Instructor: Prof. Hiroyuki Imai

**Purchasing Power Parity**

Debate

Debate

Written By

Alan M. Taylor and Mark P. Taylor

**Definition of PPP**

**Purchasing Power Parity (PPP) is a disarmingly simple theory that holds that the nominal exchange rate between two currencies should be equal to the ratio of aggregate price levels between the two countries, so that a unit of currency of one country will have the same purchasing power in a foreign country.**

**Question: Does PPP Hold?**

One very simple way of checking whether there may be discrepancies from PPP is to compare the prices of similar or identical goods from the basket in the two countries.

Possible Problems

Economist newspaper publishes the prices of McDonald's Big Mac hamburgers around the world and compares them in a common currency, the U.S. dollar, at the market exchange rate as a simple measure of whether a currency is overvalued or undervalued relative to the dollar at the current exchange rate

not be traded internationally.

The fact that many inputs can not be internationally traded.

1. Service Component: Wage

2. Property Rental Component: Cost of rent

Intuition: Neither the service-sector labor nor the property (nor the trademark sauce) is easily arbitraged internationally, and advocates of PPP have generally based their view

largely on arguments relating to international goods arbitrage. Thus, while these indices may give a lighthearted and suggestive idea of the relative value of currencies, they should be treated with caution.

Law of One Price: price of an internationally traded good should be the same anywhere in the world once that price is expressed in a common currency.

Implication: a PPP exchange rate should hold between the countries concerned

.

Possible Objections

Presence of transaction costs

Transport Cost

Taxes

Tariffs and Duties

Non-tariff barriers

PPP might hold in two senses

Absolute purchasing power parity holds when the purchasing power of a unit of currency is exactly equal in the domestic economy and in a foreign economy, once it is converted into foreign currency at the market exchange rate. However, it is often difficult to determine whether literally the same basket of goods is available in two different countries.

Relative PPP, which holds that the percentage change in the exchange rate over a given period just offsets the difference in inflation rates in the countries concerned over the same period.

Class Material Revision: Neither absolute nor relative PPP appear to hold closely

in the short run, although both appear to hold reasonably well as a long-run ,

and both appear to hold better between producer price indices than between consumer

price indices.

**Does Monetary Approach help?**

This approach assumed that the purchasing power parity exchange rate held continuously.

History Review: Under the Bretton Woods agreement that was signed after World War II, the U.S. dollar was tied to the price of gold, and then all other currencies were tied, or "pegged," to the U.S. dollar. However, in 1971, President Nixon ended the convertibility of the U.S. dollar to gold and devalued the dollar relative to gold. After the failure of attempts to restore a version of the Bretton Woods agreement, the major currencies of the world began floating against each other in March 1973.

A wave of empirical studies in the late 1970s tested whether continuous purchasing power parity did indeed hold, as well as other implications of the monetary approach to the exchange rate, and the initial results were encouraging (Frenkel and Johnson, 1978). With the benefit of hindsight, it seems that these early encouraging results arose in part because of the relative stability of the dollar during the first two or three years or so of the float (after an initial period of turbulence) and in part because ofthe lack ofa long enough run of data with which to test the theory properly. Toward the end of the 1970s, however, the U.S. dollar did become much more volatile and more data became available to the econometricians, who subsequently showed that both continuous PPP and the simple monetary approach to the exchange rate were easily rejected. One did not have to be an econometrician, however, to witness the "collapse of purchasing power parity" (Frenkel, 1981): one could simply examine the behavior of the real exchange rate.

**A more sophisticated econometric literature on long-run PPP**

The "unit root process"

We estimated the following regression equation for the real exchange rate qt over time, where Et is a random error and α and β are unknown parameters:

Interpretations and implications of the regression model

1. If β = 1, we say that the process generating the real exchange rate contains a unit root.

2. Changes in the real exchange rate would be predictable. They would be equal on average to the estimated value of α.

3. The level of the real exchange rate would not be predictable, even in the long run: since the change each period would be equal to a constant plus an unpredictable random element, the long-run level will be equal to the sum of the constant changes each period plus the sum of a large number of random elements.

1. Statistical Significance Test:

The null hypothesis

that β = 1 is a test for whether the path of the real exchange rate over time does not return to any average level and thus that long-run PPP did not hold.

2. Empirical Evidence:

Effectiveness of the Regression Model

Empirical studies employing these types of tests on real exchange rate data among major industrialized countries that emerged toward the end of the 1980s were unanimous in their failure to reject the unit root hypothesis for major real exchange rates although, as we shall see this result was probably due to the low power of the tests.

Comments on Econometric Interpretation of PPP

1. Even though null hypothesis is not rejected, it does not necessarily mean we should accept the model. Empirically, the unit root process is false, due to lack power.

2. Lack power: can it be fixed by Data from More Years and More Countries?

4. Result: Even though we could have more "power", no clear conclusion has reached.

*5. Non-linearity of interpretation(Will be discussed later)

**Modified PPP Model**

The Harrod-Balassa-Samuelson model

The Harrod-Balassa-Samuelson model

Introduction:

1. In this model, rich countries supposedly grow rich by advancing productivity in traded "modern" sectors (say, manufacturing). Mean time, all nontraded "traditional" sectors, in rich and poor countries alike, remain in technological stasis (say, haircuts)

.

2. Suppose the Law of One Price holds among traded goods and we live in a world where labor is mobile intersectorally, but not internationally. As productivity in the modern sector rises, wage levels rise, so prices of nontraded goods will have to rise (as there has been no rise in productivity in that sector).

3. If we measure the overall price index as a weighted average of traded and nontraded goods prices, relatively rich countries will tend to have "overvalued" currencies.

1. Magnitude of Harrod-Balassa Samuelson effect has been variable over time, though not clear why

2. The Harrod-Balassa-Samuelson hypothesis suggests that as per capita income rises, driven by productivity growth in tradables, then price levels should also rise: there should be a positive correlation in the scatterplot.

3. The graphs show that the cross-country relationship between income per capita and the price level has been intensifying since 1950; once close to zero, and statistically sinsignificant, the elasticity is now over one half. The null hypothesis of a zero slope can be rejected beginning in the early 1960s when Balassa and Samuelson wrote their seminal papers

1. Theoretical work suggested that exchange rates should be linked to relative changes in price levels with deviations that might be only minimal or momentary, while empirical work could find only the flimsiest evidence in support of purchasing power parity, and even these weak findings implied an extremely slow rate of reversion to PPP of, at best, three to five years.

**Conclusions**

2. The presence of nontraded goods (a manifestation of extreme transaction costs) enriches our models further. A renewed attention to the Harrod-Balassa-Samuelson effect and wealth effects leads to a modified view of PPP where the equilibrium real exchange rate itself may move over time.

3. A very general theoretical model could be developed to incorporate all of the above refinements simultaneously and its predictions studied. Empiricists could attempt to include both nonlinearities and Harrod-Balassa-Samuelson effects to get even tighter estimates of convergence speeds.

In sum, the interpretation of the consensus view of the PPP debate:

1. Short-run PPP does not hold

2. Long-run PPP may hold

Thank you for watching!

Good Luck On

Mid-Term!

The real exchange rate is the nominal exchange rate (domestic price of foreign currency) multiplied by the ratio of national price levels (domestic price level divided by foreign price level)

**More about Real Exchange rate**

The real exchange rate measures the purchasing power of a unit of foreign currency in the foreign economy relative to the purchasing power of an equivalent unit of domestic currency in the domestic

economy. Thus, PPP would, in theory, imply a real, relative-price-level-adjusted exchange rate of one

What is clear and important is that variation in the real exchange rate must indicate deviations from PPP (since otherwise it would be constant at the level consistent with PPP).

**Formal Tests of Long-Run PPP**

1. Formal tests for evidence of PPP as a long-run phenomenon have often been

based on an empirical examination of the real exchange rate. If the real exchange

rate is to settle down at any level whatsoever, including a level consistent with PPP,

it must display reversion toward its own mean. (Mean Reversion)

Definition of Mean Reversion:

In general terms, the essence of the concept is the assumption that both a stock's high(higher than average) and low(lower than average) prices are temporary and that a stock's price will tend to move to the average price over time.

Implication and Application of Mean Reversion:

1. When the current market price is less than the average price, the stock is considered attractive for purchase, with the expectation that the price will rise.

2. When the current market price is above the average price, the market price is expected to fall. In other words, deviations from the average price are expected to revert to the average.

2. Hence, mean reversion is only a necessary condition for long-run PPP: to ensure long-run absolute PPP, we should have to know that the mean toward which it is reverting is in fact the PPP real exchange rate. Still, since much of this research has failed to reject the hypothesis that even this necessary condition does not hold, this has not in general been an issue.

Random Walk Assumption

1. Early empirical studies, tested the null hypothesis that the real exchange rate does not mean revert but instead follows a random walk, the archetypal non-mean reverting time series process where changes in each period are purely random and independent.

2. Assumption: international markets are efficient , in the sense of prices and exchange rates reflecting all available information and all arbitrage opportunities being quickly

exploited.

3. Expectation: the change in the real exchange rate, since it is effectively a measure of the one-period real return from arbitraging goods between countries, should have an expected value of zero if markets are efficient.

4. Result: it's false because it has econometric weaknesses. The theoretical underpinnings of "efficient markets PPP" failed to adjust the expected return for the real cost of financing goods arbitrage. Once this arbitrage adjustment is made, efficiency requires that the expected real exchange rate change be equal to the expected real interest rate differential, and long-run PPP will be implied if the latter differential is stationary.

**PPP Puzzles**

1. The panel-data studies raise the issue of whether the hypothesis of

non-mean

reversion is being rejected because of just a few mean-reverting real exchange rates within the panel. If exchange rates do tend to converge to PPP, economists have, at least so far had a hard time presenting strong evidence to support the claim.

2. Even the studies that were interpreted as supporting the thesis that PPP holds in the long run also suggested that the speed at which real exchange rates adjust to the PPP exchange rate was extremely slow.

Solution:

1.Half-lives of adjustment: they mostly tend to fall into the range of three to five years.

2. Non-Linearity

**Non-Linearity**

1. Recall: in a linear framework, the adjustment, the speed of PPP deviations from parity is assumed to be uniform at all times and, in particular, for all sizes of deviation, and implicitly the econometric problem is reduced to the estimation of a single parameter?the half-life.

2. While this framework is very convenient, there are good reasons for suspecting that the speed of convergence toward the PPP exchange rate should be greater as the deviation from PPP rises in absolute value.

3. Adjustment may be nonlinear because of transactions costs in international arbitrage.

Possible Solution to PPP Puzzles--Non-Linearity

1. Reject the hypothesis of a unit root in favor of the alternative hypothesis of nonlinearly mean-reverting real exchange rates, and using data just for the post-Bretton Woods period, thus solving the first PPP puzzle. For modest real exchange shocks in the 1 to 5 percent range, the half-life of decay is under three years, while for larger shocks the half-life of adjustment is estimated much smaller?thus going some way toward solving the second PPP puzzle.

2. Careful examination of transaction costs