Advanced Economic Development – Recitation, Week #2

GDP/cap comparisons STATA

• Cross-country GDP/capita comparisons • Stata

Claire Palandri [email protected]

January 27, 2021

1 / 15 GDP/cap comparisons STATA Outline

1 Cross-country GDP/cap comparisons Exchange-rate (XR) conversion Purchasing Power Parity (PPP) conversion

2 STATA

2 / 15 GDP/cap comparisons STATA Cross-country GDP/cap comparisons

Goal: We want to compare GDP per capita across countries and years. → We must put these measures in the same units : convert nominal GDP in a local currency to real GDP in a common currency.

Converting across time = adjusting for inﬂation, using CPI

Nominal GDP = GDP in current prices (unit: current $). Real GDP = GDP adjusted for inﬂation (unit: constant $ of year YYYY). Inﬂation is estimated by computing the Consumer Price Index (CPI): “average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.” Cost of market basket this year CPI = Cost of market basket in base year × 100

nominal GDP real GDP = CPI × 100

Converting across space = converting currencies, using exchange rates Market exchange rate = rate in the foreign exchange market. Is based on tradable goods only... Purchasing Power Parity (PPP) conversion rate = theoretical rate at which the currency of one country would have to be converted into the currency of another country to buy the same amount of goods and services in each country. 3 / 15 GDP/cap comparisons STATA Outline

1 Cross-country GDP/cap comparisons Exchange-rate (XR) conversion Purchasing Power Parity (PPP) conversion

2 STATA

4 / 15 GDP/cap comparisons STATA XR conversion – Example

Example 2 countries: U.S., Tanzania (currency: TZS - Tanzanian Shilling) 2 years: 1994, 2000 2 goods: soap (tradable), haircut (non-tradable) Production doesn’t change across years: – U.S. GDP: 100 soaps and 100 haircuts – Tanzania GDP: 20 soaps and 50 haircuts Prices: Soap Haircut US $ 1 $ 15 1994 TAZ 1,000 TZS 1,000 TZS US $ 2 $ 30 2000 TAZ 3,000 TZS 2,000 TZS

Question: Compare the values of GDP across countries and years. Method: Express them in the same unit, e.g., $ of 1994.

5 / 15 GDP/cap comparisons STATA XR conversion – Example

Question: Compare the values of GDP across countries and years.

Method: Express the 4 values in the same unit, e.g., $ of 1994. Current GDP, local currency −→ Constant GDP (1994), US $ Option 1:

1 local currency −→ US $ (XR current year) 2 current −→ constant (deﬂate, using US CPI) Option 2:

1 current −→ constant (deﬂate, using local CPI) 2 local currency −→ US $ (XR base year)

Preliminary: compute the CPIs and the exchange rates – CPI: consider that the ‘standard consumption basket’ = 1 soap and 1 haircut. – XR: consider tradable goods only.

6 / 15 GDP/cap comparisons STATA XR conversion – Example

7 / 15 GDP/cap comparisons STATA XR conversion – Example

7 / 15 GDP/cap comparisons STATA Outline

1 Cross-country GDP/cap comparisons Exchange-rate (XR) conversion Purchasing Power Parity (PPP) conversion

2 STATA

8 / 15 GDP/cap comparisons STATA XR vs PPP conversions

Limitation: The market exchange rate only takes into account the prices of tradables. . . It does not reflect the different price levels between countries. Nontraded goods and services tend to be cheaper in low-income than in high-income countries: you can buy more haircuts and taxi rides with 1e in Lima than in New York. I.e., the purchasing power of the Euro is higher in Peru than in the U.S. =⇒ An analysis that doesn’t take into account these differences in the prices of nontraded goods across countries, will underestimate the purchasing power of consumers in low-income countries and, consequently, their overall welfare.

The Purchasing Power Parity exchange rate (PPP) tries to capture this price-level diﬀerence:

PPP = theoretical exchange rate at which the currency of one country would have to be converted into the currency of another country to buy the same amount of goods and services in each country.

It takes into account the prices of tradables and non-tradables, to capture the ability to buy the same amount of goods and services in every country.

Angus Deaton: “PPPs are price indexes that summarize prices in each country relative to a numeraire country, typically the United States. These numbers are used to compare living standards across countries, [...] to draw attention to discrepancies between rich and poor countries.”

9 / 15 GDP/cap comparisons STATA PPP conversion – Method

Approach: we create a hypothetical currency, called ‘international dollars’ (I$), which serves as a common unit of measure. I.e., a given amount of I$ will buy roughly the same amount of goods & services in any country. Therefore the PPP conversion rates are the theoretical exchange rates to translate monetary values in local currencies into I$.

cost of basket in currency c PPP = 1 in year t c1/I$,t cost of basket in I$

In practice, we consider an imaginary country (I-land), where goods are bought and sold at average international prices (using equal weights for all countries), with the I$ currency. We arbitrarily deﬁne the currency I$ to be at all times indexed on the U.S., s.t. US GDP in US$ = US GDP in I$.

10 / 15 GDP/cap comparisons STATA PPP conversion – Same example

First, let’s compute average international prices (I$):

We have (arbitrarily) deﬁned 1 I$ to be s.t. US GDP in USD = US GDP in I$. I.e., noting x the international average price of soap in I$, x satisﬁes the equation: US GDP (US$) = US GDP (I$) 100 × $1 + 100 × $15 = 100 × x + 100 × 8x 1600 = 900x

x ' 1.78 I$1994 11 / 15 GDP/cap comparisons STATA PPP conversion – Same example

First, let’s compute average international prices (I$):

x ' 1.78 I$1994 11 / 15 GDP/cap comparisons STATA PPP conversion – Same example

First, let’s compute average international prices (I$):

x ' 1.78 I$1994 11 / 15 GDP/cap comparisons STATA PPP conversion – Same example

First, let’s compute average international prices (I$):

x ' 1.78 I$1994 11 / 15 GDP/cap comparisons STATA PPP conversion – Same example

Similarly, for 2000:

12 / 15 GDP/cap comparisons STATA PPP conversion – Same example

Similarly, for 2000:

12 / 15 GDP/cap comparisons STATA PPP conversion – Same example

current price of basket (I$) Recall: CPI = base year price of basket (I$) 13 / 15 GDP/cap comparisons STATA PPP conversion – Same example

current price of basket (I$) Recall: CPI = base year price of basket (I$) 13 / 15 GDP/cap comparisons STATA Conclusion: XR vs PPP conversions

Tanzania’s GDP is valued more highly with the PPP conversion. Because for non-tradables (e.g., haircuts), international prices > local prices in poor countries. with XR, Tanzania’s GDP = $70 in 1994, $64 or $53 in 2000 with PPP, Tanzania’s GDP = $747 in 1994, $746 in 2000

Conclusion: which method is better for cross-country comparisons? It depends on the quantity and the set of countries we’re comparing: Market exchange rates (how many units of currency from country B you can buy with a unit of currency A) are easy to observe, but are relevant only for internationally traded goods... → a reasonable choice for certain quantities, such as financial flows, or levels of GDP across developed countries; but not for quantities containing nontraded items whose price differ among countries considered – e.g., GDP across developed and developing countries. PPP exchange rates (how many currency units you have to spend to buy the same amount of goods and services in each of the two countries) take into account also the prices of non-tradable goods. If we are interested in living standards, a monetary income should be considered in relation to the amount of goods & services that it can buy locally. PPPs therefore seem like the appropriate conversion method to compare overall well-being. But heavy computation... And the ’standard’ basket of goods remains arbitrary. 14 / 15 GDP/cap comparisons STATA Outline

1 Cross-country GDP/cap comparisons Exchange-rate (XR) conversion Purchasing Power Parity (PPP) conversion

2 STATA

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