Are Mexican Business Cycles Asymmetrical?

Contributor Notes

Author’s E-Mail Address: asantos2@imf.org

We use the regime-switching econometric models in Hamilton (1989) and Filardo (1994) to study business cycles in Mexico. In particular, we characterize the ups and downs of economic activity in Mexico. As a proxy for economic activity, we use the Mexican quarterly industrial production index from the second quarter of 1972 to the third quarter of 1999. We allow the transition probabilities driving changes in economic activity to be a function of fiscal, financial, and external sector indicators. Our results show that recessions in Mexico are deeper and shorter than expansions.

Abstract

We use the regime-switching econometric models in Hamilton (1989) and Filardo (1994) to study business cycles in Mexico. In particular, we characterize the ups and downs of economic activity in Mexico. As a proxy for economic activity, we use the Mexican quarterly industrial production index from the second quarter of 1972 to the third quarter of 1999. We allow the transition probabilities driving changes in economic activity to be a function of fiscal, financial, and external sector indicators. Our results show that recessions in Mexico are deeper and shorter than expansions.

I. Introduction

Economists have been long interested in business cycles. Although, there exists an extensive literature on business cycles in developed economies, not much is known about business cycles in the developing world.2 This paper investigates Mexican business cycles, in particular whether some fiscal, financial, and external sector indicators contain information about them.

Possible sources of Mexican business cycles such as political cycles, exchange rate stabilization plans, and market imperfections justify our choice of fiscal, financial, and external sector indicators as leading indicators.3 Since many of these indicators track financial crises in the early warning indicators literature, they are also good candidates for the role of leading indicators of business cycles in Mexico.4 Combining these fiscal, financial, and external sector indicators into a composite index also provides helpful information. To obtain this combination, we use principal component analysis. Since the first orthogonal principal component accounts for most of the variation in these indicators, we can easily interpret it as a composite index of vulnerabilities in the fiscal, financial, and external sectors.

We use the regime-switching econometric model in Hamilton (1989), and its extension in Filardo (1994), to estimate the average growth rates of expansions and recessions, and to assess the effectiveness of our fiscal, financial, and external sector indicators. We set the transition probabilities driving regime changes from expansions to recessions and vice versa as a function of fiscal, financial, and external sector indicators.

If structural breaks are expected to occur in a time series, regime-switching models are more appropriate to fit the data than extensions from the usual linear regression models. By not imposing deterministic changes that might be conditioned on arbitrary events chosen by the researcher, regime-switching models are a more general approach to deal with structural breaks. Regime-switching models also have the advantage that the regime probabilities obtained as a subproduct from the maximization procedure can be used to access the turning points in business cycles. As pointed in Diebold and Rudebusch (1996), despite the general interest in turning points, only regime-switching models provide the framework where the concept of turning points is meaningful.

The regime-switching models, applied to quarterly industrial production index in Mexico, from the first quarter of 1972 through the third quarter of 1999, yields interesting results. First, estimates for the positive and negative growth rates with and without our fiscal, financial, and external sector indicators show stronger recessions than expansions. Second, our estimations indicate that the economy moved from an expansion to a recession in 1982, 1985–86, and 1994 and from a recession to an expansion in 1983, 1986, and 1995.

Section II summarizes possible sources of business cycles in Mexico. Section III lists our fiscal, financial, and external sector indicators. Section IV describes the regime-switching econometric model with constant time-varying transition probabilities. Section V discusses our results. The last section summarizes the main findings of the paper.

II. Sources of Mexican Business Cycles

This section briefly reviews the Mexican economic performance from 1970 to 1999, and suggests four possible sources of business cycles in Mexico: political cycles, exchange-rate-based stabilization plans, market distortions, and external factors.

The first period reviewed, from 1970 to 1981, was characterized by an import-substitution strategy (implemented since the 1950s), mounting economic distortions, particularly in the financial sectors, restrictions to foreign direct investments, and domestic and external imbalances. In response to low growth rates in the early 1970s, the Mexican government implemented expansionary fiscal policies, which in turn accelerated inflation, appreciated the local currency in real terms, and real interest rates were kept artificially low. The resulting capital outflows pressured the foreign exchange market, and the authorities were forced to devalue in 1976. The expenditure switching and reduction effect of the devaluation was short lived as the government kept spending and borrowing, encouraged by the large oil discoveries in mid-1970s. As a result, the current account deficit widened and the external debt rose. The Mexican authorities only changed policies after the collapse of oil prices in 1981 and the increases in international interest rates.

The second period, 1982 to 1988, is a period of weak economic performance, following the government default on its external debt. In February 1982, and again six months later, the authorities devalued the peso. To tackle the crisis, the Mexican government implemented an economic program supported by the IMF in late 1982. After the introduction of the economic program, internal and external imbalances decreased, inflation receded, and real GDP increased. However, domestic and external adverse shocks (the 1985 earthquake and the fall in oil prices in 1986) undermined the adjustment efforts and increased the vulnerability of the external and fiscal positions.

In the third period, 1989 tol994, the Mexican authorities implemented an exchange-rate-based stabilization program, which was complemented by incomes policies, public finance reform measures, and financial and trade liberalizations. The successful implementation of the stabilization program led to lower inflation, higher income per capita, and large capital inflows. The latter in turn prevented a reversal of the real exchange rate appreciation. Indeed, financial liberalization—coupled with weak prudential regulation and inadequate banking supervision—increased consumer credit and consumption. Imports then grew more than exports and the current account deficit tripled. Given the short-run nature of the financing flows to Mexico, the economy became quite vulnerable in 1994 to the adverse external and domestic shocks, resulting in capital outflows and a collapse of the exchange rate and output.

In the last period, 1995 to 1999, the economy recovered. After the 1994 crisis, Mexico implemented an adjustment program with IMF support. The adjustment program included a floating exchange rate, the tightening of monetary policy, fiscal consolidation, and restrained incomes policies. In addition, authorities responded to the banking crisis with several support schemes. As a result, after 1996, the economic situation improved and real GDP grew, on average, at 5 percent per year.

The four periods above can be interpreted in terms of four possible sources that we discuss next. For example, Grier and Grier (2000) argued that, when autocratic governments rule for short periods, without the possibility of reelection, they neglect the long-run benefits of public goods and confiscate assets that generate long-term flows of resources. Autocratic governments make distorted policy decisions and reduce both the quantity and quality of public goods. Investors and consumers delay private decisions and economic activity declines as the end of the presidential term nears and uncertainty in the economy increases. In the context of autocratic governments, financial crisis is simply endogenous to the political cycle.

Another source of business cycles in Mexico is the exchange-rate-based stabilization programs, as they could have been an important source in the third period mentioned above. Empirically, as report by Calvo and Vegh (1999), exchange-rate-based stabilization plans led to consumption booms, currency overvaluations, and trade deficits in countries that implemented them. The authors also report that most stabilization strategies ended with a depletion of foreign reserves, speculative attacks, and a fall in aggregate demand. In fact, Mendoza and Uribe (1999) developed a theoretical model to explain this interaction, which worked through interest rate distortions (currency risk premium) that affect savings, investment, and labor supply decisions. The calibration of their model with Mexican data simulated the consumption increase and the real exchange rate appreciation, with a worsening trade balance and a dwindling reserve.

A third possible source of Mexican business cycles is market distortion. Mishkin (1997) suggested that asymmetric information problems worsened before the end-1994 crisis in Mexico with a series of events such as the deregulation of financial markets in early 1990s; the interest rate increases following the U.S. policy response to inflationary pressures in 1994; the increase in uncertainty following the political shocks and the stock market decline in 1994; and the deterioration of cash flows of firms and households. McKinnon and Pill (1997) suggested the unlimited government insurance to almost all bank’s liabilities also contributed to the 1994 financial crisis as it protected depositors from losses associated with new technologies and distorted banks’ borrowing and credit decisions. Domestic residents invested more than they would have otherwise done. Since the exchange rate was fixed, banks did not hedge their currency risk positions and overborrowed.

Finally, given the fact that over SO percent of Mexico’s total trade is with the United States, and that oil contributes to about one-third of the government revenue, the business cycle in the United States and terms-of-trade shocks could also have been a major source of business cycles in Mexico, specially in the second and third periods reviewed above.

III. Fiscal, Financial, and External Sector Indicators as Business Cycle Indicators

The previous sources of business cycles in Mexico suggest some interesting leading indicators of business cycles. Table 1, first column, lists our fiscal, financial, and external sector indicators. Many of these indicators also track financial crises in the early warning indicators literature.

Table 1.

Mexico: First Principal Component of Fiscal, Financial, and External Sector Indicators, 1972:Q2-99:Q3

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Source: Appendix I.

An increase in the deviations implies a real depreciation of the local currency and vice versa.

However, some indicators are computed in a slightly different way than in the early warning indicators literature.5 For instance, domestic credit change as percentage of GDP is used to capture the monetary policy stance instead of deviations from a money demand function for real cash balances.6 Instead of deviations of the real exchange rate from its trend, deviations of the real exchange rate are computed from its equilibrium value as in Dabós and Juan-Ramon (2000).7 Appendix III shows how the deviations from the equilibrium real exchange rate were obtained.

Although single indicators might not convey statistically significant information, their combination could result in a helpful index. An example is Filardo (1994) and Layton (1998), who included the Composite Index of Eleven Leading Indicators (CLI), the CLI’s diffusion index, and the Stock and Watson Experimental Index of Seven Leading Indicators in their analysis. We could use similar composite indexes of leading indicators for Mexico, but they are only available for a shorter period than is necessary in the estimations of the next sections.8

Since long series for composite indexes are not available in Mexico, we compute a composite indicator of vulnerabilities in the balance of payments and the banking sector using principal components analysis. Table 1, third column, reports our estimation results using deviations from the mean for the seventeen fiscal, financial, and external sector indicators. As seen in Table 1, the first principal component accounts for 42 percent of the variance in our indicators measured with respect to their mean (deviations). Interestingly, all factor loadings have signs that correspond to the expected ones in an aggregate composite index of vulnerability.9

Figure 1 plots our composite index from variables in Table 1. When above zero, our composite index of vulnerability is signaling pressures either on the balance of payments or on the banking sector. Note that, in all crises in September 1976, February 1982, December 1982, and December 1994, our index was signaling pressures far in advance.10 On the other hand, when below zero, no pressures on the balance of payments or on the banking sector exist.

Figure 1.
Figure 1.

Mexico: Composite Index of Vulnerabilities in the Balance of Payments and the Banking Sector, 1972:Q2-99:Q3

Citation: IMF Working Papers 2002, 150; 10.5089/9781451856972.001.A001

Source: Table 2.
Table 2.

Mexico: Expected Signs for the Effects of Fiscal, Financial and External Sector Indicators on the Transition Probabilities P11t and P22t

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Source: Table A.1Note: The indicators are: defgdp=public sector borrowing requirement (last 12-months), percent of GDP (last 12 months); M1=deviations of Ml from a money demand function; multiplier=money multiplier (Ml/base reserve), 12-month percent change; deposits-bank deposits, percent of GDP (last 12 months); realint=real interest rate on time deposits; stocks=stock index deflated by CPI, 12-month percent change; cps=credit to the private sector, percent of GDP (last 12 months); RER=deviations of the real exchange rate from its equilibrium value, where an increase in the deviations implies a real depreciation of the local currency and vice-versa.; imports=imports of goods and services, 12-month percent change; exports=exports of goods and services, 12-month percent change; tot=terms of trade, 12-month percent change; reserves=reserves, 12-month percent change; m2res=ratio M2/reserves, 12-month percent change; stres=ratio short-term debt/total external debt, 12-month percent change; U.S.realint= U.S. real interest rate; realdif=Mexican-U.S. real interest rate differential; and composite index=first principal component of the fiscal, financial, and external indicators in Table 1.

How can our fiscal, financial, and external sector indicators be useful in characterizing business cycles? These indicators can be incorporated into the laws of motion that drive changes in the phases of business cycles. This is the line of research pursued in the next sections.

IV. Regime-Switching Models with Time-Varying Transition Probabilities

In this section we use the regime-switching econometric model in Hamilton (1989) and its extension in Filardo (1994) to analyze Mexican business cycles and test the predictive power of our fiscal, financial, and external sector indicators. Hamilton (1989) proposed the regime-switching econometric model to allow different probability distributions to characterize the behavior of a variable.11 An example is the U.S. business cycles. During states of expansion, changes in GDP are centered around a positive mean, whereas, during states of contraction, changes in GDP are centered around a negative mean.

Following Hamilton (1989), we let st describe the state of the business cycle. For periods of expansion, st=l, and for periods of contraction, st=2. Since quarterly GDP for Mexico is only available since 1982, we use the seasonally adjusted industrial production index as a proxy for economic activity. We can express the current changes in the industrial production index as:

yt=gst+ut,(1)

where yt is the quarterly change in the industrial production index (in log); gst is the mean growth rate in states st; and ut is an error term with a N(0, σst2) distribution in state st. In periods of expansion (st=1), g1≥0 and the error term has a variance equal to σ12. In periods of contraction (st=2), g2<0 and the error term has a variance equal to σ22. That is:

yt=g1+ut if st=1, where utN(0,σ12), or yt=g2+ut if st=2, where utN(0,σ22)(2)

We assume that the state variable st is a first-order Markov process that evolves according to a (2x2) transition probability matrix P:

P=[p11t1p22t1p11tp22t].(3)

where:

i) p11t stands for probability of going from state 1 (expansion) at time t-1 to state 1 (expansion) at time t; ii) p12t = 1-p11t stands for the probability of going from state 1 (expansion) at time t-1 to state 2 (contraction) at time t; iii) p21t = 1-p22t stands for the probability of going from state 2 (contraction) at time t-1 to state 1 (expansion) at time t; and iv) P22t stands for the probability of going from state 2 (contraction) at time t-1 to state 2 (contraction) at time t.

Note that Hamilton (1989) has a constant transition probability matrix driving changes in states. This implies that the probability that a recession (expansion) at time t follows a recession (expansion) at time t-1 is always the same and independent of the duration of the contractionary state. However, these constant transition probabilities might not be appropriate to identify business cycles since they (i) cannot increase before a contraction or an expansion begins; (ii) do not allow for the persistence of a phase (recession or expansion) over time; and (iii) do not incorporate expected durations.

To overcome these drawbacks, Filardo (1994) extended the standard regime-switching model by allowing the transition probabilities to be time-varying. His approach set the transition probabilities as a function of indicators containing information on business cycles. He then applied the extended framework to U.S. data and found that time-varying transition probabilities are better to characterize expansions and contractions in the U.S. business cycles than constant transition probabilities.

Following Filardo (1994), we allow the transition probabilities to be time-varying and dependent on our fiscal, financial, and external sector indicators. We specify logistic function for the transition probabilities piit:

piit=exp(Xt.Φi)1+exp(Xt.Φi),(4)

where xt is a vector of exogenous variables and Φi is a vector of parameters for the sequence of states St-1=i and st=i, where i = l, 2. The logit function constrains the transition probabilities piit to lie in the interval 0< piit<1.

Table 2 shows the expected effects of our fiscal, financial, and external sector indicators on the transition probabilities. The expected signs for the indicators correspond to the main channels through which political cycles and financial crises affect economic activity. For instance, a positive sign in the second column for indicators measuring problems in the current account is consistent with a lower current account surplus (or a higher current account deficit) increasing the chances of a balance of payment crisis and, as a consequence, an output contraction or an increase in 1-p11t. A negative sign for the transition probability p22t of the same indicators implies a higher current account surplus leading to lower chances of a balance of payment crisis and an output contraction.

As shown in Table 2, the expected signs for the coefficients in the transition probabilities p11t and p2t are opposite. Filardo (1994) and Layton (1997b) emphasized that these opposite signs imply an increase in the probability of being in state st=j at time t regardless of the state at time t-1. If an indicator increases and if Φ11 and Φ22 have, respectively, positive and negative signs, then both p11t and p21t=1-p22t increase. The probability of being in state 2 at time t then decreases.

Instead of current indicators in the transition probabilities, we use lagged ones. The assumption is that lagged indicators are uncorrelated with the contemporaneous state. According to Filardo (1999), this is a reasonable assumption as long as information variables are predetermined with respect to the state of the business cycle at time t.12 If this condition is violated, we cannot extend Hamilton’s filtering method to time-varying transition probability models, hence we need to use other methods to find maximum likelihood estimates.

To accommodate autocorrelation in the residuals, we can replace the white noise error term ut with an AR(q) process:

ut=i=1qβiuti+εt,(5)

where q is the number of lags, γt is an error term with a N(0, σ12) distribution if st=1 and N(0, σ22) if st=2. This is equivalent to the following model for the series yt:

ytgst=i=1qβi(ytigsti)+εt.(6)

The parameters g1, g2, σ1, σ2, β1, β2, β2, …, and βq and the elements in vectors Φ1 and Φ2 (all comprised in the vector θ) can be estimated by the filter described in Appendix I.13

V. Results

Appendix I shows how the data set in estimations was constructed. Economic activity in Mexico is proxied by the quarterly industrial production index (seasonally adjusted with a two-sided moving average). This index is plotted in Figure 2 from the first quarter in 1972 through the third quarter in 1999.

Figure 2
Figure 2

Mexico: Industrial Production Index (SA), 1972:Q2–99:Q3 Levels and Growth Rates

Citation: IMF Working Papers 2002, 150; 10.5089/9781451856972.001.A001

Source: IMF, International Financial Statistics.

A simple inspection of Figure 2 illustrates the difficulty in classifying changes in the industrial production index as contractionary or expansionary. Even if some filter eliminates seasonality, classifying observations is still difficult. A negative change in the industrial production index after a sequence of positive changes, for instance, does not necessarily imply a contractionary phase since economic activity might still increase in the next quarter.

The estimated models contain two autoregressive coefficients:

ytgst=β1(yt1gst1)+β2(yt2gst2)+εt(7)

where εt has a N(0, σ2) distribution, and the transition probabilities piit driving changes in regime are:

piit=exp(Φi0+Φi1xt1)1+exp(Φi0+Φi1xt1)(8)

Likelihood ratio statistic tests—not shown in the text—applied to the model with constant transition probabilities led to the choice of two lags for the autoregressive process and only one variance. This simplified version increased the speed at which the GAUSS program converged.

Table 3 reports maximum likelihood estimates for the parameters in the constant and the time-varying transition probability models, their corresponding t-statistics, and the likelihood ratio tests for the null hypothesis that the time-varying transition probability models are not statistically different from the constant ones.14 If an indicator does not contain any information that helps predict business cycles, the coefficients Φ11 and Φ21 in the time-varying transition probabilities are not statistically different from zero and the likelihood ratio statistic test does not reject the null hypothesis that the time-varying model is statistically equivalent to the constant one.

Table 3.

Mexico: Maximum-Likelihood Estimates for a Two-State Regime-Switching Model, 1972:Q2–99:Q3

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Notes:The indicators are: defgdp=public borrowing sector requirement (last 12-months), percentage of GDP (last 12 months), DC=domestic credit, 12-month change as percentage of GDP (last 12 months); multiplier=Money multiplier (M1/base reserve), 12-month percentage change; deposits=bank deposits, percentage of GDP (last 12 months); realint=real interest rate on time deposits; stocks=stock index deflated by CPI, 12-month percentage change, cps=credit to the private sector, percentage of GDP (last 12 months); RER=deviations (two lags) of the real exchange rate (Peso/US$) from its eqilibrium value; imports=imports of goods and services, 12-month percentage change in the last quarter, exports=export5 of goods and services, 12-month percentage change; tot=terms of trade, 12-month percentage change; reserves=reserves, 12-month percentage change; m2res=ratio M2/reserves, 12-month percentage change; sttotaldebt=ratio short-term debt/total external debt, 12-month percentage change; USrealint= U.S. real interest rate; realdif=Mexican-U.S. real interest rate differential; and composite index=first principal component of the fiscal, financial, and external indicators in Table 1;The transition probabilities are equal to: P11t=exp(Φ1011*indicator)/(1+exp(Φ1012*indicator)); p22t=exp(Φ2021*indicator)/(1+exp(Φ2021*indicator)).The critical values for the chi-squared distribution with 2 degrees of freedom, at the 5 percent and 10 percent levels, are equal to 5.99 and 4.60, respectively; andNumbers in parentheses are t-statistics.

For the constant transition probability model, phases of contraction and expansion in Mexico are asymmetric. In times of expansion industrial production grows at average rate of 0.7 percent per quarter. In periods of contraction industrial production decreases at the average rate of 1.2 percent per quarter. Recessions are thus deeper than expansions. The estimates for the constant transition probabilities p11 and P22 are equal to 0.94 and 0.65, respectively, and are plotted as straight lines in the first panel of Figure 3. These values for the transition probabilities imply higher degree of reversion from a recession to an expansion (p21=1-0.65=0.35) than vice-versa (p12=1-0.94=0.06). In addition, the expected duration of expansions in Mexico is:

(1p11)1=(10.94)1=16.6 quarters,(9)
Figure 3.
Figure 3.

Mexico: Constant and Time-varying Transition Probabilies pllt and p22t for the Indicator Reserves and the Composite Index, 1972:Q2–93:Q3

Citation: IMF Working Papers 2002, 150; 10.5089/9781451856972.001.A001

Note: The indicators are: reserves=reserves, 12-month % change; and composite index= first principal component of the fiscal, financial, and external indicators in Table 1.The transition probabilities are computed as:P11t=exp(Φ1011*indicator)/(1+exp(Φ1012*indicator)) andp22t=exp(Φ2021*indicator)/(1+exp(Φ2021*indicator)).

while the expected duration of contractions is:

(1p22)1=(10.66)1=2.94 quarters.(10)

Figure 4 plots smoothed probabilities for state 1 or the expansionary state. Smoothed probabilities represent “the smoothed inference about the regime process was in at date t based on data obtained through some later date T.”15 If expansion is defined as a period when smoothed probabilities exceed 0.5 as in Hamilton (1989), then we can use these probabilities to construct a business cycle chronology in Mexico and compare it with other chronologies. Table 4 reports those comparisons.

Figure 4.
Figure 4.

Mexico: Smoothed Probabilies for the Expansionary State, Computed with Constant and Time-varying Transition Probabilities (TVTP) for the Indicator Reserves and the Composite Index, 1972:Q2–93:Q3

Citation: IMF Working Papers 2002, 150; 10.5089/9781451856972.001.A001

Note: The indicators are: reserves=reserves, 12-month % change; and composite index=first principal component of the fiscal, financial, and external indicators in Table 1.
Table 4.

Mexico: Turning Points in Business Cycles

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Source: Phillips, Vargas, and Zarnowitz (1996) and Figure 3.Note: The indicators are: reserves=reserves, 12-month percent change; and composite index=first principal component of the fiscal, financial, and external indicators in Table 1.

The first two columns in Table 4 contain peaks and troughs in business cycles computed by the Federal Reserve Bank of Dallas (FRBD) and by the Center for International Business Cycle Research (CIBCR) and reported in Phillips, Vargas, and Zarnowitz (1996). We obtain the other columns by identifying the turning points in the smoothed probabilities for state 1 in Figure 4. The economy would be in an expansionary (recessionary) phase only when the smoothed probabilities for state 1 are greater than 0.5 (less than 0.5) for at least 2 quarters as in Layton (1996).16 We observe that the chronology using the constant transition probabilities resembles the ones computed by the FRBD and the CIBCR. The only exceptions are the peak and the trough in the third quarters of 1993 and 1994, respectively.17 Our univariate approach to business cycles thus performs well in terms of characterizing the inflection points of business cycles when compared to the results in Phillips, Vargas, and Zarnowitz (1996).

We then ask the following question: if business cycles in Mexico follow political cycles and financial crises, can fiscal, financial, and external sector indicators that track vulnerabilities in the external and banking sectors help us to obtain more precise characterizations of business cycles? We use the time-varying regime-switching econometric model in Filardo (1994) to answer this question. Table 3, column 2 tol9, reports our results from estimations using our fiscal, financial, and external sector indicators. For the fiscal and financial indicators, the coefficients Φ11 and Φ21 are not statistically different from zero at the 5 percent level. In addition, likelihood ratio tests do not reject the null hypothesis that time-varying transition probability models with fiscal and financial indicators are equivalent to the model with constant transition probabilities. Thus, individually, our fiscal and financial indicators do not contain information that helps to characterize business cycles.

Inappropriate fiscal and financial indicators could be the cause of these weak results. Other financial and fiscal indicators may do a better job. In addition, it is rather surprising that financial indicators do not convey any information. In Mexico, asymmetric information and adverse selection problems increased after the 1990 stabilization and the following financial liberalization. The result was a financial boom, with excessive risk-taking by banks. The lending boom turned into loan losses and a deterioration of banks’ balance sheets, with the consequent constraint on banks’ ability to lend.

On the other hand, one external sector indicator, namely changes in the foreign exchange reserves, does perform well. The other external sector indicators do not add any statistically relevant information and the loglikelihood ratio statistics for these indicators do not reject the null hypothesis that the models with these indicators in the transition probabilities are equivalent to the model with constant transition probabilities. The coefficients Φ11 and Φ21 for reserves have the positive and negative signs, respectively. This implies that if foreign exchange reserves increase, the risk of currency crises decreases and the probability that the economy will remain in the expansionary state in the next period increases.

The composite index with our fiscal, financial, and external indicators contains as much information as reserves. The estimated signs for the coefficients Φ11 and Φ21 are negative and positive, respectively. An increase in the composite indicator leads to a decrease in the probabilities p11t, and 1-p22t. If the Mexican economy is in expansion at time t-1 and signs of a currency and banking crisis develop, the probability that the economy will remain in the expansionary state at time t decreases, while the probability of the economy entering a contractionary state increases.

Time-varying transition probabilities for the foreign exchange reserves indicator and the composite index are plotted in Figure 3. The time-varying transition probability p11t for both indicators shows some downward spikes, which roughly correspond to the periods of crises in September 1976, February 1982, December 1984, and December 1994. The transition probability p22t for reserves does not vary as much as the probability p11t in the period from the second quarter of 1972 to the third quarter of 1999. However, for the composite index indicator, the transition probability p22t is close to zero in the third quarter of 1987. This implies that the expansionary state is an absorbing state in the sense that the set of possible states for the next period does not include the recessionary state.

The chronologies generated by the time-varying transition probabilities with reserves and the composite index are also similar to the FRBD and the CIBCR. With the exception of the third quarter of 1993 and 1994, the number of peaks and troughs in the time-varying transition probabilities chronology is the same as in the FRBD and the CIBCR chronologies. However, the turning points are slightly different, with either a lead or a lag of one quarter. Yet, according to Figure 4, smoothed probabilities for the expansionary state in the first and second quarter of 1993 are around 60 percent for the composite index, a drop from the 99 percent level in the previous quarters. This is a sign of a mild recession in those two quarters.

Comparing our results with other econometric methodologies shows that, as pointed in Diebold and Rudebusch (1996), only regime-switching models provide the framework where the concept of turning points is meaningful. Acevedo and others (2001) identified the permanent and cyclical components of growth cycles in Mexico using the Hodrick-Prescott filter and structural vector autoregressions. Their estimates of the potential real GDP and output gap led to the periods of expansion from 1980:Q1 to 1982:Q2 and from 1991:Q1 to 1994:Q1, when average actual real GDP growth exceeded potential real GDP by 1.7 and three-fourths of a percentage point, respectively. Since the output gap measures the difference between actual and potential real GDP growth rates, both negative and small positive values for actual GDP growth rate imply fewer periods of expansion than the ones computed with regime switching models.

To assess the marginal contribution of the time-varying transition probabilities, Filardo (1994) suggested the weighted transition probabilities. These weighted transition probabilities take into account the fact that the time variation for p11t=p(st=1|st-1=1, xt) or p11t=p(st=2|st-1=2, xt) is only important when the previous state in the economy is st-1=1 or st-1=2. In addition, they also subtract the mean of the transition probabilities since we are only interested in the marginal contribution of the time varying transition probabilities. For p11t, the weighted transition probability then is:

WTP(p11t)=(p11tp¯)p(st1=1|It2,xt1),(11)

where p(st-1=1|It-2, xt-1) is the regime probability of being in state 1 at time t-1; and for p22t, the weighted transition probability is:

WTP(p22t)=(p22tp¯)p(st1=2|It2,xt1),(12)

where p(st-1=1|It-2, xt-1) is the regime probability of being in state 2 at time t-1.18

Figure 5 plots the weighted transition probabilities for both reserves and the composite index. The marginal contribution of time-varying transition probabilities is the deviations from zero. Spikes in the weighted transition probability WTP(p11t) for both reserves and the composite index correspond to the peaks in Table 4. On the other hand, the spikes in the weighted transition probability WTP(p22t) are only clear for the composite index. Therefore, Figure 5 provides evidence that reserves and a combination of fiscal, financial, and external sector indicators do contain helpful information about Mexican business cycles.

Figure 5.
Figure 5.

Mexico: Weighted Transition Probabilities WTP(pllt) and WTP(p22t) for the Indicator Reserves and the Composite Index, 1972:Q2–99:Q3

Citation: IMF Working Papers 2002, 150; 10.5089/9781451856972.001.A001

Source: Figure 3Note: The indicators are: reserves=reserves, 12-month % change; and composite index=first principal component of the fiscal, financial, and external indicators in Table 1.

VI. Conclusions

We use the regime-switching econometric methodology to analyze Mexican business cycles from 1972 to 1999. Specifically, we estimated constant and time-varying transition probability models as in Hamilton (1989) and Filardo (1994), respectively. For the time-varying transition probability model, we allowed the transition probabilities to be a function of fiscal, financial, and external sector indicators.

We obtained interesting results. First, estimates for the positive and negative industrial production growth rates in all models show deeper recessions than expansions in Mexico.

However, for the model with constant transition probabilities, estimates for these probabilities show that recessions are shorter than expansions. Second, the Mexican economy moved from an expansion to a recession in 1982, 1985–86, and 1994 and from a recession to an expansion in 1983, 1986, and 1995. This chronology of expansions and recessions closely resembled the results of other researchers.19 Finally, our smoothed probabilities did capture the inflection points in business cycles, except in the third quarters of 1993 and 1994

APPENDIX I

Mexico: Data Sources, 1972:Q2–99:Q3

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APPENDIX II

Maximum Likelihood Estimation of Regime-Switching Models

The parameters g1, g2, Φ1, Φ2, N1, N2, N3,… Nq, and the elements in vectors M11 and M22 (all comprised in the vector 2) can be estimated by the filter described in Hamilton (1994):

(i) the joint density function of yt and st is computed by multiplying the conditional density of yt by the filter probabilities:

f(yt,st,,stq|It1,xt;θ)=f(yt|st,,stq,It1;θ).p(st,,stq,|It1,xt;θ)(13)

where It-1 is the information set at time t-1 and the conditional density function f(yt|st,…, st-q,It-1; 2) is the Normal distribution:

f(yt|st,,stq,It1;θ)=12πσst2exp((ytgsti=1qβi(ytigst1))22σst2)(14)

(ii) the sum of the joint density functions over all states st yields the unconditional density function of yt:

f(yt|It1,xt;θ)=Σst=12Σst1=12Σstq=12f(yt,st,,stq|It1,xt;θ)(15)

(iii) to update filter probabilities, the following Bayesian rule is used:

p(st,,stq|It;θ)=f(yt,st,,stq|It1,xt;θ)f(yt|It1,xt;θ)(16)

(iv) finally, filter probabilities at time t+1 are obtained by multiplying the updated probability p(st,…,st-q|It; 2) by the transition probability p(st+1|st, xt+1):

p(st+1,st,,stq|It,xt+1;θ)=p(st+1|st,xt+1).p(st,,stq|It;θ)(17)

where:

p(st+1|st,xt+1)=exp(xt+1.Φstst+1)1+exp(xt+1.Φstst+1)(18)

and then summing over st-q:

p(st+1,,stq+1)|It,xt+1;θ)=stq=12p(st+1,,stq|It,xt+1;θ)(19)

Our exogenous information variables are assumed to be uncorrelated with the contemporaneous state. Violation of this condition implies that Hamilton’s filtering method cannot be extended to time-varying transition probability models, hence other methods need to be used.

As a by-product of steps (i) and (ii), the sample log-likelihood can be computed:

L(θ)=t=1Tlog(f(yt|It1,xt;θ))(20)

To minimize the number of multiple solutions - that is, the number of local maxima - extra terms that represent prior information about the means gk and variances Φk are added to the log-likelihood function as in Hamilton (1991):

L(θ)=t=1Tlog(f(yt|It1,xt,θ))k=12(ak/2)logσk2k=12bk/(2σk2)k=12ck(mkgk)/(2σk2)(21)

where mk is the prior expectation for gk, the ratio bk/ak is the prior for Φk, and the parameters ak and ck are the weights placed on priors.

Given the last regime probabilities p(sT|IT;2), smoothed probabilities are obtained through the following algorithm:

P(st|IT;θ)=P(st|It;θ)[P[P(st+1|It)(÷)P(st+1|It)]](22)

where P(.|.) stands for a (2x1) vector of filter or smoothed probabilities and where the symbols θ and 0) stand for the multiplication and division of element by element in the vectors, respectively.

APPENDIX III

Estimation of the Deviations of the Real Exchange Rate from Its Equilibrium Value

This appendix estimates deviations of the real exchange rate from its equilibrium value and is based on Dabós and Juan-Ramón (2000). They suggested the following econometric model:

RERXt=β0+β1kyt+β2ETTt+β3PROt+ut,(23)

where RERX is the log of the relative price of exports to consumer prices; ky is ratio of the net capital flow to GDP; ETT is the log of the external terms of trade; and PRO is a trend variable that captures increases in productivity.

Table A1.

Mexico: Aumented Dickey-Fuller (ADF) Test for the Oder of Integreation of the Relative Price of Exports to Consumer Price, the Ratio of Net Capital Inflows to Gross Domstic Product, and Terms of Trade, 1971 :Q3-99:Q2

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Source: Dabós and Juan-Ramón (2000).

Table A.1 shows Augmented Dickey-Fuller tests applied on RERX and ETT. We reject the null hypothesis that these series are integrated of order 2, I(2), at the 5 percent level. These tests still reveal that both variables are integrated of order one, I(1). Then, there might exist a linear cointegration among them that is stationary and yields I(0) residuals.

As in Dabós and Juan-Ramón (2000), we use the Engle and Granger (1987) methodology to test for a long-run relationship. First, we regress RERX on ky, ETT, and PRO. Table A4.2 shows parameter estimates for this regression. Then, we apply the Augmented Dickey-Fuller test on the residuals of the regression. Table A4.3 shows our results of the latter test. We reject the null hypothesis that our regression residuals contain a unit root. This implies a stationary long-run relationship between RERX, ky, ETT, and PRO.

Table A2.

Mexico: Regression Estimates for the Equihbrium Real Exchange Rate Model, 1971 :Q3-99:Q2

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Source: Dabós and Juan-Ramón (2000).
Table A3.

Mexico: Alimented Dickey-Fuller (ADF) Test for the Order of Integration of the Estimated Residuals in the Equation for the Equilibrium Real Exchange Rate, 1971:Q3-99:Q2

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Source: Dabós and Juan-Ramón (2000).

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1

The author, currently Economist in the IMF Institute, thanks Pablo Cordoba, Enzo Croce, Andrew Feltenstein, Hugo Juan-Ramón, Eliot Kalter, Sunil Sharma, Reza Vaez-Zadeh, and seminar participants at the IMF Institute for helpful comments on an earlier draft of this paper.

2

See Hoffrnaister and Roldos (1997) and Agénor, McDermott, and Prasad (1999) for a general characterization of business cycles in developing countries. See Acevedo and others (2001) for a characterization of Mexican business cycles using the HP filter, the unobservable components method, and a structural VAR with annual and quarterly real GDP data. See Mejía-Reyes (2000) for another characterization of Mexican business cycles using a regime-switching model with annual real GDP data. The latter researcher found that Mexican business cycles are asymmetrical, as we also found.

3

Mexican business cycles can also be connected to U.S. business cycles and to terms-of-trade shocks. Our set of fiscal, financial, and external sector variables is broad enough to include variables that are related to different sources of Mexican business cycles.

6

See Appendix I for data sources.

7

See Kakkar (2001) for another approach to the estimation of the equilibrium real exchange rate in Mexico.

8

Composite indexes of leading and coincident indicators of business cycles in Mexico are available in the web page dgcnesyp.inegi.gob.mx/bie.html-ssi.

9

Factor loadings are the ordinary least squares coefficients obtained from a regression of each fiscal, financial, and external sector indicator on the first principal component. See Theil (1971), pp. 46–56.

10

Kaminsky and Reinhart (1999) has a chronology of currency and banking crises for a selected group of countries.

11

For a summary on this literature, see Hamilton (1994), Chapter 23.

12

For further details, see Filardo (1999).

13
To minimize the problem of multiple local maxima, extra terms representing prior information about the means gk and variances σk are added to the log-likelihood function above as in Hamilton (1991):
L(θ)=t=1Tlog(f(yt|It1,xt;θ))k=12(ak/2)logσk2k=12bk/(2σk2)k=12ck(mkgk)/(2σk2)

where mk is the prior expectation for gk, the ratio bk/ak is the prior for σk, and the parameters ak and ck are the weights placed on priors. Values for the priors used in estimations are ak=0.2, bk=1, ck=0.1, and mk=0.

14

We undertake the estimations of the many statistical models in this section with GAUSS. The GAUSS code implemented for the estimations is a modified version of the routines maxseek and procs provided by James Hamilton. These routines incorporate changes to allow time-varying transition probabilities. The algorithm used for maximization of the likelihood function is BFGS. We perform about 1,400 estimations with different initial parameters for each model. The reported estimates in Table 5 correspond to the local maxima with the highest likelihood.

15

Hamilton (1994), p. 694. For further details, see Appendix II.

16

Layton (1996) used monthly data. His criterion for defining a contraction was that if at least five of the smoothed probabilities in a row were less than 0.5. The translation of this monthly criterion into a quarterly criterion corresponds to at least two of the smoothed probabilities in a row being less than 0.5.

17

Henriques, Sadorsky, and Verma (1998) reported that the 1993 recession in Mexico was different from the others because it was caused by a slowdown in natural resource intensive sectors.

19

In particular, the results resembled the ones by the Federal Reserve Bank of Dallas (FRBD) and by the Center for International Business Cycle Research (CIBCR) and reported in Phillips, Vargas, and Zarnowitz (1996).

Are Mexican Business Cycles Asymmetrical?
Author: Mr. Andre O Santos
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    Mexico: Composite Index of Vulnerabilities in the Balance of Payments and the Banking Sector, 1972:Q2-99:Q3

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    Mexico: Industrial Production Index (SA), 1972:Q2–99:Q3 Levels and Growth Rates

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    Mexico: Constant and Time-varying Transition Probabilies pllt and p22t for the Indicator Reserves and the Composite Index, 1972:Q2–93:Q3

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    Mexico: Smoothed Probabilies for the Expansionary State, Computed with Constant and Time-varying Transition Probabilities (TVTP) for the Indicator Reserves and the Composite Index, 1972:Q2–93:Q3

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    Mexico: Weighted Transition Probabilities WTP(pllt) and WTP(p22t) for the Indicator Reserves and the Composite Index, 1972:Q2–99:Q3