Shift-Share Designs: Theory and Inference*

We study inference in shift-share regression designs, such as when a regional outcome is regressed on a weighted average of sectoral shocks, using regional sector shares as weights. We conduct a placebo exercise in which we estimate the effect of a shift-share regressor constructed with randomly generated sectoral shocks on actual labor market outcomes across U.S. commuting zones. Tests based on commonly used standard errors with 5% nominal significance level reject the null of no effect in up to 55% of the placebo samples. We use a stylized economic model to show that this overrejection problem arises because regression residuals are correlated across regions with similar sectoral shares, independent of their geographic location. We derive novel inference methods that are valid under arbitrary cross-regional correlation in the regression residuals. We show using popular applications of shift-share designs that our methods may lead to substantially wider confidence intervals in practice.

The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten's Theorem

We provide a nonlinear characterization of the macroeconomic impact of microeconomic productivity shocks in terms of reduced‐form nonparametric elasticities for efficient economies. We also show how microeconomic parameters are mapped to these reduced‐form general equilibrium elasticities. In this sense, we extend the foundational theorem of Hulten (1978) beyond the first order to capture nonlinearities. Key features ignored by first‐order approximations that play a crucial role are: structural microeconomic elasticities of substitution, network linkages, structural microeconomic returns to scale, and the extent of factor reallocation. In a business‐cycle calibration with sectoral shocks, nonlinearities magnify negative shocks and attenuate positive shocks, resulting in an aggregate output distribution that is asymmetric (negative skewness), fat‐tailed (excess kurtosis), and has a negative mean, even when shocks are symmetric and thin‐tailed. Average output losses due to short‐run sectoral shocks are an order of magnitude larger than the welfare cost of business cycles calculated by Lucas (1987). Nonlinearities can also cause shocks to critical sectors to have disproportionate macroeconomic effects, almost tripling the estimated impact of the 1970s oil shocks on world aggregate output. Finally, in a long‐run growth context, nonlinearities, which underpin Baumol's cost disease via the increase over time in the sales shares of low‐growth bottleneck sectors, account for a 20 percentage point reduction in aggregate TFP growth over the period 1948–2014 in the United States.

The Relative Importance of Aggregate and Sectoral Shocks and the Changing Nature of Economic Fluctuations

A principal components decomposition of sectoral IP data reveals that the contribution of aggregate shocks to the variance of aggregate output declined from about 70 percent in the period 1967–1983 to about 30 percent after 1983. We develop an “islands” model with two sectors and costly labor reallocation to investigate how this change in the relative importance of shocks alters business cycle moments. A version of the model with relatively more important sectoral shocks results in a sizeable decline in the cyclicality of labor productivity and is consistent with changes in several other business cycle moments observed in the data. (JEL E13, E23, E24, E32, J21, J24)

How Important Are Sectoral Shocks?

I quantify the contribution of sectoral shocks to business cycle fluctuations in aggregate output. I develop and estimate a multi-industry general equilibrium model in which each industry employs the material and capital goods produced by other sectors. Using data on US industries' input prices and input choices, I find that the goods produced by different industries are complements to one another as inputs in downstream industries' production functions. These complementarities indicate that industry-specific shocks are substantially more important than previously thought, accounting for at least half of aggregate volatility. (JEL D12, D24, E23, E32, L14)