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Economics 310

Economics 310. Lecture 4 Least-Squares Efficiency. Shazam Omitted Variable Example. |_sample 1 20 |_read x1 x2 x3 3 VARIABLES AND 20 OBSERVATIONS STARTING AT OBS 1 |_* Generate 1000 samples with true model: Y=10+3X1-5X2+4X3+e

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Economics 310

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  1. Economics 310 Lecture 4 Least-Squares Efficiency

  2. Shazam Omitted Variable Example |_sample 1 20 |_read x1 x2 x3 3 VARIABLES AND 20 OBSERVATIONS STARTING AT OBS 1 |_* Generate 1000 samples with true model: Y=10+3X1-5X2+4X3+e |_* where e is normal with mean 0 and variance 4 |_* allocate arrays to hold the estimates |_dim bols 4 1000 stdols 4 1000 bbias 3 1000 stdbias 3 1000 |_dim binef 4 1000 stdinef 4 1000 beff 3 1000 stdeff 3 1000 |_* suppress useless output |_set nodoecho |_do #=1,1000 |_sample 1 20 |_* generate e |_genr e=nor(2) |_* generate y |_genr y=10+3*x1-5*x2+4*x3+e |_* ols estimation, supress the output with ? |_?ols y x1 x2 x3 / coef=bols:# stderr=stdols:# |_?ols y x1 x2 / coef=bbias:# stderr=stdbias:# |_endo ****** EXECUTION BEGINNING FOR DO LOOP # = 1 ****** EXECUTION FINISHED FOR DO LOOP #= 1000

  3. Omitted Variable Results |_sample 1 4 |_* unbias ols estimation |_print b ase ese stdse B ASE ESE STDSE 2.999865 0.1919761E-01 0.1821358E-01 0.3203836E-02 -5.000589 0.2234035E-01 0.2230756E-01 0.3923984E-02 4.000645 0.2231198E-01 0.2105855E-01 0.3704277E-02 10.01183 1.669633 1.576074 0.2772373 |_sample 5 7 |_* exclude relevant variable |_print b ase ese stdse B ASE ESE STDSE 4.954072 0.1622638E-01 0.6927163 0.3860903E-02 -6.515474 0.2067005E-01 0.9601574 0.5351505E-02 180.6879 1.358374 59.67985 0.3326298

  4. Irrelevant Variable Shazam Example |_* run the model for inclusion of irrelevant variable with |_* true model y=10+3x1-4x2+e |_do #=1,1000 |_sample 1 20 |_* generate error |_genr e=nor(2) |_* generate y |_genr y=10+3*x1-4*x2+e |_* ols estimation, supress the output with ? |_?ols y x1 x2 /coef=beff:# stderr=stdeff:# |_?ols y x1 x2 x3 / coef=binef:# stderr=stdinef:# |_endo

  5. Intermediate Step to get Output |_* Transpose the array so that the STAT command can be used. |_matrix bols=bols' |_matrix stdols=stdols' |_matrix bbias=bbias' |_matrix stdbias=stdbias' |_matrix beff=beff' |_matrix stdeff=stdeff' |_matrix binef=binef' |_matrix stdinef=stdinef' |_sample 1 1000 |_?stat bols bbias beff binef /mean=b stdev=ase |_?stat stdols stdbias stdeff stdinef /mean=ese stdev=stdse

  6. Results Irrelevant Variable |_sample 8 10 |_* efficient estimate reduced model |_print b ase ese stdse B ASE ESE STDSE 2.999353 0.1560298E-01 0.1508509E-01 0.2613140E-02 -4.000647 0.2129266E-01 0.2090908E-01 0.3622011E-02 10.05974 1.332989 1.299631 0.2251309 |_sample 11 14 |_* inefficient estimate reduced model |_print b ase ese stdse B ASE ESE STDSE 2.999578 0.1869003E-01 0.1829380E-01 0.3232131E-02 -4.000821 0.2226461E-01 0.2240582E-01 0.3958639E-02 -0.4610111E-03 0.2097928E-01 0.2115130E-01 0.3736992E-02 10.07941 1.589152 1.583016 0.2796858

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