Abstract
This paper re-examines the instrumental variable (IV) approach to estimating returns to education by use of compulsory school law (CSL) in the US. We show that the IV-approach amounts to a change in model specification by changing the causal status of the variable of interest. From this perspective, the IV-OLS (ordinary least square) choice becomes a model selection issue between non-nested models and is hence testable using cross validation methods. It also enables us to unravel several logic flaws in the conceptualisation of IV-based models. Using the causal chain model specification approach, we overcome these flaws by carefully distinguishing returns to education from the treatment effect of CSL. We find relatively robust estimates for the first effect, while estimates for the second effect are hindered by measurement errors in the CSL indicators. We find reassurance of our approach from fundamental theories in statistical learning.
Highlights
Over the past century, compulsory school law (CSL) was introduced in virtually every middle and high-income country (Goldin 1998; Goldin and Katz 2007)
The authors used CSL indicators as instrumental variables (Ivs) to ‘randomise’ latent ability across educational attainment groups to correct for the presumed inconsistency or beyond-sample bias in the ordinary least square (OLS) estimator
This re-specification is based on the premise of inconsistency of the OLS model specification of s with s as the valid conditional variable, thereby altering the causal interpretation of the relative to its instrumental variable (IV) counterpart
Summary
Compulsory school law (CSL) was introduced in virtually every middle and high-income country (Goldin 1998; Goldin and Katz 2007). While we find shortcomings in the CSL instruments, we delve deeper into the failure to reveal its root in equivocal causal model modifications by choosing the IV-based modelling approach This choice virtually prevents direct and careful translation of causal postulates of interest into data-consistent conditional relationships. Being constrained by the data sets provided in AK and SY, our re-examination of the CSL case clearly shows the importance of empirical model design and selection over estimator choice
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