Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 6

Let math10 denote the percentage of students at a Michigan high school receiving a passing score on a standardized math test (see also Example). We are interested in estimating the effect of per student spending on math performance. A simple model is

math10 = ?0 + ?1log(expend) + ?2log(enroll)+ ?3poverty + u,

where poverty is the percentage of students living in poverty.

(i) The variable lnchprg is the percentage of students eligible for the federally funded school lunch program. Why is this a sensible proxy variable for poverty?

(ii) The table that follows contains OLS estimates, with and without lnchprg as an explanatory variable.

Explain why the effect of expenditures on math10 is lower in column (2) than in column (1). Is the effect in column (2) still statistically greater than zero?

(iii) Does it appear that pass rates are lower at larger schools, other factors being equal? Explain.

(iv) Interpret the coefficient on lnchprg in column (2).

(v) What do you make of the substantial increase in R2 from column (1) to column (2)?

Step 1 of 6

Consider the model, the result of which is given in column (1) and column (2)

It shall be noted that is used as the proxy variable for

The column (1) is the result of the model without

The column (2) is the result of the model with

(i)

Considering as the percentage of students eligible for the federally funded school lunch program, it is considered to be a sensible proxy variable for .This is because, the federally funded school lunch program is aimed at promoting the children of the families below poverty line to attend school. In order to ensure family support as well as the interest of such children to go to school, this program ensures that the children of such families get a free lunch meal