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 COVID-19 Pandemic, which derailed the longest expansion the U.S. history and affected most macroeconomic series. 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. 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 only [25 points]; then calculate the standard deviation of the cyclical components of GDP, consumption, and investment. [25 points]. 4. Compare the impact of COVID-19 on the three variables and summarize your findings [25 points], and explain in the context of the pandemic [25 points]. The end. Detailed instructions for point 2 above (follow each step verbatim) 1. Download the excel add-in for the HP-filter. http://ideas.repec.org/c/dge/qmrbcd/165.html => 2. Make sure that the HPFilter.xla file is in the same directory as where you are going to save your excel file. Double click on HPFilter.xla to launch it in Excel and make sure to enable macros. This should enable the HP- Filter function. You will always have to first start the macro every time you use the workfile (in that same order). 3. Transpose the variables into columns and then take the natural log of each of the variables [the Excel function is =In( )]. 4. HP-filter the natural log of each variable, the function in Excel is: HP(timeseries to be filtered, value for lambda). This is an array formula (columns). Example. Suppose you want to filter 5 data points in the first five cells of column A, say A1:A5, at lambda = 1600. Enter the following formula into cell B1: = HP(A1:A5,1600) Then hit return or enter. Then, starting with cell B1, select cells B1 through B5 Hit F2. Then hit the Ctrl, Shift, and Enter buttons simultaneously. This will HP-Filter the entire set of cells from A1-A5 and place the filtered series into B1-B5. 5. For the case of GDP, the variable on column A should be the In(GDP) and column B represents the trend, In(GDP*). The next step is to compute the cycle In(GDP) - In(GDP*) in column C. Now you can plot it and calculate its standard deviation. Do the same for consumption and investment