Quiz2 Solutions

EC 303 Quiz 2

Name:______________________________ You have the entire period to complete this quiz.

(1) Consider the following regression results (education = # of years of schooling; experience = # of years of work experience; tenure = # of years at current job) from an unknown sample of people.

Table 1 (1)

(2)

(3)

Ln(wage)

Ln(wage)

Ln(wage)

-.297 (.036)

-.227 (.168)

.080 (.007)

-.110 (.056) .213 (.055) -.301 (.072) .079 (.007)

N

.029 (.005) -.00058 (.00010) .032 (.007) -.00059 (.00023) .417 (.099) 526

.027 (.005) -.00054 (.00011) .029 (.007) -.00053 (.00023) .321 (.100) 526

.082 (.008) -.0056 (.0131) .029 (.005) -.00058 (.00011) .032 (.007) -.00059 (.00024) .389 (.119) 526

R^2

.441

.461

.441

Female Married Female x Married Education Female x Education Experience Experience^2 Tenure Tenure^2 Constant

(a) Considering specification (1), answer the following questions: (i) What does the coefficient on female indicate (i.e., how would you interpret this coefficient)? Holding education, experience, and tenure constant, females earn 29.7% less than males, on average.

EC 303 Quiz 2

(ii) What does the coefficient on education indicate (i.e., how would you interpret this coefficient? Holding sex, experience, and tenure constant, each additional year of schooling generates 8% higher wages. (b) Considering specification (2), answer the following questions: (i) What does the coefficient on female indicate (i.e., how would you interpret this coefficient)? Holding education, experience, and tenure constant, single females earn 11% than single males. In order to simplify the explanation, assume the regression equation can be represented by: Yi = b 0 + b1Female+ b 2 Married+ b 3 Female´ Married Let’s start by holding married constant and examining what happens as female changes:

E(Y | female = 0,married = 0) = b 0 E(Y | female = 1,married = 0) = b 0 + b1 Taking the difference between these two equations yields the difference between single men and single women -- β1 (i) What does the coefficient on married indicate? Holding education, experience, and tenure constant, married men earn 21.3% more than single men. Using the same simplifying equation as above, this time, hold female constant at 0 and examine what happens when we change the married variable:

E(Y | female = 0,married = 0) = b 0 E(Y | female = 0,married = 1) = b 0 + b 2 Taking the difference between these two equations yields the differences between single men and married men -- β 2 (ii) What does the coefficient on (Female x Married) indicate? Holding education, experience, and tenure constant, marriage has a different effect for women then for men.

E(Y | female = 1,married = 0) = b 0 + b1 E(Y | female = 1,married = 1) = b 0 + b1 + b 2 + b 3

EC 303 Quiz 2

Taking the difference between these two equations yields the effect of marriage on females -- β 2 + b 3 . Since β 2 reflects the marriage effect for males, β 3 reflects the additional effect of marriage on females (beyond the effect for males).

(c) Considering specification (3), answer the following questions: (i) In stark contrast to the coefficient on female in specification (1), the coefficient for female in this regression is not statistically significant. Should we conclude that there is no statistically significant evidence of lower pay for women at the same levels of education, experience, and tenure within this sample? Why or why not? No, we should not draw such a conclusion. The coefficient is still relatively large and negative. The standard errors, though, are significantly larger. The key question to ask, then, is what is driving the increase in standard errors? The only difference between specification (1) and specification (3) is the inclusion of the interaction term between female and education. Given the large degree of collinearity between the female variable and the interaction, it is not surprising that the standard errors on the female coefficient increase. This interaction term, though, is insignificant and does not contribute to increase R^2. Thus, the interaction term is irrelevant and should be excluded from the regression.

(ii) Does this specification provide support for an argument that the returns to education are different for men and women within this sample? No, it does not. The interaction term is small and statistically insignificant.

(d) Do you agree with the analyst’s decision to include both experience and tenure in the regression? Why or why not? Why do you think the analyst included quadratic terms for both of these variables? I think it makes sense. The two variables capture two different determinants of wages – general job experience (which reflects the acquisition of general human capital) and firm-specific experience (which reflects the acquisition of firm specific human capital). Including quadratic terms for both of these regressors reflects the fact that both have a non-linear relationship with wages. Early in one’s career, an extra year of

EC 303 Quiz 2

experience or tenure is likely to generate larger increases in productivity (and thus wages) than the same change in experience or tenure will during later years.

(e) Do the results in this table provide convincing evidence for or against discrimination against women in the labor market? Why or why not? If not, what additional information would you like to have in order to reach a conclusion about discrimination against women? No, these results are not very compelling. First, the table includes no description of the data used to generate this table. Without a better sense of the sample from which these data were collected, it is difficult to decide how seriously to consider these results. Second, there are still a number of potentially omitted variables that may bias these results. For instance, I would like to have data that would allow me to control for differences in occupational choice or job abilities.

(2) Assume you want to investigate the effects of education spending on housing prices. You have cross-sectional data containing the average home price and total school spending per pupil for a cross-section of communities in Oregon. (a) List 5 additional variables you would add to this regression. Very briefly discuss why you would want to include each variable. Primarily, we want to add in variables that may be causing omitted variable bias. That is, variables that are correlated with both school spending and housing prices. A partial list includes: average (or median) household income for each community, a measure of education levels (e.g., the share of people with bachelors degrees), a measure for the type of community (e.g., urban, suburban, rural), measures of local economic conditions (e.g., unemployment rates, growth rates, or, alternatively, regional or county fixed effects).

(b) Write down the regression equation you would estimate if you were investigating this relationship – including any nonlinearities or transformations. How would you interpret the coefficient on school spending? A log-log specification is preferred. This would yield the elasticity of home prices with respect to school spending.

EC 303 Quiz 2

(c) Assume that the results of your regression show a positive relationship between school spending and housing prices that is both economically and statistically significant. If an advocate for increasing school spending in Spokane wrote an op-ed that included an argument, based on your research, that suggested that increasing school funding would be good for homeowners because it would increase property values by the amount you found, would you have any problem with this argument?

There are two main questions to address. First, are the results of this simple regression internally valid, and, second, are the results externally valid? There are a number of potential threats to internal validity. It is unlikely that the simple specification discussed above has included all the potentially omitted variables. It is also possible that our estimates are plagued by simultaneous causality bias (i.e., high average housing prices cause increases in school spending – e.g., via higher property taxes). Setting concerns about internal validity aside, we still need to worry about external validity. By citing our results, the advocate is essentially assuming that the relationship between school spending and housing prices is the same in Spokane as it is in the average Oregon community. However, Spokane, a relatively large city, is fairly different from the average Oregon community (which is likely a relatively small town).

(d) Suppose that instead of data on community level attributes (e.g., average house prices), you had data from the assessors within a single metropolitan area (e.g., Portland-Vancouver) that includes: •

the sales prices of specific homes

•

variables that describe the home (e.g., lot size, square feet of the house, number bedrooms, number of bath rooms, etc.)

•

the schools and school district attended by residents of this house

•

basic details about the neighborhood (e.g., views, proximity to parks, etc.)

In addition, you can merge the assessor’s data with data you obtain data from the school and school district about school test scores and spending per pupil. How could you use these data to obtain a relationship between home prices and school spending? What regression would you run? What types of controls would you include? Would you limit the sample of houses examined to include only houses meeting certain criteria (if so, what criteria would you use)? Do you think that the evidence from this regression would provide

EC 303 Quiz 2

stronger support (or better evidence) for the hypothesis that school spending affects property values? We can use these data to generate results that are more likely to be internally valid. A clever approach pursued by economist Sandra Black, restricted the sample of houses examined to those near school area boundaries. Black’s insight is that within neighborhoods, the other factors that affect housing prices are constant (e.g., crime, general neighborhood amenities (parks, stores, transportation access), the characteristics of the people in the neighborhood, etc.). As such, comparing similar houses (e.g., same lot size, same house size, same year built, etc.) in the same neighborhood on different sides of the street, where one side of the street send their kids to a better school than the other, yields a fairly clean estimate of what people are willing to pay to attend a “better” school.