Working Paper
Jonathan Roth. Working Paper. “Union Reform and Teacher Turnover: Evidence from Wisconsin's Act 10”.Abstract
This paper studies teacher attrition in Wisconsin following Act 10, a policy change which severely weakened teachers' unions and capped wage growth for teachers. I document a sharp increase in turnover after the Act was passed, driven almost entirely by the exit of older teachers, who faced strong incentives to retire before the end of pre-existing collective bargaining agreements. I find that student academic performance increased in grades with teachers who retired following the reform, and I obtain similar results when instrumenting for retirement using the pre-existing age distribution of teachers. Differences in value-added between retirees and their replacements can potentially explain some, but not all, of the observed academic improvements.
Jonathan Roth. Working Paper. “Pre-test with Caution: Event-study Estimates After Testing for Parallel Trends”.Abstract
    Researchers often test for pre-trends when using a research design that relies on a parallel trends assumption, yet typical estimation and inference does not account for this test. This paper analyzes the properties of conventional estimates conditional on having passed (i.e. not rejected) a pre-test for parallel pre-trends. I derive a formula for the bias in conventional treatment effects estimates after pre-testing, which generally differs from the unconditional bias when parallel trends is violated. Moreover, I prove that under homoskedasticity, the additional bias from pre-testing amplifies the bias in the treatment effects estimates from a monotone violation of parallel trends. Hence, pre-trends tests meant to mitigate bias in published work can actually exacerbate it. In addition, coverage rates of traditional confidence intervals can be above or below their nominal level conditional on passing the pre-test. Simulations based on a review of recent papers in leading economics journals suggest that substantial distortions from pre-testing are possible in practice. To address these issues, I develop a method of constructing corrected event-study plots that removes distortions from pre-testing or from model-selection on the basis of pre-trends. I illustrate the usefulness of these corrections in simulations and in an application to Dube et al. (2010)'s study of the minimum wage.