- A researcher is trying to model the level of UK personal consumption expenditure i.e. the total amount spent by households on goods and services for consumption. Using quarterly data from quarter 1 1997 to quarter 4 2019, the following regression model is estimated (with
*t*-ratios given below in parentheses):

where *C _{t}* is UK personal consumption expenditure in millions of £s,

*time*is a linear trend variable,

*Q2*is a dummy variable that equals 1 in the second quarter of each year and zero otherwise,

_{t}*Q3*is a dummy variable that equals 1 in the third quarter of each year and zero otherwise and

_{t}*Q4*is a dummy variable that equals 1 in the fourth quarter of each year and zero otherwise.

_{t}- Interpret and discuss the estimated values of the regression coefficients on the dummy variables
*Q2*,*Q3*and*Q4*. - Using the t-ratios given above, determine whether there is evidence of significant seasonality in UK personal consumption expenditure. Clearly explain how you reach your conclusion.

- Using two separate equations, write the estimated regression model that applies in the second quarter of each year and the regression model that applies in the third quarter of each year.

- Define and briefly explain the concept of a ‘structural break’. Explain how you could test for the existence of a structural break in personal consumption expenditure after the financial crisis of 2008. When answering the question, clearly write out the regression model that you would use (you may ignore the seasonal effects discussed above to keep things simple) and clearly define the dummy variables that are used in the model.