Time Series Econometrics

Econometrics
QUESTION 1 The file ‘TS_CWK_23.xlsx’ shows quarterly data for workforce jobs in the UK wholesale and retail service industry (000s jobs, RET_JOB) and UK Real Household expenditure (£m, HH_EXP) from 1978 Q2 to 2022 Q2 (both series have been seasonally adjusted)
a. Transform the variables so that the econometric analysis of retail/wholesale service industry jobs and real household expenditure can be made in percentage terms. State what transformation you have made. (1 MARK)
The variables were transformed using the “genr” function where "log" function was used to calculate the percentage change, and the "*100" is used to convert the change into percentage terms.
b. Test the transformed variables for stationarity using the Augmented DickeyFuller (ADF) test with 4 AR lags and interpret the test results. Perform any further transformations and tests necessary to demonstrate that stationarity in both variables has been achieved. (3 MARKS)
The stationarity in both variable is satisfied.
(Note: you should retain any transformations made in part a and b throughout the remainder of question one)
c. Model RET_JOB as a function of HH_EXP using 8 distributed lags. Test back the lags of this model using the 5% significance level. (2 MARS)
d. Interpret the value of R-squared and its statistical significance for the final model of part c. (1 MARK
The analysis indicates that UK wholesale and retail service industry (RET_JOBs) accounts for 53.67 percent variation in real household expenditure. The model is statistically significant as the p value is lower than 0.05.
e. Interpret the individual model coefficients and their statistical significance for the final model in part c. (3 MARKS)
The F-statistic of 10.93345 with a very small p-value (p<0.001) suggests that there is a significant relationship between the percentage changes in retail/wholesale service industry jobs and real household expenditure with 8 distributed lags. This implies that changes in real household expenditure have a significant effect on the number of jobs in the retail/wholesale service industry after accounting for the lagged effects.
f. Show how you calculate the long-run elasticity of retail/wholesale jobs with respect to household expenditure in the final model estimated in part c. Interpret the calculated value. (2 MARKS)
The resulting equation from the model is RET_JOBS_PCT = 0.228507 + 0.0821*HH_EXP_PCT. The values represents the mean of the 8 distributed lags.
g. Test the final model in part c for i. Up to fourth-order autocorrelation ii. Functional form misspecification iii. Normality of the residual Comment in each case on whether the model is adequately specified. (3 MARKS)
The Breusch-Godfrey Lagrange Multiplier (LM) test is used to test for higher-order autocorrelation up to fourth order. The p-value (P=0.5053) was greater than 0.05 indicating that there is no evidence of autocorrelation. Thus, the model is adequately specified.
The p-value for the Jacque-Bera test is is greater than the chosen significance level (0.05), indicating that the data meets the test of normality. The model may be adequately specified.
The p value from the Ramsey reset test was 0.0569, which is higher t...