Purchasing power parity has been the subject of many empirical studies. Much of this work has focused on recent history in developed countries. This paper reports results of tests for nonlinear, mean reversion of the real exchange rate for a less-developed country, Mexico, using a previously unexploited data set of monthly observations for 1930-1960. The test results provide weak support for PPP.purchasing power parity; nonlinear unit root

Wallace, Frederick

English

Research Papers in Economics

 
 
 
Purchasing Power Parity in Mexico: 
A Historical Note 
 
by 
 
 
Frederick H. Wallace* 
  
Professor, CENTRUM Católica 
Graduate School of Business 
Pontificia Universidad Católica of Peru 
Lima, Peru 
 
 
 
October 2009 
 
 
 
Running Title: Purchasing Power Parity in Mexico 
 
Abstract: Purchasing Power Parity in Mexico: A Historical Note 
JEL Codes: F31, C22  
Keywords: purchasing power parity, nonlinear unit root 
 
Purchasing power parity has been the subject of many empirical studies. 
Much of this work has focused on recent history in developed countries. 
This paper reports results of tests for nonlinear, mean reversion of the real 
exchange rate for a less-developed country, Mexico, using a previously 
unexploited data set of monthly observations for 1930-1960. The test results 
provide weak support for PPP. 
 
* Please direct correspondence to the author at the División de Ciencias 
Sociales y Económico-Administrativas, Universidad de Quintana Roo, 
Blvd. Bahía s/n esq. I Comonfort, col. Del Bosque, Chetumal, Quintana 
Roo, México C.P. 77019. E-mail addresses are fwalla@uqroo.mx and 
wallacefred@yahoo.com.    2 
Introduction 
Purchasing power parity (PPP) means that the cost of a market basket 
of goods is the same in different countries when measured in a common 
currency.  If barriers to trade are absent, there are no transportation costs, 
and the goods in the market basket are traded and not subject to price 
controls, then deviations from PPP are temporary and eliminated through 
arbitrage. That is, the real exchange rate will revert to its mean, generally 
assumed to be the purchasing power parity value. But empirical evidence 
for mean reversion of the real exchange rate has not been overwhelming. 
Indeed, Taylor and Taylor (2004) cite the absence of strong empirical 
support as one of two puzzles concerning PPP.
1 The second puzzle is the 
very slow adjustment speeds to PPP based on supportive evidence obtained 
assuming linear adjustment. 
Taylor (2001) shows how linear estimates of adjustment speeds can be 
biased upward when the true process is nonlinear.
2 Taylor and Taylor cite 
three reasons for nonlinear adjustments: Transactions costs, heterogeneity of 
opinion in foreign exchange markets, and the tendency of central banks to 
intervene only when the deviation of the real exchange rate from its 
(presumed) fundamental value is large. Transactions costs, for example, can 
produce a band or range within which arbitrage is not profitable so that the 
real exchange rate behaves as a unit root process. However, once the real 
                                                 
1 See Sarno y Taylor (2002) for a comprehensive survey of the evidence before 2002. 
2 The upward bias can be compounded by the degree of temporal aggregation in the data, as 
demonstrated in Taylor. A comprehensive review of the literature on nonlinear adjustment 
is beyond the scope of this note. As a start,    3 
exchange rate moves outside the band’s upper or lower threshold, the rate 
tends to return to its threshold value.
3 
This paper reports results of tests for a nonlinear unit root in the real 
exchange rate for Mexico, relative to the US dollar, during the 1930-1960 
period. The nonlinear unit root test is one developed by Sollis, Leybourne, 
and Newbold (2002), henceforth SLN. 
Historical Review and Data 
The period considered in this paper was a tumultuous one in the world 
economy as it includes the Great Depression and World War II, and these 
events most certainly impacted Mexico. According to data in Cárdenas 
(1987) real per capita GDP declined from approximately 2,553 pesos in 
1926 to 1,775 pesos in 1932.
4 Total GDP decreased sharply as well. Internal 
events also affected the economy. Gold was demonetized in 1931, as was 
silver four years later. The peso was allowed to float in 1932, and then 
subsequently fixed in value in November 1933. Indeed, during the entire 
period considered in this study the data show that nominal exchange rates 
were generally fixed; but these periods of generally fixed rates are 
interspersed with devaluations and brief interludes of floating rates. The 
government also began to take a more active, interventionist role in the 
economy in pursuing various social objectives. For example Haber (1989) 
cites instances in the 1920s when textile manufacturers were denied 
permission to shut down failing factories in order to maintain employment, 
                                                 
3 The gold points under the gold standard are an example of such threshold values which 
have long been recognized. In studies of the law of one price Sarno, Taylor, and 
Chowdhury (2004) and Juvenal and Taylor (2008) find that transactions costs are sizeable 
and vary substantially across countries and sectors. 
4 The peso depreciated during this period so that the decline in per capita GDP is even more 
dramatic when expressed in dollars; from about $1239 to $562.   4 
a policy that continued at least into the 1930s.
5 In 1938 the oil industry was 
nationalized. Not least, Mexico pursued an import substitution strategy in 
the 1950s as can clearly be seen in Figure 1 showing imports as a percent of 
GDP. Import substitution policies continued well into the 1980s. The other 
noticeable declines in imports were associated with the Great Depression, 
the expropriation of the oil industry in 1938, and World War II. 
 
The data used in the study are from Cárdenas (1994) and include 
monthly observations on the nominal exchange rate, measured as the 
Mexican peso price of a US dollar, and the wholesale price index in Mexico 
City.
6 These data have not been used previously to study purchasing power 
parity. The US producer price index, not seasonally adjusted, for the same 
period is from the database, FRED, maintained by the St. Louis Federal 
Reserve Bank.  
Test Specification and Results 
Letting 
  
pt
M  represent the log wholesale price index in Mexico, 
  
pt the 
log US producer price index, and 
  
et the log price of one US dollar in 
                                                 
5 Haber, pp. 157-158.  
6 Price indices are not available for the entire country. Mexico City was, and remains, the 
most important commercial and industrial location in the country.   5 
Mexican pesos, the log of the period t real exchange rate is given by 
equation (1).  
 
  
rt = pt
M  et   pt  (1) 
Figure 2 shows the real exchange rate over the sample period. 
 
One approach to testing for purchasing power parity is to test rt for the 
presence of a (linear) unit root. The absence of a unit root is evidence of 
mean reversion, usually regarded as evidence of reversion to its PPP value.
7 
A series of linear unit root tests are applied to the full sample and the 
January 1930-December 1951 and January 1952-December 1960 
subsamples. The subsamples are selected to isolate the period of import 
substitution, a period in which PPP is less likely to hold due to diminished 
trade. In most cases, the linear tests fail to find evidence of stationarity.
8 
There are no indications of seasonality in the data; the mean real exchange 
rate is virtually the same each month despite substantial variation in rt over 
                                                 
7 Conceptually, it is possible that the real exchange rate reverts to a mean different from its 
PPP value. See the discussion in Taylor and Taylor. 
8 Results from the augmented Dickey-Fuller test over the full sample, the Kwiatkowski, 
Phillips, Schmidt, and Shin (KPSS) test over the restricted sample January 1930-December 
1951, and the and Elliot, Rothenberg, and Stock (ERS) over the subsample January 1952-
December 1960 are supportive of PPP. Over the full sample the stationarity null for the 
KPSS test is cannot be accepted at the 1% level nor does the ERS test show evidence of 
stationarity over the full sample. Results from the Phillips-Perron unit root tests regardless 
of sample period fail to support stationarity of the real exchange rate.   6 
the sample, so that the possibility of seasonal unit roots do not need to be 
considered. 
Given the low power of linear unit root tests when the adjustment 
process is nonlinear, investigation of an alternative nonlinear approach 
seems warranted. Furthermore, the tendency of Mexico to maintain a fixed 
nominal exchange rate with devaluations at irregular intervals suggests a 
nonlinear adjustment process for the real exchange rate. A test developed by 
Sollis, Leybourne, and Newbold (2002), henceforth SLN, based on the 
smooth transition, autoregressive (STAR) model is employed. The 
underlying idea is that mean reversion will be an increasing function of 
squared deviations from the mean. The SLN test offers two advantages. 
First, it permits asymmetric adjustment so that the response to an 
overvalued exchange rate can be different from the adjustment of an 
undervalued one. Second, the test can carried out allowing for different 
delays in the adjustment response. Such delays might arise if, say, over a 
lengthy period of time the central bank expended foreign reserves in a futile 
effort to maintain a fixed rate and resorted to devaluation only after reserves 
fell below some minimum target.
9 The symmetric version of the test is 
given by equation (2) 
 
  
 zt =   .5+ 1+ exp   
2zt d
2 ( ) [ ]
 1 { }zt 1 +  i
i=1
k
   zt i + t  (2) 
where zt is the demeaned real exchange rate and the term in braces is a 
modified logistic function. The sample mean is used to construct the 
                                                 
9 Even though a central bank might implement a discrete devaluation once the real 
exchange rate is outside its target range, the prices of individual, traded goods can also 
adjust to move the real exchange rate in the direction its PPP value. Since individual goods 
are likely to have different threshold values due to different transactions costs, a test based 
on a STAR model is more appropriate than, say, a threshold autoregressive model in which 
the adjustments are abrupt.   7 
demeaned real exchange rate.
10 It is helpful to note that the SLN test is the 
equivalent to the augmented Dickey-Fuller test when the term in braces is 
equal to one. The delay parameter is an integer, 
  
d  1, that can be varied to 
allow for responses to squared deviations of the demeaned real exchange 
rate further in the past, and the number of lags, k, is selected so that εt is a 
white noise process. Of interest is the t-statistic on the estimated value of α. 
If the estimated α is significantly different from zero, the nonlinear unit root 
null cannot be accepted thus providing evidence of PPP. 
Versions of equation (2) are estimated using nonlinear least squares for 
different values of d. The estimated values of the coefficients, α and γ, are 
hardly affected by the choice of d, but the significance of the estimated α is 
sensitive to d as reported below. To determine k, lags of the dependent 
variable are added to the test equation until the marginal significance level 
of the obs.*R
2 statistic from a Lagrange multiplier test exceeds .3. By this 
criterion, 7 lags of Δzt are included in the estimations. As a check on this 
conclusion estimations are also carried out with 9 lags of Δzt. Using a Wald 
test the null hypothesis that the coefficients on lags 8 to 9 are jointly equal 
to zero cannot be rejected and none of the extra lags have individually 
significant coefficients. The number of lags needed to eliminate 
autocorrelation is not affected by changes in the delay parameter.  
Various specification were tried allowing for asymmetric adjustment of 
the real exchange rate, but none showed any evidence of different responses 
to over-valued and under-valued real rates. Hence, test results are reported 
                                                 
10 See SLN for additional discussion of the test equation. In particular, the symmetric 
version of the test is valid when the data are demeaned using the sample mean rather than 
the population mean.   8 
solely for the symmetric case. Table 1 displays the t-statistics for the 
estimated α in the SLN nonlinear test allowing for different delays and 
seven lags of the dependent variable. The number varies with the value of d, 
but there are at least 361 observations for each specification. Based on 
simulations, SLN report a 10% critical value of -2.86 for the t-statistic when 
there are 300 observations.
11 As the critical value is hardly affected by the 
number of observations, it is -2.83 for 500 observations, -2.86 is used to 
assess significance of the estimated α from equation (2). 
Table 1 t-statistics from the SLN Unit Root Test Applied to the Real 
Exchange Rate for Mexico, January 1930 to December 1960. 
 
Delay 
parameter 
t-statistic 
1  -2.610 
2  -2.540 
3  -2.538 
4  -2.575 
5  -2.771 
6  -2.772 
7  -2.770 
8  -2.867* 
9  -2.743 
10  -2.912* 
11  -2.625 
*10% significance level 
As can be seen from the results in the table, except for two of the 
specifications, those with delay parameters of 8 and 10 months, the unit root 
null cannot be rejected thus providing evidence against purchasing power 
parity. But it is interesting to note that none of the t-statistics for delay 
parameters ranging from one to eleven months are very different, they are 
all clustered in from -3 to -2.5. Those that are not significant are reasonably 
                                                 
11 See Table 1 of their paper.   9 
close to the 10% critical value. Interpreted in this fashion, the results seem 
to provide some weak support for PPP. Interestingly, when SLN apply their 
tests to monthly real exchange rates with respect to the U.S. dollar for 
seventeen countries not a single t-statistic is significant from the symmetric 
version of the test. Indeed, all but two of the t-statistics they report for the 
symmetric version are larger than -2.5. 
Examined in a different light, however, the fact that even two of the 
nonlinear unit root test results are supportive of PPP could be considered 
remarkable in light of the sample period. As noted earlier the years 1930-
1960 include a relatively long period during which import substitution 
policies were followed, nominal exchange rates were usually fixed, and the 
peso was devalued periodically; conditions that make the it more difficult to 
uncover evidence of PPP. In light of these complicating factors, any 
evidence of mean reversion can be considered surprising.  
Furthermore, that the significant t-statistics appear on specifications 
with delays of 8 and 10 months is consistent with central bank behavior 
during this period. Cárdenas cites such instances when foreign exchange 
reserves were expended to maintain the nominal exchange and the 
government resorted devaluation and brief periods of floating rates when the 
decline in reserves could not be halted.
12     
Conclusions 
Considering the difficulties of uncovering evidence of mean reversion 
during a period of mostly fixed nominal rates with occasional devaluations, 
the fact that two specifications yield t-statistics indicating stationarity of the 
                                                 
12 For example see the discussion on pages 49 and 101-102.   10 
real exchange rate and all the estimated t-statistics are close to their 10% 
critical value suggests that PPP probably did hold in Mexico during the 
1930-1960 period. The failure to find any indications of asymmetric 
adjustment may be due to its absence or may be explained by the fact that 
peso does not appear to have been over-valued often during the period.   
 
   11 
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Depresión, El Colegio de México, México, D.F. 
 
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Instituto Nacional de Estadística y Geografía (2000)  Estadísticas Históricas 
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Lopez, C.; Murray, C.J.; and Papell, D.H. (2005) State of the art unit root 
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A century of purchasing-power parity,

Additional evidence of long-run purchasing power parity with restricted structural change,

An alternative test of purchasing power parity,

Industry and Underdevelopment: The Industrialization of Mexico

Instituto Nacional de Estadística y Geografía

La Industrialización Mexicana Durante la Gran Depresión, El Colegio de México,

Potential pitfalls for the purchasing-power-parity puzzle? Sampling and specification biases in the mean-reversion tests of the law of one price,

Purchasing power parity and nonlinear adjustment,

State of the art unit root tests and purchasing power parity,

Tests for symmetric and asymmetric nonlinear mean reversion in real exchange rates,

The Economics of Exchange Rates

The purchasing power parity debate,

Threshold adjustment of deviations from the law of one price,

Purchasing power parity in Mexico: a historical note

Purchasing power parity in Mexico: a historical note

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