Working papers

“Heterogeneous Passthrough from TFP to Wages,” (with Sergio Salgado and Ming Xu) [New Draft Coming (06/2020)]

Abstract: What is the impact of firms’ productivity shocks on workers’ labor earnings? To answer this question, we propose a novel approach to identify firms’ productivity shocks that combines a nonparametric production function estimation method with a set of two-way fixed effect regressions to control for differences in labor quality across firms. We apply this method on matched employer-employee data that encompasses the entire population of workers and firms in Denmark between 1995 and 2010. Our dataset allows us to separately study workers that stay in the firm across consecutive periods from those that transition between firms, to control for workers’ endogenous job mobility decisions, and to investigate how the passthrough from firms’ shocks to wages varies across narrow population groups. We find an elasticity of workers’ hourly wages to firms’ productivity of 0.08. This implies that a positive shock to firms’ productivity of one standard deviation generates an increase of $1,100 US dollars in annual wages for the average worker in Denmark. This result also implies labor supply elasticities of around 5.6. We find that both persistent and transitory shocks to firms are passed on to wages and that there is marked asymmetry in passthrough between positive and negative productivity shocks. In fact, after controlling for workers’ endogenous mobility decisions, the elasticity of hourly wages to a negative productivity shock is twice that of a positive productivity shock of the same magnitude. This suggests that workers are more exposed to negative than to positive shocks to firms’ productivity. Furthermore, we find that the changes in wages due to variation in firm productivity are quite persistent and do not dissipate even five years after the shock. By looking at the heterogeneity of passthrough across firm and worker groups, we provide insights about the theoretical mechanisms that could explain the patterns of passthrough we observe in the data.

“Firm Productivity and Labor Quality,” (with Sergio Salgado and Ming Xu)  [Draft Coming Soon]

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.

“An Empirical Framework for Matching with Imperfect Competition,” (with Kory Kroft and Ismael Mourifié) [Work in Progress]
“MPC Heterogeneity and Firm Level Shocks,” (with Sergio Salgado and Ming Xu) [Work in Progress]

Abstract: In this paper we use firm-level shocks estimated using an employer-employee matched panel dataset from Denmark to provide new and precise estimates of the Marginal Propensity to Consume (MPC). Firm productivity shocks – estimated using a structural model – are especially useful to study MPC as they are, by construction, unexpected from the perspective of the worker and generate sizable changes in workers’ labor income. Using these firm shocks as instruments to control for the endogeneity of wages in the consumption decision, we find that an unexpected increase in wages of one dollar leads to an increase in consumption of 30 cents on average. We also find sizable variations in MPC for positive and negative income shocks and across the age and income distributions.

“How Substitutable Are Labor and Intermediates?” Job Market Paper [Draft (12/15/17)]

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.

“Trade, Occupation Sorting, and Inequality,” (with Ming Xu) [Latest Draft]

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) [Preliminary 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.

“The Impact of Research and Development on Quality, Productivity, and Welfare,” (with Amil Petrin and Frederic Warzynski) [Draft Coming Soon]

Abstract: There is a large theoretical literature that shows there may be too little or too much research and development (R&D) from the perspective of maximizing long run growth. In this paper we provide a methodology for answering this question that jointly studies production and demand for multi-product firms using detailed firm-product level dataset from Denmark. We recover estimates of marginal cost by combining the proxy techniques of multi-product production function estimation (using insights from Dhyne et al. (2017) 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). Having recovered estimates of firm-product level technical efficiency, quality, and marginal cost we get the implied markups. We estimate the relationship between quality (technical efficiency) and product (process) R&D. We then simulate the effect of a 1% increase in R&D expenditures on consumer and producer surplus. In most industries we find that too little R&D is being done from the perspective of society. In contrast, from the perspective of firms there is sufficient spending on R&D. Our findings are consistent with the theoretical story where competitors cannibalize the innovator’s profits leading to underinvestment in R&D.