International Macroeconomics 2(3)

INTERNATIONAL MACROECONOMICS

Sinchan Mitra

Purchasing power parity (PPP) hypothesis, Chapter 2, Copeland

Law of one price (LOOP) - if two goods are identical they must sell for the same price. If not, there is an opportunity for arbitrage.

Arbitrage is the process of buying or selling something in order to exploit a price differential so as to make a riskless profit.

Transaction costs. PPP hypothesis extends this basic economic

idea to the international context- but we have to keep in mind transportation costs & tariffs.

Purchasing power parity

A consumer price index is a measure of the general price level- it is defined as the weighted average of individual product prices, with weights determined by expenditure shares.

Define PPP, Pi = SPi* for all i = 1…N. Also assume

that the weights used in compiling the price indices of the domestic and the foreign country are identical. Then P = SP* where P and P* refers to the home and foreign countries price indices- this is absolute PPP.

PPP says that the general level of prices, when converted to a common currency, will be the same in every country.


Assume there are n goods produced in each country, and each of these goods has a foreign homogenous equivalent, then the overall price levels are P(t) = ∑ai Pi(t) and P*(t) = ∑ai Pi*(t) where a’s are the weights used to aggregate individual P’s and are assumed to equal across countries.

Using these P levels, we derive the condition for absolute PPP as S(t) = P(t)/P*(t). APPP says that a country’s nominal exchange rate is determined as the ratio of overall P levels of home and foreign country- forced by arbitrage in the long run.


In logs, s(t) = p(t) – p*(t) The real exchange rate is the price of

foreign relative to domestic goods and services. Formally, it is measured by Q = SP*/P.

Using the definition of real exchange rates, Q(t) = S(t) P*(t)/P(t) = 1. If absolute PPP holds, the real exchange rate should equal unity. The log of the real exchange rate should equal zero, q(t) = s(t) – p(t) + p*(t) = 0.


The three most restrictive assumptions a) Goods are identical/perfect substitutes across countries b) The weights used to construct the P levels are same across countries c) Absence of transaction costs in arbitraging goods across countries.

Easy to modify this to allow for transaction costs, s(t) = π + p(t) – p*(t). Assuming constant shipping costs π is symmetrical between home and foreign country, we can define a neutral band for the log of the exchange rate -π ≤ q(t) ≤ π.


Relative PPP, ∆s(t) = ∆p(t) - ∆p*(t). Countries with relatively high inflation will experience a depreciating currency.

Absolute PPP does not hold in practice- however exchange rates do have a long-run tendency to gravitate towards their PPP levels.

Different explanations for failure of PPP Decompose CPI based real exchange rate into

two relative P components- introduce non-traded goods P’s into our previous set up.


p(t) = a(t) p(t)T + (1-a(t)) p(t)NT (1) p*(t) = a(t) p(t)T*+ (1-a(t)) p(t)NT* (2) q(t) = s(t) – p(t) + p*(t) (3) Define a similar relationship for the p of traded

goods as q(t)T = s(t) – p(t)T + p(t)T* (4) By substituting (1), (2) and (4) into (3), we

obtain q(t)= q(t)T+(a(t) -1)[(p(t)NT- p(t)T) – (p(t)NT*- p(t)T*)] or q(t) = q(t)T+ q(t)NT,T where q(t)NT,T is the relative price of non-traded to traded goods in the home country relative to the foreign country- the internal price ratio.


Balassa- Samuelson hypotheses – for countries with faster growth rates, their non-traded goods to traded goods price ratio will rise faster- real exchange rate will appreciate. The BS hypothesis suggests that rapid economic growth is accompanied by real exchange rate appreciation because of differential productivity growth between tradable and non-tradable sectors.


Trade costs and adjustment to PPP ∆qt =f[(q*t-1 – qt-1), zt-1] π(q*t-1 – qt-1) , 0< f1<1

qt-1 is the log of the real exchange rate at time t-1 and q*t-1 is the equilibrium level at time (t-1). zt summarizes a list of other factors that may affect q*, typically other macroeconomic variables to be introduced in later models. The function f which takes a value between 0 and 1 each period, measures the extent to which the gap between q*t-1 and qt-1 is eliminated by the next period’s change in the exchange rate.


Trade costs – Iceberg model. A proportion m of every unit of good shipped is “lost” or consumed in the form of shipping costs- if the price in its country of origin is P1* and price at home is P1 , then (1-m)P1 = P1* .

Similarly, for a product being imported into the foreign country and exported from home, (1-m)P2

* = P2

P1/P2 = 1/(1-m)2 P1*/P2*-this can cause divergence in relative prices between countries. Price is different for these products but no arbitrage opportunities.


Incomplete pass-through and pricing to market

Empirical evidence, purchasing power parity

GDP (PPP) vs GDP (market exchange rates)

Why is GDP (either total GDP or per-capita GDP) almost always higher when expressed in terms of PPP exchange rates than in terms of market exchange rates?

For example – China’s GDP in official exchange rate is 5.8 trillion US $, according to PPP exchange rates it is 10 trillion US$.

India’s GDP at official exchange rate is 1.5 trillion US$, according to PPP exchange rates it is 4 trillion US$.

Financial Markets in the open economy

Domestic strategy: Invest AUD 1 in 12 month fixed deposit, receive AUD(1+r) at the end of the year.

Foreign strategy: a) Convert the AUD to US$ b) Deposit the dollars with a US bank c) At the end of the year, convert the proceeds back to AUD.

After a) we have US $1/S After b) we have US $(1+r*)1/S At stage c), liquidate the deposit and convert the

proceeds back from US $ to AUD. We have US $(1+ r*)Se/S- where Se is the expected exchange rate at the end of period t or beginning of (t+1).

Financial Markets in the open economy

The risk premium is the reward, usually in the form of an anticipated excess return , that an economic agent gets in order to persuade him to bear risk. We assume that economic agents are risk neutral.

Under this assumption, in equilibrium- the domestic and foreign strategies will have to yield the same AUD return. In other words, the investor must be indifferent between deposits in the two countries.

Financial markets in the open economy

Uncovered interest rate parity(1+r) = (1+r*)Se/S Se/S ≈ 1 + ∆se where ∆s is the rate of depreciation

of the domestic currency. (1+r) = (1+r*)(1+∆se) = 1+ r*+ ∆se + r*∆se . The

last term is very small and we disregard it. Uncovered interest parity relation r = r* + ∆se

The domestic interest rate must be higher(lower) than the foreign interest rate by an amount equal to the expected depreciation (appreciation) of the domestic currency.

Financial markets in the open economy Spot exchange rate – for current exchange. The (1-3-12 month) forward exchange rate is

the rate that appears in contracts to exchange one currency for another 1, 3 or 12 months in advance of the actual transaction.

We can replace Se by F to arrive at the covered arbitrage condition, (1+r) = (1+r*) F/S

F/S ≈ 1 +f where f is the forward premium (discount) – the proportion by which a country’s forward exchange rate exceeds (falls below) its spot rate.


Covered interest parity (1+r) = (1+r*)(1+f) OR r = r* + f The domestic interest rate must be

higher(lower) than the foreign interest rate by an amount equal to the forward discount(premium) on the domestic currency.


An investor who has a liability(an asset) denominated in a specific currency is said to have a short (long) position in that currency.

It pays to borrow (be short in) a depreciating currency and lend (be long in) an appreciating currency.

Mechanics of a “speculative attack” on a fixed exchange rate

Currency risk arises whenever an investors net position in a currency is non-zero. When a long position is matched by an equal and opposite short position in the same currency, the investor has a fully hedged or covered position in that currency.

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International Macroeconomics 2(3)