1) You have collected quarterly data for real GDP ( over time and have estimated
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1) You have collected quarterly data for real GDP ( over time and have estimated the following model: 7.866 + 0.00679·Z, (0.007) (0.00008) In y, = 20.98, SER-0.036 Standard errors (s.e.) in (parentheses) and where Zt is a deterministic time trend, which takes on the value of 1 in the 1st observation, and is increased by one for each succeeding observation to time period T. a) Describe the functional form of this model. b) Interpret the slope coefficient. Does it make sense? c) Interpret and comment on the size of the r. Are you surprised by its value? d) Do you think that given the regression r. you should use this equation to forecast real GDP beyond the sample period? e) Why or Why not? Be sure to include a discussion of stationarity, identifying any additional data transformations here that you might choose to model instead.Explanation / Answer
(a) Here the model is
ln (Real quartly GDP) = 7.866 + 0.00679 * Time
(b) Here the slope coefficient is 0.00679, that means if we increase the quarter value by 1 unit or we can say in the next quarter, we will get real quartly GDP increase by 0.000679 unit s
It make sense as their is increase in GDP as time progresses and as the dependent variable is in logarithmic scale. The slope will effect exponentially in real terms.
(c) Here the size of r2= 0.98 that means that 98% of variation in the logarithmic value of GDP as variation in the time.
(d) Yes, as the given R2which tells us that there is very strong relationship between these two variables and it can be used to forecast real GDP in the given period but for beyond that period it is not suitable as this will be an extrapolation and not regression here.
(e) Here as we know from statistical concept stationarity , here we take the assumption that the time series can be rendered approximately stationary where whose statistical properties such as mean, variance, autocorrelation, etc. are all constant over time. So we can do an additional transformation and use the dependent variable (Yt -Yt-1) to include the feature of stationarity assumption in the regression analysis
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