4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model Two-way Fixed Effects Model

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1 1 EViews ( ) Pooled OLS Fixed Effects Model random effects model F Test Pooled OLS vs Fixed Effect Model Hausman Test Time Fixed Effects Model Time Random Effects Model Two-way Fixed Effects Model Two-way Random Effects Model EViews Pooled OLS Fixed Effects Model F Test Pooled OLS vs Fixed Effect Model Random Effects Model Hausman Test Fixed Effects Model vs Random Effects Model Time Fixed Effects Model F Test Pooled OLS vs Time Fixed Effect Model Time Random Effects Model

2 4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model Two-way Fixed Effects Model F Test Pooled OLS vs Fixed Effect Model Two-way Random Effects Model Hausman Test Two-way Fixed Effects vs Two-way Random Effects /46

3 1 ( ) 1 ( ) y k l lny lnk lnl balanced panel Excel ID OBS * 1 LNY 100 LNK 100 LNL 100 * /46

4 1 ( ) & 1. Workfile Quick - Empty Group (Edit Series) 2. Excel A1 E241 * 2 3. EViews Excel obs 1 Paste *2 Excel EViews 4/46

5 1 ( ) Excel Workfile Excel Workfike 1. EViews Open - Foreign Data as Workfile Excel panel panel panel.xls Workfile Excel * 3 *3 Excel Group Object Object 5/46

6 1 ( ) Workfile Workfile Excel 1. Workfile File - New - Workfile OK Workfile structure type Unstructured/Undated Observations 240 * 4 2. Workfile * /46

7 1 ( ) Workfile Proc - Import - Read Text-Lotus-Excel Excel panel panel panel.xls Data order By Observation - series in columns * 5 Upper-left data cell a2 * 6 Name of series 5 Excel 5+ sheet name 4. Workfile *5 *6 ( Excel spreadsheet ) 1 7/46

8 1 ( ) id id spreadsheet Display format * 7 6. Numeric display Fixed decimal * 8 Decimal places 0 * 9 7. *7 id Excel *8 *9 0 8/46

9 1 ( ) Workfile EViews 1. Workfile Range 2. Workfile 9/46

10 1 ( ) Workfile Workfile structure type Dated panel * 10 Cross-section ID series id * 11 Data series obs * OK Range Sample 5. lny EViews lny lny *10 *11 id *12 obs 10/46

11 2 2 EViews 1. lny Views - Descriptive Statistics - Histogram and Stats 2. lny Views - Descriptive Statistics - Statistics by Classification * 13 Series Group for classify id * 14 *13 ststistics *14 id 11/46

12 lny Views - Descriptive Statistics - Statistics by Classification * 15 Series Group for classify dateid * *15 ststistics *16 dateid 12/46

13 2 6. ID View - Graph Individual cross-section graphs OK ID View - Graph Combined cross-section graphs OK 9. 13/46

14 Pooled OLS N T Y it = β 0 + β 1 X it + ε it, i = 1, 2,, N, t = 1, 2,, T (1) ε it ) β 1 Pooled model OLS Pooled OLS Y it = β 0 + β 1 X it + u it, i = 1, 2,, N, t = 1, 2,, T (2) u it = µ i + ε it (3) µ i 3.2 Fixed Effects Model fixed effects model random effects model fixed effects model random effects model µ i fixed effects model µ i random effects model µ i Fixed Effects Model fixed effects model (2) (3) Y it = β 0 + µ i + β 1 X it + ε it (4) fixed effects model µ i Cov(µ i, X it ) 0 (5) fixed effects model unobservable hetertogeneity * 17 *17 random effects model 14/46

15 3 3.2 Fixed Effects Model LSDV Least Square Dummy Variable (4) Y it = β 0 + µ 1 D µ N 1 D N 1 + β 1 X it + ε it (6) D i = { 1, i = j, 0, i j (7) (6) LSDV N 1 fixed effects model LSDV OLS fixed effects model Pooled OLS ˆβ 0, ˆµ OLS OLS, ˆβ 1 i N T µ i X it µ i ˆβ 1 X it Within µ i within (4) (4) t Y it Ȳi = β 1 ( Xit X i ) + (uit ū i ) (8) Ȳi = T Y it t=1 T X i, ū i, t β 0, µ i (8) OLS ˆβ 1 within fixed effects LSDV model Between Ȳ i = β 0 + β 1 Xi + ū i (9) Var (ū i ) = σ 2 µ + σ2 ε T (10) (9) OLS between fixed effects model between random effects model 15/46

16 3 3.3 random effects model 3.3 random effects model random effects model µ i Y it = β 0 + µ i + β 1 X it + ε it (11) Cov(µ i, X it ) = 0 (12) random effects model Pooled OLS u it = µ i + ε it σ µ + σ ε, i = j, t = s, cov(u it, u js ) = σ µ, i = j, t s, 0, i j pooled OLS random effects model GLS GLS ˆβ 1 GLS random effects random effects GLS Wooldridge (2009, Section 14.2) (13) 3.4 F Test Pooled OLS vs Fixed Effect Model H 0 : µ 1 = µ 2 = = µ N (14) H 1 : H 0 (15) H 0 N 1, NT N k F k X ( RSS F E RSS OLS) / (N 1) RSS OLS / (NT N k) RSS F E RSS OLS fixed effects model pooled model Residual Sum of Squares pooled OLS Greene (2007, Section 9.4.3) (16) 3.5 Hausman Test (3) random effects fixed effects Hausman test H 0 H 1 H 0 : Cov(µ i, X it ) = 0 (17) H 1 : Cov(µ i, X it ) 0 (18) 16/46

17 3 3.6 H 0 : random effects model (19) H 1 : fixed effects model (20) µ i fixed effects random effects LSDV H 0 random effects H 1 H 0 H = ˆβ RE 1 ) 2 ( ˆβ 1 F E V ar( ˆβ 1 F E ) V ar( ˆβ RE 1 ) (21) ˆβ 1 F E RE, ˆβ 1 fixed effects random effects V ar( ˆβ 1 F E ), V RE ar( ˆβ 1 ) H χ 2 (1) fixed effects model fixed effects model random effects estimaor GLS - fixed effects model fixed effects estimator LSDV 4 random effects model random effects model random effects estimaor GLS random effects model fixed effects estimator LSDV 3.7 Time Fixed Effects Model Time Random Effects Model Y it = β 0 + β 1 X it + u it (22) u it = γ t + ε it (23) fixed effects model random effects model (4) µ i (23) γ t time fixed effects model time random effects model 3.8 Two-way Fixed Effects Model Two-way Random Effects Model Two-Way fixed effects Two-way Fixed Effects Model 17/46

18 3 3.8 Two-way Fixed Effects Model Two-way Random Effects Model random effects Two-way Random Effects Model Y it = β 0 + β 1 X it + u it (24) u it = µ i + γ t + ε it (25) 18/46

19 4 EVIEWS 4 EViews 4.1 Pooled OLS lny lnk lnl Pooled OLS lny it = c + β 1 lnk it + β 2 lnl it + ε it (26) 1. Pooled OLS Workfile Quick - Estimate Equation OK Equation specification lny c lnk lnl 2. 19/46

20 4 EVIEWS 4.1 Pooled OLS 3. Name eq01 OK Workfile eq01 Object 4. View - Actual, Fitted, Residual - Actual, Fitted, Residual Graph 5. Jarque-Bera Test View - Residual Tests - Histogram-Normality 20/46

21 4 EVIEWS 4.2 Fixed Effects Model 4.2 Fixed Effects Model lny lnk lnl fixed effects model * 18*19 lny it = c + β 1 lnk it + β 2 lnl it + u it (27) u it = µ i + ε it (28) µ i dum1, dum2, * 20 LSDV model lny it = c + µ 1 dum1 i + µ 2 dum2 i + + µ 48 dum48 i + β 1 lnk it + β 2 lnl it + ε it (30) 1. Workfile Quick - Estimate Equation Equation specification lny lnk lnl * 21 *18 time fixed or random) effects *19 EViews ID EViews 0 EViews ID *20 dumj i dumj i = { 1 for i = j 0 for i j (29) *21 fixed effects model random effects model c 21/46

22 4 EVIEWS 4.2 Fixed Effects Model 2. Panel Options OK Cross-section Fixed * 22 Period None 3. *22 fixed effects model 22/46

23 4 EVIEWS 4.2 Fixed Effects Model 4. fixed effects View - Fixed/Random Effects - Cross-section Effects 5. Name eq02 OK Workfile eq02 Object 6. View - Actual, Fitted, Residual - Actual, Fitted, Residual Graph 23/46

24 4 EVIEWS 4.3 F Test Pooled OLS vs Fixed Effect Model 7. Jarque-Bera Test View - Residual Tests - Histogram-Normality 4.3 F Test Pooled OLS vs Fixed Effect Model H 0 : µ 1 = µ 2 = = µ N (31) H 1 : H 0 (32) H 0 pooled OLS 1. eq02 View - Fixed/Random Effects Testing - Redundant Fixed Effects. Likelihood Ratio * 23 *23 EViews fixed effects model 24/46

25 4 EVIEWS 4.4 Random Effects Model 4.4 Random Effects Model lny lnk lnl random effects Model * 24 lny it = c + β 1 lnk it + β 2 lnl it + u it (33) u it = µ i + ε it (34) µ i Cov (lnk it, µ i ) = 0 Cov (lnl it, µ i ) = 0 (35) 1. Workfile Quick - Estimate Equation Equation specification lny lnk lnl * 25 *24 fixed or random) time effects *25 fixed effects model random effects model c 25/46

26 4 EVIEWS 4.4 Random Effects Model 2. Panel Options OK Cross-section Random * 26 Period None 3. *26 random effects model 26/46

27 4 EVIEWS 4.4 Random Effects Model 4. random effects View - Fixed/Random Effects - Cross-section Effects 5. Name eq03 OK Workfile eq03 Object 6. View - Actual, Fitted, Residual - Actual, Fitted, Residual Graph 27/46

28 4 EVIEWS 4.5 Hausman Test Fixed Effects Model vs Random Effects Model 7. Jarque-Bera Test View - Residual Tests - Histogram-Normality 4.5 Hausman Test Fixed Effects Model vs Random Effects Model 1. (33) (34) Hausman Test H 0 : random effects model (36) H 1 : fixed effects model (37) eq03 * 27 View - Fixed/Random Effects Testing - Hausman Test of Random vs. Fixed *27 EVies Hausman Test random effects or time random effects 28/46

29 4 EVIEWS 4.6 Time Fixed Effects Model 4.6 Time Fixed Effects Model lny lnk lnl time fixed effects model * 28 lny it = c + β 1 lnk it + β 2 lnl it + u it (38) u it = γ t + ε it (39) γ γ t timedum1980, timedum1985, * 29 LSDV model lny it = c + γ 1 timedum1980 t + γ 2 timedum1985 t + + γ 5 timedum2000 t + β 1 lnk it + β 2 lnl it + ε it (41) 1. Workfile Quick - Estimate Equation Equation specification lny lnk lnl * 30 *28 fixed or random effects t τ = T 1975 timedumt 5 t { 1 for τ = t timedumt t = (40) 0 for τ t *30 time fixed effects model time random effects model c 29/46

30 4 EVIEWS 4.6 Time Fixed Effects Model 2. Panel Options OK Cross-section None Period Fixed * *31 time fixed effect model 30/46

31 4 EVIEWS 4.6 Time Fixed Effects Model 4. time fixed effects View - Fixed/Random Effects - Period Effects 5. Name eq04 OK Workfile eq04 Object 6. View - Actual, Fitted, Residual - Actual, Fitted, Residual Graph 31/46

32 4 EVIEWS 4.7 F Test Pooled OLS vs Time Fixed Effect Model 7. Jarque-Bera Test View - Residual Tests - Histogram-Normality 4.7 F Test Pooled OLS vs Time Fixed Effect Model H 0 : γ 1 = γ 2 = = γ T (42) H 1 : H 0 (43) H 0 pooled OLS 1. eq04 View - Fixed/Random Effects Testing - Redundant Fixed Effects. Likelihood Ratio * 32 *32 EViews time fixed effects model 32/46

33 4 EVIEWS 4.8 Time Random Effects Model 4.8 Time Random Effects Model lny lnk lnl time random effects model * 33 lny it = c + β 1 lnk it + β 2 lnl i,t + u it (44) u it = γ t + ε it (45) γ γ t Cov (lnk it, γ t ) = 0 Cov (lnl it, γ t ) = 0 (46) 1. Workfile Quick - Estimate Equation Equation specification lny lnk lnl * 34 *33 fixed or random effects *34 Fixed Effects Model Random Effects Model c 33/46

34 4 EVIEWS 4.8 Time Random Effects Model 2. Panel Options OK Cross-section None Period Random * *35 time random effects model 34/46

35 4 EVIEWS 4.8 Time Random Effects Model 4. time random effects View - Fixed/Random Effects - Period Effects 5. Name eq05 OK Workfile eq05 Object 6. View - Actual, Fitted, Residual - Actual, Fitted, Residual Graph 35/46

36 4 EVIEWS 4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model 7. Jarque-Bera Test View - Residual Tests - Histogram-Normality 4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model 1. (44) (45) Hausman Test H 0 : time random effects model (47) H 1 : time fixed effects model (48) 36/46

37 4 EVIEWS 4.10 Two-way Fixed Effects Model Two-way Fixed Effects Model 2 lny lnk lnl two-way fixed effects model 2 * 36 lny i,t = c + β 1 lnk i,t + β 2 lnl i,t + u i,t (49) u i,t = µ i + γ t + ε i,t (50) µ i γ t µ i γ t Cov (lnk it, µ i ) 0 Cov (lnl it, µ i ) 0 Cov (lny it, γ t ) 0 Cov (lny it, γ t ) 0 (51) LSDV model lny i,t = c + µ 1 dum1 i + µ 2 dum µ 48 dum48 + γ 1 timedum1980 t + γ 2 timedum1985 t + + γ 5 timedum2000 t + β 1 lnk i,t + β 2 lnl i,t + ε i,t (52) 1. Workfile Quick - Estimate Equation Equation specification lny lnk lnl * 37 *36 fixed effects time fixed effects *37 fixed effects model random effects model c 37/46

38 4 EVIEWS 4.10 Two-way Fixed Effects Model 2 2. Panel Options OK Cross-section Fixed * 38 Period Fixed * *38 fixed effect model *39 time fixed effect model 38/46

39 4 EVIEWS 4.10 Two-way Fixed Effects Model 2 4. fixed effects View - Fixed/Random Effects - Cross-section Effects 5. time fixed effects View - Fixed/Random Effects - Period Effects 6. Name eq06 OK Workfile eq06 Object 39/46

40 4 EVIEWS 4.10 Two-way Fixed Effects Model 2 7. View - Actual, Fitted, Residual - Actual, Fitted, Residual Graph 8. Jarque-Bera Test View - Residual Tests - Histogram-Normality 40/46

41 4 EVIEWS 4.11 F Test Pooled OLS vs Fixed Effect Model 4.11 F Test Pooled OLS vs Fixed Effect Model H 0 : µ 1 = µ 2 = = µ N γ 1 = γ 2 = = γ T (53) H 1 : H 0 (54) H 0 pooled OLS 1. eq06 View - Fixed/Random Effects Testing - Redundant Fixed Effects. Likelihood Ratio * 40 *40 EViews two-way fixed effects model 41/46

42 4 EVIEWS 4.12 Two-way Random Effects Model Two-way Random Effects Model 2 lny lnk lnl two-way random effects model 2 * 41 lny it = c + β 1 lnk it + β 2 lnl it + u it (55) u it = µ i + γ t + ε it (56) µ γ Cov (lnk it, µ i ) = 0 Cov (lnl it, µ i ) = 0 Cov (lnk it, γ t ) = 0 Cov (lnl it, γ t ) = 0 (57) 1. Workfile Quick - Estimate Equation Equation specification lny lnk lnl * 42 *41 random effects time random effects *42 fixed effects model random effects model c 42/46

43 4 EVIEWS 4.12 Two-way Random Effects Model 2 2. Panel Options OK Cross-section Random * 43 Period Random * *43 random effect model *44 time random effect model 43/46

44 4 EVIEWS 4.12 Two-way Random Effects Model 2 4. random effects View - Fixed/Random Effects - Cross-section Effects 5. time random effects View - Fixed/Random Effects - Period Effects 6. Name eq07 OK Workfile eq07 Object 44/46

45 4 EVIEWS 4.12 Two-way Random Effects Model 2 7. View - Actual, Fitted, Residual - Actual, Fitted, Residual Graph 8. Jarque-Bera Test View - Residual Tests - Histogram-Normality 45/46

46 4.13 Hausman Test Two-way Fixed Effects vs Two-way Random Effects 4.13 Hausman Test Two-way Fixed Effects vs Two-way Random Effects 1. (55) (56) Hausman Test H 0 : two-way random effects model (58) H 1 : two-way fixed effects model (59) Greene, William H. (2007) Econometric analysis: Prentice Hall, 6th edition. Wooldridge, Jeffrey M. (2009) Introductory econometrics : a modern approach: South-Western, 4th edition. 46/46

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と入力する すると最初の 25 行が表示される 1 行目は変数の名前であり 2 列目は企業番号 (1,,10),3 列目は西暦 (1935,,1954) を表している ( 他のパネルデータを分析する際もデ ータをこのように並べておかなくてはならない つまりまず i=1 を固定し i=1 の t に関 R によるパネルデータモデルの推定 R を用いて 静学的パネルデータモデルに対して Pooled OLS, LSDV (Least Squares Dummy Variable) 推定 F 検定 ( 個別効果なしの F 検定 ) GLS(Generalized Least Square : 一般化最小二乗 ) 法による推定 およびハウスマン検定を行うやり方を 動学的パネルデータモデルに対して 1 階階差

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