* This model uses the Translog Cost Function to estimate the system of input demand functions * and the cost function itself. * All elasticities are then computed from the cost function estimates. * Data input cal 1947 1 1 allocate 0 1971:1 open data klem.wks data(format=wks,org=obs, verbose) set trend = t set lpe = log(pe/pm) set lpk = log(pk/pm) set lpl = log(pl/pm) set lqy = log(qy) * Hunt and Lynk Transformation sta(noprint) lpe; set lpe = lpe-%mean sta(noprint) lpk; set lpk = lpk-%mean sta(noprint) lpl; set lpl = lpl-%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 set rc = revenue/cost set lc = log(cost/pm) sta(noprint) lc; set lc = lc-%mean set tt = trend*trend*.5 set tlqy = trend*lqy set tlpk = trend*lpk set tlpl = trend*lpl set tlpe = trend*lpe set lqylqy = lqy*lqy*.5 set lqylpk = lqy*lpk set lqylpl = lqy*lpl set lqylpe = lqy*lpe set lpklpk = lpk*lpk*.5 set lpllpl = lpl*lpl*.5 set lpelpe = lpe*lpe*.5 set lpklpl = lpk*lpl set lpklpe = lpk*lpe set lpllpe = lpl*lpe dec vec beta(39) equation 1 sk # constant trend lqy lpk lpl lpe equation 2 sl # constant trend lqy lpk lpl lpe equation 3 se # constant trend lqy lpk lpl lpe equation 4 lc # constant trend lqy lpk lpl lpe $ tt tlqy tlpk tlpl tlpe lqylqy lqylpk lqylpl lqylpe $ lpklpk lpllpl lpelpe lpklpl lpklpe lpllpe sur(noprint) 4 # 1 # 2 # 3 # 4 * Symmetry + Homogeneity Restrictions restrict(replace) 18 # 5 10 # 1.0 -1.0 0.0 # 6 16 # 1.0 -1.0 0.0 # 12 17 # 1.0 -1.0 0.0 # 1 22 # 1.0 -1.0 0.0 # 7 23 # 1.0 -1.0 0.0 # 13 24 # 1.0 -1.0 0.0 # 2 27 # 1.0 -1.0 0.0 # 8 28 # 1.0 -1.0 0.0 # 14 29 # 1.0 -1.0 0.0 # 3 31 # 1.0 -1.0 0.0 # 9 32 # 1.0 -1.0 0.0 # 15 33 # 1.0 -1.0 0.0 # 4 34 # 1.0 -1.0 0.0 # 11 35 # 1.0 -1.0 0.0 # 18 36 # 1.0 -1.0 0.0 # 10 37 # 1.0 -1.0 0.0 # 16 38 # 1.0 -1.0 0.0 # 17 39 # 1.0 -1.0 0.0 sur(create) 4 # 1 r1 # 2 r2 # 3 r3 # 4 r4 Chi-Squared(18)= 555.352101 or F(18,*)= 30.85289 with Significance Level 0.00000000 Linear Systems - Estimation by Seemingly Unrelated Regressions Annual Data From 1947:01 To 1971:01 Usable Observations 25 Log Likelihood 446.29442 Dependent Variable SK Mean of Dependent Variable 0.0534882129 Std Error of Dependent Variable 0.0044804570 Standard Error of Estimate 0.0020730804 Sum of Squared Residuals 0.0001074416 Durbin-Watson Statistic 0.731855 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 1. Constant 0.053424033 0.000374509 142.65079 0.00000000 2. TREND 0.001301178 0.000320473 4.06018 0.00004903 3. LQY -0.040902269 0.006578183 -6.21787 0.00000000 4. LPK 0.035401949 0.004109972 8.61367 0.00000000 5. LPL 0.008109458 0.008850124 0.91631 0.35950426 6. LPE -0.007226044 0.001701898 -4.24587 0.00002177 Dependent Variable SL Mean of Dependent Variable 0.2744612933 Std Error of Dependent Variable 0.0128772782 Standard Error of Estimate 0.0046712972 Sum of Squared Residuals 0.0005455254 Durbin-Watson Statistic 1.982096 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 7. Constant 0.274387980 0.000907729 302.27955 0.00000000 8. TREND 0.000044930 0.001163830 0.03861 0.96920510 9. LQY -0.028228703 0.016107902 -1.75248 0.07969209 10. LPK 0.008109458 0.008850124 0.91631 0.35950426 11. LPL 0.124671020 0.045822670 2.72073 0.00651383 12. LPE 0.010328094 0.009824054 1.05131 0.29311771 Dependent Variable SE Mean of Dependent Variable 0.0448202036 Std Error of Dependent Variable 0.0031049179 Standard Error of Estimate 0.0008415910 Sum of Squared Residuals 0.0000177069 Durbin-Watson Statistic 1.257588 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 13. Constant 0.044804456 0.000159556 280.80746 0.00000000 14. TREND 0.000730681 0.000224504 3.25464 0.00113534 15. LQY -0.028918443 0.003059305 -9.45262 0.00000000 16. LPK -0.007226044 0.001701898 -4.24587 0.00002177 17. LPL 0.010328094 0.009824054 1.05131 0.29311771 18. LPE 0.014337775 0.005091080 2.81625 0.00485872 Dependent Variable LC Mean of Dependent Variable -0.000000000 Std Error of Dependent Variable 0.276017871 Standard Error of Estimate 0.010324045 Sum of Squared Residuals 0.0026646474 Durbin-Watson Statistic 0.941040 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 19. Constant -0.003428305 0.000850348 -4.03165 0.00005539 20. TREND 0.001399572 0.000319013 4.38719 0.00001148 21. LQY 0.782700963 0.008186428 95.60958 0.00000000 22. LPK 0.053424033 0.000374509 142.65078 0.00000000 23. LPL 0.274387980 0.000907729 302.27947 0.00000000 24. LPE 0.044804456 0.000159556 280.80724 0.00000000 25. TT 0.001586918 0.000416404 3.81100 0.00013840 26. TLQY -0.030325657 0.010581320 -2.86596 0.00415745 27. TLPK 0.001301178 0.000320473 4.06018 0.00004903 28. TLPL 0.000044930 0.001163830 0.03861 0.96920510 29. TLPE 0.000730681 0.000224507 3.25461 0.00113549 30. LQYLQY 0.549903326 0.274931843 2.00014 0.04548470 31. LQYLPK -0.040902269 0.006578186 -6.21786 0.00000000 32. LQYLPL -0.028228703 0.016107902 -1.75248 0.07969209 33. LQYLPE -0.028918443 0.003059305 -9.45262 0.00000000 34. LPKLPK 0.035401949 0.004109974 8.61367 0.00000000 35. LPLLPL 0.124671020 0.045822666 2.72073 0.00651383 36. LPELPE 0.014337777 0.005091816 2.81585 0.00486488 37. LPKLPL 0.008109458 0.008850121 0.91631 0.35950413 38. LPKLPE -0.007226044 0.001701898 -4.24587 0.00002177 39. LPLLPE 0.010328094 0.009824221 1.05129 0.29312593 Covariance\Correlation Matrix of Residuals SK SL SE LC SK 4.297662e-06 0.2746148163 0.5615434265 0.3045886743 SL 2.659363e-06 2.182102e-05 0.3877998740 -0.0001705204 SE 9.797169e-07 1.524566e-06 7.082755e-07 0.2020616202 LC 6.518982e-06 -8.223635e-09 1.755637e-06 0.000107 mat beta=%beta eval hkk = (beta(1)*beta(1)-beta(1)+beta(4))/beta(1) eval hll = (beta(7)*beta(7)-beta(7)+beta(11))/beta(7) eval hee = (beta(13)*beta(13)-beta(13)+beta(18))/beta(13) eval hmm = ((1-beta(1)-beta(7)-beta(13))*(1-beta(1)-beta(7)-beta(13))-(1-beta(1)-beta(7)-beta(13))+beta(4)+beta(5)+beta(6)+beta(10)+beta(11)+beta(12)+beta(16)+beta(17)+beta(18))/(1-beta(1)-beta(7)-beta(13)) eval hkl = (beta(1)*beta(7)+beta(5))/beta(1) eval hke = (beta(1)*beta(13)+beta(6))/beta(1) eval hkm = (beta(1)*(1-beta(1)-beta(7)-beta(13))-beta(4)-beta(5)-beta(6))/beta(1) eval hlk = (beta(7)*beta(1)+beta(10))/beta(7) eval hle = (beta(7)*beta(13)+beta(12))/beta(7) eval hlm = (beta(7)*(1-beta(1)-beta(7)-beta(13))-beta(10)-beta(11)-beta(12))/beta(7) eval hek = (beta(13)*beta(1)+beta(16))/beta(13) eval hel = (beta(13)*beta(7)+beta(17))/beta(13) eval hem = (beta(13)*(1-beta(1)-beta(7)-beta(13))-beta(16)-beta(17)-beta(18))/beta(13) eval hmk = ((1-beta(1)-beta(7)-beta(13))*beta(1)-beta(4)-beta(5)-beta(6))/(1-beta(1)-beta(7)-beta(13)) eval hml = ((1-beta(1)-beta(7)-beta(13))*beta(7)-beta(10)-beta(11)-beta(12))/(1-beta(1)-beta(7)-beta(13)) eval hme = ((1-beta(1)-beta(7)-beta(13))*beta(13)-beta(16)-beta(17)-beta(18))/(1-beta(1)-beta(7)-beta(13)) eval akk = hkk/beta(1) eval all = hll/beta(7) eval aee = hee/beta(13) eval amm = hmm/(1-beta(1)-beta(7)-beta(13)) eval akl = hkl/beta(7) eval ake = hke/beta(13) eval akm = hkm/(1-beta(1)-beta(7)-beta(13)) eval alk = hlk/beta(1) eval ale = hle/beta(13) eval alm = hlm/(1-beta(1)-beta(7)-beta(13)) eval aek = hek/beta(1) eval ael = hel/beta(7) eval aem = hem/(1-beta(1)-beta(7)-beta(13)) eval amk = hmk/beta(1) eval aml = hml/beta(7) eval ame = hme/beta(13) dis akl dis ake dis akm dis alk dis ale dis alm dis aek dis ael dis aem dis amk dis aml dis ame 1.55321 -2.01886 -0.08258 1.55321 1.84011 0.16868 -2.01886 1.84011 0.37958 -0.08258 0.16868 0.37958 * Morishima Elasticity of Substitution eval mem = hme-hee eval mel = hle-hee eval mek = hke-hee eval mme = hem-hmm eval mml = hlm-hmm eval mmk = hkm-hmm eval mle = hel-hll eval mlm = hml-hll eval mlk = hkl-hll eval mke = hek-hkk eval mkm = hmk-hkk eval mkl = hlk-hkk dis mkl dis mke dis mkm dis mlk dis mle dis mlm dis mek dis mel dis mem dis mmk dis mml dis mme 0.36690 0.17606 0.27950 0.69743 0.77615 0.31754 0.54473 0.71763 0.65219 0.00707 0.16471 0.29702 * Shadow Elasticity eval skl = (-akk+2*akl-all)/((1/beta(1))+(1/beta(7))) eval ske = (-akk+2*ake-aee)/((1/beta(1))+(1/beta(13))) eval skm = (-akk+2*akm-amm)/((1/beta(1))+(1/(1-beta(1)-beta(7)-beta(13)))) eval slk = (-all+2*alk-akk)/((1/beta(7))+(1/beta(1))) eval sle = (-all+2*ale-aee)/((1/beta(7))+(1/beta(13))) eval slm = (-all+2*alm-amm)/((1/beta(7))+(1/(1-beta(1)-beta(7)-beta(13)))) eval sek = (-aee+2*aek-akk)/((1/beta(13))+(1/beta(1))) eval sel = (-aee+2*ael-all)/((1/beta(13))+(1/beta(7))) eval sem = (-aee+2*aem-amm)/((1/beta(13))+(1/(1-beta(1)-beta(7)-beta(13)))) eval smk = (-amm+2*amk-akk)/((1/(1-beta(1)-beta(7)-beta(13)))+(1/beta(1))) eval sml = (-amm+2*aml-all)/((1/(1-beta(1)-beta(7)-beta(13)))+(1/beta(7))) eval sme = (-amm+2*ame-aee)/((1/(1-beta(1)-beta(7)-beta(13)))+(1/beta(13))) dis skl dis ske dis skm dis slk dis sle dis slm dis sek dis sel dis sem dis smk dis sml dis sme 0.42076 0.37657 0.25813 0.42076 0.72585 0.27103 0.37657 0.72585 0.62852 0.25813 0.27103 0.62852 * Antonelli Elasticity of Complementarity dec symm aes(5,5) aec(5,5) shares(5,5) mat aes=%const(0) eval aes(1,1)=akk eval aes(2,1)=akl eval aes(2,2)=all eval aes(3,1)=ake eval aes(3,2)=ale eval aes(3,3)=aee eval aes(4,1)=amk eval aes(4,2)=aml eval aes(4,3)=ame eval aes(4,4)=amm do in=1,4 eval aes(5,in)=1 end do in mat shares=%const(0) eval shares(1,1)=beta(1) eval shares(2,2)=beta(7) eval shares(3,3)=beta(13) eval shares(4,4)=1-beta(1)-beta(7)-beta(13) eval shares(5,5)=1 mat aec=inv(shares*aes*shares) dis aec(2,1) dis aec(3,1) dis aec(4,1) dis aec(2,1) dis aec(3,2) dis aec(4,2) dis aec(3,1) dis aec(3,2) dis aec(4,3) dis aec(4,1) dis aec(4,2) dis aec(4,3) -15.99885 9.80208 14.14196 -15.99885 -3.19362 7.19208 9.80208 -3.19362 3.17416 14.14196 7.19208 3.17416 * Hicks Elasticity of Substitution eval skl = (-aec(1,1)+2*aec(2,1)-aec(2,2))*beta(1)*beta(7)/(beta(1)+beta(7)) eval ske = (-aec(1,1)+2*aec(3,1)-aec(3,3))*beta(1)*beta(13)/(beta(1)+beta(13)) eval skm = (-aec(1,1)+2*aec(1,4)-aec(4,4))*beta(1)*(1-beta(1)-beta(7)-beta(13))/(beta(1)+(1-beta(1)-beta(7)-beta(13))) eval slk = (-aec(2,2)+2*aec(2,1)-aec(1,1))*beta(7)*beta(1)/(beta(7)+beta(1)) eval sle = (-aec(2,2)+2*aec(2,3)-aec(3,3))*beta(7)*beta(13)/(beta(7)+beta(13)) eval slm = (-aec(2,2)+2*aec(2,4)-aec(4,4))*beta(7)*(1-beta(1)-beta(7)-beta(13))/(beta(7)+(1-beta(1)-beta(7)-beta(13))) eval sek = (-aee+2*aec(3,1)-aec(1,1))*beta(13)*beta(1)/(beta(13)+beta(1)) eval sel = (-aec(3,3)+2*aec(2,3)-aec(2,2))*beta(13)*beta(7)/(beta(13)+beta(7)) eval sem = (-aec(3,3)+2*aec(3,4)-aec(4,4))*beta(13)*(1-beta(1)-beta(7)-beta(13))/(beta(13)+(1-beta(1)-beta(7)-beta(13))) eval smk = (-aec(4,4)+2*aec(1,4)-aec(1,1))*(1-beta(1)-beta(7)-beta(13))*beta(1)/((1-beta(1)-beta(7)-beta(13))+beta(1)) eval sml = (-aec(4,4)+2*aec(2,4)-aec(2,2))*(1-beta(1)-beta(7)-beta(13))*beta(7)/((1-beta(1)-beta(7)-beta(13))+beta(7)) eval sme = (-aec(4,4)+2*aec(3,4)-aec(3,3))*(1-beta(1)-beta(7)-beta(13))*beta(13)/((1-beta(1)-beta(7)-beta(13))+beta(13)) dis skl dis ske dis skm dis slk dis sle dis slm dis sek dis sel dis sem dis smk dis sml dis sme 3.26151 3.61393 6.15328 3.26151 1.65606 6.06458 3.06810 1.65606 1.98641 6.15328 6.06458 1.98641 * Morishima Elasticity of Complementarity eval hkk=aec(1,1)*beta(1) eval hll=aec(2,2)*beta(7) eval hee=aec(3,3)*beta(13) eval hmm=aec(4,4)*(1-beta(1)-beta(7)-beta(13)) eval hkl=aec(1,2)*beta(7) eval hke=aec(1,3)*beta(13) eval hkm=aec(1,4)*(1-beta(1)-beta(7)-beta(13)) eval hlk=aec(2,1)*beta(1) eval hle=aec(2,3)*beta(13) eval hlm=aec(2,4)*(1-beta(1)-beta(7)-beta(13)) eval hek=aec(3,1)*beta(1) eval hel=aec(3,2)*beta(7) eval hem=aec(3,4)*(1-beta(1)-beta(7)-beta(13)) eval hmk=aec(4,1)*beta(1) eval hml=aec(4,2)*beta(7) eval hme=aec(4,3)*beta(13) eval mem = hme-hee eval mel = hle-hee eval mek = hke-hee eval mme = hem-hmm eval mml = hlm-hmm eval mmk = hkm-hmm eval mle = hel-hll eval mlm = hml-hll eval mlk = hkl-hll eval mke = hek-hkk eval mkm = hmk-hkk eval mkl = hlk-hkk dis mkl dis mke dis mkm dis mlk dis mle dis mlm dis mek dis mel dis mem dis mmk dis mml dis mme 4.06700 5.44539 5.67724 -0.87551 2.63809 5.48780 2.07797 1.49570 1.78101 11.74359 7.38335 4.86258 * Hicks Elasticity of Complementarity dec symm sigma(5,5) hec(4,4) dec vec sharesv(4) eval aes(5,1)=beta(21)+beta(31)/beta(1) eval aes(5,2)=beta(21)+beta(32)/beta(7) eval aes(5,3)=beta(21)+beta(33)/beta(13) eval aes(5,4)=beta(21)+(-beta(31)-beta(32)-beta(33))/(1-beta(1)-beta(7)-beta(13)) eigen aes va ma mat sigma=ma*inv(%diag(va))*tr(ma) eval sharesv(1)=beta(1) eval sharesv(2)=beta(7) eval sharesv(3)=beta(13) eval sharesv(4)=1-beta(1)-beta(7)-beta(13) eval dlnmcdlny=-1+beta(21)+beta(30)/beta(21) eval rts=1/(beta(1)*aes(5,1)+beta(7)*aes(5,2)+beta(13)*aes(5,3)+(1-beta(1)-beta(7)-beta(13))*aes(5,4)) eval hec(1,1)=sigma(1,1)/(sharesv(1)*sharesv(1))-dlnmcdlny eval hec(2,1)=sigma(2,1)/(sharesv(2)*sharesv(1))-dlnmcdlny eval hec(2,2)=sigma(2,2)/(sharesv(2)*sharesv(2))-dlnmcdlny eval hec(3,1)=sigma(3,1)/(sharesv(3)*sharesv(1))-dlnmcdlny eval hec(3,2)=sigma(3,2)/(sharesv(3)*sharesv(2))-dlnmcdlny eval hec(3,3)=sigma(3,3)/(sharesv(3)*sharesv(3))-dlnmcdlny eval hec(4,1)=sigma(4,1)/(sharesv(4)*sharesv(1))-dlnmcdlny eval hec(4,2)=sigma(4,2)/(sharesv(4)*sharesv(2))-dlnmcdlny eval hec(4,3)=sigma(4,3)/(sharesv(4)*sharesv(3))-dlnmcdlny eval hec(4,4)=sigma(4,4)/(sharesv(4)*sharesv(4))-dlnmcdlny dis hec(2,1) dis hec(3,1) dis hec(4,1) dis hec(2,1) dis hec(3,2) dis hec(4,2) dis hec(3,1) dis hec(3,2) dis hec(4,3) dis hec(4,1) dis hec(4,2) dis hec(4,3) -26.30227 0.46364 7.84448 -26.30227 -8.04829 5.37836 0.46364 -8.04829 2.32542 7.84448 5.37836 2.32542 * Pigou Elasticity of Complementarity eval hkk=hec(1,1)*beta(1)*rts eval hll=hec(2,2)*beta(7)*rts eval hee=hec(3,3)*beta(13)*rts eval hmm=hec(4,4)*(1-beta(1)-beta(7)-beta(13))*rts eval hkl=hec(1,2)*beta(7)*rts eval hke=hec(1,3)*beta(13)*rts eval hkm=hec(1,4)*(1-beta(1)-beta(7)-beta(13))*rts eval hlk=hec(2,1)*beta(1)*rts eval hle=hec(2,3)*beta(13)*rts eval hlm=hec(2,4)*(1-beta(1)-beta(7)-beta(13))*rts eval hek=hec(3,1)*beta(1)*rts eval hel=hec(3,2)*beta(7)*rts eval hem=hec(3,4)*(1-beta(1)-beta(7)-beta(13))*rts eval hmk=hec(4,1)*beta(1)*rts eval hml=hec(4,2)*beta(7)*rts eval hme=hec(4,3)*beta(13)*rts eval mem = hme-hee eval mel = hle-hee eval mek = hke-hee eval mme = hem-hmm eval mml = hlm-hmm eval mmk = hkm-hmm eval mle = hel-hll eval mlm = hml-hll eval mlk = hkl-hll eval mke = hek-hkk eval mkm = hmk-hkk eval mkl = hlk-hkk dis mkl dis mke dis mkm dis mlk dis mle dis mlm dis mek dis mel dis mem dis mmk dis mml dis mme 5.50215 7.32908 7.83287 -2.69043 3.70879 8.41571 2.34297 1.85571 2.44954 8.19892 6.22217 3.77505 * Hotelling-Lau ES dec symm hles(4,4) do in=1,4 do jn=1,in eval hles(in,jn)=(beta(21)-1)*(aes(in,jn)-aes(5,in)*aes(5,jn)/(beta(21)*dlnmcdlny)) end do jn end do in dis hles(2,1) dis hles(3,1) dis hles(4,1) dis hles(2,1) dis hles(3,2) dis hles(4,2) dis hles(3,1) dis hles(3,2) dis hles(4,3) dis hles(4,1) dis hles(4,2) dis hles(4,3) -0.33087 0.44004 0.02712 -0.33087 -0.34647 0.32854 0.44004 -0.34647 -0.00874 0.02712 0.32854 -0.00874 * FRES eval hkk=hles(1,1)*beta(1) eval hll=hles(2,2)*beta(7) eval hee=hles(3,3)*beta(13) eval hmm=hles(4,4)*(1-beta(1)-beta(7)-beta(13)) eval hkl=hles(1,2)*beta(7) eval hke=hles(1,3)*beta(13) eval hkm=hles(1,4)*(1-beta(1)-beta(7)-beta(13)) eval hlk=hles(2,1)*beta(1) eval hle=hles(2,3)*beta(13) eval hlm=hles(2,4)*(1-beta(1)-beta(7)-beta(13)) eval hek=hles(3,1)*beta(1) eval hel=hles(3,2)*beta(7) eval hem=hles(3,4)*(1-beta(1)-beta(7)-beta(13)) eval hmk=hles(4,1)*beta(1) eval hml=hles(4,2)*beta(7) eval hme=hles(4,3)*beta(13) eval mem = hme-hee eval mel = hle-hee eval mek = hke-hee eval mme = hem-hmm eval mml = hlm-hmm eval mmk = hkm-hmm eval mle = hel-hll eval mlm = hml-hll eval mlk = hkl-hll eval mke = hek-hkk eval mkm = hmk-hkk eval mkl = hlk-hkk dis mkl dis mke dis mkm dis mlk dis mle dis mlm dis mek dis mel dis mem dis mmk dis mml dis mme -0.07938 -0.03820 -0.06025 -0.22228 -0.22656 -0.04134 -0.11879 -0.15403 -0.13890 -0.31224 -0.12314 -0.33475 wr