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1、Class 6, Page 7Class 6: Auxiliary regression and partial regression plots. More independent variables? I. Consequences of Including Irrelevant Independent VariablesWhat are the consequences of including irrelevant independent variables? In other words, should we always include as many independent va
2、riables as possible? The answer is no. You should always have good reasons for including your independent variables. Do not include irrelevant independent variables. There are four reasons: A. Missing Theoretically Interesting FindingsB. Violating the Parsimony Rule (Occoms Razor)C. Wasting Degrees
3、of FreedomD. Making Estimates Imprecise. (e.g., through collinearity).Conclude: Inclusion of irrelevant variables reduces the precision of estimation. II. Consequences of Omitting Relevant Independent VariablesSay the true model is the following:.But for some reason we only collect or consider data
4、on y, x1 and x2. Therefore, we omit x3 in the regression. That is, we omit x3 in our model. The short story is that we are likely to have a bias due to the omission of a relevant variable in the model. This is so even though our primary interest is to estimate the effect of x1 or x2 on y. Give you a
5、n example. For a group of Chinese youths between ages 20-30: y = earningsx1 = educationx2 = party member statusx3 = ageIf we ignore age, the effects of education and party member status are likely to be biased (1) because party members are likely to be older than non-party members and old people ear
6、n more than the young. (2) because older people are likely to have more education in this age interval, and older people on average earn more than young people. But why? We will have a formal presentation of this problem.III: Empirical Example of Incremental R-SquaresXie and Wus (2008, China Quarter
7、ly) study of earnings inequality in three Chinese cities: Shanghai, Wuhan, and Xian in 1999. See the following tables:Table 1: Percent Variance Explained in Logged EarningsVariablesDFR2 DR2(1) DR2(2) City217.47*18.11*19.12*Education Level57.82*5.49*4.46*Experience+Experience220. 230.170.05Gender14.7
8、8*4.84*3.05*Cadre Status13.08*2.27*0.63*Sector33.54*2.18*1.80*Danwei Profitability (linear)112.52*9.30*Danwei Profitability (dummies)412.89*N = 1771Note: DF refers to degrees of freedom. DR2(1) refers to the incremental R2 after the inclusion of Danweis financial situation (linear). DR2(2) refers to
9、 the incremental R2 after the inclusion of all the other variables. * p 0.001, * p0.01, * p0.05, based on F-tests. Source: 1999 Three-City Survey. Table 2: Estimated Regression Coefficients on Logged EarningsVariables Observed Effects Adjusted Effects b SE(b) b SE(b)City (Shanghai=excluded) Wuhan-0.
10、465*0.033-0.539*0.028 Xian-0.628*0.034-0.658*0.028 Constant9.402* 0.024Education Level (no schooling=excluded) Primary 0.536*0.2160.414*0.170 Junior high0.737*0.2020.447*0.161 Senior high0.770*0.2010.592*0.161 Junior college1.049*0.2030.778*0.162 College1.253*0.2070.923*0.166 Constant8.120*0.210Expe
11、rience+Experience2 Experience (x1000)-11.2356.0292.4214.775 Experience2 (x1000)0.288*0.144-0.0170.114 Constant9.113*0.059Gender (male=excluded) Female-0.276*0.029-0.225*0.023 Constant9.144* 0.019Cadre Status (non-cadre=excluded) Cadre0.375*0.0500.185*0.042 Constant8.992*0.015Sector (government+publi
12、c=excluded) State owned-0.133*0.037-0.0430.030 Collectively owned-0.397*0.057-0.224*0.045 Privately owned0.0270.0470.114*0.037 Constant9.129*0.031Danwei Profitability (linear)0.256*0.0160.227*0.013 Constant8.270*0.050Danwei Profitability (dummies) (very poor=excluded) Relatively poor 0.1000.062 Aver
13、age 0.405*0.054 Fairly good 0.702*0.059 Very good 0.918*0.108 Constant 8.624*0.050Constant8.237*0.171R2 (N = 1771) 43.92%Note: Observed effects on logged earnings are derived from bivariate models. Adjusted effects are derived from a multivariate model including all variables.* p 0.001, * p0.01, * p0.
