International Macroeconommics Chapter 3: Exchange Rate, The Monetary Approach in the Long Run Department of Economics, UCDavis
Outline Goods Market Equilibrium: PPP 1 Goods Market Equilibrium: PPP 2 3 4
Outline Goods Market Equilibrium: PPP 1 Goods Market Equilibrium: PPP 2 3 4
An Example CPI consumer price index: price paid by a typical consumer for a basket of goods and servies Inflation percentage change of price index (CPI) 1970 1990 Inflation CPI CA C$100 C$392 292% CPI US $100 $336 236% Exchange Rate 1 C$/$ 1.16 C$/$ CPI CA (in$) $100 $338 238%
An Example Is it a coincidence? No In the Long-run, prices and exchange rate will always adjust so that the purchasing power of each currency remain comparable over basket of goods. When price in Canada expressed in c$ goes up more than the price in the U.S. expressed in $, C$ depreciated relative to $ so they still has same purchasing power.
The Intuition No arbitrage condition in goods market Assumptions: No trade frictions, free competition, identical goods Then price must be equal in all locations for any good when expressed in common currency. Example: A diamond of given quality, e5000 in Paris E $/euro = 1.2 No arbitrage: a diamond with same quality in N.Y. must sells for $6000
LOOP Microeconomic version of the no-arbitrage condition in goods market. Consider a single good in two different locations Law of one price (LOOP): the price of the good in each market must be the same (once expressed in same currency units) p US = p EU E $/euro
PPP Macroeconomic version of the no-arbitrage condition in goods market. LOOP holds for every good in the CPI basket Purchasing Power Parity (PPP): overall price level in each market must be the same (once expressed in same currency units) P US = P EU E $/euro
Real Exchange Rate Definition: Relative price across countries. q US/EU = E $/europ EU P US (previous edition use a different notation: q EU/US ) Real Exchange rate: How many US baskets are needed to purchase one European basket. Nominal Exchange rate: How many dollars are need to exchange for one euro.
US is the home country: q US/EU, home has experienced a real depreciation. q US/EU, home has experienced a real appreciation. PPP holds if and only if real exchange rate is 1.
PPP as a theory of ex-rate determination Rearrange PPP: E $/euro = P US P EU PPP makes a clear prediction about exchange rate: exchange rate at which two currencies trade equals the relative price levels of the two countries. Example: a basket of goods cost $120 in the U.S., the same basket of goods cost e100. PPP predicts an exchange rate of $1.2 per e.
PPP as a theory of ex-rate determination
Relative PPP Absolute PPP: price levels and exchange rate E $/euro = P US P EU Relative PPP: change of price levels (inflations) and change of exchange rate (appreciation/depreciation) E $/euro,t E $/euro,t = π US,t π EU,t
Relative PPP Rate of depreciation of the nominal exchange rate equals the inflation differential. Example 1970 1990 Annual Inflation Annual depreciation of C$ CPI CA C$100 C$392 7.07% CPI US $100 $336 6.25% Ex-rate 1 C$/$ 1.16 C$/$ 0.74% Relative PPP predicts that higher inflation in home country relative to foreign will depreciates the home currency.
Absolute PPP and Relative PPP PPP, whether in absolute or relative form, suggests that price levels in different countries and exchange rates are tightly linked. Absolute PPP: prices and exchange rate are linked in their absolute levels. Relative PPP: prices and exchange rate are linked in the rates at which they change. Relative PPP is derived from Absolute PPP If absolute PPP holds, then relative PPP also holds. When aosolute PPP fails, we may also abserve relative PPP.
Test of PPP Goods Market Equilibrium: PPP Relative PPP is a useful guide to the relationship between prices and exchange rates in the long run, over horizons of many years or decades.
Test of PPP Goods Market Equilibrium: PPP PPP holds less well in the short run, over horizons of just a few years.
Why PPP fails in the short run? Transaction costs: transportation cost, tariff. Nontraded goods: goods that are nontradable. A big mac includes trades goods such as raw foods and nontraded goods such as labor. Imperfect competition: goods may not be identical with brand names, copyrights, and legal protections. Arbitrage can be shut down by regulation. Price stickiness: price is sticky in the short run and may not respond to fluctuating exchange rate.
Outline Goods Market Equilibrium: PPP 1 Goods Market Equilibrium: PPP 2 3 4
Recap the essential elements of monetary theory. PPP: in the long run, exchange rate is determined by the ratio of price levels in two countries. What determines those price levels? Quantity theory: price levels are determined by the relative demand and supply of money.
What is Money? Money perform three key functions: Store of value Money is an asset, it pays no interests, but has value in the future. unit of account All prices in an economy are quoted in money. medium of exchange Money is the most liquid asset: can be easily converted to goods and services.
The Measurement of Money What accounts as money? M0 Base Money: currency in circulation, reserves of commercial banks. M1 Narrow Money: currency in circulation, checking accounts, traveler s check. M2 Broad Money: M1, saving accounts, small time deposits. In this course, when we refer to money M, we mean M1: The stock of liquid assets that are routinely used to finance transactions.
The Supply of Money Central bank controls money supply (M=M1) Central bank directly control base money (M0) by issuing notes and coins. Centra bank indirectly control M1 by using monetary policy to influence the behavior of the private banks. To simplify, we assume central bank controls M1.
The Demand of Money We demand money because we need money to conduct transactions. Assume amount of transactions is proportional to nominal income. Money demand is proportional to nominal income. Example: If an individual s income doubled from $100, 000 to $200, 000, we expect this person s demand for money also double.
The Demand of Money Money demand is proportional to nominal income. Demand for money (in $) = a constant nominal income (in $) M d = L PY Demand for real money (in baskets of goods)= a constant real income (in baskets of goods) M d P = L Y
Equilibrium in the Money Market Equilibrium: Supply = Demand In nominal term: M = M d = L PY M = L PY In real term: M P = L Y Example: US nominal income is $15 trillion, has money $1.5 trillion. The constant term is 0.1. Each $ allows the economy to transact nominal GDP worth $10. We say the velocity of money is 10 (1/L).
A Simple of Price Quantity Theory: In the long run, prices are flexible and will adjust to put the money market in equilibrium. P US = M US L US Y US P EU = M EU L EU Y EU If M rises by a factor of 10, real income stays the same, with more money chasing the same quantity of goods, price will rise also by a factor of 10.
A Simple of Price Quantity Theory: Growth rate of money supply: µ US,t. Growth rate of real income: g US,t. Inflation: π US,t. P US = M US L US Y US π US,t = µ US,t g US,t Inflation is the excess of money supply growth over real output growth When money supply growth is higher than real output growth, we have more money chasing fewer goods and this leads to inflation.
A Simple of Price
Test of the quantity theory
Outline Goods Market Equilibrium: PPP 1 Goods Market Equilibrium: PPP 2 3 4
A Simple of Exchange Rate Long-run Monetary approach of exchange rate: E = $/EU Exchange rate P US P EU Ratio of price levels! M US $ # & " L = US Y US % =! M EU $ # & " L EU Y EU % ( M US / M EU ) ( L US Y US / L EU Y EU ) Relative nominal money supplies divided by relative real money demands M US increases P US increases E $/euro increases. $ depreciates against e y US increases P US decreases E $/euro decreases. $ appreciates against e
A Simple of Exchange Rate Long-run Monetary approach of exchange rate in relative form: ΔE $/ t E $/,t Rate of depreciation of the nominal exchange rate = π US,t π EU,t Inflation differential = ( µ g US,t US,t ) ( µ EU,t g EU,t ) ( ) = µ US,t µ EU,t g g US,t EU,t. Differential in nominal money supply growth rates ( ) Differential in real output growth rates All else equal, faster money supply growth rate in the U.S., $ will depreciate more rapidly. All else equal, faster real output growth rate in the U.S., $ will appreciate more rapidly.
Test of the Monetary Theory
Outline Goods Market Equilibrium: PPP 1 Goods Market Equilibrium: PPP 2 3 4
Money Demand Previously, M d = L PY Now L is decreasing in i, M d = L(i) PY There is an opportunity cost of holding money. i increases, opportunity cost of holding money increases, demand of money decreases. In real term, M d P = L(i) Y
Money Market Equilibrium M P Real money supply = L( i) Y Real money demand
Fisher Effect Goods Market Equilibrium: PPP Relative PPP UIP e ΔE / E$/ Expected rateof dollar depreciation Δ E = e πus πeur $ e E e $/ $/ Expected rate of dollar depreciation Expected inflation differential = i$ Net dollar interest rate i Net euro interest rate Fisher Effect i$ i Nominalinterest rate differential = e e πus πeur Nominalinflation rate differential (expected)
Fisher Effect Goods Market Equilibrium: PPP i$ i Nominalinterest rate differential = e e πus πeur Nominalinflation rate differential (expected) In the long run, when prices are flexible, a rise in the expected inflation rate in a country will lead to an equal rise in its nominal interest rate. According to PPP, a rise in expected inflation leads to expected depreciation of home currency. According to UIP, if home currency is expected to depreciate, home nominal interest rate must rise to offset the extra lose such that assets market is in equilibrium.
Test of the Fisher Effect
Real Interest Rate Parity Real Interest Rate: Inflation adjusted return on an interest-bearing asset. r e US = i $ π e US Rearrange the Fisher Effect equation: Real Interest Rate Parity: i $ π e US = i euro π e EU r e US = r e EU If PPP and UIP both hold, then expected real interest rates are equalized across countries.
Test of Real Interest Rate Parity
The Fundamental Equation under the General Model M US P LUS ( i$ ) Y US US ( MUS / M EUR ) E $/ = = = P ( ( ) EUR M LUS i$ ) YUS / LEUR ( i ) Y EUR EUR Ratio of price levels L ( ) Relative nominal money supplies EUR i Y EUR Exchange rate divided by demands Relative real money