It has a been a while since I have posted. During that period I was working on my partial treatise draft, which I handed in on Friday and obtaining some preliminary results. In the partial treatise draft I had completed the introduction and motivation, literature review and methodology chapters. I had also presented some details on the data collection and some preliminary results. The first three chapters are no means complete and I will be refining them further along the weeks incorporating in the comments that I obtain from Dr.Poon.
Since the partial draft I have been further working on my results. The preliminary results which I have obtained so far are attached below. They include an estimation of the translog model for the 1981-2002 period and 1989-2002 period as well as the AES obtained for both periods.
Regression Results of Translog 1981-2002
Coefficients | Estimate | Std. Error | t value | Pr(>|t|) |
β_{o} | 1.935069 | 4.095545 | 0.472482 | 0.637037 |
β_{SK} | -3.59742 | 0.601137 | -5.98435 | 8.40E-09 |
β_{HK} | 3.196295 | 0.540743 | 5.910936 | 1.24E-08 |
β_{OK} | -3.08555 | 0.595171 | -5.18431 | 4.79E-07 |
β_{L} | 4.412228 | 0.777771 | 5.672913 | 4.25E-08 |
β_{SKHK} | -0.07981 | 0.056434 | -1.41422 | 0.158668 |
β_{SKOK} | 0.29958 | 0.052916 | 5.661461 | 4.51E-08 |
β_{SKL} | 0.040585 | 0.030756 | 1.319565 | 0.18831 |
β_{KHOK} | -0.25008 | 0.043943 | -5.69116 | 3.87E-08 |
β_{HKL} | -0.0316 | 0.026971 | -1.17163 | 0.242572 |
β_{OKL} | -0.36169 | 0.038045 | -9.50682 | 2.96E-18 |
β_{SKSK} | 0.056274 | 0.028064 | 2.005184 | 0.046131 |
β_{HKHK} | 0.039415 | 0.030344 | 1.29895 | 0.195279 |
β_{OKOK} | 0.304332 | 0.038915 | 7.82046 | 1.97E-13 |
β_{LL} | -0.00655 | 0.027073 | -0.24209 | 0.808926 |
T_{1982} | -0.07036 | 0.083668 | -0.841 | 0.401232 |
T_{1983} | -0.18504 | 0.088161 | -2.09891 | 0.03693 |
T_{1984} | -0.23224 | 0.094434 | -2.45932 | 0.014667 |
T_{1985} | -0.2968 | 0.101679 | -2.91895 | 0.003866 |
T_{1986} | -0.40875 | 0.108416 | -3.7702 | 0.000208 |
T_{1987} | -0.55139 | 0.11776 | -4.68233 | 4.88E-06 |
T_{1988} | -0.64727 | 0.124346 | -5.20538 | 4.33E-07 |
T_{1989} | -0.73405 | 0.127711 | -5.74775 | 2.90E-08 |
T_{1990} | -0.8428 | 0.132905 | -6.3414 | 1.22E-09 |
T_{1991} | -0.94061 | 0.136498 | -6.89099 | 5.40E-11 |
T_{1992} | -1.02249 | 0.139904 | -7.30853 | 4.56E-12 |
T_{1993} | -1.06997 | 0.142023 | -7.53379 | 1.16E-12 |
T_{1994} | -1.10585 | 0.143281 | -7.71804 | 3.73E-13 |
T_{1995} | -1.13752 | 0.143058 | -7.95148 | 8.63E-14 |
T_{1996} | -1.1319 | 0.143119 | -7.90879 | 1.13E-13 |
T_{1997} | -1.15017 | 0.143922 | -7.99162 | 6.70E-14 |
T_{1998} | -1.1646 | 0.146581 | -7.94509 | 8.99E-14 |
T_{1999} | -1.20425 | 0.150877 | -7.98168 | 7.13E-14 |
T_{2000} | -1.28412 | 0.158085 | -8.12293 | 2.91E-14 |
T_{2001} | -1.37719 | 0.162579 | -8.47092 | 3.07E-15 |
T_{2002} | -1.41934 | 0.167084 | -8.49475 | 2.63E-15 |
I_{service} | 0.515471 | 0.038752 | 13.30167 | 3.11E-30 |
AES for 1981-2002
| σ^{SKHK } | σ^{SKKO} | σ^{SKL} | σ^{HKOK} | σ^{HKL} | σ^{OKL} |
Mean value | 0.098557 | 0.6739457 | ^{1.209937} | ^{1.209937} | ^{-3.77287} | -0.281779 |
p-value | 0.4502 | ^{0.07933} | ^{0.3311} | ^{0.1038} | ^{0.1031} | 0.4289 |
Regression Results of Translog 1989-2002
Coefficients | Estimate | Std. Error | t value | Pr(>|t|) |
β_{o} | -2.76934 | 3.496849 | -0.79195 | 0.429738 |
β_{SK} | -4.91899 | 0.733963 | -6.70197 | 4.73E-10 |
β_{HK} | 3.282922 | 0.436596 | 7.519358 | 6.17E-12 |
β_{OK} | -3.70208 | 0.628954 | -5.8861 | 2.82E-08 |
β_{L} | 6.466395 | 0.809478 | 7.988354 | 4.68E-13 |
β_{SKHK} | 0.254486 | 0.070287 | 3.620682 | 0.000411 |
β_{SKOK} | 0.317701 | 0.061771 | 5.143242 | 9.01E-07 |
β_{SKL} | 0.29704 | 0.043638 | 6.806945 | 2.74E-10 |
β_{KHOK} | -0.22608 | 0.03697 | -6.11539 | 9.20E-09 |
β_{HKL} | -0.16539 | 0.029004 | -5.7024 | 6.82E-08 |
β_{OKL} | -0.37694 | 0.041219 | -9.14489 | 6.61E-16 |
β_{SKSK} | -0.21684 | 0.04987 | -4.34821 | 2.64E-05 |
β_{HKHK} | -0.05881 | 0.027685 | -2.12441 | 0.035406 |
β_{OKOK} | 0.33207 | 0.042761 | 7.765808 | 1.60E-12 |
β_{LL} | -0.13565 | 0.023766 | -5.70765 | 6.65E-08 |
T_{1990} | -0.13121 | 0.047436 | -2.76602 | 0.006446 |
T_{1991} | -0.24256 | 0.049593 | -4.89092 | 2.74E-06 |
T_{1992} | -0.32922 | 0.052037 | -6.32657 | 3.21E-09 |
T_{1993} | -0.36548 | 0.053528 | -6.82791 | 2.46E-10 |
T_{1994} | -0.38471 | 0.054356 | -7.07753 | 6.62E-11 |
T_{1995} | -0.39591 | 0.054812 | -7.22317 | 3.05E-11 |
T_{1996} | -0.37964 | 0.055736 | -6.81141 | 2.68E-10 |
T_{1997} | -0.37973 | 0.057315 | -6.6253 | 7.03E-10 |
T_{1998} | -0.36279 | 0.060596 | -5.98709 | 1.73E-08 |
T_{1999} | -0.39968 | 0.064078 | -6.23743 | 5.02E-09 |
T_{2000} | -0.46585 | 0.070161 | -6.6397 | 6.53E-10 |
T_{2001} | -0.57207 | 0.072914 | -7.84578 | 1.03E-12 |
T_{2002} | -0.61339 | 0.076199 | -8.0499 | 3.33E-13 |
I_{service} | 0.508949 | 0.030608 | 16.62825 | 7.34E-35 |
AES for 1989-2002
| σ^{SKHK } | σ^{SKKO} | σ^{SKL} | σ^{HKOK} | σ^{HKL} | σ^{OKL} |
Mean value | ^{-5.033649} | ^{-1.590819} | ^{4.832529} | ^{-11.34981} | ^{21.34182} | ^{4.966173} |
p-value | ^{0.2039} | ^{0.1658} | ^{0.04353} | ^{0.1566} | ^{0.1376} | ^{0.1783} |
Two different time periods have been used since an accurate deflator for the data from 1981-1989 could not be obtained form the ABS. Since we had to estimate these numbers there is a strong possibility that we will introduce significant measurement error into the model. Since the data set being used in a panel data set i.e. a cross section of industries observed across time, the measurement error is attenuated in the model. Consequently our parameter estimates will be biased, inconsistent and inefficient and any inferences drawn about them will be invalid.
Dr.Poon has also asked me to estimate the translog model using random effects. The purpose of this is to check whether the fixed effect model we are currently using is a suitable choice via a statistical test called the Hausman test. However, this is not possible since we need to obtain the between estimator. The between estimator measures the variability between different industries. Since we are estimating 14 parameters but only have 12 industries we cannot obtain the between estimator. I have emailed Dr.Poon about this and am awaiting his reply as to how he would like me to proceed regarding this.
Dr.Poon has also asked me if could try and estimate another model called the Constant Elasticity of Substitution (CES) model using the Eview software package. The results of this model will then be compared to the translog model. I have tried to estimate this model but once again come across problems. The error that was being generated was that a near singular matrix was formed. This means that there is collinearity present and that there the regressors are dependent. I suspect that this is due to the high correlation between the Hardware Capital and Software Capital in excess of 85%. I have emailed Dr.Poon about this and am awaiting his reply.
I am also researching testing for aggregation error. My treatise is not just focused on testing the complementarity between Software Capital and other production inputs but also testing whether Software Capital and Hardware Capital can be aggregated into a single IT measure. The argument is that if these two production inputs are not perfect substitutes they cannot be aggregated into one measure since we will be omitting the complementarity that they add to business value. Dr.Poon has provided me with the following readings to review:
- McGukin, R. H. and Stiroh, K. J. (2002) Economic Enquiry, 40, 42-59.
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