The Elephant in the Room: the Impact of Labor
Obligations on Credit Risk∗
Jack Favilukis†
Xiaoji Lin‡
Xiaofei Zhao§
September 28, 2015
Abstract
We study the impact of labor market frictions on credit risk. Our central finding is that labor
market variables are the first-order effect in driving both of the aggregate time series and the
cross sectional variations of credit risk. Recent studies have highlighted a link between credit
risk and macroeconomic/firm-level variables such as investment growth, financial leverage,
volatility, etc. We show that labor market variables (wage growth or labor share) can forecast
the aggregate credit spread as well as or better than alternative predictors. Furthermore,
firm-level labor expense growth rates and labor share can predict Moody-KMV expected
default frequency (EDF) in the cross-section across a wide range of countries. A model with
wage rigidity and endogenous long-term defaultable debt can explain these links as well as
produce large credit spreads despite realistically low default probabilities. This is because
pre-committed payments to labor make other committed payments (such as debt) riskier; for
this reason variables related to pre-committed labor payments have explanatory power for
credit risk.
JEL classification: E23, E44, G12
Keywords: Wage rigidity, long-term debt, credit risk, labor market frictions, labor leverage,
financial leverage, wage growth, labor share
∗
First draft: November 2013. We thank Frederico Belo, Murillo Campello, Murray Carlson, Sergey Chernenko,
Andres Donangelo, Andrea Eisfeldt, Isil Erel, Bob Goldstein, Philippe Mueller, Christopher Polk, René Stulz, Eric
Swanson, Sheridan Titman, Andrea Vedolin, Mike Weisbach, and Lu Zhang for helpful comments. All errors are
our own.
†
Finance Division, University of British Columbia, 2053 Main Mall, Vancouver, BC, V6T 1Z2, Canada. Tel:
604-822-9414 and E-mail: jack.favilukis@sauder.ubc.ca
‡
Department of Finance, Ohio State University, 2100 Neil Ave, 846 Fisher Hall, Columbus, OH 43210. Tel:
614-292-4318 and E-mail: lin.1376@osu.edu
§
Jindal School of Management, University of Texas at Dallas, 800 West Campbell Road, SM 31, Richardson,
TX 75080. Tel: 972-883-5971 and E-mail: xiaofei.zhao@utdallas.edu
1
1
Introduction
We study the impact of labor market frictions on credit risk. Our central finding is that labor
market variables are the first-order effect in driving both of the time series and the cross section
of variations in credit risk. When wages are rigid, the operating leverage effect caused by smooth
wages increases firms’ default risk because precommitted wage payments make debt payment
riskier.
Consistent with this view, we show that labor market variables (wage growth and labor share)
which capture the strength of operating leverage when wages are sticky, significantly forecast the
aggregate Baa-Aaa credit spread in the U.S. More specifically, a 1 percentage point increase in
the wage growth (labor share) is associated with a decrease (increase) of 15 (11) basis points in
credit spread. The predictability of labor market variables is stronger than or comparable to the
standard credit risk predictors including market volatility, term spread, financial leverage, etc.
For example, the adjusted R2 of wage growth in predicting credit spread is 28%, substantially
larger than that of market volatility (22%) and term spread (2%) and is close to that of financial
leverage (37%). Furthermore, wage growth drives out the predictability of real variables including
investment growth, a key variable used in the recent investment-based models to link credit risk
to the real economy. In the cross section, we show that firm-level labor market variables are
important predictors of credit risk measured by the Moody-KMV expected default frequency
(EDF) across a wide range of countries, including U.S., Canada, and major European and Asian
Pacific countries. Controlling for variables that are known to have explanatory power for firmlevel credit risk, labor expense growth rate and labor share remain strong factors in explaining
the cross sectional variations of future EDFs. More specifically, firms with higher labor expense
growth rates (higher labor share) are associated with lower (higher) future EDFs. These relations
are stronger for firms with measures of higher wage rigidity, implying wage rigidity is a key driving
force of the result. Taken together, our results suggest the crucial role of labor market variables
as the key determinants of both the aggregate and the cross sectional variations of credit risk.
To understand the link between labor market and credit risk, we propose a dynamic stochastic
general equilibrium (DSGE) model with heterogeneous firms. Different from the standard models,
in our model the labor market is not frictionless, rather wages are rigid. More specifically, wage
contracts are staggered, which prevent firms from immediately adjusting their labor expenses in
response to new shocks. Sticky wages capture the fact that wages are smoother than output
and are imperfectly correlated with output in the data. On the financing side, firms issue longterm debt to finance investment and labor expenses. In particular, firms only issue new debt
infrequently before the existing debt matures, making debt payment sticky and hence firms’ cash
flow extra risky.
In the model, the predictability of labor market variables for the credit spread arises
2
endogenously due to the interaction between operating leverage and financial leverage. In economic
downturns, productivity and output fall by more than wages, causing an increase in labor leverage.
High expected payments to labor make equity more likely to default in bad times, especially when
the wage bill is relatively high. Thus, the model implies that labor share (positively) and wage
growth (negatively) are natural predictors of credit risk.
More specifically, in the model firms default if the realized firm value is below zero. This occurs
if the firm’s idiosyncratic productivity is below a cutoff value, which itself depends on the state
of the economy. In economic downturns, profit falls more than output, which makes it harder for
firms to pay off precommitted debt payment. This raises the default threshold of idiosyncratic
productivity, which in turn increases the default probability and the credit risk premium. Thus
the model produces large credit spreads despite realistically low default probabilities, providing
a novel explanation for the credit spread puzzle. Furthermore, wage growth negatively whereas
labor share positively predicts credit spread because times of low wage growth or high labor share
are associated with high operating leverage and hence high credit risk premium. The model
endogenously generates time-variations in credit spread.
This intuition is consistent with anecdotal evidence. For example, regarding the bankruptcy
of American Airlines in 2012, the Wall Street Journal writes “Bankruptcy seems to be helping
American do what practically every other bankrupt airline has done – reduce its labor costs to
competitive levels. Those costs are ... the highest of any major airline operating in the U.S.
today. American spends $600 million more on wages than its peers.” 1 American’s CEO Thomas
W. Horton said “Achieving the competitive cost structure we need remains a key imperative in this
process, and as one part of that, we plan to initiate further negotiations with all of our unions to
reduce our labor costs to competitive levels.” Similarly, regarding the bankruptcy of United in 2002,
a UBS analyst said “Excess debt, burdensome labor contracts, expensive pension obligations... are
all high on the list of what ails airlines. Bankruptcy can certainly address these other issues.” 2
The model is calibrated to match aggregate-level and firm-level real quantity moments. The
model generates a sizable aggregate credit spread and a low aggregate default probability consistent
with the data. Most important, the model with wage rigidity and long-term debt successfully
replicates the predictability of wage growth and labor share for the credit spread observed in the
data. Taken together, our results show that labor market frictions have significant impact for
credit risk. In addition to successfully replicating the observed predictability in credit spread,
the model also produces a sizable equity premium and equity volatility consistent with the data
(the mechanism is similar to Favilukis and Lin 2015a). Thus the model with wage rigidity and
corporate debt provides a coherent explanation for the two major asset pricing puzzles in a unified
1
James K. Glassman, Wall Street Journal Op/Ed, October 16, 2012, ”Once It Emerges From Bankruptcy, Let
American Airlines Stay American.”
2
Sam Buttrick in interview to CNNMoney, December 9, 2002 ”United hits turbulance of bankruptcy.”
3
framework–the equity premium puzzle and the credit spread puzzle.
Related literature: While the macroeconomic literature on wages and labor is quite large (e.g.,
Pissarides 1979, Calvo 1982, Taylor 1983, Taylor 1999, Shimer 2005, Hall 2006, Gertler and
Trigari 2009), there has been little work done relating labor market frictions to credit risk.
Notable exceptions include Gilchrist and Zakrajsek (2012) who show credit spread predicts future
movement in unemployment rate.
We integrate labor market frictions with credit risk.
In
particular, our paper differs from these macro papers in that we study implications of staggered
wage setting on corporate bond pricing, while the models in labor economics fail to match the
asset prices observed in the data; this is a problem endemic to most standard models.
The literature of structural models on credit risk highlights the roles of financial leverage,
asset volatility, and macroeconomic risk as the key determinants of credit spread (e.g., CollinDufresne and Goldstein 2001; Hackbarth, Miao and Morellec 2006; Chen, Collin-Dufresne, and
Goldstein 2009; Chen 2010). We are complementary to these work by endogenizing cash flows
through firms’ investment, hiring/firing, and financing decisions. More importantly, as is shown
in Favilukis and Lin (2015a, b), wage rigidity is crucial to match cash flow dynamics in DSGE
models, thus our paper makes structural models of credit risk viable in a production economy.
Some recent investment-based models attempt to link credit risk to firms’ real investment decisions.
In particular, Gomes and Schmid (2010) explore the propagation mechanism of movements in bond
markets into the real economy. Gourio (2013) studies the impact of disaster risk on credit risk in
a DSGE model. Kuehn and Schmid (2013) study the interaction between investment and credit
spread. Gilchrist, Sim, and Zakrajsek (2014) study the relations between uncertainty, investment,
and credit risk in a DSGE model. Bai (2015) explores the link between unemployment and credit
risk. We are different from these papers by explicitly modelling the interactions between staggered
wage contract and corporate debt pricing.
Our empirical findings relate to the empirical literature on the determinants of credit spread.
Collin-Dufresne, Goldstein, and Martin (2001) show that standard credit spread forecasters have
rather limited explanatory power. Elton et al (2001) find that expected default accounts for a
small fraction of the credit risk premium. We show that labor market variables, in particular,
wage growth, have as strong explanatory power as financial leverage and stock market volatility
in predicting the Baa-Aaa spread and the cross sectional variations in firms’ EDFs. Our findings
suggest that exploring the link between labor market frictions and credit risk can shed light to
the empirical puzzle documented in Collin-Dufresne, Goldstein, and Martin (2001).
Our paper also relates to the recent literature exploring the relations between labor frictions
and equity returns. Belo, Lin, and Bazdresch (2013) study the impact of labor frictions on the
relationship between hiring rates and the cross section of returns. Petrosky-Nadeau, Zhang, and
Kuehn (2013) explore how search frictions in the style of Mortensen and Pissarides (1994) affect
4
asset pricing in a general equilibrium setting with production. Gomes, Jermann, and Schmid
(2013) study the rigidity of nominal debt which creates long term leverage that works in a similar
way to our labor leverage. We differ in that we explicitly study credit risk and wage rigidity.
2
Empirical Evidence
In this section we explore the explanatory power of labor market variables (wage growth and labor
share) for credit risk both in the time series U.S. aggregate data and the firm-level data cross a
wide range of countries.
2.1
Time Series Analysis
We first describe the data, then the empirical specifications and the results.
2.1.1
Data and Variable Definitions
Credit spread We use the Moody’s Baa corporate bond yield in excess of Aaa corporate bond
yield from the Federal Reserve. As in Chen, Collin-Dufresne, and Goldstein (2009), the Baa-Aaa
spread should be mostly due to credit risk, assuming that the component of the credit spread due
to taxes, call/put/conversion options and the lack of liquidity in the corporate bond markets, is
of similar magnitude for Aaa and Baa bonds.
Wage growth We use the growth rate in the real wages and salaries per full-time equivalent
employee from NIPA table 6.6.
Labor share Labor share is the ratio of aggregate compensation of employees to GDP.
Controls The empirical finance literature has uncovered a list of variables that forecast
credit spread. We measure financial leverage as the book value of credit market instruments of
nonfinancial business sector divided by the sum of the market value of equity in the nonfinancial
corporate business sector and the credit market instruments from the Flow of Funds Accounts.
Stock market volatility is the annualized volatility of monthly CRSP stock market returns in excess
of riskfree rate. Term spread is the difference between the ten-year Treasury bond yield and the
three-month Treasury bill yield from the Federal Reserve. Spot rate is the one-year Treasure bill
rate. Our sample is from 1948 to 2014.3
Panel A in Table 1 reports the descriptive statistics for the variables mentioned above. Credit
spread has an annual mean of 95 basis points and a volatility of 40 basis points. It has a first3
We start in 1948 because financial leverage from Flow of Funds is available after 1946. We do not start in 1946
to avoid the influence of the WWII on our results. However, the predictability of wage growth for credit spread
holds in a longer sample starting from 1929.
5
order autocorrelation at 0.74, suggesting that credit spread is persistent. Wage growth has mean of
1.5% and a standard deviation of 1.4%. It has a first-order autocorrelation at 0.47, less persistent
than credit spread. Labor share has a mean and standard deviation at 0.55 and 1.2%, respectively.
Investment growth has a volatility of 6.3%. Turning to financial variables, the mean, volatility and
persistence of price-to-earnings ratio, term spread and spot rate are consistent with the estimate
in the literature. Financial leverage is persistent with an autocorrelation at 0.88.
Panel B in Table 1 presents the correlations of all variables of interest with real GDP growth,
and their cross correlations. Credit spread has a correlation with GDP growth at −0.51, suggesting
that it is countercyclical. Wage growth and investment growth are procyclical with correlations
with GDP growth at 0.41 and 0.76, respectively; both of them negatively correlate with credit
spread with correlations at -0.42 and -0.49, respectively. But wage growth is only mildly positively
correlated with investment growth at 0.2. This implies that wage growth contains different
information than investment growth in explaining credit spread even though all of them negatively
correlate with credit spread. Both labor share and financial leverage are negatively correlated
with GDP growth with correlations at -0.14 and -0.01, respectively; however labor share and
financial leverage themselves are weakly correlated at 0.25, suggesting they contain different
information despite both being countercyclical. Consistent with the existing literature, credit
spread is positively correlated with financial leverage, market volatility, and the term spread.
It is also evident in Figure 1 that credit spread is highly countercyclical and moves in the
opposite direction to the wage growth, while labor share somewhat leads credit spread but moves
in the same direction as credit spread.
2.1.2
Empirical Specifications and Results
In this subsection, we explore the predictability of wage growth and labor share for credit spread
in three steps. All regressions are at an annual frequency. First, we run univariate regressions of
one year ahead credit spread, CSt+1 , on current wage growth, ∆Wt , labor share, LSt at year t;
second, we run horse race regressions of either wage growth or labor share with a control one at
a time; thirdly, we conduct a multivariate regression with all the predictors at the right hand side
including lagged credit spread which controls for the persistency in credit spread.
Univariate regressions Specification 1 in panels A and B in Table 2 reports the univariate
regression results. Wage growth negatively forecasts credit spread with a slope coefficient at
−15.4 which is more than 4 standard deviations away from zero. Furthermore, the adjusted R2 is
0.28, which is significantly larger than that implied by market volatility (0.22) and slightly smaller
than that of financial leverage (0.37), suggesting that the explanatory power of wage growth is as
strong as the conventional predictors (Univariate results for other controls are not tabulated but
are available upon request). Labor share positively predicts credit spread with the slope coefficient
6
of 10.66 which is more than 2 standard deviations away from zero.
4
Horse race regressions Specifications 2 to 8 in panels A and specifications 2 to 7 of panel B in
Table 2 present the horse race regression results of wage growth and labor share with a control
one at a time. Wage growth remains statistically significant in predicting credit spread after
controlling for all other predictors including financial leverage, market volatility, price-to-earnings,
and term premium. Furthermore, investment growth even turns insignificant (specification 3).
This is perhaps surprising given that the recent literature has emphasized the role of investment
in driving credit spread, however our result shows that wage growth drives out the predictive
power of investment growth, thus wage growth is more informative in explaining the movement of
credit spread than investment. Similarly, labor share remains significant at 5% significance level
with other controls at the right hand side.
Multivariate regressions Specification 9 in panel A and specification 8 in panel B present the
multivariate kitchen sink regression for wage growth and labor share that includes all controls,
respectively. In these regressions, the adjusted R2 is above 0.73; recall that wage growth alone
attains an R2 of 0.28. Wage growth remains significant after controlling for all variables; however
labor share is no longer significant due to high correlation with lagged credit spread. Given that
there are 10 regressors and 66 years of annual observations, this regression may very well be
overfitted.
2.2
Cross Sectional Analysis
We describe the firm-level international data first, and then the cross-sectional regression results.
2.2.1
Data
Our accounting data come from Compustat North America (for U.S. and Canadian firms) and
Compustat Global (for firms from other countries) Fundamentals Annual files. Similarly, the
security data come from CRSP and Compustat Global Security Daily respectively. We use MoodyKMV’s Expected Default Frequency (EDF) data to measure the default probability for global firms
from 1992 to 2011, which is also the sample period for most of our firm-level analysis.
In Table 3, we report the number and percentage of annual (firm-year) observations that have
non-missing labor expenses (Compustat variable XLR), hiring (Compustat EMP), and EDF for
each of the thirty-nine countries. We follow Gao, Parsons, and Shen (2013) to filter out outliers
4
As for the controls in the univariate regressions which are tabulated here, investment growth negatively forecasts
credit spread, but the adjusted R2 is only 0.03, far below the adjusted R2 implied by wage growth (it is also smaller
than the adjusted R2 implied by labor share at 0.09). Both financial leverage and stock market volatility positively
predict credit spread, consistent with Collin-Dufrene, Goldstein, and Martin (2001). However, price-to-earnings
ratio, term spread, and spot rate do not significantly predict credit spread.
7
and categorize the countries into seven different regions. First of all, we can see that for the US,
only 7% (= 9588/135632) of observations have non-missing labor expenses. If we further require
non-missing hiring and EDF data, this percentage drops to 3.5%. Therefore, the sample with
labor expenses based on US firms is quite small and it is difficult to make a general conclusion
from an exercise based on US only sample. This is the main reason that we expand our scope to
global firms for our firm-level analysis. Once we gather data from other countries, we can see a
lot of them in fact have decent coverage of labor expenses, especially European countries. Japan
is an exception — only 2 annual observations with XLR available — therefore our analysis does
not include Japan.
Table 4 reports the summary statistics (mean and standard deviation) for our main variables
of interest: EDF , ∆XLR, and LS, where ∆XLRt = (XLRt − XLRt−1 )/XLRt−1 is the labor
expenses growth rate from year t − 1 to year t and LSt = XLRt /Salet measures the labor share
at year t using the ratio of labor expenses to sales. As we can see from Table 4, both ∆XLR and
LS show quite a bit of variation across regions. In general, developed countries have higher labor
share and lower labor expenses growth whereas developing countries have lower labor share and
higher labor expenses growth.5
2.2.2
Empirical Findings
Before conducting the empirical analysis, it is worth discussing the measure of labor expenses
XLR. According to its definition from WRDS, this item is a supplementary Income Statement
item (i.e., not a standardized item) and may include other expenses beyond wages and salaries
(such as incentive compensations). Moreover, due to the supplementary nature of this variable,
firms could choose to report different components in different years. However, this is the accounting
variable that is most closely related to wages and salaries. Therefore, we work with this measure
but impose a filter to make sure that we use observations with consistent labor expenses number.
More specifically, we identify a firm-year observation as an outlier and exclude it from the crosssectional analysis if the growth rate of labor expenses per employee (XLR/EM P ) is outside the
range of (−50%, 300%).6 In other words, if the annual labor expenses per employee growth rate
is beyond 300% or less than −50%, it is likely that either the firm has reported a labor expense
number with components different from previous year or it may simply be a data error. In this
sense, the filter is very similar to the one used by Hou, Karolyi, and Kho (2011) when they filter
5
Both ∆XLR and LS are winsorized at 1% and 99% percentiles. The mean values of un-winsorized variables
are much higher — an indication of outliers in labor expenses.
6
The reason we use labor expenses per employee but not total labor expenses for the filtering purpose is because
it is much more difficult to judge whether changes in total labor expenses contain an error by just examining its
magnitude. However, the labor expenses per employee should be much more stable and a dramatic change is likely
to be an outlier.
8
out outliers in monthly stock returns in international data.
To understand the impact of labor expenses on default risk, we first conduct firm-level timeseries analysis. This is accomplished by calculating the correlation between ∆XLR and EDF
(Corr(∆XLR, EDF )) for each individual company using its time-series observations. Then
we present the distribution of this correlation at country and aggregate level in Table 5. The
summary statistics reported include mean, standard deviation, number of firms, and t-statistic
corresponding to test H0 : Corr(∆XLR, EDF ) = 0. We also calculate the correlation between
LS and EDF for each firm and report the corresponding summary statistics on Corr(LS, EDF )
in Table 5. The average value of Corr(∆XLR, EDF ) is -0.19 for all countries (12,280 firms
together) with a t-stat of -39.89. This suggests that a decrease in labor expenses is associated
with higher default risk. It is quite strong and robust across countries (statistically significant for
30 countries and those insignificant ones have very small number of firms in the sample). The
average value of Corr(LS, EDF ) is 0.11 for all countries (12,004 firms together) with a t-stat of
21.29. This indicates that an increase in labor share is associated with higher default risk. The
average value of this correlation is also positive and statistically significant for the majority of the
countries (though the pattern is weaker than that of Corr(∆XLR, EDF )). These two time-series
correlations strongly support that labor obligations are very important determinants of credit risk.
Next, we use Fama-MacBeth (1973) cross-sectional regressions to analyze the predictability
of labor obligations on credit risk by controlling for a list of well-known determinants of credit
and distress risk. We regress default risk measure in year t + 1 on labor expenses growth and
labor share in year t, controlling for other firm-characteristics. For example, when we use labor
expenses growth (or labor share) as a determinant for default risk, we run the following crosssectional regression
EDFi,t+1 = a + b × ∆XLRit (or LSit ) + b1 × Xit + it ,
(1)
where Xit is a vector of determinants for default and distress risk used by previous studies such
as Altman (1968), Zmijewski (1984), Collin-Dufresne, Goldstein, and Martin (2001), Shumway
(2001), Campbell, Hilscher, and Szilagyi (2008), among others. Specifically, we control for the
following firm characteristics in year t: leverage, stock return volatility, working capital, retained
earnings, EBIT, sales, net income, current asset to liability ratio, investments, relative firm size,
market capitalization. We also control for individual firm’s stock excess return and the market
return for its country in year t. Detailed descriptions of these variable constructions are provided
in the appendix. To further understand the impact of labor expense rigidity on the marginal
effect of labor expenses growth on default risk, we also create a measure for labor expense rigidity.
We calculate the volatility of labor expenses growth rate (V ol(∆XLR)) for each firm using its
9
time-series observations. Then we define a variable Rigid and set Rigid = 1 if V ol(∆XLR) is
below its 25% percentile in its country, otherwise we set Rigid = 0. We then interact Rigid with
∆XLR and rerun the above regression with this additional interaction term.
The regression results are reported in Table 6. Panel A presents the results based on ∆XLR.
The results in columns (1)-(6) are based on all countries; in columns (7)-(8) are based on European
countries; in columns (9)-(10) are based on other countries. As expected, the coefficient associated
with ∆XLR is negative and highly statistically significant. For example, in column (6) when we
include all control variables, the coefficient estimate for ∆XLR is -0.85 with a t-stat of -12.87.
This is consistent with the conclusion from our time-series analysis in Table 5: a decrease in labor
expenses predicts a higher default risk, and this effect is beyond the traditional firm characteristics
in existing literature. In the same column, the coefficient estimate associated with Rigid × ∆XLR
is -1.24 with a t-stat of -3.99. This suggests that firms with rigid labor expense would experience
a much larger increase in default risk for the same percentage decrease in labor expenses, all else
being equal. The results are robust and qualitatively similar for European and non-European
countries.
Panel B presents the results based on LS. To capture a sudden change in labor share (in
particular sudden increases in labor share due to drops in sales), we create a dummy variable
LSIncrease for each firm-year observation. It is set to equal to 1 if it is above the 75th percentile of
labor share changes in its country year, and 0 otherwise. We then interact the labor share with
this dummy variable in our analysis. As we can see from Panel B, the coefficient estimates for LS
and LSIncrease × LS are both positive when there are no control variables or when we control for
leverage and stock return volatility, suggesting an increase in labor share predicts higher default
risk and this increase is much bigger for firms with sudden rapid increase in labor share. However,
when we control for all the other variables, the LS becomes insignificant, potentially because the
control variables absorb the profitability shocks that affect labor share. However, the coefficient
on LSIncrease × LS still remains positive and statistically significant, reflecting the effects of wage
rigidity and labor adjustments costs that are not absorbed by the other control variables.
The impact of labor obligations on credit risk is likely to be higher when a firm is experiencing
distress and needs to cut down labor expenses. To test whether labor expense cut plays an
important role in the relation between labor obligations and default risk, we create a variable
XLRCut which takes the value of 1 if the firm’s ∆XLR is below the 25% percentile of ∆XLR in
its country, and 0 otherwise. Then we interact XLRCut with ∆XLR and LS and rerun the crosssectional predictive regressions as in Table 6. The results are reported in Table 7. From column
(2) of the table we can see that the coefficient estimate associated with XLRCut × ∆XLR is
-3.51 with a t-stat of -7.77, suggesting that the impact of labor expenses growth on default risk is
highly asymmetric — labor expense cut plays a main role in the negative relation between ∆XLR
10
and default risk. If we move to column (4), we can see the coefficient estimate associated with
XLRCut × LS is 2.12 with a t-stat of 14.7. This again suggests that the impact of labor share
on default risk is mainly from labor expenses cutting.
3
Model
In this section, we present a dynamic general equilibrium model with heterogenous firms to
understand the economic mechanism that drives the empirical links between labor market variables
and firms’ credit risk. We begin with the household’s problem. We then outline the firm’s problem,
the economy’s key frictions are described there. Finally we define equilibrium.
In the model financial markets are complete, therefore we consider one representative household
who receives labor income and financial income, chooses between consumption and saving, and
maximizes utility as in Epstein and Zin (1989).
11
1− 1
1
1−
ψ
1− ψ
ψ
1−θ 1−θ
+ βEt [Ut+1 ]
Ut = max (1 − β)Ct
(2)
where Ct is average consumption and β is subjective discount factor. For simplicity, we assume
that aggregate labor supply is inelastic: Nt = 1. Risk aversion is given by θ and the intertemporal
elasticity of substitution by ψ.
3.1
Firms
The interesting frictions in the model are on the firm’s side. We assume a large number of firms
(indexed by i and differing in idiosyncratic productivity) choose investment, labor, and debt to
maximize the present value of future dividend payments where the dividend payments are equal
to the firm’s after-tax profit (output net of wage bills, operating costs, and debt payment) net of
investment plus new issuance of debt. Output is produced from labor and capital. Firms hold
beliefs about the discount factor Mt+1 , which is determined in equilibrium.
3.1.1
Technology
Firm i’s output is given by
Yti = Zti α(Kti )η + (1 − α)(Xt Nti )ηρ
11
η1
.
(3)
Output is produced with CES technology from capital (Kti ) and labor (Nti ) where Xt is labor
augmenting aggregate productivity, Zti is the firm’s idiosyncratic productivity, ρ determines the
1
degree of return to scale (constant return to scale if ρ = 1), 1−η
is the elasticity of substitution
between capital and labor (Cobb-Douglas production if η = 0), and (1 − α)ρ is labor share in
production.
The process for Xt is non-stationary but its growth rate is stationary, this is in the spirit of
the exogenous shock process in long run risk models of Bansal and Yaron (2004), Kaltenbrunner
and Lochstoer (2010), and Croce (2014). We specify the growth rate of aggregate productivity
(∆ log Xt+1 ) to be the following
∆ log Xt+1 = (1 − ρX ) µX + ρX ∆ log Xt + X
t+1 ,
(4)
which is consistent with long run risk. ∆ is the first-difference operator, X
t+1 is an independently
and identically distributed (i.i.d.) standard normal shock, and µX and ρX are the average growth
rate and autocorrelation of the growth rate of aggregate productivity, respectively.
Idiosyncratic productivity log Zti follow an AR(1) process
i
log Zt+1
= ρZ log Zti + Zt+1 ,
(5)
where Zt+1 is an i.i.d. standard normal shock that is uncorrelated across all firms in the economy
and independent of X
t+1 , and ρZ is the autocorrelation of idiosyncratic productivity.
3.1.2
The Wage Contract
The wage contract here builds on Favilukis and Lin (2015a). In standard production models wages
are reset each period and employees receive the marginal product of labor. We assume that any
employee’s wage will be reset this period with probability 1 − µ.7 When µ = 0 our model is
identical to models without rigidity: all wages are reset each period, each firm can freely choose
the number of its employees, and each firm chooses Nti such that its marginal product of labor is
equal to the wage. When µ > 0 we must differentiate between the spot wage (wt ) which is paid to
all employees resetting wages this year, the economy’s average wage (wt ), and the firm’s average
wage (wit ). The firm’s choice of employees may no longer make the marginal product equal to
either average or spot wages because firms will also take into account the effect of today’s labor
choice and today’s wage on future obligations.
7
Note that this is independent of length of employment. This allows us to keep track of only the number of
employees and the average wage as state variables, as opposed to keeping track of the number of employees and
the wage of each tenure. This way of modeling wage rigidity is similar in spirit to Gertler and Trigari (2009), but
for tractability reasons, we do not model search and match frictions.
12
When a firm hires a new employee in a year with spot wage wt , with probability µ it must
pay this employee the same wage next year; on average this employee will keep the same wage for
1
1−µ
years. All resetting employees come to the same labor market and the spot wage is selected
to clear markets. The firm chooses its total labor force Nti each period. These conditions lead to
a natural formulation of the firm’s average wage as the weighted average of the previous average
wage and the spot wage:
i
i
) + wit−1 µNt−1
wit Nti = wt (Nti − µNt−1
(6)
i
i
Here Nti − µNt−1
is the number of new employees the firm hires at the spot wage and µNt−1
is the
number of tenured employees with average wage wit−1 .8
Note that the rigidity in our model is a real wage rigidity, although our channel could in
principle work through nominal rigidities as well. There is evidence for the importance of both
real and nominal rigidities. Micro-level studies of panel data sets comparing actual and notional
wage distributions show that nominal wage changes cluster both at zero and at the current
inflation rate, with sharp decreases in the density to the left of the two mass points. Barwell
and Schweitzer (2007), Devicenti, Maida and Sestito (2007), and Bauer, Goette and Sunde (2007)
find that downward real wage rigidity is substantial in Great Britain, Germany, and Italy, and that
the fraction of real wage cuts prevented by downward real wage rigidity is more than five times
greater than the fraction prevented by downward nominal wage rigidity. In a recent international
wage flexibility study, Dickens, Goette, and Groshen (2007) find that the relative importance of
downward real wage rigidity and downward nominal wage rigidity varies greatly across countries
while the incidences of both types of wage rigidity are about the same.
3.1.3
The debt contract
The firm uses long-term defaultable debt to finance investment and wage bills. More specifically,
in each period the firm chooses to issue a level of new coupon payment κit+1 for next period.
The firm may only issue κit+1 if it is currently debt free, i.e., κit = 0. If the firm currently has
outstanding debt, i.e., the current coupon κit is above zero, then the firm will not change its
coupon payment (κit =κit+1 ), in other words the firm will not issue new debt, unless one of the
following two conditions occur: i) Debt randomly expires between t and t+1, which happens with
probability pexp , ii) The firm chooses to default at the start of t+1. A firm’s debt cannot expire
before it has paid its first coupon payment. The probability of debt expiration also determines
8
i
i
cannot be interpreted as tenured employees. In this case
It is possible that Nti < µNt−1
, in which case µNt−1
we would interpret the total wage bill as including payments to prematurely laid-off employees. Note that the wage
i
bill can be rewritten as wit Nti = wit−1 Nti + (µNt−1
− Nti )(wit − wt ), here the first term on the right is the wage paid
to current employees and the second term represents the payments to prematurely laid off employees. An earlier
i
version of the paper included the constraint Nti ≥ µNt−1
, the results were largely similar.
13
the expected maturity of the debt, i.e., the average length of the debt contract is
1
.
pexp
The firm
defaults at t if its cum-dividend market value Vt+1 is below 0. Additionally, if there is a positive
amount of debt outstanding, the firm’s dividend cannot be so high so that the firm’s ex-dividend
value is less than or equal to zero, consistent with the covenants that limit the dividends firms
may pay.
In the event of bankruptcy, creditors inherit a debt free firm, of which the firm’s cum-dividend
0
. The market price of bond is determined in equilibrium and depends
value is denoted by Vt+1
on the aggregate state (discount rate) and the firm’s individual state (probability of default). In
particular, the bond pricing follows the equation below,
0
Ψit = Et Mt+1 1{exp} × 0 + 1{Vt+1 <0} × Vt+1
+ 1 − 1{exp} − 1{Vt+1 <0} κit+1 + Ψit+1 ,
(7)
where Ψit is the price of debt with coupon payment κit+1 , 1{exp} is an indicator function that takes
the value of one when the debt expires and zero otherwise, and 1{Vt+1 <0} is an indicator function
that takes the value of one when the firm is insolvent and zero otherwise.
3.1.4
Accounting
The equation for after-tax profit is
Π(Kti ) = (1 − τ ) Yti − wit Nti − zt − κit + τ δKti
(8)
Π(Kti ) is after-tax profit, which is output less labor, operating costs, and coupon payment, plus
tax shield on capital depreciation. Operating costs are defined as zt = f ∗ Kt ; they depend on
aggregate (but not firm specific) capital.9 Labor costs are wit Nti .
Capital adjustment costs are convex given by
Φ(Iti , Kti )
=υ
Iti
Kti
2
Kti ,
where υ > 0. The total dividend paid by the firm is
Dti = Π(Kti ) − Iti − Φ(Iti , Kti ) + Ψit 1{Issue} ,
9
(9)
Because productivity is non-stationary, all model quantities are non-stationary and we cannot allow for a
constant operating cost as it would grow infinitely large or infinitely small relative to other quantities. All quantities
in the model must be scaled by something that is co-integrated with the productivity level, such as aggregate capital.
We have also experimented with using the spot wage (wt ) or aggregate productivity (Xt ) and the results appear
insensitive to this.
14
which is after-tax profit less investment, capital adjustment costs plus the cash from newly issued
debt where 1{Issue} is an indicator function that takes the value of one when the firm issues new
coupon and zero otherwise.
3.1.5
The Firm’s Problem
We now formally write down firm i’s problem. The firm maximizes the present discounted value
of future dividends
(
Vti = max
)
max
i
i ,κi
It+j
,Nt+j
t+j+1
Et [
X
i
Mt+j Dt+j
], 0 ,
(10)
j=0,∞
subject to the standard capital accumulation equation
i
Kt+1
= (1 − δ)Kti + Iti ,
(11)
as well as equations (3), (6), (8), and (9).
3.1.6
Credit Spread
We define the credit spread CSt in the model as the difference between the yield ζ B
t on the
defaultable debt and the yield of a comparable bond without default risk, ζ t , i.e.,
CSt = ζ B
t − ζ t,
with ζ B
t =
3.2
κit+1
Ψit
and ζ t =
κit+1
Ψit (saf e)
(12)
where Ψit (saf e) is the price of the bond without default risk.
Equilibrium
We assume that there exists some underlying set of state variables St which is sufficient for
this problem. Each firm’s individual state variables are given by the vector Sti . Because the
household is a representative agent, we are able to avoid explicitly solving the household’s
maximization problem and simply use the first order conditions to find Mt+1 as an analytic
function of consumption or expectations of future consumption. For instance, with CRRA utility,
ψ1 −θ
−θ
− ψ1 Ct+1
Ct+1
Ut+1
Mt+1 = β Ct
while for Epstein-Zin utility Mt+1 = β Ct
.10
1
1−θ
Et [Ut+1 ] 1−θ
10
Given a process for Ct we can recursively solve for all the necessary expectations to calculate Mt+1 . The
appendix provides more details.
15
Equilibrium consists of:
• Beliefs about the transition function of the state variable and the shocks: St+1 = f (St , Xt+1 ).
• Beliefs about the realized stochastic discount factor as a function of the state variable and
realized shocks: M (St , Xt+1 ).
• Beliefs about the aggregate spot wage as a function of the state variable: w(St ).
• Beliefs about the price of debt, as a function of the state today and the firm’s choice of
coupon next period: Ψit St , Sti , κit+1
• Firm policy functions (which depend on St and Sti ) for labor demand Nti , investment Iti and
coupon κit .
It must also be the case that given the above policy functions all markets clear and the beliefs
turn out to be rational:
• The firm’s policy functions maximize the firm’s problem given beliefs about the wages, the
discount factor, and the state variable.
• The labor market clears:
P
Nti = 1
• The goods market clears: Ct =
P
(Yti − Iti ) =
P
Πit + wit Nti + zt + Φit − Iti + Tt . Note
that here we are assuming that all costs are paid by firms to individuals and are therefore
consumed, the results look very similar if all costs are instead wasted.
• The beliefs about Mt+1 are consistent with goods market clearing through the household’s
Euler Equation.11
• Beliefs about the transition of the state variables are correct. For instance if aggregate
P
capital is part of the aggregate state vector, then it must be that Kt+1 = (1 − δ)Kt + Iti .
4
Model Solution
We solve the model at a quarterly frequency using a variation of the Krusell and Smith (1998)
algorithm, we discuss the solution method in the appendix. The model requires us to choose
the preference parameters: β (time discount factor), θ (risk aversion), ψ (intertemporal elasticity
of substitution); the technology parameters: α and ρ (jointly determine labor share in output
11
For example, with CRRA Mt+1 = β
P
Dt+1,i
P +wt Nt+1,i +Φt+1,i +Ξt+1,i +Ψt+1,i
Dt,i +wt Nt,i +Φt,i +Ξt,i +Ψt,i
16
−θ
and degree of return to scale),
1
1−η
(elasticity of substitution between labor and capital), δ
(depreciation), f (operating cost); the adjustment cost parameters: ν (capital adjustment cost),
and the debt contract parameter: pexp (debt expiration probability). Finally we must choose our
key parameter µ which determines the frequency of wage resetting. Below we justify our choices
of these parameters. Table 8 presents parameters of the benchmark calibration.
Preferences We set β = 0.98 to match the level of the risk free rate. We set θ = 8 to get
a reasonably high Sharpe Ratio, while keeping risk aversion within the range recommended by
Mehra and Prescott (1985). The intertemporal elasticity of substitution ψ also helps with the
Sharpe Ratio, it is set to 2 close to that in Bansal and Yaron (2004), who show that values above
1 are required for the long run risk channel to match asset pricing moments as this ensures that
the compensation for long-run expected growth risk is positive.
Technology The technology parameters are fairly standard and we use numbers consistent
with prior literature. We jointly choose α = 0.45 and ρ = 0.77 so that labor share and profit share
are consistent with empirical estimates.12 Similarly we set η = −1 to match empirical estimates
of the elasticity of substitution between labor and capital. The elasticity of substitution between
1
labor and capital is 1−η
= 0.5. In a survey article based on a multitude of studies, Chirinko (2008)
argues this elasticity is between 0.4 and 0.6.13 We set δ = 0.025 to match annual depreciation.
Operating cost zt = f ∗Kt is a fixed cost from the perspective of the firm, however it depends
on the aggregate state of the economy, in particular aggregate capital. We choose f = 0.019 to
match the average market-to-book ratio in the economy, which we estimate to be 1.33 (details
of this estimation are in Favilukis and Lin 2015a). While we think it is realistic for this cost to
increase when aggregate capital is higher (during expansions), the results are not sensitive to this
assumption. The results look very similar when zt is simply growing at the same rate as the
economy.14 Note that fixed costs in the production process also effectively constitute a form of
operating leverage. However, its quantitative effect on credit spread is minimal.
Capital adjustment costs We choose the capital adjustment costs ν = 5 to match
the volatility of aggregate investment.
Higher adjustment costs always help increase equity
12
Labor share is (1 − α)ρ = 0.42. Profit share is (1 − α)(1 − ρ) = 0.13 implying returns to scale of 0.87. Gomes
(2001) uses 0.95 citing estimates of just under 1 by Burnside (1996). Burnside, Eichenbaum, and Rebelo (1995)
estimate it to be between 0.8 and 0.9. Khan and Thomas (2008) use 0.896, justifying it by matching the capital
to output ratio. Bachmann, Caballero and Engel (2013) use 0.82, justifying it by matching the revenue elasticity
of capital.
13
One concern may be that the estimate of η would itself be affected by frictions, such as the one in our paper.
However, several of the studies cited by Chirinko (2008) are done with micro-level data specifically to account
for frictions, therefore η is the exact model analog of their estimate. Furthermore, we have repeated the exercise
in Caballero (2004) to estimate η from aggregate quantities in our model by regressing log(Y /K) on the cost of
1
is 0.5 if the cost of capital is defined as the return on capital, and 0.41 if it is the
capital. The estimate of 1−η
interest rate plus the log of Tobin’s Q.
14
Recall that the model is non-stationary, therefore zt cannot be a constant and must be scaled by something
that is cointegrated with the size of the economy.
17
volatility but they decrease aggregate investment volatility. This restriction on matching aggregate
investment limits how much work capital adjustment costs can do in helping to match financial
moments.
Debt contract We calibrate the debt expiration probability pexp = 0.025, which implies that
the maturity of the debt contract is 40 quarters, close to the average estimate in Guedes and Opler
(1996). Corporate tax rate τ is set to 0.3 close to that in Jermann and Quadrini (2012).
Productivity shocks In order for the long run risk channel to produce high Sharpe ratios,
aggregate productivity must be non-stationary with a stationary growth rate. We specify the
growth rate of aggregate productivity (∆ log Xt ) to be a symmetric 3-state Markov process with
autocorrelation 0.27, unconditional mean of 0.02, and unconditional standard deviation of 0.055.
We choose these numbers to roughly match the autocorrelation, growth rate, and standard
deviation of output. Aggregate productivity is then log(Xt+1 ) = log(Xt ) + ∆ log Xt+1 which
is consistent with long run risk.15
The volatility of idiosyncratic productivity shocks log Zti depends on the model’s scale, that is
which real world production unit (firm, plant) is analogous to the model’s production unit. There
is no consensus on the right scale to use, for example the annual autocorrelation and unconditional
standard deviation are 0.69 and 0.40 in Zhang (2005), 0.62 and 0.19 in Gomes (2001), 0.86 and
0.04 in Khan and Thomas (2008), while Pastor and Veronesi (2003) estimate that the volatility
of firm-level profitability rose from 10% per year in the early 1960s to 45% in the late 1990s.
We have experimented with various idiosyncratic shocks and find that our aggregate results are
not significantly affected by the size of these shocks. In our model, log Zti is a 3-state Markov
process with autocorrelation and unconditional standard deviation of 0.75 and 0.23 respectively.
We believe these shocks make our production units closest to real world firms because, as will be
discussed below, these shocks allow us to match various firm moments, such as the cross-sectional
variation of investment rate and stock returns.
Frequency of wage resetting In standard models wages are reset once per period and
employees receive the marginal product of labor as compensation. This corresponds to the µ = 0
case. However, wages are far too volatile in these models relative to the data. We choose the
frequency of resetting to roughly match the volatility of wages in the data. This results in µ = 0.90
or an average resetting frequency of ten quarters.
We also believe that this number is realistic, for example Rich and Tracy (2004) estimate that
a majority of labor contracts last between two and five years with a mean of three years, they cite
several major renewals (United Auto Workers, United Steel Workers) which are at the top of the
range. Anecdotal evidence suggests that assistant professors, investment bankers, and corporate
15
Our process for TFP growth is analogous to a discretized AR(1) process, Bansal and Yaron (2004) use a slightly
more complicated formulation where consumption growth is ARMA(1,1). When the short-run and long-run shocks
in Bansal and Yaron (2004) are perfectly correlated, their process becomes identical to ours.
18
lawyers all wait approximately this long to be promoted. Even if explicit contracts are written
for a shorter period than our calibration (or not written at all), we believe that four years is a
reasonable estimate of how long the real wage of many employees stays unchanged. Campbell and
Kamlani (1997) conducted a survey of 184 firms and find that implicit contracts are an important
explanation for wage rigidity of U.S. manufacturing workers, especially of blue-collar workers. For
example, if the costs of replacing employees (for employers) and the costs of finding a new job
(for employees) are high, the status quo will remain, keeping wages the same without an explicit
contract. Another example are workers who receive small raises every year, keeping their real wage
constant or growing slowly; indeed, Barwell and Schweitzer (2007) show that this type of rigidity
is quite common. Such workers do not experience major changes to their income until they are
promoted, or let go, or move to another job. Hall (1982) estimates an average job duration of
eight years for American workers, Abraham and Farber (1987) estimate similar numbers just for
non-unionized workers (presumably unionized workers have even longer durations).
Given the importance of this parameter for our model, it is useful to note the difference between
job length and the separation rate. As mentioned above, average job length is around eight years
for American workers. A separation rate is the probability of a worker separating from her job
in any particular period. Estimates of separation rates for the US range from 1.1%/month by
Hobijn and Sahin (2009), to 3.4%/month by Shimer (2005), with most being around 3%/month.
If separations were equally likely for all workers, this would imply an average job length of around
2.8 years - far shorter than our calibrated contract length or job length in the data. This apparent
difference is due to a small number of workers who frequently transition between jobs, while a
majority of workers stay in their jobs for a long time. For example, Hall (2005) writes “Separation
rates are sensitive to the accounting period because a small fraction of jobs but a large fraction
of separations come from jobs lasting as little as a day.” Hobijn and Sahin (2009) show that 15%
of jobs have a tenure below 6 months; Davis, Faberman, and Haltiwanger (2006) show that if one
estimates separations based on workers who have held their job for a full quarter (as opposed to
all separations), the quarterly separation rate falls from 24% to 10.7%. On the other hand, as
mentioned above, estimates of average job length are around 8 years for U.S. workers.
Since, for computational reasons, in our model separation is equally likely for all workers, we
can either relate µ to estimated separation rates which will imply that model job length is too
low relative to the data, or to estimated job and contract lengths, which will imply that model
separation rates are too low relative to the data. We believe that the latter is more relevant for
our model. Note that workers who separate frequently are likely to be low paid, temporary or
part time workers who do not significantly contribute to the firm’s wage bill. The majority of the
firm’s wage bill is likely paid to high skilled and long-tenured workers and the obligations to these
workers are likely to be quite sticky.
19
5
Model Results
In this section, we study the model implications for both equity volatility and credit spread
predictability.
5.1
Aggregate Quantities
Here we discuss our benchmark model, which combines long-run risk, infrequent wage
renegotiation, long-term defaultable debt, and a calibrated CES production function. Quarterly
variables are aggregated to annual frequency to be consistent with the data. Table 9 presents
the real aggregate quantities in the data and the model. The benchmark model does a good job
at matching many macroeconomic moments. For example, it produces smooth consumption and
volatile investment. In the data, consumption is about half as volatile as GDP, and investment
is three times more volatile than GDP both in HP filtered levels and in growth rates. The
model implied consumption volatility is slightly higher than the data and investment volatility is
fairly close to the data. In addition, the persistence of consumption (consumption growth) and
investment (investment growth) are reasonably close to the data moments as well.
Turning to wage volatility, recall that in standard models where wages are reset every period,
as is shown in Favilukis and Lin (2015a), the volatility of hourly compensation is twice as high
as in the data and its correlation with output is far too high. Because labor income comprises
such a large fraction of output, this flaw is very significant quantitatively and is responsible for
many of this model’s failures at matching financial data.16 While in our benchmark model with
wage rigidity, because wages are negotiated infrequently, the average wage is no longer equal to
the marginal product of labor but rather a weighted average of past spot wages, this results in
average wages being much smoother than the marginal product of labor. The model implied wage
volatility relative to that of GDP is 0.49, close to the data moment at 0.44. Moreover wages are
imperfectly correlated with GDP; the correlation of HP filtered wage (wage growth) with GDP
(GDP growth) is 0.82 (0.85), somewhat higher than the data 0.60 (0.61), but represents a big
improvement relative to the standard models where this correlation is perfect at one. We believe
that almost any model in which average wages are smoother than the marginal product of labor
16
Unlike the first generation of RBC models, which did a very poor job matching financial moments (the well
known Equity Premium Puzzle), this model can produce a high Sharpe Ratio through the long run risk channel.
First proposed by Bansal and Yaron (2004) in an endowment economy and later incorporated into a production
economy by Croce (2014) and Kaltenbrunner and Lochstoer (2010), the long run risk channel makes the economy
appear risky to households because (i) a high intertemporal elasticity of substitution makes households care not
only about instantaneous shocks to consumption growth but also shocks to expectations of future consumption
growth, (ii) shocks to the growth rate (as opposed to the level in standard models) of productivity are persistent
causing expectations of future consumption growth to vary over time. But because the volatility of equity is so
low, the equity premium (which is the Sharpe Ratio multiplied by the volatility of equity) is also quite low.
20
will have results qualitatively similar to those discussed below. We view infrequent renegotiation
as simply one of multiple mechanisms responsible for the relatively smooth wages in the data.
5.2
Equity Volatility
Profits are approximately equal to output minus wages. In a standard model wages are highly
volatile and highly pro-cyclical (the marginal product of labor is perfectly correlated with output).
This results in profits being too smooth. Dividends are approximately equal to profits minus
investment. Because profits are relatively small in magnitude while investment is pro-cyclical,
dividends in a standard model are counter-cyclical and highly volatile, exactly the opposite of
what we observe in the data. Because profits are smooth and dividends are counter-cyclical, the
firm’s equity is also very smooth in standard models. In other words, pro-cyclical wages act as a
hedge for the firm’s shareholders, making equity seem very safe.
When wages become smoother than the marginal product of labor, profits become more volatile
and more pro-cyclical relative to the standard model. Volatile and pro-cyclical profits lead to procyclical dividends. With smoother wages no longer being as strong of a hedge, equity volatility
looks closer to the data as well. Table 10 presents the unconditional asset pricing moments of the
wage rigidity model. The rigidity model, combining infrequent renegotiation and CES production
function, has an equity volatility of 8.9% representing a significant improvement over the standard
models despite somewhat below the 19.89% in the data.17 A common problem of production
models that were able to produce high equity volatilities is that they also resulted in highly
volatile risk free rates (for example Jermann (1998) and Boldrin, Christiano and Fisher (2001) .
Note that risk free rates in our models are all sufficiently smooth. Furthermore, due to the high
volatility of equity, our model is not only able to match the high Sharpe Ratio (like Croce (2014)
and Kaltenbrunner and Lochstoer (2010)) but also gets close to the actual equity premium; the
model combining infrequent renegotiation and CES production function has an equity premium
of 4.5%, close to the data.
5.3
Credit Spread
As in Favilukis and Lin (2015a), our benchmark model fixes or greatly reduces all of the problems
with the standard model in matching wage volatility, and equity volatility. In the following, we
will also focus on the novel empirical predictions of the model on the forecastability of credit
spread.
17
The model implied equity volatility is short of magnitude because both labor and debt are frictionlessly adjusted.
Adding adjustment costs on these margins will make equity volatility even closer to the data.
21
Because wages are set infrequently, the average wage is no longer equal to the marginal product
of labor but rather a weighted average of past spot wages, this results in average wages being
much smoother than the marginal product of labor. Smoother wages imply volatile profit which
in turn increases the default probability and credit risk premium. Table 10 presents the credit
risk moments implied by the model. The model implied financial leverage is 0.31, close to the
data moment at 0.44. The credit spread is 2.9%, within the historical range of the credit spread
while lies on the upper part of the distribution. The average default probability is 1.3%, close to
the mean estimate at 1.5% in the data, which also falls within the historical estimates reported in
Giesecke et al (2011).
Turning to the predictability of the credit spread, Panel B in Table 11 presents the predictive
regression results. In the model, wage growth negatively forecasts credit spread with the slope
at -11.03, which is fairly close to the data counterpart at -15.4. Similarly, labor share positively
forecasts credit spread with the slope coefficient at 10.20, which is also close to the data slope of
10.66. Taken together, the model does a reasonably good job generating a sizable credit spread
despite low default probability, thus providing a novel explanation for the credit spread puzzle.
Furthermore, the benchmark model also quantitatively generates time-variations in credit spread
that is consistent with data.
5.4
Intuition
To gain some intuition for why wage rigidity matters for credit risk premium and its predictability,
we will compare the default decision in the frictionless model to the model with wage rigidities.
The firm defaults if its realized firm value Vt is below zero. This occurs if all else being equal, the
firm’s idiosyncratic productivity Z is below a cutoff value Z ∗ , which itself depends on the state of
the economy including the aggregate the firm-specific state variables. Mathematically, the cutoff
value Z ∗ is a function of states, which can be characterized as
i
Z ∗ St , Kti , Nt−1
, κit ; wit
= arg min [Vt (St , Sti ) > 0]
Z
= arg min (1 − τ ) Yti − wit Nti − Ψit − κit + τ δKti − Iti − Φ(Iti , Kti ) + Ψit 1{Issue} + Et Mt+1 Vt+1 > 0
Z
(13)
The default decision can be described as follows
Z ≥ Z ∗ stay
Z < Z ∗ default
22
(14)
All else equal, the model with rigidity implies a higher default probability than the frictionless
model. When a negative aggregate productivity shock hits the economy, gross profit Yti − wit Nti in
the model without wage rigidity will fall roughly proportional to output, whereas the gross profit
will fall by more than output in the wage rigidity model. This implies that all else being equal, the
cutoff value of idiosyncratic productivity for default in the frictionless model is lower than that of
wage rigidity model, i.e.,
∗
Zf∗rictionless < Zrigidity
(15)
Equation (15) implies that the default region in idiosyncratic productivity for the frictionless
model is smaller than the wage rigidity model, which is described in equation (16),
∗
−∞, Zf∗rictionless ⊂ −∞, Zrigidity
.
(16)
This relationship will directly translate into a higher default probability for the firm in the wage
rigidity model, which in turn results in higher credit risk premium since aggregate productivity
shocks carry a positive price of risk. This economic channel leads to a sizable credit spread in
the wage rigidity model. Furthermore, the operating leverage effect caused by wage rigidities is
not constant over time. Times of low wage growth or high labor share are associated with high
labor leverage and hence are associated with high credit risk premium. This happens because
during bad (good) times, wages fall (rise) by less than output leading to an increase (decrease)
in operating leverage, thus wage growth negatively whereas labor share positively predicts future
credit spread in the model.
6
Conclusion
Labor market variables have significant impact in driving the credit spread fluctuations. We show
that wage growth and labor share strongly forecast credit risk as well as or better than the standard
predictors including financial leverage and market volatility both in the time series and the cross
section of firms across a wide range of countries. We build a DSGE model with wage rigidities and
long-term defaultable debt that can explain this link. This is because pre-committed payments to
labor make other committed payments (such as debt) riskier; for this reason variables related to
pre-committed labor payments forecast credit risk.
Our results have implications for asset pricing, labor economics, and macroeconomics literature.
Our findings suggest that labor market frictions, in particular, wage rigidity can have a significant
impact on corporate bond prices. Credit market variables, which are typically ignored in the labor
economics literature, can thus be a useful source of information for quantifying frictions in labor
23
markets. Our results suggest that incorporating time-varying credit risk in current DSGE models
can be important for an accurate understanding of labor market dynamics over the business cycle.
24
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28
A
A.1
Numerical Solution
Making the Model Stationary
Note that the model is not stationary. In order to solve it numerically, we must rewrite it in
terms of stationary quantities. We will show that a normalizing all non-stationary variables by Ztρ
implies a stationary competitive equilibrium. We will do this in two steps. First we will show that
if the firm believes that the stochastic discount factor is stationary and that aggregate quantities
(in particular the spot wage) normalized by Ztρ are stationary than the firm’s policy functions
normalized by Ztρ will also be stationary. Second we show that these policy functions imply that
these aggregate quantities are indeed stationary when normalized by Ztρ .
The firm’s problem is:
i
i
, κit , W t−1 ; Zt , Kt , St , W t−1 ) = maxIti ,Nti ,κit+1 (1 − τ ) Yti − wit Nti − zt − κit + τ δKti
V (Zti , Kti , Nt−1
i
i
i
, Nti , κit+1 , W t ; Zt+1 , Kt+1 , St+1 , W t )]
, Kt+1
+Et [Mt+1 V (Zt+1
(17)
i
i
i
Where Zt is the idiosyncratic productivity, Kt is the firm’s individual capital, Nt−1 is the firm’s
i
employment last period, κit is the current coupon payment paid, W t−1 is the firm’s average wage last
period, Zt is aggregate productivity, W t−1 is the aggregate average wage from last period, and Wt is
the spot wage this period. Following Krusell and Smith (1998) the state space potentially contains
all information about the joint distribution of capital and productivity. Kt and St summarize this
distribution. We explicitly write its first moment Kt as an aggregate state variable and let St
be a vector of any other relevant moments normalized by the mean (i.e. the normalized second
moment is E[(Kti − Kt )2 ]/Kt2 ).
Households have beliefs about the evolution of the aggregate quantities Mt+1 , Kt , and St
and about the spot wage as a function of the aggregate state. Aggregate wage evolves as
W t = µW t−1 + (1 − µ)Wt . The individual state variables evolve as:
i
Kt+1
= (1 − δ)Kti + Iti
i
Wt =
Ki
(18)
i
i
i
W t−1 Nt−1
µ+(Nti −Nt−1
µ)Wt
i
Nt
Ii
κi
i
t
Let us define kti = Z ρt , kt = ZKρt , iit = Ztρ , κ̂it = Ztρ ,wt = W
, wit = ZWρ t , and wt = ZWρ t (not that
Ztρ
t
t
t
t
t+1
t+1
the timing of wit and wt differs from the others). We will now show by induction that the value
function is linear in Ztρ . Suppose this is true at t+1:
i
ρ
i
i
i
i
V (Zt+1
, Kt+1
, Nti , κit , W t ; Zt+1 , Kt+1 , St+1 , W t ) = Zt+1
V (Zt+1
, kt+1
, Nti , κit+1 , wit ; 1, kt+1 , St+1 , wt )
29
Than we can rewrite the firm’s problem as:
i
V (Zti , kti , Nt−1
, κ̂it , wit−1 ; 1, kt , St , wt−1 ) = maxiit ,Nti ,κit+1 (1 − τ ) Yti − wit Nti − zt − κit + τ δKti
ρ
i
i
+Et [ ZZt+1
Mt+1 V (Zt+1
, kt+1
, Nti , κ̂it+1 , wit ; 1, kt+1 , St+1 , wt )]
t
(19)
−ρ
Zt+1
and the individual state
where the aggregate wage evolves as wt = (µwt−1 + (1 − µ)wt ) Zt
variables evolve as:
−ρ
i
kt+1
= ((1 − δ)kti + iit ) ZZt+1
t
i i
−ρ
(20)
i −N i
w
N
µ+(N
µ)w
t
Zt+1
t
t−1 t−1
t−1
wit =
i
Zt
Nt
ρ
As long as ZZt+1
, Mt+1 , kt+1 , and wt+1 are stationary this is a well defined stationary problem
t
i
where the firm’s optimal policy (iit and Nti ) will also be stationary. But this implies that kt+1
and
P i
kt+1 = kt+1 are stationary as well, confirming the firm’s beliefs.
It is similarly straight forward to show that the stochastic discount factor is stationary. First
of all note that Mt+1 is related to the growth rate of consumption, so it should be stationary.
More formally:
11
1− 1
1
1−
ψ
1− ψ
ψ
1−θ 1−θ
+ βEt [Ut+1 ]
U t = Ct
(21)
1 −θ 1
ψ
Ut+1
Mt+1 = β
Ct+1
Ct
1
1−θ 1−θ
Et [Ut+1
]
−ψ
Define ct = ZCρt and ut = ZUρt and note that the firm’s optimal policy implies that ct is stationary.
t
t
Now we can rewrite the above equations as:
ut =
1− 1
ct ψ
+ βEt [
Z
Mt+1 = β
t+1
Zt
Et [
Z
t+1
Zt
Zt+1
Zt
ρ
ρ
ρ
ut+1
1− 1
ψ
1−θ
1−θ
ut+1
]
! ψ1 −θ
1
1−θ
u1−θ
t+1 ]
1
1− 1
ψ
ct+1
ct
− ψ1 Zt+1
Zt
− ψρ
(22)
which are stationary as long as ct is stationary.
Next, we must show that the spot wage is stationary. The firm’s first order condition for labor
implies:
wt =
Zti
α(kti )η
+ (1 −
α)(Nti )ρη
1−η
η
(1 −
α)ρ(Nti )ρη−1
ρ
Zt+1
∂Vt+1
+ Et [
Mt+1
]
Zt
∂Nti
(23)
For every firm, the right hand side is well defined and stationary, therefore the wage is too. To
jointly find the wage and each firm’s choice of Nti one must solve a system of N equations. N-1
equations where the right hand side of the first order condition for firm 1 is set equal to firm i
30
P i
(i=2,N), and the labor market clearing equation
Nt = 1.
There remains one last complication, is St stationary? This is related to a more general problem
of the validity and accuracy of the Krusell and Smith (1998) algorithm. We cannot give an explicit
answer as it is not clear what exactly St must contain. Krusell and Smith (1998) argue that St
should contain higher order moments of the distribution since they fully describe the distribution.
Since we define St to be normalized by its first moment, it is likely that these normalized higher
moments are stationary. We have also checked the behavior of several simulated higher order
moments and they appear stationary. In practice our numerical algorithm (described in the next
section) only considers the first moment so St is an empty set, which is stationary by definition.
A.2
Numerical Algorithm
We will now describe the numerical algorithm used to solve the stationary problem above. We
will first describe the algorithm used to solve a model with CRRA utility and then the extension
necessary to solve the recursive utility version. The algorithm is a variation of the algorithm in
Krusell and Smith (1998).
The aggregate state space is potentially infinite because it contains the full distribution of
capital across firms. We follow Krusell and Smith (1998) and summarize it by the average aggregate
capital kt and the state of aggregate productivity ∆Zt ; because past wages matter, we augment
the aggregate state space with the previous period’s average wage wt−1 . Each of these is put on
a grid, with the grid sizes of 20 for capital, 9 for past wage, and 13 for coupon. Productivity is a
3-state Markov process. We also discretize the firm’s individual state space with grid sizes of 25
i
), and 5 for last period’s average wage
for individual capital (kti ), 11 for last period’s labor (Nt−1
(wit−1 ). Individual productivity is a 2-state Markov process. We chose these grid sizes after careful
experimentation to determine which grid sizes had the most effect on Euler equation errors and
predictive R2 .
For each point in the aggregate state space (kt , wt−1 , ∆Zt ) we start out with an initial belief
about consumption, spot wages, and investment (ct , wt , and it ); note that this non-parametric
approach is different from Krusell and Smith (1998).18 From these we can solve for aggregate
−ρ
capital next period kt+1 = ((1 − δ)kt + it ) ZZt+1
for each realization of the shock. Combining
t
kt+1 with beliefs about consumption as a function of capital we can also solve for the stochastic
18
The standard Krusell and Smith (1998) algorithm instead assumes a functional form for the transition, such as
log(k t+1 ) = A(Zt ) + B(Zt )log(kt ) and forms beliefs only about the coefficients A(Zt ) and B(Zt ) however we find
that this approach does not converge in many cases due to incorrect beliefs about off-equilibrium situations and
that our approach works better. Without heterogeneity and infrequent resetting we would not need beliefs about
wt because it would just be the marginal product of aggregate capital. Similarly, we would not need beliefs about
ct as we could solve for it from yt = ct + it where yt is aggregate output, however aggregate output is no longer a
simple analytic function of aggregate capital.
31
ct+1
ct
−θ Zt+1
Zt
−θρ
. This is enough information to solve
discount factor next period: Mt+1 = β
the stationary problem described in the previous section. We solve the problem by value function
iteration with the output being policies and market values of each firm for each point in the state
space.
The next step is to use the policy functions to simulate the economy. We simulate the economy
for 5500 periods (we throw away the initial 500 periods). In addition to the long simulation, we
start off the model in each point of the aggregate state space. We must do this because unlike
Krusell and Smith (1998), the beliefs in our algorithm are non-parametric and during the model’s
typical behavior it does not visit every possible point in the state space. From the simulation
we form simulation implied beliefs about ct , wt , and it at each point in the aggregate state space
by averaging over all periods in which the economy was sufficiently close to that point in the
state space. Our updated beliefs are a weighted average of the old beliefs and the new simulation
implied beliefs.19 With these updated beliefs we again solve the firm’s dynamic program; we
continue doing this until convergence.
In order to solve this model with recursive preferences an additional step is required. Knowing
ct and kt+1 as functions of the aggregate state is not alone enough to know Mt+1 because
in addition to consumption growth, it depends on the household’s value function next period:
ψ1 −θ
− ψ1 Ut+1
Ct+1
. However this problem is not difficult to overcome. After
Mt+1 = β Ct
1
1−θ
Et [Ut+1 ] 1−θ
each simulation step we use beliefs about ct and kt+1 to recursively solve for the household’s value
function at each point in the state space. This is again done through value function iteration,
however as there are no choice variables this recursion is very quick.
We perform the standard checks proposed by Krusell and Smith (1998) to make sure we have
found the equilibrium. Although our beliefs are non-parametric, we can still compute an R2
analogous to a regression; all of the R2 are above 0.999. We have also checked that an additional
state variable (either the cross-sectional standard deviation of capital or lagged capital) does not
alter the results.
A.3
Variable Construction
Our firm-level control variables are constructed as follows:
• W CT A: Working capital is the ratio of Compustat item WCAP to total assets (Compustat
item AT).
19
The weight on the old belief is often required to be very high in order for the algorithm to converge. This is
because while rational equilibria exist, they are only weakly stable in the sense described by Marcet and Sargent
(1989). However, we find that this is only a problem when capital adjustment costs are very close to zero.
32
• RET A: Retained earnings is the ratio of Compustat item RE to total assets.
• EBIT T A: EBIT is the ratio of Compustat item EBIT to total assets.
• Leverage: Financial leverage is defined as (DLT T + DLC)/AT , where DLT T and DLC
are Compustat items for long-term and short-term debt respectively. We also calculate an
alternative measure using (DLT T + DLC)/(DLT T + DLC + AT + T XDIT C − P ST K −
LT ) but find that empirically the correlation between these two measures is high (95%
correlation). Therefore we only report the results based on our main definition of financial
leverage.
• ST A: Sales is the ratio of Compustat item SALE to total assets.
• N IT A: Net income is the ratio of Compustat item NI (for North America) and NICON (for
Global) to total assets.
• CACL: Current ratio is the ratio of Compustat item ACT (current assets) to LCT (current
liabilities).
• σ: Stock return volatility is the standard deviation of monthly returns. For US firms, stock
returns are retried from CRSP. For firms in other countries, we use data from Compustat
Global Security Daily to calculate stock return in month t as
RETt =
P RCCDt /AJEXDIt × T RF Dt − P RCCDt−1 /AJEXDIt−1 × T RF Dt−1
P RCCDt−1 /AJEXDIt−1 × T RF Dt−1
where P RCCDt is the closing price at month end, AJEXDIt and T RF Dt are the
corresponding share and return adjustment factors.
• Invest: Investment ratio is defined as the ratio of Compustat item CAPX to lagged PPENT
(Property, Plant and Equipment).
• M CAP : The market capitalization of a firm at year for is defined as the logarithm of the
product of year end closing price (PRCCD) and shares outstanding (CSHOC).
• RSIZE: Relative size is defined as the logarithm of the ratio of company’s market
capitalization to the total market capitalization in its country at the year end. In other
words, it is a company’s weight in its country’s value-weighted market portfolio.
• Rm : The return on the value-weighted market portfolio for each country at annual frequency.
• Rexcess : The excess return of a firm’s stock is defined as the difference between firm’s raw
return (RET ) and the value-weighted market portfolio return (Rm ).
33
4
Credit Spread
∆W
LS
3
2
1
0
−1
−2
−3
1950
1960
1970
1980
1990
2000
2010
Figure 1: Labor Market Variables and Credit Spread
This figure plots the Baa-Aaa credit spread, wage growth (∆W ) and labor share (LS). Wage growth is the growth
rate of real wages & salaries per employee; labor share is the total compensation scaled by GDP, and credit spread is
the Moody’s Baa-Aaa corporate bond yield. Sample is from 1948 to 2014. The grey bars are the NBER recessions.
All variables are standardized to allow for an easy comparison in one plot.
34
Table 1
Descriptive Statistics
Panel A reports the descriptive statistics of the variables of interests. Panel B reports the cross correlations
of the variables. Credit spread (CS) is the Moody’s Baa-Aaa corporate bond yield. Wage growth (∆W )
is the growth rate of real wages & salaries per employee; labor share (LS) is the aggregate compensation
divided by GDP; investment growth (InvGr) is the growth rate of real private nonresidential fixed
investment; P/E is the equity price to earnings ratio from Shiller; term spread (TS) is the long-term
government bond yield (10 year) minus the short-term government bond yield (1 year); financial leverage
(FinLev) is book value of nonfinancial credit instruments divided by the sum of the market value of
equities and credit instruments of nonfinancial corporate sector. Market volatility (MktVol) is the annual
volatility of CRSP value-weighted market premium; spot rate (SoptRate) is the real 1 year government
bond yield from Shiller’s webpage. GDP growth (GDPGr) is the real GDP growth from NIPA. Wage
growth, labor share, investment growth, term spread, credit spread, and spot rate are in percentage
terms. Sample is from 1948 to 2014.
Panel A Summary Statistics
∆W
LS
InvGr
P/E
TS
FinLev
MktVol
SpotRate
CS
Mean
s.d
AC
1.5
55.29
4.46
16.58
1.37
0.44
0.14
1.57
0.95
1.42
1.23
6.31
16.16
1.28
0.09
0.05
2.73
0.4
0.47
0.86
0.2
0.82
0.44
0.88
0.33
0.56
0.74
Panel B Cross Correlations
GDPGr
∆W
LS
∆W
LS
InvGr
P/E
TS
FinLev
MktVol
SpotRate
0.41
-0.14
-0.1
InvGr
0.76
0.2
-0.06
P/E
0.07
0.2
0.21
0.06
TS
-0.16
0.01
-0.21
-0.29
-0.07
FinLev
-0.01
-0.54
0.25
-0.15
-0.18
0.09
MktVol
-0.32
-0.2
0.32
-0.32
0.11
-0.02
0.38
SpotRate
-0.12
0.16
0.3
-0.07
0.12
0.02
0.19
0.08
CS
-0.51
-0.42
0.22
-0.49
-0.08
0.25
0.62
0.45
35
0.3
Table 2
Labor Market Variables and Credit Spread
This table reports the predictive regression of variables of interests for credit spread. Credit spread (CS)
is the Moody’s Baa-Aaa corporate bond yield. Wage growth (∆W ) is the growth rate of real wages
& salaries per employee; labor share (LS) is the aggregate compensation divided by GDP; investment
growth (InvGr) is the growth rate of real private nonresidential fixed investment; P/E is the equity price to
earnings ratio from Shiller; term spread (TS) is the long-term government bond yield (10 year) minus the
short-term government bond yield (1 year); financial leverage (FinLev) is book value of nonfinancial credit
instruments divided by the sum of the market value of equities and credit instruments of nonfinancial
corporate sector. Market volatility (MktVol) is the annual volatility of CRSP value-weighted market
premium; spot rate (SR) is the real 1 year government bond yield from Shiller’s webpage. GDP growth
(GDPGr) is the real GDP growth from NIPA. [t] are heteroscedasticity and autocorrelation consistent
t-statistics (Newey-West). Sample is from 1948 to 2014.
Panel A Wage growth
∆W
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
-15.4
-14.47
-14.82
-8.08
-13.04
-14.86
-15.29
-16.67
-4.29
-4.15
-4.41
-3.75
-2.86
-4.32
-4.92
-4.9
-3.68
-3.4
LS
8.52
0.14
3.13
0.08
InvGr
-0.63
0.53
-1.24
1.43
FinLev
2.17
1.12
4.77
2.26
MktVol
2.84
0.56
6.35
1.29
P/E
0
0.01
-0.49
1.55
TS
-5.36
-10.61
-1.62
-4.06
SpotRate
4.63
0.26
2.61
0.41
lag CS
0.67
7.74
2
R
0.28
0.34
0.28
0.42
36
0.41
0.28
0.3
0.37
0.74
Labor Market Variables and Credit Spread (Contd)
Panel B Labor Share
LS
[1]
10.66
2.15
InvGr
[2]
10.33
2.09
-1.2
-2.45
FinLev
[3]
6.33
1.46
[4]
6.33
1.45
[5]
11.14
2.04
[6]
9.83
2.19
[7]
9.28
1.83
2.71
5.73
MktVol
3.14
4.68
P/E
-0.01
-1.06
TS
-3.79
-0.71
SpotRate
2.24
0.98
lag CS
R2
0.09
0.11
0.4
0.24
37
0.13
0.09
0.10
[8]
0.08
0.24
0.34
0.76
1.67
3.2
0.32
0.75
0.01
2.11
-11.53
-3.93
-0.46
-0.95
0.7
8.1
0.73
Table 3: No. of annual observations with non-missing labor expenses, hiring, and EDF
This table reports the number of annual (firm-year) observations for each individual country.
In particular, the number of annual
observations with non-missing labor expenses (Compustat variable XLR), hiring (Compustat variable EMP), and the EDF is reported
in the column titled “# Obs w XLR/EMP/EDF”. The percentage of observations with non-missing labor expenses, hiring, and EDF is
reported for each country (column titled “Within country % of obs w XLR/EMP/EDF”). The last column titled “For all countries % of
obs w XLR/EMP/EDF” presents the percentage of observations with non-missing labor expenses, hiring, and EDF contributed by each
country to the final sample of all observations with non-missing labor expenses, hiring, and EDF (total # of obs = 63274).
Start
Year
End
Year
All
Obs
# Obs
w XLR
Country
Region: Europe
Austria
1992
2011
1425
1318
Belgium
1992
2011
1769
1597
Denmark
1992
2011
2244
2048
Finland
1992
2011
1995
1897
France
1992
2011
10855
10055
Germany
1992
2011
11151
10005
Greece
1994
2011
2443
1443
Italy
1992
2011
3631
3425
Netherlands
1992
2011
2756
2492
Norway
1992
2011
3021
2607
Poland
1994
2011
3722
2699
Portugal
1992
2011
857
771
Spain
1992
2011
2216
2149
Sweden
1992
2011
5712
4798
Switzerland
1992
2011
3485
3176
United Kingdom
1992
2011
26546
21034
Region: North America
Canada
1992
2011
23575
3228
United States
1992
2011
135632
9588
Region: Japan
Japan
1992
2011
50011
2
Region: Asia Pacific (ex. Japan)
Australia
1992
2011
19885
11285
China
1992
2011
27448
1210
Hong Kong
1992
2011
3468
2363
India
1992
2011
29938
26949
Indonesia
1992
2011
4017
2705
Malaysia
1992
2011
12457
7986
New Zealand
1992
2011
1633
563
Philippines
1992
2011
2198
1296
Singapore
1992
2011
7903
5210
S. Korea
1993
2011
8701
75
Taiwan
1992
2011
14520
214
Thailand
1992
2011
5749
3171
Region: Other America (ex. Canada and U.S.)
Argentina
1992
2011
934
352
Brazil
1992
2011
4558
2039
Chile
1992
2011
2171
346
Mexico
1992
2011
1674
282
Region: Middle East
Israel
1992
2011
2975
2058
Pakistan
1994
2011
2814
2033
Turkey
1992
2011
1905
854
Region: Africa
South Africa
1992
2011
3761
1893
Total
451755
157216
Within
For all
# Obs
w EMP
# Obs
w EDF
# Obs
w XLR/EMP/EDF
Country
% of obs
w XLR/EMP/EDF
Countries
% of obs
w XLR/EMP/EDF
1152
1348
1844
1716
7122
7884
1073
2261
2414
2189
304
495
1580
3296
2721
20157
981
1224
1457
1544
8105
7200
1724
2584
2085
1900
1457
643
1674
3041
2378
18954
796
932
1216
1342
5393
5053
498
1631
1800
1436
135
403
1273
2045
1867
15372
55.86
52.69
54.19
67.27
49.68
45.31
20.38
44.92
65.31
47.53
3.63
47.02
57.45
35.80
53.57
57.91
1.26
1.47
1.92
2.12
8.52
7.99
0.79
2.58
2.84
2.27
0.21
0.64
2.01
3.23
2.95
24.29
10989
115652
11908
69610
975
4747
4.14
3.50
1.54
7.50
33883
42403
0
0.00
0.00
4515
1031
1969
5927
2440
4267
337
1191
2425
62
213
2071
12018
10755
1812
6603
2377
9084
1029
995
5211
5916
10868
3240
2385
486
1019
2786
1169
3024
147
551
1591
32
20
908
11.99
1.77
29.38
9.31
29.10
24.28
9.00
25.07
20.13
0.37
0.14
15.79
3.77
0.77
1.61
4.40
1.85
4.78
0.23
0.87
2.51
0.05
0.03
1.44
79
956
381
646
667
671
1303
993
36
115
49
63
3.85
2.52
2.26
3.76
0.06
0.18
0.08
0.10
711
524
906
1008
993
1443
362
242
481
12.17
8.60
25.25
0.57
0.38
0.76
1700
2330
894
23.77
1.41
250431
260188
63274
38
Table 4: Summary statistics on labor expenses and EDF
This table reports the summary statistics on EDF, labor expenses growth, and labor share. We define labor expenses
growth as ∆XLR = (XLRt − XLRt−1 )/XLRt−1 and labor share as LSt = XLRt /Salet for year t. We report the mean
and standard deviation of these variables within each country; we also report the same summary statistics for all countries
in the last row “Total”.
EDF
∆XLR
LS
Country
Mean St.D. Mean St.D. Mean St.D.
Region: Europe
Austria
1.57
3.90
0.01
0.35
0.26
0.12
Belgium
1.25
3.14
0.06
0.46
0.22
0.15
Denmark
1.36
3.49
0.11
0.38
0.27
0.17
Finland
1.03
2.81
0.04
0.36
0.27
0.16
France
1.94
4.15
0.04
0.35
0.28
0.18
Germany
2.47
5.45
0.07
0.39
0.27
0.17
Greece
3.72
6.10
0.05
0.42
0.17
0.13
Italy
1.38
3.21
0.01
0.39
0.20
0.12
Netherlands
1.30
3.71
0.06
0.36
0.26
0.17
Norway
2.50
5.50
0.17
0.41
0.26
0.17
Poland
2.40
4.80
0.19
0.37
0.18
0.13
Portugal
2.27
4.52
0.00
0.32
0.19
0.14
Spain
0.85
2.38
0.03
0.31
0.21
0.13
Sweden
1.74
4.22
0.15
0.39
0.32
0.21
Switzerland
0.82
2.74
0.06
0.27
0.26
0.13
United Kingdom
2.07
4.50
0.20
0.53
0.23
0.18
Region: North America
Canada
4.13
7.59
0.18
0.51
0.26
0.20
United States
2.78
6.13
0.10
0.25
0.30
0.18
Region: Japan
Japan
2.31
4.23
0.07
NA
0.27
0.01
Region: Asia Pacific (ex. Japan)
Australia
2.50
5.16
0.56
1.20
0.26
0.24
China
0.87
1.74
0.24
0.35
0.09
0.08
Hong Kong
1.79
3.73
0.31
0.67
0.13
0.13
India
4.03
6.34
0.23
0.54
0.10
0.11
Indonesia
6.70
9.50
0.28
0.71
0.08
0.08
Malaysia
2.98
5.44
0.09
0.31
0.12
0.09
New Zealand
1.62
4.23
0.12
0.42
0.21
0.16
Philippines
5.69
9.01
0.18
0.63
0.13
0.14
Singapore
2.59
4.41
0.15
0.47
0.15
0.12
S. Korea
4.15
6.51
0.24
0.80
0.07
0.09
Taiwan
1.74
3.29
0.27
0.51
0.10
0.12
Thailand
3.52
6.76
0.08
0.25
0.13
0.10
Region: Other America (ex. Canada and U.S.)
Argentina
4.38
7.18
0.29
0.46
0.13
0.09
Brazil
3.68
7.06
0.23
0.58
0.11
0.12
Chile
1.55
4.17
0.16
0.38
0.11
0.10
Mexico
2.91
6.12
0.45
1.21
0.04
0.08
Region: Middle East
Israel
1.92
4.13
0.28
0.79
0.15
0.16
Pakistan
5.82
8.92
0.22
0.53
0.07
0.06
Turkey
1.68
2.81
0.23
0.58
0.08
0.08
Region: Africa
South Africa
3.60
6.98
0.30
0.73
0.17
0.12
Total
2.57
5.3939
0.18
0.56
0.19
0.17
Table 5: Time-series correlation between labor expenses and EDF
This table reports the distribution of the firm-level time-series correlation between labor expenses growth and EDF
(Corr(∆XLR, EDF )), and the correlation between labor share and EDF (Corr(LS, EDF )). For every firm, we calculate
Corr(∆XLR, EDF ) and Corr(LS, EDF ) using its time-series observations. Then we report the mean and standard
deviation of these two correlations within each country; we also report the same summary statistics for all countries in the
last row “Total”. The t-stat is for testing whether Corr(∆XLR, EDF ) = 0 or Corr(LS, EDF ) = 0.
Corr(∆XLR, EDF )
Country
Mean St.D. No of firms t-stat
Region: Europe
Austria
-0.34
0.48
102
-7.08
Belgium
-0.15
0.50
121
-3.20
Denmark
-0.23
0.45
137
-6.02
Finland
-0.21
0.38
139
-6.45
France
-0.21
0.46
822
-12.73
Germany
-0.25
0.45
723
-14.68
Greece
-0.16
0.61
152
-3.24
Italy
-0.13
0.50
272
-4.46
Netherlands
-0.18
0.50
189
-5.07
Norway
-0.26
0.55
212
-6.91
Poland
-0.27
0.60
195
-6.24
Portugal
-0.17
0.46
60
-2.83
Spain
-0.15
0.45
155
-4.07
Sweden
-0.24
0.54
311
-7.94
Switzerland
-0.22
0.44
212
-7.26
United Kingdom -0.23
0.51
1917
-19.84
Region: North America
Canada
-0.17
0.67
268
-4.07
United States
-0.17
0.64
712
-6.96
Region: Japan
Japan
Region: Asia Pacific (ex. Japan)
Australia
-0.19
0.53
1265
-12.78
China
-0.14
0.57
87
-2.35
Hong Kong
-0.16
0.51
170
-4.03
India
-0.20
0.54
1279
-13.31
Indonesia
-0.11
0.51
214
-3.01
Malaysia
-0.16
0.51
885
-9.70
New Zealand
-0.26
0.60
92
-4.22
Philippines
-0.03
0.49
87
-0.61
Singapore
-0.16
0.52
519
-6.77
S. Korea
0.23
0.75
9
0.92
Taiwan
0.97
1
Thailand
-0.10
0.58
289
-2.95
Region: Other America (ex. Canada and U.S.)
Argentina
-0.03
0.56
38
-0.34
Brazil
-0.11
0.65
78
-1.45
Chile
0.05
0.95
39
0.31
Mexico
-0.04
0.82
22
-0.21
Region: Middle East
Israel
-0.19
0.52
107
-3.83
Pakistan
-0.02
0.53
103
-0.38
Turkey
-0.17
0.58
105
-2.97
Region: Africa
South Africa
-0.20
0.59
192
-4.67
40
Total
-0.19
0.53
12280
-39.89
Corr(LS, EDF )
St.D. No of firms
t-stat
0.09
0.02
0.08
0.20
0.16
0.16
0.19
0.17
0.11
0.13
0.10
0.09
0.27
0.21
0.11
0.15
0.54
0.58
0.51
0.44
0.53
0.53
0.59
0.53
0.52
0.55
0.59
0.49
0.49
0.55
0.50
0.58
103
121
135
139
827
721
165
272
191
209
198
60
158
309
209
1895
1.71
0.30
1.87
5.41
8.46
7.94
4.15
5.31
2.86
3.28
2.34
1.48
6.79
6.53
3.26
10.89
0.05
0.09
0.74
0.68
117
692
0.77
3.63
0.05
0.12
0.16
0.13
-0.07
0.06
-0.02
0.01
0.09
0.00
0.74
0.04
0.66
0.61
0.54
0.57
0.55
0.54
0.60
0.56
0.52
0.85
0.70
0.55
1004
88
175
1277
223
908
91
89
530
14
7
300
2.53
1.92
3.85
8.06
-2.02
3.28
-0.24
0.19
3.96
0.00
2.79
1.30
0.21
0.16
0.01
0.38
0.54
0.63
0.87
0.74
42
79
77
37
2.48
2.32
0.06
3.16
0.05
-0.04
0.07
0.56
0.51
0.61
109
104
118
0.92
-0.75
1.26
0.14
0.60
211
3.40
0.11
0.58
12004
21.29
Mean
Table 6: Labor expenses and default risk
This table reports the results of cross-sectional regressions using labor expenses to predict default risk. Panel A reports
the results based on labor expenses growth (∆XLR). We regress the default risk (EDF ) in year t+1 on labor expenses
growth and other control variables in year t. We also interact the labor expenses with a labor expense rigidity measure
Rigid. To calculate Rigid, we first calculate the time series volatility of labor expenses growth for each individual firm.
Then we define a firm’s labor expenses as rigid if its labor expense volatility is below 25% percentile in its country
(i.e., Rigid = 1), otherwise we set Rigid = 0. The other variables include leverage (Leverage), stock volatility (σ),
working capital (W CT A), retained earnings (RET A), EBIT (EBIT T A), sales (ST A), net income (N IT A), current
asset to liability (CACL), investment (Invest), stock excess return (Rexcess ), relative size (RSIZE), market return
(Rm ), market capitalization (M CAP ). Panel B reports the results based on labor share (LS). We also interact the
labor share with a indicator variable for rapid increase in labor share LSIncrease . To calculate LSIncrease , we first
calculate the change in labor share for each firm-year observations. Then we define a labor share as experiencing
rapid increase if its change is above below 75% percentile in its country for that year (i.e., LSIncrease = 1), otherwise
we set LSIncrease = 0. All the other variables are the same as in Panel A. The details of the variable constructions
can be found in the appendix. All the results are estimated using Fama-MacBeth (1973) cross-sectional regressions.
The t-statistics reported in the parentheses below each coefficient estimate are heteroscedasticity and autocorrelation
consistent t-statistics (Newey-West). Statistical significance levels of 1%, 5%, and 10% are indicated with ***, **, and
* respectively.
Panel A:
(1)
∆XLR
(2)
All countries
(3)
(4)
-1.10*** -0.95*** -1.08***
(-7.84) (-7.22) (-11.25)
Rigid × ∆XLR
-2.65***
(-6.67)
Control variables:
Leverage
σ
W CT A
RET A
EBIT T A
ST A
N IT A
CACL
Invest
Continued on Next Page. . .
(5)
(6)
European countries
(7)
(8)
Other countries
(9)
(10)
-1.00*** -0.91*** -0.85*** -1.01*** -0.94*** -0.81***
(-11.03) (-14.08) (-12.87) (-10.81) (-9.94)
(-3.11)
-1.44***
-1.24***
-1.04**
(-3.72)
(-3.99)
(-2.42)
5.45*** 5.45*** 4.74*** 4.72***
(4.75) (4.73) (4.10) (4.07)
5.96*** 5.94*** 4.75*** 4.73***
(18.66) (18.62) (13.41) (13.36)
-1.74*** -1.74***
(-7.15) (-7.12)
0.02
0.02
(0.28) (0.27)
-2.18** -2.16**
(-2.18) (-2.14)
0.41*** 0.41***
(7.52) (7.68)
-0.88** -0.89**
(-2.82) (-2.82)
-0.05*** -0.05***
(-7.93) (-8.01)
0.04
0.04
41
3.65***
(4.00)
4.18***
(8.70)
-1.71***
(-4.44)
0.01
(0.06)
-2.28
(-1.39)
0.39***
(6.91)
-2.04**
(-2.30)
-0.05***
(-6.80)
0.05
3.65***
(3.97)
4.16***
(8.79)
-1.70***
(-4.51)
0.01
(0.06)
-2.25
(-1.35)
0.40***
(7.17)
-2.04**
(-2.27)
-0.06***
(-6.15)
0.05
6.19***
(4.49)
5.82***
(4.57)
-1.64***
(-11.13)
-0.47
(-1.19)
-1.77*
(-2.09)
0.41***
(18.03)
-0.37**
(-2.25)
-0.21**
(-2.11)
-0.13**
-0.77***
(-2.98)
-2.21***
(-4.33)
6.14***
(4.40)
5.78***
(4.56)
-1.64***
(-10.85)
-0.46
(-1.18)
-1.77*
(-2.05)
0.42***
(19.26)
-0.38**
(-2.18)
-0.21**
(-2.12)
-0.13**
Table 6 – Continued
Rexcess
RSIZE
Rm
M CAP
Obs
Avg. R2
45588
0.007
45588
0.010
(1)
(2)
Panel B:
LS
LSIncrease × LS
1.43**
(2.09)
45385
0.196
45385
0.197
All countries
(3)
(4)
(1.22)
-3.60***
(-16.23)
-0.23***
(-3.81)
-2.01**
(-2.49)
-0.09
(-1.41)
(1.20)
-3.59***
(-16.21)
-0.23***
(-3.81)
-1.96**
(-2.39)
-0.09
(-1.37)
45385
0.301
45385
0.302
(5)
(6)
(1.15)
(1.16)
(-2.16)
-2.90*** -2.88***
-2.49
(-11.98) (-12.12) (-1.40)
-0.11** -0.12** -0.30***
(-2.24)
(-2.28)
(-7.36)
-2.60*** -2.53***
3.92
(-6.51)
(-6.47)
(0.95)
-0.26** -0.25** -0.11***
(-2.59)
(-2.56)
(-4.34)
31061
0.316
31061
0.318
European countries
(7)
(8)
14324
0.362
(-2.23)
-2.47
(-1.37)
-0.30***
(-6.84)
4.45
(1.09)
-0.11***
(-4.32)
14324
0.363
Other countries
(9)
(10)
0.22 1.32*** 0.61*** -0.40
-0.72
-0.45
(0.32) (7.00) (3.24) (-0.60) (-1.01) (-0.99)
2.81***
1.69***
0.81***
(9.92)
(11.43)
(10.44)
-0.61
(-1.22)
0.43***
(3.36)
-0.46
(-0.56)
-1.32
(-1.68)
2.34***
(3.22)
5.26*** 5.27*** 4.14*** 4.15***
(5.05) (5.10) (4.36) (4.38)
6.08*** 6.01*** 4.66*** 4.64***
(14.47) (14.39) (11.60) (11.64)
-1.52*** -1.53***
(-7.49) (-7.46)
-0.09
-0.09
(-0.87) (-0.92)
-4.92*** -4.80***
(-4.29) (-4.22)
0.41*** 0.41***
(7.73) (7.88)
-1.74** -1.72**
(-2.34) (-2.33)
-0.04*** -0.04***
(-3.91) (-4.24)
-0.01
-0.01
(-0.27) (-0.44)
-3.60*** -3.57***
(-10.51) (-10.44)
-0.22*** -0.22***
3.22***
(3.88)
4.16***
(7.80)
-1.48***
(-4.63)
-0.10
(-0.50)
-4.40***
(-3.26)
0.39***
(7.54)
-2.48**
(-2.26)
-0.03***
(-4.06)
-0.05
(-1.23)
-2.93***
(-10.74)
-0.10**
5.12***
(3.98)
5.67***
(4.23)
-1.42***
(-11.20)
-0.41
(-1.43)
-6.86***
(-4.49)
0.45***
(12.52)
-1.85**
(-2.11)
-0.28*
(-2.05)
-0.07
(-0.65)
-2.02
(-0.94)
-0.30***
5.20***
(3.97)
5.63***
(4.13)
-1.41***
(-10.42)
-0.41
(-1.44)
-6.46***
(-4.41)
0.50***
(10.31)
-1.87**
(-2.11)
-0.30**
(-2.10)
-0.08
(-0.78)
-1.88
(-0.86)
-0.31***
Control variables:
Leverage
σ
W CT A
RET A
EBIT T A
ST A
N IT A
CACL
Invest
Rexcess
RSIZE
Continued on Next Page. . .
42
3.21***
(3.91)
4.16***
(7.77)
-1.48***
(-4.56)
-0.10
(-0.50)
-4.50***
(-3.40)
0.39***
(7.33)
-2.48**
(-2.24)
-0.03***
(-4.07)
-0.05
(-1.22)
-2.93***
(-10.73)
-0.10**
Table 6 – Continued
Rm
M CAP
Obs
Avg. R2
43470
0.007
43470
0.014
43338
0.192
43338
0.196
(-4.14)
-2.37***
(-4.55)
-0.08
(-1.49)
(-4.17)
-2.42***
(-4.84)
-0.08
(-1.48)
43338
0.312
43338
0.313
43
(-2.34)
(-2.37)
-2.80*** -2.88***
(-5.95)
(-5.82)
-0.25** -0.25**
(-2.63)
(-2.64)
29867
0.327
29867
0.327
(-6.08)
4.17
(0.81)
-0.06
(-1.71)
(-7.01)
3.72
(0.80)
-0.05
(-1.22)
13471
0.379
13471
0.386
Table 7: Impact of labor expenses cutting and default risk
This table reports the results of analyzing whether labor expenses cutting in year t affects the impact of
labor expenses on default risk in year t + 1. We interact labor expenses growth (∆XLR) and labor share
(LS) with a labor firing measure XLRCut and test whether the interaction term has any impact on
the predictability of default risk (EDF ) in year t + 1. We set XLRCut= 1 if the labor expenses growth
is below 25% percentile of its distribution in each country (this percentile is negative for most countries
with an average of -4% and a median of -4.4%), and set XLRCut= 0 otherwise. The regressions are
similar to those in Table 6. The control variables are the same as in Table 6. All the results are estimated
using Fama-MacBeth (1973) cross-sectional regressions. The t-statistics reported in the parentheses below
each coefficient estimate are heteroscedasticity and autocorrelation consistent t-statistics (Newey-West).
Statistical significance levels of 1%, 5%, and 10% are indicated with ***, **, and * respectively.
∆XLR
XLRCut × ∆XLR
(1)
-0.32***
(-3.85)
-4.32***
(-7.43)
LS
XLRCut × LS
Control variables:
Leverage
σ
5.51***
(4.72)
5.71***
(18.11)
W CT A
RET A
EBIT T A
ST A
N IT A
CACL
Invest
Rexcess
RSIZE
Rm
M CAP
Obs
Avg. R2
45385
0.204
All countries
(2)
(3)
-0.29**
(-2.42)
-3.51***
(-7.77)
0.48*
(1.76)
3.37***
(11.84)
4.74***
(4.06)
4.59***
(12.84)
-1.73***
(-6.99)
0.03
(0.35)
-2.08**
(-2.11)
0.43***
(7.94)
-0.87***
(-2.97)
-0.05***
(-9.67)
0.03
(0.75)
-3.58***
(-17.14)
-0.23***
(-3.80)
-1.99**
(-2.37)
-0.08
(-1.30)
45385
0.307
5.19***
(4.90)
5.93***
(14.64)
43338
0.201
-0.89
(-1.26)
2.12***
(14.70)
European countries
(5)
(6)
-0.37***
(-4.03)
-2.98***
(-7.26)
-0.82*
(-1.75)
1.88***
(13.24)
Other countries
(7)
(8)
0.12
(0.31)
-6.16***
(-3.50)
-0.95
(-1.27)
2.28***
(4.35)
4.11***
(4.25)
4.59***
(11.65)
-1.54***
(-7.65)
-0.08
(-0.83)
-4.72***
(-4.25)
0.41***
(8.02)
-1.70**
(-2.36)
-0.04***
(-4.13)
0.02
(0.60)
-3.61***
(-11.14)
-0.22***
(-4.11)
-2.40***
(-4.48)
-0.08
(-1.47)
43338
0.316
3.65***
(3.96)
4.05***
(8.74)
-1.66***
(-4.45)
0.03
(0.14)
-2.16
(-1.31)
0.41***
(7.36)
-2.06**
(-2.31)
-0.06***
(-6.90)
0.03
(0.75)
-2.91***
(-11.75)
-0.11**
(-2.13)
-2.58***
(-6.57)
-0.25**
(-2.54)
31061
0.322
6.09***
(4.20)
5.61***
(4.46)
-1.61***
(-10.25)
-0.42
(-1.16)
-1.79**
(-2.17)
0.48***
(13.32)
-0.40**
(-2.56)
-0.22**
(-2.15)
-0.23**
(-2.76)
-3.18**
(-2.43)
-0.30***
(-6.99)
4.81
(1.03)
-0.11***
(-4.08)
14324
0.371
(4)
44
3.28***
(3.92)
4.13***
(7.76)
-1.65***
(-4.28)
-0.11
(-0.54)
-3.93***
(-3.18)
0.39***
(7.03)
-2.26**
(-2.34)
-0.03***
(-3.16)
-0.02
(-0.34)
-2.95***
(-11.80)
-0.10**
(-2.27)
-2.72***
(-5.80)
-0.25**
(-2.64)
29867
0.329
5.08***
(3.96)
5.64***
(4.26)
-1.42***
(-11.34)
-0.42
(-1.42)
-6.72***
(-4.36)
0.44***
(13.05)
-1.80**
(-2.10)
-0.28*
(-2.08)
-0.00
(-0.02)
-2.02
(-0.94)
-0.30***
(-6.43)
3.83
(0.76)
-0.06
(-1.60)
13471
0.384
Table 8
Calibration
The benchmark model parameters are listed in this table.
Parameter
Description
Benchmark
Preferences
β
θ
ψ
Time Preference
0.98
Risk Aversion
8
IES
2
Production
(1 − α)ρ
α + ρ − αρ
Labor Share
0.42
Returns to Scale
0.87
1
1−η
Labor Capital Elasticity
0.50
δ
υ
f
µ
τ
pexp
Depreciation
0.025
Capital Adj. Cost
5
Operating Cost
0.019
Probability No Resetting
0.90
Corporate tax rate
0.3
Debt expiration probability
0.025
45
Table 9
Aggregate Macroeconomic Moments
This table compares macroeconomic moments from the data to the model. All reported
correlations are with HP filtered GDP (y) except for growth rates of variables, in these cases
correlations are reported with the growth rate of GDP. In the data, y is real GDP, c is consumption,
i is private non-residential fixed investment plus durables, and w is compensation per hour. The
1
= 0.5),
model in Panels B has a calibrated elasticity of substitution between labor and capital ( 1−η
exp
wage rigidity (µ = 0.9) and long-term debt (p = 0.025). Note that the table reports the volatility
of quantities relative to GDP volatility. The volatility of HP filtered GDP in the data is 3.55%,
the model is calibrated to match this number.
Panel A: Data
x
σ(x)
σ(y)
ρ(x, y)
AC(x)
σ(∆x)
σ(∆y)
ρ(∆x, ∆y)
AC(∆x)
y
c
i
w
1.00
0.51
3.04
0.44
1.00
0.72
0.07
0.60
0.57
0.53
0.55
0.36
1.00
0.53
2.84
0.49
1.00
0.79
0.27
0.61
0.54
0.50
0.39
0.32
x
σ(x)
σ(y)
ρ(x, y)
AC(x)
σ(∆x)
σ(∆y)
ρ(∆x, ∆y)
AC(∆x)
y
c
i
w
1
0.74
3.17
0.49
1
0.87
0.83
0.82
0.6
0.6
0.51
0.71
1
0.82
2.84
0.66
1
0.89
0.77
0.85
0.67
0.72
0.38
0.88
Panel B: Model
Table 10
Unconditional Financial Moments
This table presents the unconditional financial moments of the data and the model. Rf is the riskfree
rate, Rexc is the market excess return, SR is the sharpe ratio, Lev is the aggregate financial leverage, CS
is credit spread in percentage term with the range of estimate in the data. DefProb is the percentage
default probability from Giesecke et al (2011).
Data
Model
E[Rf ] σ(Rf ) E[Rexc ] σ(Rexc )
0.69
3.81
6.84
19.89
2.88
2.11
4.49
8.85
46
SR Lev
0.34 0.44
0.51 0.31
CS
DefProb
0.38-4.19 0.3-3.99
2.91
1.27
Table 11
Simulated Labor Market Variables and Credit Spread
This table reports the predictive regression of variables of interests for credit spread in the mode. [t] are
heteroscedasticity and autocorrelation consistent t-statistics (Newey-West).
∆W
[t]
LS
[t]
Adj. R2
Panel A Data
-15.4
-4.15
10.66
2.15
0.28
0.09
47
Panel B Model
-11.03
-5.07
10.19
4.50
0.36
0.24