Calibration and IV Estimation of a Wage Outcome Equation in a Dynamic Environment

We consider an artificial population of forward looking heterogeneous agents making decisions between schooling, employment, employment with training and household production, according to a behavioral model calibrated to a large set of stylized facts. Some of these agents are subject to policy interventions (a higher education subsidy) that vary according to their generosity. We evaluate the capacity of Instrumental Variable (IV) methods to recover the population Local Average Treatment Effect (LATE) and analyze the economic implications of using a strong instrument within a dynamic economic model. We also examine the performances of two sampling designs that may be used to improve classical linear IV; a Regression-Discontinuity (RD) design and an age-based sampling design targeting early career wages. Finally, we investigate the capacity of IV to estimate alternative "causal" parameters. The failure of classical linear IV is spectacular. IV fails to recover the true LATE, even in the static version of the model. In some cases, the estimates lie outside the support of the population distribution of returns to schooling and are nearly twice as large as the population LATE. The trade-off between the statistical power of the instrument and dynamic self-selection caused by the policy shock implies that access to a "strong instrument" is not necessarily desirable. There appears to be no obvious realistic sampling design that can guarantee IV accuracy. Finally, IV also fails to estimate the reduced-form marginal effect of schooling on wages of those affected by the experiment. Within a dynamic setting, IV is deprived of any “causal” substance.