Ppp implied exchange rate formula

Lecture 2 Purchasing Power Parity and Real Exchange Rates

Learning Objectives

Understand what PPP tells us about exchange rate

determination

Gain knowledge of absolute PPP and relative PPP and their

application

Be able to examine PPP conditions empirically and explain the

consequences of violating these conditions

Comprehend effective exchange rates and competitiveness of nations

Reading: Madura and Fox, Ch 8

The Law of One Price (LOOP)

Prices in the open economy:

* The Law Of One Price suggests that the price of a given good is the same across all

countries when expressed in terms of the same currency.

(e.g., if a bottle of shampoo costs $3 in the US and =0.60 then it will cost

£1.8 in the UK)

That is,

so the LOOP implies that the exchange rate can be written as:

The LOOP makes the following assumptions:

- competitive markets

- markets free from trade restrictions

- no transportation costs exist

S£/$

3

Purchasing Power Parity (PPP)

A generalization of the LOOP for all goods in one economy.

That is: the general level of prices when converted to a common currency will be the same across all countries.

Or simply,

Purchasing power parity states:

Which implies that the PPP exchange rate is given by

(eg, for the PPP implies that )

S£/$

4

Absolute Purchasing Power Parity

The relationship between the prices of goods and services and

exchange rates is known as Purchasing Power Parity (PPP)

Absolute purchasing power parity (PPP)

PPP states that

The same goods or basket of goods

Should sell at the same price in different countries

When measured in a common currency:

Ph= Sh/f Pf

OR

where Ph is the home price and Pf the foreign price.

Absolute Purchasing Power Parity

For example

If an ounce of gold costs $300 in the U.S. and the exchange rate is £0.62/$, what is the price of gold in the U.K.?

P£=S£/$ P$ = £0.62/$ * $300 = £186

5-6

Absolute Purchasing Power Parity

Problems:

* It is not easy to attach an unambiguous meaning to an index of

different prices

* The “baskets” used in different countries are not identical

* The changes in the “baskets” used in different countries are not

identical

* The choice of the base period can have important implications

Thus the absolute version of PPP is not always a convenient concept

Relative Purchasing Power Parity

How would we expect the exchange rate to change

If two countries experience different price changes (inflation)

Relative purchasing power parity (PPP)

Relative Purchasing Power Parity

Alternatively, taking logs, relative purchasing power parity (PPP)

The relative PPP (the equation)

the % change in the exchange rate (S)

is equal to the % change in the domestic price level

minus the % change in the foreign price level.

We usually refer to the % change in the price level as the rate of inflation,

So, the relative PPP says the % change in the exchange rate (S)

Equals the inflation differential between the domestic and foreign

10

Relative Purchasing Power Parity

Price indices

Usually consumer price indices (CPI)

Used for the measurement of inflation

Relative PPP

Indicates that the home currency will depreciate

if inflation in the home country is higher than that in the foreign country,

Indicates that the home currency will depreciate to an extent

equal to the inflation differential between the two countries.

11

Relative Purchasing Power Parity

Example

If inflation in the US was 2% and Inflation in Japan was 0%

According to relative PPP

The yen should appreciate by 2 %

The US dollar should depreciate by 2 %

PPP: US and UK

.

12

13

Why we may experience deviations from PPP in practice?

transportation costs ≠ 0

restrictions on trade

not all goods are traded

imperfect competition

different countries use different baskets to measure inflation

14

Why we may experience deviations from PPP in practice?

Transportation costs

A simplified version would be to treat transportation costs as linearly related to the distance that goods are shipped.

The further the distance the goods have to travel the higher those costs are.

So more proximate countries are more likely to adhere to PPP

2. Trade Restrictions

Tariffs (i.e, taxes on goods crossing international borders). Their effect is similar to the transportation costs, that is, they increase the price of a given good in the destination country.

Why we may experience deviations from PPP in practice?

3. Tradables and Nontradables

Non-tradables /Non-traded goods

are those for which inter-regional (or international) price differentials

cannot be eliminated.

This is because the transaction costs involved

are so high relative to the cost of the goods (services)

that makes it non-feasible to trade it.

16

Why we may experience deviations from PPP in practice?

4. Imperfect Competition

The focus for most of the current research

Monopolistic competition & Pricing-to-Market (PTM)

(price discrimination, international market segmentation)

It would be impossible to adjust prices with a frequency that would match the frequency of the exchange rates change.

The costs of changing prices are often referred to as menu costs.

17

Why we may experience deviations from PPP in practice?

5. PPP and price indices

Which price index to use

Does the choice of price index (say CPI vs. RPI)

Affect the performance of the PPP exchange rate?

Different countries use different baskets

The same good may have different weights

In the baskets of different countries

This affects both absolute and relative PPP measures

How do PPP deviations affect countries’ competitive positions in the world market?

The implications of the deviations from PPP

If exchange rate changes satisfy PPP

competitive positions of countries will remain unaffected following exchange rate changes.

Otherwise, exchange rate changes will affect relative competitiveness

If a country’s currency appreciates (depreciates) by more than is warranted by PPP,

It will hurt (strengthen) the country’s competitive position in the world market.

Empirical Evidence

PPP predicts fairly well, both in absolute and relative form

at the level of one heavily traded commodity for which the governments involved do not interfere with trade.

Examples would be wheat, gold

Thus for something like wheat

LOOP is a pretty good approximation.

PPP holds better for high inflation countries (McNown and Wallance, 1989; Zhou, 1997).

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Empirical Evidence (continued)

• PPP predicts better over the long run than the short run (Froot and Rogoff,

1995; Sarno and Taylor, 2002; Coakley, 2005).

– According to Froot and Rogoff (1995), for major industrialized countries it

takes about four years on average for a deviation from PPP to be reduced by

half.

• PPP predicts better for traded goods than non-traded goods.

PPP predicts poorly using CPI, but it holds better using TPI (Xu, 2003)

BigMacPPP

The MacPPP Standard

The Big Mac as a Price Index

Advantages:

Standard product globally

Local suppliers used reducing transit costs

Surprisingly close to more complicated indexes

Implied BigMacPPP Rates

Overvaluations/Undervaluations

21

Table 1: BigMacPPP in 2010 Big Mac index

Big Mac PPP

The Big Mac Index : A Guide

• The first column indicates the price of a Big Mac in local currency for any

given country. For example, $3.58 in the US and Yuan 12.51 in China.

• The second column indicates the price of a Big Mac in terms of US$ for any

given country.

For example, the price of a Big Mac in terms of US$ for China is $1.83

Big Mac PPP

The third column is the implied PPP value of the US$ against currency of the

given country and emerges by using the PPP definition of the exchange rate i.e.

the exchange rate implied by the ratio of the two prices (or price levels).

• The fourth column is the actual exchange rate.

Why the price of a Big Mac in terms of US$ for China is $1.83 ?

MacPPP - Exercise

• The fifth column uses the actual exchange rate and the PPP-implied exchange

rate to obtain a measure of currency over(under) valuation against the US$.

Consider China again:

What is the interpretation? Do you think the Chinese currency is under/overvalued?

2 minutes!

The Real Exchange Rates (RER)

What is the real exchange rate?

-- It is defined as the actual/nominal exchange rate multiplied by the ratio of the price levels

Real Exchange Rate (Q or in logs q )

where ,

So,

27

The Real Exchange Rates (RER)

The real exchange rate is a useful concept and a simple

means to gauge the strength of currencies.

If absolute PPP always held, the real exchange rate Q

would equal 1.

Home currencies are over valued and foreign currencies

are under valued, then: Q < 1

(  )

What is the real exchange rate of in Big Mac PPP case?

Effective exchange rates

Measure the value/strength of a currency against a trade-weighted 'basket' of other currencies, relative to the base date.

Suppose country i has m trading partners , the effective exchange rate of country i, is:

Ei is the effective exchange rate of country i,

Si,j is the nominal exchange rate between countries i and j,

wi,j is the weight average of country i in relation to country j.

Effective Exchange rates

Effective Exchange rates

Effective exchange rates are useful for gauging whether a currency has appreciated overall relative to trading partners.

For example, in 2015 the Chinese RMB depreciated about 8% against the US dollar. However, more of China's trade is with Asia and Europe than with the United States, and meanwhile the dollar appreciated against those currencies. Therefore, the net effect of the Chinese currency actually appreciated approximately 10% relative to its trading partners.

Effective Exchange rates

The weights

Measure the relative importance

Of each of the other countries

As a trading partner

In the case of the UK,

The trade weights reflect aggregated trade flows

Cover 27 countries.

The base date for the index is 2005, and is set at 100.

More details of how Effective Exchange rates are calculated may be found at the Bank of England webs site.

30

Effective Exchange rates

The weight for each country is derived from three components.

For example

The weight of the US dollar in the sterling index, where the three factors used are:

US competition in the UK domestic market

UK competition in the US domestic market

Competition between US and UK manufactured goods in third country markets

Effective Exchange rates

The effective exchange rate

Is an artificial index

It is based on a specific base period.

Does not indicate the absolute level of competitiveness

Just as price indices do not show actual price levels

So better to use in the examining changes in competitiveness

The Real Effective Exchange Rates (REER)

International competitiveness

Is affected not only by the exchange rate

But also by domestic and foreign price movements.

For example,

The nominal effective exchange rate of the yen remains unchanged,

The relative competitiveness of Japanese goods increases

If the inflation rate of the rival exporting countries surpasses that of Japan

Japanese exporters receive more real income for their goods

The Real Effective Exchange Rates (REER)

The real effective exchange rate

Each of the bilateral exchange rates

Is adjusted by the price indices of the two countries

To give real exchange rates

Real bilateral exchange rates

Replace nominal bilateral exchange rates in the effective exchange rate formula

To derive real effective exchange rates

Source: Bank of England. Index set at Jan 2005 = 100

35

Real Effective Exchange Rate £

1990-01 1990-02 1990-03 1990-04 1990-05 1990-06 1990-07 1990-08 1990-09 1990-10 1990-11 1990-12 1991-01 1991-02 1991-03 1991-04 1991-05 1991-06 1991-07 1991-08 1991-09 1991-10 1991-11 1991-12 1992-01 1992-02 1992-03 1992-04 1992-05 1992-06 1992-07 1992-08 1992-09 1992-10 1992-11 1992-12 1993-01 1993-02 1993-03 1993-04 1993-05 1993-06 199 3-07 1993-08 1993-09 1993-10 1993-11 1993-12 1994-01 1994-02 1994-03 1994-04 1994-05 1994-06 1994-07 1994-08 1994-09 1994-10 1994-11 1994-12 1995-01 1995-02 1995-03 1995-04 1995-05 1995-06 1995-07 1995-08 1995-09 1995-10 1995-11 1995-12 1996-01 1996-02 1996-03 1996-04 1996-05 1996-06 1996-07 1996-08 1996-09 1996-10 1996-11 1996-12 1997-01 1997-02 1997-03 1997-04 1997-05 1997-06 1997-07 1997-08 1997-09 1997-10 1997-11 1997-12 1998-01 1998-02 1998-03 1998-04 1998-05 1998-06 1998-07 1998-08 1998-09 1998-10 1998-11 1998-12 1999-01 1999-02 1999-03 1999-04 1999-05 1999-06 1999-07 1999-08 1999-09 1999-10 1999-11 1999-12 2000-01 2000-02 2000-03 2000-04 2000-05 2000-06 2000-07 2000-08 2000-09 2000-10 2000-11 2000-12 2001-01 2001-02 2001-03 2001-04 2001-05 2001-06 2001-07 2001-08 2001-09 2001-10 2001-11 2001-12 2002-01 2002-02 2002-03 2002-04 2002-05 2002-06 2002-07 2002-08 2002-09 2002-10 2002-11 2002-12 2003-01 2003-02 2003-03 2003-04 2003-05 2003-06 2003-07 2003-08 2003-09 2003-10 2003-11 2003-12 2004-01 2004-02 2004-03 2004-04 2004-05 2004-06 2004-07 2004-08 2004-09 2004-10 2004-11 2004-12 2005-01 2005-02 2005-03 2005-04 2005-05 2005-06 2005-07 2005-08 2005-09 2005-10 2005-11 2005-12 2006-01 2006-02 2006-03 2006-04 2006-05 2006-06 2006-07 2006-08 2006-09 2006-10 2006-11 2006-12 2007-01 2007-02 2007-03 2007-04 2007-05 2007-06 2007-07 2007-08 2007-09 2007-10 2007-11 2007-12 2008-01 2008-02 2008-03 2008-04 2008-05 2008-06 2008-07 2008-08 2008-09 2008-10 2008-11 2008-12 2009-01 2009-02 2009-03 2009-04 2009-05 2009-06 2009-07 2009-08 2009-09 2009-10 2009-11 2009-12 2010-01 2010-02 2010-03 2010-04 2010-05 2010-06 2010-07 2010-08 2010-09 2010-10 2010-11 2010-12 2011-01 2011-02 2011-03 2011-04 2011-05 2011-06 2011-07 2011-08 2011-09 2011-10 2011-11 2011-12 2012-01 2012-02 2012-03 2012-04 2012-05 2012-06 2012-07 2012-08 2012-09 2012-10 2012-11 2012-12 2013-01 2013-02 2013-03 2013-04 2013-05 2013-06 2013-07 2013-08 2013-09 2013-10 2013-11 2013-12 2014-01 2014-02 2014-03 2014-04 2014-05 2014- 06 2014-07 2014-08 2014-09 2014-10 2014-11 2014-12 2015-01 2015-02 2015-03 2015-04 2015-05 2015-06 2015-07 2015-08 2015-09 2015-10 2015-11 2015-12 2016-01 2016-02 2016-03 2016-04 2016-05 2016-06 2016-07 112.23 114.55 111.63 113.47 115.44000000000001 118.39 121.76 124.61 123.17999999999999 124.41000000000001 123.95 122.64 122.76 122.86 121.52 124.5 124.02 122.24000000000001 121.41000000000001 122.25 123.08 122.54 123.02 123.47 122.16 122.16999999999999 121.24000000000001 123.76 125.66999999999999 125.53 124.64999999999999 123.95 119.01 109.81 106.47 108.71000000000001 107.96000000000001 102.89 104.61 108.61999999999999 109.09 107.79 109.28 109.31 109.33 108.4 108.61 109.71000000000001 109.9 108.16 107.6 107.8 107.8 107.95 105.91000000000001 105.98 106.44000000000001 107.25 107.19 107.4 106.75 105.51 103.63 102.38 102.58 102.3 101.33 102.89 103.6 102.8 101.76 101.73 101.57 102.26 102 102.34 103.36 105.17999999999999 104.47 103.76 105.67999999999999 108.08 112.32 114.39 115.9 117.3 117.09 119.71000000000001 119.31 120.94000000000001 124.78 122.84 121.05 121.96000000000001 125.6 127.06 126.83 126.61999999999999 128.81 129.66999999999999 126.24000000000001 128.42000000000002 127.55 127.31 126.89 123.7 123.36 123.55 121.75 122.9 125.59 125.88 127.19 127.33 124.89 125.11999999999999 126.98 127.64999999999999 127.8 128.76 129.34 129.20999999999998 128.63 130.78 128.60999999999999 124.49000000000001 124.61 126.08 124.83 128.16 126.07 125.47 122.77 122.09 123.11999999999999 124.05 125.11999999999999 125.1 125.25 123.73 124.98 124.35 124.61 124.98 124.96000000000001 125.36 124.4 125.05 123.2 121.3 123.11 123.39 124.81 125.14 124.26 124.05 121.56 119.85 117.61999999999999 116.95 114.9 116.81 116.29 116.09 116.39 117.29 118.02 118.28 120.23 123.09 122.63 122.69 122 123.41000000000001 123.4 122.66999999999999 120.47 119.05 118.8 120.85 119.31 120.51 120.11 121.24000000000001 120.63 121.89 118.74000000000001 119.61 120.47 119.38 119.72 119.88 118.61 118.95 117.73 117.38 120.58 120.16999999999999 120.03 122.82 123.22 123.7 124.28 125.73 126.64 126.26 124.11999999999999 124.55 124.14 125.19 125.38 124.8 123.01 122.29 120.61 119.1 114.26 113. 98 111.32 109.43 109.66999999999999 110.11999999999999 110.19 109.85 108.31 108.07 101.88 95.2 92.89 96.03 93.52 95.61 97.76 101.8 101.82 101.69 98.8 96.32 98.45 98.22 99.440000000000012 99.14 95.64 98.38 98.8 101.57 101.69 103.56 101.39 98.59 100.8 101.01 101.64 102.7 100.16 99.7 99.89 98.740000000000009 98.81 100.08 100.09 100.28 101.6 102.71000000000001 103.13 103.24000000000001 103.07 104.78 106.36 105.16 107.11 107.23 106.9 106.52 107.08 107.03 105.3 102.4 101.42 103.11 103.61999999999999 103.49000000000001 102.54 103.63 105.79 105.73 107 108.19 109.41000000000001 109.88 108.8 109.72 110.51 111.85 113.41000000000001 112.61999999999999 112.51 112.72 112.46000000000001 113.14 114.33 117.22 117.66 117.44000000000001 118.51 119.34 121.61999999999999 121.71000000000001 118.85 118.41000000000001 121.53 118.89 114.85 112.26 110.53 109.06 111.16 108.85 101.94000000000001
Effective Exchange Rate £

1994-01 1994-02 1994-03 1994-04 1994-05 1994-06 1994-07 1994-08 1994-09 1994-10 1994-11 1994-12 1995-01 1995-02 1995-03 1995-04 1995-05 1995-06 1995-07 1995-08 1995-09 1995-10 1995-11 1995-12 1996-01 1996-02 1996-03 1996-04 1996-05 1996-06 1996-07 1996-08 1996-09 1996-10 1996-11 1996-12 1997-01 1997-02 1997-03 1997-04 1997-05 1997-06 1997-07 1997-08 1997-09 1997-10 1997-11 1997-12 1998-01 1998-02 1998-03 1998-04 1998-05 1998-06 1998-07 1998-08 1998-09 1998-10 1998-11 1998-12 1999-01 1999-02 1999-03 1999-04 1999-05 1999-06 1999-07 1999-08 1999-09 1999-10 1999-11 1999-12 2000-01 2000-02 2000-03 2000-04 2000-05 2000-06 2000-07 2000-08 2000-09 2000-10 2000-11 2000-12 2001-01 2001-02 2001-03 2001-04 2001-05 2001-06 2001-07 2001-08 2001-09 2001-10 2001-11 2001-12 2002-01 2002-02 2002-03 2002-04 2002-05 2002-06 2002-07 2002-08 2002-09 2002-10 2002-11 2002-12 2003-01 2003-02 2003-03 2003-04 2003-05 2003-06 2003-07 2003-08 2003-09 2003-10 2003-11 2003-12 2004-01 2004-02 2004-03 2004-04 2004-05 2004-06 2004-07 2004-08 2004-09 2004-10 2004-11 2004-12 2005-01 2005-02 2005-03 2005-04 2005-05 2005-06 2005-07 2005-08 2005-09 2005-10 2005-11 2005-12 2006-01 2006-02 2006-03 2006-04 2006-05 2006-06 2006-07 2006-08 2006-09 2006-10 2006-11 2006-12 2007-01 2007-02 2007-03 2007-04 2007-05 2007-06 2007-07 2007-08 2007-09 2007-10 2007-11 2007-12 2008-01 2008-02 2008-03 2008-04 2008-05 2008-06 2008-07 2008-08 2008-09 2008-10 2008-11 2008-12 2009-01 2009-02 2009-03 2009-04 2009-05 2009-06 2009-07 2009-08 2009-09 2009-10 2009-11 2009-12 2010-01 2010-02 2010-03 2010-04 2010-05 2010-06 2010-07 2010-08 2010-09 2010-10 2010-11 2010-12 2011-01 2011-02 2011-03 2011-04 2011-05 2011-06 2011-07 2011-08 2011-09 2011-10 2011-11 2011-12 2012-01 2012-02 2012-03 2012-04 2012-05 2012-06 2012-07 2012-08 2012-09 2012-10 2012-11 2012-12 2013-01 2013-02 2013-03 2013-04 2013-05 2013-06 2013-07 2013-08 2013-09 2013-10 2013-11 2013-12 2014-01 2014-02 2014-03 2014-04 2014-05 2014-06 2014-07 2014-08 2014-09 2014-10 2014-11 2014-12 2015-01 2015-02 2015-03 2015-04 2015-05 2015-06 2015-07 2015-08 2015-09 2015-10 2015-11 2015-12 2016-01 2016-02 2016-03 2016-04 2016-05 2016-06 2016-07 99.07 97.990000000000009 97.89 97.910000000000011 98.19 98.740000000000009 97.92 97.7 98.32 99.79 99.63 99.39 99.33 98.34 96.93 95.710000000000008 95.39 95.35 95.02 95.86999999999999 96.39 96.14 95.3 94.84 95.22 95.910000000000011 95.64 95.85 96.79 98.460000000000008 98.53 97.669999999999987 99.11999999999999 101.54 105.79 107.56 109.63 110.71000000000001 110.42 112.64 112.34 113.67999999999999 118.01 115.77 114.36999999999999 115.82 119.56 121.21000000000001 122.42 121.89 123.72 124.08 120.84 123.53 123.4 122.97 123.1 120.4 119.64999999999999 119.79 119.04 120.3 122.41000000000001 122.57 123.47 123.57 121.97 122.61999999999999 124.41000000000001 125.61 125.36999999999999 126.06 127.99000000000001 127.55 127.11 128.83000000000001 126.32 123 123.9 125.14 123.26 126.6 124.64 124.64999999999999 123.22 122.6 123.77 124.89 125.22 125 125.96000000000001 124.36999999999999 125.96000000000001 125.81 125.8 126 126.41000000000001 126.81 126.05 126.78 125.34 124.16 126.99000000000001 127.02 128.51 129.01 128.09 127.83 126.84 125.2 123.07 121.93 120.22 122.5 121.6 120.92 121.25 122.67999999999999 123.61999999999999 124.14 127.03 130.07 129.66 129.53 129.16 130.84 130.89000000000001 129.99 127.76 126.61999999999999 126.41000000000001 128.19 126.33 127.43 127.59 128.72 127.55 128.37 124.6 125.59 126.77 125.55 125.21000000000001 125.25 124.44000000000001 124.27 123.61 123.48 127.24000000000001 126.92 126.81 129.15 129.30000000000001 129.31 129.6 130.79 132.09 131.41 129.53 130.39000000000001 129.75 130.55000000000001 131.41 130.58000000000001 129.06 128.25 127.07 124.76 120.32 119.53 117.88 115.49000000000001 115.34 115.36999999999999 115.4 113.42 111.33 111.14999999999999 104.04 98.09 96.11999999999999 98.95 96.61 98.61999999999999 100.63 104.94000000000001 104.35 104.27 101.46000000000001 99.11 101.14 100.27 100.92 100.03 96.43 98.68 98.490000000000009 100.88 101.39 102.86 101.02 98.75 100.57 99.97 100.17999999999999 101.21000000000001 99.8 98.92 99.03 98.01 97.72 98.940000000000012 98.64 99.02 100.24000000000001 100.74000000000001 100.82 100.67999999999999 101.16999999999999 102.67999999 999999 104.2 103.36999999999999 104.44000000000001 104.43 104.71000000000001 103.92 103.86 103.8 102.06 98.990000000000009 98.14 99.42 99.7 100.55 99.27 100.51 102.73 102.64999999999999 103.74000000000001 104.95 106.16 106.61999999999999 106.47 107.16999999999999 107.94000000000001 108.98 110.23 109.02 108.74000000000001 108.59 108.22 108.96000000000001 109.32 112.09 112.55 112.02 113.72 114.75 116.36 117.06 115.2 114.6 116.74000000000001 114.75 111.32 108.9 107.44000000000001 106.28 108.64999999999999 106.43 99.440000000000012
Conclusion

Examined how deviations from PPP might inform exchange rate movements

Considered the difference between absolute PPP and relative PPP

And examined their application

Considered PPP conditions empirically

Explained the consequences of violating these conditions

Have real effects – can result in re-allocation of resources

Also indicate where consumers may be paying too much / little for goods and services

Outlines the competitive environment for producers

Business School

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