When to use matching and weighting or regression in instrumental variable estimation? Evidence from college proximity and returns to college

Standard two-stage least squares (2SLS) regression remains dominant in instrumental variables estimation of causal effects even though the literature has shown that 2SLS may be inconsistent when effects are heterogenous and the instrument is only valid when conditioning on covariates. To show that this is not merely a hypothetical threat, this paper re-estimates the returns to college using college proximity as an instrument based on the data from Card (Aspects of labour market behavior: essays in honour of John Vanderkamp, University of Toronto Press, Toronto, 1995). The results show that 2SLS yields systematically larger estimates of the returns to college than more flexible estimators based on the instrument propensity score. In the full sample, differences amount to about 50 to 100%. This is due to the implicit conditional-variance weighting performed by 2SLS. Moreover, in line with the theoretical prediction by Sloczynski (When should we (not) interpret linear IV estimands as LATE? IZA discussion papers 14349, Institute of Labor Economics (IZA), 2021), findings suggest that the impact of the conditional-variance weighting is larger when instrument groups are not roughly the same size. Thus, it is advised to use 2SLS with caution and use estimators based on the instrument propensity score instead when groups are of different size and covariates are predictive of the instrument.