Purchasing Power Parity FX 2

Example: Iphone 6 (March 2015, taken from seekingalpha.com). Rt = 𝑺𝒕 PIPhone,f/PIPhone,d (d=US)  Rt=1 under Absolute PPP • Empirical Evidence: Simple informal test: Test: If Absolute PPP holds  Rt = 1. In the Big Mac example, PPP does not hold for the majority of countries.  Absolute PPP, in general, fails (especially, in the short-run). • Absolute PPP: Qualifications (1) PPP emphasizes only trade and price levels. Political/social factors, financial problems, etc. are ignored. (2) Implicit assumption: Absence of trade frictions (tariffs, quotas, taxes, etc.). Q: Realistic? - On average, transportation costs add 7% to the price of U.S. imports of meat and 16% to the import price of vegetables. - Many products are heavily protected, even in the U.S. For example, peanut imports are subject to a tariff as high as 163.8%. 12 • Absolute PPP: Qualifications Some everyday goods protected in the U.S.: - Peanuts (shelled 131.8%, and unshelled 163.8%). - Paper Clips (as high as 126.94%) - European Roquefort Cheese, cured ham, mineral water (100%) - Japanese leather (40%) - Sneakers (48% on certain sneakers) - Chinese tires (35%) - Canned Tuna (as high as 35%) - Synthetic fabrics (32%) - Steel (25%) - Indian wood furniture (25%) - Italian footwear & eyeglasses (25%) - Brooms (quotas and/or tariff of up to 32%) - Trucks (25%) & cars (2.5%) • Absolute PPP: Qualifications Some Japanese protected goods: - Rice (778%) - Sugar (328%) - Powdered Milk (218%) - Beef (38.5%, but can jump to 50% depending on volume). Some European protected goods: - Knitted Clothes (100%) - Fresh Cheese (48.3%) - Bovine Meat, boneless (41%) - Fresh or dried grapefruit (25%) - Atlantic Salmon (25%) 13 • Absolute PPP: Qualifications (3) PPP is unlikely to hold if Pf and Pd represent different baskets. This is why the Big Mac is a popular choice. (4) Trade takes time (contracts, information problems, etc.). (5) Internationally non-traded/non-tradable (NT) goods –i.e. haircuts, home and car repairs, medical services, real estate. The NT good sector is big: 50%60% of consumption (big weight in CPI basket). Then, in countries where NT goods are relatively expensive, the CPI basket will be relatively expensive. Thus, PPP will find these countries' currencies overvalued relative to currencies in low NT cost countries. Note: In the short-run, cars will not be taken to Mexico to be repaired, but in the long-run, resources (capital, labor) will move.  Over-/under-valuation: An indicator of movement of resources. • Absolute PPP: Qualifications The NT sector also has an effect on the price of traded goods. For example, rent and utilities costs affect the price of a Big Mac: 25% of Big Mac due to NT goods. • Empirical Fact Price levels in richer countries are consistently higher than in poorer ones. This fact is called the Penn effect. Many explanations, the most popular: The Balassa-Samuelson (BS) effect. • Borders Matter You may look at the Big Mac Index and think: “No big deal: there is also a big dispersion in prices within the U.S., within Texas, and, even, within Houston!” True. Prices vary within the U.S. For example, in 2015, the price of a Big Mac (and Big Mac Meal) in New York was USD 5.23 (USD 7.45), in Texas as USD 4.39 (USD 6.26). 14 But, borders play a role, not just distance! Engel and Rogers (1996) computed the variance of LOOP deviations for city pairs within the U.S., within Canada, and across the border. Conclusion: Distance between cities within a country matter, but the border effect is significant. To explain the difference between prices across the border using the estimate distance effects within a country, they estimate the U.S.-Canada border should have a width of 75,000 miles! This huge estimate has been revised downward, but a large positive border effect remains. • Balassa-Samuelson Effect Labor costs affect all prices. We expect average prices to be cheaper in poor countries than in rich ones because labor costs are lower. This is the Balassa-Samuelson effect: Rich countries have higher productivity and, thus, higher wages in the traded-goods sector than poor countries do. But, firms compete for workers. Then, wages in NT goods and services are also higher  Overall prices are lower in poor countries. 15 • For example, in 2000, a typical McDonald’s worker in the U.S. made USD 6.50/hour, while in China made USD 0.42/hour. In 2021, the same numbers for a cashier are USD 10/hour and USD 1.76. • Balassa-Samuelson effect: A positive correlation between PPP exchange rates (overvaluation) and high productivity countries. Incorporating the Balassa-Samuelson effect into PPP: 1) Estimate a regression: Big Mac Prices against GDP per capita. PBM (in USD)t = α + β GDP_per_capitat + εt Big Mac Prices vs GDP per capita: July 2022 7.0000 Uruguay 6.5000 Switzerland 6.0000 5.5000 5.0000 4.5000 4.0000 3.5000 3.0000 2.5000 Japan 2.0000 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Points on Red line: Fitted (Expected) Big Mac Prices, given a GDP per person. 𝑃BM,GDP-adj = 𝛼 + β GDP_per_capitat 16 Incorporating the Balassa-Samuelson effect into PPP: 2) Compute fitted values: 𝑃BM,GDP-adj = 𝛼 + β GDP_per_capitat Big Mac Prices vs GDP per capita: July 2022 7.0000 Uruguay 6.5000 Switzerland 6.0000 5.5000 5.0000 4.5000 𝛼 + β GDP_per_capitat 4.0000 3.5000 Difference between Actual & Expected BM Prices 3.0000 2.5000 Japan 2.0000 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 GDP-adjusted over/under valuation: (BM Price/𝑃BM,GDP-adjusted ) – 1. Incorporating the Balassa-Samuelson effect into PPP: Computations Using data from The Economist for July 2022, we estimate the red line: 𝑃BM,GDP-adj = 3.045895 + 0.0000332 * GDP_per_capitat Now, we can compute the “Expected BM prices, given the GDP of a given country.” Let’s compute the above value for Uruguay. Uruguay’s GDP per capita in July 2022 was USD 15,169.153. Then, 𝑃BM,GDP-adj (Uruguay) = 3.045895 + 0.0000332 * 15,169.153 = 3.549511 That is, the expected BM in Uruguay in July 2022, given its GDP per capita, was USD 3.55. Since the observed local BM price was UYU 255, which translates to USD 6.08 (= UYU 255 * 41.91 USD/UYU), then the GDPadjusted over/under valuation was: 6.08 / 3.549511 – 1 = 71.29% (71.29% overvalued) 17 Incorporating the Balassa-Samuelson effect into PPP: July 2011 Same computation for July 2011. BM PriceGDP-adjusted Difference between Actual & Expected BM Prices Points on Red line: GDP-adjusted Big Mac Prices (BM PriceGDP-adjusted). Incorporating the Balassa-Samuelson effect into PPP: The GDP adjustment can make a difference. 18 Example: Raw vs GDP-Adjusted Big Mac Index in Dec 2022. • Pricing-to-Market Krugman (1987): Positive relationship between GDP and price levels is caused by Pricing-to-market –i.e., price discrimination. Producers discriminate: Same good is sold to rich countries at higher prices than to poorer countries. Alessandria and Kaboski (2008): U.S. exporters, on average, charge the richest country a 48% higher price than the poorest country. But pricing-to-market struggles to explain why PPP does not hold among developed countries with similar incomes. For example, Baxter and Landry (2012) report that IKEA prices deviate 16% from the LOOP in Canada, but only 1% in the U.S. 19 Example: Pricing to Market? Pret A Manger (August 2019, from The Economist). Comparing: St PPM,London & PPM,Boston. Main PPP criticism Absolute PPP does not incorporate transaction costs and frictions. Relative PPP allows for fixed transaction costs/frictions (say, a fixed USD amount). Relative PPP The rate of change in the prices of products should be similar when measured in a common currency (as long as trade frictions are unchanged): 𝑒 –1 ,, (Relative PPP) where, 𝐼 = foreign inflation rate from t to t+T. 𝐼 = domestic inflation rate from t to t+T. Note: 𝑒 , , is an expectation; what we expect to happen in equilibrium from t to t+T. • Linear approximation: 𝑒 ,,  𝐼 𝐼  one-to-one relation 20 Relative PPP • Linear approximation: 𝑒 ,,  𝐼 𝐼  one-to-one relation Example: From t=0 to t=1, prices increase 10% in Mexico relative to prices in Switzerland. Then, St should also increase 10%. If 𝑆  𝐒𝐭𝐏𝐏𝐏 𝟏 = E[𝑆 = 9 MXN/CHF ] = 9.9 MXN/CHF. Suppose at t=1, 𝑆 increases 13.33%. Then, 𝑺𝒕 𝟏 = 10.2 MXN/CHF > 𝐒𝐭𝐏𝐏𝐏 𝟏 = 9.9 MXN/CHF  According to Relative PPP, the CHF is overvalued. ¶ Notation: E[𝑆 value. ] = Expected value of 𝑆 (model-based), a predicted Example: Forecasting St (USD/ZAR) using PPP (ZAR=South Africa). It’s Dec 2022. You have the following information: CPIUS,2022 = 104.5, CPISA,2022 = 100.0, 𝑺𝒕 𝟐𝟎𝟐𝟐 = .2035 USD/ZAR. You are given the 2023 CPI’s forecast for the U.S. and SA: E[CPIUS,2023] = 110.8 E[CPISA,2023] = 102.5. You want to forecast S2023 using the relative (linearized) version of PPP. E[IUS,2023] = (110.8/104.5) - 1 = .06029 E[ISA,2023] = (102.5/100) - 1 = .025 E[S2023] = 𝑺𝟐𝟎𝟐𝟐 * (1 + 𝑒 , , ) = 𝑺𝟐𝟎𝟐𝟐 * (1 + E[IUS] - E[ISA]) = .2035 USD/ZAR * (1 + .06029 - .025) = .2107 USD/ZAR.. 21 • Under the linear approximation, 𝑒 𝐼 ,,  𝐼 𝐼 , we have a PPP Line 𝐼 PPP Line  B (FC appreciates)  A (FC depreciates) 45º 𝑒 , , (DC/FC) Look at point A: 𝑒 , , > 𝐼 𝐼 ,  Priced in FC, the domestic basket is cheaper  pseudo-arbitrage (trade) against foreign basket  FC depreciates • Relative PPP: Implications (1) Under relative PPP, Rt remains constant (it can be different from 1!). (2) Without relative price changes, an MNC faces no real operating FX risk (as long as the firm avoids fixed contracts denominated in FC). • Relative PPP: Absolute versus Relative - Absolute PPP compares price levels. Under Absolute PPP, prices are equalized across countries: “A mattress costs GBP 200 (= USD 320) in the U.K. and BRL 800 (= USD 320) in Brazil.” - Relative PPP compares price changes. Under Relative PPP, exchange rates change by the same amount as the inflation rate differential (original prices can be different): “U.K. inflation was 2% while Brazilian inflation was 8%. Meanwhile, the BRL depreciated 6% against the GBP. Then, relative cost comparison remains the same.” 22