Nonlinear Models of Measurement Errors
نویسندگان
چکیده
Measure errors in economic data are pervasive and nontrivial in size. The presence of measurement errors causes biased and inconsistent parameter estimates and leads to erroneous conclusions to various degrees in economic analysis. The importance of measurement errors in analyzing the empirical implications of economic theories is highlighted in Milton Friedman’s seminal book on the consumption theory of the permanent income hypothesis (Friedman (1957)). In Friedman’s model, both consumption and income consist of a permanent component and a transitory component that can arise from measurement errors or genuine fluctuations. The marginal propensity to consume relates the permanent component of consumption to the permanent income component. Friedman showed that because of the attenuation bias, the slope coefficient of a regression of observed consumption on observed income would lead to an underestimate of the marginal propensity to consume. Bias in nonlinear models is more complex than the attenuation bias in linear models. Using a small error expansion, Chesher (1991) obtained an approximation formula to characterize the bias in a general nonlinear regression model when the regressor is measured with error and the measurement error distribution is not necessarily normal. The approximate bias depends on the derivatives of the regression function with respect to the mismeasured Departments of Economics, New York University, Stanford University and UC Berkeley, USA. The au-
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