Nikolas Mittag

A Simple Method to Estimate Large Fixed Effects Models Applied to Wage Determinants and Matching

Models with high dimensional sets of fixed effects are frequently used to examine, among others, linked employer-employee data, student outcomes and migration. Estimating these models is computationally difficult, so simplifying assumptions that cause bias are often invoked to make computation feasible and specification tests are rarely conducted. I present a simple method to estimate large two-way fixed effects (TWFE) and worker-firm match effect models without additional assumptions. It computes the exact OLS solution including estimates of the fixed effects and makes testing feasible even with multi-way clustered errors. An application using German linked employer-employee data illustrates the advantages: The data reject the assumptions of simpler estimators and omitting match effects biases estimates including the returns to experience and the gender wage gap. Specification test detect both problems. Firm fixed effects, not match effects, are the main channel through which job transitions drive wage dynamics, which underlines the importance of firm heterogeneity for labor market dynamics.

A Method of Correcting for Misreporting Applied to the Food Stamp Program

Survey misreporting is known to be pervasive and bias common statistical analyses. In this paper, I first use administrative data on SNAP receipt and amounts linked to American Community Survey data from New York State to show that survey data can misrepresent the program in important ways. For example, more than 1.4 billion dollars received are not reported in New York State alone. 46 percent of dollars received by house- holds with annual income above the poverty line are not reported in the survey data, while only 19 percent are missing below the poverty line. Standard corrections for measurement error cannot remove these biases. I then develop a method to obtain consistent estimates by combining parameter estimates from the linked data with publicly available data. This conditional density method recovers the correct estimates using public use data only, which solves the problem that access to linked administrative data is usually restricted. I examine the degree to which this approach can be used to extrapolate across time and geography, in order to solve the problem that validation data is often based on a convenience sample. I present evidence from within New York State that the extent of heterogeneity is small enough to make extrapolation work well across both time and geography. Extrapolation to the entire U.S. yields substantive differences to survey data and reduces deviations from official aggregates by a factor of 4 to 9 compared to survey aggregates.