Home Assignment Macroeconomics Gdp

Macroeconomics 3
Home assignment 1

Exercise 9.1
Data description

Country: Mexico
Indicator: Real GDP per capita (Constant Prices: Chain series) (I$ in 2005 Constant Prices)
Name of variable: rdgp
Frequency: Annual
Period: 1950-2007
Number of observations: 58

Our first task is to compute the trend component of GDP:
Let’s use the method described in Doepke’s book.
First of all we need to compute the growth rate of real GDP for each period: we will create new variable GRATET it shows us the economic growth in period t. GRATEt=RGDPt+1RGDPt

Now we are supposed to apply a method called exponential smoothing (which is described in our Textbook) to get smooth versions of our data:
GRATESM1=GRATE1,
GRATESMt=0.5*GRATEt-1+0.5*GRATESMt-1 for t>1

Now we should apply the same method to real GDP, but additionally we will use the smooth growth rates we just computed:
TREND1=RGDP1,

TRENDt=0.5*GRATESMt-1*TRENDt-1+0.5*RGDPt-1 for t>1

And we can receive the following results:
We can check whether we’ve done everything correctly or not by using an automatic procedure of exponential smoothing in EViews. The method of smoothing is Holf-Winters method with parameters alpha and beta being equal to 0,5.
The results are absolutely the same.

Exercise 9.2

Now we have to compute the cyclical component of GDP. As it is stated in our textbook, this is simply the difference between GDP and its trend. We will use log-differences instead of absolute differences.
Let’s create our new log-variables.

Now we can compute our cyclical pattern: CYCLYEt=LNRGDPt-LNTRENDt

Exercise 9.3

Now we Have to examine our cycles more closely. Let’s define our “peaks” (years when the cyclical component is higher than in the two preceding and following years): 2,7,11,16,19, 21, 24, 30, 36,41, 45, 48, 52, 55, 57. These were the numbers of periods where we observed peaks. Thus, have about 15 cycles in our data with the average length of the cycle being