By Manuel Arellano
Panel facts econometrics makes use of either time sequence and cross-sectional info units that experience repeated observations through the years for a similar contributors (individuals might be staff, families, businesses, industries, areas, or countries). This e-book reports crucial issues within the topic. the 3 components, facing static types, dynamic versions, and discrete selection and similar versions are prepared round the subject matters of controlling for unobserved heterogeneity and modelling dynamic responses and blunder components.About the SeriesAdvanced Texts in Econometrics is a exclusive and quickly increasing sequence during which top econometricians determine contemporary advancements in such components as stochastic chance, panel and time sequence information research, modeling, and cointegration. In either hardback and reasonable paperback, each one quantity explains the character and applicability of a subject matter in better intensity than attainable in introductory textbooks or unmarried magazine articles. each one definitive paintings is formatted to be as obtainable and handy when you will not be acquainted with the designated fundamental literature.
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Additional resources for Panel Data Econometrics (Advanced Texts in Econometrics)
49) where vi = (yi − Xiβ − ηiι). Thus, the log likelihood of a cross-sectional sample of independent observations is a function of β, σ2, and η1, . . 25) have . will not be a consistent estimator of σ for large N and small T panels. 51) , we Thus has a negative (cross-sectional) large sample bias given by σ2/T. This is an example of the incidental parameter problem studied by Neyman and Scott (1948). The problem is that the maximum likelihood estimator need not be consistent when the likelihood depends on a subset of (incidental) parameters whose number increases with sample size.
The crucial feature of the models in this section is that the unobservable variables are additive terms. ) is some nonlinear link function (as in exponential, logit, and probit regression), and structural equations with non-additive errors, like discrete choice models with endogenous explanatory variables (panel data models with nonlinear effects are surveyed in Arellano and Honoré, 2001). 64) which can be stacked over time for individual i to give yi = g(xi, β) + ι ηi + vi. 65) If A1 holds but A2 does not, so that 13 A speciﬁcation of this type was ﬁrst considered by Mundlak (1978).
1) where μ is an intercept, , and ηi and vit are independent of each other. The cross-sectional variance of yit in any given period is given by . This model tells us that a fraction of the total variance corresponds to differences that remain constant over time while the rest are differences that vary randomly over time and units. Dividing total variance into two components that are either completely ﬁxed or completely random will often be unrealistic, but this model and its extensions are at the basis of much useful econometric descriptive work.