Econometrics-I-9

# Erpzz mean of x constant 04186 00704 5949 0000 age

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| Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ |Constant| .04186*** .00704 5.949 .0000 | |AGE | .00030*** .919581D-04 3.209 .0013 43.5257| |EDUC | .01967*** .00045 44.180 .0000 11.3206| |MARRIED | .07947*** .00239 33.192 .0000 .75862| |WHITEC | .04819*** .00225 21.465 .0000 .29960| +--------+------------------------------------------------------------+ ™    10/27

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Part 9: Hypothesis Testing - 2 F Statistic for Chow Test --> Calc ; k = col(x) ; List; dfd = (tm + tf - 2*k) ; Chowtest = ((sall - sm - sf)/k) / ((sm+sf)/dfd) ; FCrit = Ftb(.95,k,dfd) \$ DFD = 27316.000000 CHOWTEST = 64.281630 FCRIT = 2.214100 ™    11/27
Part 9: Hypothesis Testing - 2 Use Dummy Variables ™    12/27

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Part 9: Hypothesis Testing - 2 Wald Test for Difference ™    13/27
Part 9: Hypothesis Testing - 2 Specification Test: Normality of p Specification test for distribution p Standard tests: n Kolmogorov-Smirnov: compare empirical cdf of X to normal with same mean and variance n Bowman-Shenton: Compare third and fourth moments of X to normal, 0 (no skewness) and 34 (meso kurtosis) p Bera-Jarque – adapted Bowman/Shenton to linear regression residuals ™    14/27

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Part 9: Hypothesis Testing - 2 Testing for Normality ™    15/27 2 1 1 3 2 4 2 3 4 Normality Test for Random Variable e ( ) ( ) s = , m , e = 0 for regression residuals ( / ) [( / ) 3] Chi-squared[2] = 6 20 n n j i i i i j e e e e n n m s m s = = - - = - +
Part 9: Hypothesis Testing - 2 The Stochastic Frontier Model              ui > 0, usually assumed to be |N[0,s ]|              vi may take any value.   symmetric  distribution,  such  as  the  normal  distribution, is usually assumed for vi. ™    16/27 ( ) ln + = + . i v i i i i i i i i i = f y e TE = + v u y + α - α x x x ε β β

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Part 9: Hypothesis Testing - 2 Application to Spanish Dairy Farms Input Units Mean Std. Dev. Minimum Maximum Milk Milk production (liters) 131,108 92,539 14,110 727,281 Cows # of milking cows 2.12 11.27 4.5 82.3 Labor # man-equivalent units 1.67 0.55 1.0 4.0 Land Hectares  of  land  devoted  to  pasture  and  crops. 12.99 6.17 2.0 45.1 Feed Total  amount  of  feedstuffs  fed  to  dairy  cows (tons) 57,941 47,981 3,924.1 4 376,732 N = 247 farms, T = 6 years (1993-1998) ™    17/27
Part 9: Hypothesis Testing - 2 Stochastic Frontier Model ™    18/27

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Part 9: Hypothesis Testing - 2 ™    19/27
Part 9: Hypothesis Testing - 2 ™    20/27

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Part 9: Hypothesis Testing - 2 Nonnested Regression Models p Davidson and MacKinnon: If model A is correct, then predictions from model B will not add to the fit of model A to the data.

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