In difference-in-differences applications, identification of the key parameter often arises from changes in policy by a small number of groups. In contrast, typical inference assumes that the number of groups changing policy is large. We present an alternative inference approach for a small (finite) number of policy changers, using information from a large sample of nonchanging groups. Treatment effect point estimators are not consistent, but we can consistently estimate their asymptotic distribution under any point null hypothesis about the treatment. Thus, treatment point estimators can be used as test statistics, and confidence intervals can be constructed using test statistic inversion.

In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between "economic time" and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.

This paper presents a spatial econometric method for characterizing productivity comovement across sectors of the U.S. economy. Input‐output relations provide an economic distance measure that is used to characterize interactions between sectors, as well as conduct estimation and inference. We construct two different economic distance measures. One metric implies that two sectors are close to one another if they use inputs of other industrial sectors in nearly the same proportion, and the other metric implies that sectors are close if their outputs are used by the same sectors. Our model holds that covariance in productivity growth across sectors is a function of economic distance. We find that (1) positive cross‐sector covariance of productivity growth generates a substantial fraction of the variance in aggregate productivity, (2) cross‐sector productivity covariance tends to be greatest between sectors with similar input relations, and (3) there are constant to modest increasing returns to scale. We test and reject the hypothesis that these correlations are due to a common shock.

This paper investigates the role of social learning in the diffusion of a new agricultural technology in Ghana. We use unique data on farmers' communication patterns to define each individual's information neighborhood. Conditional on many potentially confounding variables, we find evidence that farmers adjust their inputs to align with those of their information neighbors who were surprisingly successful in previous periods. The relationship of these input adjustments to experience further indicates the presence of social learning. In addition, applying the same method to input choices for another crop, of known technology, correctly indicates an absence of social learning effects. (JEL D83, O13, O33, Q16)

Instrumental variable (IV) methods are widely used to identify causal effects in models with endogenous explanatory variables. Often the instrument exclusion restriction that underlies the validity of the usual IV inference is suspect; that is, instruments are only plausibly exogenous. We present practical methods for performing inference while relaxing the exclusion restriction. We illustrate the approaches with empirical examples that examine the effect of 401(k) participation on asset accumulation, price elasticity of demand for margarine, and returns to schooling. We find that inference is informative even with a substantial relaxation of the exclusion restriction in two of the three cases.

In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between “economic time” and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.

We develop and estimate a model of student study time choices on a social network. The model is designed to exploit unique data in the Berea Panel Study. Study time data allow us to quantify an intuitive mechanism for academic social interactions: own study time may depend on friend study time in a heterogeneous manner. Social network data allow us to embed study time and resulting academic achievement in an estimable equilibrium framework. We develop a specification test that exploits the equilibrium nature of social interactions and use it to show that novel study propensity measures mitigate econometric endogeneity concerns.