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Empirical Economics

Erschienen in:

21.02.2019

Testing functional forms of the lifetime income process in the presence of factor loadings

verfasst von: Yuri Ostrovsky

Erschienen in: Empirical Economics | Ausgabe 1/2020

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Abstract

I show that a covariance-based test typically used to distinguish between lifetime income models known as Heterogeneous Income Profiles and Restricted Income Profiles will lead to erroneous conclusions in the presence of time-varying factor loadings on the permanent earnings component. The magnitude of a potential estimation bias associated with this test is examined using a Monte-Carlo simulation exercise.

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In the literature on earnings inequality, \(y_{iht}\) usually represents “detrended” individual earnings computed either as residuals from the first-stage regression of individual log earnings \(Y_{iht}\) on a polynomial function of age or experience (Haider 2001) or as deviations of \(Y_{iht}\) from mean log earnings in each age-cohort or year-cohort cell (Baker and Solon 2003; Ostrovsky 2010, 2012). Education can be explicitly accounted for either by including education dummies in the first-stage regression (Haider 2001) or by using education as an additional cell dimension during the first-stage “demeaning” (Hoffmann 2013).

This is essentially the point of the Shin and Solon’s (2011) criticism of earlier papers in which the transitory variance component of earnings was obtained by differencing \(\mathrm{Cov}(y_{it,}y_{it-s})\) from \(\mathrm{Var}(y_{it})\), a method that works well only if \(p_{t}\) is constant over time.

For instance, using the parameter estimates reported in Moffitt and Gottschalk (2012) and also conservatively assuming that \(\Delta p_{t}=\Delta p_{t-s}=0.04\) (less than two thirds of the average absolute annual change in \(p_{t}\)reported by Moffitt and Gottschalk) and \(p_{t-s}=1.1\), this will be equal to 0.04 * 0.04 * 0.09 + 0.04 * 1.1 * 0.0027 \(\approx \) 0.00026, well within the range of usual estimates for \({\hat{\sigma }}_{\beta }^{2}\).

Advantages of using the identity matrix as a weighting matrix are discussed in Altonji and Segel (1996).

The variance of \(\beta \) is not always overestimated. Experimenting with different sequences of \(p_{t}\), I also discovered that, for certain sequences, \({\hat{\sigma }}_{\beta }^{2}\) can be severely underestimated.

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Titel: Testing functional forms of the lifetime income process in the presence of factor loadings
verfasst von: Yuri Ostrovsky
Publikationsdatum: 21.02.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 1/2020
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-019-01625-4

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