Problem Set #1 ECON 322, Prof. DeBacker Due Thursday, September 6, 8:30 a.m.

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1 Problem Set #1 ECON 322, Prof. DeBacker Due Thursday, September 6, 8:30 a.m. NOTE:You are encouraged to work on this problem set in a group of up to four members. When finished, each group should turn in one copy of the problem set directly to me by the beginning of class on the due date. A completed problem set should list the names of the group members who worked on the assignment. As noted in the syllabus, no late assignments will be graded. 1. Hands dirty with data (8 points). In this problem, you will retrieve and manipulate macroeconomic data and verify some relationships that inform macroeconomic theory. (a) Go the Federal Reserve Bank of St. Louis Federal Reserve Economic Data (FRED) website at and download the following three data series into an Excel file. You can then do the subsequent analysis using Excel, Stata, or other software of your choice: Real Gross Domestic Product (GDPC1), percent change from year ago, deviation from trend. Make sure you set the units of account to percent change from year ago on the Edit Graph menu. Otherwise, you will simply have to manually calculate the percent change from a year ago from the quarterly levels. You transform this series to deviation of GDP growth from trend in the following way. If you look at the GDP percentage change series, you ll notice that the average percentage change (growth rate) is above zero. So calculate the average growth rate for the whole series. Then the deviation from trend equals the growth rate minus the average growth rate. This measure shows how the economy is growing relative to its average or natural rate. Total Non-farm Payroll Employment (PAYEMS), year over year percentage change. Make sure you set the units of account to percent change from year ago. Follow the same procedure from above in creating the series for deviation from trend in employment growth. Because the GDP series is quarterly and the employment series is monthly, you ll need to transform the employment series to quarterly. Just set each quarter s employment equal to the average of the three months employment growth rate. This is an option when you are selecting the data to download from FRED. Consumer Price Index for All Urban Consumers (CPIAUCSL), all items less food and energy, year over year percentage change. Make sure you set the units of account to percent change from year ago. Follow the same procedure from above in creating the series for deviation from trend in employment growth. Also, follow the same procedure as with the PAYEMS series to transform CPIAUCSL from a monthly series to a quarterly series. 1

2 M1 Money Stock (M1SL), percent change from year ago. Make sure you set the units of account to percent change from year ago on the download page. (b) Create a chart that plots both Real GDP (% chg. from year ago, deviation from trend) and total non-farm payroll employment (% chg. from year ago) from 1948Q1 to 2015Q1. Calculate the correlation of the two series over the period 1948Q1 to 2015Q1. How do you explain the two series being related in this way? (c) Create a chart that plots both the CPI (% chg. from year ago) and M1 Money Stock (% chg. from year ago) from 1960Q1 to 2015Q1. Calculate the correlation of the two series over the period 1970Q1 to 2015Q1. (d) Now create a 10-year average CPI annual growth rate by putting a formula in each cell starting in 1960Q1 that averages the past 40 quarters of annual growth rates. Create the same 10-year average annual growth rate series for M1 Money Stock but starting in 1970Q1. Create a chart that plots both the 10-year average annual CPI growth rate and the 10-year average annual M1 Money Stock growth rate from 1970Q1 to 2015Q1. Calculate the correlation of the two series over the period 1970Q1 to 2015Q1. How do you explain the difference in the correlations between part (c) and part(d)? (Hint: Has to do with short-term and long-term.) 2. Chapter 2, working with price indices (2 points): Consider an economy that produces and consumes bread and automobiles. In the following table are data for two different years Quantity Price Quantity Price Automobiles 100 $50, $60,000 Bread 500,000 $10 400,000 $20 (a) Using 2000 as the base year, compute the following statistics for each year: nominal GDP, real GDP, the implicit price deflator for GDP, and a fixed-weight price index such as the CPI. (b) How much did prices rise between 2000 and 2010? Compare the answers given by the Laspeyres and Paasche price indexes. Explain the difference. (c) Suppose you are a senator writing a bill to index Social Security and federal pensions. That is, your bill will adjust these benefits to offset changes in the cost of living. Will you use the GDP deflator or the CPI? Why? 3. Chapter 2 related employment question (3 points): Suppose an economy is made up of 100 people who are in the following mutually exclusive categories shown in Table 1: (a) What is the percent of the workforce not in the labor force? 2

3 (b) What is the labor force participation rate? (c) What is the unemployment rate? Table 1: Employment categories for fake economy Number Category 5 under 16 years old 5 disabled 5 have been unemployed for a long time and have decided to stop looking for a job 5 stay-at-home spouses 10 retired 50 currently working 10 have jobs that are currently off for the summer 5 had to leave jobs temporarily because of hurricane Sandy 5 not employed and looking for work 3

4 4. Chapter 3, Problems and Applications (4 points): #4, #11 5. Chapter 3, Equilibrium in the Goods Market (2 points): Consider an economy describe by the following equations: Y = C + I + G Y = 5, 000 G = 1, 000 T = 1, 000 C = (Y T ) I = 1, r (a) In this economy, compute private savings, public saving, and national saving. (b) Find the equilibrium interest rate. (c) Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving. (d) Find the new equilibrium interest rate. 6. Chapter 7, Problems and Applications (4 points): #1, #7 7. Chapter 7, Labor Market Regulation (3 points): Consider an economy with the following Cobb-Douglas production function: Y = K 1 3 L 2 3 The economy has 1,000 units of capital and a labor force of 1,000 workers. (a) Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock (Hint: Review Chapter 3.) (b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employment, output, and the total amount earned by workers? (c) Now suppose that Congress, concerned about the welfare of the working class, passes a law requiring firms to pay workers a real wage of one unit of output. How does this real wage compare to the equilibrium wage? (d) Congress cannot dictate how many workers firms hire at the mandated wage. Given this fact, what are the effects of this law? Specifically, what happens to employment, output, and the total amount earned by workers? (e) Will Congress succeed in its goal of helping the working class? Explain. (f) Do you think that this analysis provides a good way of thinking about a minimum wage law? Why or why not? 8. Chapter 7, Steady State Unemployment (6 points): Assume, as in the example in the book, that the job separation rate s is 0.01 (1%) per month and that the job finding rate f is 0.2 (20%) per month. 4

5 Assume that the labor force is 100 million. (a) What is the steady state unemployment rate for this economy? (b) Given that L = 100 million, what is the steady state number of employed E and unemployed U? (c) If U.S. immigration policy changed today (period t = 1) such that we allowed more people to enter the country and L increased to 110 million from its initial value of 100 million. Assume that these new entrants would be unemployed first and then find jobs at the job finding rate f. Create a table (maybe in Excel) that shows how E, U, and U/L evolve over time, given s = 0.01 and f = 0.2, starting at t = 1 and ending when the unemployment rate reaches its steady state rounded to the nearest thousandth. (d) In the table from the previous scenario, how many periods does it take for the unemployment rate to reach its steady state level rounded to the nearest thousandth? Appendix: How to get data from FRED: Once you find the desired series at the FRED website, click on the series ID (e.g., CPI- AUCSL) which should take you to the series data page. Use the Edit Graph button choose the units you want the data in, the frequency you want the data in (e.g., quarterly). Then click Download and select the format you want to download the data in (e.g. Excel).. How to calculate moving averages in Excel: In Excel, this is done by using the =AVERAGE() function and then copy and pasting it down. E.g. Suppose cells A1-A40 contain the CPI numbers for all quarters of year 1-year 10. Use the function AVERAGE() to calculate the average for 40 quarters- put in cell B40; =AVERAGE(A1:A40). Quarter 2 of year 10 is in cell A41. Paste the formulate from B40 into B41. It will update itself and read =AVERAGE(A2:A41). Paste the formula in the rest of the cells in column B and each cell will contain an average of the previous 40 quarters. Calculating the correlation coefficient in Excel: In Excel, you calculate the correlation between two series by using the =CORREL(series1,series2) command. 5