PS1

Problem Set 1 — Macroeconomics I

Part of: Macro-Economics Companion notes: Lec_01-Data Review Questions 1–4 for submission; the rest are for the TA session.

Value Added (Phone Supply Chain) — for submission

Consider the following prices (in Shekels) for a phone sold in Israel. The retail price is 3,000. Prior to selling the phone to the consumer, the retailer pays 2,500 to an importer. The importer's costs are 1,700 that are paid to the manufacturer in China. The Chinese manufacturer uses intermediate goods that were purchased in Vietnam for 500 and other intermediate goods that were purchased in China for 300.

(a) What is the Israeli retailer's value added?

(b) What is the Israeli importer's value added?

(c) What is the Chinese manufacturer's value added?

(d) How much of the tablet's retail value shows up in Israel's GDP according to the product (value-added) approach? How much in China's GDP?

(e) Where does the tablet show up in the expenditure components of Israel's GDP? How much of its retail value shows up in Israel's GDP according to the expenditure approach?

(f) If we count Israel's net exports (or trade balance) with each individual country, how does the tablet affect Israel's trade balance with China? With Vietnam?

GDP Growth and the Deflator — for submission

Consider an economy that produces three products: apples, oranges, and machines. Production and price data are:

(a) What is the growth rate of nominal GDP from 2010 to 2020?

(b) What is the growth rate of real GDP at 2010 prices?

(c) What is the growth rate of real GDP at 2020 prices?

(d) What is the GDP deflator in 2010 and 2020 if you calculate real GDP based on 2010 prices?

(e) What is the GDP deflator in 2010 and 2020 if you calculate real GDP based on 2020 prices?

(f) What is the inflation rate (based on the GDP deflator) associated with the price levels of (d) and (e)?

CPI Inflation — for submission

Continue with the same data as in Question 2. Now let's calculate Consumer Price Index inflation in the economy. Assume that there are 1,000 identical households in the economy, and each of them consumes the same basket of consumption goods (i.e. only the fruit, not the machines, enter the CPI calculations).

(a) Assume that the "representative consumption basket" is the one reflected by the quantities of 2010. What is the price of this basket in 2010? In 2020?

(b) Assume that the "representative consumption basket" is the one reflected by the quantities of 2020. What is the price of this basket in 2010? In 2020?

(c) What is the inflation rate associated with the prices in (a) and (b)?

(d) Why are the inflation rates different?

(e) What is the reason for the different inflation rates in this question relative to the inflation rates based on the GDP deflator?

Average Growth Rates: GDP vs. GDP per capita — for submission

The Penn World Table (PWT) is a database with information on various economic variables for more than 180 countries and over time. Its strength is that it is a serious attempt to have comparable figures across countries and over time.

Download the recent version (11.0) from https://www.rug.nl/ggdc/productivity/pwt/?lang=en.

Pick any two countries that you like. For each country use:

• rgdpna — Real GDP at constant 2017 national prices (mil. 2017 USD)
• pop — Population (millions)

Divide real GDP by population, so that you have a series of real GDP per capita for each country.

(i) What is the average growth rate of GDP for each of the two countries between 1990 and the latest year that you have (for most countries 2022 or 2023, but for some the most updated may be earlier)?

(ii) What is the average growth rate of GDP per capita for each country between 1990 and the latest year?

• Which growth rate is larger: GDP or GDP per capita? In case of a difference, why do you think it exists?
• If you were asked to describe (to a friend or a relative) the growth experience of a country, would you use GDP or GDP per capita? Briefly explain.

(iii) Now calculate the average growth rates of GDP per capita by decade for each country (see table below), and briefly describe how different these growth rates are relative to your calculations in part (ii).

(TA session)

PPP vs. Nominal Exchange Rates — all numbers in this example are invented.

Assume that in 2015 China's GDP per capita was 8,000 yuan, and that the market exchange rate between the yuan and the U.S. dollar was 8 yuan per dollar.

Assume that in the same year Albania's GDP per capita was 20,000 Albanian Lek (that's the name of the currency) and the U.S. dollar was traded for 4 Lek per dollar.

Also assume that a representative product costs $1 in the US, 4 yuan in China, and 10 Lek in Albania.

(a) What is the market value of China's GDP per capita in U.S. dollars? What is the market value of Albania's GDP per capita in US dollars?

(b) What is the "purchasing power exchange rate" between the yuan and the U.S. dollar? Between the Albanian Lek and the U.S. dollar?

(c) What is China's PPP GDP per capita? What is Albania's PPP GDP per capita?

(d) Which country looks richer according to the calculation in part (a)? And according to part (c)? Explain the source of the difference and why it is usually better to use the PPP measure rather than the nominal one.

(e) Give one example of a measurement problem when calculating the PPP exchange rate.

(TA session)

Quarterly vs. Annualised Growth — growth rates in the data and how they are reported.

Go to https://fred.stlouisfed.org and search for real GDP, so that you can see the quarterly real gross domestic product series for the US. Use the data points for the second quarter of 2020 and the third quarter of 2020 to calculate the growth rate.

When the data on GDP growth for the third quarter of 2020 was released, the "headline number" reported was around 33% GDP growth. Is this identical to your calculation? Explain.

(TA session)

CPI vs. GDP Deflator with Real Data — related to Questions 2 and 3, but with real data.

The Federal Reserve Bank of St. Louis maintains a data source called FRED, with a lot of macro data for the US and other countries: https://fred.stlouisfed.org

Using FRED, download two data series: (i) Consumer Price Index: Total All Items for the United States; and (ii) Gross Domestic Product: Implicit Price Deflator. For both series, use quarterly and seasonally adjusted data, starting from the earliest date possible.

(a) Download the data and calculate the inflation rate based on CPI and the inflation rate based on the GDP deflator.

(b) Plot the two inflation rates (time on the x-axis, the index on the y-axis). Are there any noticeable differences?

(c) Compute the correlation coefficient between the two inflation series. How similar are they? Explain why you would expect them to be similar or different. (To calculate the correlation you must use the same time period for both series.)

(d) Explain why it is important to use seasonally adjusted data when calculating inflation rates. (To illustrate, search for Consumer Price Index for All Urban Consumers: All Items — available with and without seasonal adjustment — and zoom in on a short period of a few years.)

(TA session)

Expected Real Rates from TIPS

In class we described the reasoning behind the equation for the expected real interest rate:

where $\mathbb{E}[r]$ is the expected real interest rate, $i$ is the nominal interest rate, and $\pi^e$ is expected inflation.

Sometimes it is useful to use data on market prices to calculate the expected inflation according to financial markets. In principle, this can be done by rearranging the equation:

If we have market prices for the nominal and expected real rate, the calculation is easy. One such price involves indexed vs. non-indexed government bonds. In the US, the Treasury issues "regular" bonds that are not indexed, as well as "Treasury Inflation-Protected Securities" (TIPS).

(a) Explain why a regular bond can be used as a proxy for the nominal rate, and the indexed bond as a proxy for real rates.

(b) Explain why it is important that the two bonds are issued by the same borrower and have similar maturities.

(c) Go to https://fred.stlouisfed.org and search for the 5-year, 10-year, and 30-year Breakeven Inflation Rate (three separate series). These are "…what market participants expect inflation to be in the next 5/10/30 years, on average." Plot the three series from the earliest available point.

(d) Do the three appear to be positively correlated?

(e) Focusing on the recent spike around 2022: why do you think the 5-year expectations are higher than the other two? Why do you think expected inflation is lower than what inflation was? Why do you think that over the longer term inflation is expected to be close to 2%?