In this exercise, we use a subset of the data compiled by Everaert and Pozzi \({ }^{18}\) to forecast growth in per capita private consumption (CONSN) and growth in per capita real disposable income (INC) in France. Their data are annual from 1971 to 2007 and are stored in the data file france_ep.

a. To forecast consumption growth consider the autoregressive model

Estimate this model for \(p=1,2,3\), and 4. In each case, use 33 observations to ensure the same number of observations for each value of \(p\). Based on significance of coefficients, autocorrelation in the residuals, and the Schwarz criterion, choose a suitable value for \(p\).

b. For the choice of \(p\) in part (a), reestimate the model using all available observations and use it to find 95\% interval forecasts for \(\operatorname{CONSN}_{2008}, \operatorname{CONSN}_{2009}\) and \(\operatorname{CONSN}_{2010}\).

c. To forecast income growth, consider the ARDL model

Estimate this model for \(p=1,2\) and \(q=1,2\). In each case, use 35 observations to ensure the same number of observations for all values of \(p\) and \(q\). Use the Schwarz criterion to choose between the four models. In the model of your choice, are the coefficient estimates significantly different from zero at a \(5 \%\) level? At a \(10 \%\) level? Does the correlogram of residuals suggest that there is any serial correlation?

d. Use the model chosen in part (c) to find \(95 \%\) interval forecasts for \(I N C_{2008}, I N C_{2009}\), and \(I N C_{2010}\), given that \(H O U R S_{2008}=H O U R S_{2009}=-0.0066\).

Transcribed Image Text:

P CONSN, = 6+0 CONSN,_,+ e s=1