Publication: Research › Paper – Annual report year: 2012
We use data from the Danish National Travel Survey (NTS) and merge it with administrative register data that contains very detailed information about incomes. This gives a unique opportunity to learn about the magnitude and nature of the measurement error in income reported by the respondents in the Danish NTS compared to income from the administrative register (correct measure). We find that the classical measurement error model (for the logarithm to income) is valid except in the tails of the income distribution where those with low (high) income tends to over (under) report. In addition we find that the marginal distribution of the measurement errors is symmetric and leptokurtic and hence has a higher peak around zero and thicker tails than a normal distribution.
In a linear regression model where the explanatory variable is measured with error it is well-known that this gives a downward bias in the absolute value of the corresponding regression parameter (attenuation), Friedman (1957). In non-linear models it is more difficult to obtain an expression for the bias as it depends on the distribution of the true underlying variable as well as the error distribution. Chesher (1991) give some approximations to very general non-linear models and Stefanski & Carroll (1985) in the logistic regression model. Using these results we find that the bias in logit models can be substantial with the magnitude of measurement error found in income from the NTS survey.
A way to solve the problem with the measurement error is to use instruments. These are additional variables (not already in the model) that are uncorrelated with the measurement error part of income and correlated with the underlying true income. If the data contains information about the expenditure on consumption items such as housing or other consumption goods (that do not affect the discrete choice of interest directly) and we find it plausible that the possible measurement errors in these expenditures are uncorrelated with the measurement in income these will be valid instruments. However, in the Danish NTS there is only limited information about such expenditures (we know if the household owns or rents their home) so finding a good instrument will be difficult. Another possibility is to use technical instruments (understood as a function of the variables already in the model) by using the properties of the measurement errors and the model for measured income. Lewbel (1997) shows that if the distribution of the measurement errors is symmetric and the distribution of the underlying true income is skewed then there are valid technical instruments. We investigate how this IV estimation approach works in theory and illustrate it by simulation studies using the findings about the measurement error model for income from the NTS.
|State||Published - 2012|
|Event||Kuhmo Nectar Conference and Summer School on Transportation Economics 2012 - Berlin, Germany|
|Conference||Kuhmo Nectar Conference and Summer School on Transportation Economics 2012|
|Period||18/06/2012 → 22/06/2012|
Chesher, A. 1991. The effect of measurement error. Biometrika, 78, 451–462.
Friedman, M. 1957. A Theory of the Consumption Function. Princeton University Press.
Lewbel, A. 1997. Constructing instruments for regressions with measurement error when no additional data is available, with an application to R&D. Econometrica, 65, 1201-1213.
Stefanski, L.A. and R.J. Carroll, 1990, Covariate measurement error in logistic regression, Ann. Statist., 13, 1355-51.
- National travel survey, Nonclassical measurement error, Nonlinear models