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Quantitative Research Method

Q1. Multiple regression: Determinants of wages
Use multiple regression model to determine which factors explain wages. Preliminary study finds that age is a factor that determines wage. The other three variables considered are years of education, years of apprentice trainings in firms and a different measure for the apprentice trainings. Use the data mult_reg.xls

Research Question:
1. Is age a determinant of productivity?
2. Is apprentice training more efficient than education in raising the level of wage?
Econometric model:
Please state your econometric model with appropriate assumptions.

Hypothesis testing
Please state the hypotheses you are testing and the rationale for these

Basic statistics:
Please provide the following information in an appropriate table and explain their implications.
Mean, standard deviation, skewness, kurtosis, Jarque-Bera normality test
Model estimates:

Run regressions and report your findings. Please put your t-stats in brackets and indicate significance with *, **, *** for significance at 10%, 5% and 1% respectively.

Which is the best model and why?

Diagnostic tests:
Please do the following tests and explain their implications.
1. Auto-correlation test
2. Collinearity check
Q2. Time Series Analysis of Price and Earnings
You are given time series of price (lnP) and earnings (lnE), and you would like to analyse the value relevance of earnings. Specifically, you are first required to determine if the time series are stationary or integrated with order one, and in the latter case if they are co-integrated. Then, dependent on the outcome of the above analyses, an appropriate autoregressive distributed lag (ARDL) model or ECM is to be fitted.Use the date Timeseries.xls.
Research Question: Can change in price be explained by earnings?
Preliminary tests:
1. Test for presence of unit root
2. Test for cointegration

Econometric model:
The econometric model will depend on the outcome of unit root tests and cointegration test.

Hypotheses testing
Test for significance of relevant coefficients, i.e., the coefficient of change in earnings and (if appropriate) the coefficient of error from the cointegrating relationship.

Basic statistics:
Mean, standard deviation, skewness, kurtosis, Jarque-Bera normality test

Model estimates (t-stats in brackets):
Which is the best model?

Diagnostic tests:
Auto-correlation test


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