Working papers

“An Empirical Framework for Matching with Imperfect Competition,” (with Kory Kroft, Elena Mattana and Ismael Mourifié) [NEW DRAFT (May 2024)]

Abstract: This paper builds, identifies and estimates a model of the labor market that features strategic interactions in wage setting and two-sided heterogeneity in order to shed light on the sources of wage inequality. We provide a tractable characterization of the model equilibrium and demonstrate its existence and uniqueness. This characterization of the equilibrium allows us to derive a rich set of comparative statics and to gauge the relative contributions of worker skill, preference for amenities and strategic interactions to equilibrium wage inequality. Using instrumental variables, we establish identification of labor demand and supply parameters and estimate them using matched employer-employee data from Denmark. Using our estimated structural model, we perform a series of counterfactual analyses in order to provide a quantitative evaluation of the main sources of wage inequality in Denmark.

“Dynamic Wage Setting: The Role of Monopsony Power and Adjustment Costs,” (with Elena Mattana, Sergio Salgado and Ming Xu) [New draft soon. Updated Slides (June 2024), Previous draft with old title (August 2023)]

Abstract: How much do adjustment costs, labor market power and production complementarities matter for wage setting and passthrough? We develop a general theoretical framework and empirical identification strategy illustrating how firm productivity impacts wages in imperfect labor markets. We estimate firm-level distributions of productivity, worker ability, markdowns, passthrough and labor-supply elasticities using Danish data. Typical firms respond to 1% productivity increases by lowering markdowns 1.7% and increasing marginal productivity 2.1% — increasing wages by 0.4%. Adjustment costs induce firms to hoard workers and increase markdowns in response to negative shocks. Labor market power and adjustment costs reduce passthrough, decreasing wage volatility by 77%.

“Scalable vs. Productive Technologies,” (with Guangbin Hong, Joachim Hubmer, Serdar Ozkan, Sergio Salgado) [FIRST DRAFT (July 2024)]

Abstract: Do larger firms have more productive technologies or are their technologies more scalable, or both? We use administrative data on Canadian and US firms to estimate flexible nonparameteric production functions. Our estimation results in a joint distribution of output elasticities of capital, labor, and intermediate inputs—therefore, returns to scale (RTS)—along with total factor productivity (TFP). We find significant heterogeneity in both RTS and TFP across firms. Larger firms operate technologies with higher RTS, both across and within industries. Higher RTS for large firms are entirely driven by higher intermediate input elasticities. Descriptively, these align with higher intermediate input revenue shares. We then incorporate RTS heterogeneity into an otherwise standard incomplete markets model with endogenous entrepreneurship that matches the observed heterogeneity in TFP and RTS. In this model, we find that the efficiency losses of financial frictions are more than twice as large relative to the conventional calibration that loads all heterogeneity on TFP and imposes a common RTS parameter.

“Heterogeneous Passthrough from TFP to Wages,” (with Sergio Salgado and Ming Xu)  [Latest Draft (Sept 2023)]
R&R at the Journal of Labor Economics

Abstract: We examine the passthrough of firms’ idiosyncratic productivity shocks to workers’ wages using rich matched employer-employee data from Denmark which allows us to control for unobserved worker and firm heterogeneity. We find an average elasticity of incumbent workers’ hourly wages to firms’ productivity of 0.08. The passthrough of firm shocks to wages is strongly asymmetric, in that wages are twice as responsive to negative shocks as to positive shocks. Failing to account for workers’ endogenous mobility underestimates the passthrough of negative shocks and reverses the asymmetry. Passthrough decreases with labor market share and productivity but increases with income and ability. Recessions reduce passthrough from positive shocks to zero but do not affect passthrough of negative shocks. Workers with wage growth after switching to a new firm typically move from low to high productivity firms; In contrast, workers with a decline in wages after switching move between firms of similar productivity.

“How Substitutable Are Labor and Intermediates?”  [Latest Draft (Oct 2023)]

Abstract: Empirical models of production often impose input complementarity and rule out an extensive margin in the decision to “make or buy” inputs. This paper develops a simple model of production which generalizes the standard Cobb-Douglas approach and allows labor and intermediates of similar types (or “tasks”) to be complements, substitutes, or (importantly) outsourced entirely. Modeling this “make or buy” decision directly allows me to correct for selection bias resulting from the endogenous outsourcing decision and to characterize the extensive margin of factor demand. I take the model to unique Danish data on task-level purchases of disaggregated labor (e.g. truck drivers), goods, and services (e.g. shipping) and find that labor and intermediates are gross substitutes. Estimated elasticities of substitution range from 1.5 to 4, with positive cross-price elasticities between 0 to 2 across inputs and industries. Aggregating across firms, I show that demand for labor is becoming increasingly price elastic over time, driven by growing outsourcing and specialization. To illustrate the importance of allowing for substitution, I examine the effect of an increase in minimum wages in the Danish manufacturing industry, finding that ignoring outsourcing underestimates disemployment by 40%. This also has important implications for estimating productivity. I estimate the effect of recent decreases in Danish import tariffs on firm productivity and show that controlling for substitution triples the results relative to benchmark models which only control for price effects.

“The Effect of R&D on Quality, Productivity, and Welfare,” (with Amil Petrin and Frederic Warzynski) [NBER Working Paper]

Abstract: In this paper we provide a methodology that jointly studies production and demand for multi-product firms using detailed firm-product level data from Denmark. We estimate marginal cost by combining production function estimation with a cost function that allows for quasi-fixed inputs. We use a discrete choice demand model that extends insights from Berry, Levinsohn and Pakes (1995) to obtain a measure of the demand shock (quality). We estimate the relationship between product (process) R&D and quality (efficiency), and find strong evidence that process innovation is related to higher efficiency, while product innovation is associated with higher product quality. We discuss the welfare implications of these two distinct innovation activities.

“Firm Productivity and Labor Quality,” (with Sergio Salgado, Frederic Warzynski and Ming Xu)  [Work in Progress]

Abstract: In this paper we argue that a large fraction of the observed dispersion in firm productivity can be accounted for by differences in labor quality. In order to investigate this claim, we propose an estimation method that combines a non parametric production function estimation with a series of two-way fixed effect wage regressions with time-varying firm fixed effects which allow us to control for differences in labor quality across firms and time. We implement this method on a large employer-employee matched panel dataset from Denmark and find that around 60% of the dispersion in productivity can be explained by cross-sectional differences in the quality of labor. A similar fraction of the dispersion in idiosyncratic shocks to firm productivity can be attributed to changes in the quality of the labor force hired by the firm. Using these labor quality-adjusted measures of productivity, we find a significant degree of positive assortative matching between high ability workers and high productivity firms. High productivity firms also tend to pay higher wages per unit of ability than low productivity firms. We also find that firms react to productivity shocks by adjusting both the quantity and quality of their labor force. We then discuss the degree to which cross-sectional wage inequality may be driven by dispersion in firm productivity.

“Trade, Occupation Sorting, and Inequality,” (with Luke Rawling and Ming Xu) [Work in Progress]

Abstract: Firms react to changes in factor prices with intensive and extensive-margin employment adjustments at the occupational-level. We study the distributional and aggregate consequences of this make-or-buy dynamic by developing a novel network model of heterogeneous firm-to-firm trade where the boundary of each firm depends on factor prices and firm-occupation comparative advantage in input-production. We show that the model can be easily aggregated and taken to industry-level data, and use the calibrated model to examine recent trends in employment, wages and trade in the USA. We use public OES and CPS data to show empirical evidence that a significant fraction of the growth in wage inequality in the USA is due to changes in firm/industry specialization and occupation sorting. To understand and measure the underlying causes of these trends, we calibrate the model to occupation and industry data from the OES and input-output tables. The results suggest that 1/3rd of the increases in wage inequality stem from decreases in inter-industry trade frictions with the remaining 2/3rds stemming from changes in technology and labor supply. Falling trade frictions are also responsible for all of the increases in occupational sorting and concentration. Had trade frictions been held at their 2002 level, productivity growth would have led to an increase in vertical integration, rather than the decrease observed in the data.

“Allowing for Heterogeneous Preferences over Unobserved Quality in Random Coefficient Models,” (with Amit Gandhi, Kyoo-il Kim and Amil Petrin) [Latest Draft]

Abstract: In this paper we study a class of random utility models that allows for horizontal product differentiation to enter an otherwise purely vertically differentiated market. The model generalizes the standard random coefficient model by allowing for consumer heterogeneity to interact with a product’s unobserved attribute. We seek to establish three basic results concerning this model that is relevant for empirical work. First, the discrete choice demand literature to date allows for heterogeneous preferences on observed characteristics, but not on unobserved characteristics. This is potentially problematic, as in empirical settings much of demand loads on unobserved product quality. Allowing for heterogeneous preferences over this unobserved quality (which might represent reliability, marketing, style, or other unmeasured product characteristics) thus has an obvious economic interpretation which is useful for the purposes of measuring product quality and demand. Second, a key issue in generalizing the model in this way is that the standard computation method, following Berry (1994) and Berry, Levinsohn, and Pakes (1995) (henceforth BLP), does not apply to this model, as the conditions under which the proposed mapping is a contraction are no longer generally satisfied. Third, we build on work by Berry et al. (2013) and Berry and Haile (2014) and establish conditions under which the generalized model is both identified and has a globally convergent solution method.

“MPC Heterogeneity and Firm Level Shocks,” (with Sergio Salgado, Bastian Schulz and Ming Xu) [Work in Progress]