economic and statistic question

21 Jul economic and statistic question

1. The significance level is .

(a) Probability of a type I error

(b) Probability of rejecting a true null

(c) The tolerance for making a mistake in hypothesis testing

(d) All of the above

2. Suppose I want to estimate an equation where y is a function of x with OLS and my coefficients can be interpreted as percent change in y for a one unit change in x. Which form should I use?

(a) level-log

(b) level-level

(c) log-level (d) log-log

3. Suppose the R2 from estimating x1 = α0 + α1x2 + e is 0.94. If I estimate the equation: y = β0 + β1x1 + β2x2 + e, what potential problem will I likely have?

(a) βˆ1 will be biased

(b) Heteroskedastic errors

(c) V ar(βˆ1) will be high

(d) All of the above

4. Suppose you estimate the equation: y = β0 + β1x1 + e when the true model is:y = α0 + α1x1 + α2x2 + e. Which statement is true?

(a) If Cov(x1,x2) = 0 and α2 6= 0, then β1 will be biased.

(b) If Cov(x1,x2) = 0 and α2 = 0, then β1 will be biased. (c) If Cov(x1,x2) 6= 0 and α2 6= 0, then β1 will be biased.

(d) All of the above.

5. Including irrelevant variables will .

(a) Increase Variance of estimates

(b) Introduce heteroskedasticity

(c) Cause bias of βˆ

(d) All of the above

6. Suppose, I estimate the equation y = β0 + β1x + β2x2 + e. Which result would indicate diminishing returns.

(a) βˆ1 > 0 and βˆ2 < 0

(b) βˆ1 > 0 and βˆ2 > 0

(c) βˆ1 < 0 and βˆ2 > 0

(d) None of the above

7. Given the null:H0 : β1 = β2 = β3 = 0. How many restrictions are there in an F-test?

(a) 4 (b) 3 (c) 2

(d) 1

8. Which is true of using incorrect functional form?

(a) Estimates are not necessarily BLUE (b) Coefficients can be biased.

(c) There is potential for heteroskedasticity.

(d) All of the above.

9. Given data on wage, race, gender, and education. Which functional form is used if the returns to education are expected to be linear in percentage change?

(a) Quadratic Terms

(b) Logged dependent variable

(c) Interaction Terms

(d) Dummy Variables

10. Which of the following was not one of the criteria that we used in specification searches?

(a) Look for potential omitted variable bias.

(b) Look at the R2.

(c) Use theory to determine functional form.

(d) Evaluate as many different functional forms as the data allows.

Table 1: Word Bank

T-test	H0 : β = 0	Significance Level	Significance Interval	Statistical Significance
F-test	H0 : β ≥ 0	Joint Significance	Unrestricted Model	Confidence Level
P-Value	Restrictions	Hypothesis Test	H0 : β1 = β2 = 0	Confidence Interval
Multicollinearity	Variance Inflation Factor	Heteroskedasticity	Homoskedasticity	Restricted Model

Choose the answer from the word bank that best fits the description.

11. Statistic used to test for multicollinearity:

12. Test for multiple linear hypotheses :

13. Includes all values γ at which H0 : β = γ cannot be rejected 14. Lowest significance level at which H0 : β = 0 can be rejected:

.

15. Probability of rejecting a null that is in fact true:

Open Answer

Directions

Open answer questions refer to the regression results in Table 2. When asked to complete a test, this includes declaring relevant hypotheses, solving for appropriate test statistics, finding the correct critical values, and properly applying the decision rule. Points will be awarded for each portion. A detailed description of the table, formulas for test statistics, and distribution tables are attached.

Questions

1. Interpreting coefficients: (15 Points)

(a) Interpret the coefficient on Hispanic in Column 1. (b) Interpret the coefficient on Hispanic in Column 3.

(c) Interpret the coefficient on Female*Grade in Column 2.

(d) Interpret the coefficient on Female in Column 2.

(e) Interpret the coefficient on Log Parent’s Income Column 2

2. Hypothesis Testing: (25 Points)

(a) Test the joint significance of the ice cream variables.

(b) Find a 95% confidence interval for the coefficient on ASVAB in column 1.

(c) Conduct an F-Test on the joint significance of all included variables in column 1.

(d) Use any column to test whether Black workers earn more than workers of mixed race.

(e) It is standard practice in reporting regression results to put stars on coefficients according to their respective p-values where p < 0.01 = ∗∗∗, p < 0.05 = ∗∗, and p < 0.10 = ∗. How many stars (1,2, or 3) would be on the ASVAB coefficient in column 1? Show work to support your answer.

3. (5 pts) Give two examples of evidence to include or not include a quadratic term for experience?

4. (5 pts) Find the missing coefficient in column 3.

5. (5 pts) Do students with higher ASVAB scores have higher education? Use the regression results in Table 2 to explain your answer.

Test Statistics

 Tables for looking up critical values are attached.

Table Description

The data for table 1 is taken from the 1997 NLSY.

In column 1, the dependent variable is the individual’s income in dollars.

In columns 2-5, the dependent variable is the natural log of the individual’s income in dollars.

Experience is age minus highest grade completed.

Female*Grade is the female dummy times the highest grade completed variable.

ASVAB is the armed services vocational aptitude battery. It is a test given to all respondents meant to evaluate intelligence.

Parent’s income is the income earned by the respondent’s parents when he/she was a child.(in dollars)

Respondents were asked their favorite ice cream flavor. Options were Chocolate, Vanilla, Strawberry, Butter Pecan, or None of these. Dummy variables for favorite ice cream flavor are included in all but column 5.

Respondents were asked to check the race/ethnicity group which best describes them. Options were Black, Hispanic, Mixed Race, or Non-Black/Non-Hispanic. Dummy variables for race/ethnicity were included in each column.

Coefficients are shown with standard errors in parentheses. The R2, RSS, and observations are in the bottom part of the Table.

Exam 2 v2 Econ 4400

Name:

1.6.11.

2.7.12.

3.8.13.

4.9.14.

5.10.15.

1. (a)

(b)

(c)

(d)

(e)

2. (a)

(b)

(c)

(d)

(e)

3.

4.

5.

Table 2: Income Regressions

	(1)	(2)	(3)	(4)	(5)
	Income	Log Income	Log Income	Log Income	Log Income
Experience	2508.4	0.0581	0.0581	0.0650	0.0576
	(401.1)	(0.0127)	(0.0127)	(0.0127)	(0.0127)
Experience Squared	-30.00	-0.000942	-0.000942	-0.00116	-0.000943
	(3.977)	(0.000125)	(0.000125)	(0.000117)	(0.000125)
Highest Grade Completed	3855.3	0.0962	0.0962	0.113	0.0958
	(456.9)	(0.0145)	(0.0145)	(0.0141)	(0.0145)
Female	-14708.6	-0.715	-0.715	-0.703	-0.721
	(4216.1)	(0.134)	(0.134)	(0.134)	(0.134)
Female*Grade	93.97	0.0242	0.0242	0.0232	0.0244
	(280.6)	(0.00888)	(0.00888)	(0.00891)	(0.00888)
ASVAB	0.146	0.00000360	0.00000360		0.00000356
	(0.0242)	(0.000000765)	(0.000000765)		(0.000000763)
Parent’s Income	0.105 (0.0135)
Log Parent’s Income		0.0912	0.0912	0.102	0.0918
		(0.0175)	(0.0175)	(0.0174)	(0.0175)
Chocolate	1406.7	0.0403	0.0403	0.0173
	(2034.8)	(0.0645)	(0.0645)	(0.0645)
Vanilla	2762.7	0.0738	0.0738	0.0540
	(2085.8)	(0.0661)	(0.0661)	(0.0662)
Strawberry	609.6	0.0199	0.0199	-0.00201
	(2135.5)	(0.0677)	(0.0677)	(0.0678)
Butter Pecan	942.7	-0.0108	-0.0108	-0.0272
	(2516.7)	(0.0799)	(0.0799)	(0.0801)
Black	-2325.9	-0.148	-0.0709	-0.145	-0.0746
	(1487.9)	(0.0475)	(0.176)	(0.176)	(0.176)
Hispanic	1990.8	0.103	???	0.136	0.177
	(1504.0)	(0.0482)	(0.176)	(0.177)	(0.176)
Mixed Race (non-Hispanic)	-43.87	-0.0766
	(5476.4)	(0.172)
Constant	-57019.2	7.182	7.105	6.928	7.153
	(12387.9)	(0.419)	(0.451)	(0.451)	(0.447)
R2	0.189	0.164	0.164	0.158	0.164
RSS	2.30305e+12	2250.7	2250.7	2268.2	2252.8
N	2867	2867	2867	2867	2867

Standard errors in parentheses