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Journal of Econometric Methods

Ed. by Giacomini, Raffaella / Li, Tong

Mathematical Citation Quotient (MCQ) 2018: 0.06

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Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation

Sule Alan / Bo E. Honoré / Luojia Hu
  • Economic Research Department, Federal Reserve Bank of Chicago, 230 S. La Salle Street, Chicago, IL 60604, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Søren Leth-Petersen
  • Department of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K. and SFI, The Danish National Centre for Social Research, Herluf Trolles Gade 11, DK-1052, Denmark
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-04-09 | DOI: https://doi.org/10.1515/jem-2012-0012


This paper constructs estimators for panel data regression models with individual specific heterogeneity and two-sided censoring and truncation. Following Powell the estimation strategy is based on moment conditions constructed from re-censored or re-truncated residuals. While these moment conditions do not identify the parameter of interest, they can be used to motivate objective functions that do. We apply one of the estimators to study the effect of a Danish tax reform on household portfolio choice. The idea behind the estimators can also be used in a cross sectional setting.

Keywords: censored regression; panel data; truncated regression; JEL Code: C20; C23; C24


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About the article

Corresponding author: Sule Alan, College of Administrative Sciences and Economics, Koc University, Istanbul, 34450, Turkey, E-mail:

Published Online: 2013-04-09

Published in Print: 2014-01-01

1930 is the latest year for which this linkage is feasible.

Of course one could combine the insight in (4) and (5) to get even more general moment conditions. See also the discussions in Arellano and Honoré (2001) and Honoré and Hu (2004).

Clearly, one can also use the fact that differences in functions of the re-censored residuals will be orthogonal to functions for the explanatory variables. As discussed in Arellano and Honoré (2001), one can also construct moment conditions based on symmetry under the additional assumption that (εi1, …,εiT) is exchangeable conditional on (xi1, …,xiT). This is the motivation for the approach in Honoré (1992).

Consistency follows from theorem 4.1.1 of Amemiya (1985) and asymptotic normality from, for example, theorem 3.3 of Pakes and Pollard (1989).

Strictly speaking, Manski (1987) only considers the binary choice model, while Han (1987) deals with a more general model. However, Abrevaya (1999a) has demonstarted how the approach in Manski (1987) can be generalized to deal with models like the ones in Han (1987).

Ridder (1990). See also Heckman and Honoré (1989).

Bakija (2000) uses the limited panel module of the American Survey of Consumer Finances (SCF) to study portfolio changes around the 1988 tax reform. However, his data set is very small (984 households) and unrepresentative due to the well-known attrition problem in the SCF panel module; see Kennickell and Woodburn (1997). More important in this context, the estimators applied do not exploit the full potential of the panel data in handling unobserved heterogeneity. Ioannides (1992) also employs the 1983–1986 SCF panel module but does not control for unobserved heterogeneity.

Alan and Leth-Petersen (2006) document that the reduced value of the interest deduction led households to liquidate financial assets to lower their mortgage debt. This was possible because pre-payment of mortgage debt is not restricted in Denmark.

Approximately 20% of the population belong in the top bracket.

The median household in the sample holding stocks received dividends corresponding to 2% of the value of the stocks. The median household in the sample holding bonds received interest payments from these corresponding to 10% of the value of the bonds.

For assessing portfolio reshuffling renters could have been included. We have chosen to leave them out of this analysis because there are only a few renters (898) with positive financial wealth of at least 5000 DKK in 1984. Moreover, renters generally do not provide a good comparison group for homeowners, since different preference parameters may govern their behavior.

See Alan and Leth-Petersen (2006) for a more detailed analysis.

An alternative identification strategy could be based on comparing the behavior of households in different tax brackets. Households in the lowest tax bracket faced only very small changes in marginal tax rates on capital income, and households in the middle tax bracket faced different changes in marginal tax rates than households in the highest tax bracket. In our case this is not a natural approach to follow. High- and low-income people are different in terms of wealth levels and portfolio composition and possibly different with respect to preference parameters such as the discount rate and the level of risk aversion. Households in lower tax brackets therefore do not represent a natural control group for high-income households.

As explained in Honoré (2008), the parameter estimates for both the random effects and the fixed effects models can be converted to marginal effects by multiplying them by the fraction of observations that are not censored.

Since both the difference in the re-censored residuals and u are continuous in d, it is not necessary to distinguish between closed and open intervals in the following discussion.

Citation Information: Journal of Econometric Methods, Volume 3, Issue 1, Pages 1–20, ISSN (Online) 2156-6674, ISSN (Print) 2194-6345, DOI: https://doi.org/10.1515/jem-2012-0012.

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