Ước lượng hiệu quả các biến không thay đổi theo thời gian và hiếm khi thay đổi trong phân tích bảng mẫu hữu hạn với hiệu ứng cố định theo đơn vị
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#biến không thay đổi theo thời gian #hiệu ứng cố định #ước lượng OLS #mô hình dữ liệu bảng #mô phỏng Monte CarloTài liệu tham khảo
This has been suggested by Amemiya and MaCurdy (1986), Breusch, Mizon, and Schmidt (1989), Baltagi and Khanti-Akom (1990), Baltagi, Bresson, and Pirotte (2003), and Oaxaca and Geisler (2003).
We also varied the number of units (N = 15, 30, 50, 70, 100) and the number of time periods (T = 20, 40, 70, 100). We report these results only in the online appendix. The number of possible permutations of these settings is 2000 that would have led to 2000 times the aggregated number of estimators used in both experiments times 1000 single estimations in the Monte Carlo analyses. In total, this would have given 18 million regressions. However, without loss of generality, we simplified the Monte Carlos and estimated “only” 980,000 single regression models.
We follow standard practice by this notation. However, from equation (4) it follows that the FE estimate of the unit effects propels much more to the estimated unit effects. To avoid confusion and maintain consistence with standard textbooks, we stick to this notation—needless to say that it does not make much sense.
Acemoglu Daron , Johnson Simon , Robinson James , and Thaicharoen Yunyong . 2002. Institutional causes, macroeconomic symptoms: Volatility, crises and growth. NBER working paper 9124.
None of the three main textbooks on panel data analysis (Baltagi 2001; Wooldridge 2002; Hsiao 2003) refers explicitly to the inefficiency of estimating rarely changing variables in a FE approach Thomas Plümper and Vera E. Troeger
We reran all Monte Carlo experiments on rarely changing variables for different sample sizes. Specifically, we analyzed all permutations of N = {15, 30, 50, 70, 100} and T = {20, 40, 70, 100}. The results are shown in Table A2 of Appendix A. All findings for rarely changing variables remain valid for larger and smaller samples, as well as for N exceeding T and T exceeding N.
z 3 in section 5 is rarely changing, the between and within SD for this variable are changed according to the specifications in Figs. 2–4.
Green Donald, 2001, Dirty pool, International Organization, 55
This article is about time-series–cross-sectional (TSCS) data as defined by Beck and Katz (1995) and Beck (2001). Yet, our procedure can also be applied to panels with short time series. Note that demeaning can be problematic when the number of periods is low.
In Section 5, we assume that one z variable is rarely changing and thus almost time invariant.
Note that the estimated coefficients of the time-varying variables remain unbiased even in the presence of correlated unit effects. However, the assumptions underlying a FE model must be satisfied (no correlated time-varying variables may exist).
King, 1994, Designing social inquiry: Scientific inference in qualitative research, 10.1515/9781400821211
Wilson Sven E. , and Butler Daniel M. 2007. A lot more to do: The sensitivity of time-series cross-section analyses to simple alternative specifications. Political Analysis 10.1093/pan/mpl012.
Wooldridge, 2002, Econometric analysis of cross section and panel data
Hsiao, 1987, Econometrics, 95
The online appendix (see the Political Analysis Web page for online appendices) demonstrates that this result also holds true when we vary the sample size. The fevd model performs best even with a comparably large T and N.
The RE model is unbiased only when the pooled-OLS model is unbiased as well. However, the RE model is, under broad conditions, more efficient than the pooled-OLS model.
This procedure is superficially similar to that suggested by Hsiao (2003, 52). However, Hsiao only claims that his estimate for time-invariant variables is consistent as N approaches infinity. We are interested in the small sample properties of our estimator and thus explore TSCS data. Hsiao (correctly) notes that his estimate is inconsistent for TSCS. Moreover, he neither provides SEs for his estimate nor compares his estimator to others Time-Invariant and Rarely Changing Variables
Baltagi, 2001, Econometric analysis of panel data
We also compared the vector decomposition and the FE model to pooled-OLS and the RE model. Since all findings for time-invariant variables carry over to rarely changing variables, indicating that the vector decomposition model dominates pooled-OLS and RE models, we report the results of the RE and pooled-OLS Monte Carlos only in the online appendix.