In this box you will work with the HP-filter. This is a procedure to decompose economic variables into a trend and a cycle. The HP-filter allows for a flexible time-varying trend, in contrast to imposing a constant trend over long periods of time ---say, decades. Since long-term trends change (eventually), this provides a better measure of the cycles i.e. deviations from trend.

The purpose of the box is to calculate the co-movement and volatility of consumption and investment relative to GDP, all measured in real terms. For this exercise you will use table 1.1.6 from BEA.gov once again; starting in 1960:Q1 to the latest available year at a quarterly frequency. The smoothing parameter (lambda) for quarterly data is 1,600.

The box has to describe the nature of the filter and report the correlation and volatility of the cyclical components of GDP, consumption, and investment over time. The focus will be on the Great Moderation which is known as the period under which the U.S. economy experienced a break in the volatility of most of its macroeconomic variables. The literature has identified it as beginning in the mid-1980s, and ending in 2008 with the Great Recession. Part of the exercise is to identify the Great Moderation in the data and see whether the 2008 broke that trend; that is, has the U.S. economy become as volatile as before 1984, or has the moderation persisted?

To create the box follow these steps:

1. Go to NIPA Table 1.1.6 in the Bureau of Economic Analysis website (bea.gov), and download the quarterly data for GDP, consumption, and investment for the period 1960:Q1 to latest available.
2. Use the HP-filter to calculate the trend of the three variables for the whole period, and then for the periods 1960-83; 1984-2007; and 2008 to latest available. Use a value of 1,600 for lambda.
3. Detrend the original series and plot the three variables in the same graph for the entire sample period [25 points]; then calculate the standard deviation of the cyclical component of GDP, consumption, and investment for each of the periods and present in a table [25 points].
4. Compare the four sample periods, summarize your findings [25 points] and explain in the context of the Great Moderation [25 points].