This paper surveys recent advances in drawing structural conclusions from vector autoregressions (VARs), providing a unified perspective on the role of prior knowledge. We describe the traditional approach to identification as a claim to have exact prior information about the structural model and propose Bayesian inference as a way to acknowledge that prior information is imperfect or subject to error. We raise concerns from both a frequentist and a Bayesian perspective about the way that results are typically reported for VARs that are set-identified using sign and other restrictions. We call attention to a common but previously unrecognized error in estimating structural elasticities and show how to correctly estimate elasticities even in the case when one only knows the effects of a single structural shock.

Ample evidence indicates that a person’s human capital is important for success on the labor market in terms of both wages and employment prospects. However, unlike the efforts to identify the impact of school attainment on labor-market outcomes, the literature on returns to cognitive skills has not yet provided convincing evidence that the estimated returns can be causally interpreted. Using the PIAAC Survey of Adult Skills, this paper explores several approaches that aim to address potential threats to causal identification of returns to skills, in terms of both higher wages and better employment chances. We address measurement error by exploiting the fact that PIAAC measures skills in several domains. Furthermore, we estimate instrumental-variable models that use skill variation stemming from school attainment and parental education to circumvent reverse causation. Results show a strikingly similar pattern across the diverse set of countries in our sample. In fact, the instrumental-variable estimates are consistently larger than those found in standard least-squares estimations. The same is true in two “natural experiments,” one of which exploits variation in skills from changes in compulsory-schooling laws across U.S. states. The other one identifies technologically induced variation in broadband Internet availability that gives rise to variation in ICT skills across German municipalities. Together, the results suggest that least-squares estimates may provide a lower bound of the true returns to skills in the labor market.