Urgent Econometrics test

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Deferred Examination - July 2020

Econometric Methods and Modelling

EMET8005

Reading Time: 15 minutes

Writing Time: 2 Hours Scanning and Uploading Time: 45 minutes

Permitted materials: Non-programmable Calculators

You must attempt to answer all questions. Use your papers to answer both Part A and Part B Questions

Supplementary statistical tables are provided at the end.

This examination is worth 60 marks and it is worth 60% of the total assessment.

DO NOT TAKE THIS PAPER FROM THE EXAM ROOM

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Part A: Multiple choice questions: (20 x 1 = 20 marks) Answer ALL questions: (Please choose the best possible answer)

Q1. The LM (Lagrange Multiplier) test for heteroskedasiticity generates a test statistic N * R2 ~χ2(S-1). Where is the R2 in the test statistic measured? a) the original econometric model when estimated using the White correction technique b) the average from all the auxiliary regressions estimated with each explanatory variable as a function of the other explanatory variables c) the original econometric model before any test of heteroskedasticity has been performed d) the auxiliary regression of residuals as a function of the explanatory variables generating the heteroskedasticity Q2. If you run a LM test for heteroskedasiticity and reject the null hypothesis, what should you conclude? a) at least one coefficients in the auxiliary regression is significantly different from zero, the assumption ( ) ( ) 2 i ivar y var e σ= = is unlikely to be true b) there is no evidence of heteroskedasticity, the assumption ( ) ( ) 2 i ivar y var e σ= = is most likely true c) there is heteroskedasticity present and it is correctly specified as tested d) there is heteroskedasticity, but it is not linear in the explanatory variables

Q3. Which assumption is most likely to be violated with times series data:

a) ( ) 0tE e = b) 2( )tVar e σ=

c) ( ), 0, t scov e e t s= ≠

d) ( )2 0,te N σ Q4. How do you calculate the total multiplier for a finite distributed lag model:

0 1 1 2 2 ,t t t t q t q ty x x x x e− − −= α +β +β +β + +β + where q is the number of lags? a) qβ

b) 0 q

ss β

=∑ c) 1

q ss

β =∑

d) 0qβ β−

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Q5. Which of the following is not a valid criterion for choosing p and q in an ARDL model?

a) fewest number of lags that eliminates serial correlation b) statistical significance of coefficient estimates c) minimization of AIC and SC d) maximization of R2 Q6. Which of the following is NOT a reason nonlinear least squares is used to estimate an AR(1) model? a) linear least squares is not possible since the transformation that allows the new error term to be uncorrelated is no longer linear in parameters b) using OLS to estimate the untransformed model provides incorrect standard errors c) the algorithmic nonlinear optimization is less complicated to compute when error terms are correlated d) minimizing the sum of squares of uncorrelated error terms produces an estimator that is unbiased and consistent Q7. If the assumption that cov(x,e) = 0 is not true, what are the implications of least squares estimators? a) still BLUE for all sample sizes b) consistent and normally distributed in very large sample sizes c) unbiased, but not BLUE for small samples d) inconsistent; parameter estimates do not converge to true values regardless of sample size. Q8. If you reject the null hypothesis when performing a Hausman test, what should you conclude? a) at least one of the explanatory variables is endogenous b) there are no endogenous variables c) the 2SLS estimation has corrected the endogeneity in the initial model d) the 2SLS second stage equation still has endogenous variables Q9. Why should augmented Dickey-Fuller tests always be used when performing econometric analysis? a) the augmented tests allow for more degrees of freedom b) so we can test hypotheses using a t-distribution c) since no assumptions about the sign of ρ are needed to perform a one-tailed test d) to confirm that error terms are not autocorrelated Q10. How do you check for cointegration of two series? a) estimate a regression of one series as function of the other, then perform an augmented Dickey- Fuller test on estimated residuals b) estimate a regression of one series as a function of the other and test the significance of the parameter estimates c) test the significance of the covariance between the two series d) subtract one series from the other and check for stationarity of the difference

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Q11. What is a spurious regression?

a) statistically significant but meaningless results generated by regression analysis of non-stationary data b) the results generated by regression analysis of a stationary variable dependent on a non-stationary series c) regression analysis where endogenous and exogenous variables are reversed d) regression analysis that is impossible due to lack of identification Q12. Which non-stationary time series has a constant mean but non-constant variance?

a) random walk b) AR(1) with linear trend c) random walk with drift d) deterministic trend

Q13. If you perform a Chow test to compare two regressions and reject the null hypothesis, what should you conclude? a) there is not sufficient evidence that the regressions are significantly different b) the regression equations are statistically different c) the regression equations are equivalent d) it depends on how you set up the null hypothesis

Q14. What is the tradeoff researchers’ face when deciding how to deal with heteroskedasticity? a) Goldfeld-Quandt overstates heteroskedasticity but LM leads to more Type I errors b) White’s robust estimator should be used for hypothesis testing, but GLS is better for interval estimation c) GLS gives minimum variance, but results are more difficult to interpret d) White’s robust estimator requires no assumptions about the structure of the variance, but it is not as efficient as GLS estimates when the right structure is imposed on the variance Q15. The following economic model predicts whether a voter will vote for an incumbent school board member

1 2 3 4 5INCUMBENT MALE PARTY MARRIED KIDSβ β β β β= + + + + where INCUMBENT = 1 if the voter votes for them, 0 otherwise, MALE = 1 if the voter is a male, PARTY indicates the voter is registered with the same political party as the incumbent, MARRIED = 1 for married voters, 0 otherwise, and KIDS is the number of school age kids living with the voter. If you hypothesize males and females might have a different willingness to vote for a candidate registered with a different political party, which variable should you add to the economic model to allow you to test the hypothesis? a) MALE * PARTY b) MALE * MARRIED c) MARRIED * KIDS d) MARRIED * PARTY

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Q16. What are the consequences of using least squares when heteroskedasticity is present? a) no consequences, coefficient estimates are still unbiased b) confidence intervals and hypothesis testing are inaccurate due to incorrect standard errors c) all coefficient estimates are biased for variables correlated with the error term d) it requires very large sample sizes to get efficient estimates Q17. Which of the following is not a common cause of endogeneity?

a) measurement error b) simultaneous equations c) omitted variables d) continuous variables Q18. If series y and z have similar stochastic trends, but are otherwise unrelated, they are said to be

a) cointegrated b) cotrending c) converging d) jointly stationary

Q19. If you model has heteroskedastic error terms, but you do not know the functional form of the variance equation, what should be done? a) use White’s Robust Estimator b) use weighted least squares c) try different functional forms for the variance until the Lagrange Multiplier falls 10% d) add observations to the dataset and estimate again Q20. You have estimated the following simple regression model y = 379 + 1.44 x3 What is the elasticity when x = 8.49? a) 263.19 b) 311.39 c) 2.10 d) -24.7

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Part B: (Answer all the questions) Short answer/Numerical questions: Note: For all the below hypothesis tests, carefully state the (i) null and the alternative hypothesis, (ii) test statistics and the corresponding critical value, (iii) Rejection region, (iv) Decision rule and (v) Conclusion. Use 5% level of significance while carrying out the necessary tests.

Q1.

(a) State all of the assumptions of the multiple linear regression model. [3 marks] (b) State the Gauss-Markov Theorem. [1 marks]

corresponding covariance matrix are given by

2 3 ,

b b b

       =       −  

 3 2 1

cov 2 4 0 1 0 3

(b) − 

 = −     

Test the following hypothesis and state the conclusion:

1 2 3 4β β β− + = (against the alternative 1 2 3 4β β β− + ≠ ) [3 marks]

Q2. Table 1 shows the regression estimates using the data on 4682 houses that were sold in Stockton, California from Jan 1991 to December 1996. The regression model for house price includes as explanatory variables, the size of the house (SQFT), the age of the house (AGE), and the annual indicator (dummy) variables, omitting the indicator variable for 1991.

(a) Discuss the estimated coefficients on the indicator variables. [2 marks]

(b) What would have happened if we had included an indicator variable for 1991?

[2 marks]

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Table 1: 1 2 3 1 2 3 4 592 93 94 95 96PRICE SQFT AGE D D D D D eβ β β δ δ δ δ δ= + + + + + + + +

Dependent Variable: PRICE Method: Least Squares Date: 09/25/15 Time: 13:26 Sample: 1 4682 Included observations: 4682

Variable Coefficient Std. Error t-Statistic Prob. C 21456.20 1839.040 11.66707 0.0000

SQFT 72.78780 1.000145 72.77726 0.0000 AGE -179.4623 17.01123 -10.54964 0.0000 D92 -4392.846 1270.930 -3.456403 0.0006 D93 -10435.47 1231.800 -8.471727 0.0000 D94 -13173.51 1211.477 -10.87393 0.0000 D95 -19040.83 1232.808 -15.44509 0.0000 D96 -23663.51 1194.928 -19.80329 0.0000

R-squared 0.593567 Mean dependent var 109561.4

Adjusted R-squared 0.592958 S.D. dependent var 35411.80 S.E. of regression 22592.68 Akaike info criterion 22.89035 Sum squared resid 2.39E+12 Schwarz criterion 22.90137 Log likelihood -53578.30 Hannan-Quinn criter. 22.89422 F-statistic 975.1484 Durbin-Watson stat 2.027764 Prob(F-statistic) 0.000000

Q3. Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for houses. In this question we consider an equation where monthly change in the new one-family houses sold in the US depends on the last month’s change in the 30-year conventional mortgage rate. Let HOMES be the number of new houses sold (in thousands) and IRATE be the mortgage rate. Their monthly changes are denoted by 1t t tDHOMES HOMES HOMES −= − and

1t t tDIRATE IRATE IRATE −= − . Using data from January 1992 to March 2010, the following least squares regression estimates is obtained:



12.077 53.51 218 ( ) (3.498) (16.98)

t tDHOMES DIRATE observations se

−= − − =

(a) Interpret the estimate -53.51. [1 marks]

(b) Let t̂e denote the residuals from the above equation. Use the following estimated equation to conduct LM test for first-order autoregressive errors.

1ˆ ˆ0.1835 3.210 0.3306 0.1077 ( ) (16.087) (0.0649) 218

t t te DIRATE e R se observations

−= − − − = =

[3 marks]

Q4. A sample of 200 Chicago households was taken to investigate how far American households tend to travel when they take vacation. Measuring distance in miles per year, the following model was estimated: 1 2 3 4MILES INCOME AGE KIDS eβ β β β= + + + + .

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(a) Ordering the observations according to descending values of INCOME, and applying least squares to the first 100 observations, and again to the second 100 observations, yields the sum square errors 7 71 22.9471 10 and 1.0479 10SSE SSE= × = × respectively. Use the Goldfeld Quandt test to test for heterokedastic errors. Include specification of the null and the alternative hypothesis.

[3 marks] (b) Tables 2 and 3 contain two sets of estimates: those from least squares and those least squares

with White’s standard errors respectively. How do White’s standard errors compare with the least squares standard errors?

[2 marks] Table 2: Least square estimates

Dependent Variable: MILES Method: Least Squares Date: 09/25/15 Time: 14:11 Sample: 1 200 Included observations: 200

Variable Coefficient Std. Error t-Statistic Prob. C -391.5480 169.7752 -2.306273 0.0221

INCOME 14.20133 1.800256 7.888506 0.0000 AGE 15.74092 3.757370 4.189346 0.0000 KIDS -81.82642 27.12960 -3.016131 0.0029

R-squared 0.340605 Mean dependent var 1054.230

Adjusted R-squared 0.330512 S.D. dependent var 552.7990 S.E. of regression 452.3125 Akaike info criterion 15.08642 Sum squared resid 40098973 Schwarz criterion 15.15239 Log likelihood -1504.642 Hannan-Quinn criter. 15.11312 F-statistic 33.74740 Durbin-Watson stat 1.948060 Prob(F-statistic) 0.000000

Table 3: Least square estimates with White standard errors

Dependent Variable: MILES Method: Least Squares Date: 09/25/15 Time: 14:14 Sample: 1 200 Included observations: 200 White heteroskedasticity-consistent standard errors & covariance

Variable Coefficient Std. Error t-Statistic Prob. C -391.5480 142.6548 -2.744724 0.0066

INCOME 14.20133 1.938857 7.324589 0.0000 AGE 15.74092 3.965735 3.969232 0.0001 KIDS -81.82642 29.15438 -2.806660 0.0055

R-squared 0.340605 Mean dependent var 1054.230

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Q5. To examine the quantity theory of money, Brum (2005) specified the equation:

1 2 3INFLAT MONEY OUTPUT eβ β β= + + +

where INFLAT is the growth rate of general price level, MONEY is the growth rate of the money supply, and OUTPUT is the growth rate of the national output. Table 4 shows the regression estimates for this specification.

(a) It is argued that OUTPUT may be endogenous. Four instrumental variables are proposed, INITIAL = initial level of real GDP, SCHOOL = a measure of the population’s educational attainment, INV = average investment share of GDP, and POPRATE = average population growth rate. Table 5 shows the least squares regression estimates, where OUTPUT is regressed on the four proposed instruments and money. What is the usefulness of this regression?

[2 marks]

(b) The residuals obtained from the regression in table 5 is saved as VHAT. Table 6 shows the least squares regression estimates for the following specification:

1 2 3INFLAT MONEY OUTPUT VHAT eβ β β γ= + + + + . Is the variable OUTPUT endogenous? Perform the appropriate test to justify your answer.

[3 marks]

Table 4: Regression output for 1 2 3INFLAT MONEY OUTPUT eβ β β= + + +

Dependent Variable: INFLAT Method: Least Squares Date: 10/01/15 Time: 14:26 Sample: 1 76 Included observations: 76

Variable Coefficient Std. Error t-Statistic Prob. C -0.234214 0.979925 -0.239012 0.8118

MONEY 1.033131 0.009042 114.2565 0.0000 OUTPUT -1.662006 0.250566 -6.633003 0.0000

R-squared 0.994797 Mean dependent var 25.35395

Adjusted R-squared 0.994654 S.D. dependent var 58.94767 S.E. of regression 4.309966 Akaike info criterion 5.798411 Sum squared resid 1356.034 Schwarz criterion 5.890413 Log likelihood -217.3396 Hannan-Quinn criter. 5.835179 F-statistic 6978.325 Durbin-Watson stat 2.305899 Prob(F-statistic) 0.000000

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Table 5: Regression output for 1 2 3 4 5 6+ + + OUTPUT MONEY INITIAL SCHOOL INV POPRATE eα α α α α α= + + +

Dependent Variable: OUTPUT Method: Least Squares Date: 10/01/15 Time: 14:49 Sample: 1 76 Included observations: 76

Variable Coefficient Std. Error t-Statistic Prob. C 2.552969 1.231741 2.072650 0.0419

MONEY -0.004796 0.003846 -1.247059 0.2165 INITIAL -0.270930 0.156711 -1.728848 0.0882 SCHOOL -1.160768 0.883908 -1.313222 0.1934

INV 12.90258 3.602194 3.581866 0.0006 POPRATE -0.438909 0.279795 -1.568681 0.1212

R-squared 0.241115 Mean dependent var 2.997368

Adjusted R-squared 0.186909 S.D. dependent var 2.026950 S.E. of regression 1.827732 Akaike info criterion 4.119685 Sum squared resid 233.8423 Schwarz criterion 4.303691 Log likelihood -150.5480 Hannan-Quinn criter. 4.193223 F-statistic 4.448129 Durbin-Watson stat 2.298671 Prob(F-statistic) 0.001414

Table 6: Regression output for 1 2 3 + INFLAT MONEY OUTPUT VHAT eδ δ δ γ= + + + Dependent Variable: INFLAT Method: Least Squares Date: 10/01/15 Time: 14:50 Sample: 1 76 Included observations: 76

Variable Coefficient Std. Error t-Statistic Prob. C -1.093985 1.852740 -0.590468 0.5567

MONEY 1.035059 0.009744 106.2265 0.0000 OUTPUT -1.394200 0.549880 -2.535463 0.0134

VHAT -0.338844 0.618526 -0.547825 0.5855 R-squared 0.994818 Mean dependent var 25.35395

Adjusted R-squared 0.994602 S.D. dependent var 58.94767 S.E. of regression 4.330777 Akaike info criterion 5.820567 Sum squared resid 1350.405 Schwarz criterion 5.943237 Log likelihood -217.1815 Hannan-Quinn criter. 5.869592 F-statistic 4607.713 Durbin-Watson stat 2.279388 Prob(F-statistic) 0.000000

Q6. Tables 7, 8, 9, 10 and 11 use quarterly data on real GDP for Mexico ( )MEXICO and the United States ( )USA from the first quarter of 1980 to the fourth quarter of 2006. Both series have been standardised so that the average value in 2000 is 100. For all the Augmented Dickey-Fuller tests shown in Tables 7, 8, 9 and 10, the maximum lag was set to 12 and the optimal lag was selected based on Schwarz Information Criteria (SIC).

(a) Tables 7 and 8 respectively show the augmented Dickey-Fuller tests for real GDP of Mexico ( )MEXICO and the first difference of real GDP of Mexico ( )DMEXICO . What is the order of integration for the real GDP of Mexico series?

[2 marks]

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(b) Tables 9 and 10 respectively show the augmented Dickey-Fuller tests for real GDP of United

States ( )USA and the first difference real GDP of United States ( )DUSA . What is the order of integration for the real GDP of United States series?

[2 marks]

(c) The real GDP of Mexico series is regressed on a constant and the real GDP of United States series and the residual from this regression is saved as RESID1. Table 11 shows the Engle- Granger cointegration test results for the RESID1 series. Perform the test for cointegration between real GDP of Mexico series and the real GDP of United States series based on this table. Is Mexico’s real GDP cointegrated with, or spuriously related to, United State’s real GDP?

[3 marks]

Table 7: Augmented Dickey-Fuller test for MEXICO

Augmented Dickey-Fuller Test Equation Dependent Variable: D(MEXICO) Method: Least Squares Date: 10/01/15 Time: 16:22 Sample (adjusted): 1980Q2 2006Q3 Included observations: 106 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. MEXICO(-1) -0.050233 0.034328 -1.463327 0.1464

C 2.792020 1.824431 1.530351 0.1290 @TREND("1980Q1") 0.033181 0.018275 1.815591 0.0723

R-squared 0.042695 Mean dependent var 0.548001

Adjusted R-squared 0.024107 S.D. dependent var 1.492569 S.E. of regression 1.474469 Akaike info criterion 3.642366 Sum squared resid 223.9280 Schwarz criterion 3.717747 Log likelihood -190.0454 Hannan-Quinn criter. 3.672918 F-statistic 2.296879 Durbin-Watson stat 2.138751 Prob(F-statistic) 0.105702

Table 8: Augmented Dickey-Fuller test for DMEXICO

Augmented Dickey-Fuller Test Equation Dependent Variable: D(DMEXICO) Method: Least Squares Date: 10/15/15 Time: 13:53 Sample (adjusted): 1980Q3 2006Q3 Included observations: 105 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. DMEXICO(-1) -1.087853 0.098718 -11.01976 0.0000

C 0.604425 0.155236 3.893599 0.0002 R-squared 0.541070 Mean dependent var 0.028202

Adjusted R-squared 0.536614 S.D. dependent var 2.200205 S.E. of regression 1.497733 Akaike info criterion 3.664646 Sum squared resid 231.0500 Schwarz criterion 3.715198 Log likelihood -190.3939 Hannan-Quinn criter. 3.685131 F-statistic 121.4351 Durbin-Watson stat 1.936655 Prob(F-statistic) 0.000000

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Table 9: Augmented Dickey-Fuller test for USA

Augmented Dickey-Fuller Test Equation Dependent Variable: D(USA) Method: Least Squares Date: 10/01/15 Time: 16:24 Sample (adjusted): 1980Q4 2006Q3 Included observations: 104 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. USA(-1) -0.034918 0.021006 -1.662248 0.0996

D(USA(-1)) 0.203167 0.096837 2.098019 0.0384 D(USA(-2)) 0.238088 0.092945 2.561614 0.0119

C 1.876773 0.979015 1.917002 0.0581 @TREND("1980Q1") 0.023465 0.012967 1.809568 0.0734

R-squared 0.196178 Mean dependent var 0.620606

Adjusted R-squared 0.163701 S.D. dependent var 0.486742 S.E. of regression 0.445123 Akaike info criterion 1.265949 Sum squared resid 19.61528 Schwarz criterion 1.393083 Log likelihood -60.82935 Hannan-Quinn criter. 1.317455 F-statistic 6.040406 Durbin-Watson stat 1.920008 Prob(F-statistic) 0.000216

Table 10: Augmented Dickey-Fuller test for DUSA

Augmented Dickey-Fuller Test Equation Dependent Variable: D(DUSA) Method: Least Squares Date: 10/15/15 Time: 13:59 Sample (adjusted): 1980Q4 2006Q3 Included observations: 104 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. DUSA(-1) -0.531156 0.107798 -4.927305 0.0000

D(DUSA(-1)) -0.254101 0.090823 -2.797778 0.0062 C 0.336985 0.078910 4.270502 0.0000 R-squared 0.399479 Mean dependent var 0.006269

Adjusted R-squared 0.387587 S.D. dependent var 0.575831 S.E. of regression 0.450627 Akaike info criterion 1.272068 Sum squared resid 20.50952 Schwarz criterion 1.348348 Log likelihood -63.14752 Hannan-Quinn criter. 1.302971 F-statistic 33.59359 Durbin-Watson stat 1.922546 Prob(F-statistic) 0.000000

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Table 11: Engle-Granger cointegration test using RESID1

Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID1) Method: Least Squares Date: 10/15/15 Time: 14:07 Sample (adjusted): 1980Q2 2006Q3 Included observations: 106 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. RESID1(-1) -0.087832 0.042258 -2.078484 0.0401 R-squared 0.038830 Mean dependent var 0.038588

Adjusted R-squared 0.038830 S.D. dependent var 1.448945 S.E. of regression 1.420535 Akaike info criterion 3.549333 Sum squared resid 211.8815 Schwarz criterion 3.574460 Log likelihood -187.1147 Hannan-Quinn criter. 3.559517 Durbin-Watson stat 2.189454

Q7. Table 12 shows the regression output for the following specification:

2 2 1 2 3 4 5 6ln( )WAGE EDUC EDUC EXPER EXPER HRSWK eβ β β β β β= + + + + + +

where, variables hourly wage WAGE, years of education EDUC , years of experience EXPER and hours worked per week HRSWK are collected from 2008 Current Population Survey (CPS). Table 13 shows the regression output from the following restricted specification: 21 4 5 6ln( )WAGE EXPER EXPER HRSWK eβ β β β= + + + +

Table 12: 2 21 2 3 4 5 6ln( )WAGE EDUC EDUC EXPER EXPER HRSWK eβ β β β β β= + + + + + +

Dependent Variable: LOG(WAGE) Method: Least Squares Date: 08/13/15 Time: 16:47 Sample: 1 1000 Included observations: 1000

Variable Coefficient Std. Error t-Statistic Prob. C 1.387825 0.228769 6.066488 0.0000

EDUC 0.010510 0.029992 0.350429 0.7261 EDUC^2 0.002851 0.001073 2.656293 0.0080 EXPER 0.037192 0.004765 7.805352 0.0000

EXPER^2 -0.000574 8.38E-05 -6.855775 0.0000 HRSWK 0.006828 0.001568 4.354194 0.0000

R-squared 0.259891 Mean dependent var 2.856988

Adjusted R-squared 0.256168 S.D. dependent var 0.580619 S.E. of regression 0.500758 Akaike info criterion 1.460596 Sum squared resid 249.2544 Schwarz criterion 1.490042 Log likelihood -724.2980 Hannan-Quinn criter. 1.471788 F-statistic 69.80912 Durbin-Watson stat 2.012761 Prob(F-statistic) 0.000000

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Table 13: 21 4 5 6ln( )WAGE EXPER EXPER HRSWK eβ β β β= + + + +

Dependent Variable: LOG(WAGE) Method: Least Squares Date: 08/13/15 Time: 16:49 Sample: 1 1000 Included observations: 1000

Variable Coefficient Std. Error t-Statistic Prob. C 2.022752 0.089933 22.49180 0.0000

EXPER 0.037806 0.005282 7.156950 0.0000 EXPER^2 -0.000627 9.28E-05 -6.751409 0.0000 HRSWK 0.009406 0.001726 5.450627 0.0000

R-squared 0.088432 Mean dependent var 2.856988

Adjusted R-squared 0.085686 S.D. dependent var 0.580619 S.E. of regression 0.555186 Akaike info criterion 1.664965 Sum squared resid 306.9986 Schwarz criterion 1.684596 Log likelihood -828.4825 Hannan-Quinn criter. 1.672426 F-statistic 32.20754 Durbin-Watson stat 2.003548 Prob(F-statistic) 0.000000

(a) Suppose you want to test the hypothesis that a year of education has the same effect on ln( )WAGE as a year of experience. What null and alternative hypothesis would you set up?

[3 marks]

(b) Write down the restricted model in (a), assuming that the null hypothesis is true.

[2 marks]

(c) Test the null hypothesis that 2 3andβ β are jointly insignificant (against the alternative that at least one of them is significantly different from zero).

[3 marks]

END OF THE EXAMINATION PAPER

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Critical Values for the Dickey–Fuller Test

Critical Values for the Cointegration Test

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