Please help with Econometrics HW True or False: The OLS estimator is unbiased. T

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Please help with Econometrics HW

True or False: The OLS estimator is unbiased. This means the estimate produocd by the OLS estimator is close to the truth. True of False: The interpretation of beta1 in yi = beta0 + beta1 ln zi + ei is that a 1% change in x lends to a beta1/100 unit change in y. Explain the following statement: 'I am contemplating between using a log-level and a level model. I think I should use the log-level model since the TSS from the log-level model is smaller, meaning R2 is higher than the level-level model." Explain the following statement: "The more linearly related two variables in my data are, the higher the variance of their respective OLS estimators are." I have collected data from the Massachusetts Comprehensive Assessment System (MCAS) from the Massachusetts Department of Education. My key variable of interest in the cumulative 4th grade score on the MCAS (totse4) across schools in the state of Massachusetts. The variables I am considering using are the percentage of students eligible in each school for a free lunch (Inchpet), the number of students per computer in each school (studpe), the total spending in each school per student in $ (totday), and the student-teacher ratio of each school (sttchratio). I have estimated three models which appear in Table 1. Standard errors for each coefficient estimate appear in parentheses beneath each estimate. (6, 3 each) Please interpret the coefficient estimates for Model (1). No explanation is required for the intercept. Suppose I were to measure total spending in $1.000 instead of $ in Mode) (1). What would the coefficient estimate be and explain if the R2 would change in this model. How do you explain the reduction of the coefficient estimate for studpe in Model (2) relative to Model (1)? Interpret the coefficient estimate on Inchpet in Model (2). Keep in mind that Inchpet is measured in percentage points. Using sound economic arguments, explain why you think this coefficient estimate is negative?

Explanation / Answer

1)True, Yes OLS estimators are unbaised as E(Beta cap) =beta

2)True ,as model is lnYo = betao +beta1*lnZ+e , so if you differentiate this we get

dY/Y =beta1*dZ/Z =>beta1 = (dY/Y)/(dZ/Z) so 1% change in Y leads to beta1/100 units change in Z

3)Yes, this statement tells about how well data fits yhe model.If R^2 of log level model is higher than level model,this indicates coefficient of determination is high(R^2 is high) .So data is well fitted for log level model.So it is good to use log level model

4) As variance of OLS estimator beta cap is proportional to r^2 , which defines strengthg of linear relationship between x and y. So OLS estimators variance will be higher if r^2 is higher. Higher r^2 denotes that variables rae more linearly related

5)
a) this coefficients represents that with 1% change in independent variable i.e X1, X2 and x3 , how much dependent variable Y will change

b) Each coefficient esyimate will be multiplied by 1000 , so new coefficient = old estimated coefficients *1000

and R^2 of the model will not change as only scale of the variable changed but not data pattern

c)As dependent variable is different in model 1 and model2 and also as log is introduced in model 2 . So coefficient of studpe has reduced.

d) this coefficient tells us that with 1% change in lunch pet(i.e 1% change in number of students eligible for free lunch , )cumulative 4th grade score of MCAS changes by coefficient of estimator times of lunchpet. Coefficient estimate is negative as this indicates with no of students increasing for eligibility of free lunch,cumulative 4th grade scores across schools of Massacheussets is decreasing. Economic argument here is due to no of students increased for free lunch. So In budget allocated to school, Significant amount goes for free lunch making other resources not efficiently used i.e spending on other academic related things decreased there by decreasing cumulative 4th grade score

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