Homework 8

Questions

1. The following model shows the relationship between the value of a companys exports (measured in thousands of dollars[1]) and a number of other variables:

Tax is the amount of tax a company pays (in thousands of dollars); Manuf is an indicator variable equal to 1 if the company is in the manufacturing industry (0, otherwise), Service is an indicator variable equal to 1 if the company is in the service sector (0, otherwise). The omitted category is the retail sector

a. Interpret the intercept.

b. Interpret the coefficient of TAX

c. Interpret the coefficients of Manuf and Service

d. Everything else equal, what is the expected difference between the value of exports by a typical company in the manufacturing sector and a company in the service sector?

2. You are analyzing the impact of local Marketing expenditure for a vegan restaurant chain on the Sales of its branches in that market. You are worried that the exclusion of Preference for Meat in a local market from the following model creates an omitted variable bias. Assume a higher Preference for Meat in a local market leads to lower Sales of the branches of this vegan restaurant in that market. Moreover, assume that the higher Preference for Meat in a local market, the more Marketing expenditure is done by the branches in that market. Given this information, do you expect the true effect of Marketing expenditure on Sales to be more or less than the estimated value in the model (i.e., more or less than 2.5)? Explain your answer.

3. The F-statistic for the following hypothesis test is 3.1. Assuming the sample size is very large, are we able to reject the null hypothesis at 1% significance level. Explain your answer. Use the relevant critical value table in the slides or at the end of the textbook.

, , , , and

vs.

, , , , or

4. The model below shows the determinants of hourly wage (HW) for the first job college graduates find upon graduation. Assume the students in our sample can have one of the four majors: STEM, Business, Arts, and Others. We have created corresponding indicator variables with the same names and used some of them in the model. In the following model we also have Other Variables, which is a placeholder for any variable that is not related to a students major (e.g., gender).

a. We are wondering if a students major matters at all in determining their hourly wage in their first job after college. Write down the corresponding null and alternative hypotheses. (Hint: this is a joint hypothesis)

b. If the F-statistic for this hypothesis test is 2.90, determine whether a students major matters at all or not. Use 5% significance level and assume we have a large sample. Use the relevant critical value table in the slides or at the end of the textbook. Be very clear about your conclusion, i.e., does a students major matters or not (in terms of its impact on the hourly wage of the first job upon graduation)

Reminders:

Assume all sample sizes are large and any hypothesis test is a two-sided one.

When a variable is measured in thousands of dollars, it means the value of, for example, 200 that we observe in the database means $200,000.

xportsC=800.3TaxC+25 Manu C15 Service C Sales i=100+2.5 Marketing i+ Residual i H0:B1=B2 B3=B4+B5 B6=0 B7=B8 B9=1 H1:B1=B2 B3=B4+B5 B6=0 B7=B8 B9=1 HWi=B0+B1STEEM+B2 xportsC=800.3TaxC+25 Manu C15 Service C Sales i=100+2.5 Marketing i+ Residual i H0:B1=B2 B3=B4+B5 B6=0 B7=B8 B9=1 H1:B1=B2 B3=B4+B5 B6=0 B7=B8 B9=1 HWi=B0+B1STEEM+B2