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We study the identification and estimation of covariate‐conditioned average marginal effects of endogenous regressors in nonseparable structural systems when the regressors are mismeasured. We control for the endogeneity by making use of covariates as control variables; this ensures conditional independence between the endogenous causes of interest and other unobservable drivers of the dependent variable. Moreover, we recover distributions of the underlying true causes from their error‐laden measurements to deliver consistent estimators. We obtain uniform convergence rates and asymptotic normality for estimators of covariate‐conditioned average marginal effects, faster convergence rates for estimators of their weighted averages over instruments, and root‐n consistency and asymptotic normality for estimators of their weighted averages over control variables and regressors. We investigate their finite‐sample behavior using Monte Carlo simulation and apply new methods to study the impact of family income on child achievement measured by math and reading scores, using a matched mother–child subsample of the National Longitudinal Survey of Youth. Our findings suggest that these effects are considerably larger than previously recognized, and depend on parental abilities and family income. This underscores the importance of measurement errors, endogeneity of family income, nonlinearity of income effects, and interactions between causes of child achievement.

We revisit the production function estimators of Olley and Pakes (1996) and Levinsohn and Petrin (2003). They use control functions to address the simultaneous determination of inputs and productivity. Both assume that input demand is a monotonic function of productivity holding capital constant and then invert this function to condition on productivity during estimation. If the observed capital variable is measured with error, input demand will not generally be monotonic in the productivity shock holding observed capital constant. We develop consistent estimators of production function parameters in the face of this measurement error. Our identification and estimation results combine the nonlinear measurement error literature with Wooldridge (2009)'s joint estimation method to construct a proxy for productivity that addresses simultaneity. Our approach directly extends to the case where other inputs like intermediates or labor are observed with error.

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