ECON20110 Econometrics Semester 2 2018/19
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ECON20110 Econometrics
Semester 2 2018/19
= Information and model used for questions 1 and 2 =
Consider a model of the price of whiting (a type of fish) sold at the local market. You have the following information on catches for the past 111 days:
· price - the price paid (in f) per kilogram sold,
· quan - the quantity of whiting sold, in kilograms,
· stormy - dummy variable, =1 if high wind and waves, =0 otherwise,
· rainy - dummy variable, =1 if raining on shore on day of catch, =0 otherwise, · weekday - dummy variable, =0 if day of catch is Saturday or Sunday, =1 otherwise.
The model is:
lpricet = β0 + β1 lquant + β2 stormyt + β3rainyt + ut (1)
where lprice and lquan are the natural logarithms of price and quan respectively.
1. The model in (1) is estimated using OLS with the following regression output from R:
Call:
lm(formula = lprice ~ lquan + stormy + rainy, data = fish)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.3746 0.3902 0.96 0.3392
lquan -0.0880 0.0444 [A] [B]
stormy 0.3973 [C] 4.97 2.5e-06
rainy [D] 0.0765 2.85 0.0052
Residual standard error: 0.334 on [E] degrees of freedom Multiple R-squared: 0.254,Adjusted R-squared: 0.233 F-statistic: 12.1 on 3 and [E] DF, p-value: 6.64e-07
(a) Some values are missing from the output above. What are the values for [A] to [E]? [10 MARKS]
(b) Interpret the estimated coefficients βˆ1 and βˆ2 .
[5 MARKS]
(c) You suspect that the model for the price paid for fish at the market as given in model (1) is different at the weekend than during the week. Describe how you could test whether there is a structural difference between a model for weekdays and a different model for the weekend. Be clear on any additional regressions you would need to run, any additional assumptions required, your null and alternative hypotheses, and the appropriate test statistic and associated distribution.
[10 MARKS]
2. (a) A colleague is helping you with your analysis and provides you with the following output from R.
Breusch-Godfrey test for [... output missing ...]
data: reg_fish
LM test = 51, df = 2, p-value = 8e-13
What is your colleague testing? Describe how the Breusch-Godfrey test is performed. Clearly state the auxiliary regression, the null and alternative hypotheses, the relevant test statistic and its distribution, and your decision rule.
What do you conclude?
[12 MARKS]
(b) In addition to the OLS estimates from Question 1 you also obtain the Newey-West standard errors:
> coeftest(reg_fish, vcov = NeweyWest)
t test of coefficients:
(Intercept) lquan stormy rainy
Estimate Std. Error t value
0.3746
-0.0880
0.3973
0.2183
Pr(>|t|)
0.23869
0.01485
0.00062
0.01640
Based on your conclusions in part (a) perform the following hypothesis tests. Be clear to state the test statistic and relevant distribution, your decision rule, and your conclusion.
(i) H0 : β1 = 0 versus HA : β1 0 (use 5% significance level)
[4 MARKS]
(ii) H0 : β2 > 0.5 versus HA : β2 < 0.5 (use 10% significance level)
[4 MARKS]
(c) Given your conclusions from part (a) what can you say about the distribution of the estimator βˆ1 ?
[5 MARKS]
3. (a) The monthly inflation and unemployment rates for the UK from January 2006 to April 2018 are plotted below. Also plotted are the auto-correlation functions for each time-series.
Making use of the above plots, why might you have concerns about using OLS to estimate the following model
inflationt = α0 + α 1unemploymentt + ut ? (2)
[10 MARKS]
(b) Suppose that Yt follows the stationary AR(1) model Yt = 2.5 + 0.7Yt − 1 + ut where ut is i.i.d. with E[ut] = 0 and Var(ut ) = 9.
(i) Compute the unconditional mean and variance of Yt .
[6 MARKS]
(ii) Compute the first two autocorrelations of Yt .
[4 MARKS]
(iii) Suppose that YT =102.3. Compute E[YT+2|IT ], where IT = {YT , YT − 1 , YT −2 , . . . }. [5 MARKS]
4. Consider the choice of joining the labour force, or not, faced by married women with or without young children. The variable infl takes the value 1 if the woman is working and 0 otherwise. We assume that the choice of working is based on the husband’s wage (hwage), the number of years of education for the woman (educ), and the number of young children in the house (kidslt6).
The estimated model using OLS is
i一nfl = 0.08 - 0.016 hwage + 0.054 educ - 0.224 kidslt6.
(0.033)
(3)
(a) (i) Interpret the estimated coefficients for the variables educ and kidslt6.
[4 MARKS]
(ii) Donna, Halley and Sherri are all friends who went to university together (educ = 17) and their husbands all earn the same (hwage = 7.48). However, Donna has no children, Halley has one young child, and Sherri has two young children. What are the predicted probabilities that each is working?
[4 MARKS]
The summary information for the fitted values i一nfl from the above regression
in R are as follows:
> summary(fitted.values(inlf_reg))
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.198 0.478 0.598 0.568 0.658 0.934
(iii) With reference to your answer in part (a)(ii) and the summary information above, give two reasons why linear probability models may not be suitable for estimating models with binary dependent variables.
[7 MARKS]
(b) When testing the null hypothesis H0 : βeduc < 0.05 versus HA : βeduc > 0.05 you obtain a p-value of 0.31. When discussing your findings with a friend they make the following statement.
”That means there is a 31% probability the true value of βeduc is larger than 0.05”.
Explain why this interpretation is incorrect and briefly explain how a Bayesian ap- proach does provide the interpretation they are after. What additional piece of information would they require to estimate this probability?
[10 MARKS]
2022-05-25