Monetary Policy and Real Currency Appreciation: A BEER Model for the Mexican Peso

International Economic JournalVol. 25, No. 1, 91–110, March 2011

Monetary Policy and Real CurrencyAppreciation: A BEER Model

for the Mexican Peso

CARLOS A. IBARRA

Universidad de las Americas Puebla, Economics, Ex Hacienda Santa Catarina Martir,Cholula, 72820 Mexico

(Received 26 February 2009; final version received 19 April 2010)

ABSTRACT A notable feature of the Mexican economy since the late 1980s was the persistentreal appreciation of the peso. The appreciation – a key development that helps to explainMexico’s slow rate of economic growth – took place despite changes in the exchange-rateregime, yet with an unchanging focus of monetary policy on gradually reducing the inflationrate. Thus, the frequent assumption that only real-side variables (as opposed to monetaryones) have a lasting or ‘long-run’ effect on the real exchange may not suit the recent Mexicancase. The paper presents the results of an econometric study of exchange rate determina-tion in Mexico for the period 1990Q1–2006Q4. The study is based on the so-called BEER(Behavioral Equilibrium Exchange Rate) model, which relies on Johansen’s cointegrationmethodology and jointly considers real-side and monetary determinants. The estimationresults – in the form of two- and three-equation cointegration models – show that, control-ling for the influence of real-side determinants, the peso–dollar interest differential had astatistically and economically significant long-run effect on the peso’s real exchange rate.

KEY WORDS: Real currency appreciation, real exchange rate, monetary policy, Mexican peso, BEERmodel, Johansen’s cointegration methodologyJEL CLASSIFICATIONS: C32, F31, F35, F41, O54

1. Introduction

A notable feature of the Mexican economy since the late 1980s was the persis-tent appreciation of the peso in real terms. For a small open economy, this is a

Correspondence Address: Carlos A. Ibarra, Universidad de las Americas Puebla, Economics, ExHacienda Santa Catarina Martir, Cholula, 72820 Mexico. Email: [email protected]

1016-8737 Print/1743-517X Online/11/010091–20 © 2011 Korea International Economic AssociationDOI: 10.1080/10168737.2010.487539

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key development. The appreciation not only makes exports less competitive –a drawback for a country pursuing an export-led growth strategy – but it alsoaffects negatively profit margins, and hence investment, in the tradables sector (seeEichengreen, 2008, and Rodrik, 2008 for general analyses, and Ibarra, 2008a forevidence on the Mexican case). The appreciation thus helps to explain Mexico’sproblem of slow economic growth.

The appreciation took place across different exchange-rate regimes (a crawlingpeg, a crawling band, and finally a float) but with the constant of a gradualprocess of disinflation. After a sharp reduction of inflation in 1989, and separatedby the 1994–1995 economic crisis, there were two phases of gradual disinflation.In the first phase the annual inflation rate fell from 20% in 1990 to 7% in 1994;meanwhile, the Bank of Mexico’s real exchange rate index – a multilateral ratioof foreign to local consumer prices – fell from 119.1 to 90.4 (1988–2006 average =100). In the second phase the inflation rate fell from 34% in 1996 to 5% in 2002,while the real exchange rate index dropped from 112.6 to 72.8. After the end of thesecond phase, the real exchange rate reversed, partially, its previous appreciation,reaching a level of 86.9 in 2006.

Despite the setting of prolonged disinflation, it has been frequently argued thatthe real currency appreciation was unrelated to the stance of monetary policy. Inthe mid 1990s the Mexican authorities insisted that the appreciation reflected theboost to productivity triggered by structural reforms (see for example Bank ofMexico, 1995). More recently, the appreciation has been attributed to large laborremittances and the high price of oil (see IMF, 2006). An exception is Galindo& Ros (2008), who argue that an asymmetric response of monetary policy toexchange rate changes contributed to the appreciation of the peso during theperiod 1995 to 2004.

Downplaying the role of monetary policy follows from the proposition thatonly real-side variables can have a lasting influence on the real exchange rate.1But the neglect of monetary factors seems unsuitable in Mexico’s case, giventhe country’s prolonged disinflationary process and the overriding emphasis ofmonetary policy on that goal (see Ramos & Torres, 2005; Ibarra, 2008b). Infact, the episode provides an opportunity to study whether a sustained shift inmonetary policy can have lasting effects on the real exchange rate.

The paper presents the results of an econometric study of exchange rate deter-mination in Mexico. The study is based on the so-called BEER (BehavioralEquilibrium Exchange Rate) model, a model that jointly considers real-side andmonetary determinants and that relies on Johansen’s cointegration methodology– a natural econometric framework to test for the existence of lasting or ‘long-run’ effects. The period under analysis starts in 1990Q1 (to focus on the periodof free capital mobility in Mexico, as required by the risk-adjusted interest paritycondition underlying the BEER model) and ends in 2006Q4.

1See Williamson (1994) for a discussion of the proposition, Kildegaard (2006) for an example appliedto Mexico, and Frankel (2007) for a recent counter-example. The proposition does not imply, ofcourse, that an appreciation caused by real-side variables, such as an oil windfall or a surge inforeign capital inflows, will not have negative growth effects, particularly in the tradables sector(see Krugman, 1987).

Monetary Policy and Real Currency Appreciation 93

The estimation results, in the form of two- and three-equation cointegrationmodels, show significant long-run effects of monetary policy on the real exchangerate in Mexico; in particular, they show that – controlling for the influence ofreal-side determinants like the oil price, government consumption, and relativemanufacturing production – a rise in the nominal interest differential appreci-ates the currency by two channels: directly, through a rise in the real interestdifferential; and indirectly, through a fall in the inflation differential.

The rest of the paper is organized as follows. Section 2 provides the macroeco-nomic background; section 3 briefly reviews the BEER model and the econometricmethodology; section 4 presents the estimation results; and section 5 summarizesthe paper. An appendix details the data sources and definitions.

2. Real Exchange Rate and Macroeconomic Performance in Mexico

Table 1 presents selected indicators of macroeconomic performance in Mexicosince 1988 – after the country liberalized its trade regime – averaged over periodsthat track the country’s growth cycle. The table includes three measures of thereal exchange rate: the multilateral ratio of foreign to Mexican consumer prices;the bilateral ratio between the US and Mexico; and the relative unit labor cost inthe manufactures between the two countries.2

Interrupted only by the 1994–1995 currency crisis and by the end of the secondphase of disinflation in 2002, there is a clear tendency for the peso to appreciatein real terms. In addition, within this tendency it is possible to single out periodswith relatively high (depreciated) exchange rate levels: 1988–1992 and 1997–2000,and periods with low levels: 1993–1994 and 2001–2006.

The fact that the three measures tell the same story is important. If the appre-ciation revealed by relative consumer prices merely reflected productivity growthdifferentials, the relative labor cost should be stable – which is not the case.For instance, while the multilateral ratio indicates an appreciation of about21% between 1997–2000 and 2001–2006, the relative labor cost also indicatesan appreciation, of about 32%.

The real exchange rate leads the growth cycle of the Mexican economy, both inabsolute terms and relative to the US economy.3 In the periods with a depreciatedcurrency, Mexico’s average GDP growth rate exceeds the US rate by more thanone point; when the currency appreciates, the Mexican growth rate falls – bothover time and with respect to the US rate. The pattern characterizes both theentire economy and the manufacturing sector.

Given the upward trend of the export share after trade liberalization, the simpleaverages of Table 1 cannot uncover the effect of the appreciation on manufacturedexports. Moreover, the share of exports in GDP jumped after the enactmentof the North American Free Trade Agreement in 1994 and the currency crisis

2See Chinn (2006) for a discussion of alternative measures of the real exchange rate.3The real exchange rate indices in Table 1 are lagged one year to better visualize their effect onmacroeconomic performance.

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Table 1. Selected macroeconomic indicators

1988–1992 1993–1994 1997–2000 2001–2006

Real effective exchange rate (1988 − 2006 = 100)(a) average 128.1 94.8 104.5 82.5(b) beginning/end 160/108.9 102.2/87.5 122.6/92.6 82/88

Bilateral real exchange rate (1988–2006=100)(a) average 119.6 88.5 105.6 90.6(b) beginning/end 152.5/99.6 91.1/86 117.6/96.2 89.8/92.3

Relative manufacturing unit labor cost a/(a) average 90.2 60.1 91.4 62.4(b) beginning/end 117.6/70.9 62.8/57.5 105.2/78.3 68.7/60.4

Annual GDP growth rate(a) average 3.67 3.20 5.56 2.30(b) Mexico-US growth differential 1.13 −0.15 1.36 −0.25

Manufacturing production index(a) average annual growth rate 5.1 1.9 7.2 0.8(b) Mexico-US growth differential 3.2 -3.3 0.7 −0.8

Manufactured exports(a) average share of GDP 8.5 11.1 25.1 28.7(b) beginning/end 8.1/9.2 10.2/12 21.5/28.2 27.8/31.2

Trade balance(a) average share of GDP −1.0 −4.5 −0.7 −3.2(b) beginning/end 2.2/−4.8 −3.9/−5.1 0.8/−2.5 −3.2/−4.0

a/ 1996Q4 = 100.The real exchange rate and unit labor cost series are lagged one year. The real exchange rate indices are ratios offoreign to Mexican consumer prices. The bilateral exchange rate and the unit labor cost are US/Mexico ratios.Sources: Real effective exchange rate: Bank of Mexico (BOM); bilateral real exchange rate: BOM and USBLS; relative unit cost: Mexico’s Institute of Statistics (INEGI); GDP: INEGI and US BEA; manufacturingproduction: BOM and US Federal Reserve; trade data: BOM and INEGI.

of 1994–1995, almost doubling between 1994 and 1997. The table does show,however, that manufactured exports gradually lost dynamism, rising by onlythree points of GDP during 2001–2006.

Lacking a trend, the ratio of the trade balance to GDP shows more clearly thepossible influence of the real exchange rate. For instance, the average trade deficitrose from less than one point of GDP during 1997–2000 to more than three pointsduring 2001–2006, despite the high price of oil. Since the Mexican GDP growthrate fell from 5.6% to 2.3%, the rise in the trade deficit cannot be attributed toan acceleration in economic growth.

3. The BEER Model

What are the factors that explain the tendency of the peso to appreciate in realterms? The so-called BEER (Behavioral Equilibrium Exchange Rate) model pro-vides a framework to test for the possible influence of both monetary and real-sidevariables on the real exchange rate. Moreover, for estimation purposes, the model


relies on Johansen’s cointegration methodology, which seeks to detect lasting or‘long-run’ effects (see Clark & MacDonald, 1998; MacDonald, 2007).4

The model is based on a risk-adjusted interest parity condition betweendomestic and foreign assets, which in nominal terms can be written as:

NERt = NERet − NIRDt + ρt, (1)

where NERt is the natural log of the nominal exchange rate (in pesos per dollar),NERe

t is the log rate currently expected for the end of the investment period,NIRDt is the difference between the domestic (peso) and the foreign (dollar)nominal interest rates, and ρt is a risk premium or expected excess return on pesoinvestments.

The parity condition can be expressed in real terms by adding and subtractingthe difference between the expected domestic and foreign inflation rates. Usingthe current difference as a proxy for the expected one, as is standard in the BEERliterature, the result is:

RERt = RERet − NIRDt + INFDt + ρt, (2)

where RER is the real exchange rate – the ratio of foreign to local prices – andINFD is the inflation differential.

Note that rather than including the real interest differential, equation (2) keepsits components – the nominal interest differential and the inflation differential –separated. This follows from the observation that, while the rest of the variablesin the models have a unit root (see below), the real interest differential is station-ary. If no further restrictions are imposed, the specification allows the estimatedcoefficients on the components of the real interest differential to differ in absolutevalue; this may be useful if, for instance, the unobserved risk premium respondsto the inflation differential (for instance, because of Mexico’s problematic historywith inflation control). In any event, the outcome of imposing symmetry on theestimated coefficients is explored at the end of section 4.

Equation (2) implies that the real exchange rate is positively related to the infla-tion differential and negatively to the nominal interest differential. The negativesign of the latter relationship is important for the correct interpretation of the esti-mation results. If there is fear of floating, monetary authorities may lean againstthe wind – that is, they may adjust the interest rate to stabilize the exchange rate(see Calvo & Reinhart, 2002) – making the interest rate ultimately depend on theexchange rate, rather than the other way around. Empirically, this would imply apositive relationship between the interest differential and the exchange rate – incontrast to the prediction from the interest parity condition. By supporting oneinterpretation over the other, the sign of the estimated coefficient can be used tosettle the question.

Starting from the parity condition, the BEER approach consists of (a) posit-ing a number of real-side determinants of the risk premium and the expected

4The definition of ‘long-run’ can be a matter of debate (see Driver & Westaway, 2004). In whatfollows, a long-run relationship is understood as a relationship in levels (as opposed to first differ-ences) between the real exchange rate and its determinants within the specific horizon of 17 yearsof quarterly observations spanning 1990 to 2006.

96 C.A. Ibarra

real exchange rate, and (b) estimating equation (2) by cointegration techniques.Following Kildegaard (2006) and Dabós and Juan-Ramón (2000), our analysiswill consider three real-side variables: the ratio of Mexico’s manufacturing pro-duction index to the US index (RIMP, in natural logs), the international price of oilin real dollar terms (OIL, also in natural logs), and Mexico’s ratio of governmentconsumption to GDP (GOVCOR).5

The manufacturing production ratio – intended to capture the Balassa–Samuelson effect – is a proxy for relative productivity in the tradables sector.A rise in relative productivity increases the consumer price index by its effect onwages and prices in the non-tradable sector, and therefore it is expected to reducethe real exchange rate. Under the assumption that it is biased toward non-tradablegoods, a rise in government consumption should have the same effect.

The oil price is included on account of the large share of oil in Mexico’s non-manufactured exports. There are several possible effects. Since a higher price ofoil improves the current account balance, the real value of the peso must rise tokeep the balance – and hence the country’s rate of debt accumulation – constant.Alternatively, a rise in the oil price produces a foreign-exchange windfall thatpushes up the local currency. Finally, the windfall can increase the demand fornon-tradable goods and raise the consumer price index.

Equation (2) was estimated following Johansen’s cointegration methodology(see Juselius, 2006, for a detailed presentation). The starting point is the followingk-lag VAR for a set of non-stationary variables:

yt = π1yt−1 + · · · + πkyt−k + ϕzt + ut, (3)

where yt is an (n × 1) vector of endogenous variables observed at time t, zt is a (q ×1) vector of exogenous and deterministic variables, and πi and φ are coefficientmatrices. Diagnostic tests can be applied to the residual vector ut in order toassess the VAR’s statistical fit.

There can be up to r < n linearly independent stationary combinations – orcointegration relationships – between the n + q non-stationary variables, wherethe value of r is determined by the so-called trace test. Conditional on this value,the VAR can be reformulated and estimated by maximum likelihood as a vectorerror-correction model:

�yt = αβ ′xt−k + δ1�yt−1 + · · · + δk−1�yt−k+1 + ut, (4)

where x is an [(n + q) × 1] vector containing the n endogenous variables plus theq exogenous and deterministic variables.

5BEER studies usually include the country’s net foreign assets (NFA) position among the determi-nants of the real exchange rate. Since there are no readily available quarterly series for Mexico’sNFA position, one was constructed using the current account balance as a proxy for the changein NFA. The constructed series resembled closely the annual series presented by Lane and Milesi-Ferretti (2006); compared with the rest of the variables in the models though, it had a higher degreeof integration, making its inclusion problematic. Following Fazio et al. (2007) the current accountbalance itself was considered as a proxy for NFA, but its estimated coefficient tended to have thewrong sign in the real-exchange-rate equation (a result also obtained by those authors). See Note14 for the inclusion of government debt as a possible determinant of the risk premium.


The [r × (n + q)] matrix β ′ contains the cointegration coefficients, while therows of β ′x correspond to the cointegration equations. The (n × r) matrix αcontains the speed-of-adjustment coefficients, which measure how each of theendogenous variables reacts to deviations from each of the cointegration equa-tions.6 The cointegration equations are identified by restricting the value of someelements of β and α, a restriction that can be statistically assessed by a likelihoodratio (LR) test.

There are potentially six endogenous variables in our model: the bilateralreal exchange rate,7 the interest and inflation differentials, the manufacturingproduction ratio, the oil price, and government consumption. Weak exogeneitytests indicate that the oil price can be considered as exogenous at 5% signifi-cance.8 In addition, there are reasons to consider government consumption alsoas exogenous. First, economic reasoning suggests that fiscal policy has a large dis-cretionary component. Second, including the variable as endogenous yields poorestimation results: its coefficient on the real exchange rate cointegration equationis wrongly signed, while the coefficient on the manufacturing production ratiobecomes non-significant (results available upon request).

For the above reasons, the oil price and government consumption are enteredas exogenous variables. In the initial specification the models also include a con-stant, a linear trend, and a 0–1 CRISIS dummy for the first quarter of 1995 –although whether those variables remain in the final specification depends ontheir statistical significance and on the results of the LR test. The constant andtrend are intended to capture other possible influences, such as the unobservedrisk premium, on the endogenous variables.

4. Results and Analysis

The risk-adjusted interest parity condition underlying the BEER model is anadequate description of assets market equilibrium only in a context of free capitalmobility. Our analysis will thus be restricted to the period 1990Q1–2006Q4, whichroughly begins with the liberalization of the capital account in Mexico.

Table 2 presents the unit-root test results. In general, it is not possible to rejectthe hypothesis that the variables are non-stationary, and therefore that cointegra-tion is the appropriate estimation framework. Table 3 presents the diagnostics forthe original VARs, consisting of tests for normality and absence of serial corre-lation, ARCH patterns, and heteroscedasticity in the residuals. Given the use ofquarterly series, the VARs were estimated with four lags to control for seasonal

6To avoid confusion, keep in mind that the number of cointegration equations in Johansen’s reduced-rank regression methodology is always smaller than the number of endogenous variables in theVAR.7While the series for the multilateral rate are available from the Bank of Mexico, the bilateralUS–Mexico ratio must be used to be consistent with the peso–dollar interest differential.8The LR test statistic was 5.65, with a p-value of 0.0592. Note that, somewhat surprisingly, thetest would reject the (weak) exogeneity of the oil price at 10% significance, despite the oil pricebeing determined in the world market with no influence from the Mexican economy. The weakexogeneity tests were carried out within an otherwise unrestricted cointegrated VAR, estimatedunder the assumption of two cointegration relationships (see trace test results below).

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Table 2. Unit-root tests 1990Q1-2006Q4, 68 observations

Augmented Dickey-Fuller Phillips-Perron

Level with Level withLevel trend First difference Level trend First difference

GOVCOR −1.3486 −6.5978*** −9.9524*** −4.1997*** −6.775*** −16.4637***INFD −2.9386** −3.6801** −4.0628*** −1.9291 −2.5336 −4.0628***NIRD −2.7953* −3.5217** −4.0415*** −2.5626 −3.1013 −8.0553***OIL −0.8234 −1.8891 −4.0907*** −0.8065 −1.8869 −7.5356***RER −2.4880 −2.5116 −8.8412*** −2.6211* −2.7153 −8.8263***RIMP −1.9938 −3.2997* −5.4137*** −1.4259 −2.6791 −5.2355***

***,**,*: The unit root hypothesis is rejected at 1%, 5%, 10%.The ADF tests included an intercept, while the number of lags was determined by the Schwarz Info Criterion.The PP tests were performed with an intercept, Bartlett kernel, and Newey-West bandwidth. Both sets of testsused MacKinnon critical values.

effects.9 Except for some degree of non-normality in some of the equations forthe interest differential, the results are satisfactory.

4.1 General Results

Table 4 presents the estimation results for a sequence of models. Model A startswith the real exchange rate and the interest and inflation differentials as endoge-nous variables; and a constant, linear trend, and CRISIS dummy as deterministiccomponents. The sequence adds the manufacturing production ratio (model B),the oil price (model C), government consumption (model D), and finally all thevariables together (model E). Models F and G, also included in the table, will beexplained below.

In all the models, the trace test indicates the existence of two cointegration rela-tionships, which after the imposition of identifying restrictions – amply acceptedby the LR test – can be interpreted as long-run equations for the inflation differ-ential and the real exchange rate. The critical values for the trace test were takenfrom Pesaran et al. (2000), who control for the number of exogenous variables inthe model. If, instead, the Juselius (2006) critical values are used, then in modelsE and G the trace test indicates the existence of a third cointegration relationship,which can be interpreted as an equation for the manufacturing production ratio.10

In the different models the negative and highly significant alpha coefficientsindicate that the inflation differential and the real exchange rate adjust over timetoward their long-run levels as determined by the cointegration equations. Inmodels E and G, the alpha coefficient in the error-correction equation for themanufacturing production ratio indicates a statistically significant but very slow

9An F-test showed that no lag could be eliminated; in addition, removing the fourth lag introducedserial correlation in the residuals.10The trace statistic was corrected for small-sample bias using the factor suggested by Johansen(2002) (see note in Table 4). Following standard practice, the cointegration relationships are reportedin the form β ′x = 0. The estimations were carried out in PcGive 10.

Monetary

Policyand

RealC

urrencyA

ppreciation99

Table 3. VAR diagnostics 1990Q1-2006Q4, 68 observations

AR 1-5 Normal ARCH 1-4 Hetero AR 1-5 Normal ARCH 1-4 HeteroF-test χ2-test F-test F-test F-test χ2-test F-test F-test

Model A Model DRER equation 0.8088 3.0181 0.2312 0.4425 RER equation 0.7849 2.4501 0.2604 0.4169INFD equation 1.7617 0.1608 0.7515 1.4215 INFD equation 1.9142 0.1579 0.7269 1.2316NIRD equation 0.7246 11.51*** 1.2471 0.3205 NIRD equation 0.8255 9.871*** 1.5783 0.3274

Model B Model ERER equation 0.184 2.301 0.1399 0.4157 RER equation 0.0961 1.0218 0.0749 0.1983INFD equation 1.2582 0.6434 0.3943 0.8788 INFD equation 1.3619 0.8405 0.3955 0.5722NIRD equation 0.8737 8.775** 1.1796 0.2972 NIRD equation 1.4443 1.5773 0.5203 0.2732RIMP equation 1.3773 1.0105 0.926 0.2384 RIMP equation 1.2782 0.8621 0.8544 0.1981

Model C Model GRER equation 1.0709 2.5114 0.1197 0.4874 RER equation 0.4124 1.1827 0.0868 0.2394INFD equation 1.6983 0.22 0.7438 1.3161 INFD equation 1.3337 0.8359 0.8436 0.8123NIRD equation 1.115 5.148* 0.5215 0.5552 NIRD equation 1.1137 2.411 0.3113 0.251

RIMP equation 1.1418 2.386 0.8113 0.3461

***,**,*: the null hypothesis of well-behaved residuals is rejected at 1%, 5%, 10% of significance. Model F, not included in the table, consists of the same equationsof model A.

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Table 4. BEER models Johansen’s ML estimation, 1990Q1-2006Q4, 68 observations

Model A Model B Model C Model D

Eq. (A.1) Eq. (A.2) Eq. (B.1) Eq. (B.2) Eq. (C.1) Eq. (C.2) Eq. (D.1) Eq. (D.2)

Beta coefficients on endogenous variablesRER 1 −64.684 1 −55.765 1 −42.512 1 −41.907

(8.8282) (7.1864) (10.857) (10.493)NIRD 0.0198 0 0.0265 0 0.0922 0 0.0219 0

(0.0079) (0.0053) (0.0262) (0.0072)INFD −0.0144 1 −0.0116 1 −0.0252 1 −0.0128 1

(0.0075) (0.0029) (0.0262) (0.0072)RIMP n.i n.i 4.8928 43.553 n.i n.i n.i n.i

(0.9739) (6.5619)

Beta coefficients on exogenous and deterministic variablesConstant −4.4964 260.3 −29.778 0 −7.1921 163.61 −4.9351 160.76

(0.0614) (40.874) (5.0637) (1.0697) (49.889) (0.4544) (48.097)Trend 0 0.2168 0.0126 0.2951 0 0.2098 0 0.2123

(0.0461) (0.0027) (0.0411) (0.0535) (0.0524)CRISIS −3.6295 −19.198 −1.4618 −16.867 −14.070 −83.061 −3.8125 −83.717

(0.2356) (6.9692) (0.0929) (6.6997) (0.9307) (8.9905) (0.2552) (8.9368)OIL n.i. n.i. n.i. n.i. 0.6993 0 n.i. n.i.

(0.3334)GOVCOR n.i n.i n.i n.i n.i n.i 3.0655 0

(3.2207)

Alpha coefficients in error-correction equations�RER −0.1153 0 −0.2683 0 −0.0292 0 −0.1084 0

(0.0074) (0.0139) (0.0019) (0.0070)�NIRD −8.7842 0 −19.799 0 −2.2438 0 −8.2939 0

(0.722) (1.662) (0.18) (0.6785)�INFD 0 −0.1994 0 −0.2055 0.7757 −0.18 2.9593 −0.1821

(0.036) (0.039) (0.2169) (0.0353) (0.8344) (0.0362)�RIMP n.i n.i 0.0265 0 n.i n.i n.i n.i

(0.0065)

Monetary

Policyand

RealC

urrencyA

ppreciation101

LR test of 2.27 (3) 5.43 (4) 0.54 (3) 0.29 (3)restrictions [0.519] [0.246] [0.91] [0.962]

Trace tests,H0: r <=

0 134.01 [42.34]* 161.78 [63.00] * 138.01 [49.36] * 135.48 [49.36] *1 28.30 [25.77] * 42.14 [42.34] ** 30.26 [30.72] ** 29.21 [30.77] **2 6.19 [12.39] 20.53 [25.77] 7.20 [15.44] 6.86 [15.44]3 7.06 [12.39]

Model E Model F Model G

Eq. (E.1) Eq. (E.2) Eq. E.3) Eq. (F.1) Eq. (F.2) Eq. (G.1) Eq. (G.2) Eq. (G.3)

Beta coefficients on endogenous variablesRER 1 −45.914 −1.0980 1 −64.684 1 −43.558 −1.0981

(17.578) (0.0098) (8.8282) (17.939) (0.0097)NIRD 0.0329 −0.5248 0 0.0120 0 0.0082 −0.5525 0

(0.0058) (0.1909) (0.0053) (0.0036) (0.1952)INFD −0.0093 1 0 −0.0120 1 −0.0082 1 0

(0.0034)RIMP 6.1920 −49.972 1 n.i n.i 0.8794 −48.834 1

(1.0761) (21.042) (0.3624) (21.587)

Beta coefficients on exogenous and deterministic variablesConstant −37.050 447.65 0 −4.4333 260.3 −9.2036 431.95 0

(5.6406) (154.86) (0.0280) (40.874) (1.8674) (158.41)Trend 0.0152 0 0 0 0.2168 n.i. n.i. n.i.

(0.0030) (0.0461)CRISIS −1.6380 −18.707 1.491 −2.5496 −19.198 −1.7016 −19.293 1.4952

(0.1084) (6.4201) (0.3509) (0.1667) (6.9692) (0.1131) (6.5962) (0.3503)OIL 0.0464 0 0 n.i. n.i 0.0495 0 0

(0.0463) (0.0443)GOVCOR 3.1944 0 0 n.i n.i 2.144 0 0

(1.7472) (1.5232)

(Continued)

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Table 4. Continued

Model E Model F Model G

Eq. (E.1) Eq. (E.2) Eq. E.3) Eq. (F.1) Eq. (F.2) Eq. (G.1) Eq. (G.2) Eq. (G.3)

Alpha coefficients in error-correction equations�RER −0.2314 0 0 −0.1637 0 −0.2435 0 0

(0.0117) (0.0104) (0.015)�NIRD −17.22 0 0 −12.432 0 −18.435 0 0

(1.3911) (1.0345) (1.5473)�INFD 0 −0.2197 0 0 −0.1994 0 −0.2139 0

(0.0444) (0.036) (0.0433)�RIMP 0 0 −0.0299 n.i n.i 0 0 −0.0299

(0.0054) (0.0054)LR test of 12.82 (11) 2.95 (4) 8.92 (10)

restrictions [0.305] [0.567] [0.54]Trace tests,

H0: r <=0 169.81 [81.20] * 134.01 [42.34]* 141.98 [72.15] *1 47.16 [56.43] a/ 28.30 [25.77]* 34.78 [49.43] c/2 25.01 [35.37] b/ 6.19 [12.39] 16.61 [30.46] d/3 9.72 [18.08] 5.82 [15.27]

* (**): Rejects the null at the 5% (10%) significance level, based on the critical values in Pesaran et al. (2000) (5% critical values are shown in brackets).Critical values at 5% (10%) of significance from Juselius (2006):a/ 42.77 (39.73); b/ 25.73 (23.32); c/ 35.07 (32.25); d/ 20.16 (17.98).1) The trace statistic was corrected for small-sample bias using the factor [T − n(k − 1)]/T (see Johansen, 2002), where k is the number of lags in the VAR, n isthe number of endogenous variables, and T is the number of observations.2) Standard errors are reported in parenthesis below the alpha and beta coefficients. In the LR test, the number of restrictions is shown in parenthesis and thep-value in brackets.3) The beta coefficients are the coefficients of the cointegration equations, while the alpha coefficients are the speed of adjustment coefficients of the error-correctionequations. The table reports the cointegration equations in the form β ′x = 0, with the coefficient on the dependent variable normalized to one. See equations (3)and (4) in the text for further explanation.n.i.: not included.


adjustment of that variable toward its long-run level. The slow adjustment prob-ably reflects the fact that – through the choice of variables – the models were setup to study the equilibrium in the assets market rather than the determination ofthe production level. Ibarra (2008c) shows, for instance, that an acceptable modelfor industrial production in Mexico must include investment and manufacturedexports, besides the real exchange rate.

In the cointegration equations for the inflation differential and the manufactur-ing production ratio, the real exchange rate is the most significant determinant.The real exchange rate has a positive effect on the production ratio, with an elas-ticity practically equal to one (Ibarra, 2008c provides evidence that the channelsfor this effect are investment and manufactured exports). The real exchange ratealso has a positive effect on the inflation differential.11 The estimated coefficientimplies that a 10% appreciation tends to decrease the inflation differential inabout 6.4 to 4.2 percentage points (see equations A.2 and D.2).

4.2 RER Determination

Considering now the cointegration equation for the real exchange rate, the coef-ficients on the three real-side determinants show the expected negative sign. Onlythe manufacturing production ratio, though, is always statistically and econom-ically significant; moreover, its inclusion improves the overall estimation results:both the interest-differential coefficient in the real-exchange-rate cointegrationequation and the speed of adjustment of the real exchange rate toward its long-runlevel rise (compare models B and E, with model A).

The negative coefficient on the manufacturing production ratio presumablyreflects the Balassa–Samuelson effect. Figure 1 shows that the rise in the produc-tion ratio contributed to the real appreciation of the peso during 1990–1991 andagain in the second half of the 1990s. The estimated coefficient in equation E.1,for instance, implies that the rise in the production ratio explains about 7.7 points(0.0124 times 6.192) of the 19% appreciation recorded during 1998–2001. Note,however, that the manufacturing production ratio – since it was falling – cannotexplain the strong appreciation observed during 1992–1993.

There is some evidence of an oil-price effect on the real exchange rate. Thenegative coefficient in equations C.1 and E.1 implies that the oil price mayhave contributed to the peso appreciation during 1999–2000 and 2004–2006. Theappreciation registered in the 1990s, though, is necessarily unrelated to the evo-lution of oil, which mostly tended to fall (see Figure 2). In addition, equation C.1– the only one where the oil price is statistically and economically significant – isnot entirely satisfactory: the speed of adjustment of the real exchange rate drops

11In most models the interest differential in the inflation equation has a non-significant coefficient. Ifin equation E.2 the interest differential – which shows a significant positive coefficient – is eliminated,then the real exchange rate coefficient rises strongly, from 45.9 to 88.3; this suggests that the positivecoefficient on the interest differential is capturing some of the inflationary effect of the real exchangerate during periods of financial turbulence – when the interest differential and the real exchangerate move in the same direction. Eliminating the interest differential, however, is rejected at 10% bythe LR test. In the inflation equation of models E and G, the manufacturing production ratio has apositive coefficient, presumably reflecting a cost-push factor.

104 C.A. Ibarra

Figure 1. Real exchange rate and manufacturing production ratio, 1990Q1–2006Q4.Note: The series are 4-quarter, left-sided moving averages.Source: See appendix.

Figure 2. Real exchange rate and oil price, 1990Q1–2006Q4.Note: The series are 4-quarter, left-sided moving averages.Source: See appendix.

from 0.2683 in equation B.1 to 0.0292, and the CRISIS coefficient turns unrealis-tically large. The lack of a robust effect of the oil price on the peso’s real exchangerate may reflect the decline of this commodity in Mexico’s international trade.12

12The share of oil in goods exports fell from more than 60% in the early 1980s to less than 10%twenty years later. The variable has been problematic in previous studies. Kildegaard (2006) founda significant but positively-signed oil price coefficient in a cointegration analysis for the period


Figure 3. Real exchange rate and government consumption, 1990Q1–2006Q4.Note: The series are 4-quarter, left-sided moving averages.Source: See appendix.

The negative coefficient on government consumption suggests that this vari-able contributed to the peso appreciation during 1992–1993 and 1998–2001 (seeFigure 3), but the effect is probably small. The coefficient in equation E.1 – the onewhere it approaches statistical significance – implies that the rise in governmentconsumption during 1998–2001 tended to appreciate the peso by about 1.4%(3.1944 times 0.007) – against a total appreciation of 19%.

Figure 4 reveals a complex relationship between the real interest differentialand the real exchange rate. At times of financial turbulence – like 1994–1995(the Tequila crisis) and 1998–1999 (the Russian crisis) – the variables move in thesame direction, probably reflecting the policy use of the interest rate to cushionthe impact on the exchange rate. Over prolonged periods, though, they tend tomove in opposite directions. For instance, the appreciation of the peso duringthe early 1990s, and again in the wake of the 1995 crisis, took place against thebackdrop of a rising interest differential.

The link is captured in the estimated long-run equations for the real exchangerate, which show a positive relationship of that variable with the inflationdifferential and a negative one with the nominal interest differential. The resultobtains whether the real-side variables are excluded (model A), included one byone (models B to D), or simultaneously (model E).

Finding a negative relationship between the exchange rate and the interestrate is important, for it implies that causality runs from the interest rate to theexchange rate, thus validating the risk-adjusted parity condition underlying theBEER model. As mentioned in section 3, a positive relationship would signal that

1969–2000; Dabós and Juan-Ramón (2000) obtained a similar result in a regression analysis for theperiod 1982Q1–1998Q4 – using the international terms of trade rather than the oil price. Edwards(1994) and Elbadawi (1994) discuss theoretically why the terms of trade coefficient may have anambiguous sign.

106 C.A. Ibarra

Figure 4. Real exchange rate and real interest differential, 1990Q1–2006Q4.Note: Real interest rate differential (RIRD)=NIRD-INFD. The series are 4-quarter, left-sidedmoving averages.Source: See appendix.

the interest differential is in fact being determined by the exchange rate – a policyof leaning against the wind.

Taken together, the equations for the inflation differential and the real exchangerate imply that the nominal interest differential has a long-run effect on thereal exchange rate by two channels: directly, through a rise in the real interestdifferential; and indirectly, through a fall in the inflation differential.

To exemplify, consider model A. The direct channel, captured by the realexchange rate equation (A.1), shows that a rise of 5 points in the interest dif-ferential eventually leads to a real currency appreciation of 10% (5 × 0.0198).The indirect channel operates through inflation: a 10% real currency apprecia-tion decreases the inflation differential by 6.5 points (0.1 × 64.684; see equationA.2), which in turn tends to produce a further 9% appreciation (6.5 × 0.0144).Naturally, the specific numbers must be taken with caution, but they do suggestthat variations in the interest differential can have economically significant effectson the real exchange rate.13

To have an idea of the historical effects in the Mexican case, consider that thereal interest differential rose by 7.5 percentage points during 1998–2001, resultingfrom a fall of 14.9 points in the inflation differential but of only 7.4 points in thenominal interest differential. According to the estimated coefficients in equationA.1, this tended to produce a real appreciation of 6.8% – that is, about one thirdof the appreciation recorded in that period.

13Interestingly, our point estimates for the interest-differential coefficient in the long-run equationfor the real exchange rate are very similar to those obtained by Frankel (2007) in his study of theSouth African rand (his point estimates range from 0.019 to 0.022 for the pre-liberalization period).


Figure 5. Real exchange rate and BEER, 1990Q1–2006Q4.Note: The series are 4-quarter, left-sided moving averages.Source: Bank of Mexico and model G (see Table 4).

Note, however, that using the coefficients of equation E.1 – instead of A.1 –would predict a depreciation of about 10%. This counter-intuitive result comesfrom the fact that the coefficient on the interest differential is much larger thanthat on the inflation differential – contrary to what was initially expected.14 Apossible response to the unexpected result consists of imposing symmetry onthe coefficients for the nominal interest rate and the inflation differentials, andchecking whether this restriction is statistically acceptable.

Two models were estimated under the symmetry restriction: model F, whichexcludes the real-side determinants of the real exchange rate (originally, modelA), and model G, which includes all the variables (originally, model E). The newmodels are accepted by the LR test with p-values that are even higher than thoseobtained in the original models; moreover, the speed-of-adjustment coefficientsare now larger, particularly in model F (compared with model A).15

The estimated coefficients in the new models have the expected sign, indicatingthat a rise in the real interest rate differential – irrespective of whether it comesfrom a rise in the nominal interest rate or a fall in the inflation differential – tends

14A larger coefficient on the inflation differential was expected under the assumption that theinflation differential could be a significant determinant of the unobserved risk premium. Followingthe BEER literature, model A was re-estimated with the addition of the government’s total debt (inpercentage of GDP) as a possible determinant of the risk premium (results available upon request).As expected – given the stationarity of the new variable – the trace test indicated the existence of anew, third cointegration relationship, which captured a positive relationship between governmentdebt and the interest differential. The estimated coefficient on the government’s debt in the long-run equation for the real exchange rate showed the expected positive sign, but no economic orstatistical significance. Compared with model A, the other coefficients in the real exchange rateequation remained unchanged, including those on the interest and the inflation differentials.15The trend had to be removed from model G for the LR test to accept the symmetry restriction.

108 C.A. Ibarra

to produce a lasting currency appreciation. The point estimate of 0.0082 – to usethe smallest of those obtained in models F and G – implies that the observed riseof 7.5 points in the real interest differential during 1998–2001 tended to producea real appreciation of 6.2% – representing, again, about one-third of the actualappreciation recorded in the period.

As a summary of the different effects, Figure 5 shows the actual real exchangerate together with the estimated BEER series from model G. The figure suggeststhat, after controlling for the influence of real-side and monetary factors, thepeso was overvalued in about 9% by 2002. This is in addition to the alreadymentioned effect of the rise in the real interest differential. Understanding thestrong appreciation of the peso in the late 1990s and early 2000s is clearly a topicfor further research.

5. Conclusions

In a setting of prolonged disinflation, since the late 1980s the Mexican peso experi-enced a tendency to appreciate in real terms. Controlling for the effect of real-sidevariables, such as relative manufacturing production, government consumption,and the oil price, the paper showed that monetary policy – as reflected in theinterest differential – had a lasting effect on the peso’s real exchange rate.

A frequent assumption in the academic literature and the policy debate is thatmonetary factors – in contrast to real-side determinants – cannot have a lastingeffect on the real exchange rate. The premise does not seem suitable in Mexico’scase, however, given the country’s experience of prolonged disinflation and thesustained focus of monetary policy on that goal.

To test the joint influence of real-side and monetary variables, the paper esti-mated a BEER (Behavioral Equilibrium Exchange Rate) model for the Mexicanpeso. The model not only considers both types of variables, but relies onJohansen’s cointegration methodology – a natural framework to uncover long-run effects on the real exchange rate. The period under analysis starts in 1990Q1(to concentrate on the period of free capital mobility in Mexico, as required bythe risk-adjusted interest parity condition underlying the BEER model) and endsin 2006Q4.

In different combinations, the core of the estimated models consisted of the realexchange rate – the inverted consumer-price ratio between Mexico and the US –and the nominal interest differential, the inflation differential, and the manufac-turing production ratio between the two countries, all as endogenous variables;and the international price of oil in real terms and Mexico’s ratio of governmentconsumption to GDP as exogenous variables.

Johansen’s methodology yielded models of two cointegration relationshipsthat can be interpreted as long-run equations for the real exchange rate andthe inflation differential; in some models the estimation produced an additionalequation, for the manufacturing production ratio. The models show that themanufacturing production ratio and the inflation differential depend positivelyon the real exchange rate, while the real exchange rate – controlling for the effectof real-side variables – depends negatively on the nominal interest rate differentialand positively on the inflation differential. Taken together, the equations for the


inflation differential and the real exchange rate imply that a rise in the nominalinterest differential appreciates the currency by two channels: directly, through arise in the real interest differential; and indirectly, through a fall in the inflationdifferential.

The effect of the interest differential on the real exchange rate is economicallysignificant. Using the estimated coefficients in the cointegration equation for thereal exchange rate shows, for instance, that the 7.5 point rise in the real interestdifferential recorded during 1998–2001 accounts for about one-third of the realappreciation observed in the period.

Acknowledgements

Financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT), project 47140-S, is gratefullyacknowledged.

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Appendix. Data Sources and Definitions

CRISIS: 0–1 dummy equal to 1 in the first quarter of 1995.

GOVCOR: Residual from a regression of GOVCO on a set of (three) centeredseasonals, without a constant, for the period 1980Q1–2006Q4. GOVCO is theratio of the public sector’s total current expenditure to GDP. Source: Mexico’sMinistry of Finance (SHCP) and Institute of Statistics (INEGI).

INFD: Difference between the Mexican and the US inflation rate, in percentagepoints. The inflation rate equals the 12-month variation rate in the consumerprice index. Source: Calculated with data from Bank of Mexico (BOM) and USBLS.

NIRD: Difference between the Mexican Treasury bill rate (91-day CETE rate)and the US federal funds rate, in percentage points and annual terms. Source:Calculated with data from BOM and the US Federal Reserve.

OIL: Natural logarithm of the international price of oil in real dollars. Thenominal price series was deflated using the US producer price index. The nominalprice corresponds to the simple average of the spot quotations of Dated Brent,West Texas Intermediate, and Dubai Fateh. Source: IMF and US BLS.

RER: Natural logarithm of the bilateral real exchange rate of the Mexican peso,calculated as the product of the nominal peso-dollar exchange rate and the USconsumer price index, divided by the Mexican consumer price index. Source:Calculated with data from BOM and US BLS.

RIMP: Natural logarithm of the ratio of Mexico’s manufacturing productionindex to the US index. The data was seasonally-adjusted by the original source.Source: BOM and the US Federal Reserve.

All the series except GOVCOR are quarterly averages of monthly data.

Documents

Monetary Policy and Real Currency Appreciation: A BEER Model for the Mexican Peso