Lectures in Applied Econometrics 11

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Transcript of Lectures in Applied Econometrics 11

7

11.

11.

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1948-1994, 47 .

L PL PK INTM PINTM 1

2

TC = PL*L + PK*K + PINTM*INTM ( )

. .

:, :, COBB & DOUGLASLTC=B0+B1*LPL+B2*LPK+B3*LPINTM+B4*LY1+B5*LY2+B6*T

L .

:

1, 2, 3, 4, 5 > 0

1 + 2 + 3 = 1

= 4 + 5 = = 6 = :GENR TC=PL*L+PK*K+PINTM*INTM

GENR LTC=LOG(TC)

GENR TREND=YEAR-1947

SHOW TREND

GENR LTC1=LOG(TC/PINTM)

GENR LPL1=LOG(PL/PINTM)

GENR LPK1=LOG(PK/PINTM)

GENR LY1=LOG(Y1)

GENR LY2=LOG(Y2)

PLOT LY1 LY2

GENR LPL=LOG(PL)

GENR LPK=LOG(PK)

GENR LPINTM=LOG(PINTM)

LS LTC C LPL LPK LPINTM LY1 LY2 TREND

.Dependent Variable: LTC

Method: Least Squares

Sample: 1948 1994

Included observations: 47

VariableCoefficientStd. Errort-StatisticProb.

C-1.573215 0.367905-4.276139 0.0001

LPL 0.346870 0.053620 6.469015 0.0000

LPK 0.403960 0.013506 29.91007 0.0000

LPINTM 0.653860 0.049561 13.19296 0.0000

LY1-0.049945 0.052259-0.955714 0.3450

LY2 0.568832 0.184039 3.090818 0.0036

TREND-0.030114 0.005022-5.996204 0.0000

R-squared 0.999138 Mean dependent var 11.27868

Adjusted R-squared 0.999008 S.D. dependent var 0.740460

S.E. of regression 0.023318 Akaike info criterion-4.542576

Sum squared resid 0.021749 Schwarz criterion-4.267022

Log likelihood 113.7505 F-statistic 7724.171

Durbin-Watson stat 1.458718 Prob(F-statistic) 0.000000

Dependent Variable: LTC1

Method: Least Squares

Sample: 1948 1994

Included observations: 47

VariableCoefficientStd. Errort-StatisticProb.

C-0.203740 0.326916-0.623218 0.5366

LPL1 0.135304 0.044400 3.047419 0.0040

LPK1 0.395888 0.017132 23.10794 0.0000

LY1 0.152012 0.044469 3.418336 0.0014

LY2 0.249888 0.221494 1.128196 0.2658

TREND-0.010779 0.004294-2.510432 0.0161

R-squared 0.985936 Mean dependent var 0.646683

Adjusted R-squared 0.984221 S.D. dependent var 0.237056

S.E. of regression 0.029778 Akaike info criterion-4.071380

Sum squared resid 0.036355 Schwarz criterion-3.835190

Log likelihood 101.6774 F-statistic 574.8585

Durbin-Watson stat 0.727376 Prob(F-statistic) 0.000000

SSR unrestricted 0.021749

SSR restricted 0.036355

J = 1

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95% ( ) 4.08

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R2 .

1.40 , , . .

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Equation: Untitled

Null Hypothesis:C(2)+C(3)+C(4)=1

F-statistic 26.86191Probability 0.000007

Chi-square 26.86191Probability 0.000000

. AR(2) .

Dependent Variable: LTC

Method: Least Squares

Sample(adjusted): 1950 1994

Included observations: 45 after adjusting endpoints

Convergence achieved after 28 iterations

VariableCoefficientStd. Errort-StatisticProb.

C-0.684450 0.546698-1.251971 0.2187

LPL 0.227770 0.055256 4.122109 0.0002

LPK 0.377345 0.030477 12.38114 0.0000

LPINTM 0.552812 0.052693 10.49113 0.0000

LY1 0.049225 0.050822 0.968578 0.3392

LY2 0.033374 0.183285 0.182087 0.8565

TREND-0.012766 0.004900-2.605373 0.0133

AR(1) 0.733566 0.177447 4.134001 0.0002

AR(2)-0.045285 0.143578-0.315402 0.7543

R-squared 0.999428 Mean dependent var 11.32050

Adjusted R-squared 0.999301 S.D. dependent var 0.728809

S.E. of regression 0.019264 Akaike info criterion-4.884284

Sum squared resid 0.013360 Schwarz criterion-4.522951

Log likelihood 118.8964 F-statistic 7867.594

Durbin-Watson stat 1.882320 Prob(F-statistic) 0.000000

Inverted AR Roots .67 .07

Wald Test:

Equation: Untitled

Null Hypothesis:C(2)+C(3)+C(4)=1

F-statistic 3.269573Probability 0.078936

Chi-square 3.269573Probability 0.070576

5%.

Berndt, E. R., 1991, The practice of econometrics: Classic and contemporary, Addison-Wesley. 9, . translog, Leontief .

Kumbhakar, S. C., and C. A. K. Lovell, 2000, Stochastic frontier analysis, Cambridge, Cambridge University Press. . , . . 78. , . . 75.

Kumbhakar, S. C. and E. G. Tsionas, 2005, Measuring Technical and Allocative Inefficiency in the Translog Cost System: a Bayesian Approach, Journal of Econometrics 126, 355-384.

L=wx+[y-f(x)] L=wx+[f(x)-y]. f(x).

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