Financial Shocks, Cyclicality of Labor Productivity and the Great Moderation

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1 Financial Shocks, Cyclicality of Labor Productivity and the Great Moderation October 28, 2014 Abstract The nature of the business cycle has sharply changed since the onset of great moderation with decline in output volatility coinciding with vanishing procyclicality of labor productivity. I combine the insights of the Real Business Cycle (RBC) theory, which features productivity shocks that lead to procyclicality of labor, with the recent work on labor and finance to provide a unifying theory for these patterns. In my model, the firm needs to finance its wage bill and capital in advance by borrowing against its assets before its revenues are realized. The basic intuition that overturns the prediction of an RBC model i.e., a negative productivity shock reduces both output and labor productivity- is that a negative financial shock tightens the borrowing constraint of firms, which lowers labor demand as the wage bill has to be financed in advance and raises labor productivity. Thus, the shift in importance of financial shocks relative to TFP shocks implies a decline in the procyclicality of labor productivity, an increase in the volatility of hours relative to output, and a decline in the correlation between labor productivity and hours. I quantitatively assess the importance of this mechanism in a DSGE model with borrowing constrained entrepreneurs facing both financial shocks and TFP shocks. I calibrate the model and show that increased quantitative importance of financial shocks captures the sharp changes brought about by the Great Moderation. There is some empirical support for this mechanism in the cross-section of 12 OECD countries. 1 Introduction The cyclical behavior of labor productivity (output per unit of labor) has long played an important role in theories of the business cycle. 1 However, the strong procyclicality of labor productivity has vanished in the past three decades leading to extensive reexamination of these theories, as well as a search for the underlying cause of this change. 2 Gali and Gambetti (2009) [19] documentsthatthischangetookplace around the onset of the period of the great moderation when output volatility sharply decreased, the relative volatility of labor to output increased and the correlation of labor and labor productivity decreased. Figure (1) depicts these changes. While there are numerous studies on the great moderation and its underlying 1 RBC theories view this as evidence for importance of technology shocks while Keynesian theories interpret it as a sign of labor hoarding and evidence of slack in the economy. See Bernanke and Parkinson (1990) [7] for an extended discussion. 2 More surprisingly, during the recent great recession labor productivity didn t fall or even increased by some accounts while output fell sharply.see Daley and Hobijn (2010) [15] and Brugemann et al (2011) [11] 1

2 causes, a unifying theory capable of explaining all these changes is still needed. In this paper I combine the insights of the real business cycle theory, which features productivity shocks that lead to procyclicality of labor, with the recent work on labor and finance to provide such a unifying theory. I develop an otherwise standard RBC model with financial frictions where the firm has to finance its wage bill along with capital in advance by borrowing against its assets before the revenues are realized. The inclusion of the wage bill in the borrowing constraint is motivated by recent research on effects of disruptions in financial markets which provides strong evidence of the effect of financial constraints on labor decisions at the firm level (Chodorow Reich (2013) [13] andbenmelechetal(2011)[4]). I show that this augmented model can capture the cyclical changes in the past three decades because financial shocks have become more important relative to productivity shocks. The basic intuition that overturns the prediction of an RBC model -anegativeproductivityshockreducesbothoutputandlaborproductivity-isthatanegativefinancialshock tightens the borrowing constraint of firms, which lowers labor demand as the wage bill has to be financed in advance. This in turn raises labor productivity. Hence, adverse financial shocks result in lower output and higher labor productivity σy ρ(labor Prodcutvity, Output) q1 1960q1 1970q1 Date 1980q1 1984q1 1990q1 2000q1 1950q1 1960q1 1970q1 Date 1980q1 1984q1 1990q1 2000q1 (a) standard deviation of output (b) correlation of labor productivity and output ρ(labor Productivity, Labor) σy/σl q1 1960q1 1970q1 Date 1980q1 1984q1 1990q1 2000q1 1950q1 1960q1 1970q1 Date 1980q1 1984q1 1990q1 2000q1 (c) correlation of labor productivity and labor (d) standard deviation of labor relative to output Figure 1: Standard deviations and correlations are computed using 40 quarter rolling window estimators. Output is real business value added from BEA, labor is total aggregate weekly hours worked from BLS and labor productivity is defined as output per unit of labor. Data series used are quarterly and are filtered using an HP filter with a smoothing parameter of 1600 (standard parameter for filtering quarterly data). 2

3 The simplicity of this model allows me to extract the productivity and financial shocks readily from the data with minimal parametric assumptions. Productivity shocks are extracted by de-trending Solow residuals, as is common in the RBC literature. Similarly, financial shocks are extracted by log linearizing the borrowing constraint equation around the steady state. This allows me to study the shock processes through time, independent of the parameters and performance of the model. I estimate the shock processes separately for two distinct periods: and I find that while financial shocks have the same volatility across the two periods, the volatility of productivity shocks drops significantly in the latter period. Thus, the role of financial shocks as drivers of the business cycles have become more prominent. Next, I use my model to demonstrate quantitatively that the change in the shock processes is able to capture the cyclical changes in the data. I calibrate the model to match specific data moments in the pre-1984 period. I then feed in the recovered shock processes for the entire time period and study the performance of my framework when faced with these shocks. The model quantitatively captures all the aforementioned cyclical changes while it does a good job matching other moments which are not targeted. In the model, an increase in the relative importance of financial shocks compared to productivity shocks increases the volatility of total credit outstanding relative to output. Figure 2 plots the relative volatility of total credit to the non-financial sector relative to output. There is a large upward coinciding with the change of the cyclical features depicted in Figure 1. σb/σy q1 1960q1 1970q1 Date 1980q1 1984q1 1990q1 2000q1 Figure 2: Relative volatility of credit to output. Credit is total outstanding credit market instruments of NFB from Flow Funds and output is real business value added from the BEA. Data series used are quarterly and are filtered using an HP filter with a smoothing parameter of 1600 (standard for quarterly data). Standard deviations are computed using 40 quarter rolling window estimators. As a robustness check for significance of financial shocks as drivers of business cycles, I extend the baseline model to include inter-temporal, labor supply, and investment specific shocks which are popular in DSGE models. I estimate the parameters and the shock processes separately for pre and post 1984 sample periods using Bayesian methods. Among the additional shocks, inter-temporal shocks are significant drivers of the variation in labor and output, investment specific shocks explain a large fraction of the variation in investment, while labor supply shocks are negligible for all variables. The presence of the additional shocks notwithstanding, financial and productivity shocks remain important drivers of the cycle in both periods and the estimated volatility of productivity shocks drops by roughly 50% with the onset of the great moderation. 3

4 Ifurtherdemonstratethatalthoughintertemporalshocksinducesimilardynamicstofinancialshocksfor labor productivity, the extended model without financial shocks can not capture key features of the cyclical changes. I simulate the model for 1984:2013 absent the estimated financial shocks. When all the shocks are included in the simulation the model can capture the dynamics of the aggregate variables. Moreover the effect of financial shocks on the dynamics predicted by the model for post 1984 is very significant; not only the dynamics of credit to the business sector would have been sharply different without financial shocks but also the dynamics of hours and output would have looked completely different. Especially the model simulated without financial shocks loses the expansion in hours and output from mid 90s till early 2000s. Iusemymodeltostudytherecentgreatrecession. Arathersurprisingobservationduringtherecent recession was that labor productivity didn t fall at all or even increased by some accounts (Daly Hobjin (2010) and [15] Brugemann(2010)[11]). I show that the model also predicts a small drop in labor productivity during the recent crisis while it assigns most of the drop in output and labor to the tightening of the borrowing constraint of the firms. Specifically, the model attributes more than half of the drop in output and 80% of the drop in hours worked to financial shocks alone while it predicts a small drop in labor productivity. In this sense the model is able to generate a consistent narrative of the recent recession mainly caused by financial shocks, while at the same time it explains why labor productivity remained almost unchanged. Finally, in order to provide reduced form evidence for the importance of financial shocks in shaping the cyclical behavior of labor productivity, I use cross-sectional data on total credit outstanding, output, and total hours worked for 12 OECD countries. 3 Iproxytherelativevolatilityoffinancialshockstoproductivity shocks for each country with the volatility of total private sector credit relative to the volatility of GDP of that country. I break the sample for each country to pre and post 1984 and study the relationship between the change in this proxy and the change in the procyclicality of labor productivity across the two time periods. I find that countries which experienced a larger increase in the relative volatility of debt to GDP also experienced a larger breakdown in the correlation of labor productivity and output. The change in the volatility of debt relative to output can explain 40% of the cross country variation in the change in the correlation of labor productivity and output. This suggestive evidence supports the main hypothesis of this paper, that the change in procyclicality of labor productivity in developed countries can be understood through the more prominent role of financial conditions as the driver of the business cycle. The paper is organized as follows: Section 2 provides a literature review of the causes of the great moderation and the role of financial shocks since the great moderation. Section 3 describes the model and derives the equilibrium conditions of the model. Section 4 describes the calibration procedure using pre 1984 data for the US and looks at the predicted moments of the model for the period after 1984 with the recovered shocks from the data and evaluates the performance of the model. Section 5 studies the extension of the benchmark model with multiple shocks, and investigates the importance and dynamics introduced by financial shocks during the past three decades. Section 6 provides preliminary evidence for the mechanism proposed in this paper from international data. Section 7 concludes. 3 Data for total credit outstanding for each country is from the BIS. Output is real GDP from OECD stats and hours worked per individual are used from Ohanian Raffo (2012) [31] 4

5 2 Literature Review This paper is at the intersection of several literatures in macroeconomics and finance. The main contribution of this paper is connecting the results of the recent literature on effects of finance and financial shocks on labor market outcomes in corporate finance to the behavior of labor productivity at the macro level during the past three decades. To my knowledge this is the first paper which emphasizes the importance of the dynamics induced by financial shocks through the working capital channel for understanding the behavior of labor productivity. I believe the result that the relative importance of financial shocks has increased in the past three decades compared to the rest of the post war period is novel contribution to the extensive macro finance literature. Naturally, this paper falls in the literature on the Great Moderation and its causes and it is among the very few papers which explains the drop in volatility of output at the same time that it captures the changes in cyclical behavior of labor and labor productivity. A review of each of these individual literatures can be found below. 2.1 Labor and Finance The recent financial crisis and the ensuing large and sharp drop in employment led to a focus on the effects of financial shocks on labor. Chodorow Reich (2013) [13] usesbank-firmleveldatafromsyndicatedloans and identifies firms which have Lehman Brothers as their lead syndicator as firm which should experience the most adverse fund supply. After controlling for various firm level measures he finds that such firms experienced significantly larger drop in employment (around 3%) at the height of the recession compared to very similar firms that didn t have Lehman as their lead syndicator. The paper rationalizes this difference through the working capital channel. Greenstone and Mas (2012) [24] alsofindstrongevidenceofeffectsof bank credit supply shocks on employment outcomes at the county level. Bentolila et al (2013) [5] employ bank-firm level data on spanish firms and banks and find that the firms connected to the weakest banks had the largest drop in employment, around 13% more than the firms connected to healthy banks. Other studies which do not only analyze the recent recession and study the labor market effects of financial shocks in general find similar results. Benmelech et al (2011) [4] identifytheeffectoffinancial distress on labor decision at the firm level by drawing on methods identifying the effect of cash flow shocks on investments. They find that distressed firms (firms with large amount of debt due for instance) sharply cut employment in the face of bad cash flow shocks. Moreover, they find that this drop in labor is not fully explained by the drop in investment, pointing to a direct effect of financial distress on labor rather than just through the investment decisions of the firms. Boeri et al (2012) [9] alsostressestheeffectoffinancial shocks on firm employment through the liquidity and working capital channel. They show that highly levered firms and sectors experience largest drops in employment during financial recessions or crises. In short the literature on effects of finance and financial shocks on labor points to a strong relationship between the two through the working capital / liquidity channel. 2.2 The Causes of the Great Moderation McConnell Perez (2000) [30], Blanchard Simon (2000) [8] and and Stock Watson(2002)[37] were the first among many others pointing to the large drop in volatility of output during the past three decades com- 5

6 pared to the earlier post war period. Form the outset, four potential explanations where offered for this change; change in monetary policy, change in inventory behavior of the firms, good luck (drop in volatility of exogenous shocks), and financial innovation. Boivin Giannoni (2006) [10] and Clarida et al (2000) [14] findasignificantchangeinconductandeffect of monetary policy in the post 1980 time period using a VAR approach. However, other empirical and structural studies that include monetary policy as an explanation among other explanations for the drop in volatility of output find that the contribution of monetary policy, if any, has been rather small. Stock and Watson (2003) [37] usinganempiricaldfmapproachfindthatmonetarypolicycanaccountfor10-20% of the drop for output volatility. Premiceri (2005) [33], using a stochastic volatility empirical framework, also finds evidence for a change in conduct of monetary policy, but the role of this change is not significant. Sims Zha (2006) [35] findlittleevidenceofchangesinmonetarypolicyasanimportantfactorbehindthedropin output volatility as well. The role for better inventory management as a significant contributor to the drop in output volatility has been advocated by McConnell Perez (2000) [30] and Kahn, McConnell and Perez-Quiros (2001, 2002) [29]. The main observation behind this claim is the apparent drop in volatility of production over sales and the negative coemovement between sales and inventories post However, this hypothesis is undermined by the research following these papers. Stock Watson (2003) [38] showthatatfrequenciesoffourquarter or longer the relative volatility of sales to production hasn t changed much. Herrara Pesavento (2006) [25] shows that once different components of manufacturing inventories are separated, the inventory of manufactured goods does not show any negative comovement with sales. Also, as Ramey and Vine (2006) [34] propose,changesinthepersistenceofsalesprocessescanleadtothesameobservationsaboutthe behavior of inventories. All in all, the aforementioned papers cast doubt on the effect of better inventory management practices on output volatility. Some papers in the literature point to changes in financial market regulations between the 70s to 80s as the main reason behind the drop in volatility of output. Dynan et al (2006) [16] documentsthree changes in the post 1984 period which could be associated with better access to credit: (1) the response of household consumption and business investment to cash flow has decreased substantially, (2) volatility of various measures of interest rates has sharply dropped, especially after the introduction of regulation Q, and (3) VAR estimations show smaller responses of mortgages and fixed business investment to interest rates. 4 Campbell Hercowitz (2005) [12] build a model in which better access to credit makes the correlation between mortgages and output smaller and reduces volatility as well. The last and very common proposed hypothesis for the Great Moderation is good luck which asserts that the economy was hit by smaller shocks during the period of the great moderation compared to before. A plethora of both empirical and structural papers which allow for a structural break in the variance of the shocks have found that the majority of of the decline in output volatility can be explained by smaller shocks, either productivity shocks (Gambetti et al (2008) [21],Ariasetal(2007)[2] ),investmentspecificshocks (Justiniano and Premiceri (2008)[28]) and a combination of smaller various shocks (Stock Watson (2003) [37], Sims and Zha (2006) [35], SmetsandWouters(2007)[36], Fernandez Villaverde (2011) [17]). 4 The low variation in interest rates in the second sample could be possible for negligible and insignificant coefficients the authors find. 6

7 2.3 Financial Shocks Post 1984 The results form the past two sections that financial shocks played an important role in business cycles since the outset of the great moderation is against some of the earlier studies on the great moderation which proposed financial innovation as a significant contributor to the drop in volatility of output 5.Howeverthis result is not particular to this paper. Becker and Ivashina (2014)[3] combinethedatafromthesurveyof bank officers with the composition of liabilities of large firms between bank loans and bonds to uncover credit 6 supply shocks and find evidence in favor of credit supply tightening in the past three recessions as well. Gilchrist and Zackarjsek (2012) [22] constructameasureofexcesspremiumusingcorporatebonddateand find that the shock to this variable can explain a large fraction of output and hours in a VAR setting. On the structural side, Jermann and Quadrini (2011)[26] construct a model with similar borrowing constraint and financial shocks in a New Keynesian DSGE setting and find that financial shocks can explain alargefractionofthevolatilityofoutput(46%)andhours(35%). FuentesAlbero(2013)[18] investigatesthe sources of the great moderation in a New Keynesian DSGE model where she allows for changes in efficiency of financial sector, monetary policy and volatility of shocks. She finds evidence of better access to external finance and an increase in the relative importance of financial shocks for business cycles. Interestingly, in her framework the increased access to finance contributes to the rise in relative importance of financial shocks. 3 Model In this section I introduce a simple neoclassical model with financial frictions and productivity and financial shocks. There are two types of agents in the model; households and entrepreneurs. Households supply labor, save in financial assets and consume. Entrepreneurs have access to a production technology specific to them and borrow funds from households to produce using capital and labor. Households are relatively more patient than entrepreneurs which naturally makes households savers and entrepreneurs borrowers. Financial markets are incomplete as debt contracts are the only available financial instrument and are subject to a collateral constraint. I start with describing Entrepreneur s problem first. 3.1 Entrepreneur s Problem Entrepreneurs are the only agents who have access to the production technology in this model. They enter period t with capital stock k t and debt stock b t.eachperiodtheychooseconsumptionc E t, Investment I t, labor input (h t ) and borrowing (b t+1 ) to maximize their expected utility. All entrepreneurs have access to the same CRS production function F (k t,l t )=A t kt h 1, where A t represents the time-varying firm-specific productivity. The law of motion for the capital stock of an entrepreneur follows t where k t+1 =(1 )k t + f(i t 1,I t ) 5 A short review of this literature is provided in the introduction of the paper 6 They only look at the data post 1985 since the earliest available date for the survey is around that date. 7

8 f(i t 1,I t )=(1 S( I t ))I t I t 1 Here, S( It I t 1 )I t represents the adjustment cost of investment and S(1) = S 0 (1) = 0, S 00(.) < 0. These properties insure that in a deterministic steady state both the level of adjustment costs and marginal adjustment cost are equal to zero while drastic adjustment in investment remains costly. Specifically I use the following functional form for S: S(x) = 1 (exp(applex)+exp( applex) 2) 2 Similarly, the labor is subject to quadratic adjustment costs of the form 2 l (l t l t 1) 2 l t 1. The only financial instrument available is collateralized debt contracts where the maximum borrowing capacity of a firm is equal to a fraction of its capital stock t k t+1 where t is exogenous. I assume that the amount of working capital (w t l t ) a firm uses each period affects its borrowing capacity for intertemporal debt (b t+1 ). This assumption captures the idea that changes in the borrowing capacity of firms affect not only intertemporal debt holdings, but also the amount they can raise to finance working capital as well. The borrowing constraint can be written as: b t+1 apple t k t+1 w t h t (1) The form of the borrowing constraint assumed in this model deserves some justification, as including working capital in the borrowing constraint is new. However, several recent studies have provided evidence showing that financial constraint affect labor decisions of the firm through such working capital. Identifying credit supply shocks at the firm level, Chodorow-Reich (2013) [13] shows that during the recent crisis firms which received large credit supply shocks cut current employment at their firms significantly more than others. Such reductions in labor seen at the more constrained firms is interpreted through its effect on working capital availability of these firms. In a separate study, Gilchrist et al (2012) [23] show that firms which were more likely to be constrained increased their output prices compared to firms which were less likely to be constrained. In such a setting, financial shocks affect the marginal cost of production through the working capital channel. The assumption of an exogenous process for the financial constraint is a reduced form way of capturing the variation in capital requirements for firms during different stages of the business cycle. There is ample evidence that collateral requirements for firms gets tightened during recessions, as can be seen in Survey of Financing Officers by the Federal Reserves. The economic justification for such variation could be because of lower recoverability of capital in recessions, or shocks to the liquidation technology of the economy. Finally the exogenous state variables t = e b t and A t = e zt evolve exogenously according to an AR(1) process: " # " #" # " z t z 0 z t 1 = + ˆ t 0 ˆ t 1 " t t # " " t t # N 2 " " " 2 Note that the AR(1) process is given the maximum freedom to have any structure, and the shocks are distributed iid across time. Denote the exogenous state variables by s t = {z t, ˆ t } and the endogenous! 8

9 state variables by ŝ t = {k t,i t 1,h t 1,b t }. The entrepreneur s decision making problem can be expressed recursively as follows: V (s t, ŝ t )= max k t+1,i t,h d t,b t+1,ce t log(c E t c E t 1)+ E E t V (s t+1, ŝ t+1 ) (2) s.t c E t + I t = A t kt ht 1 l (h d t h d t w t h 1) 2 t + b t+1 R t b t (3) 2 h t 1 k t+1 =(1 )k t + f(i t 1,I t ) (4) b t+1 apple t k t+1 w t l t (5) In order to avoid cumbersome equations, define gt n ht ht 1 = h t 1 (the growth rate in labor input), t = u 0 (c E t ) the Lagrangian multiplier on the budget constraint, µ t the Lagrangian multiplier on the borrowing constraint, and t as the marginal benefit of an extra unit of capital for tomorrow We have the following optimality conditions for the decisions of the entrepreneurs: <b t+1 >: µt =1 ER t t+1 E t ( t+1 ) t <h t >: F h (k t,h t )=w t (1 + µt )+ lg n t t E E t( t+1 lg n t t+1) <k t+1 >: t = t µt + t+1 E E t t t ( F t k (h t+1,k t+1 )+(1 ) t+1 ) t+1 <I t >:1=f 2 (I t 1,I t ) t + E t E t{ t+1 ( t+1 f 1(I t t+1 t,i t+1 ))} Equation (10) is the optimality condition for borrowing where µt captures the shadow value of one more t unit of a dollar today which tells us how binding the borrowing constraint is. Due to the working capital constraint, the marginal cost of labor depends on the severity of the binding borrowing constraint which µ shows up as w t t. Therefore any shock that makes the entrepreneur more financially constrained affects t the shadow cost of labor and labor demand through this channel. The marginal cost of a unit of labor also includes labor adjustment costs today and the expected adjustment cost in the future. Interpreting t as the unit cost of an extra unit of capital from the FOC with respect to investment, The t FOC for capital gives us the optimality condition for capital where the right hand side denotes the marginal µ benefit of an extra unit of capital tomorrow, and capital has the collateral value of t t. Therefore, any t changes in how much an entrepreneur is constrained is translated into the optimality condition of capital and hence firm investment. 3.2 Households Problem At each date t, householdschoosetheirconsumptionc h t,laborsupplyh s t and savings a t+1 to maximize their expected utility. Household earn wages w t on their labor and enjoy returns R t on their asset holdings from last period. Their maximization problem is: 9

10 max c t,a t+1,l t E t 1X s=t s t h u(c h t,h t ) (6) s.t c h t + a t+1 = w t h t + R t a t (7) Throughout this paper I use the following preferences for households 7 : u(c h t,h t )= (ch t c h t 1) 1 1 h 1+ 1 t 1+ 1 Iassumethathabitformationisexternaltothehouseholds;thatisthehouseholdsdon ttakeintoaccount the effect of their consumption today for tomorrow. In this class of preferences, is the Frisch labor supply elasticity and 1 is the intertemporal elasticity of substitution. Equations 4 and 5 characterize the labor supply decision and the inter temporal decision of the households. (8) u ht h 1 " = t u ct (c t c t 1 ) 1 = w t (9) (c t c t 1 ) = h R t+1 E t (c t+1 c t ) (10) 3.3 Equilibrium Definition: Arecursiveequilibriumisasetofpolicyfunctionsforhouseholds{c h t (s t, ŝ t ),h s t (s t, ŝ t ),a t+1 (s t, ŝ t )}; policy functions for the entrepreneurs {c E t (s t, ŝ t ),h d t (s t, ŝ t ),I t (s t, ŝ t ),b t+1 (s t, ŝ t ),k t+1 (s t, ŝ t )} ;prices{w t (s t, ŝ t ),R t+1 (s t, ŝ t )} ;andalawofmotionofendogenousandexogenousaggregatestates(s t, ŝ t ) which satisfy the household s and entrepreneur s bellman equations; goods, labor and bond markets clearing conditions, and the policy functions are consistent with the law of motion of aggregate state variables. 4 Quantitative Assessment 4.1 Data In this section I describe the data used for construction of shock processes, calibration of the model and computation of moments in the data. Investment is total investment by private non financial businesses from Federal Flow of Funds statistics. This data is more suitable for the model at hand as it excludes investment in residential buildings and consumption of durables by households. Similarly, capital stock data is measured using the investment series plus depreciation series (consumption of fixed capital by non financial businesses) from Flow of Funds statistics. The initial level of capital stock is chosen so that the capital stock relative to output does not show any trend. For borrowing of Entrepreneurs I use seasonally adjusted total credit to non-financial businesses from Flow of Funds statistics. For labor I use aggregate weakly hours worked in non-farm businesses and for 7 The primary reason behind using GHH preferences in this model is that it makes wages only a function of labor demand and not household consumption. There preferences are one of the standard preferences used in the RBC literature. 10

11 wages I use average hourly wage per worker, both from BLS. For output I use real business value added, and consumption is total consumption (including durables), both from BEA. Interest rate data is the real return computed from 3-month treasury bill data adjusted for ex-post inflation Calibration The parameters of the model can be divided into two groups: static and dynamic parameters. The static parameters {, E, h, 0,, } can be pinned down by matching the first moment (average) of some variables in the data with the steady state of the model, while the dynamic parameters of the model {,apple,, } do not affect the steady state. Static Parameters: Before setting the parameters of the model it is worth noting that the borrowing constraint of the entrepreneurs is binding in the steady state of the model as long as E < h.toseethisnote that if in the steady state, the optimality condition for borrowing by firms implies that µss = max{0, H E }, ss H and therefore the difference between the discount factor of households and the entrepreneurs determines the tightness of the firm s borrowing constraint. In this model, the condition E < h will always hold and therefore the borrowing constraint binds in the steady state. Ichoose h =0.99 which translates to an average annual real interest rate of 4%. is set to 0.02 to match an average depreciation rate of capital of around 8%. I set to match an average non financial firm debt to output ratio of 60%, which is the average in the period This, coupled with a capital stock to annual output ratio of around 2.3 (Evans 1999) and a labor share of 60% in the data, leads to an approximate value of 0.45 for. Iset E to match the empirical estimate of average before taxes net annual return to physical capital of 8.5% for as in Poterba (1998) [32]. To see how E is related to this measure note that combining equations 10 and 14 in the steady state gives: F K = 1 E H (1 ( H E )) 1=MPK Since and are already set, E is pinned down from the above equation at E = is set to match an average labor share of 60% which from labor demand equation 12 evaluated at the steady state implies wl y = F l l (1+ µss )y = (1 ) and therefore =0.39. Finally is set to match a labor supply of 0.30 in (1+ µss ) ss ss equilibrium which depends on the estimated value of labor supply elasticity, h and. Table1listsall the calibrated static parameters of the model. 4.3 Shock Process Extraction The derivation of the shock processes in this model is straightforward; the productivity shock series is derived from the production function, while the financial shock series is derived by log-linearization of the borrowing constraint around the steady state. 9 Note that the derivation of the financial shock process is valid as long 8 Note that since in my model there is only one interest rate this choice is reasonable. The model should be thought as grouping intermediaries and firms into one group and therefore measures of risk-less short term interest rates are appropriate. In future extensions of the model where I distinct between the funding costs of the intermediaries and firms a different measure of interest rate should be used for funding cost of firms. 9 Note that given the adjustment cost function assumed, the capital stock derived using the perpetual inventory method depends on the adjustment cost parameter. In the appendix I show that the capital stock and hence the shock process derived 11

12 Parameter Numerical value Data counterpart h % annual interest rate equilibrium debt to capital stock - steady state labor supply Average labor share = Depreciation rate E Return to Capital Stock of 8.5% Table 1: Steady state parameters and their data counterparts. Note that these parameters are jointly determined. h and E denote the discount factor of households and Entrepreneurs respectively, Cobb-Douglas production function, 0 is the parameter of the borrowing constraint and is the depreciation rate, is the parameter of capital stock in the is the utility parameter. as the borrowing constraint is binding. I confirm that the borrowing constraint is binding when the shocks are fed to the model ex-post. The two equations below show how the shock series are constructed where ˆx t denotes log deviations from a deterministic trend: ẑ t =ŷ t ˆk t (1 )ĥt (11) ˆ t = b + w l (ŵ t + b + w lˆbt b ˆl t ) ˆkt (12) + w l After deriving the process for ẑ t and ˆ t, I estimate the shock process from the AR(1) process below: " # " #" # " z t z 0 z t 1 = + ˆ t 0 ˆ t 1 " t t # " " t t # N 2 " " " 2 Once the shock series are uncovered I estimate the process separately for two sub periods : and Table 3 show the shock processes estimated for each period. As it can be seen from this table, while in the earlier period (before 1984) productivity shocks were significantly more volatile than financial shocks, In the latter period the volatility of the shock processes is very similar. In this sense the relative importance of financial shocks to productivity shocks has grown in the latter period. 1960: :2007 " z " Table 2: Estimated shock process for 1960:1984 and 1984:2007. z and are the persistence parameters for productivity shocks and financial shocks respectively, and " and are the volatility of productivity and financial shocks. " denotes the cross correlation between the two shocks.! (13) using a wide range of adjustment cost parameters stays the same. 12

13 4.4 Calibration Using Pre 1984 Data Using the derived shock processes, I calibrate the dynamic parameters of the model (apple,,,, certain second moments in the data for the period of 1960:1984. ) to match Once these parameters are chosen, we can investigate the prediction of the model for the moments of interest for the post 1984 period when it is simulated using the shock processes derived in previous subsection. Table 3 describes the set of moments chosen to calibrate these parameters and a heuristic argument for why each moment is chosen. Table 4 examines the rest of the moments predicted for pre 1984 data. The calibrated parameter for labor supply ( ) is 2.2 which is within the ballpark of the estimates in the RBC literature. The adjustment cost on investment apple is around 2.34 which is smaller number than most of the literature. This is mostly because my measure of investment in this calibration does not include durable consumption. As fixed capital business investment is more volatile compared to durable consumption, ceteris parabus the investment adjustment cost parameter should be smaller in my calibration so the model produces the volatility of investment as defined in the data. affects the volatility of labor to output most of all and Iset =0.48 which helps to match the relative volatility of labor to output of 0.9 for pre 1984 period. The habit persistence parameter is set to roughly match the relative volatility of total consumption to output, and the value of 1 is within the bounds found in the literature. Parameter Data Moment before 84 Model apple=2.34 =0.48 =0.48 =2.2 =1 (I) =3.14 (y) 3.15 (h) =0.91 (y) 0.91 (c) =0.62 (y) 0.62 (w) =0.51 (y) 0.53 (r) =0.23 (y) 0.24 Table 3: Calibration of the dynamic parameters of the model and the data counterparts targeted. All parameters are determined jointly. All the moments in the data are computed from the deviation from a deterministic trend. denotes the standard deviation and I,h,c,w,r denote investment, hours, consumption, wages and real interest rate as described in the data section of the paper. Table 4 describes the performance of the model vis-a-vis the data for moments that were not targeted for calibration. The model performs reasonably well in matching the volatility of debt to that of GDP, and the correlation of hours and investment with output although they were not targeted as part of the calibration done here. Also, the model predicts a correlation of output and labor productivity of 0.45 (0.51 in the data) and a correlation of hours and labor productivity of (-0.03 in the data). The model somewhat underperforms in matching the autocorrelation of labor, however on this dimension the performance is the same as most RBC models. 4.5 Performance for post 1984 data Using the calibrated parameters of the model I evaluate the performance of the model for the period of 1984:2007 when the recovered shocks for post the 1984 period are fed into the model. Specifically, I examine whether the model can generate moments similar to ones observed in the data for the post 1984 period, and whether it can capture the change in the cyclical behavior of labor productivity. Table 5 reports the 13

14 Data Moments Before 84 Model (y) ( y,y) h ( y,h) h (I,y) (h, y) ( db,y) y (y, y 1 ) (h, h 1 ) (I,I 1 ) Table 4: Moments from the data for 1960:1984 period v.s model generated moments using the shock process recovered for the same period. denotes the standard deviation, denotes correlation and the (-1) subscript denotes the lag of variables. y db,y,b,i,h, denote labor productivity, output, debt stock, investment, total hours worked and debt flow relative to output. h y moments generated from the model and the moments in the data both for the period. Data Moments After 84 Model (y) (h) (y) (c) (y) (I) (y) ( y,y) h ( y,h) h (I,y) (l, y) ( db,y) y (h, h 1 ) (I,I 1 ) Table 5: Moments from the data for 1985:2007 period v.s model generated moments using the shock process recovered for the same period. denotes the standard deviation, denotes correlation and the (-1) subscript denotes the lag of variables. y db,y,b,i,h, denote labor productivity, output, debt stock, investment, total hours worked and debt flow relative to output. h y Given the parsimony of the model, the simulated moments are remarkably in line with the observed (h) moments in the data for almost all variables of interest. Specifically, the model predicts (y) =1.16 (versus 1.2 in the data), ( y h,y)= 0.11 (versus in the data), and ( y h,h)= 0.66 (versus in the data). The volatility of output predicted by this model is also very close to that of the data. This is the sense in which this model is able to generate the key changes associated with the great moderation through the reduction in the importance of productivity shocks relative to financial shocks. As Table 5 shows, the model generates a large drop in the volatility of output, the correlation of labor productivity and output and the correlation of labor productivity and labor and the increase in relative volatility of labor compared to output. 4.6 Impulse Responses To gain a better insight into the working of the model it is instructive to look at the impulse response of endogenous variables to each shock. Figure (3) plots the impulse response of output, consumption, 14

15 investment, labor, and debt flow to output - both to a negative financial shock and a negative productivity shock. After an adverse financial shock, labor drops more than output while after a productivity shock the reverse is true. The reason for this is intuitive: financial shocks affect labor directly through the working capital constraint which spills over to output, while productivity shocks affect output directly, while their effect on labor is through their effect on the marginal product of labor. Therefore, a financial shock tends to make labor productivity countercyclical while a productivity shock makes labor productivity more procyclical. The two shocks have different effects on debt flows as well. A financial shock has a larger effect on debt flows compared with a productivity shock. This effect is quite mechanical: financial shocks affect debt flows directly through the borrowing constraint while productivity shocks affect them mainly through the demand for investment and consumption smoothing of entrepreneurs. Another point worth mentioning is the lower persistence of the effect of financial shocks compared to productivity shocks, while the persistence of the underlying shock processes is similar. This difference is due to the nature of the two shocks; the effect of a negative financial shock can be partially absorbed by retaining more of the income of the firm, while a productivity shock fundamentally changes the output frontier which won t recover till the effect of the shock has completely dissipated. 5 x 10 3 Outout 1 x 10 3 Hours 0.02 Labor Productivity x 10 3 Investment 4 x 10 3 Debt Flow µ Figure 3: Impulse Responses to a productivity shock (blue line) and a financial shock (red line). The parameter values are set from the calibration described in the previous two subsections. The IRFs are computed after a negative one standard deviation innovation to productivity and financial shocks. The intuition provided above for the impulse response of labor to productivity and financial shocks carries to the implications for a change in volatility of financial shocks relative to productivity shocks. Figure (4) shows how ( h y ), ( y h,y) and ( y h,h) change as ( z )variesfrom0to2. AscanbeseeninFigure(3), ( h )increasesas( ) increases while ( y y z h,y) and ( y h,h) both decrease in ( ). The increase in relative z 15

16 importance of financial shocks to productivity shocks changes the moments in the direction of dynamic implications of financial shocks. This is why the model correctly predicts a decline in the procyclicality of labor productivity for the period compared to as ( z )decreasesfromaround2to relative volatility of labor to output correlation of labor productivity with output correlation of labor productivity with hours σν σϵ Figure 4: Relative volatility of labor to output (blue), correlation of labor productivity and output (red) and correlation of labor productivity and labor (black) as a function of the volatility of financial shocks relative to productivity shocks. " 5 Extended Model with Multiple shocks This section extends the baseline model to a framework with multiple shocks that are standard in DSGE models. Specifically I add preference, investment, and labor supply shocks to the baseline model. As in the previous section, I divide the data into two sub-periods (pre-84 and post-84), and estimate the dynamic parameters of the model and the shocks processes for each period separately. Then I ask: do financial and productivity shocks explain a large chunk of the variation in output and labor? Which parameters or shock processes show a significant difference across the two periods? The answer to these questions are not necessarily the same as the ones in previous section as these additional shocks could potentially have similar dynamic implications and render financial or productivity shocks insignificant. However, as I show below, financial shocks remain an important driver of business cycles, and have increased in importance as the volatility of labor productivity shocks has declined. 5.1 Extended Model Iaddthreenewshockstothebasicmodel: demandshocks,investmentspecificshocks,andlaborsupply shocks. These shocks enter the utility function of the households and the capital accumulation equation: 1 u(c t,l t )=A p,t log(c t c t 1 ) A l1+ t l,t

17 K t+1 =(1 )K t + µ t (1 S( I t ))I t I t 1 Where A p,t and A l,t are preference and labor supply shocks respectively and µ t is the investment specific shock. Shocks are iid and follow a log normal AR(1) process: x t = x t 1 + " x,t " x,t N(0, 2 x) Since the addition of these shocks does not change the first order conditions of the model in a substantial way, I relegate the first order conditions to the Appendix. 5.2 Estimation IusebayesianestimationtechniquesasexplainedinAnandSchorfeide(2007)[1] toestimatetheshock processes and the dynamic parameters of the model. 10 Since the model includes 5 shocks, I use the following five series to estimate the shock processes and dynamic parameters of the model: gross private business investment (excluding inventories), real business value added, real total consumption of households (durable and non-durables), net increase in the outstanding credit market instruments of non-financial businesses, and aggregate weekly hours divided by population. All series are constructed by dividing each nominal series by its deflator and detrended by a quadratic trend. 11 Iestimatethemodelseparatelyfortwoepisodes: and Iallowallofthedynamic parameters and shock processes to vary across the two periods while the static parameters are borrowed from the previous section. The priors for dynamic parameters include the range of estimates in the literature and allow relatively flat priors. Table (6) describes the prior and posteriors estimated in each sub-sample for each parameter. The estimation of dynamic parameters across the two sub-samples are very close to each other, and there seems to be no significant differences between the estimates. The only notable difference is the estimate of the investment adjustment cost parameter. Nonetheless, the model in the second period using the mode value of the estimated parameter from the first sub-sample gives us similar estimates for the shock processes. Therefore, there is not much evidence of a significant change in parameters across the two periods. However, the standard deviation of the productivity shock process falls by almost half in line with the result from the previous section. Financial shocks also display a small rise and the process for the other shocks is almost unchanged. Therefore in the extended model, the sources of the decline in volatility of real variables is dominantly due to a reduction in volatility of productivity shocks. The result that the reduction in volatility of productivity shocks is responsible for the period of the great moderation is in line with some of the studies on sources of the great moderation. For example, Smets and Wouters (2007)[36] usinganewkeynesianmodelalsofindthatthesignificanceofproductivity shocks as drivers of business cycles has decreased significantly when they divide their sample to and Nonetheless, the cause of the great moderation is still controversial. For example Boivin Gianonni (2006) [10] make the case for better conduct of monetary policy in the latter period, while Justiniano et al 10 For a short explanation of the method please refer to the Appendix?? 11 The case using a linear trend is very close to the one using a quadratic trend. 17

18 Parameter Prior Posterior (pre 1984) Posterior (post 1984) Mode Mode h Igamma(1,1) Normal(2,2) Normal(1,1) apple Normal(1.4,1.4) Beta(0.5,0.5) z Beta(0.8,0.1) Beta(0.8,0.1) µ Beta(0.8,0.1) c Beta(0.8,0.1) l Beta(0.8,0.1) z IGamma(0.003,0.025) IGamma(0.003,0.025) µ IGamma(0.003,0.025) c IGamma(0.003,0.025) l IGamma(0.003,0.025) Table 6: Priors and Posteriors of Parameters Estimation for and (2008) [28] findasignificantdecreaseinimportanceofinvestmentspecificshockspost1984astheunderlying cause of the great moderation. 12 Table (8) presents the variance decomposition for the contribution of each shock to selected endogenous variables for each period separately. All shocks except labor supply shocks are significant drivers of cycles at business cycle frequencies. Productivity, financial, and intertemporal shocks explain most of the variation in output, labor, and labor productivity in both time periods. While the explanatory power of productivity shocks decreases in the latter period, financial and intertemporal shocks explain more of the variation in output and labor, while investment specific shocks explain an even larger fraction of the variation in investment. The reason is that in absence of other frictions, investment specific shocks can only affect output through their effect on the capital stock and therefore their effect on output is limited. The uncovered productivity and financial shock processes for both periods are very close to the uncovered shock processes derived in the previous section, although they are estimated using a different technique. [Since I don t 2investment and debt flow are flows of debt stock and capital stock and should capture their variation to some extent.] The similarity in the estimated processes across the two models lends further credibility to the importance of inclusion of financial shocks in the model. Table (8) compares selected simulated moments of the extended model with the moments in the data for each period. The extended model captures the volatility of output and relative volatility of labor to output quite well however, it exaggerates the volatility of investment and consumption to output. It also delivers the change in procyclicality of labor productivity, but it underestimates this moment in both periods. In order to understand the extent to which financial shocks influence the performance of the model, I estimate the extended model without financial shocks for each sub period and estimate the model without financial shocks using the debt outstanding series. The estimated results in Table (A.3) show that the 12 I don t find much evidence of a change in volatility of investment shocks. In this framework investment specific shocks don t have much effect on output or labor as it is well known from Justiniano et al (2010) [27] that real rigidities are essencial for propagation of investment shocks. 18

19 Productivity Financial Consumption Labor Investment Output Consumption Investment Labor Labor Productivity Debt Stock Debt Flow Interest Rate Debt Flow Output (a) Unconditional Variance Decomposition for Productivity Financial Consumption Labor Investment Output Consumption Investment Labor Labor Productivity Debt Stock Debt Flow Interest Rate Debt Flow Output (b) Unconditional Variance Decomposition for Table 7: Unconditional Variance Decomposition for (Fig. a) and (Fig. b) using the estimated shock process and the mode of the estimated values from the bayesian estimation procedure. estimated variance of all shocks, especially labor supply shocks, increases compared to the case when financial shocks were not included. The increase in variance of labor supply shocks is mostly to explain the variation in labor and output that was captured by financial shocks before. This result is interesting as many of the prototype neoclassical models which included labor supply shocks find an important role for this shock while as seen here, considering financial shocks and using the debt series in identification nullifies these shocks. 5.3 Dynamic Performance of The Extended Model To understand how financial shocks affect the performance of the model I re-estimate the model using the whole sample from 1985 to I uncover shocks using a standard Kalman filter and set the dynamic parameters of the model at their mode values. Next I run two simulation exercises: I feed all the uncovered shocks to the model and once I feed the model with all the shocks other than financial shocks. Through this experiment we can both check the dynamic performance of the model in general and specifically understand the contribution of financial shocks to the fluctuations post 1985 and. Figure (5) plots the simulated series for each of the two exercises mentioned above versus the data. Figure (5) shows that when the model is simulated with all uncovered shock series, it does a reasonable job at capturing the dynamics of the fluctuations, though it can not completely match the level as in the data. The importance of financial shocks for the dynamics post-1985 can be seen by comparing the results of the two simulations with the dynamics realized in the data. The model performs significantly better when 19

20 Data Before 84 Model before 84 Data after 84 Model after 84 (y) (h) (y) (c) (y) (I) (y) ( b) (y) ( b, y) (lp, y) (lp, h) (I,y) (l, y) (h t,h t 1 ) (I t,i t 1 ) Table 8: Moments generated by the uncovered shock processes. All variables in the model are computed as the deviation from steady state values. The moments in the data are computed using an HP filter with smoothing parameter of financial shocks are included. Specifically, the predictions of the model are greatly improved for the debt series as shown in figure 5(d). Including financial shocks also enables the model to do a much better job of capturing fluctuations in hours worked as the model won t match the increase in hours worked in late 90s without financial shocks. The effect of financial shocks in the recent crisis are of specific interest since financial factors arguably played a larger role in the recent recession and naturally one would expect financial shocks in this model play a great role. When financial shocks are not included, the model predicts an output drop of around 5% from the peak to trough of the recent recession compared with 10% for the case with financial shocks and 12% in the data. More interestingly, without financial shocks the model predicts an increase in hours worked (around 2%) and a large drop in labor productivity (around 8%), whereas in the data total hours worked falls sharply (around 10%) and the drop in labor productivity is rather small (around 2%). When financial shocks are included, the drop in hours and labor productivity are comparable to that of the data; 8% and 2%. The last point on the response of labor productivity during the recent crisis is of special interest as the fact that labor productivity almost didn t change (when measured in levels, not deviations from the trend) came as a surprise and received a lot of attention. 13 Through the lens of this framework, the reason that labor productivity did not change while output sharply fell is due to the sudden and sharp tightening of the borrowing constraint of the firms which cut labor sharply primarily because of the working capital requirement. Thus this framework gives a consistent narrative of the recent recession while resolving the controversy surrounding the behavior of labor productivity during the recent recession. 6 Reduced Form Evidence In this section I provide some preliminary cross sectional evidence for the hypothesis that a larger role for financial shocks might be the culprit for the reduction in procyclicality of labor productivity. It is well known 13 See Brugemann et al (2010) 20