* This model uses the Translog Distance Input Function to estimate the system of input demand functions. * Then we compute the Hicks Elasticity of Substitution for the four inputs. * The materials equation is dropped due to singularity and we normalize on materials quantity to impose homogeneity in inputs. * Data input cal 1947 1 1 allocate 0 1971:1 open data klem.wks data(format=wks,org=obs, verbose) set trend = t set lqe = log(qe/qm) set lqk = log(qk/qm) set lql = log(ql/qm) set lqy = log(qy) * Hunt and Lynk Transformation sta(noprint) lqe; set lqe = lqe-%mean sta(noprint) lqk; set lqk = lqk-%mean sta(noprint) lql; set lql = lql-%mean sta(noprint) lqy; set lqy = lqy-%mean sta(noprint) trend; set trend = trend-%mean set se = pe*qe/cost set sm = pm*qm/cost set sl = pl*ql/cost set sk = pk*qk/cost instruments constant z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 trend equation 1 sk # constant trend lqy lqk lql lqe equation 2 sl # constant trend lqy lqk lql lqe equation 3 se # constant trend lqy lqk lql lqe sur(noprint,instruments) 3 # 1 # 2 # 3 * Symmetry Restrictions restrict(replace) 3 # 5 10 # 1.0 -1.0 0.0 # 6 16 # 1.0 -1.0 0.0 # 12 17 # 1.0 -1.0 0.0 sur(create) 3 # 1 r1 # 2 r2 # 3 r3 Chi-Squared(3)= 16.803936 or F(3,*)= 5.60131 with Significance Level 0.00077548 Linear Systems - Estimation by Seemingly Unrelated Regressions Annual Data From 1947:01 To 1971:01 Usable Observations 25 Log Likelihood 357.02283 Dependent Variable SK Mean of Dependent Variable 0.0534882129 Std Error of Dependent Variable 0.0044804570 Standard Error of Estimate 0.0034557463 Sum of Squared Residuals 0.0002985546 Durbin-Watson Statistic 1.545513 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 1. Constant 0.053488213 0.000676954 79.01304 0.00000000 2. TREND 0.001628572 0.000713939 2.28111 0.02254199 3. LQY -0.029621336 0.017445674 -1.69792 0.08952311 4. LQK -0.016424291 0.014422160 -1.13882 0.25477689 5. LQL 0.028717957 0.013568648 2.11649 0.03430285 6. LQE 0.020896291 0.004498841 4.64482 0.00000340 Dependent Variable SL Mean of Dependent Variable 0.2744612933 Std Error of Dependent Variable 0.0128772782 Standard Error of Estimate 0.0036179060 Sum of Squared Residuals 0.0003272311 Durbin-Watson Statistic 1.436739 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 7. Constant 0.274461293 0.000695231 394.77737 0.00000000 8. TREND 0.002082023 0.000726039 2.86764 0.00413540 9. LQY 0.024727521 0.017737764 1.39406 0.16329926 10. LQK 0.028717957 0.013568648 2.11649 0.03430285 11. LQL 0.111845515 0.026627812 4.20033 0.00002665 12. LQE -0.011238347 0.007980059 -1.40830 0.15904117 Dependent Variable SE Mean of Dependent Variable 0.0448202036 Std Error of Dependent Variable 0.0031049179 Standard Error of Estimate 0.0009842374 Sum of Squared Residuals 0.0000242181 Durbin-Watson Statistic 1.578249 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 13. Constant 0.044820204 0.000195848 228.85189 0.00000000 14. TREND 0.000008163 0.000271536 0.03006 0.97601757 15. LQY -0.011392521 0.006040163 -1.88613 0.05927769 16. LQK 0.020896291 0.004498841 4.64482 0.00000340 17. LQL -0.011238347 0.007980059 -1.40830 0.15904117 18. LQE 0.007519971 0.008824973 0.85212 0.39414531 Covariance\Correlation Matrix of Residuals SK SL SE SK 0.00001194218 -0.2560396301 -0.3595432098 SL -0.00000320115 0.00001308924 0.6315828340 SE -0.00000122291 0.00000224899 0.00000096872 gra 3 # r1 # r2 # r3 set psk = sk-r1 set psl = sl-r2 set pse = se-r3 set r4 = -r1-r2-r3 set psm = sm-r4 gra 2 # se # pse gra 2 # sm # psm gra 2 # sl # psl gra 2 # sk # psk eval am=(1-%beta(1)-%beta(7)-%beta(13)) eval bkm=-%beta(4)-%beta(5)-%beta(6) eval blm=-%beta(10)-%beta(11)-%beta(12) eval bem=-%beta(16)-%beta(17)-%beta(18) eval bmm=-bkm-blm-bem * Elasticities eval skl = ((%beta(1)-%beta(4))/(%beta(1)**2)+2*%beta(5)/(%beta(1)*%beta(7))+(%beta(7)-%beta(11))/(%beta(7)**2))/((1/%beta(1))+(1/%beta(7))) eval ske = ((%beta(1)-%beta(4))/(%beta(1)**2)+2*%beta(6)/(%beta(1)*%beta(13))+(%beta(13)-%beta(18))/(%beta(13)**2))/((1/%beta(1))+(1/%beta(13))) eval skm = ((%beta(1)-%beta(4))/(%beta(1)**2)+2*bkm/(%beta(1)*am)+(am-bmm)/(am**2))/((1/%beta(1))+(1/am)) eval sle = ((%beta(7)-%beta(11))/(%beta(7)**2)+2*%beta(12)/(%beta(7)*%beta(13))+(%beta(13)-%beta(18))/(%beta(13)**2))/((1/%beta(7))+(1/%beta(13))) eval slm = ((%beta(7)-%beta(11))/(%beta(7)**2)+2*blm/(%beta(7)*am)+(am-bmm)/(am**2))/((1/%beta(7))+(1/am)) eval sem = ((%beta(13)-%beta(18))/(%beta(13)**2)+2*bem/(%beta(13)*am)+(am-bmm)/(am**2))/((1/%beta(13))+(1/am)) dis skl dis ske dis skm dis sle dis slm dis sem 1.36565 1.47382 1.16291 0.72817 0.34248 0.77318