Profile-score Adjustements for Nonlinearfixed-effect Models
AbstractMaximum-likelihood estimates of nonlinear panel data models with fixed effects are generally not consistent as the number of units, N, grows large while the number of time periods, T, stays fixed. The inconsistency can be viewed as a consequence of the bias of the score function, where the unit-specific parameters have been profiled out. We investigate ways of adjusting the profile score so as to make it unbiased or approximately unbiased. This leads to estimators, solving an adjusted profile score equation, that are fixed-T consistent or have less asymptotic bias, as T ! 1, than maximum likelihood. One approach to adjusting the profile score is to subtract its bias, evaluated at maximum- likelihood estimates of the fixed effects. When this bias does not depend on the incidental parameters, the adjustment is exact. Otherwise, it does not eliminate the bias entirely but reduces its order (in T), and it can be iterated, reducing the bias order further. We examine a range of nonlinear models with additive fixed effects. In many of these, an exact bias adjustment of the profile score is possible. In others, suitably adjusted profile scores exhibit much less bias than without the adjustment, even for very small T.
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Bibliographic InfoPaper provided by Sciences Po in its series Sciences Po publications with number info:hdl:2441/eu4vqp9ompqllr09j0031f620.
Date of creation: 15 Mar 2011
Date of revision:
adjusted profile score; bias correction; fixed effects; nonlinear models.;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Longitudinal Data; Spatial Time Series
- C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
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