Are Labor Intensive Assets Riskier?

Transcription

1 Are Labor Intensive Assets Riskier? Preliminary and incomplete draft All comments are welcome Miguel Palacios November 18, 2011 Abstract An empirical analysis suggests that labor intensive firms are riskier, yet they do not seem proportionally more volatile. This result is inconsistent with operational leverage explaining the riskiness of labor intensive firms, since an increase in beta would be associated with a proportional increase in volatility. In this paper I document the evidence described above and develop a simple production model in which changes in labor intensity are associated with changes in beta and disproportionally smaller changes in volatility. The empirical results are not only statistically significant at the 1% level, they are also economically significant. Regressions of an industry s beta on the industry s labor intensity suggests that a 10% increase in labor intensity is associated with 4% - 6% increase in beta. I also document that increases in labor intensity over time are associated with increases in the riskiness of industries over time. The empirical analysis uses aggregate compensation and production information by industry published in the National Income and Product Accounts tables between 1947 and 1997 and COMPUSTAT data on wages between 1950 and The financial support of The Dean Witter Foundation and the White Foundation is gratefully acknowledged. I would like to thank Jonathan Berk, Pierre Collin-Dufrense, Greg Duffee, Thomas Gilbert and Adam Szeidl for insightful conversations and suggestions. Any errors remain my own. Owen Graduate School of Management, Vanderbilt University. miguel.palacios@owen.vanderbilt.edu. Phone: +1(615) Address: st Avenue South, Nashville, TN, (USA). 1

2 1 Introduction Wages are the largest single item affecting a firm s cash flows. Employee compensation is about 60% of GDP in the United States, and us such it is the single largest expense in the economy. Labor is mobile, seeking higher wages were these are available. As a result, we can expect that the wages firms pay move systematically, making them an important source of risk. But, what is the direction of the exposure to wages and who does it affect most? Wages have been viewed as a source of operating leverage and thus the conclusion has been that firms with a higher ratio of wages to production should be riskier. The operating leverage argument is based on the idea that wages are sluggish, so that in good times firm owners get an extra dividend in the form of the difference between labor s marginal product and the wage. Thus, in good times dividends grow faster than wages. On the other hand, in bad times firms owners end up absorbing the difference between labor s decreases marginal product and the wage. As a result, in bad times, dividends fall faster than wages. In the presence of sluggish wages, firms with high ratios of wages to production will be riskier. Several theoretical models (Harris and Holmstrom (1982), Marcus (1984), Berk, Stanton and Zechner (2006)) suggest that, in the absence of markets for trading future claims to labor income, firms can act as the institution through which a risk exchange between employers and employees takes place. Under the assumption that investors are less risk averse than employees, it follows that wages will have some form of insurance. 1 In these models wages end up being a form of operational leverage. High operational leverage then leads to higher betas. Yet, operational leverage also has implications for an asset s volatility. The link between a firm s beta and operational leverage implies that volatility should also increase with operational leverage. The empirical evidence I present in this paper fails to find a strong relationship between volatility and labor intensity, whereas it finds an economically significant relationship between beta and labor intensity. Not finding a relationship between 1 Both idiosyncratic and systematic. 2

3 volatility and labor intensity suggests that operational leverage does not alone explain the impact that labor intensity has on a firm s risk. The operational leverage hypothesis certainly was never the only explanation for the way in which wages affect beta. We routinely observe firms hiring and firing employees, with wages fluctuating permanently, far from the debt-like nature that wages would show if they were insurance. Furthermore, even if wages were a form of insurance, firms continually need to make decisions involving estimates of future uncertain wages. A model that incorporates this uncertainty explicitly will go beyond a model that ignores such variations. Finally, a growing body of work suggests that human capital the present value of labor income is less risky than equity. 1 For instance, Palacios (2011) shows that this result can be obtained in a standard general equilibrium model without frictions. I will refer to this characteristic of human capital as the systematic safety of human capital. To understand how the systematic safety of human capital affects the riskiness of particular firms, consider the following. Under the standard assumption of decreasing returns to scale in capital and wage rates proportional to capital s productivity, a positive shock to capital leads to a fall in its productivity, and as a result, to a fall in the wage rate per unit of capital. The impact that such a shock has on the production of a small firm depends on the characteristics of the own firm. In particular, if a firm is highly labor intensive, the firm s managers will spot an opportunity and hire aggresively, boosting the firm s output and the firm s dividends. The dividend growth experienced by this firm takes place, however, at the same time that the representative agent s marginal utility is low capital received a positive shock making the firm risky. The case of a capital intensive firm is the opposite. Changes in the wage rate per unit of capital does not make too much a difference, since wages make up a small fraction of the firm s production. Managers in the capital intensive firm are insensitive to variations in wages in the market and dividends end up being insensitive as well. Even though the capital intensive firm s dividends might go up slightly when the aggregate wage per unit of capital falls, the effect is not as important 1 For example, Lustig, Van Nieuwerburgh and Verdelhan (2010) 3

4 as that for the labor intensive firm. As a result, labor intensive firms will be riskier than capital intensive ones. Even though a positive correlation exists between labor intensity and beta, one cannot conclude that high labor intensity causes high betas. While the evidence presented here is highly suggestive, it is possible that some other ommitted variable is responsible for my findings. However, the results on volatility show that the most likely omitted variable, one related to operating leverage, is not likely driving the results. As long as no simple alternative explanation emerges, the evidence provided here does point to a causal relationship between labor intensity and beta. The empirical analysis uses data combining portfolio betas and labor intensity of different industries. First, I use data from the NIPA tables to find the average labor intensity of different industries. The analysis reveals a wide dispersion of labor intensity between industries. This dispersion provides power to a regression using labor intensity as the independent variable and the industry beta as the dependent variable. The results of the regression imply that labor intensity is positively related to beta and that labor intensity can explain 20% of the variation in beta. On a second analysis, I calculate annual betas using daily stock returns, and annual labor intensity using data from COMPUSTAT on wages and revenues. The second analysis results in panel regressions where, besides studying the relationship between labor intensity and beta between industries, one can study the relationship between labor intensity and beta over time. I show this intuition in a partial equilibrium setting in which a firm with constant elasticity of substitution between labor and capital optimally reacts to economy-wide changes in wages. A key ingredient of the production function is that the elasticity of substitution between labor and capital is less than one, unlike the frequently used Cobb-Douglas production function where the elasticity is equal to one. When the elasticity of substitution equals one, the labor intensity of the firm is invariant to changes in wages. The empirical evidence presented here shows that this is not the case, and other work already stresses a value below unity for this elasticity. In the model labor intensity changes over time, and 4

5 this change implies that the riskiness of the firm, as measured by beta, and its volatility do not move in lockstep. The rest of the paper is structured as follows: section 2 discusses related literature; section 3 presents a simple model in which labor intensity changes over time, and derives the implications for a firm s returns, beta, and volatility. Section 4 describes the empirical analysis and results, section 5 provides additional discussion and section 6 concludes. 2 Related Literature The impact of wages on asset pricing and portfolio choice has received increasing attention in recent years. Most of the work has focused on analyzing the impact that the presence of exogenous labor income would have in equilibrium prices and portfolio choice. Since Mayers (1972), who extended the CAPM to account for idiosyncratic labor income, the approach followed by researchers has been to take assets risk and agent s wages as exogenous, and then conclude on the effect that wages have on the agent s demand for risky assets, and thus asset prices. Models that continued to build on this tradition, with important improvements such as intertemporal analysis, cointegrated movements of the relevant variables, heterogeneous agents with idiosyncratic income, and the choice of leisure (Bodie et al (1992), Koo (1998), Viceira (2001), Santos and Veronesi (2004 and 2006), Benzoni, Collin-Dufresne and Goldstein (2004), Constantinides and Duffie (1996)) all specify exogenously the wage process. With the exception of Mayers (1972) who was interested in the impact of labor income on the cross-section of asset returns, posterior work taking into account labor income has focused on settings with only one risky asset to analyze the equity premium or an individual s portfolio allocation between a risky and a safe asset. On the cross-section of asset returns and wages, the starting point is Mayers (1972). His model predicted that the betas predicted by the CAPM would be different than those obtained including labor income. However, Fama and Schwert (1977) showed that the im- 5

6 pact predicted by the model was negligible. In contrast, the CAPM holds (by assumption) in the model I present here, and the empirical analysis suggest that labor intensity explains a significant fraction of variation in an asset s beta. Gourio (2011) is closely related to this paper, though he stresses operational leverage as the mechanism through which higher labor intensive firms end up being riskier. As I explain above, operational leverage seems to not explain all the impact that labor intensity has on firms since volatility does not seem to be as sensitive to labor intensity as a firm s risk. The most important variable that emerges from the model is labor intensity, i.e., the fraction of production that is paid to wages. This variable is positively correlated, and conceptually similar, to Santos and Veronesi s (2006) ratio of labor income to consumption and Lettau and Ludvigson s (2001) cay. These authors models, and their empirical tests, find that their related aggregate variables can explain some of the cross-section of asset returns. The model here uses industry-level information to calculate the relevant labor income-related variable for each industry rather than an aggregate factor. 3 Model The economic setting is a continuous-time partial equilibrium model in which firms take their capital, wages, the stochastic discount factor, and production function as given. Managers maximize the value of the firm by choosing the amount of labor involved in production at every instant. The dynamics of dividends, as well as the equilbirium price and expected return on a claim of the firm s dividends can be determined as a function of the manager s hiring decision. Once the model has been solved one can relate changes in expected returns and volatility to changes in labor intensity. 6

7 3.1 Aggregate dynamics I assume a frictionless competitive economy with complete markets. Denote by (Ω, I, P) a fixed complete probability state, and the stochastic process (B t ) t 0, a standard 2-dimensional Brownian motion with respect to the filtration (F t ). The first element of the Brownian motion will be denoted by db Z and the second by db y. The correlation between the shocks is ϕ Z,y. The first component of the brownian motion captures changes to a firm s productivity, whereas the second one contains shocks to the ratio of a firm s productivity and aggregate wages. I model the dynamics of the stochastic discount factor as being perfectly negatiely correlated to changes in the ratio of wages to productivity. I make this assumption for simplicity, but it can easily be relaxed to obtain stronger results. Empirically, wage growth is highly correlated with consumption growth, so this assumption would be consistent with the cannonical model. The dynamics of the stochastic discount factor in this economy are: dλ t Λ t = rdt σ λ db y (1) where λ t is the stochastic discount factor, r is the risk-free rate, and σ λ is the volatility of the stochastic discount factor. 3.2 Small firm s dynamics and value I focus attention now on a small firm that observes aggregate wages and the stochastic discount factor, and uses this information to optimally choose the labor it hires. The small firm s capital is fixed and normalized to 1 and all production net of wages is given back to shareholders as dividends. The instantaneous production flow results from a Constant Elasticity of Substitution (CES) production function in capital and labor. Concretely, F (L t, Z t ) is given by: F (L t, Z t ) = Z t ((1 α) + αl ρ t ) 1 ρ, (2) 7

8 where Z t is the firm specific total factor productivity, α measures the relative importance of labor, and 1 1 ρ is the elasticity of substitution between capital and labor, and L t is the amount of labor employed by the firm. Note that the capital stock is fixed (to one) whereas both productivity and labor change over time. Importantly for the purposes of the model, the firm s labor intensity, defined as the ratio of wages to production, will vary depending on the stte of the economy. As a result, optimal reaction to changes in wages will cause the share of production going to capital and labor to change over time. An exception to the previous statement is the case when ρ = 0, in which case the production function collapses into the well known Cobb-Douglas production function. In that case, labor intensity is constant over time and determined by the parameter α. The CES production function imposes some restrictions on the process of the ratio of wages to productivity. In particular, under some parameters, if the ratio of wages to productivity is small enough, the manager will want to hire an infinite amount of workers. This situation is clearly inconsistent with the partial equilibrium model and I address it by reducing the volatility of the ratio wages to productivity as the ratio becomes small. Such an assumption is consistent with the behavior of the ratio of wages to productivity in a general equilibrium model in which the small firm grows to become the only firm in the economy. As a small firm, wages are determined mostly by productivity shocks to the rest of the economy. As a large firm, however, wages are mostly determined by the firm s own productivity shocks, reducing the volatility of the ratio of wages to productivity. Thus, I model the dynamics of the ratio of aggregate wages to productivity y t (k, ) as: dy t = µ y dt + y t kdb y (3) The drift of y t does not change significantly the results of the model, so I choose µ y = 0 as a benchmark, corresponding to a firm whose productivity grows in expectation at the same rate of the economy. I choose k in the diffusion term so that the volatility of the ratio of wages to productivity is 0 when the manager would like to hire all the working population 8

9 in the economy (normalizing the population to 1). This assumption implies that the firm can potentially grow to the point where it is the only employer in the economy, and when this happens, no other competitor arises again. The dynamics of the firm s specific productivity is exogenous and assumed to be a geometric brownian motion. Thus, dz i,t = Z i,t µ Z dt + Z t σ Z db Z (4) The shocks to Z T are correlated with the shocks to relative wages y t, with the correlation equal to ϕ Z,y. This correlation parameter captures the relationship between the firm s productivity, wages, and the stochastic discount factor. When ϕ Z,y > 0, the firm behaves procyclically, with productivity increasing in good times, more than the increase in wages associated with a boom. This is plausibly the most relevant case, and therefore in the numerical calibrations I assume this correlation to be positive. Consider now the manager s maximization problem. Taking the capital stock, the ratio of wages to productivity y t, the stochastic discount factor λ t as given, the manager chooses labor to maximize the value of the firm. The manager s problem therefore is: max {L τ } t E t [ 0 ] λ τ (F (Z τ, L τ ) Z τ y τ L τ )dτ (5) Using the first order condition implied by equations (2) and (5), the manager s optimal labor demand is: ) ρ (( y 1 ρ α α L(y t ) = 1 α ) 1 ρ (6) The optimal demand for labor is not well defined, or implies a demand for labor larger than the one available in the economy, for all ratios of wages to productivity y t. In particular, 9

10 the demand for labor will be equal to one when: ( y α) ρ 1 ρ α = 1 α, (7) so depending on ρ demand can be higher than one. The dynamics of y t discussed before are defined so as to avoid this problem. By choosing k = α the demand for labor increases as wages fall relative to the firm s productivity, but will exceed the population of the economy. Once the manager chooses the optimal amount of labor, the instantaneous dividend payment resulting from substituting labor from equation (6) in the production function is: d t = Z t ((1 α) + αl ρ t ) 1 ρ (1 ψ(lt )), (8) where ψ(l t ) Lρ t α 1 α+αl ρ t is the fraction of total output paid to labor. ψ(.) is the function for labor intensity of the firm. Unlike the standard Cobb-Douglas production model, labor intensity will change over time, driven by changes in the relative value of wages to the firm s productivity. Whether a firm becomes more or less labor intensive as the ratio of wages to productivity changes depends on the sign of ρ. When labor and capital are substitutes (ρ > 0), labor intensity increases when wages grow relative to the firm s productivity. The opposite is true when labor and capital are complements (ρ < 0). The standard Cobb-Douglas case corresponds to labor intensity being invariant with respect to changes in the value of relative wages. After deriving the dividend flow generated by the firm we can find the value of the firm. The following proposition gives the result. Proposition 1 Assuming the function v(y t ) exists, is continuous and twice-differentiable in the interval y (α, ), then the value of equity of the firm is given by V (y t, z t ) = z t v(y t ), where v(y t ) solves the following: 0 = (1 α + αl(y t ) ρ ) 1 ρ (1 ψ(yt )) 10

11 v(y t )(r µ Z + σ λ σ Z ϕ Z,y ) + v (z t )(yµ y + y k( σ λ σ y + σ y σ Z ϕ Z,y ) + (9) v (z t )(y k) σ2 y 2, with boundary conditions equal to: v(α) = v(h) = 1 r µ Z + σ λ σ Z ϕ Z,y (10) (1 α) 1 ρ r µ Z + σ λ σ Z ϕ Z,y α 1 ρ if ρ < 0 h = if ρ 0 The boundary conditions in proposition (1) follow from the two extreme cases in which managers hire all the population (L(y) = 1) or when the demand for labor is zero (L(y) = 0). The dynamics of y t are such that when y t = α, there is no further change in y and the firm behaves as the only firm in the economy thereafter, employing all of the economy s population. In that case, given the dynamics of Z t and λ t, the value of the firm is that of one with a constant discount rate and growth in which the beginning dividend is given by the profits of a firm with labor of one. When y t = h, the opposite situation arises, as the manager does not want to hire any labor. In this case the value of the firm is also that of a firm with a constant return and growth with an initial dividend equal to the profits of a firm that hires no labor. The expected return of a claim to the firm s dividends is only a function of v(y t ) and the parameters of the model. The following corollary delivers the result: Corollary 1 The excess return of the firm s equity, r e, is given by: r e,t r f,t = σ λ σ Z ϕ Z,y + y kσ λ σ y v (y t ) v(y t ) (11) 11

12 Corollary (1) decomposes the firm s excess return into two components. The first component is a premium paid for the riskiness coming from the covariance between the firm s productivity and the stochastic discount factor. For an average firm this term will be positive, as the average firm produces more in good times. The second term captures the risk premium resulting from the exposure that the firm has to relative wages. The exposure depends on the volatility of relative wages and on changes in labor intensity associated with changes in relative wages (captured by v (y t) v(y t) ). Defining β as the covariance between the stochastic discount factor and the asset s return, we obtain expressions for the asset s β and volatility: β = σ Zϕ Z,y + v y kσ (y t) y v(y t) (12) σ λ ( ) 2 σ r = σz 2 + (y v (y t k)σy 2 t ) + 2 v y t kσ y σ Z ϕ (y t ) Z,y (13) v(y t ) v(y t ) Equations (12) and (13) make clear that there will not be a one-to-one relationship between the firm s β and its volatility. Whereas these two will be positively correlated, they will not be proportional to each other. This key result distinguishes the model from one in which labor affects riskiness through operational leverage. When operational leverage drives the relationship bewteen β and volatility, these two end up being proportional to each other. 3.3 Model results In this section I present key features of the model through a numerical example. In the example I show the relationship between wages and labor intensity, and build on this to show the relationship between labor intensity with beta, and labor intensity with the asset s volatility. The key features of the model are the variation between labor intensity and relative wages, and the changes in beta and volatility as a function of labor intensity. For this example (it is not a calibration) I use parameters that result in a range of volatilities for the firm between 14% and 20%, to use the market s volatility of 16% as a reference, 12

13 and a volatility of productivity of 10%. The volatility of the stochastic discount factor and of the productivity shocks is.1. The correlation between shocks to wages and shocks to productivity is.4, in line with the relatively low correlation observed between asset returns and consumption. The importance of labor in the production function, given by α, is.5. This choice for α ensures that the labor intensity of the firm varies between.5 and 1. Finally, the risk-free rate is 2% and the growth rate of productivity is 1.6%. The only parameter not specified yet is the elasticity of substitution between labor and capital ρ. The value of ρ changes the results significantly and merits some discussion. When ρ = 0, the firm has a Cobb-Douglas production function, implying that the labor intensity remains constant. Given that the empirical analysis shows that labor intensity is, in general, not constant, the point of this example is to show what happens when ρ 0. Previous work suggests that the elasticity of substitution between labor and capital is less than unity, which implies a negative value for ρ. When ρ < 0 labor intensity grows as relative wages grow. Given the parameters explained above, Figure (1) shows the relationship between labor intensity and relative wages when ρ =.3. Now consider the relationship between labor intensity and the firm s beta. Figure (2) shows how the firm s beta changes at the same time that its labor intensity changes. The relationship is not linear, increasing throughout most of the possible values of labor intensity. 2 The relationship between volatility and labor intensity is somewhat different. Figure (3) shows that, even though the relationship between labor intensity and volatility is also increasing, the change is not nearly as large as with beta. Figure (4) makes this relationship transparent. The figure depicts the ratio of beta to volatility. As can be seen, the relationship is increasing, showing that as labor intensity increases, beta increases at a faster rate than volatility. The simple model delivered a result that contrasts an explanation based on oper- 2 The relationship is decreasing near the lowest range for labor intensity. This is due to the volatility of dividends growing to infinity as labor intensity approaches α. 13

14 ational leverage to explain the relationship between a firm s beta and its labor intensity with an explanation rooted in a production model without frictions. Unlike the operational leverage explanation, the model is capable of explaining changes in beta that are not followed by proportional changes in volatility. The empirical section that follows provides the evidence that motivated the model of this section. 4 Empirical Analysis The model presented in the previous section predicts that an asset s beta will vary with labor intensity. I present two sources of evidence that support this hypothesis. First, using data from the NIPA tables I construct a series of labor intensity by industry. Then, I show that industries with higher labor intensities are associated with higher betas. Second, using data from Compustat, I construct a series of labor intensity by company. I then construct portfolios by industry and calculate each industry s labor intensity. To calculate beta for any given year, I use daily stock returns and market returns for that year. This computation produces a panel of industries, labor intensity and betas over time. The panel regressions show that an increase in labor intensity over time is associated with an increase in beta. Finally, I show that the results are not largely driven by the volatility in the stock returns, implying that the effect of higher betas associated with higher labor intensities is mostly a result of an increase in the correlation between stock returns and market returns. The following sections describe the data and the econometric procedure in more detail. 4.1 Data The data to test the implications of the model comes from three different sources: (1) macroeconomic data comes from the NIPA tables, (2) company data, in particular its level of debt, assets and wages, comes from COMPUSTAT, and (3) return and market capitalization data comes from CRSP database. Macroeconomic data is annual for individual 14

15 industries and quarterly for aggregate information of wages and production. Data from Compustat is annual, and CRSP data is monthly and daily. The macroeconomic data used goes from 1947 to is the first year for which government publishes compensation and production data by industry. The end of the sample, 1997, corresponds to the year before government changed the definition of its industries, switching from SIC to NAIC codes. I use macroeconomic data to estimate the labor intensity of different industries. In the NIPA tables one can find an industry s production and total compensation, for every year going back to An industry s labor intensity for a given year is calculated as that year s total compensation divided by the same year s production. Table 1 summarizes the characteristics of each industry in the sample period. Table 1 reveals a wide dispersion in labor intensity among different industries during the sample period. The smallest average for which there were enough stocks to build an industry portfolio was real estate with a labor intensity of.05, while the largest average labor intensity corresponded to social services with a labor intensity of.97. Whereas these were the extremes in the list, the average was.61 and the standard deviation between industries was.19. I use annual Company data from Compustat to calculate an unlevered beta, which can then be used in the regressions. In theory, debt should have a first order effect on a stock s beta, and thus it needs to be controlled for when testing the model. I assume that debt remains constant through the year, using the same value for every month of the year. Leverage is calculated as the book value of debt adjusted for cash holdings, as reported in Compustat, divided by the sum of market value of equity and book value of debt. I use monthly data from CRSP to obtain stock returns. I build value-weighted portfolios grouping stocks according to the SIC code groups found in the NIPA tables. Market returns and the monthly risk-free rate are also obtained from CRSP. For the panel regression, I use daily data from CRSP to find an annual estimate of a portfolio s beta and volatility. 15

16 Once I calculate portfolio s i beta, βt, i either using monthly returns between 1947 and 1997, or each year, using daily returns from that year, I calculate an unlevered beta assuming a stock s debt is riskless. Whereas this is clearly not true for corporate debt, the average leverage in the resulting portfolios is not very high, suggesting that the assumption need not be too far from reality. 4.2 Estimation The main empirical prediction of the model is that an asset s beta will depend on the asset s labor intensity. The first estimation uses monthly data between 1947 and 1997 to estimate the average labor intensity and average portfolio betas by industry. The second estimation is a panel regression using annual betas and labor intensity by industry Average industry labor intensity and beta For the first analysis, I start by estimating the following regression: β i = β 0 + γ α i + ρ X i + ε i (14) Betas in equation (14) are the coefficients of regressing monthly excess (over the risk-free rate) portfolio returns on monthly excess market returns. Alphas are the average labor intensity for each industry. The results of the regression of equation (14) are shown on panel A of Table 5. The coefficient γ relating labor intensity and beta is significant at the 1% level. With a magnitude of.6, it says that a 1% increase in labor intensity is associated with a.06 increase in beta. Interestingly, the coefficient relating leverage and beta is not significant, while γ remains significant whether debt is included or not in the regression. The R 2 of the regression is 20%, implying that labor intensity goes a long way in explaining the crosssection variation in beta between industries. These results can be more easily understood by looking at Figures 2 and 3, which depict the positive relationship between labor intensity 16

17 and beta. Figure 4 depicts the negligible relationship between leverage and beta. A portfolio s beta is a function of leverage, and thus one could unlever that beta to calculate an unlevered beta β i u. The model presented above implies that the this is the beta that increases with labor intensity. Assuming riskless debt, an estimate of a portfolio s unlevered beta is β i u = β i (1 w i d), (15) where w i d is the average weight of debt for industry i during the sample period. Panel B of Table 5 shows that α i is successful explaining variations in βu. i The coefficient associated with labor intensity is significant at the 5% level and its magnitude, though not as high as with the raw beta, is.46. Controlling for market size doe not change the results. The previous analysis has several weaknesses. First, betas, leverage, and market capitalizations are changing over time. An analysis that masks their variations using only their averages is suspect to miss important variations. Second, significant intra-industry variation in labor intensity may exist, or systematic differences between an industry s labor intensity and the public firms in that industry can be present. Both would affect the results. More subtly, a third unobserved variable may be correlated with beta and labor intensity, so that riskier industries just happen to have higher labor intensity. To address this issues, I construct an annual measure of labor intensity by firm, and then analyze the resulting panel data. The procedure and results are explained in the next section Panel data I construct a series of annual observations for industry portfolios. Each observation consists of the portfolio s beta, average return, leverage, market capitalization and labor intensity. I estimate the portfolio s beta, average return and market capitalization, using all the daily 17

18 observations available on CRSP on a given calendar year. The estimate of the portfolio s leverage and labor intensity comes from the annual observations available in COMPUSTAT. Leverage is debt divided by debt plus equity, where debt is adjusted subtracting the firm s cash. Labor intensity is wages divided by revenue. The regression is: β i t = β i + γ α i,t + ρ X i,t + ε i,t (16) One advantage of using the data on firm wages to construct labor intensity is that it allows us to use labor intensity and betas of only the firms that are being traded, rather than making an assumption of the labor intensity of the firms using macroeconomic data. Another advantage is that I can use data between 1950 and 2007, instead of just to However, there is also an important disadvantage: the data for wages is voluntary, and therefore many firms do not report it. I construct the industry portfolios using only firms that have wages available. An observation for an industry will exist if at least 10 firms in the industry who were traded on more than 50 days on a given year provided wage information. This filter reduces the number of observations to 1543 year-industry observations. Also, the measure of firm-specific data calculated from COMPUSTAT is about half of the one derived from macroeconomic data. There are at least two possible explanations for this. One possibility is that the figure reported in the NIPA tables includes forms of compensation that are not included in what firms report. A second explanation is that smaller, non traded firms, are more labor intensive. Understanding these differences is important. However, for the present analysis, it will be enough to state that the results hold with what the firms report, and that the coefficients obtained with either sources of data (NIPA and firm-specific) are, at least, of the same order of magnitude. The qualitative results are also similar. Table 7 shows the results of the panel regression. Panel A presents the results of the fixed-effects estimation in which none of the regressors conclusively explains variations in 18

19 beta. However, the between group regressions (which are analogous to the analysis already presented) still show labor intensity significant at the 5% level. The coefficient results around.8, also consistent with the analysis of the previous section. Unlike the previous results, leverage appears significant at the 10% level. I repeat the panel regressions using unlevered betas as dependent variables. I calculate an unlevered beta for each portfolio each year using the year s estimate of beta (which was calculated using daily returns) and leverage. The equation used to calculate the unlevered betas is: β i u,t = β i t(1 w i d,t). (17) The panel regression using unlevered betas shows coefficients associated with labor intensity significant at the 1% level. Panel A of Table 8 shows the results of the fixed-effects regressions. The magnitude of the coefficient in the regression that does not control for size is.41, consistent with the.46 obtained using the data from the NIPA tables. The coefficient is significant at the 5% level in the between groups regressions, shown in Panel B of Table 8. In this case the estimates are much higher, at about Labor intensity and volatility A positive relationship between labor intensity and beta could be due to a positive relationship between labor intensity and volatility, a positive relationship between labor intensity and the correlation between industry shocks and aggregate shocks, or both. To advance our understanding on what is driving the results between labor intensity and beta, I test in this section whether a relationship exists between labor intensity and volatility. The test consists in performing the same regressions as in equation (14), but using return volatility for each industry as the dependent variable instead of beta. The analysis is otherwise identical from that of the previous section. The analysis using labor intensity 19

20 from the NIPA tables is σ i = σ 0 + γ α i + ρ X i + ε i (18) and the panel regression when using daily betas and labor intensity using firm data is σ i t = σ i + γ α i,t + ρ X i,t + ε i,t (19). Consider first the regressions using average monthly volatilities and labor intensities by industry (Equation (18)). Panel A of Table 6 shows the results of regressing industry average monthly returns for the period against industry average annual labor intensity. Consistent with the theory, leverage is significant at the 10% and 5% levels in explaining variations in the volatility of porftolio returns. Not surprisingly, though not necessarily predicted by theory, market capitalization shows up significant at the 1% level. Critically for what we are studying in this paper, labor intensity does not appear to explain volatility at all in these regressions. Moreover, the estimated coefficients are much smaller than those associated with debt. As with beta, theory predicts that equity s volatility depends on leverage, so that the analysis for the hypothesis relating volatility and labor intensity should also use a measure of unlevered volatility. To unlever an industry s portfolio volatility, I make the same assumption about riskless debt so that a portfolio s unlevered volatility is σ i u,t = σ i t(1 w i d,t). (20) Panel B of Table 6 shows the results of regressing unlevered volatility on labor intensity. The conclusion remains the same, with labor intensity not explaining variations in unlevered volatility. The most important change between the regressions with raw volatility and unlevered volatility, is the effect of leverage. In these regressions leverage does not explain 20

21 the cross-section of unlevered volatilities. Now consider the panel regressions using annual measures of volatility and labor intensity. Panel A of Table 9 shows the results of the fixed-effects regressions. Consistent with theory, the coefficient associated with leverage is significant at the 1% level. As an industry increases it s level of debt, the volatility of its returns also increases. Labor intensity appears significant at the 5% level, with coefficients half as large as those obtained for leverage. Panel B shows the results of the between groups regressions, where leverage is still significant at the 1% level, while labor intensity becomes insignificant. Finally, Table 10 repeats the panel regressions using unlevered volatility instead of raw volatility. Labor intensity does appear significant at the 5% level, while leverage becomes insignificant. The coefficient associated with labor intensity is relatively small (.005), implying that the effect, though significant, is small. To put things in perspective, a portfolio with annual volatility of 18% will exhibit a daily volatility of %. An increase of 10% in labor intensity would increase it s daily volatility to %. In contrast, the previous results suggest that an increase of 10% in labor intensity would increase beta by.04, a change two orders of magnitude larger. 5 Discussion The empirical results of the previous section point to a relationship between labor intensity and beta, consistent with the model presented in the theoretical section. But the analysis presented here does not allow us to establish a causal relationship conclusively. A third, unobserved, variable could be driving labor intensity and beta simultaneously. However, if such a variable exists, it needs to provide a good explanation for why industries with higher labor intensity exhibit higher betas, and why an industry s beta increases as its labor intensity increases. The model has a simple explanation, based on employees having more flexibility on which industry to work than firms choosing on which industries to deploy their capital. 21

22 If the conclusion that labor intensive firms are riskier is accepted, the next step is to ask whether the reasoning behind the model is valid. An alternative explanation is that firms with higher labor intensity have higher operational leverage. The much weaker relationship, insignificant in some cases, that appears to exist between volatility and labor intensity sheds light on this question. Since the order of magnitude is much larger for the positive relationship between labor intensity and beta, the implication is that labor intensive firms exhibit higher correlation with the market. Operational leverage would predict higher volatility, but not higher correlation. The result obtained in this paper, therefore, suggest that operational leverage is not the main reason why labor intensive firms are riskier. 6 Conclusion Labor intensity can explain a significant fraction of the variation of beta between portfolios. This paper presented a model providing why labor intensity can explain some of the variation of beta and provided empirical evidence that a significant relationship exists. In particular, regressing the beta of industry portfolios and their average labor intensity between 1950 and 1997 finds that labor intensity explains 20% of the variation between portfolio betas. The success of this regression stands out in contrast to the failure of debt to be related to beta. The panel results also suggest that a positive relationship exists between labor intensity and beta. Labor intensive industries tend to have higher betas, and industries that become more labor intensive see their betas increase. The more surprising result is that the relationship does not exist when the analysis is made with volatility. This suggests that what drives the result is not an effect of operational leverage (which would affect return volatility) but a systematic movement of wages in the economy. Given the positive relationship between labor intensity and beta, the results suggest that aggregate wages are less risky than the cash flows firms generate. This result is consistent with the theoretical 22

23 model I present in Palacios (2010), where I show that a general equilibrium model calibrated to match the observed ratio of wages to consumption, consumption volatility, and equity volatility, implies a lower excess return for claims to aggregate wages than claims to equity. These results have implications for practitioners and researchers. For practitioners, labor intensity can be used to estimate beta when other alternatives are not available. Researchers, for example, could use labor intensity as a conditioning variable when estimating expected asset returns. In both cases the value of the results presented here is that labor intensity can give us information about beta not available elsewhere. 23

24 References Constaninides, G. and D. Duffie (1996). Asset pricing with heterogeneous consumers. The Journal of Political Economy 104 (2), Fama, E. and W. Schwert (1977). Human capital and capital market equilibrium. Journal of Financial Economics 4 (1), Gourio, F. (2011). Putty-clay technology and stock market volatility. Journal of Monetary Economics 58 (2), Harris, M. and B. Holmstrom (1982). A theory of wage dynamics. The Review of Economic Studies 49 (3), J. Berk, R. S. and J. Zechner (2009). Human capital, bankruptcy and capital structure. Journal of Finance. Koo, H. K. (1998). Consumption and portfolio selection with labor income: continuous-time approach. Mathematial Finance 8 (1), Lettau, M. and S. Ludvigson (2001). Resurrecting the (c)capm: A cross-sectional test when risk premia are time-varying. The Journal of Political Economy 109 (6), Lustig, H., S. Van Nieuwerburgh, and A. Verdelhan (2010). The wealth-consumption ratio. Working Paper, UCLA. Marcus, A. (1984). Efficient risk sharing, non-marketable labor income and fixed-wage contracts. European Economic Review 25, Mayers, D. (1972). Non-marketable assets and capital market equilibrium under uncertainty, in Studies in the Theory of Capital Markets, M.C. Jensen, ed., Praeger, Palacios, M. (2010). The value and the risk of aggregate human capital. Working paper, Vanderbilt University. Santos, T. and P. Veronesi (2006). Conditional betas. Working paper 19 (1), Z. Bodie, R. Merton, W. S. (1992). Labor supply flexibility and portfolio choice in a life cycle model. 16, Appendix A: Proof of proposition 1 To be completed. A 24

25 Figure I Relationship between relative wages and labor intensity Labor intensity and relative wages in the production model with the following parameters: α =.5, ρ =.6, σ λ =.1,σ Z =.1, σ y =.04, ϕz, y =.4, µ Z =.016, r =

26 Figure II Relationship between beta and labor intensity Beta as a function of labor intensity in the production model with the following parameters: α =.5, ρ =.6, σ λ =.1,σ Z =.1, σ y =.04, ϕz, y =.4, µ Z =.016, r =

27 Figure III Relationship between volatility and labor intensity Volatility as a function of labor intensity in the production model with the following parameters: α =.5, ρ =.6, σ λ =.1,σ Z =.1, σ y =.04, ϕz, y =.4, µ Z =.016, r =

28 Figure IV Relationship between volatility and labor intensity Volatility as a function of labor intensity in the production model with the following parameters: α =.5, ρ =.6, σ λ =.1,σ Z =.1, σ y =.04, ϕz, y =.4, µ Z =.016, r =

29 Figure V Annual Market Returns and Aggregate Labor Intensity Annual market returns and average annual aggregate labor intensity between 1950 and Average annual labor intensity is the average of quarterly labor intensity. Labor intensity is calculated as the ratio of compensation and GDP as published in the NIPA tables Market return Y/GDP Date Market return Y/GDP 29

30 Figure VI Industry Labor Intensity vs Beta Industry labor intensity is the average over the sample period, calculated from the annual information published in the NIPA tables. Each year s labor intensity is the ratio of the industry s compensation and the industry s production. Beta for an industry is the coefficient of the regression of monthly industry portfolio excess returns on monthly market excess returns over the sample period Industry Beta Industry Labor Intensity 30

31 Figure VII Industry Labor Intensity plus leverage vs Beta Industry labor intensity is the average over the sample period, calculated from the annual information published in the NIPA tables. Each year s labor intensity is the ratio of the industry s compensation and the industry s production. An industry s leverage is the average over the sample period of annual industry leverage. Annual industry leverage is calculated as the weighted average of each company s leverage in an industry s portfolio. Debt data from each company comes from Compustat s annual database. Firm value is the sum of market value as it appears in CRSP plus debt. A company s leverage is calculated as the ratio of debt and firm value. Beta for an industry is the coefficient of the regression of monthly industry portfolio excess returns on monthly market excess returns over the sample period Industry Beta Industry Labor Intensity + Industry Leverage 31

32 Figure VIII Industry Leverage vs Beta An industry s leverage is the average over the sample period of annual industry leverage. Annual industry leverage is calculated as the weighted average of each company s leverage in an industry s portfolio. Debt data from each company comes from Compustat s annual database. Firm value is the sum of market value as it appears in CRSP plus debt. A company s leverage is calculated as the ratio of debt and firm value. Beta for an industry is the coefficient of the regression of monthly industry portfolio excess returns on monthly market excess returns over the sample period Industry Beta Industry Leverage 32

33 Table I Summary Statistics by Industry Industries as they appeared in the NIPA tables between Prod/GDP is the fraction of GDP produced by the industry. α is the industry s average labor intensity over the sample period. Annual labor intensity is calculated using the ratio of total compensation and production for the industry. σ is the standard deviation of α over the sample. Industry SIC Prod/GDP α σ Max Min Private Industries 87.3% Agriculture, forestry, and fishing 1.6% Farms Agricultural serv., forestry, and fishing Mining 1.6% Metal mining Coal mining Oil and gas extraction Nonmetallic minerals, except fuels Construction % Manufacturing 16.9% Durable goods 9.8% Lumber and wood products Furniture and fixtures Stone, clay, and glass products Primary metal industries Fabricated metal products Machinery, except electrical Electric and electronic equipment Motor vehicles and equipment Other transportation equipment Instruments and related products Miscellaneous manufacturing industries Nondurable goods 7.1% Food and kindred products Tobacco products Textile mill products Apparel and other textile products Paper and allied products Printing and publishing Chemicals and allied products Petroleum and coal products Rubber and misc. plastics products Leather and leather products