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# ERF Training Workshop Panel Data 4

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Raimundo Soto - Catholic University of Chile

ERF Training on Advanced Panel Data Techniques Applied to Economic Modelling

29 -31 October, 2018
Cairo, Egypt

Published in: Government & Nonprofit
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### ERF Training Workshop Panel Data 4

1. 1. ERF Training Workshop Panel Data 4 Raimundo Soto Instituto de EconomΓ­a, PUC-Chile
2. 2. FIRST-DIFFERENCES ESTIMATOR β’ Another alternative to tackle the heterogeneity problem of π¦ππ‘ = πΌπ + π½π₯ππ‘ + πππ‘ consists in first- differencing the model π¦ππ‘ β π¦ππ‘β1 = πΌπ + π½π₯ππ‘ + πππ‘ β πΌπ + π½π₯ππ‘β1 + πππ‘β1 βπ¦ππ‘= π½βπ₯ππ‘ + βπππ‘ β’ Hence, the first-difference estimator is simply π½ πΉπ· = βπ₯ππ‘β²βπ₯ππ‘ β1βπ₯ππ‘β²βπ¦ππ‘ 2
3. 3. FIRST-DIFFERENCES ESTIMATOR β’ This estimator is consistent if πΈ[π₯ππ‘ πππ‘] = 0 but slightly less efficient than the within estimator β Notice: the restriction is πΈ π₯ππ‘ πππ‘ and the exogeneity of π₯ππ‘ is not needed as is the case in the within estimator (e.g., it allows for correlation between π₯ππ‘ y πππ‘β2). β’ Notice that the residual βπππ‘ is autocorrelated even if πππ‘ is not. Thus t-statistics are distorted β’ All information on non-time varying variables is lost. β’ First observation of each individual is lost 3
4. 4. FIRST-DIFFERENCES ESTIMATOR RESULTS 4 _cons .0337766 .0045505 7.42 0.000 .0248557 .0426975 D1. -.0998219 .1910678 -0.52 0.601 -.4743976 .2747537 l_popt D1. -.0134668 .0029968 -4.49 0.000 -.0193419 -.0075917 l_infl2 D1. -.2939159 .0468332 -6.28 0.000 -.3857292 -.2021026 l_realgdp D.l_money Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 162.369352 5064 .032063458 Root MSE = .17805 Adj R-squared = 0.0113 Residual 160.435782 5061 .031700411 R-squared = 0.0119 Model 1.93357008 3 .644523359 Prob > F = 0.0000 F( 3, 5061) = 20.33 Source SS df MS Number of obs = 5065
5. 5. 5 * p<0.1, ** p<0.05, *** p<0.01 t statistics in parentheses Observations 5436 5436 5436 5436 5065 (39.10) (-31.67) (5.14) (-18.82) (7.42) Constant 3.315*** -7.845*** 2.450*** -4.160*** 0.0338*** (-0.52) D.Population -0.0998 (-4.49) D.Inflation -0.0135*** (-6.28) D.Real GDP -0.294*** (0.24) (2.56) (0.30) (2.62) Population 0.00144 0.0732** 0.00875 0.0564*** (-20.94) (-5.92) (-6.24) (-7.92) Inflation -0.165*** -0.0281*** -0.406*** -0.0403*** (-2.36) (25.09) (-0.37) (21.47) Real GDP -0.00867** 0.385*** -0.00630 0.258*** Pooled Within Between Random FirstDif (1) (2) (3) (4) (5)
6. 6. FIT β’ The R2 statistics is valid to undertake comparisons between the pooled model pooled and the fixed effects model. β’ Using R2 statistics to undertake comparisons between the fixed effects model and the random effects model is invalid, because the individual effects πΌπ are random variables in FE but are part of the error term in the RE model. 6
7. 7. HETEROSKEDASTICITY TESTS β’ We would like to test whether π2 (i) = π2 , for all π = 1, β¦ , π β’ This only makes sense in the fixed effects model 7 Prob>chi2 = 0.0000 chi2 (163) = 3.3e+05 H0: sigma(i)^2 = sigma^2 for all i in fixed effect regression model Modified Wald test for groupwise heteroskedasticity . xttest3 It is heteroskedastic
8. 8. UNBALANCED PANELS β’ When dealing with the estimation of the model π¦ππ‘ = πΌπ + π½π₯ππ‘ + πππ‘ We tacitly assumed that we observed data for π = 1, β¦ π at each instant of time π‘ = 1, β¦ , π β’ What if there are missing data? β It depends on how the data got lost 8
9. 9. UNBALANCED PANELS β’ From a mechanic point of view, the within estimator is not sensitive to missing data, since as long as you can compute: π π€ π₯π₯ = π=1 π π‘=1 π π₯ππ‘ β π₯π β² π₯ππ‘ β π₯π π π€ π₯π¦ = π=1 π π‘=1 π π₯ππ‘ β π₯π β² π¦ππ‘ β π¦π You can obtain: π½ π€ = π π€ π₯π¦ π π€ π₯π₯ 9
10. 10. UNBALANCED PANELS β’ Computing the estimator is not the main issue, but why data is missing. β’ Let π ππ‘ indicate if one observation exists or is missing. That is π ππ‘ takes value 1 if the observation exists and 0 otherwise. β’ Let us remove the mean of each individual using the available data; π¦ππ‘ = π¦ππ‘ β 1 π π π=1 π π ππ π¦ππ π₯ππ‘ = π₯ππ‘ β 1 π π π=1 π π ππ π₯ππ ππ = π‘=1 π π ππ‘ 10
11. 11. UNBALANCED PANELS β’ The FE estimator is π½ π€ = (ππ)β1 π₯ππ‘Β΄ π₯ππ‘ β1 (ππ)β1 π₯ππ‘Β΄ π¦ππ‘ = πβ1 π=1 π π‘=1 π π ππ‘ π₯ππ‘Β΄ π₯ππ‘ β1 πβ1 π=1 π π‘=1 π π ππ‘ π₯ππ‘Β΄ π¦ππ‘ = π½ + πβ1 π=1 π π‘=1 π π ππ‘ π₯ππ‘Β΄ π₯ππ‘ β1 πβ1 π=1 π π‘=1 π π ππ‘ π₯ππ‘Β΄πππ‘ 11
12. 12. UNBALANCED PANELS β’ The FE estimator will be consistent if and only if ππππ πβ1 π=1 π π‘=1 π π ππ‘ π₯ππ‘Β΄πππ‘ = 0 β’ It requires no correlation between π₯ππ‘ and πππ‘ β’ It requires no correlation between π ππ‘ and πππ‘. That is: β The nature of heterogeneity must be uncorrelated to choice β Feedback must be absent for choice to be exogenous β’ In summary, E(πΌ) must not depend on π ππ‘ 12