Unit 5 ECONF16 (assignment answer key)(1)

# It from the model can cause omitted variables bias

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it from the model can cause omitted variables bias which, as the sample evidence indicates, seems to be the case here. Omitted variables bias seems to be a dominant story here; the standard errors although slightly higher in Model (c) have not changed so much. Recall the formula from HW #2: ~ β 1 ^ β 1 ^ β 1 100 you now know (from HW #4) that the numerator is the “estimated bias” and we can think about interpreted the bias by seeing not only the level change in the coefficient but the % change. Using this formula, when lhseval is omitted, the estimated coefficient on lincome changes by 358%! It changes the estimated coefficient on prppov by 631%! Note also that adjusted R2 for Model (c) is 0.1757 and Model (b) 0.0870. Taken jointly, the information of bias and fit, Model (c) should be considered the better model here. Thus, lincome and prppov should be considered INSIGNIFICANT to soda prices. Note: I also ran VIF analysis in STATA but in the results no values were above 10 and overall did not indicate that multicollinearity would be a topic of focus in this particular model selection. 7

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Software Output: #2 _cons -19.315 31.04662 -0.62 0.536 -81.04399 42.414 bdrms 15.19819 9.483517 1.60 0.113 -3.657582 34.05396 sqrft .1284362 .0138245 9.29 0.000 .1009495 .1559229 price Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 917854.506 87 10550.0518 Root MSE = 63.045 Adj R-squared = 0.6233 Residual 337845.354 85 3974.65122 R-squared = 0.6319 Model 580009.152 2 290004.576 Prob > F = 0.0000 F(2, 85) = 72.96 Source SS df MS Number of obs = 88 . regress price sqrft bdrms _cons 4.766027 .0970445 49.11 0.000 4.573077 4.958978 bdrms .0288844 .0296433 0.97 0.333 -.0300543 .0878232 sqrft .0003794 .0000432 8.78 0.000 .0002935 .0004654 lprice Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 8.01760352 87 .092156362 Root MSE = .19706 Adj R-squared = 0.5786 Residual 3.30088884 85 .038833986 R-squared = 0.5883 Model 4.71671468 2 2.35835734 Prob > F = 0.0000 F(2, 85) = 60.73 Source SS df MS Number of obs = 88 . regress lprice sqrft bdrms 8
_cons 4.766027 .0970445 49.11 0.000 4.573077 4.958978 bdrms .0858013 .0267675 3.21 0.002 .0325804 .1390223 new .0003794 .0000432 8.78 0.000 .0002935 .0004654 lprice Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 8.01760352 87 .092156362 Root MSE = .19706 Adj R-squared = 0.5786 Residual 3.30088884 85 .038833986 R-squared = 0.5883 Model 4.71671468 2 2.35835734 Prob > F = 0.0000 F(2, 85) = 60.73 Source SS df MS Number of obs = 88 . regress lprice new bdrms #3. (a) _cons -1.463333 .2937111 -4.98 0.000 -2.040756 -.8859092 prppov .38036 .1327903 2.86 0.004 .1192999 .6414201 lincome .1369553 .0267554 5.12 0.000 .0843552 .1895553 prpblck .0728072 .0306756 2.37 0.018 .0125003 .1331141 lpsoda Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 2.87875005 400 .007196875 Root MSE = .08137 Adj R-squared = 0.0801 Residual 2.62840943 397 .006620679 R-squared = 0.0870 Model .250340622 3 .083446874 Prob > F = 0.0000 F(3, 397) = 12.60 Source SS df MS Number of obs = 401 . regress lpsoda prpblck lincome prppov (1 missing value generated) . generate lincome = ln(income) (8 missing values generated) . generate lpsoda = ln(psoda) 9

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_cons -.8415149 .2924318 -2.88 0.004 -1.416428 -.2666019 lhseval .1213056 .0176841 6.86 0.000 .0865392 .1560721 prppov .0521229 .1344992 0.39 0.699 -.2122989 .3165447 lincome -.0529904 .0375261 -1.41 0.159 -.1267657 .0207848 prpblck .0975502 .0292607 3.33 0.001 .0400244 .155076 lpsoda Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 2.87875005 400 .007196875 Root MSE = .07702 Adj R-squared = 0.1757 Residual 2.34926197 396 .00593248 R-squared = 0.1839 Model .529488085 4 .132372021 Prob > F = 0.0000 F(4, 396) = 22.31 Source SS df MS Number of obs = 401 . regress lpsoda prpblck lincome prppov lhseval (1 missing value generated) . generate lhseval = ln(hseval) Mean VIF 4.62 prpblck 1.95 0.512342 lhseval 3.19 0.313105 prppov 5.63 0.177699 lincome 7.72 0.129451 Variable VIF 1/VIF . vif 10

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