# Econometrics - Heteroskedasticity

**Topics:**Regression analysis, Studentized residual, Heteroscedasticity-consistent standard errors

**Pages:**11 (3099 words)

**Published:**April 1, 2013

TRAN THI ANH NGUYET 28 March, 2013

1. The data set CEOSAL2.DTA contains information on 177 CEOs. In this sample, the average annual salary is $865,864,400 with the smallest and largest being $100,000 and $5,299,000,000, respectively. Another most interesting variable is sales with the average being $3,5329,463,000, and its the smallest and largest being $29,000 and $51,300,000. Using the data set, the following OLS regression is obtained: (1) . ˆ lnsalary = 4.58 + 0.192.lnsales + 0.094.lnmktval + 0.017.ceoten − 0.009comten 0.253 .0398 0..0489 0.0055 0.0033

reg lnsalary lnsales lnmktval ceoten comten

Source Model Residual Total ln_salary ln_sales ln_mktval ceoten comten _cons . SS 22.5202805 42.1259326 64.6462131 Coef. .1918844 .0940901 .0169211 -.009415 4.576374 df 4 172 176 MS 5.63007012 .244918213 .367308029 t 4.82 1.92 3.05 -2.82 18.05 P>|t| 0.000 0.056 0.003 0.005 0.000 Number of obs F( 4, 172) Prob > F R-squared Adj R-squared Root MSE = = = = = = 177 22.99 0.0000 0.3484 0.3332 .49489

Std. Err. .039824 .0489194 .0055389 .0033341 .2535074

[95% Conf. Interval] .1132777 -.0024696 .0059882 -.0159959 4.075988 .2704911 .1906498 .0278541 -.002834 5.07676

Interprete the result. OLS Coeﬃcients The main variable of interest is lnsales. If all other factors are unchanged, 10 more percentage of annual sales increases salary per year of a CEO by 1.92%. By mean of level changes, $353,294,630 increase in annual sales, on average, raises the CEO’s salary by $101,740,800. This seems like a reasonably large inﬂuence. β2 = 0.94 means that whenever the market value of the ﬁrm is 10% higher, the CEO’s salary is predicted to rise about 0.94%, holding other factors ﬁxed. In comparison with 1.92%, this is not a huge eﬀect, but it should not negligible, either. The variable ceoten is years as CEO with the current company and comten is total years with the company with the OLS estimators being 0.0169 and −0.0094, respectively. Other factors ﬁxed, one more year as a CEO with the ﬁrm increases his salary by about 1.69% . However, another year with the ﬁrm but not as a CEO, lowers approximately his salary by 0.094%. The ﬁrst one is likely as our expectation since , but the second one, the eﬀect of comten at ﬁrst seems strange. “Superstar” eﬀect hypothesis of Rosen (1990) states that the market must identify new talent and reassign control over careers from older to younger generations. It means that when a ﬁrm hires a CEO on labor market with long-time experience working as non-CEO, it is likely he was not hired as a “superstar” (CEO) by other ﬁrms. Therefore, the ﬁrm may have no willingness to bid up his salary. If the model supposed is not mispeciﬁed or problematic, the intercept coeﬃcient seems less practically meaningful as all independent variables have no change, the annual salary is still predicted to increase about 4.57%. It is a very large number in comparison with inﬂuences of changes in sales and the ﬁrm’s market value. Otherwise, if there is any omitted variables, this change might be more meaningful.

Statistical Signiﬁcance The t statistic on lnsales, ceoten and comten are 4.82, 3.05, and−2.82 that are large enough in magnitude to conclude that all these variables are statiscally signiﬁcant at the 5% level. What about the statistical signiﬁcance of the market value variable? The t statistic on lnmktval = 1.92 and it is likely not to be high to imply that lnmktval is statistically signiﬁcant at 5% with 2-sided test. However, when we expand the signiﬁcance level to 10%, with 177 − 6 = 171 df for the 2-sided alternative, H0 : β = 0, the 10% critical value is about 1.645. Hence, lnmktval is almost signiﬁcant against the 2-sided alternative at the 10% level. In fact, we will show later that some outliers and inﬂuential observations make the less satistical signiﬁcance of lnmktval. R-squared R2 = 0.3484, this means that the 4 predictors together explain about 34.84% of the percentage change in...

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