Assume your loss function is quadratic. With your estimated VAR, produce a static forecast for the period 2008q1 to 2019q4

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Instructions. Please type your answer key before turning it in. Don't forget to include your name and to include every graph/output that is requested in this activity. Make sure that you take screenshots of your output (Windows button + PrtScn. Then just paste).

Go to https://fred.stlouisfed.org/ and download the quarterly series gdpc1, which is the US Real Gross Domestic Product, and download the unemployment rate unrate. Download both series in quarterly fre- quency as an EXCEL file. Import your files into tha same Eviews file. The goal of this exercise is to help you get acquainted with vector autoregressions (VAR). Imagine that you are making forecasts just before the great recession in 2008-2009. Throughout this exercise, the estimating sample remains 1980q1 to 2007q4, and the prediction or forecasting sample remains 2008q1 to 2019q4. The prediction sample is somewhat long and normally we could reestimate the model as more information was available (think of recursive or the rolling forecasting environment). For simplicity we only consider this fixed forecasting environment where we only estimate the model once and then do some forecasting.

1. Create the variable lngdp (genr lngdp = log(gdpc1)) time series. Then present a graph for lngdp and another one for unrate for the period 1980q1 - 2019q4.

2. For the sample period 1980q1 to 2007q4, perform a unit root test on lngdp and on unrate. According to this particular sample and from your output estimates, are these time series stationary or non-stationary?

3. Now you difference your data. Since the difference in the natural log of a variable is approximately a growth rate, when you difference lnGDP you obtain a quarterly growth rate. Construct the quarterly difference in lnGDP (will be defined by ggdp) with the formula ggdp=ln(GDP t)−ln(GDP t—1). In Eviews

this is obtained as genr ggdp = lngdp-lngdp(-1). Also construct the variable "quarterly change in

unemployment rate" as dunrate = (unratet unratet—1) , which in Eviews is obtained with the instructions genr dunrate = unrate-unrate(-1). Plot your series ggdp and dunrate for the period 1980q1 - 2019q4. Note: before you difference the data, first select a bigger sample (So we don't lose observations when we

restrict the sample later). Thus use the following sequence of commands (click enter after typing each line) smpl 9all

genr ggdp = lngdp-lngdp(-1) genr dunrate = unrate-unrate(-1)

Then you can plot your series for the period 1980q1 to 2019q4

4. Using the sample of 1980q1 to 2007q4, perform the relevant unit root tests on the new variables (on ggdp and dunrate). Remember that we studied 3 different specifications of the unit roots. Make sure you use the appropriate one. Interpret the results (what do you conclude with these statistical tests?)

5. Estimate a VAR(1) model for ggdp and dunrate, where your estimating sample is 1980q1 to 2007q4. Show your output.

6. Is your VAR(1) the most appropriate model? Replicate the following output and explain which would be the most appropriate VAR.

7. Within the output of your VAR(1), do changes in the unemployment rate Granger−cause the growth in GDP? Do growth in GDP Granger−causes changes in the unemployment rate? Use the standard significance level of 5%. Replicate the following output and explain.

8. Produce the impulse response functions of your estimated model.

9. Assume your loss function is quadratic. With your estimated VAR, produce a static forecast for the period 2008q1 to 2019q4 for ggdp and for dunrate. Present the graphs of both your forecast and the original series for the prediction sample (2008q1 to 2019q4).

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