econometrics sample test 2 Janek

OLS the parameters of picture. Var BUSTRAVL rep urban trans by bus, INCOME avr inc/cap, DENSITY density of city and LANDAREA land area of the city. For significance level of 10%, test for the normal distribution of the errors using the Jarque-Bera test.

ols BUSTRAVL const INCOME DENSITY LANDAREA ENTER ols BUSTRAVL const INCOME DENSITY LANDAREA --vcv ENTER series ehat1=$uhat ENTER normtest ehat1 --jbera ENTER normtest ehat1 --all ENTER scalar cv1=critical(c, 2,0.1)

Selected result 1: Below report: the estimated model, the Jarque Bera test statistic, the p-value and your conclusion from the test.

Jarque-Bera test statistic = 0.102925, p-value = 0.949839, conclusion: we do not reject the null hypothesis. The errors are normally distributed.

2. Using significance level of 5%, perform two F tests: 1) to check the overall significance of the model, 2) to verify the null hypothesis that, after controlling for DENSIT Y, variables INCOME and LANDAREA are jointly insignificant.

ols BUSTRAVL const INCOME DENSITY LANDAREA Escalar SSEul=$ess Escalar DFul=$df Eols BUSTRAVL const DENSITY Escalar SSErl=$ess Escalar Ftest=((SSErl-SSEul)/2)/(SSEul/DFul) Escalar cv21=critical(f, 2, DFul,0.05) Escalar pva121=pvalue(f, 2, DFul, Ftest)

Selected result 2: Below: provide the values of the test statistics, the corresponding p-values and your conclusions from these tests.

1) F(3, 36) =43.12917, p-value=5.24e-12, conclusion: we reject the null hypothesis. At least one explanatory variable is significant. 2) F(2, 36) = 21.7016, p-value = 6.55183e-007. We reject the null hypothesis.

3. For significance level of 5%, perform a test (a t test or an F test) of the hypotheses in the picture. Write down the test statistic value, the p-value and the final conclusion.

ols BUSTRAVL const INCOME DENSITY LANDAREA ENTER restrict ENTER 20*b[3]-b[4]=0 ENTER end restrict Selected result: F(1, 36) = 0.0280562, p-value = 0.867914. We do not reject the null hypothesis.

4. Calculate the 90% interval estimate for Beta2 + 2Beta3. Report the interval below.

scalar lambda_hat1=$coeff(INCOME)+2*$coeff(DENSITY) ENTER scalar se_lambda_hat1=sqrt($vcv[2,2]+(2)^2*$vcv[3,3]+2*2*$vcv[2,3]) ENTER scalar lb=lambda_hat1-critical(t,$df,0.05)*se_lambda_hat1 ENTER scalar ub=lambda_hat1+critical(t,$df,0.05)*se_lambda_hat1

Selected result 4:

(0.586014; 0.931244)

5. Using significance level of 1%, test for heteroskedasticity of the error term using the Breusch-Pagan test. Obtain robust standard errors. Below report the test statistic value, the p-value, your conclusion from the test and robust standard errors.

ols BUSTRAVL const INCOME DENSITY LANDAREA ENTER modtest --breusch-pagan ENTER scalar cv51=critical(c, 2,0.01) ENTER ols BUSTRAVL const INCOME DENSITY LANDAREA --robust

Selected result 5:

test statistic = 5.535870, p-value = 0.001412. We reject the null hypothesis. The errors are heteroskedastic. Robust s.e.: 1448.41, 0.0900911, 0.0636698, 2.27958.

6. Construct a dummy variable with a name FARE_IND taking value 1 if bus fare costs more than 1.2 (FARE >1.2) and 0 otherwise. Estimate the parameters of the model in the picture. Below interpret BetaHat5.

series FARE_IND=(FARE>1.2) ENTER ols BUSTRAVL const INCOME DENSITY LANDAREA FARE_IND selected result: BetaHat5 = -1328.63

7. Using AIC select a better model from the two in the picture. Compute variance inflation factors (VIFs) for the larger model. Below indicate which model should be selected and whether there is collinearity problem in the larger model.

ols BUSTRAVL const INCOME DENSITY LANDAREA ENTER ols BUSTRAVL const DENSITY LANDAREA Selected result: First model should be selected, there is no collinearity problem.