Gross Domestic Product (GDP) is a measure of overall activity in the economy. It is defined as the value at the final point of sale of all goods and services produced during a given period by both domestic and foreign-owned enterprises. GDP data for the 1950-2004 period shown in Figure 6.3 offer the basis to test the abilities of simple constant change and constant growth models to describe the trend in GDP over time. However, regression results generated over the entire 1950-2004 period cannot be used to forecast GDP over any subpart of that period. To do so would be to overstate the forecast capability of the regression model because, by definition, the regression line minimizes the sum of squared deviations over the estimation period. To test forecast reliability, it is necessary to test the predictive capability of a given regression model over data that was not used to generate that very model. In the absence of GDP data for future periods, say 2005-2010, the reliability of alternative forecast techniques can be illustrated by arbitrarily dividing historical GDP data into two subsamples: a 1950-99 50-year test period, and a 2000-04 5-year forecast period. Regression models estimated over the 1950-99 test period can be used to “forecast” actual GDP over the 2000-04 period. In other words, estimation results over the 1950-99 sub period provide a forecast model that can be used to evaluate the predictive reliability of the constant growth model over the 2000-04 forecast period.
A. Use the regression model approach to estimate the simple linear relation between the natural logarithm of GDP and time (T) over the 195099 sub period, where
in Gap = b0 + b1Tt + us
and in Gap is the natural logarithm of GDP in year t, and T is a time trend variable (where T1950 = 1, T1951 = 2, T1952 = 3, . . ., and T1999 = 50); and u is a residual term. This is called a constant growth model because it is based on the assumption of a constant percentage growth in economic activity per year. How well does the constant growth model fit actual GDP data over this period?
B. Create a spreadsheet that shows constant growth model GDP forecasts over the 2000-04 period alongside actual figures. Then, subtract forecast values from actual figures to obtain annual estimates of forecast error, and squared forecast error, for each year over the 2000-04 period.
Finally, compute the correlation coefficient between actual and forecast values over the 200004 period. Also compute the sample average (or root mean squared) forecast error. Based upon these findings, how well does the constant growth model generated over the 195099 period forecast actual GDP data over the 200004 period?