Applied work often studies the effect of a binary variable (“treatment”) using linear models with additive effects. I study the interpretation of the OLS estimands in such models when treatment effects are heterogeneous. I show that the treatment coefficient is a convex combination of two...

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight...

Rainfall is a truly exogeneous variable and hence popular as an instrument for many outcomes. But by its very nature, rainfall in nearby areas tends to be correlated. I show theoretically that if there are also spatial trends in outcomes of interest, this may create spurious correlation. In...

In this paper we study a class of weighted estimands, which we define as parameters that can be expressed as weighted averages of the underlying heterogeneous treatment effects. The popular ordinary least squares (OLS), two-stage least squares (2SLS), and two-way fixed effects (TWFE) estimands...

One of the perceived advantages of difference-in-differences (DiD) methods is that they do not explicitly restrict how units select into treatment. However, when justifying DiD, researchers often argue that the treatment is "quasi-randomly" assigned. We investigate what selection mechanisms are...

This paper proposes a difference-in-differences approach for disentangling a total treatment effect on some outcome into a direct impact as well as an indirect effect operating through a binary intermediate variable - or mediator - within strata defined upon how the mediator reacts to the...

We propose a novel approach for causal mediation analysis based on changes-in-changes assumptions restricting unobserved heterogeneity over time. This allows disentangling the causal effect of a binary treatment on a continuous outcome into an indirect effect operating through a binary...

In this paper, we assess the impact of firms introducing part-time work schemes for gradual labour market exit of elderly workers on their employees' labour market outcomes. The analysis is based on unique linked employer-employee data that combine high-quality survey and administrative data....

How should researchers adjust for covariates? We show that if the propensity score is estimated using a specific covariate balancing approach, inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and inverse probability weighted regression adjustment (IPWRA)...