Business Networks, Production Chains, and Productivity: A Theory of Input-Output Architecture (2013)
Revision Requested, Econometrica
This paper develops a theory in which the network structure of production - who buys inputs from whom - is the endogenous outcome of individual choices, and studies how these choices shape productivity and the organization of production. Entrepreneurs produce using labor and exactly one intermediate input; the key decision is which other entrepreneur's good to use as an input. Their choices collectively determine the economy's equilibrium input-output structure. Despite the network structure, the model is analytically tractable, allowing for sharp characterizations of productivity and various micro-level characteristics. When the share of intermediate goods relative to labor in production is high, star suppliers emerge endogenously. This raises aggregate productivity as, in equilibrium, more supply chains are routed through higher-productivity techniques. As new techniques are discovered, entrepreneurs substitute across suppliers in response to changing input prices. Larger firms experience smaller reductions in cost but are important in propagating cost savings through the network.
Revision Requested, Econometrica [Online Appendix]
We develop a framework to estimate the aggregate capital-labor elasticity of substitution by aggregating the actions of individual plants, and use it to assess the decline in labor's share of income in the US manufacturing sector. The aggregate elasticity reflects substitution within plants and reallocation across plants; the extent of heterogeneity in capital intensities determines their relative importance. We use micro data on the cross-section of plants to build up to the aggregate elasticity at a point in time. Our approach places no assumptions on the evolution of technology, so we can separately identify shifts in technology and changes in response to factor prices. We find that the aggregate elasticity for the US manufacturing sector has been stable since 1970 at about 0.7. Mechanisms that work solely through factor prices cannot account for the labor share's decline. Finally, the aggregate elasticity is substantially higher in less-developed countries.
Published and Forthcoming
Review of Economic Dynamics, 2013. [Working Paper]
Measured total factor productivity often declines sharply during financial crises. In 1982, the Chilean manufacturing sector suffered a severe contraction in output, most of which can be accounted for by a falling Solow residual. This paper uses establishment data from the Chilean manufacturing census to examine the decline in measured TFP. To quantify the contribution of resource misallocation, I develop a measure of allocational efficiency along the lines of Hsieh & Klenow (2009) and derive the appropriate measure of aggregate productivity to which it should be compared. Across specifications, within-industry allocational efficiency either remained constant or improved in 1982, while a decline in between-industry allocational efficiency accounts for about one-third of the reduction in TFP. Industries more sensitive to domestic demand -- durables and industries with low exports -- experienced larger declines in measured TFP. This finding is consistent with large adjustment costs and underutilization of inputs. Reduced capital utilization played a substantial role, accounting for 25-50 percent of the decline in measured TFP.
Journal of Economic Theory, 2012. [Working Paper]
A prominent feature of the Kiyotaki and Wright (1989) model of commodity money is the multiplicity of dynamic equilibria. We show that the frequency of search is strongly related to the extent of multiplicity. Holding fixed the average number of meetings in a given unit of time, we vary the frequency of search by altering the interval between search opportunities. To isolate the role of frequency of search in generating multiplicity, we focus on symmetric dynamic equilibria in a symmetric environment, a class for which we can sharply characterize several features of the set of equilibria. For any finite frequency of search this class retains much of the multiplicity, but when agents search continuously there is a unique dynamic equilibrium. For each frequency we are able to characterize the entire set of equilibrium payoffs, strategies played, and dynamic paths of the state variables consistent with equilibrium. Indexed by any of these features, the set of equilibria converges uniformly to the equilibrium of the continuous search limit. We conclude that when search is frequent, the unique limiting equilibrium is a good approximation to any of the more exotic equilibria.
We derive the optimal labor income tax schedule for a life cycle model with deterministic productivity variation and complete asset markets. An individual chooses whether and how much to work at each date. The government must finance a given expenditure and does not have access to lump sum taxation. We develop a solution method that uses the primal approach to solve for the optimal non-linear tax function. The average tax rate determines when an individual will work while the marginal tax rate determines how much she will work. Even in the absence of redistributive concerns, the optimal tax schedule has an increasing average tax rate at low levels of income to encourage labor market participation. The marginal tax rate at the top is strictly positive. Finally, the model is used to assess the effects of changing the current tax schedule to the optimal one. Under the preferred parameters, this delivers a welfare gain equivalent to 0.67 percent of lifetime consumption.