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The Aggregate Implications of Regional Business Cycles *

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The Aggregate Implications of Regional Business Cycles * Martin Beraja Erik Hurst Juan Ospina University of Chicago March 15, 2016 Abstract We argue that it is difficult to make inferences about the drivers
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The Aggregate Implications of Regional Business Cycles * Martin Beraja Erik Hurst Juan Ospina University of Chicago March 15, 2016 Abstract We argue that it is difficult to make inferences about the drivers of aggregate business cycles using regional variation alone because (i) the local and aggregate elasticities to the same type of shock are quantitatively different and (ii) purely aggregate shocks are differenced out when using cross-region variation. We highlight the importance of these issues in a monetary union model, and by contrasting the behavior of US aggregate time-series and cross-state patterns during the Great Recession. In particular, using household and retail scanner data for the US, we document a strong relationship across states between local employment growth and local nominal and real wage growth. These relationships are much weaker in US aggregates. In order to identify the shocks driving aggregate (and regional) business cycles we develop a methodology that combines regional and aggregate data. The methodology uses theoretical restrictions implied by a wage setting equation that holds in many monetary union models with nominal wage stickiness. We show how to estimate this equation using cross-state variation thus linking particular regional patterns to particular aggregate shock decompositions. Applying the methodology to the US, we find that a combination of both demand and supply shocks are necessary to account for the joint dynamics of aggregate prices, wages and employment during the period while only demand shocks are necessary to explain most of the observed cross-state variation. We conclude that the wage stickiness necessary for demand shocks to be the primary cause of aggregate employment decline during the Great Recession is inconsistent with the flexibility of wages estimated from cross-state variation. *First draft: May A previous version of this paper circulated as The Regional Evolution of Prices and Wages During the Great Recession . We thank Mark Aguiar, Manuel Amador, David Argente, Mark Bils, Juliette Caminade, Elisa Giannone, Adam Guren, Simon Gilchrist, Paul Gomme, Bob Hall, Marc Hofstetter, Loukas Karabarbounis, Pat Kehoe, Virgiliu Midrigan, Elena Pastorino, Harald Uhlig, Joe Vavra and Ivan Werning for their very helpful comments and suggestions. Finally, we thank seminar participants at the Bank of England, Berkeley, the Board of Governors of the Federal Reserve, Boston University, Brown, Chicago, Chicago Federal Reserve, Columbia, Duke, Harvard, IEF Workshop, Michigan, Minneapolis Federal Reserve, Minnesota Workshop in Macroeconomic Theory, MIT, NBER s Summer Institute EF&G, NBER s Summer Institute Prices Program, Northwestern, Princeton, Rochester, St. Louis Federal Reserve, UCLA, Yale s Cowles Conference on Macroeconomics. Any remaining errors are our own. and 1 Introduction A large and growing literature is exploiting regional variation to learn about the determinants of aggregate economic variables. 1 However, we argue that making inferences about the aggregate economy using only regional variation is complicated by two issues. First, we show that, in a monetary union model, local and aggregate elasticities to the same type of shock are quantitatively different both because of factor mobility and general equilibrium forces. This discrepancy makes it problematic to use local shock elasticities estimated from regional data to ascertain the importance of a given aggregate shock. Second, purely aggregate shocks get differenced out when using cross-region variation. As a result, it is not possible to learn anything about these aggregate shocks by exploiting variation across regions. Furthermore, we provide evidence of both these issues by contrasting the behavior of US aggregate time-series and cross-state patterns during the Great Recession. We document a strong relationship across states between local employment growth, and local nominal and real wage growth. These relationships are much weaker in US aggregates. In summary, we cannot expect to understand the joint evolution of aggregate variables by using cross-regional variation alone. Therefore, we present a methodology that uses regional data along with aggregate data in order to identify aggregate shocks driving business cycles. The methodology exploits theoretical restrictions implied by a wage setting equation that hold in many monetary union models with wage stickiness. In turn, the extent to which aggregate wages are sticky is a key restriction in identifying the type of shocks driving aggregate fluctuations (e.g., demand vis a vis supply shocks) 2. Under certain conditions, we show how to use cross-region variation in wages, prices, and employment to estimate this wage setting equation thus parameterizing the theoretical restrictions and linking regional business cycles to shock decompositions of aggregate business cycles. Using household and retail scanner data for the US, we construct state-level wage and price indices as well as a measure of employment. Given the strong comovement of wages and employment across states, our estimates of the wage setting equation suggest that wages are relatively flexible thus limiting the contribution of demand shocks to aggregate employment decline during the Great Recession. Instead, we find that a combination of demand and other shocks are necessary to account for the joint dynamics of aggregate prices, wages and employment during the period. In particular, the relative stability of aggregate wages in the time-series compared to state-level wages is not caused by wage stickiness, but because different aggregate shocks have relatively offsetting effects on aggregate wages. We conclude that the wage stickiness necessary for demand shocks to be the primary cause of aggregate employment decline during the Great Recession is inconsistent with the flexibility of wages estimated from cross-state variation. 1 For recent examples, see Autor et al (2013), Charles et al (2015), Hagedorn et al (2015), Mehrotra and Sergeyev (2015), Mian and Sufi (2014) and Mondragon (2015). 2 We refer to a demand shock as a shock that moves employment and real wages in opposite directions and moves employment and prices in the same direction. In the model of the monetary union we develop below, these shocks can be formalized as shocks to the household s discount rate or as shocks to the aggregate nominal interest rate rule. Our model also allows for a productivity/markup shock and a shock to household preference for leisure. 1 The paper is organized as follows. In Sections 2 and 3, we begin by documenting a series of new facts about the variation in nominal and real wages across US states during the Great Recession. Using data from the 2000 US Census and the American Community Surveys (ACS), we construct state-level nominal wage indices during the 2000 to 2012 period. We restrict our sample to full time workers with a strong attachment to the labor force. We adjust our wage measures to cleanse them from observable changes in labor force composition over the business cycle. In order to construct a measure of real wages we deflate our nominal wage indices with state-level price indices created using data from Nielsen s Retail Scanner Database. The Retail Scanner Database includes weekly prices and quantities for given UPC codes at over 40,000 stores from 2006 through While the price indices we create from this data are based mostly on consumer packaged goods, we show how under certain assumptions the indices can be scaled to be representative of a composite local consumption good. Furthermore, we show that an aggregate price index created with the retail scanner data matches the BLS s Food CPI nearly identically. Using our indices, we show that states that experienced larger employment declines between 2007 and 2010 had significantly lower nominal and real wage growth during the same time period. These cross-state patterns stand in sharp contrast with the well documented aggregate time-series trends for prices and wages during the same time period. As both aggregate output and employment contracted sharply in the US during the period, aggregate nominal wage growth remained robust and real wage growth did not break trend. 3 In sum, while aggregate wages appear to be sticky during the Great Recession, state-level wages do not. In Section 4, we present a monetary union model that we use for two purposes. First, a calibrated version of the model allows us to sign the elasticities to a given shock and quantify the differences between aggregate and local elasticities. Second, the model makes explicit assumptions that are sufficient to estimate the parameters in an aggregate wage setting equation using cross-state variation in employment, wages and prices. As we highlight below, these parameters help us identify the underlying aggregate drivers of the joint dynamics of employment, wages and prices. The model has many islands linked by trade in intermediate goods which are used in the production of a non-tradable final consumption good. The only asset is the economy is a one-period, non-state contingent nominal bond. The nominal interest rate on this asset follows a rule that endogenously responds to aggregate variables and is set at the union level. Labor is the only other input in production, which is not mobile across islands. We assume that nominal wages are only partially flexible. This is the only nominal rigidity in the model. Finally, the model includes multiple shocks: a shock to the household s discount rate, shocks to non-tradable and tradable productivity/markup, a shock to the household s preference for leisure, and a monetary policy shock. Aside from the monetary policy shock, all shocks have both local and aggregate components. By definition the weighted average of the local shocks sum to zero. We show that, under relatively few assumptions, the log-linearized economy aggregates. This allows us to study the aggregate and lo- 3 The robust growth in nominal wages during the recession is viewed as a puzzle for those that believe that the lack of aggregate demand was the primary cause of the Great Recession. For example, this point was made by Krugman in a recent New York Times article ( Wages, Yellen and Intellectual Honesty , NYTimes 8/25/14). 2 cal behavior separately, a property that we will exploit when estimating the aggregate and regional shocks through our methodology. Using a calibrated version of the model, we show that local employment elasticities to a local discount rate shock are two to three times larger than the aggregate employment elasticity to a similarly sized aggregate discount rate shock. This implies that elasticities often estimated for demand shocks (i.e., our discount rate shock) using cross-region variation are likely to dramatically overstate the elasticities of aggregate variables to demand shocks in the aggregate. The key general equilibrium forces in the model that may dampen aggregate elasticities are the endogenous response of nominal interest rates to aggregate variables and trade in the intermediate input. We show that local and aggregate elasticities get much closer together when the interest rate does not endogenously respond to changes in aggregate prices or employment (as when the economy is close to the zero lower bound). 4 In Section 5, we turn to estimation of aggregate shocks. We present a procedure that allow us estimate the shocks in a larger class of monetary union models than the benchmark model outlined above, thus imposing less a-priori structure and making the analysis more persuasive. In particular, we consider models where the aggregate and local equilibria can be represented as a structural vector autoregression (SVAR) in price inflation, nominal wage inflation, and employment with three shocks. We refer to the three shocks as the discount rate shock (which is a combination of the discount rate and monetary policy shock), the productivity/markup shock (which is a combination of the productivity/markup shocks in the tradable and non tradable sectors) and the leisure shock (which is the shock to leisure preference). In order to identify the aggregate shocks, we estimate a SVAR and impose certain properties of our benchmark monetary union model. Our results will be consistent with monetary union models that satisfy all of these. First, we use the aggregate wage setting equation to derive a series of linear restrictions linking the reduced form errors to the underlying structural shocks. Second, we use the sign of the joint-response of employment, wages and prices (on impact) to a discount rate and a productivity/markup shock. 5 These two, together with the usual shock-orthogonality conditions, are sufficient to identify the structural shocks. The methodology requires parameterizing the structural wage setting equation. We use statelevel data on prices, wages and employment during the period to estimate the two parameters in our base specification, i.e., the Frisch elasticity of labor supply and the degree of wage stickiness. Across a variety of specifications and identification procedures, including instrumenting for local labor demand shocks, we estimate only a modest degree of wage stickiness. These estimates are much smaller than estimates of wage stickiness obtained using only aggregate time-series data. 4 A similar point is made in Nakamura and Steinsson(2014) with respect to local estimates of fiscal multipliers. 5 We view this methodology as an additional contribution of our paper. Beraja (2015) presents an extension of this scheme to a more general class of models. These are part of a growing literature developing hybrid methods that, for instance, constructs optimal combinations of econometric and theoretical models (Carriero and Giacomini (2011), Del Negro and Schorfheide (2004)) or uses the theoretical model to inform the econometric model s parameter (An and Schorfheide (2007), Schorfheide(2000)). Our procedure is closest in spirit to the procedure recently developed in Baumeister and Hamilton (2015). 3 With the parameterized aggregate wage setting equation, we use the SVAR identification procedure described above to estimate the shocks driving aggregate employment, prices, and wages during the Great Recession. Our results suggest that during the early part of the recession ( ) roughly 30 percent of the aggregate employment decline can be attributed to the discount rate shock (i.e., the demand shock). The leisure shock explains roughly 30 percent of the decline in aggregate employment while the productivity/markup shock explains the remaining 40 percent. Over a longer period ( ), however, the discount rate shock cannot explain any of the persistence in employment decline. Instead, it is the productivity/markup and labor supply shocks that explain why employment remained low from In sum, while demand shocks may have been important in the early part of the recession, they cannot explain the persistently low levels of employment in the US after Furthermore, we find that the aggregate leisure shock - not sticky wages - explains why aggregate wages did not fall during the Great Recession. Our paper contributes to many literatures. First, our work contributes to the recent surge in papers that have exploited regional variation to highlight mechanisms of importance to aggregate fluctuations. For example, Mian and Sufi (2011 and 2014), Mian, Rao, and Sufi (2013) and Midrigan and Philippon (2011) have exploited regional variation within the US to explore the extent to which household leverage has contributed to the Great Recession. 7 Nakamura and Steinsson (2014) use sub-national US variation to inform the size of local government spending multipliers. Blanchard and Katz (1991), Autor et al. (2013), and Charles et al. (2015) use regional variation to measure the responsiveness of labor markets to labor demand shocks. Our work contributes to this literature on two fronts. First, we show that local wages also respond to local changes in economic conditions at business cycle frequencies. Second, we provide a procedure where local variation can be combined with aggregate data to learn about the nature and importance of certain mechanisms for aggregate fluctuations. With respect to the latter innovation, our paper is similar in spirit to Nakamura and Steinsson (2014). Second, our paper contributes to the recent literature trying to determine the causes of the Great Recession. In many respects, our model is more stylized than others in this literature in that we include a broad set of shocks without trying to uncover the underlying micro-foundations for these shocks. However, the shocks we chose to focus on were designed to proxy for many of the popular theories about the drivers of the Great Recession. For example, our discount rate shock can be thought of as reduced form representation of tightening of household borrowing limits. For example, such shocks have been proposed by Eggertsson and Krugman (2012), Guerrieri and Lorenzoni (2011) and Mian and Sufi (2014) as an explanation of the 2008 recession. Likewise, our 6 Christiano et al (2015a) estimate a New Keynesian model using data from the recent recession. Although their model and identification are different from ours, they also conclude that something akin to a supply shock is needed to explain the joint aggregate dynamics of prices and employment during the Great Recession. Likewise, Vavra (2014) and Berger and Vavra (2015) document that prices were very flexible during the Great Recession. They also conclude that something more than a demand shock is needed to explain aggregate employment dynamics given the missing aggregate disinflation. 7 There has been an explosion of papers using regional data to better understand aggregate dynamics during the Great Recession. Some recent papers include: Giroud and Mueller (2015), Hagedorn et al. (2015), Mehrotra and Sergeyev (2015), and Mondragon (2015). 4 productivity/markup shock can be interpreted as anything that changes firms demand for labor. In a reduced form sense, credit supply shocks to firms, such as those proposed by Gilchrist et al (2014), would be similar to our productivity/markup shock. Finally, our leisure shock can be seen as a proxy for increased distortions in the labor market due to changes in government policy (e.g., Mulligan (2012) or as a reduced form representation of a skill mismatch story within the labor market (e.g., Charles et al. (2013, 2015)). 2 Creating State-Level Price And Wage Indices 2.1 State-Level Wage Index To construct nominal wage indices at the state level, we use data from the 2000 Census and the American Community Surveys (ACS). The 2000 Census includes 5 percent of the US population while the ACS s includes around 600,000 respondents per year between 2001 and 2004 and around 2 million respondents per year between 2005 and The large coverage allows us to compute detailed labor market statistics at the state level. For each year of the Census/ACS data, we calculate hourly nominal wages for prime-age males with a strong attachment to the labor force. In particular, we restrict our sample to only males between the ages of 21 and 55, who were employed at the time of the Census, who reported usually working at least 30 hours per week, and who worked at least 48 weeks during the prior 12 months. Then, for each individual in the resulting sample, we divide total labor income earned during the prior 12 months by a measure of annual hours worked during prior 12 months. 8 Despite our restriction to prime-age males with a strong attachment to the labor force, the composition of workers on other dimensions may still differ across states and within a state over time. The changing composition of workers could be explaining some of the variation in nominal wages across states over time. To cleanse
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