long run (Purchasing Power Parity: PPP)

Exchange rates in the long run (Purchasing Power Parity: PPP)

Jan J. Michalek

The law of one price:

 i – for a product i;

 P

= E

* P

 Or equivalently:

 E

= P

/ P

 Idea: The same product should have the same price at competitive markets (no trade barriers and low transport costs)

 but there are many reservations

 JJ Michalek

Empirical verification of law of one price: butter

Empirical analysis of law of one price: price in

grams of silver per hectoliter f charcoal

PPP theory: absolute version

Theory of PPP: Purchasing power parity (PPP): the exchange rate is equal to relations of purchasing power among analyzed countries

If P

: Prices in Poland P

: Prices in Germany Then PPP foresees that:

E

= P

/ P

or more general: E=P/P*

According to PPP: rise in domestic price level leads to the proportional depreciation of domestic currency.

Another notation:

P

= E

*P

 JJ Michalek

PPP theory: relative version

Exchange rates equals to relative prices

Relative PPP theory: percentage change in the exchange rate = difference in the percentage changes in relative prices:

where

is the rate of inflation in time t.: 

= (P

-P

)/P

 E

 E

 / E

 

 

 JJ Michalek

Purchasing Power Parity: once again in two versions



Purchasing power parity comes in 2 forms:



Absolute PPP: purchasing power parity that has already been discussed. Exchange rates equal price levels across countries.

E

= P

/P



Relative PPP: changes in exchange rates equal changes in prices (inflation) between two periods:

(E

- E

)/E

= 

- 

where 

= inflation rate from period t-1 to t

Model based on PPP:

monetary approach

P_PL = M^s_PL/L(R_PLN,Y_PL); and the same abroad;

Where L(RPLN,YPL) is the real aggregate demand for money.

Fundamental equation of the monetary approach:

 

 







 







PL PLN s G

G S G PL PL

PLN LR Y LR Y

M P M

P

E _/ / ^, ,

long run changes in the ex-rate is fully determined by the relative supplies of those monies an the relative real demand for them

Or in the abbreviated form::





S G S

PLN PL R R Y Y

M

E _/ M 





 





where: (.) is the relative aggregate demand for monies in Germany in relation to Poland.

 JJ Michalek

Monetary Approach to Exchange Rates



To the degree that PPP holds and to the degree that prices adjust to equate real money supply with real money demand, we have the following prediction:



The exchange rate is determined in the long run by prices, which are determined by the relative supply of money across countries and the relative real demand of money across countries.

Monetary Approach

to Exchange Rates (cont.)

Predictions about changes in:

1.

Money supply: a permanent rise in the domestic money supply



causes a proportional increase in the domestic price level,



causing a proportional depreciation in the domestic currency (through PPP).



same prediction as long run model without PPP

2.

Interest rates: a rise in the domestic interest rate



lowers domestic money demand,



increasing the domestic price level,



causing a proportional depreciation of the domestic

currency (through PPP).

PPP and interest rate: exchange rate and the Fisher effect

Real interest rate: interest rate reflecting real productivity of economy = nominal interest rate corrected by expected rate of inflation: (but we do know the actual);



= (P

– P)/P

P

: expected price level (one year perspective);

P: current price level; 

: expected rate of inflation r

= R – 

lub

R = r

+ 

Fisher effect: Under ceteris paribus assumption: a rise in the domestic expected inflation rate will eventually cause rise in the interest rate that deposits of its currency offer.

 JJ Michalek

Figure 15-2: Inflation and Interest Rates in Switzerland, the United States, and Italy, 1970-2000

A Long-Run Exchange Rate

Model Based on PPP

Figure 15-2: Continued

A Long-Run Exchange Rate Model Based on PPP

Figure 15-2: Continued

A Long-Run Exchange Rate Model Based on PPP

Figure 15-2: Continued

Problems with empirical verification of PPP

 trade barriers and transportation costs exist in real economy;

 There are different basket of consumptions in different countries;

 imperfect (monopolistic) competition exist:

oligopolistic price practices undermine the law of one price.

 JJ Michalek

The real exchange rate

Real ex-rate (PLN to €): brad summary measure of the price in Polish prices goods and services to the other.

Real ex-rate = (EPLN/€ * PG) / PP

P P E P

P q E

PL G PLN PLN

*

/   

 ^



real ex-rate : measures the basket of expenditure in Pl to German one

A real appreciation: of the PPLN against € indicates decrease in the relative price of products purchased in Germany, or a rise in the zloty’s German purchasing power compared with the Polish one

In accordance with absolute version of PPP, the real ex-rate must be equal 1:

While in accordance with relative version of PPP real ex-rate must be constant (but not





/

/   _PLN  _PLN  _{G PL}

G

PLN PPLP q E P P

E _{  }

 JJ Michalek

Exchange rate fluctuations

Figure 3(c): Bilateral exchange rates and export competitiveness: 12 month percentage changes, Germany-U.S.

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

1973 DEC 1975 MAR 1976 JUN 1977 SEP 1978 DEC 1980 MAR 1981 JUN 1982 SEP 1983 DEC 1985 MAR 1986 JUN 1987 SEP 1988 DEC 1990 MAR 1991 JUN 1992 SEP 1993 DEC 1995 MAR 1996 JUN 1997 SEP

ger/us.er ger/us.exppr

 JJ Michalek

Changes in real exchange rates

Year

Consume r price

index (CPI) in

USA

Consume r price

index (CPI) in

U.K.

Nominal exchang

e rate

Real exchange

rate

Changes of real exchange rate

Inflation rate in

USA

Inflation rate in

UK P P* E q=(EP*)/P [q(t)-q(t-1)]/q(t-1)

1961 36,3 19,3 2,80 1,489

1962 36,7 20,1 2,81 1,539 3,38 1,1 4,1

1963 37,2 20,5 2,80 1,543 0,26 1,4 2,0

1964 37,6 21,2 2,79 1,573 1,95 1,1 3,4

1965 38,3 22,2 2,80 1,623 3,17 1,9 4,7

1966 39,4 23,0 2,79 1,629 0,35 2,9 3,6

1967 40,5 23,6 2,75 1,602 -1,61 2,8 2,6

1980 100,0 100,0 2,33 2,330

1981 110,4 111,9 2,03 2,058 -11,69 10,4 11,9

1982 117,2 121,5 1,75 1,814 -11,83 6,2 8,6

1983 120,9 127,1 1,52 1,598 -11,92 3,2 4,6

1984 126,1 133,5 1,34 1,419 -11,22 4,3 5,0

1985 130,6 141,6 1,30 1,409 -0,64 3,6 6,1

1986 133,1 146,4 1,47 1,617 14,71 1,9 3,4

 JJ Michalek

Empirical Evidence on PPP and the Law of One Price

Figure 15-3: The Dollar/DM Exchange Rate and Relative U.S./German Price Levels, 1964-2000

Shortcomings of PPP (cont.)

Beyond Purchasing Power Parity: A General Model of Long-Run Exchange Rates

Figure 15-5: The Real Dollar/Yen Exchange Rate, 1950-2000

Explaining the Problems with PPP

Figure 15-4: Price Levels and Real Incomes, 1992

Figure 15-6: Sectoral Productivity Growth Differences and the Change in the Relative Price of Nontraded Goods, 1970-1985

Beyond Purchasing Power Parity: A General Model of Long-Run Exchange Rates

International Fischer effect

If people expect relative PPP to hold, the difference between the interest rates offered by PLN and euro deposits will equal the difference between the inflation rates expected in Poland and Germany:

 

e PL PLN PLN

e

PLN

E E

E



/

   

And combining the expected version of relative PPP with interest parity condition:





 _PLN^e / _PLN/

/

PL

R E E E

R   

we receive the international Fisher effect:

e e PL PLN

R

R 

   

i.e.: the currency depreciation is expected to offset the international inflation difference

 JJ Michalek

The monetary model of exchange rate changes

We can get the nominal exchange rate (as a function of real ex-rate):

 

G PLN PL

PLN q P P

E

Org _{/ /} 5

. 15

and comparing this with fundamental equation of monetary approach we get:

 

 







 







PL PLN s G

G S G PL PL DM

PLN LR Y LR Y

M P M

P

E _/ / ^, ,

i.e. exchange rates fluctuations reflect changes in relative supply and demand for money or in the abbreviated form:





S G S

PLN MPLM R R Y Y

E _/   _,



 





where: (.) is the aggregate relative demand for money in G in relation to PL:

 JJ Michalek

General model

of exchange rate changes

If we assume that the PPP does not hold (and changes in real ex-rate are possible) then we get general equation for long term changes:

 The general model (equation) of exchange rate changes:

 PLN G PL

S G S PLN PL

PLN q M M R R Y Y

E / /   ,



 







If the PPP does not hold  the expected change in the real ex-rate is equal to:

And comparing this with “normal” interest parity:

We get the following equation:

  



e PL PLN PLN e

PLN

PLN R q q q

R

Or



 (



) /

    11

. 15

and this means: that the difference in interest rates depend on:

1. expected changes in real exchange rates 2. expected differences in expected rtes of inflation

      



PL PLN PLN e PLN PLN PLN e

PLN q q E E E

q

Or ( _/ _/)/ _/ _/ _/ / _/   10

. 15





 _PLN^e / _PLN/ / _PLN/

PLN R E E E

R   

 JJ Michalek

The general model of exchange rate changes: continued

I f we denote the expected rate of real depreciation of PLN to € as:







 ( q

  q

) / q

Then the long run exchange rate level can be written as:

     

 

e G e PL e S G S PL PLN

PLN

q M M Y Y

E

Or / , /

12 .

15



       

 JJ Michalek

Nominal exchange change rate in the long run: Monetary approach

1. PPP: 2. Equilibrium at domestic monetary markets

3. Equation of the exchange rate

4. Interest parity combined with the PPP

5. Equation of the long run equilibrium:

monetary approach

G PL DM

PLN P P

E _/  / S





PL

PL M LR Y

P  / ,





S G

G M LR Y

P  / _,

   

 



 

 





 









 







PL PL G S G S PL

PL PL S G

G S PL G PLN PL

Y Y R M R

M

Y R L Y R M L P M E P

,

, /

/ ,









e G e PLN PLN R R  _ 







 JJ Michalek

Price Levels and Incomes

Relative unit labour costs (inverse of

real exchange rates) in Eurozone