The 'business cycle' is not a regular cycle like a sine function. It refers to the fact that the economy as a whole has ups and downs. We can see this quite easily by looking at a measure of the total economy such as the GDP. Many aspects of the economy commonly tend to move more-or-less together, such as employment, retail sales, the stock market, etc. But we know from many decades of evidence across many countries that they do not all move one-for-one. Some aspects of the economy tend to go up and down more than others. They are more volatile and the standard deviations of their growth rates are larger.

Let's use some real data to check this out. We will use data from FRED:https://fred. stlouisfed.org/They also have an Excel add-inhttps://fred.stlouisfed.org/fred-addin/along with a user guide. You can use that add-in or you can use their menus in your browser to get the necessary data. The variables you want are

Variable Name FRED Code

GDP GDPC1

Consumption PCEC

Investment GPDI

If you are not using the Excel add-in, you can also get these variables the 'long way'. 1) Go to FRED, 2) Type GDPC1 in the search box in the upper right hand corner of the web page. This gives you a link. 3) click on that link and you get a graph, 4) click on the col orful button 'EDIT GRAPH', 5) Choose 'ADD LINE', 6) Enter the code for Consumption, 7) click on the add data series button, 8) Repeat this process for Investment. You should now see a graph with the three colored lines. It also shows vertical grey bars which show recessions. 9) In the upper right hand corner of the page you should see a 'DOWNLOAD' button which allows you to download in various formats. Pick the Excel data format so that you can use the data. Save it somewhere on you computer that you can find! You should now have the data in a nice Excel file on your computer.

Using this data, in Excel for each series compute the discretely-compounded rates of growth over the period 1950Q1 to 2017Q4 inclusive. The formula you want is:

g_{t= (}x_t x_t1

x_t1)100 = (x_t/x_t11)100

Notice that the 100 at the end converts the quarterly growth rate into a percentage. No tice that in order to get the first time period growth rate you need data from 1949Q4. Put the three growth rates into their own columns.

For each of the following questions you will do the calculations and plotting once in Excel. You will submit your written answers in a Word file. You will also submit the Excel file that justify what you wrote in the Word file.

1. For each of the growth rates calculate the mean and standard deviation. How do the standard deviations compare to each other?

2. What are the correlations among the three values? Do you agree with the claim that the variables 'move up and down together but have different volatilities'? Use a graph to illustrate your answer.

3. Calculate the continuously compounded growth rate of GDP. The formula you want is

_t= (lnx_tlnx_t1)100

How do the mean and standard deviation compare to those calculated with the discretely compounded growth rate? Why are they so similar?