I translate familiar concepts of discrete-time time-series to contnuous-time equivalent. I cover lag operators, ARMA models, the relation between levels and differences, integration and cointegration, and the Hansen-Sargent prediction formulas.

This paper reviews recent methodological developments in the empirical analysis of imperfectly competitive markets highlighting outstanding problems. Some of these problems are econometric; e.g. the need for a deeper understanding of the small sample properties of our estimators. Most of the...

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use...

It is standard practice in empirical work to allow for clustering in the error covariance matrix if the explanatory variables of interest vary at a more aggregate level than the units of observation. Often, however, the structure of the error covariance matrix is more complex, with correlations...

This paper develops methods for assessing the sensitivity of empirical conclusions regarding conditional distributions to departures from the missing at random (MAR) assumption. We index the degree of non-ignorable selection governing the missingness process by the maximal Kolmogorov-Smirnov...

This paper empirically assesses the wage effects of the Job Corps program, one of the largest federally-funded job training programs in the United States. Even with the aid of a randomized experiment, the impact of a training program on wages is difficult to study because of sample selection, a...

This paper discusses inference for rational expectations models estimated via minimum distance methods by characterizing the probability beliefs regarding the data generating process (DGP) that are compatible with given moment conditions. The null hypothesis is taken to be rational expectations...

In this paper, we explore ways of combining experimental data and non-experimental methods to estimate the differential effects of components of training programs. We show how data from a multi-site experimental evaluation in which subjects are randomly assigned to any treatment versus a control...

Nonlinearity is an important consideration in many problems of finance and economics, such as pricing securities, computing equilibrium, and conducting structural estimations. We extend the transform analysis in Duffie, Pan, and Singleton (2000) by providing analytical treatment of a general...

This paper first considers the impact on world food prices of the changes in restrictions on trade in staple foods during the 2008 world food price crisis. Those changes--reductions in import protection or increases in export restraints--were meant to partially insulate domestic markets from the...