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st: Test for the difference in the coefficients of two models that usedifferent samples - Stochastic Frontier Analysis


From   "Pavlos C. Symeou" <p.symeou@jbs.cam.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   st: Test for the difference in the coefficients of two models that usedifferent samples - Stochastic Frontier Analysis
Date   Wed, 03 Oct 2007 11:44:03 +0100

Dear Statalisters,

I am conducting Stochastic Frontier Analysis using "Frontier 4.1", a software developed by Tim Coelli, instead of STATA because the latter still does not allow for the estimation of particular model specifications the former does. Frontier 4.1 is an unfriendly to use software (Dos-based) which allows various changes in the specification of a model, however, it produces limited information that conserves statistical inference and model testing flexibility. I am estimating a translog multi-input multi-output model based on Coelli (1995) according to which, the inefficiency term is attempted to be explained by a number of variables (Zs). I want to examine whether the size of the economy has an effect on the level of inefficiency that exists in the markets I examine (telecoms in particular). In addition, I am examining whether the existence of a Regulatory Authority and the Liberalization of the market affect the efficiency of the sector. Therefore, I include these three dummy variables (Smallness, it takes 1 if economy is small and 0 otherwise; NRA, it takes 1 if there is a Regulatory Authority and 0 otherwise; Liberalization, it takes 1 if the market is open and 0 otherwise) in the model. The estimates of this model are quite useful; however, I believe that estimating two distinct models (one using data for small economies only, and one using data for large economies only) will allow me to draw more specific conclusions for each group of economies and the impact that NRA and Liberalization have on each group's efficiency (another way to address this might be to include interaction variables between (Smallness and NRA) and (Smallness and Liberalization) but this could cause multicollinearity between the variables). Now, my problem is that, if I want to estimate two models using the two subsamples I am not able to compare the statistical significance of the difference in the respective coefficients between the two models because Frontier 4.1's results are limited to each model's. Namely, even when the coefficients for each model are statistically different to zero I cannot imply that the coefficients for the same variables in the two models are not the same and then conclude that there are actually differences between small and large economies. A sample of the output for the two models that use different data is presented below. I need to know whether given the information below (basically the only useful information one can get from Frontier 4.1's output) someone can built a statistical test to test statistical significance of the difference in the coefficients of the two models. Or maybe, someone knows another way to make statistical inference about the difference in the coefficients of two models that use different data.


Large Economies
Small Economies

betas SE t-ratio

betas SE t-ratio
Constant Deterministic -11.172 1.247 -8.960
Constant Deterministic -2.275 2.558 -0.889
time 0.216 0.111 1.944
time -0.040 0.213 -0.189
timeSQ 0.009 0.003 2.694
timeSQ 0.004 0.006 0.573
lny2star -0.660 0.181 -3.638
lny2star 0.317 0.288 1.102
lny3star -0.054 0.201 -0.271
lny3star -0.272 0.356 -0.762
lnx1 0.778 0.252 3.087
lnx1 0.528 0.431 1.226
lnx2 0.967 0.174 5.548
lnx2 0.174 0.232 0.749
tlnx1 0.034 0.013 2.549
tlnx1 0.045 0.020 2.205
tlnx2 -0.044 0.011 -4.209
tlnx2 -0.025 0.012 -2.130
tlny2star -0.013 0.009 -1.455
tlny2star -0.016 0.012 -1.295
tlny3star -0.001 0.010 -0.099
tlny3star 0.002 0.016 0.143
lny2starSQ -0.003 0.009 -0.378
lny2starSQ -0.008 0.012 -0.710
lny3starSQ -0.016 0.008 -1.913
lny3starSQ 0.004 0.014 0.282
lny2starBYlny3star 0.011 0.013 0.845
lny2starBYlny3star 0.011 0.024 0.457
lnx1SQ -0.038 0.018 -2.037
lnx1SQ -0.078 0.033 -2.387
lnx2SQ -0.011 0.007 -1.702
lnx2SQ -0.009 0.006 -1.445
lnx1BYlnx2 0.022 0.022 1.023
lnx1BYlnx2 0.078 0.022 3.576
lnx1BYlny2star 0.036 0.022 1.660
lnx1BYlny2star -0.024 0.026 -0.918
lnx1BYlny3star -0.073 0.019 -3.891
lnx1BYlny3star -0.069 0.032 -2.139
lnx2BYlny2star 0.024 0.015 1.639
lnx2BYlny2star -0.008 0.016 -0.484
lnx2BYlny3star 0.049 0.014 3.420
lnx2BYlny3star 0.069 0.022 3.113
Constant Stochastic 11.193 1.556 7.195
Constant Stochastic 3.379 0.767 4.404
lib_fixed -0.144 0.124 -1.161
lib_fixed 0.002 0.096 0.023
lib_internet 0.264 0.175 1.508
lib_internet 0.030 0.092 0.326
lib_mobile -0.914 0.178 -5.138
lib_mobile -0.216 0.089 -2.440
NRA 0.010 0.117 0.088
NRA 0.101 0.077 1.312
log_openness -0.141 0.128 -1.095
log_openness -0.435 0.077 -5.636
log_score -2.725 0.346 -7.879
log_score -0.252 0.179 -1.410
d_gdp_large -0.059 0.005 -11.194
d_pop -0.046 0.008 -5.926
d_pop_large 0.003 0.001 2.768
d_arable 0.000 0.000 4.080
d_arable_large 0.007 0.002 3.037
d_gdp 0.008 0.001 7.982
sigma-squared 0.967 0.090 10.778
sigma-squared 0.238 0.025 9.660
gamma 0.882 0.026 34.030
gamma 0.284 0.133 2.140









log likelihood function = -698.243


log likelihood function = -350.915










LR test of the one-sided error = 180.715


LR test of the one-sided error = 227.709










number of cross-sections = 84.000


number of cross-sections = 60.000










number of time periods = 15.000


number of time periods = 14.000










total number of observations = 927.000


total number of observations = 547.000










mean efficiency = 0.663


mean efficiency = 0.660




Yours truly,

Pavlos

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