State with reason whether the following statements are TRUE/FALSE/UNCERTAIN

Home Assignment #3

Assignment #1 (2 points)

1) In choosing the various functional forms, we can pay no attention to stochastic disturbance term e_i.

FALSE, in choosing the various functional forms, great attention should be paid to the stochastic disturbance term e_i.

The CLRM explicitly assumes that the disturbance term has zero mean value and constant (homoscedastic) variance and that it is uncorrelated with the regressor(s). It is under these assumptions that the OLS estimators are BLUE. Further, under the CNLRM, the OLS estimators are also normally distributed. One should therefore find out if these assumptions hold in the functional form chosen for empirical analysis. After the regression is run, the researcher should apply diagnostic tests, such as the normality test (Chapter 5, Gujarati).This point cannot be overemphasized, for the classical tests of hypothesis, such as the t, F, and , rest on the assumption that the disturbances are normally distributed. This is especially critical if the sample size is small.

2) In log-lin models to interpret slope coefficient we have to divide it by 100. To accept or decline the argument -show your work.

FALSE, to interpret slope coefficient we have to divide it by 100 in lin-log models, but in log-lin models we have to multiply it by 100.

In log-lin model ( ) the slope coefficient measures the relative change in Y for a given absolute change in the value of the regressor, that is . If we multiply the relative change in Y by 100, will then give the percentage change in Y for an absolute change in X.

For example, we have an estimating the influence of education and experience on wages: , then we can say that if education / experience increases by 1 year, then wage will change by 9,8 % / 1,0 %.

3) A dummy variable is a binary variable used to distinguish between two groups (categories) and the coefficient estimate on the dummy variable estimates the difference between two groups (categories).

TRUE, a dummy variable is the variable that takes on the value zero or one and (in the simplest case) is defined to distinguish between two groups, and the coefficient estimate on the dummy variable estimates the ceteris paribus difference between the two groups. Allowing for more than two groups is accomplished by defining a set of dummy variables.

4) If there are n groups, then n +1 dummy variables should be included into the model.

FALSE, if there are n groups, then n-1 dummy variables should be included into the model.

Assignment #2 (2 points)

Suppose you want to study the behavior of sales of a product, say, automobiles over a number of years and suppose someone suggests you try the following models:

Where Y_t = sales at time t, t= time, measured in years. The first model postulates that sales is a linear function of time, where the second model states that it is a quadratic function of time.

(1) Discuss the properties of these models.

In the first model, where sales is a linear function of time, the rate of change of sales is postulated to be a constant, equal ,regardless of time t. In the second model the rate of change is not constant because , which depends on time t.

(2) How would you decide between the two models?

The simplest thing to do is plot Y against time. If the resulting graph looks parabolic, perhaps the quadratic model is appropriate.

(3) In what situations will the quadratic model be useful?

This model might be appropriate to depict the earnings profile of a person. Typically, when someone enters the labor market, the entry-level earnings are low. Over time, because of accumulated experience, earnings increase, but after a certain age they start declining.

(4) Obtain data for automobile sales in Ukraine over the past 14 years.

4.1 Construct a scattergram and a scattergram with line (x-years, y – sales of automobiles). What can you say about the data?

4.2 Estimate the regressions for both models. Interpret.

4.3 Which of the models fits the data better? Which functional form you would finally prefer?

Assignment #3 (2 points)

You are given the following regression results:

Can you find out the sample size underlying these results? (Hint: Recall the relationship between R², F and t values.)

Recalling the relationship between the t and F distributions, we know that from the first equation:

. Therefore, .

Now we can use the formula: .

Solving this equation for we can get .

We can also find out the sample size in another way. We can use the formula: , where is the for a model which doesn’t include variable and is the for a model with this added variable. Also the square of t-statistic for is equal F. Therefore: ,

,

So, we have find that the sample size is equal 16.

Assignment #4 (2 points)

Suppose you collect data from a survey on wages, education, experience, gender and race (white or black). In addition you ask for information about alcohol usage. The original question is: “On how many separate occasions last month did you drink alcohol?”

(1) Write an equation that would allow you to estimate the effects of alcohol consumption on wage, while controlling for other factors. You should be able to make statements such as, “Alcohol consumption ten more times per month is estimated to change wage by X%.”

To be able to do such interpretation we should have a log-lin model:

(2) Write a model that would allow you to test whether alcohol consumption has different effects on wages for black and white. How would you test that there are no differences in the effects of alcohol consumption for black and white?

Then we would have the following regression:

shows how alcohol usage on average influences the wages. shows whether there is a difference of alcohol influence on wages when you are white. If the coefficient , it means that there are no differences in the effects of alcohol usage between white people and black people. The influence of alcohol drinking for white people , for black people just , when .

(3) Write a model that would allow you to test whether alcohol consumption has different effects on wages for a white woman and a black man. Be specific.

We can write the next model:

, where .

Here the base category is the black man.

The sum ( ) shows a difference in the effect of alcohol consumption on wages when the persons are the black man and the white woman.

(4) Suppose you think it is better to measure alcohol consumption by putting people into one of four categories: nonuser, light user (1 to 5 times per month), moderate user (6 to 10 times per month), and heavy user (more than 10 times per month). Now, write a model that allows you to estimate the effects of alcohol consumption on wage.

We can do it by doing the next equation:

Here the base group is nonuser. So we need the dummy variables for other three groups: light user, moderate user and heavy user:

From the equation above, “light users” are estimated to earn % more (less if coefficient would be negative) than non-users, holding all other factors (level of education, experience, gender and race) are fixed.

(5) Use the model in part (4), explain in detail how to test the null hypothesis that alcohol consumption has no effect on wage. Be very specific and include a careful listing of degrees of freedom.

To get known whether the alcohol usage has any effect on wages, we should take the regression and use F test and test the hypothesis that: .

If all these three coefficients would be equal to zero at the same time, it means that alcohol consumption has no effect on wages.

Principle for including dummy-variables to indicate different groups: if the regression model is to have different intercepts for, say, n groups or categories, we need to include n-1 dummy variables in the model along with an intercept.

(6) What are potential problems with drawing causal inference using the survey data that you collected?

As an example it could be causality problem. The alcohol consumers mostly belong to low wages group, which will push to the bias in conclusion “the more you drink alcohol the lower the wages”.

Assignment #5 (2 points)

Using the data in WAGE2.RAW of Wooldridge database, estimate the model:

(1) Report the results in usual form. What type of model is it?

(2) Are the coefficients statistically significant? Interpret

(3) What can you say about the model in general. Interpret R², F-statistics?

(4) Holding other factors fixed what is approximate difference in monthly salary between blacks and nonblacks? Is this difference statistically significant?

(5) Add the variables exper² and tenure² to the equation and show that they are jointly insignificant at even 20% significance level.

(6) Extend the original model to allow the return on education to depend on race and test whether the return on education does depend on race.

(7) Again, start with the original model, but now allow wages to differ across four groups of people: married and black, married and nonblack, single and black, and single and nonblack. What is estimated wage differential between married blacks and married nonblacks?

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