% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti One-sample test of pr
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1 % 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti One-sample test of proportion x: Number of obs = 1029 Variable Mean Std. Err. [95% Conf. Interval] x p = proportion(x) z = Ho: p = 0.4 Ha: p < 0.4 Ha: p!= 0.4 Ha: p > 0.4 Pr(Z < z) = Pr( Z > z ) = Pr(Z > z) = (a), (b) Granger 1
2 ( year) 30 ) t (t = 2008, 2012) 24 (i = 1,..., 24) Y it log Y it ( ly) K it log K it ( lk) L it log L it ( ll) (a) (year = 2008) log Y it = β 0 + β 1 log K it + β 2 log L it + ϵ it, t = 2008, i = 1,..., 24. (i) (ii) (iii) 5% (iv) 5% (v) ϵ it (b) D it ( d) t = , t = D it log K it ( dlk) D it log L it ( dll) log Y it = β 0 + β 1 log K it + β 2 log L it + α 0 D it + α 1 (D it log K it ) +α 2 (D it log L it ) + ϵ it, t = 2008, 2012, i = 1,..., 24. (i) (ii) 5% (iii) VIF 3 (c) log Y it = β 0 + β 1 log K it + β 2 log L it + ϵ it, t = 2008, 2012, i = 1,..., 24. (i) 3 4 2
3 2: STATA (2). regress ly lk ll if year==2008 Source SS df MS Number of obs = F( 2, 21) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = ly Coef. Std. Err. t P> t [95% Conf. Interval] lk ll _cons test (lk+ll=1) ( 1) lk + ll = 1 F( 1, 21) = 0.65 Prob > F = estat hettest Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of ly chi2(1) = 0.00 Prob > chi2 =
4 3: STATA (3). regress ly lk ll d dlk dll Source SS df MS Number of obs = F( 5, 42) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE =.3001 ly Coef. Std. Err. t P> t [95% Conf. Interval] lk ll d dlk dll _cons test (d dlk dll) ( 1) d = 0 ( 2) dlk = 0 ( 3) dll = 0 F( 3, 42) = 0.13 Prob > F = estat vif Variable VIF 1/VIF dlk dll d lk ll Mean VIF : STATA (4). regress ly lk ll Source SS df MS Number of obs = F( 2, 45) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = ly Coef. Std. Err. t P> t [95% Conf. Interval] lk ll _cons
5 ( ), 73.4% ( 2838 ), 84.9% ( 3221 ) p X, p Y (a) 5 p X 95% (b) 5 Std. Err. (c) 5% (d) (c) 1% (e) p 5: STATA (1). prtesti Two-sample test of proportions x: Number of obs = 2838 y: Number of obs = 3221 Variable Mean Std. Err. z P> z [95% Conf. Interval] x y diff under Ho: diff = prop(x) - prop(y) z = Ho: diff = 0 Ha: diff < 0 Ha: diff!= 0 Ha: diff > 0 Pr(Z < z) = Pr( Z < z ) = Pr(Z > z) =
6 2. (a) (b) (c) (d) ( : ) (lm), GDP( :10 ) (ly) q1,q2,q3 qj j 1, (a) 1 (b) (c) 6 (d) 6 ) (e) 7 2 (f) (e) (g) (h) 10 6
7 1: lm ly 1994q1 1998q3 2003q1 2007q3 2012q1 time lm ly 6: STATA (2). regress ly L.ly L2.ly L3.ly L4.ly L.lm L2.lm L3.lm L4.lm q1 q2 q3 Source SS df MS Number of obs = F( 11, 57) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = ly Coef. Std. Err. t P> t [95% Conf. Interval] ly L L L L lm L L L L q q q _cons
8 7: STATA (3). estat hettest Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of ly chi2(1) = 0.52 Prob > chi2 = estat durbinalt Durbin s alternative test for autocorrelation lags(p) chi2 df Prob > chi H0: no serial correlation 8: STATA (4). regress ly L.ly L2.ly L3.ly L4.ly L.lm L2.lm L3.lm L4.lm q1 q2 q3 if tin(2001q1,2012q1) Source SS df MS Number of obs = F( 11, 33) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = ly Coef. Std. Err. t P> t [95% Conf. Interval] ly L L L L lm L L L L ( ))---. estat durbinalt Durbin s alternative test for autocorrelation lags(p) chi2 df Prob > chi H0: no serial correlation 8
9 9: STATA (5). var ly lm if tin(2001q1,2012q1), lags(1/4) exog(q1 q2 q3) Vector autoregression Sample: 2001q1-2012q1 No. of obs = 45 Log likelihood = AIC = FPE = 2.98e-07 HQIC = Det(Sigma_ml) = 9.97e-08 SBIC = Equation Parms RMSE R-sq chi2 P>chi ly lm Coef. Std. Err. z P> z [95% Conf. Interval] ly ly L L L L lm L L L L q q q _cons lm ly L L L L lm L L L L q q q _cons
10 10: STATA (6). vargranger Granger causality Wald tests Equation Excluded chi2 df Prob > chi ly lm ly ALL lm ly lm ALL GDP % , 0.7 µ (a) 11 µ 95% (b) 11 Std. Err. (c) 10 GDP % 1.6% 5% (d) (c) 1% (e) p 11: STATA (1) One-sample t test Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] x mean = mean(x) t = Ho: mean = 1.6 degrees of freedom = 155 Ha: mean < 1.6 Ha: mean!= 1.6 Ha: mean > 1.6 Pr(T < t) = Pr( T > t ) = Pr(T > t) = UFJ 2,
11 2. (a) (b) AIC, BIC 11
12 (, id) (%, loan) ) (%, land) 3 loan land 2, (a) 2, 3 (b) 12 (c) 12 (d) 12 ) (e) 13 (f) 14 (g) 14 land 95% (h) 15 (i) 15 land 5% (j) 5% (k) 5% (l) (m) Hausman (specification) 5% 12
13 2: Aichi Chiba Hyogo Kanagawa Kyoto Osaka Saitama Shiga Tokyo Year LOAN LAND Graphs by Prefecture 3: Aichi Chiba Hyogo Kanagawa Kyoto Osaka LOAN Saitama Shiga Tokyo LAND Graphs by Prefecture 13
14 12: STATA (2) Source SS df MS Number of obs = F( 1, 88) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = loan Coef. Std. Err. t P> t [95% Conf. Interval] land _cons : STATA (3) Between regression (regression on group means) Number of obs = 90 Group variable: id Number of groups = 9 R-sq: within = Obs per group: min = 10 between = avg = 10.0 overall = max = 10 F(1,7) = 0.03 sd(u_i + avg(e_i.))= Prob > F = loan Coef. Std. Err. t P> t [95% Conf. Interval] land _cons : STATA (4) Fixed-effects (within) regression Number of obs = 90 Group variable: id Number of groups = 9 R-sq: within = Obs per group: min = 10 between = avg = 10.0 overall = max = 10 F(1,80) = corr(u_i, Xb) = Prob > F = loan Coef. Std. Err. t P> t [95% Conf. Interval] land _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(8, 80) = 3.47 Prob > F =
15 15: STATA (5) Random-effects GLS regression Number of obs = 90 Group variable: id Number of groups = 9 R-sq: within = Obs per group: min = 10 between = avg = 10.0 overall = max = 10 Random effects u_i ~ Gaussian Wald chi2(1) = corr(u_i, X) = 0 (assumed) Prob > chi2 = loan Coef. Std. Err. z P> z [95% Conf. Interval] land _cons sigma_u sigma_e rho (fraction of variance due to u_i) 16: STATA (6) Breusch and Pagan Lagrangian multiplier test for random effects loan[id,t] = Xb + u[id] + e[id,t] Estimated results: Var sd = sqrt(var) loan e u Test: Var(u) = 0 chi2(1) = Prob > chi2 = : STATA (7) ---- Coefficients ---- (b) (B) (b-b) sqrt(diag(v_b-v_b)) fixed random Difference S.E. land b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient under Ho; obtained from xtreg Test: Ho: difference in coefficients not systematic chi2(1) = (b-b) [(V_b-V_B)^(-1)](b-B) = 0.22 Prob>chi2 =
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