ECN 235B Monetary Theory / Professor Òscar Jordà
Winter 2006 / Economics, U.C. Davis

Problem Set 1 – Due: January 19

1.  Comparing different detrending methods

The goal of this exercise is to examine the short-run dynamic correlations of detrended output and interest rates. Hence, you will need to download data for real GDP (be specific in documenting what series you are downloading and justify your choice), potential GDP (hence you should download the GDP series that is compatible with the potential GDP variable), and data on the 10 year T-Bond rate (document your choice). All of these series are easily available from the St. Louis Fed’s website FRED. Next, detrend the ln(GDP) data (obviously, ln(potential GDP) does not need to be detrended as it is itself a measure of trend GDP) using the following three methods:

·  A linear trend

·  The HP filter

·  The Baxter and King filter

·  ln(GDP)-ln(potential GDP)

With each detrended GDP measure, compute the following:

  1. Plot the correlation at different leads and lags between detrended GDP and interest rates. You can plot all four correlations (one for each detrending method) in the same graph. Calculate the correlations for up to 8 leads and lags.
  2. Plot detrended GDP (for each method) with the NBER recession dates and compare each method.
  3. Compare ln(potential GDP) with the linear trend and quadratic trend models fitted to actual ln(GDP) and comment on the differences/similarities.

Notice parts a, b, and c, really only require that you turn in one page for each at most.

2.  Monte Carlo exercise: comparing all three methods.

This exercise consists in generating synthetic data and then to compare how different detrending methods affect the short-run correlations of the data. Hence, generate data for the following model:

for e and u two independent normal random variables with mean zero and standard deviation of 1 and with . Generate samples of size 200 for 100 Monte Carlo replications. With these data, construct the observed yt as where is constructed as:

Given this set-up, compute the following:

·  Compute the correlation between and it for up to 8 leads and lags and average across Monte Carlos. Notice that the average and the 95th and 5th largest values give you 2 standard error bands on the theoretical values of these correlations. These are handy in getting a sense on the inherent variability in your DGP when you compare correlations from the sections below.

·  For each trending method, use a linear trend, the HP filter and the BK filter to obtain the estimated cyclical component. For each cyclical component thus estimated, calculate the correlation with it for eight leads and lags. Take the Monte Carlo Average and compare with the theoretical values.

·  Briefly comment on your results, emphasizing whether a) you can recover the original cycle when the detrending method differs from that in the DGP; and b) whether the cyclical properties of the estimated cycle are preserved.

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