Estimating currency misalignment using the Penn effect: It is not as simple as it looks

• Author: Menzie Chinn,Xin Nong,Yin‐Wong Cheung
• DOI: http://doi.org/10.1111/infi.12113
• Published date: 01 December 2017
• Date: 01 December 2017

DOI: 10.1111/infi.12113

ORIGINAL MANUSCRIPT

Estimating currency misalignment using the Penn

effect: It is not as simple as it looks

Yin-Wong Cheung

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Menzie Chinn

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Xin Nong

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1

Department of Economics and

Finance, City University of Hong Kong,

Hong Kong

2

Department of Economics, Robert M.

La Follette School of Public Affairs,

University of Wisconsin, Madison,

Wisconsin

3

Department of Government, University

of Texas at Austin, Austin, Texas

Correspondence

Menzie Chinn, Department of

Economics, Robert M. La Follette School

of Public Affairs, University of

Wisconsin, Madison, WI.

Email: mchinn@lafollette.wisc.edu

Abstract

We investigate the robustness of the Penn effect—the

finding that the price level is higher in countries with a

higher per capita income—over different samples, mea-

sures, and specifications. Testing for the Penn effect has

been hampered by the imprecision of the price measures, so

that use of different versions of the data set can lead to

substantially different results. We find that the price level-

income elasticity is fairly consistently estimated across data

sets. However, there is some evidence that the relationship

is non-linear. For developed economies, the quadratic

term implies an inverted U-shap ed relationship. Devel-

oping economies, on the other han d, display a U-shaped

relationship. Estimates of misalignment diff er, depending

on the choice of specification an d data sets. It appears that

the Renminbi (RMB) was fairly valued by 2011. In

contrast, the RMB's value was un dervalued in 2005, and

overvalued in 2014.

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INTRODUCTION

The issue of currency misalignment is a perennial one. As long as countries strive to reallocate

aggregate demand in their own favour, disputes will arise regarding the degree to which currency

values are ‘fair’. The problem, of course, is what constitutes such a fair value; each different model

yields its own valuation.

One key strand of methodologies involves the comparison of price levels as a means of inferring the

proper currency value. Absolute purchasing power parity (PPP) is one particularly simple, and

particularly inappropriate, price criterion. After all, the proposition that similar bundles of goods

should be equally priced when denominated in a common currency is one of the most frequently

violated ones.

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© 2017 John Wiley & Sons Ltd wileyonlinelibrary.com/journal/infi International Finance. 2017;20:222–242.

A more commonly used criterion is the Penn effect. One of the most well-documented empirical

regularities in the international finance literature—the finding that the price level is higher in countries

with a higher per capita income—is consistent with a variety of theoretical frameworks, including a

Balassa–Samuelson mechanism, and demand side forces including a preference for non-tradable goods

at higher incomes (i.e. non-homotheticity).

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In this paper, we seek to document whether indeed the Penn effect is as robust as is typically

conceived, over different samples, measures, and specifications. Testing for the Penn effect has been

hampered by the imprecision with which the price data are measured. This means that new versions of

the data set can lead to substantially different results.

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Further, some recent work has suggested the

presence of a non-linear Penn effect, namely a quadratic link between income and real exchange rate.

To anticipate our results, we find that the elasticity of the relative price level to per capita income is

fairly consistently estimated, across data sets. However, there is some evidence that the relationship is

non-linear; a statistically significant quadratic term, implying a U-shaped relationship, is estimated.

The nature of the non-linearity displayed by developed and developing economies differs. For

developed economies, the quadratic term implies an inverted U-shaped relationship between real

exchange rate and income. Developing economies, on the other hand, display a U-shaped relationship.

Additional analyses suggest that the non-linearity is likely driven by variation across countries rather

than by variation within a country. The estimated quadratic term is robust to the addition of select

economic covariates in the regressions.

In the case of China, the inclusion of a significant quadratic term, unsurprisingly, has implications

for the magnitude of the estimated degree of misalignment, particularly when the full country sample is

used in determining the exchange rate norm. Estimates of misalignment for other currencies will differ

as well, to varying degrees, depending on the choice of linear versus quadratic specification. The

choice of data sets also has a material impact on the estimates.

In terms of the Chinese currency, it appears that the Renminbi (RMB) was fairly valued by 2011. In

contrast, the RMB's value was undervalued in 2005, and overvalued in 2014 if one uses a one standard

error threshold; not so if one uses a two standard error convention. Hence, depending on one's

perspective regarding the proper significance level to apply to policy questions, the deviation was

statistically significant (Frankel, 2006) or not (Cheung, Chinn, & Fujii, 2007).

Looking forward, according to our estimates, as long as Chinese per capita growth exceeds that of

the United States, then the long-run equilibrium value of the RMB will continue to rise. The pace of

increase is about 0.25 for each 1% increase in relative per capita income, holding constant other factors

such as financial openness and levels of corruption.

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BACKGROUND

At the heart of the debate over the right way of determining the appropriate exchange rate level are

contrasting ideas of what constitutes an equilibrium exchange rate, what time frame the equilibrium

condition pertains to, and, not least, what econometric method to implement.

Most of the extant studies fall into some familiar categories, either relying upon some form of

relative PPP or cost competitiveness calculation, the modelling of deviations from absolute PPP,

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composite model incorporating several channels of effects (sometimes called behavioural equilibrium

exchange rate models), or flow equilibrium models. These alternative approaches are reviewed in, for

example, Cheung et al. (2007), and Cheung, Chinn, and Fujii (2010a).

In this study, we appeal to a simple, and apparently robust, relationship between the real exchange

rate and per capita income. We then elaborate the analysis by stratifying the data by level of income,

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