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name: <unnamed>
log: /Users/baum/Documents/Courses 2009-2010/EC771 S2010/771reg.smcl
log type: smcl
opened on: 22 Jan 2010, 09:41:44
.
. // EC771reg cfb 0122
. // illustration of regression by OLS, MM, ML
.
. sysuse auto, clear
(1978 Automobile Data)
. g gpm = 1 / mpg
. replace weight = weight / 1000
weight was int now float
(74 real changes made)
.
. // solution by OLS regression
. regress gpm foreign weight
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 2, 71) = 113.97
Model | .009117618 2 .004558809 Prob > F = 0.0000
Residual | .00284001 71 .00004 R-squared = 0.7625
-------------+------------------------------ Adj R-squared = 0.7558
Total | .011957628 73 .000163803 Root MSE = .00632
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gpm | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
foreign | .0062205 .0019974 3.11 0.003 .0022379 .0102032
weight | .016254 .0011827 13.74 0.000 .0138958 .0186122
_cons | -.0007348 .0040199 -0.18 0.855 -.0087504 .0072807
------------------------------------------------------------------------------
. estat vce
Covariance matrix of coefficients of regress model
e(V) | foreign weight _cons
-------------+------------------------------------
foreign | 3.990e-06
weight | 1.400e-06 1.399e-06
_cons | -5.415e-06 -4.640e-06 .00001616
.
. // solution by method of moments
. // GMM criterion will be minimized to zero as the model
. // is exactly identified (3 moment conditions, 3 parameters)
. gmm (gpm - {xb:foreign weight} - {b0}), ///
> instruments(foreign weight) wmatrix(unadjusted) nolog
Final GMM criterion Q(b) = 4.70e-33
GMM estimation
Number of parameters = 3
Number of moments = 3
Initial weight matrix: Unadjusted Number of obs = 74
GMM weight matrix: Unadjusted
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| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/xb_foreign | .0062205 .0019565 3.18 0.001 .0023859 .0100552
/xb_weight | .016254 .0011585 14.03 0.000 .0139835 .0185245
/b0 | -.0007348 .0039376 -0.19 0.852 -.0084524 .0069827
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Instruments for equation 1: foreign weight _cons
. // note that the VCE estimates are large-sample
. // and thus do not agree with those of OLS
. estat vce
Covariance matrix of coefficients of gmm model
| xb_foreign | xb_weight | b0
e(V) | _cons | _cons | _cons
-------------+------------+------------+------------
xb_foreign | | |
_cons | 3.828e-06 | |
-------------+------------+------------+------------
xb_weight | | |
_cons | 1.344e-06 | 1.342e-06 |
-------------+------------+------------+------------
b0 | | |
_cons | -5.195e-06 | -4.452e-06 | .0000155
.
. // solution by maximum likelihood
. // For linear regression assuming normally distributed errors,
. // ln L = sum [ ln phi( (y_i - x_i b) / sigma ) - ln sigma ]
. // where phi( ) is the density of N(0, 1)
. // The three-parameter form of Stata's normalden(x, m, s) function
. // returns [ phi((x-m)/s) / s ], so we may call it directly
. // to evaluate the likelihood of each observation
. program drop _all
. program mynormalreg_lf
1. version 11
2. args lnf mu sigma
3. quietly replace `lnf' = ///
> ln(normalden( $ML_y1, `mu', `sigma' ) )
4. end
.
. ml model lf mynormalreg_lf (gpm = foreign weight) /sigma
. ml maximize, nolog
initial: log likelihood = -<inf> (could not be evaluated)
feasible: log likelihood = -46.676799
rescale: log likelihood = 168.74536
rescale eq: log likelihood = 192.31154
Number of obs = 74
Wald chi2(2) = 237.57
Log likelihood = 271.21503 Prob > chi2 = 0.0000
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gpm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
eq1 |
foreign | .0062205 .0019565 3.18 0.001 .0023859 .0100552
weight | .016254 .0011585 14.03 0.000 .0139835 .0185245
_cons | -.0007348 .0039376 -0.19 0.852 -.0084524 .0069827
-------------+----------------------------------------------------------------
sigma |
_cons | .006195 .0005092 12.17 0.000 .005197 .0071931
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. // estimate of /sigma may be compared with RMS Error from OLS
. // but degrees of freedom differ
. // note that the VCE estimates, based on /sigma, are large-sample
. estat vce
Covariance matrix of coefficients of ml model
| eq1 | sigma
e(V) | foreign weight _cons | _cons
-------------+------------------------------------+------------
eq1 | |
foreign | 3.828e-06 |
weight | 1.344e-06 1.342e-06 |
_cons | -5.195e-06 -4.452e-06 .0000155 |
-------------+------------------------------------+------------
sigma | |
_cons | -4.394e-14 -4.034e-14 6.192e-14 | 2.593e-07
.
. log close
name: <unnamed>
log: /Users/baum/Documents/Courses 2009-2010/EC771 S2010/771reg.smcl
log type: smcl
closed on: 22 Jan 2010, 09:41:44
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