4) Consider the following model for how state employment depends on the tax reve

Question

4) Consider the following model for how state employment depends on the tax revenue mix: log(employment)-A + Ashare-property + .share-income + Bs hare-sales + u , where share pop is the share of property taxes in total tax revenue; share income is the share of income taxes, and share sales is the share of sales taxes. The share of tax revenue from all other sources (share_other) is omitted. The shares have all been multiplied by 100 so that a value of 50 for share-property would indicate that 50% of total tax revenue comes from property taxes, for example. 15 points: 5/5/5) (i) Explain why share_other is omitted. (ii) Provide a careful interpretation ofp, ii Suppose share_income and share sales are highly correlated. How would you expect this correlation to affect the bias and variance of the OLS estimator for P,? In principle, how could you mitigate any potential concerns about the effect of this correlation on the bias and variance?

Explanation / Answer

1. in the given model 3 factors are taken as explanatory variables. They are share property, share income and share sales. In the given regression model includes the variable u. In the regression model, u is the random term or the disturbance term. because it disturbs the exact relationship between the independent and dependent variables. in other words the model itself includes a random factor for representing the disturbances and that is why the variable 'share others' is omited. the purpose of that variable is served by the random variable term 'u'.

2. in the given model, the slope coefficient 2 is a measure of elasticity. that means it measures the relative change in dependent variable (here employment) to a given absolute change in corresponding explanatory variable (here share income).

3. the term multicollinearity is used to denote the presence of linear relationship among the explanatory. here, share income and share sales are two explanatory variables. if they are correlated, multicollinearity is there.

estimated coefficients will be unbiased even in the presence of multicollinearity. but estimator will lack its best property. in other worsd variance will large and thus estimators will lack efficiency.

measures to mitigate multicollinearity

1. increase the size of the sample.

2. transform the single equation model into simultaneous regression model. The reduced form method can be applied to avoid multicollinearity

3. linearly combine these independent variables

4.use of extraneous information  

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.