Working papers

“How Substitutable Are Labor and Intermediates?” Job Market Paper [Draft (12/1/17)]

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.