Financial Conditions and Labor Productivity over the Business Cycle

Financial Conditions and Labor Productivity over the Business Cycle Carlos A. Yépez September 5, 26 Abstract The cyclical behavior of productivity has noticeably changed since the mid- 8s. Importantly, the substantial decline in the co-movements of average labor productivity and total factor productivity have proved difficult to explain. We offer a novel explanation and argue that this change is due to credit frictions and financial shocks. We provide VAR evidence that financial shocks have an important effect on labor productivity. We develop a financial frictions model that explains the observed behavior of productivity. The key mechanism hinges on the effect of binding collateral constraints on labor demand. Keywords: Credit market frictions; Credit shocks; Productivity; Business Cycles. JEL codes: E22, E32, E44, J23, J24 An earlier version of this paper was entitled Financial cycles and labor productivity over the business cycle. I am grateful to the editor, an anonymous referee, Dan Tortorice and George Hall for their thoughtful comments and suggestions. Department of Economics. University of Manitoba. 5 Fletcher Argue Bldg., Winnipeg, MB. R3T 5V5. E-mail: carlos.yepez@umanitoba.ca

Introduction The substantial decline in the cyclicality of output, labor, and labor productivity (output per hour) in the U.S. since the mid-8s has been an important area of inquiry in the study of business cycles. Although many explanations have been proposed, there are still no definitive answers. On the one hand, some studies have provided evidence for a smaller role of technology shocks on aggregate fluctuations since the mid-8s (Stock and Watson 22; Smets and Wouters 27). On the other hand, studies have argued in favor of an important, yet diminishing, contribution of non-technology shocks on the dynamic behavior of productivity (Galí 999; Galí and Gambetti 29). More recently, a burgeoning literature has focused on the important role of credit market conditions on real activity (Gilchrist and Zakrajšek 22; Jermann and Quadrini 22; Liu et al. 2; Christiano et al. 24). Gilchrist and Zakrajšek 22 posit that financial shocks in the form of an excess bond premium component of credit spread (henceforth ebp), play a prominent role in explaining fluctuations of real variables, and that the contribution of these shocks has increased since the mid-8s. The present study adds to this literature by examining the impact of financial shocks on labor productivity. For our empirical analysis, we run a VAR with the following endogenous variables: () log-difference of real output per capita per hour; (2) log-difference of hours worked (non-farm business sector); (3) excess bond premium (in percentage points); and (4) the effective (nominal) federal funds rate. The full sample period is 973q-2q3..4 productivity growth (post-84) productivity growth (pre-84).2 percentage points -.2 5 5 2 5 5 2 quarters after shock 95% CI cumulative orthogonalized irf Figure. Dynamic response of labor productivity to financial shock (pre-84 and post-84) The author gratefully acknowledges the thoughtful suggestion of an anonymous referee.

Figure shows the dynamic response of labor productivity to a -standard deviation increase in the ebp both for the post-84 period (left panel) and the pre-84 period (right panel). Notably, and in contrast to the pre-84 subsample, the graph for the post- 84 period indicates that labor productivity experiences a significant and persistent short-run drop (about -standard deviation) when the ebp rises. This novel finding is consistent with the notion that financial shocks have played an important role on labor productivity since the mid-8s. 2 Recent studies confirm that labor and productivity have historically been mildly positively correlated, but since the mid-8s, have become counter-cyclical (Barnichon 2; Gali and van Rens 2; McGrattan and Prescott 22; Sarte et al. 25). This empirical observation is dubbed as the labor productivity puzzle, and it is in stark contrast to the pro-cyclical relationship between labor and productivity predicted by the canonical real business cycle (RBC) model. In a related vein, Fernald and Wang 25 document a decline in the co-movement of TFP since the mid-8s. Gali and van Rens 2 posit the hypothesis that more flexible U.S. labor markets can be reconciled with the productivity puzzle when (unobservable) variable worker effort is taken into account. A challenge to such explanation is that it implies a counter-factual increase in the variation of employment relative to hours (Fernald and Wang, 25). In terms of the cyclical properties TFP, the seminal study of Basu et al. 26 finds that unobservable margins of adjustment in the form of factor (capital and labor) utilization explain a large part of the observed pro-cyclicality of TFP. Similarly, Fernald and Wang (25) advance further evidence to show that reduced variation in factor utilization explains the diminishing co-movement between TFP and output. Within the RBC framework, non-technology shocks are a necessary component in order to account for the behavior of labor productivity (Christiano and Eichenbaum 992; Galí 999; Sarte et al. 25). In a similar vein, in the New Keynesian model, Barnichon 2 argued that a decline in the contribution of supply shocks relative to demand shocks since the mid-8s could explain the counter-cyclicality of labor productivity. Our study contributes to this literature by examining a source of fluctuations that has hitherto been overlooked as a plausible explanation to the productivity co-movement puzzle, namely financial shocks. This study is motivated by the observation that finance and financial innovation have played a predominant role in the economy since the 98s. Thus, we ask, how do financial conditions -defined as the combination of credit constraints and financial shocks- impinge on the cyclical properties of productivity? This paper is closely related to Jermann and Quadrini 22 who hint toward an important link between financial conditions and productivity. In particular, credit 2 Additional results and details of the empirical analysis are available in the online appendix. 2

market imperfections where firms face liquidity constrains on their working capital bills can force firms to reduce employment when credit is tight, and similarly, increase scale and hire more workers when credit is cheap. Similar to these authors, our study assumes that firms are liquidity constrained. Importantly, we add to this literature by examining the implications of credit constraints and financial shocks (henceforth, financial conditions) on the co-movement properties of productivity, TFP, labor, and output. This paper proceeds as follows. Section 2 describes the model and its calibration. Section 3 analyzes the model and its dynamic behavior. Section 4 concludes. 2 Model The environment is a real business cycle (RBC) model with credit constraints in the spirit of Kiyotaki and Moore 997. There are two types of agents, unconstrained households and constrained entrepreneurs. The former work and choose how much to consume and save each period. The latter are liquidity constrained and borrow from the former in order to produce and consume. 2. Households Households enjoy consumption and leisure, they derive income from work and accumulate wealth by saving. Their objective function is given by: s.t. max c s t,nt (β s ) t U(c s t, n t ) t= c s t + b t+ R t = w t nt + b t, () with b t+ B for some number B. Given prices, w t the real wage, and R t the real interest rate, each period the household chooses how much to consume c s t and how many hours to work n t, where β s denotes the household s discount factor. Preferences incorporate habit in consumption, a typically used feature to capture the hump-shaped response of output to productivity shocks. Thus, U( ) = [ (c s t h c s t ) σ σ ι n+φ t +φ ], where h is the habit parameter, ι is the (dis)utility 3

weight of labor, and φ is the inverse Frisch elasticity of labor supply. The corresponding efficiency conditions are: w t = U n t U c s t (2) E t [m t+ ] = R t (3) Equation (2) is the standard intra-temporal condition that equates the real wage to the marginal rate of substitution, while equation (3) is the standard Euler equation, where the term E t [m t+ ] = β s E t [ Uc s t+ discount factor. 2.2 Entrepreneurs U c s t ] denotes the household s stochastic Entrepreneurs run firms in the economy and derive utility from consumption c e t. They invest i t in new capital projects and hire labor n t. Furthermore, entrepreneurs are more impatient than households, β e < β s. Hence, the former are borrowing constrained while the latter are not. The entrepreneur s problem is given by: s.t. max c e t (β e ) t U(c e t) t= y t n t w t b t + b t R t = c e t + i t (4) Entrepreneurial production is given by y t = z t (u t k t ) α n α t, where k t and n t are capital and labor inputs respectively, z t is technology, and α is the capital share of income. In addition, consistent with a widely accepted extension of the RBC model, we add a capacity utilization u t margin to production. 3 As in Jermann and Quadrini 22, entrepreneurs are liquidity constrained. That is, entrepreneurs require an intra-period loan in order to finance their working capital bills at the beginning of each period and before the realization of revenues. Entrepreneurial liquidity each period is set to l t = y t, and is subject to a financial friction in the form of a limited enforcement constraint (LEC) given by: ξ t k t+ b t+ R t + l t (5) 3 For a theoretical formulation see King and Rebelo (999). For an empirical basis see Basu, et al. (24). 4

Equation (5) establishes that inter- and intra-temporal debt (RHS) cannot exceed the liquidation value of capital used as collateral (ξ t k t+ ). That is, due to limited enforcement, creditors can only recoup a fraction ξ t of collateral in case of entrepreneurial default. In addition, capital accumulation follows the law of motion: k t+ = ( δ(u t ))k t + i t (6) with the standard regularity condition δ (u) u >. Finally, productivity (z δ (u) t) and financial (ξ t ) shocks follow a standard VAR() process Ω t = {z t, ξ t } = AΩ t + ɛ t, with ɛ t i.i.d. N(, Σ 2 ). The efficiency conditions that solve the entrepreneur s problem are: y nt = w t ( q t ) (7) ξ t q t = E t [ m e t+ ( δ(ut+ ) + y kt+ ( q t+ ) )] (8) E t [ m e t+ ] = R t q t (9) δ (u t ) = y k t u t () where y nt denotes the marginal product of labor (MPL), the marginal product of capital (MPK) is y kt, µ t is the shadow price associated with the limited enforcement constraint (LEC), U c e t is the marginal utility of consumption, and E t [m e t+] [ β e Uc ] e E t+ t denotes the entrepreneur s stochastic discount factor. U c e t Equation (7) equates the marginal product of labor to the liquidation-adjusted real wage w t /( q t ). That is, the cost of labor adjusted by q t µt U c e t, the shadow price of credit in consumption units. Equation (8) relates the liquidation-adjusted value of an additional unit of capital q t ξ t, with its future expected marginal productivity. Equation (9) relates the entrepreneurial stochastic discount factor to the liquidationadjusted interest rate R t /( q t ). Last, equation () is the optimality condition with respect to capital utilization. 2.3 Calibration We calibrate the model to U.S. data for the period 984:Q-2:Q2 (see appendix A for a description of the data). Table 2 in Appendix B summarizes the values of structural parameters. One set of parameters is calibrated to values typically used 5

in related studies. Namely, the capital share of income parameter is α =.36, the rate of depreciation is δ =.25, the habit persistence parameter of both households and entrepreneurs is h =.84. As in Jermann and Quadrini 22, we set the inverse-frisch elasticity of labor supply parameter to ν =.568. Correspondingly, we set the relative utility weight of labor ι = 6.637 so that the steady state of per capita hours work is one third. Another set of parameters is simulated to match long-run averages in the data. Specifically, the elasticity of marginal depreciation with respect to utilization is set at φ =.84 to match a long-run annual capitaloutput ratio target of 2. we set the subjective discount factor of the household β s =.988 to match an average (annual) interest rate of 4.86%. Similarly, we set the subjective discount factor of the entrepreneur β e =.983 to match an implied (liquidity adjusted) credit spread of 52 bps. Last, we calibrate the enforcement constraint parameter to ξ =.393 to match a long-run of debt-to-gdp ratio of 2.53 as observed in the data. Table 3 in Appendix B summarizes the steady state implied by the calibrated model. Finally, we calibrate the two shock processes as follows. we set the persistence of productivity and financial shocks as in Jermann and Quadrini 22 (see matrix A below), and then set the values of the volatility of TFP (σ z =.3) and the volatility of financial shocks (σ z =.45) to match i) output volatility in the data at σ y =.9, and ii) a relative contribution of financial shocks to the volatility of labor productivity at 5% in line with the VAR evidence in the post-84 period. 4 Finally, we also assume a low and positive TFP spillover (ρ ze =.9) suggestive of a small but positive interaction between productivity and financial conditions. The shocks follow a VAR() process: Ω t = AΩ t + ɛ t, with Ω t = [z t, ξ t ], ɛ t i.i.d. N(, Σ 2 ). The matrices A and Σ are given by: [ ] [ ].9457.32.3 A = and Σ =..9.973.45 3 Results In this section we first we analyze the key channel that drives the dynamic behavior of productivity in the short run. Next, we discuss the distinct responses of the model economy to two types of shocks, namely, TFP and financial shocks. Last, we examine the quantitative fit of the model in terms of the predicted unconditional co-movements of productivity and TFP. 4 Details about the empirical analysis are available in the online appendix. 6

3. Credit constraints and productivity The introduction of financial frictions in the form of a binding LEC constraint has an important effect on the demand for labor. Recall from equation (7): MP L t = w t ( q t ) The above relationship equates the value marginal product of labor to the real wage adjusted by the wedge q t. When the LEC constraint binds, the shadow price of credit in units of consumption q t rises, which drives up the wedge and the liquidity adjusted cost of labor. Hence, as the cost of labor increases in response to a negative credit shock, the MP L t must be higher if firms are to hire additional labor. As a result, the increase in the wedge forces liquidity-constrained firms to reduce employment at any given level of TFP and capital, thereby breaking the tight link between productivity and labor demand. 3.2 Model dynamics In this subsection we first discuss the dynamic responses of the economy to two distinct sources of fluctuations, TFP and financial shocks. Second, we examine the fit of the model in terms of the key unconditional moments of labor and productivity. TFP shock Figure shows the dynamic responses to a negative one standard deviation shock to TFP. Due to consumption habit, when TFP falls there is a humpshaped decline in output and consumption. Moreover, the firm s reduction in investment is dampened due to the adjustment of the capacity utilization margin. Importantly, since the negative TFP shock reduces the liquidity requirements of the firm, it loosens LEC constraint as shown by the fall in the relative shadow price q t. Thus, the MP L t required to hire additional workers falls, and labor briefly increases on impact. As a result, labor productivity falls leading to a pro-cyclical response, similar to the prediction of the canonical RBC model. 7

.2.4. Output 2 4. 2 4.5 Labor Utilization.5 2 4. Consumption.2 2 4 Productivity 2 2 4.5 Shadow price (q).5 2 4.5 Investment.5 2 4.5 MPL 2 4.2 TFP.4 2 4 Figure Impulse responses to a negative TFP shock Output 2 4.5.5 2 4 Labor Utilization 2 4.2 Consumption.4 2 4 Productivity 2 4 Shadow price (q) 2 4 Investment 2 4.5 MPL.5 2 4.2 TFP.4 2 4 Figure 2 Impulse responses to a negative financial shock 8

Financial shock Figure 2 shows the impulse responses to a (one standard deviation) negative financial shock. A worsening of financial conditions tightens the LEC constraint, reduces investment, output and consumption. Tight credit also pushes up the relative shadow price of the LEC constraint q t. Through this latter effect, the wedge increases and the liquidation-adjusted cost of labor rises as shown by the increase in MP L t. As a result, firms reduce their demand for labor and lower their investment for any given level of aggregate productivity, which explains the increase in labor productivity on impact; this effect is transitory as productivity eventually falls in line with aggregate economic activity. To summarize, in response to a negative financial shock productivity is counter-cyclical, and productivity and labor co-move negatively. Unconditional moments Our empirical findings point out that financial shocks have become more prominent since 984. 5 To the extent that U.S. firms rely on credit, financial shocks can exacerbate the effects of the collateral channel. One important consideration about our model is that the LEC constraint need not always bind. In the online appendix we examine in detail the conditions under which the LEC binds. We show that i) positive productivity shocks that increase the liquidity needs of the firm, and ii) negative financial shocks, make the LEC bind. Furthermore, we show that negative productivity shocks and positive financial shocks loosen the constraint. In this study we take a simplified approach to match moments. Namely, based on the evidence on the importance of financial shocks since the mid-8s, we assume that the collateral channel is always binding, whereas for the period prior to 984 we rule out the collateral channel. 6 Table summarizes the moment matching exercise of two model specifications. First, the benchmark model with financial and TFP shocks when the LEC always binds (H.A. model), which is calibrated to post-84 data. Second, the model where we drop the impatient households from the model, ruling out the collateral channel (R.A. model). This latter model is calibrated to pre-84 data and only includes TFP shocks. 5 We also know that financial conditions have contributed to the last three recessions in the U.S. Namely, the Savings & Loans crisis of the early 9s, the dotcom bubble of the early 2s, and the global financial crisis of 28. 6 A caveat of our matching exercise is the strong assumption of whether the collateral channel binds or not. Nevertheless, examining the two polar regimes is informative as the true model of the economy is likely to lie between the two. 9

For the post-84 period, the H.A. model does a good job at matching i) the negative co-movement between labor and productivity; ii) acyclical labor productivity; and iii) the weak co-movement between TFP and labor. On the other hand, the R.A. model is consistent with the strong co-movements of TFP and pro-cyclical productivity, although it greatly overestimates the co-movement between labor and productivity prior to 984. 7 ( tfp, y) * ( tfp, n) * ( p, y) ( p, n) (y) H.A..4 -.. -.5. Post-84.6.2. -.5. R.A..... 2. Pre-84.9.6.6.2 2. Table. Model Fit Data for periods 948:Q-983:Q4 and 984:Q-2:Q2. Statistics from cyclical component of HP filter at quarterly frequency. * TFP statistics from Fernald and Wang (25), HP-filtered, periods 95:Q-983:Q4 and 984:Q-25:Q2. Overall, our theoretical results suggest that i) credit market frictions provide a plausible mechanism to help rationalize the puzzling behavior of productivity; and ii) the source of fluctuations in our case, financial shocks is crucial for understanding the declining co-movements of productivity and TFP. 3.3 Sensitivity Analysis Recent studies suggest that the relative importance of non-productivity shocks may be an important determinant of the cyclical behavior of TFP and productivity (Gali and Gambetti, 29; Barnichon, 2; Fernald and Wang, 25). To check this proposition, we examine the sensitivity of the results to changes in the relative volatility between financial and TFP shocks. Table 4 in Appendix C summarizes the results. As the relative volatility of financial shocks increases, the pro-cyclicality of both TFP and productivity drops. Similarly, the negative co-movements between 7 In the light of our earlier discussion, a form of occasionally binding collateral constraint could have better captured the cyclical properties of labor productivity and TFP prior to 984, as ignoring this channel greatly overestimates the positive co-movements of these variables.

TFP and labor, and productivity and labor drop, with the former falling by a larger magnitude. In line with the empirical evidence presented earlier, these results suggest that a plausible increase in the relative importance of financial shocks over the last few decades, due for instance to de-regulation and the rise of financial innovation since the 98s, may be consistent with the observed decline in the cyclicality of both productivity and TFP. 4 Conclusion This study provides an novel explanation to the observed decline in the pro-cyclicality of productivity since the mid-8s. Recent literature has emphasized the role of variable factor utilization, changes in the behavior of inventories, increase in the flexibility of labor markets, and changes in the structure of the economy to explain these facts. Our study contributes by providing an alternative explanation that emphasizes the importance of financial conditions on real outcomes. Specifically, financial conditions defined as the combination of credit constraints and financial shocks, introduce a wedge between the marginal rate of substitution and the marginal product of labor, which increases when credit constraints tighten and leads to a decline in labor demand for any given level of TFP and capital. Our results point toward a plausible explanation in which the growing dependence of the economy on financial conditions helps rationalize the puzzling behavior of employment and productivity over the business cycle. A full examination of the model s historical fit before and after 984 is interesting as well as challenging, as it requires the application of non-linear estimation techniques. Such exercise can provide additional evidence for the collateral channel based on estimated historical paths of key variables. This is an area that we intend to explore in future research.

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A Data sources The macro series are from St. Louis Fed FRED database and include real GDP, private consumption expenditures, gross private domestic investment, nonfarm business sector hours worked, and the effective (nominal) federal funds rate. Productivity data is real output per capita per hour and per worker from the Bureau of Labor statistics (BLS). The time series cover the period 947Q:2Q3, data is seasonally adjusted at quarterly frequency. The financial variables include debt (Credit Market Instruments) from the Flow of Funds Accounts at the Federal Reserve Board (FRB) and the corporate bond premium (the difference between BAA Moody's corporate bond yield and T-Bill rate yield) from the St. Louis Fed. The excess bond premium data is from Gilchrist and Zakrajsek (22). The time series cover the period 973Q:2Q3, data is seasonally adjusted at quarterly frequency.

B Calibration Description Parameter Value Preferences Household Discount factor* s.988 Entrepreneur Discount factor* e.983 Habit persistence parameter h.85 Relative utility weight of labor* 6.637 Inverse Frisch-elasticity of labor.568 supply Entrepreneurial firms Effective capital share.36 SS Depreciation rate.25 Elasticity of marginal depreciation w.r.t. Utilization*.64 LEC friction Enforcement constraint parameter*.393 Sources: Jermann and Quadrini (22). *Simulated. Table 2. Model Parameters Description Model Consumption-to-GDP ratio C / Y.777 Capital-to-GDP ratio K / 4Y 2.23 Loans-to-GDP ratio B / Y 2.535 Credit Spread CS.5 Interest Rate (% p.a.) R 4.868 Table 3. Steady State

C Sensitivity Analysis f ( tfp, y) z ( tfp, n) ( p, y) ( p, n).5.7 -..6 -.3.5 -..3 -.4.5.4 -.. -.5 Table 4. Sensitivity to the relative volatility between financial (f) and tfp (z) shocks. Statistics from cyclical component of HP filter at quarterly frequency. tfp denotes total factor productivity, y is output per capita, n is number of hours worked, and p is output per hour.