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From |
"Pavlos C. Symeou" <[email protected]> |

To |
[email protected] |

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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