First of all, I would like to apologize for showing the results in Spanish, but I couldn’t find the way to change Gretl’s language. However, all the explanations are in English, so I hope there is no problem to understand the results.
Secondly, I would just inform you that the time-series data that I have used is “U.S. macro data, 1950-2000” from Greene Sample folder in Gretl.
Before building the model…
I would try to explain the variable “Real GDP” using the variables “Real consumption expenditures”, “Real Private-Sector Investment”, “Real government expenditure”, “Unemployment rate” and “Inflation rate”. To do so, the first thing we should do is to check if there is correlation risk between the independent variables. We will use the Correlation Matrix to figure out this:
Since the coefficient of correlation between the variables Real Consumption, Real Private-Sector Investment and Real Government expenditure is very close to 1, it means that those variables are providing almost the same information, so I would delete some of them, and check the coefficient of correlation again.
Once Real Private-Sector investment and Real Government Expenditure have been deleted from the correlation matrix, the coefficients of correlations between variables are acceptable now, and we can be sure that every variable gives different information about the model.
However, I could have also used another statistic to check is there was any correlation between variables: Collinearity Test. It gives us the possibility to asset if the correlation is strong or not.
The result shows that there are values higher than 10 which might indicate collinearity risk between variables Real consumption, Real Private-Sector Investment and Real Government Expenditure. So, the final conclusion has been the same using two different tests. There isn’t (or at least, we haven’t gone through it in class yet) any specific method to decide which variable should be removed from the model. Since they three are much correlated, it doesn’t really matter which ones I choose to remove. So I have chosen to keep variable Real Consumption in the model, and delete Real Private Sector Investment and Real Government Expenditure.
Building the model…
Now that I know which ones are the best variables to explain the dependent variable, Real GDP, I can build the model by Ordinary Least Squared Method:
As it is showed, the output provides information about the parameters, so the model would look like: Realgdp = 286.11 + 1.45041realcons – 15.2677unemp + 3.39928infl + Ɛ
The coefficients of the parameters explain how the dependent variable would behave if they are increased by one unit. So the interpretation would be the following: * The dependent variable Real GDP would be increased by 1.45041 if the independent variable Real Consumption increases in 1 unit. * The dependent variable Real GDP would be decreased by 15.2677 if the independent variable Unemployment Rate increases in 1 unit. * The dependent variable Real GDP would be increased by 3.39928 if the independent variable Inflation Rate increases in 1 unit.
To check if the independent variables are significant in the model, I could just take a look at the stars (***) that show right next to the p-value of each independent variable. Since all the variables have a three stars rate, it is possible to assume that they are all significant in the model. However, if I would like to ensure their significance, it would be possible to analyze the situation by paying attention to the F statistic. It gives the possibility to check if the whole group of variables (Real consumption, Unemployment Rate and Inflation Rate) is significant or, instead, if it should be removed from the model. As we can see on the previous image, the value of the F statistic is 119.915’5, and its p-value is zero. Since the p-value is so small, the final conclusion would be that the...