows, is an empirical question, however. The sign cannot be determined ex ante from Equation (13) because it depends on the relative strength of the opposing discount rate and expected cash flow forces, which are likely to correlated in the data (e.g., driven by common aggregate shocks, such as aggregate TFP shocks). Hence, to quantify the relative importance of the discount rate and short- and long-term cash flow forces for explaining the variation of the hiring rate that we observe in the data, in the next subsection, we follow Campbell and Shiller (1988) (on price-to-dividend ratio) and show how to map the hiring rate predictability regressions into a variance decomposition of the firm’s hiring rate.

1.4 Empirical implications

Equation (13) motivates our empirical analysis. According to this equation, a firms’ hiring rate contains information about the firm’s future stock returns |$\{r_{t+j}\}_{j=1}^{\infty }$|⁠, future short-term cash flows (⁠|$ dl_{t+1} $|⁠), and future long-term cash flows, |$\{\Delta d_{t+j}\}_{j=2}^{\infty }$|⁠. For tractability, we apply the model to aggregate-level data. According to this interpretation, Equation (13) provides a natural link between the aggregate hiring rate with both aggregate stock returns and aggregate dividends in the economy.⁵

1.4.1 Discount rate and cash flow predictability

1.4.2 Hiring rate variance decomposition

To provide an economic interpretation of the predictability regressions, we can rearrange Equation (13) and map the univariate predictability results into a variance decomposition of the firm’s hiring rate time-series variation.

The left-hand side of Equation (16) is the full time-series variation of the hiring rates. The three terms on the right-hand side of Equation (16) represent the fraction of the variation in the hiring rate that is explained by the variation in discount rates (future stock returns), by variation in future long-term (as captured by cumulated future dividend growth starting in year 2 onward) cash flows, and short-term (as captured by next period dividend-to-labor ratio) cash flows, respectively.

We will examine this decomposition in the empirical Section 3 below.

2. Empirical Procedures

This section describes the empirical specifications and the data used in the empirical analysis.

2.1 Empirical specifications

To examine the link between aggregate hiring, discount rates, and cash flows, we use standard short- and long-horizon predictive regressions described in Equation (14), up to the |$N=$| 5-year horizon. We conduct both in-sample (IS) and out-of-sample (OOS) tests. In IS tests, we report the regression |$R^{2}$|⁠, the regression slope coefficients at the different horizons, and adjust standard errors according to Newey and West’s ( 1987) procedure. For OOS tests, we use the first half of the sample as the starting training period, which is expanded forward. OOS |$ R^{2} $| are calculated relative to historical mean forecasts. A negative out-of-sample |$R^{2}$| means that the out-of-sample errors are larger than the errors obtained using the historical mean of the predicted variable as the forecast estimate. To compute the statistical significance of the OOS performance, we calculate the New Encompassing OOS test statistic from Clark and McCracken (2001), following the construction methodology described in Kelly and Pruitt (2013).

2.2 Accounting and financial data

Our main variables of interest are the aggregate hiring rate, stock market return, dividend growth, and dividend-to-labor ratio.

To construct the aggregate hiring rate, we use accounting information from the CRSP and Compustat Merged Annual Industrial Files. We include firms with common shares (shrcd|$=10$| and |$11$|⁠), that are traded on NYSE, AMEX, and NASDAQ (exchcd=|$1,2,$| and |$3$|⁠), and with nonmissing contemporaneous or lagged Compustat variable employment EMP (i.e., nonmissing hiring rate information). We include firms whose primary standard industry classification (SIC) is between 4900 and 4999 (utility firms) or between 6000 and 6999 (financial firms). We provide robustness checks for excluding financial and utility firms in the Internet Appendix.

Aggregate stock market excess returns are given by the Center for Research in Security Prices (CRSP) value-weighted excess return from Kenneth French’s website. To compute the level of returns, we add the risk-free rate (1-month Treasury-bill rate also from Kenneth French’s website). Aggregate dividends are given by the CRSP dividends, including both cash dividends and share repurchases.⁹ Stock returns (in level) and dividend growth are constructed in logarithm and deflated by inflation as measured by the Consumer Price Index for All Urban Consumers (CPIAUCSL downloaded from FRED of St. Louis Fed). Annual real returns and dividend growth are accumulated monthly real returns and dividend growth from January to December. Finally, the annual dividend-to-labor ratio is measured as annual real dividend over aggregate employment in that year. The annual dividend-to-price ratio is measured as the ratio of annual dividend to December price.

2.3 Descriptive statistics

Table 1 shows the summary statistics of the main variables used in the empirical tests. Aggregate gross hiring rate (in log) has a mean of |$-1.25$| and volatility of |$10\%$|⁠. It is moderately persistent with autocorrelation of |$0.49$| and is positively correlated with the price-to-dividend ratio, with a correlation of 0.31.

Figure 1 shows the time-series plots for aggregate gross hiring rate, next 5-year stock market return, next 5-year real dividend growth, next-year dividend-to-labor ratio, and price-to-dividend ratio. We will study these links formally in the predictability regressions in the next section, but these plots are informative about the characteristics of these variables. All series are scaled to have zero mean and standard deviation of one. Shaded areas are NBER-indicated recessions. Aggregate gross hiring has a negative correlation with the next 5-year stock market return of |$-0.44$|⁠, a negative correlation to the next 5-year aggregate dividend growth of |$-0.50 $|⁠, a positive correlation to next-year dividend-to-labor ratio of |$0.31 $|⁠, and a positive correlation to the price-to-dividend ratio of |$0.18$|⁠. Both hiring and price-to-dividend ratio are procyclical, while the expected stock market return (as proxied by the next 5-year cumulated stock market return) is countercyclical.

Figure 1

Time-series plots 

This figure shows the annual time-series plots of the aggregate gross hiring rate (solid lines in the plots), the aggregate stock market returns over the next 5 years (dashed line in the top-left plot), the aggregate dividend growth over the next 5 years (dashed line in the top-right plot), the 1-year-ahead real aggregate dividend-to-labor ratio (dashed line in the bottom-left plot), and the 1-year-ahead price-to-dividend ratio (dashed line in the bottom-right plot). All series are expressed in logs and normalized to have a mean of zero and a standard deviation of one over the sample period presented. The sample covers the period 1963 to 2019. Shaded vertical bars represent recessions as reported by the National Bureau of Economic Research.

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3. Empirical Findings

In this section, we document our main findings on the link between aggregate hiring, discount rates, and cash flows in the time series.

3.1 Return predictability

Table 2, panel A, shows the results from the predictive regressions of aggregate stock market excess returns on the aggregate gross hiring rate of publicly traded firms in the U.S. economy. The table shows that the aggregate hiring rate predicts the aggregate stock market excess return with a negative slope across all horizons. Although economically and statistically significant at most investment horizons, the predictability is particularly strong at longer horizons. For example, at the 5-year horizon, the slope coefficient is |$ -1.46$|⁠, which is statistically significant at the |$1\%$| level, and the IS|$\ R^{2}$| is approximately |$22\%$|⁠. The OOS |$R^{2}$| at the 5-year horizon is also quite high, about |$24\%$|⁠, and significantly outperforms the historical mean according to the Clark and McCracken (2001) test statistic.

Equation (13) in the model links the hiring rate to the level of returns, not to excess returns. Hence, we need the slope coefficient of the predictability regression in levels to perform the aggregate hiring rate variance decomposition. Table 2, panel B, shows that the results are very similar when the level of real stock returns is used instead of excess returns (the hiring rate does not predict the real risk-free rate, not tabulated).

Interestingly, the results reported here contrast with the findings in Chen and Zhang (2011), who document only a mild predictive power of employment growth for stock market returns. The main difference in the analysis is that Chen and Zhang (2011) use employment data from Current Employment Statistics (CES) at BLS, which includes the employment of all firms in the economy, that is, publicly traded and privately held firms. In the Internet Appendix, we report the updated results from Chen and Zhang (2011) for our sample period from 1963 to 2019. At the 5-year horizon, the IS|$\ R^{2}$| is about half, 8.26|$\%$|⁠, of the |$R^{2}$| we obtain when we use the hiring rate for publicly traded firms only. In addition, the total hiring rate has relatively low OOS predictability. The OOS |$R^{2}$| is 9.39|$\%$|⁠, versus 24|$\%$| using our hiring rate measure, and the forecast does not significantly outperform the historical mean according to the Clark and McCracken (2001) test statistic.

Why does the inclusion of privately traded firms in Chen and Zhang (2011) negatively affects the return predictability results using aggregate employment growth? While we cannot provide a definitive answer, one reason might be mechanical. By construction, the aggregate stock market is composed of publicly traded firms only, so our hiring rate that only includes publicly traded firms is better aligned with the predicted variable. Another reason could be due to the existence of frictions that affect private and publicly traded firms, and hence their hiring behavior, differently. For example, financial constraints might be more severe for private firms, which might impede the response of private hiring to changes in aggregate discount rates. A full understanding of this effect is beyond the scope of this paper but is an interesting research question for future research.

Taken together, the results reported here show that hiring of publicly traded firms and aggregate discount rates (future returns) are negatively related.

3.2 Cash flow predictability

We now examine the link between hiring rates and future cash flows. Panel A of Table 3 shows that the aggregate hiring rate predicts aggregate dividend growth with a negative slope across all horizons, and especially at longer-horizons. At the 5-year horizon, the aggregate hiring rate slope coefficient is |$-1.1$| and statistically different from zero at the |$1\%$| level, and with an IS|$\ R^{2}$| of about 20|$\%$|⁠. The OOS|$\ R^{2}$| is about |$17\%$| and significantly outperforms the historical mean according to the Clark and McCracken (2001) test statistic.

We also predict dividend growth starting in the second year (⁠|$j=2$|⁠), to be consistent with Equation (13) in the model. Panel B of Table 3 shows that the results are broadly similar to those reported in panel A.

Finally, panel C shows that the hiring rate predicts future next period dividend-labor ratio with a positive slope and an IS |$R^{2}$| of |$15.44\%$|⁠. That is, hiring and aggregate short-term cash flows are positively related. The OOS|$\ R^{2}$| is, however, quite low, and the forecast does not beat the simple historical mean according to the Clark and McCracken (2001) test statistic. This result is not surprising given the time-series behavior of the dividend-to-labor ratio reported in the left panel in Figure 1. While the dividend-to-labor ratio appears stationary in the full sample, it exhibits a clear downward trend in the first two decades of the sample. This downward trend has a strong impact on the out-of-sample results because the first half of the sample is the starting training sample. In light of this evidence, the full IS|$\ R^{2}$| is likely to be more relevant for detecting the link between hiring and short-term cash flows.

The negative cash flow slope coefficients shown in panel B in Table 3 (but not in panel C) might seem to contradict the theoretical relation presented in Equation (13) which shows that, all else equal, higher future cash flows should be associated with more hiring today. As noted, this negative sign does not contradict the theory because expected cash flows and expected stock returns are likely to be correlated in practice, hence the empirical slope here depends on the relative magnitude of the opposing discount rate and cash flow forces in the data. Hence, the sign of these predictability slopes provides additional moments that any valid candidate model should be able to match. Accordingly, in the quantitative model section below, where we solve endogenously for the optimal hiring rate, discount rates and cash flows, we examine whether the model can replicate the empirical patterns reported here (and what features of the model are important to replicate the results).

Taken together, the results reported here show that hiring and long-term cash flows are negatively related, while hiring and short-term cash flows are positively related.

3.3 Hiring rate variance decomposition

We use the previous predictability results to quantify the relative importance of the different economic drivers of the aggregate hiring rate time-series variation through the lens of the predictive system of Equations 17 and implied variance decomposition given by Equation (18).

Following the analysis in Section 1.4, the three terms |$ -\beta _{r}^{lr}$|⁠, |$\beta _{d}^{lr}$|⁠, and |$\beta _{dl}$| in the variance decomposition given by Equation (18) are linked to the hiring rate slope coefficients in the predictability regressions reported in Table 2 (panel B) and Table 3 (panels B and C). In addition, we need the parameter |$\rho \equiv $||$\exp (\overline{pd} )/(1+\exp (\overline{pd})),$| which is |$0.96$| in our sample, and the persistence of the hiring rate parameter, as given by the slope coefficient in the last equation in the system of Equations 17. Estimating this equation, we find a slope coefficient of |$\beta _{hl}=0.49$| (the autocorrelation coefficient of aggregate hiring rate as reported in Table 1), with a |$p$|-value of |$.00$| and a regression |$R^{2}$| of |$24\%$| (not tabulated).

Table 4 reports the aggregate gross hiring rate variance decomposition. The first row of the table shows the raw decomposition coefficients, that is, |$-\beta _{r}^{lr}$|⁠, |$\beta _{d}^{lr}$|⁠, and |$\beta _{dl}$|⁠. The difference between one and the sum of the three coefficients is treated as a residual.¹⁰ In practice, the residual arises because of approximation and/or specification errors (e.g., the adjustment cost function might not be quadratic) or because of noise in the data. The second row of the table shows the scaled coefficients so that the three parts without the residual sum up to one. ¹¹

By construction, the signs of the coefficients for the (minus) returns and on long-term and short-term cash flows are consistent with those of the predictive regressions. The novel insight from Table 4 is a quantitative one. In terms of magnitude, changes in discount rates and short-term cash flows (next year dividend-to-labor ratio) are the main drivers of the time-series variation in the aggregate hiring rate. In particular, and perhaps surprisingly, the contribution of long-term expected cash flows (cumulated future dividend growth) for hiring rate variation is close to zero. Focusing on the second row, in which the coefficients are scaled, the fraction of the variation of hiring rates explained by discount rates is |$42.09\%$|⁠, the fraction explained by short term cash flows is |$61.46\%$|⁠, and the fraction explained by long-term cash flows is just |$-3.55\%$|⁠.

3.4 Robustness checks

We perform a series of additional empirical analyses to establish the robustness of the main findings. The Internet Appendix reports the full set of results, which we briefly summarize here.

First, we check how the assumption of a constant quit rate in the construction of the gross hiring rate affects our results. The time-varying quit rate data are from JOLTS, but it is only available from 2001 to 2019. We construct a time-varying quit rate for the early period from 1963 to 2000 using the OLS regression relationship between the quit rate and several macroeconomic variables (real gross domestic product [GDP] growth, unemployment rate, vacancy rate, and labor market tightness) in the recent period, and then extrapolating the regression backward. We perform the same set of empirical analysis using this broader measure of gross hiring rate with the time-varying quit rate. The hiring rate variance decomposition results are broadly consistent with those obtained using a constant quit rate, with a slight increase in the fraction explained by discount rates and a slight decrease in the fraction explained by short-term cash flows. We use the gross hiring rate with a constant quit rate as the baseline measure because it is cleaner, as it does not require any estimation (and avoids look-ahead bias).

We also use the aggregate gross hiring rate to run horse race predictions with other well-known return predictors in the literature. Although this analysis is outside the scope of the model (in this class of models, most return predictors should be highly–or even perfectly–correlated given the relatively low number of exogenous aggregate shocks, hence the multivariate predictability regressions are difficult to interpret), the results show that our gross hiring rate remains a significant predictor for the stock market excess returns when, closely following the analysis in Chen and Zhang (2011), we include the aggregate dividend-price ratio, the logarithm of consumption-to-wealth ratio (CAY) from Lettau and Ludvigson (2001), 3-month Treasury-bill rate (TB), term premium (TRM, the difference between the 10-year Treasury-bond yield and the 3-month Treasury-bill rate), and default premium (DEF, the difference between BAA- and AAA-rated corporate bond yields). The hiring rate predictability results are also robust to the inclusion of the aggregate physical capital investment rate.

In addition to the aggregate-level analysis, we also perform a variance decomposition of industry-level hiring rates, using the Fama and French 10 industry classification. We find that the negative relation between hiring and discount rates is pervasive across all industries. In addition, the main drivers of the hiring rate time-series variation across industries are discount rate and short-term expected cash flows, albeit with some variation across industries. In particular, consistent with the aggregate level analysis, the long-term expected cash flow component has essentially no contribution for the industry-level hiring rate variation.

We also investigate the role of aggregation on the results. Our model is specified at the firm-level, but the empirical analysis is at the aggregate level. We show that our empirical aggregate gross hiring rate is an employee-weighted average of the firm-level gross hiring rate. There is a wedge between this measure and the aggregate gross hiring rate assuming an aggregate firm. That is, our measure includes an aggregation error. In the Internet Appendix we show that the aggregation error is small and smooth over time, and hence it has a negligible impact on the results.

Finally, the empirical results also appear to be robust to other reasonable variations in the measurement of the variables and empirical procedures. For example, the return predictability results are very similar if we use the returns of the S&P 500 instead of the returns of all CRSP firms, or if the aggregate gross hiring rate is constructed excluding finance and utility firms. In addition, the return predictability results reported here change very little when we account for the lag of accounting information for hiring and allow for a 6-month lag by constructing an alternative annual real returns and dividend growth accumulated from July to June in the spirit of Fama and French, and several studies in the return predictability literature.

4. Quantitative Analysis

In this section, we estimate and calibrate the model parameters. We then create artificial data from the model and replicate the empirical procedure to study the model implications for the relationship between aggregate hiring, discount rates, and cash flows.

The quantitative analysis that we report here serves two purposes. First, as noted in Section 3.2, the model-implied sign of the relationship between aggregate hiring and future returns, or aggregate hiring and future cash flows given by Equation (13) cannot be determined ex ante. This is because, in the real data, the sign depends on the relative strength of the opposing discount rates and cash flows effects on the hiring rate, which are jointly endogenously determined, and likely to be correlated. Thus, by using simulated data and replicating the empirical procedures, we investigate the extent to which the empirical findings reported in the empirical section are consistent with the economic mechanisms in the model.

Second, this quantitative analysis allows us to analyze the role of key model ingredients, such as labor market frictions or time-varying price of risk, for the ability of the model to replicate the empirical findings (predictability results and variance decomposition), and hence understand the economic mechanisms driving the patterns observed in the real data.

4.1 Stochastic processes

We use the firm-level model (including the assumed functional forms) specified in Section 1 to generate a panel of firms similar to the Compustat sample, and we then aggregate the endogenous firm-level variables (hiring, stock returns, and dividends) as in the empirical section to replicate the empirical analyses. To proceed, we need to specify the stochastic processes. We assume that total factor productivity |$A_{t}$| contains an aggregate-level component, |$X_{t}$|⁠, and a firm-specific component, |$Z_{t},$| such that |$A_{t}=X_{t}Z_{t}$|⁠.

Notably, the SDF here is different from Zhang (2005) in that the model implied interest rates are constant, whereas the SDF in Zhang (2005) implies an overly volatile term premium. Our approach thus allows us to focus on risk premiums for cash flows as the main driver of the results in the model, as well as avoid parameter proliferation.

We use this equation to guide our discussion on the predictability of expected returns. In particular, |$\lambda _{t}$| is driven by the SDF and |$ \beta _{t}$| is driven the endogenous covariance between stock returns and the aggregate states, which is directly affected by labor adjustment costs.

4.2 Model estimation

We estimate almost all model parameters except the time-preference coefficient and the quit rate which can be easily calibrated from the data. The time-preference coefficient |$\beta$| is set to |$0.999345$| to match the annual average real risk-free rate of |$0.786\%$| from 1963 to 2019. The monthly labor quit rate, |$\delta $|⁠, is set to |$2.14\%$|⁠, which matches the average aggregate worker quit rate in the JOLTS sample from December |$2000$| to December |$2019$|⁠.

Instead of assuming a constant-returns-to-scale production function as in Section 1, we take the returns to scale parameter |$\alpha$| as a deep parameter of the model and estimate it in the data. We estimate this parameter, the adjustment cost parameter, the price of risk parameters in the stochastic discount factor, the persistence and volatility of aggregate productivity parameters, the wage function parameters, and the persistence and volatility of firm-specific productivity parameters. We define this set as |$\Theta =\left( \alpha,c_{H},\gamma _{0},\gamma _{1}, \rho_x, \sigma_x, \nu, w_1, \rho_z, \sigma_z\right).$|¹³ We solve the model at the monthly frequency. To make the aggregate moments in the model comparable to those in the data, we aggregate the simulated firm-level data from the model across firms and over time in the same way as in the real data.¹⁴

Naturally, the choice of target moments is important for the efficiency of the SMM estimator. In particular, moments that are informative about the underlying structural parameters should be included. Column 1 in Table 5 presents the targeted moments, which include the 1-year and 3-year prediction slopes for stock returns (⁠|$\beta_{r,1}$| and |$\beta_{r,3}$|⁠), the 1-year and 3-year prediction slopes for real dividend growth (⁠|$\beta_{d,1}$| and |$\beta_{d,3}$|⁠), the 1-year prediction slope for dividend-to-labor ratio (⁠|$\beta_{dl}$|⁠), the mean and volatility of market excess returns (⁠|$E(R_e)$| and |$SD(R_e)$|⁠), pooled standard deviations of cross-sectional demeaned net hiring rates (⁠|$SD\left(\log(L'/L)_{i,t}\right)$|⁠) and cross-sectional demeaned stock returns (⁠|$SD\left(R_{i,t}\right)$|⁠) from merged data set of CRSP and Compustat, and correlations of real dividend growth to both one- and three-lagged real output growth (⁠|$Corr\left(\log(Y_{t-1}/Y_{t-2}),\log(D_t/D_{t-1})\right)$| and |$Corr\left(\log(Y_{t-3}/Y_{t-4}),\log(D_t/D_{t-1})\right)$|⁠).¹⁵|$^,$|¹⁶

In general, the variations of the estimated parameter values affect all of the above asset pricing and real quantity moments but, to a first order, we find that the prediction slopes for returns, dividend growth, and dividend-to-labor ratio help mainly for identifying the returns to scale parameter |$\alpha$|⁠, the adjustment cost parameter |$c_{H}$|⁠, and the persistence and volatility of aggregate productivity parameters |$\rho_x$| and |$\sigma_x$|⁠; the asset pricing moments for returns help mainly for identifying the price of risk parameters |$\gamma _{0}$| and |$\gamma _{1}$| in the SDF; the correlations between dividend growth and output growth help mainly for identifying wage function parameters |$\nu$| and |$w_1$|⁠; and the pooled standard deviations of firm net hiring rates and stock returns help mainly for identifying the persistence and volatility of idiosyncratic productivity parameters |$\rho_z$| and |$\sigma_z$|⁠. In addition, the asset pricing moments also help for identifying |$\rho_x$| and |$\sigma_x$|⁠, and the pooled standard deviation of firm net hiring rates also help for identifying |$c_{H}$|⁠. Since the moments are in various categories, their standard errors vary significantly. To avoid that certain moments dominate the estimation, we use an identity matrix as the weighting matrix |$W$| in the SMM estimation. This approach also allows us to directly focus on economically interesting moments. (Optimal SMM uses linear combinations of the moments as target moments to improve efficiency, but this approach makes the interpretation of the model fit on each specific moment more difficult).

4.2.1 Parameter estimates

Table 6, column 2 presents the estimated parameters for the baseline model. The estimated returns to scale parameter is |$ \alpha =0.76$|⁠, while the estimated adjustment cost is |$c_{H}=20267$|⁠. This adjustment cost parameter may appear large, but the implied adjustment cost to the annual aggregate output ratio is on average |$1.09\%$|⁠, close to the low end of the estimated labor adjustment cost reported in Bloom (2009). The estimated parameters of the SDF are |$\gamma_{0}=2.93$| and |$\gamma_{1}=-16.70$|⁠. The estimated parameters of aggregate productivity are |$\rho_x=0.96$| and |$\sigma_x=0.05$|⁠. The estimated parameters of wage function are |$\nu=1.38$| and |$w_1=0.63$|⁠. The estimated parameters of idiosyncratic productivity are |$\rho_z=0.98$| and |$\sigma_x=0.21$|⁠.

4.2.2 Model fit

Table 5, column 2, reveals that the baseline model fits the data well (we examine the alternative model specification in Section 4.4 below). The model-implied prediction slopes for 1-year and 3-year returns, 1-year and 3-year dividend growth, and 1-year dividend-to-labor ratio are |$-0.22$|⁠, |$-0.57$|⁠, |$-0.05$|⁠, |$-0.79$|⁠, and |$1.01$|⁠, which are all close to the data. The model-implied equity premium and excess return volatility are |$6\%$| and |$20\%$|⁠, close to data moments |$7\%$| and |$17\%$|⁠. The model-implied cross-sectional standard deviations of firm-level net hiring rates and stock returns are |$16\%$| and |$51\%$|⁠, which also matches the data well. Finally, the model-implied correlations of real dividend growth to one- and three-lagged real output growth are |$0.29$| and |$-0.23$|⁠, matching the data well. Taken together, the model matches the target moments well and with economically reasonable parameter values.

4.3 Model-implied link between hiring, discount rates, and cash flows

We replicate the key predictive regressions and hiring rate variance decomposition reported in the empirical section using artificial data generated from the baseline model.

4.3.1 Return predictability

Table 7, panel B, shows that the estimated baseline model generates a stock return predictability pattern that is consistent with the data. The aggregate gross hiring rate negatively predicts future aggregate stock market returns from 1-year horizon to 5-year horizons. As in the data, the model-implied |$R^{2}$| increases with the predictability horizon, although the |$R^{2}$|s are somewhat higher than in the data. For example, at the 5-year horizon, the |$ R^{2}$| is |$29\%$| in the model and |$22\%$| in the data. The model-implied prediction slopes also increase (in absolute value) with the horizon, but are somewhat smaller than the data at the long 4-year and 5-year horizons. For example, at the 5-year horizon, the prediction slope is |$-0.65$| in the model and |$-1.46$| in the data.

4.3.2 Cash flow predictability

Table 7, panel B, shows that the baseline model also matches the cash flow predictability patterns in the data very well. Aggregate hiring negatively predicts aggregate dividend growth at all horizons. The model-implied |$R^{2}$|s and slopes are quantitatively close to those in the data. The model also predicts the next period dividend-to-labor ratio with a positive slope, although the |$R^{2}$| is somewhat higher than in the data.

4.3.3 Hiring rate variance decomposition

Table 8, second row (baseline model), reports the model-implied variance decomposition of aggregate gross hiring rates. The reported coefficients are scaled and sum up to one. The baseline model performs well in matching the aggregate hiring rate variance decomposition. As in the data, the main drivers of the variation in the aggregate hiring rate are discount rates and short-term cash-flows, about |$38\%$| and |$67\%$|⁠, respectively, with very little (and slightly negative) contribution from long-term cash flows, about |$-5\%$|⁠. Thus, as in the data, changes in discount rates and expected short-term cash flows drive most of the time-series variation in the aggregate hiring rate, with almost no contribution from changes in expected long-term cash flows.

4.4 Inspecting the mechanism

To understand the economic forces driving the overall good fit of the model, we study the policy functions and evaluate the quantitative performance of three alternative model specifications.

4.4.1 Policy functions

Figure 2 plots optimal hiring, expected return, and payout against labor (left) and aggregate productivity (right) in the baseline model. On optimal hiring policy (top-two panels), we see that firms hire more in good times (high aggregate productivity states) than in bad times; moreover, big firms hire more than small firms. On expected returns (middle-two panels), firms have lower expected returns in good times than bad times. The payout policy (bottom-two panels) contains two regions: payout region and equity issuance region, in which there is no payout. Conditional on aggregate productivity, payout increases with firm size: small firms issue, while big firms payout. In addition, firms increase payout when productivity increases. However, firms reduce payout to enter into issuance region when productivity further increases. This is because wage bills and adjustment costs outgrow output for firms, which also leads to a payout policy that is hump-shaped in productivity.

Figure 2

Policy functions 

This figure shows policy functions for hiring (⁠|$H$|⁠), expected return (⁠|$E(R)$|⁠), and payout plotted against the state variables labor (⁠|$L$|⁠) and total factor productivity (TFP, |$X$|⁠). Average |$X$| is mean TFP, and high (low) |$X$| indicates one grid higher (lower) than the average |$X$|⁠. Average |$L$| is labor at the stochastic steady state in simulation, and high (low) |$L$| indicates five grids higher (lower) than the average |$L$|⁠.

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The dynamics of firm’s optimal hiring, payout policies, and expected returns links the aggregate hiring rate to both future stock returns and cash flows, as documented in the data. When aggregate productivity is high, a significant fraction of firms hire, leading to an increase in aggregate labor used; in addition, expected returns are low due to low price of risk and low systematic risk loadings (betas). As a result, current hiring and expected returns (hence, future returns) are negatively correlated. High aggregate productivity states are also the times when many firms are in the payout region, as firms’ revenue is sufficient to cover wage payments and adjustment costs. As a result, current labor hiring and short-term cash flows are positively correlated. Because aggregate productivity is persistent, high aggregate productivity states are followed by high aggregate productivity states for a while. Over time, firms reduce dividend payout to enter into issuance region; this happens because wages and adjustment costs outgrow output, which causes dividend to decline over time, hence labor hiring negatively predicts future aggregate cash flow growth.

4.4.2 Performance of alternative model specifications

We also analyze the quantitative performance of the following three alternative model specifications:

• A model with frictionless labor (no labor adjustment cost, |$c_H=0$|⁠)

• A model with a constant price of risk (⁠|$\gamma _{1}=0$|⁠)

• A model with constant hours and wages (⁠|$S_t=40*52/12$| and |$W_t=1$|⁠)

These three specifications shut down key model features one at a time, thus allowing us to inspect the relative importance of each feature in the model. Different from the standard comparative static analysis (namely, changing one parameter at a time) that is done in this literature to inspect the model mechanism, we reestimate all the parameters in the restricted models by SMM, which is a time-consuming task. This reestimation approach allows the other nonrestricted model parameters to adjust, and hence allows us to evaluate more properly the quantitative importance of each model component in driving the results.

The model without labor adjustment cost performs significantly worse than the baseline model. Table 5, column 3, shows that the criterion function increases almost 60 times relative to the baseline model reported in column 2. For example, the implied hiring rate is too volatile, |$52\%$| here versus |$16.3\%$| in the baseline, and |$17\%$| in the data. Importantly, the return predictability slopes are too small, |$-$|0.02 here at the 1-year horizon versus |$-$|0.22 in the baseline, and |$-$|0.33 in the data, which show the return predictability slopes, and hence asset prices, are informative about the size of labor adjustment costs (more generally, labor market frictions) in the economy. Some of the dividend predictability slopes have the wrong sign, 0.07 here at the 1-year horizon versus |$-$|0.57 in the baseline and |$-$|0.64 in the data (see also Table 7, panel C). As a result, Table 8 (third row labeled No adj cost) shows that, the (scaled) contributions of discount rates and long-run cash flow for the hiring rate variance decomposition are completely off relative to the baseline model and the data.¹⁷ Clearly, labor adjustment costs are important for the model to simultaneously match the quantity moments (e.g., hiring rate volatility) and the asset pricing moments (e.g., return predictability) in the data.

The model with a constant price of risk also performs worse than the baseline model, although not as poorly as the model without labor adjustment costs. Table 5, column 4, shows that the criterion function increases about 15 times relative to the baseline model reported in column 2. For example, the return predictability slopes are too small, 0 here at the 1-year horizon versus |$-$|0.22 in the baseline model, and |$-$|0.33 in the data. Interestingly, the prediction slopes for dividend growth and dividend-to-labor ratio matches the data about as well as in the baseline. Together with the previous analysis of the no labor adjustment cost model, this result reveals that, in the model, the link between dividend (cash flow) dynamics and hiring are mostly determined by the labor adjustment cost friction, but not so much by time-varying risk. Given the estimated predictability slopes, Table 8 (fourth row labeled Constant Price of Risk), shows that, in this model, the variation of the hiring rate that is explained by variation in discount rates is too small, 0.05|$\%$| here versus 38|$\%$| in the baseline model, and 42|$\%$| in the data, and the variation in the hiring rate that is explained by short-term expected cash flows is too high, |$109\%$| here versus |$67\%$| in the baseline model and |$61\%$| in the data (the variation explained by long-term expected cash flows is very small, similar to the baseline model and the data). Thus, without time-varying risk, the variability of the hiring rate in the model is almost fully determined by variation in short-term expected cash flows, with no role for variation in discount rates, in contrast with the data.

Turning to the analysis of the model with constant hours and wages, Table 5, column 5, shows that the criterion function increases about five times relative to the baseline model reported in column 2. Hence, this specification performs worse than the baseline, but not as poorly as the previous two alternative specifications. For example, the excess return volatility is too small, |$10\%$| here versus |$20\%$| in the baseline, and |$16.5\%$| in the data, and so is the hiring rate volatility, |$11.7\%$| here versus |$16.3\%$| in the baseline, and |$16.9\%$| in the data. Also, Table 7, panel E, shows that the predictability |$R^2$|s for dividend growth at all horizons are smaller than in the baseline model and in the data. Table 8 (fifth row, labeled Constant Hours), shows that, relative to the baseline model, variation in discount rates explains a lower fraction of the variation in hiring rate, 31|$\%$| here versus 38|$\%$| in the baseline model, and 42|$\%$| in the data, that variation in long-term expected cash flows contributes positively to the variation in the hiring rate, |$3\%$| here versus |$-5\%$| in the baseline model, and |$-4\%$| in the data, and that the contribution of the variation in short-term expected cash flows to explain the variation in the hiring rate is about the same as the baseline model, |$67\%$| here versus |$67\%$| in the baseline model, and |$61\%$| in the data. Thus, allowing for endogenous hours (and hence wages), helps improve the quantitative fit of the model, but it does not have a first-order effect on the model qualitative results.