storage display value variable name type format label variable label ------------------------------------------------------------------------------- county int %9.0g county identifier year byte %9.0g 81 to 87 crmrte float %9.0g crimes committed per person prbarr float %9.0g 'probability' of arrest prbconv float %9.0g 'probability' of conviction prbpris float %9.0g 'probability' of prison sentenc avgsen float %9.0g avg. sentence, days polpc float %9.0g police per capita density float %9.0g people per sq. mile taxpc float %9.0g tax revenue per capita west byte %9.0g =1 if in western N.C. central byte %9.0g =1 if in central N.C. urban byte %9.0g =1 if in SMSA pctmin80 float %9.0g perc. minority, 1980 wcon float %9.0g weekly wage, construction wtuc float %9.0g wkly wge, trns, util, commun wtrd float %9.0g wkly wge, whlesle, retail trade wfir float %9.0g wkly wge, fin, ins, real est wser float %9.0g wkly wge, service industry wmfg float %9.0g wkly wge, manufacturing wfed float %9.0g wkly wge, fed employees wsta float %9.0g wkly wge, state employees wloc float %9.0g wkly wge, local gov emps mix float %9.0g offense mix: face-to-face/other pctymle float %9.0g percent young male d82 byte %9.0g =1 if year == 82 d83 byte %9.0g =1 if year == 83 d84 byte %9.0g =1 if year == 84 d85 byte %9.0g =1 if year == 85 d86 byte %9.0g =1 if year == 86 d87 byte %9.0g =1 if year == 87 lcrmrte float %9.0g log(crmrte) lprbarr float %9.0g log(prbarr) lprbconv float %9.0g log(prbconv) lprbpris float %9.0g log(prbpris) lavgsen float %9.0g log(avgsen) lpolpc float %9.0g log(polpc) ldensity float %9.0g log(density) ltaxpc float %9.0g log(taxpc) lwcon float %9.0g log(wcon) lwtuc float %9.0g log(wtuc) lwtrd float %9.0g log(wtrd) lwfir float %9.0g log(wfir) lwser float %9.0g log(wser) lwmfg float %9.0g log(wmfg) lwfed float %9.0g log(wfed) lwsta float %9.0g log(wsta) lwloc float %9.0g log(wloc) lmix float %9.0g log(mix) lpctymle float %9.0g log(pctymle) lpctmin float %9.0g log(pctmin) clcrmrte float %9.0g lcrmrte - lcrmrte[_n-1] clprbarr float %9.0g lprbarr - lprbarr[_n-1] clprbcon float %9.0g lprbconv - lprbconv[_n-1] clprbpri float %9.0g lprbpri - lprbpri[t-1] clavgsen float %9.0g lavgsen - lavgsen[t-1] clpolpc float %9.0g lpolpc - lpolpc[t-1] cltaxpc float %9.0g ltaxpc - ltaxpc[t-1] clmix float %9.0g lmix - lmix[t-1]
Estimoi lineaarinen malli POLS estimaattorilla (pooled ordinary least squares) kayttaen kaikkia vuosia 81-87. Mallissa vastemuuttuja on log(crmrte) ja selittavat muuttujat ovat log(prbarr), log(prbconv), log(prbpris), log(avgsen) ja log(polpc).
file<-"http://cc.oulu.fi/~jklemela/panel/cornwell.raw" data<-read.table(file=file) y<-log(data[,3]) x1<-log(data[,4]) x2<-log(data[,5]) x3<-log(data[,6]) x4<-log(data[,7]) x5<-log(data[,8]) reg.model<-lm(y ~ x1+x2+x3+x4+x5) summary(reg.model) Call: lm(formula = y ~ x1 + x2 + x3 + x4 + x5) Residuals: Min 1Q Median 3Q Max -1.93632 -0.19952 0.02951 0.25318 1.29941 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -2.20673 0.23869 -9.245 < 2e-16 *** x1 -0.72151 0.03671 -19.655 < 2e-16 *** x2 -0.54928 0.02627 -20.909 < 2e-16 *** x3 0.23797 0.06643 3.582 0.000367 *** x4 -0.06520 0.05535 -1.178 0.239281 x5 0.36252 0.02996 12.100 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.3789 on 624 degrees of freedom Multiple R-squared: 0.5658, Adjusted R-squared: 0.5624 F-statistic: 162.7 on 5 and 624 DF, p-value: < 2.2e-16 ###################################### K<-6 n<-length(y) x<-matrix(0,n,K) x[,1]<-1 x[,2]<-x1 x[,3]<-x2 x[,4]<-x3 x[,5]<-x4 x[,6]<-x5 A<-t(x)%*%x invA<-solve(A,diag(1,K)) b<-invA%*%t(x)%*%y b [1,] -2.20673453 [2,] -0.72151130 [3,] -0.54927675 [4,] 0.23797055 [5,] -0.06519926 [6,] 0.36252309 ########################################### county<-data[,1] year<-data[,2] uc<-unique(county) uy<-unique(year) N<-length(uc) T<-length(uy) residu<-matrix(0,N,T) for (i in 1:N){ xi<-x[((i-1)*7+1):(i*7),] yi<-y[((i-1)*7+1):(i*7)] residu[i,]<-yi-xi%*%b } Ahat<-matrix(0,K,K) for (i in 1:N){ xi<-x[((i-1)*7+1):(i*7),] Ahat<-Ahat+t(xi)%*%xi } Ahat<-Ahat/N Bhat<-matrix(0,K,K) for (i in 1:N){ xi<-x[((i-1)*7+1):(i*7),] ui<-matrix(residu[i,],T,1) Bhat<-Bhat+t(xi)%*%ui%*%t(ui)%*%xi } Bhat<-Bhat/N sighat2<-mean(residu^2) invAhat<-solve(Ahat,diag(1,K)) avar.robust<-invAhat%*%Bhat%*%invAhat/N avar<-sighat2*invAhat/N ################################### sdhats<-matrix(0,K,1) tstats<-matrix(0,K,1) pvals<-matrix(0,K,1) for (k in 1:K){ sdhats[k]<-sqrt(avar[k,k]) tstats[k]<-b[k]/sdhats[k] pvals[k]<-2*(1-pnorm(abs(tstats[k]))) } sdhats tstats pvals > sdhats [,1] [1,] 0.23755308 [2,] 0.03653369 [3,] 0.02614469 [4,] 0.06611309 [5,] 0.05508736 [6,] 0.02981777 > tstats [,1] [1,] -9.289438 [2,] -19.749203 [3,] -21.009110 [4,] 3.599447 [5,] -1.183561 [6,] 12.157956 > pvals [,1] [1,] 0.000000000 [2,] 0.000000000 [3,] 0.000000000 [4,] 0.000318895 [5,] 0.236586851 [6,] 0.000000000 # robustit #################### sdhats<-matrix(0,K,1) tstats<-matrix(0,K,1) pvals<-matrix(0,K,1) for (k in 1:K){ sdhats[k]<-sqrt(avar.robust[k,k]) tstats[k]<-b[k]/sdhats[k] pvals[k]<-2*(1-pnorm(abs(tstats[k]))) } sdhats tstats pvals > sdhats [,1] [1,] 0.85072888 [2,] 0.10845868 [3,] 0.06977112 [4,] 0.10549265 [5,] 0.10197897 [6,] 0.11856455 > tstats [,1] [1,] -2.5939340 [2,] -6.6524070 [3,] -7.8725522 [4,] 2.2558022 [5,] -0.6393402 [6,] 3.0576012 > pvals [,1] [1,] 9.488471e-03 [2,] 2.883382e-11 [3,] 3.552714e-15 [4,] 2.408302e-02 [5,] 5.226016e-01 [6,] 2.231163e-03 ################################# OLS-kaavat Ahatb<-t(x)%*%x/(N*T) sighat2<-sum(residu^2)/(N*T-K) invAhatb<-solve(Ahatb,diag(1,K)) avarb<-sighat2*invAhatb/(N*T) sdhats<-matrix(0,K,1) tstats<-matrix(0,K,1) pvals<-matrix(0,K,1) for (k in 1:K){ sdhats[k]<-sqrt(avarb[k,k]) tstats[k]<-b[k]/sdhats[k] pvals[k]<-2*(1-pnorm(abs(tstats[k]))) } sdhats tstats pvals > sdhats [,1] [1,] 0.23869243 [2,] 0.03670891 [3,] 0.02627009 [4,] 0.06643018 [5,] 0.05535157 [6,] 0.02996078 > tstats [,1] [1,] -9.245097 [2,] -19.654934 [3,] -20.908828 [4,] 3.582265 [5,] -1.177912 [6,] 12.099923 > pvals [,1] [1,] 0.0000000000 [2,] 0.0000000000 [3,] 0.0000000000 [4,] 0.0003406274 [5,] 0.2388318499 [6,] 0.0000000000