Abstract
This paper examines whether reported income generates biases for studies on economic mobility and poverty dynamics. Using a linear measurement error model capturing mean-reverting measurement error, this study finds that substantial classical measurement error exists in reported data, leading to a bias toward zero in the estimate of income dynamics. Time-invariant non-classical measurement error and unobserved heterogeneity offset the effect of classical measurement error. This study also identifies the standard deviation of the measurement error, which is estimated to be about 70% of that of the equation error in the income model, suggesting that random measurement error is substantial.
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Notes
Estimating \(\gamma \) and \(\beta \) never requires an assumption of homoskedasticity, but \(\varepsilon _{it}\) will be restricted to be homoskedastic for the variance of measurement error decomposition introduced in Sect. 2.3. This study also proposes specification tests to examine the AR(1) model, which will be introduced shortly. The tests also examine if the errors in the model is serially correlated.
If one is willing to ignore measurement error, the AR(1) model in this paper can be also derived from the earnings dynamics model in the macroeconomics literature by linking the current and lagged income through the AR(1) shock components. This study cannot exclude the possibility that the persistence of income is indeed solely from the persistence of shocks (or of time-varying omitted variables) after controlling observed and unobserved (if fixed) individual characteristics
If external IVs are valid while internal IVs are not, the use of only external IVs can also present consistent estimates. External IVs are also used for both estimates using the internal IVs that include and exclude \(y_{it-2}\) to identify measurement error avoiding a potential weak instruments problem.
Note that the error term can be regarded to be MA(2) in level, but this paper takes it as MA(1) for a differenced term (i.e., \(\Delta v_{it-1} \equiv \psi _{it-1} \)).
It can be shown that summing ARMA(p, q) processes yields a ARMA(p, q) process. The composite error could be the sum of MA(1) equation error and MA(1) measurement error.
General sequential exogeneity means that \(\varepsilon _{it}\) is uncorrelated with the current or past values of the household heads’ satisfaction, but this study does not assume that \(\varepsilon _{it}\) is uncorrelated with the current value of the external instrument.
The EWMD estimation method has been extensively used in the labor/macroeconomics literature identifying different types of error variances (e.g., Meghir and Pistaferri (2004)).
All income is after-tax income in units of 10,000 won (\(\approx 9\) dollars) for the year 2000.
Since adding one could be criticized as an arbitrary choice, additional robustness checks are conducted. The estimates of \(\gamma \) show robustness according to adding the numbers from 0.05 to 2.
Other variables change over two years only for 1 to 5% of all observations (i.e., 95–99% are time-invariant and so zero by first-differencing), while 10% out of all observations change household size over two years. Only household size is included to control for possible economies of scale.
Note that the external IVs (income satisfaction at t-2 and t-3) are also used for the purpose of comparison with the other results in addition to the internal IVs, \(y_{it-2}\) and \(y_{it-3}\). However, it is worth note here that the number of IVs in this study are limited; only up to two lags of income and income satisfaction variables are used. The earlier values of the instruments (that is, t-4 and so on) can be also used, but it is well known that too many instruments can cause severe overfitting biases (Bun et al. 2015). The literature found that omitting distant lags based on the overidentification tests can help avoid the potential problem of too many instruments (Bond 2002; Windmeijer 2005). In particular, Windmeijer (2005) finds that using only two lags of the dependent variable as instruments appeared to decrease the average bias by 40% relative to the estimator that made use of the full set of instruments. With the same reason, time-varying characteristics of previous periods (i.e., \(x_{it-s}\)) are also not used as instruments.
The result is available upon request.
The estimate is 1.19 with .16 bootstrap standard errors obtained by 1,000 repetitions.
They use the OLS method with validation data. Bound and Krueger and Bollinger use CPS-SSA matched files, and Bound et al use the PSID validation study.
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Acknowledgements
I would like to thank John Strauss, John Gibson, John Ham, Jungmin Lee, David McKenzie, Roger Moon, Jeffrey Nugent, Masao Ogaki, Geert Ridder, and participants at North American Summer Meeting of the Econometric Society, Asian Meeting of the Econometric Society, Northeastern Universities Development Consortium Conference, Southern Economic Association Annual Meeting, Pacific Conference for Development Economics, and seminars at Chinese University of Hong Kong, Sogang University, University of Southern California. All remaining errors are mine.
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The author declares no specific funding for this study and no conflicts of interest. Since this study uses non-experimental and publicly available survey data, no additional ethical approval is required.
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Lee, N. Measurement error and its impact on estimates of income dynamics. Empir Econ 63, 2539–2550 (2022). https://doi.org/10.1007/s00181-022-02218-4
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DOI: https://doi.org/10.1007/s00181-022-02218-4