Testing for Keynesian Labor Demand

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Previous articleNext article FreeTesting for Keynesian Labor DemandMark Bils, Peter J. Klenow, and Benjamin A. MalinMark BilsUniversity of Rochester and NBER Search for more articles by this author , Peter J. KlenowStanford University and NBER Search for more articles by this author , and Benjamin A. MalinFederal Reserve Bank of Minneapolis Search for more articles by this author University of Rochester and NBERStanford University and NBERFederal Reserve Bank of MinneapolisPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionA leading proximate explanation for plunging employment during the Great Recession is plummeting demand for goods. According to this Keynesian labor demand hypothesis, when producers face unexpectedly low demand for their goods they respond by laying off workers rather than lowering their output prices. The underlying source of Keynesian labor demand could be nominal price stickiness and/or countercyclical desired markups. See Keynes (1939) for his embrace of both justifications.1We test for Keynesian labor demand across US industries in recent decades (1990 to 2011). To do so, we exploit how durability varies across seventy consumption and investment categories to predict relative goods demand movements over the business cycle. Relative demand shocks allow us to test whether markups move in the direction predicted by Keynesian labor demand.2 We also exploit information on which goods are luxuries versus necessities to predict relative demand, and take into account how price flexibility and capital-intensity of production vary across industries.According to consumer theory, durability should be a powerful determinant of the cyclical expenditures on a good. The more durable a good, the smaller is the average flow of expenditures on the good relative to the accumulated stock. For a good that lasts N years, increasing the stock by 1 percent requires an N percent increase in expenditures on the good relative to replacement expenditures. Thus any common macro shock (such as to technology or monetary policy) should hit demand for durables more dramatically. Similarly, demand for luxuries should be more cyclical than demand for necessities.Under sticky prices, firms should accommodate shifts in relative demand by firing or hiring workers rather than adjusting their prices. If capital is less flexible than labor in the short run, firms in flexible-price industries should adjust their prices more and adjust their production less than do sticky-price industries—controlling for the size of the demand shift they face. If target markups are countercyclical, however, then price stickiness may not be essential for a Keynesian labor demand response to goods demand shocks.We test for Keynesian labor demand using a variety of data. We use US National Income and Product Accounts (NIPA) and insurance industry estimates of durability for seventy goods covering around 60 percent of GDP. These include most consumer and investment goods and services, but exclude government purchases and housing consumption. We estimate whether a good is a luxury or a necessity using cross-sectional Engel curves from the US Consumer Expenditure Survey. We assess price flexibility using US Consumer Price Index (CPI) and Producer Price Index (PPI) microdata on the frequency of price changes by good.We use quarterly NIPA data on consumption and investment from 1990 to 2011 to test whether durability and luxuriousness succeed in predicting the cyclicality of expenditures. Durability is a strong predictor. Bringing in data from the US Current Employment Survey, we find that durability is also highly correlated with employment growth across industries—including during the Great Recession. Finally, we incorporate the US Bureau of Labor Statistics KLEMS data on production, prices, and inputs across detailed industries. This allows us to contrast movements in labor’s productivity with its real wage, identifying whether producers move away from constant-markup labor demand in response to goods demand shocks.We find that industries producing goods that are more durable, while displaying much more cyclical employment and output, exhibit countercyclical relative markups. This countercyclical increase in markups is sufficiently large that relative prices of durables do not fall in recessions. (By contrast, sectoral total factor productivity [TFP] movements play little role in explaining the lack of cyclicality in durables’ relative prices.) Our evidence rejects flexible-price labor demand under a constant markup, but is consistent with Keynesian labor demand. This cyclical pricing for durables could reflect intentional markup movements, rather than being the byproduct of price stickiness. In fact, a model with countercyclical intended markups for durables, but flexible pricing in general, would arguably explain the data better than a sticky-price model.Despite its prominence in business cycle theorizing, there have been surprisingly few tests for Keynesian labor demand. Most have been based on aggregate time series, such as Galí and Rabanal (2004) and Basu, Fernald, and Kimball (2006). More recently, a number of studies have exploited regional variation to test whether goods demand drives employment. Examples include Feyrer and Sacerdote (2011), Nakamura and Steinsson (2011), and Mian and Sufi(2012). Mulligan (2010) looks at seasonal movements in labor supply and employment. Our study complements these by looking at cross-industry evidence. Thus, our approach is similar to Shea (1993) and Nekarda and Ramey (2011), who examine the impact of an industry’s downstream demand (Shea) and its share of government purchases (Nekarda and Ramey) on industry price and quantity. Chang, Hornstein, and Sarte (2009) examine how employment responds to industry-specific productivity shocks, and how that response depends on the use of inventories and pricing frequency in the industry.The rest of the paper is organized as follows. In section II, we lay out a dynamic stochastic general equilibrium (DSGE) model to illustrate the key forces that motivate our demand predictors. Section III briefly describes the data sets we use. Section IV presents the main results, and section V concludes.II. ModelIn this section we use a multisector DSGE model to demonstrate how relative demand shocks affect markups under Keynesian versus classical labor demand. Here the source of Keynesian labor demand is sticky prices, rather than countercyclical intended markups. We incorporate heterogeneity in the durability of goods, the capital intensity of firms’ production, and the frequency of price changes. After sketching the key model features, we use a simplified version of the model to illustrate analytically how movements in relative quantities and prices across sectors differ depending on whether the model is Keynesian or classical (i.e., sticky or flexible prices).3 We then calibrate and simulate the full-blown model to get some quantitative sense of these movements.A. FirmsDurable (Yd) and nondurable (Yn) final goods are produced from intermediate goods, which are produced by two types of firms: those with high- and low-capital-intensity technologies. Competitive final goods producers use the following production functionwhere Yjf,t are composite intermediate goods produced (by competitive firms) according towhere ε > 1. Individual intermediate goods producers are monopolistically competitive and produce using a constant returns to scale (CRS) production functionwhere kjf,t(l) and njf,t(l) are capital and labor services employed by firm l in sector jf at time t, Ajf,t is sector-specific TFP, j = {d,n} indexes the type of good produced, and f = {h,l} denotes the technology used. Sectoral price indices, Pj,t and Pjf,t, expressed as functions of individual prices pjf,t(l), can be derived via standard cost minimization.Capital and labor flow freely between firms in the same sector, which implies, under CRS production, that nominal marginal costs and capital-labor ratios will be equated across firms in the same sector. However, as will become clear when we discuss household supply of factor inputs, imperfect capital mobility will allow marginal costs to vary across sectors. Furthermore, different production technologies across sectors imply different slopes for sectoral marginal cost curves. In particular, firms that produce with more capital-intensive technologies (larger αf) will require a greater increase in the flexible labor factor to effect a given short-run increase in production (i.e., their marginal cost curves are steeper).Finally, goods prices are sticky. We use the Calvo (1983) assumption whereby monopolistically competitive firms change their prices with a constant probability of (1 – θif). We allow θjf to vary by sector, and will also consider perfect price flexibility (θjf = 0, ∀jf ).B. HouseholdsHouseholds get utility from nondurable and durable consumption and disutility from working. Let Cn,t denote nondurable consumption, Cd,t durable consumption expenditures, the stock of the durable consumption good, and Nt labor supply. Households maximize expected discounted utilityand the stock of the durable consumption good evolves according towhere δ is the depreciation rate and S′′ governs adjustment costs on durables expenditures. Following Barsky, House, and Kimball (2007), the functional forms for household preferences arewhere σ is the intertemporal elasticity of substitution, ψ determines the relative preference for nondurables versus durables, η is the elasticity of substitution between the two goods, ϕ is the Frisch labor supply elasticity, and χ governs the level of disutility from labor supply.Greater durability implies that any increase in consumption requires a more dramatic increase in expenditure. To increase consumption of the durable good by 1 percent from a steady state level requires an annual increase in expenditure of 1/δ percent, whereas a 1 percent increase in nondurables consumption requires only a 1 percent increase in expenditure. This motivates our use of durability as a shifter of goods demand and, because a larger increase in expenditure will call forth a larger increase in hours worked, labor demand as well.The household also owns the economy’s stock of physical capital (Ks), sets the utilization rate of capital (u), and rents capital services to firms in a competitive market. The relationship between capital services, utilization, and the physical capital stock isThe accumulation equation for capital mirrors that for durables consumption:where Ijf,t denotes investment that adds to the sector-jf capital stock. Note that Ijf,t is distinct from investment expenditures, which are given byInvestment expenditures include maintenance costs arising from capital utilization, . The cost function a(ṡ) is increasing, convex, and zero in steady state. In addition, investment is affected by investment-specific productivity ; greater productivity means less expenditure is required to achieve a given increase in the capital stock.Importantly, we have assumed each sector has a separate capital stock, which means that capital is (partially) fixed in the short run. Capital services can adjust immediately due to time-varying utilization, but utilization costs make utilization less than perfectly flexible. Capital stocks adjust fully over time, but the speed depends on investment adjustment costs.Households also supply labor to firms in each sector, and this process is intermediated by monopolistically competitive unions who have the power to set wages (Erceg, Henderson, and Levin 2000). The unions face Calvo frictions, altering wages with a constant probability of 1 – θw. Because wage stickiness does not vary by sector and labor supply across sectors is assumed to be perfectly elastic (Nt = ∑j,fNjf,t ), (nominal) wages Wt will be equalized across sectors.C. Analytical DiscussionBefore presenting numerical simulations, we use a stripped-down version of our model to analytically illustrate how cyclical movements in relative sector quantities, prices, and markups behave under sticky versus flexible prices. We assume the economy starts in steady state and evaluate the immediate response to an expansionary aggregate shock at time t. The stripped-down model features a constant aggregate capital stock, with the distribution of capital services across sectors fixed at time t but perfectly mobile by t + 1 (fixed capital utilization and no investment adjustment costs). We also assume durables goods are very long-lived (δ sufficiently small that the shadow value of durables is nearly invariant to short-lived shocks, as in Barsky, House, and Kimball 2007).With sufficiently long-lived durables, household optimization requireswhere hatted variables are log deviations from steady-state values. Furthermore, the law of motion for durables implies ; all produced goods are consumed ; the production functions are ; marginal costs are ; and markups are given by . Combining these expressions, we haveWe first consider a flexible-price economy. Markups are constant at μj = ε/(ε – 1). If sectors have the same capital intensities, equation (2) shows that labor will expand more in the durables sector. Thus, relative output, marginal costs, and prices also increase. Note that these relative movements do not depend on the underlying shock causing the expansion, but the movements are even larger if the source is a positive aggregate TFP shock.The results differ under sticky prices. Take the extreme of fixed prices, so that relative prices do not move. Equation (1) implies an increase in relative durables output, and thus labor and marginal costs. Therefore, relative markups are countercyclical. If prices are not perfectly rigid but are equally sticky in the two sectors, one can show that relative output, labor, and prices are procyclical, while relative markups are countercyclical.4 Thus, the primary (qualitative) difference between flexible and sticky prices is the behavior of relative markups.We have derived these predictions for relative movements in durables holding other characteristics—such as price flexibility, capital intensity, and TFP—fixed across sectors. This is important. For example, if durables prices were perfectly flexible and nondurables perfectly rigid, the relative durables markup would be procyclical and, under some parameters, relative labor could be countercyclical. Likewise, if the aggregate expansion was caused by a shock to durables TFP (Ad,t > An,t), one can show that, under sticky prices, the relative durables markup would again be procyclical (e.g., assuming η = 1 and αj = α). In our subsequent empirical analysis, therefore, we will control for variables that might be correlated with durability.So far, we have analyzed the response of durables relative to nondurables, but the model also predicts relative movements across goods on other dimensions, holding durability constant. Optimal demand by final (durable or nondurable) goods producers implieswhere h and l denote high- and low-capital-intensity firms. Assuming equally sticky prices in the two subsectors, one can derive the following expression for relative markupsso that higher-capital-intensity production implies a countercyclical markup. The sign of the relative movements in other variables depends on parameter values, although the more capital-intensive good typically has higher marginal costs and prices, but lower output.We can also use equation (3) to analyze how differences in price stickiness affect relative movements, now letting h and l denote firms with high and low price stickiness. We get the following relationship between relative labor and relative markups:That is, relative labor (and thus output and marginal costs) will move in the opposite direction of relative markups (and prices). Whether the relative markups are procyclical or countercyclical, however, depends on the nature of the underlying shock. Monetary (TFP) shocks that put upward (downward) pressure on prices will lead to countercyclical (procyclical) markups for the sector with stickier prices.D. Quantitative ResultsWe now calibrate and simulate the full-blown model. This allows us to move away from stark assumptions, such as the complete short-run fixity of capital, and consider realistic features like capital utilization and investment adjustment costs. We consider an empirically relevant amount of durability, capital intensity, and price stickiness in order to get a quantitative sense of the size of movements of key variables across sectors.Table 1 summarizes our model calibration. The parameters governing household preferences (σ, η, ϕ) and desired markups are set to standard values, and y is set to produce a steady-state nondurable-to-durable consumption ratio of 2.96. The annual depreciation rate of 5 percent matches the (weighted) average life span of durables in our data (i.e., twenty years). We set the household’s annual discount rate (3.34 percent) to match an investment-to-output ratio of 0.16, given the depreciation rate and an empirical aggregate capital share of 0.322. When we consider high- and low-capital intensity sectors, we use capital shares of ah = 0.475 and al = 0.169, which are the weighted average capital shares for consumption categories above and below the median capital share, respectively. Consistent with the microdata underlying the US CPI, the average price changes every four months, while high- and low-frequency firms set prices roughly every two and a half and twelve months. Wages are assumed to change once a year.Table 1. Model ParametersView Table ImageThe curvature of the utilization adjustment cost function is pinned down by the relationship between relative sector utilization rates and relative labor-to-capital ratios:Using Gorodnichenko and Shapiro (2011) data on twenty two-digit manufacturing sectors over the past thirty years, we regress utilization rates on labor-capital ratios (and time effects) to estimate an elasticity of 0.33, corresponding to a′′ = 2.0. Online appendix C has details (http://www.nber.org/data-appendix/c12756/appendix.pdf). For durables expenditure adjustment costs we set S′′ = 0.455/δ to match Cooper and Haltiwanger’s (2006) estimate of the elasticity of the investment rate with respect to Tobin’s Q.Finally, we need to calibrate the exogenous shock processes and the Taylor rule that governs monetary policy. With one exception, these parameters are monthly transformations of the quarterly estimates of Smets–Wouters (2007).5 We choose a larger volatility for the neutral technology shock to match the cyclicality of the aggregate labor share (i.e., inverse markup), but since our primary focus is on conditional impulse response functions, alternative calibrations of the volatility do not change the insights we draw from the model.Figures 1 to 4 show impulse responses to an expansionary monetary policy shock.6 We plot relative movements in output, labor, prices, and markups, where we measure markups using the inverse of the labor share. (Note that, under Cobb–Douglas production, fluctuations in markups are equivalent to fluctuations in the labor share. However, our test does not hinge on Cobb–Douglas production, and we will explicitly consider departures from it in our empirical analysis.) For scaling purposes, we also show the response of aggregate output (thin line). Figure 1 shows the relative durable-to-nondurable responses under sticky prices. For this exercise, the average capital intensity and price-change frequency in the two sectors are the same.7 Relative output (thick solid and labor are procyclical, while the relative price response is also positive but by sticky prices. Relative markups are countercyclical, two first and most price markups are more countercyclica

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