Abstract
This paper focuses on the Mexican economy, its output fluctuations, and analyzes the country's external competitiveness in the context of medium-term external current account sustainability. The study also presents different measures of the fiscal deficit, including the traditional budget balance, and reviews measures on the fiscal stance and fiscal impulse. It examines the evolving relationship between inflation and the exchange rate, using fixed and time-varying coefficient models. The paper describes the methodology, provides the rationale for estimating time-varying parameter models, and presents the estimation results.
I. Potential GDP in Mexico1
A. Introduction
1. In most countries, over a sufficiently long time period, economic growth shows two distinct characteristics—a stable, upward trend in output and some variation in output around that trend. In Mexico, these features are also present, although the fluctuations have on occasion been so pronounced that they have jeopardized the sustainability of growth. Thus, the identification of the distortions that generate such deviations from trend is central to designing an appropriate macroeconomic policy framework.
2. The characterization of policies as either procyclical or counter cyclical depends on the stage of the business cycle in which the economy finds itself. For example, a restrictive monetary policy would be considered procyclical in a phase of decelerating growth since it would accentuate the contraction in aggregate demand. In contrast, the same policy would be considered counter cyclical in an expansion phase, as it would tend to attenuate the expansion in aggregate demand.
3. The importance of knowing with precision the phase and characteristics of the business cycle of an economy has motivated various lines of research in the literature. The first systematic study of the business cycle was that of Burns and Mitchell (1946). They treated each cycle as a separate episode, which had an expansion phase, in which the economy moved from a “valley” to a “peak,” and a contraction phase, in which the economy moved from a peak to a valley. The business cycle was then characterized by the average length of its expansion and contraction phases, the amplitude of its fluctuations, and by the behavior of other economic variables over the cycle period.
4. Burns and Mitchell defined a recession for the U.S. economy as an episode in which there was a substantial decline in economic activity for a representative group of productive sectors that lasted more than three consecutive months. This definition was later refined, giving rise to the empirical rule of thumb that a recession exists when economic growth is negative for two consecutive quarters.
5. The methodology of Burns and Mitchell was eventually discarded because it was considered subjective and because the data series that it generated did not have sufficiently well defined statistical properties. Currently, the analysis of economic fluctuations assumes that the variables follow a linear stochastic process with constant coefficients. This new focus has permitted a greater integration of macroeconomic and econometric theory.
6. The Keynesian approach, and later the monetarist approach, became the principal theoretical models for the design of economic policies aimed at affecting the evolution of economic variables, and hence their fluctuations. Assuming that monetary and fiscal authorities could influence the interaction of economic agents, the volatility of economic activity could be reduced, while its growth rate could be boosted. The existence of market imperfections is another argument, developed more recently, to justify active policy intervention.
7. Although the macroeconomic theory developed in the context of these models justified the use of procyclical and counter cyclical policies to limit the negative effects of economic volatility, Prescott (1986) indicated that the authorities’ capacity to influence such effects was minimal. His work suggested that economic fluctuations in the industrial countries existed principally because of random disturbances to total factor productivity.2 The most striking point made by Prescott was the irrelevance of certain counter cyclical policies since, according to the evidence, the characteristics of the observed fluctuations of the U.S. economy would not have been significantly different in the absence of such policies. Furthermore, according to Prescott, the cost of implementing such policies, on more than one occasion, had been greater than the benefits.3
8. Prescott’s work stirred an important debate about the nature and effects that random disturbances have on output growth, including the search for better ways to measure such effects. In the last 20 years, a number of econometric techniques have been formulated to identify separately the cyclical and permanent components of economic series. Such a decomposition enables identification of the characteristics of economic fluctuations and, at the same time, evaluation of the efficacy of economic policies.4
9. This paper will focus on the Mexican economy, which has seen important output fluctuations, whose characteristics and determinants merit further research. Real GDP growth averaged nearly 7 percent during 1950-81, a period of over 30 years. Following the debt crisis of the early 1980s, there was a distinct downward shift in the growth rate, with real GDP growth averaging a mere 1.3 percent during 1982-95, a period which saw a variety of internal and external shocks.5 The high degree of fluctuations experienced in the past complicate the estimation of potential output growth in Mexico. The identification of permanent and cyclical components of growth cycles is central to this exercise. Knowing potential output growth, and the stage of the cycle, are two important pieces of information that policymakers require in designing the appropriate stance of monetary and fiscal policies.
10. The econometric techniques presented in this paper aim at decomposing the GDP6 series in a statistically efficient manner. In this context, given an estimate of the magnitude of output fluctuations, the paper also aims at relating the business cycle to other economic variables. The paper aims at identifying key links between policies and economic variables in order to be able to consolidate the benefits of economic expansions, offset the negative effects of contraction phases, and more broadly, contribute to the design of policies that lay the foundations for sustainable growth.
11. It should be noted that some of the econometric techniques employed in this paper assume certain theoretical properties that may not fully exist in the Mexican economy such as full information and completeness of markets. Nonetheless, the results obtained appear to be quite robust. Thus, the exercise described in this paper should contribute to a better understanding of potential output growth in Mexico.
12. This chapter describes various econometric procedures and different analytic specifications to determine the characteristics of a time series and decompose it into its cyclical and trend components. The chapter is structured as follows. Section B provides a description of the general procedures used to extract the various components of the real GDP series. Section C summarizes the estimation results of the cyclical and permanent components of GDP and compares the results obtained through the various procedures. A key result is that the magnitude of potential GDP growth and the output gap was similar under two out of the three methodologies employed. Section D concludes.
B. Techniques to Estimate Potential GDP and the Output Gap
13. A number of analytical tools exist that help to identify business cycle traits. In particular, the deviations from trend observed during contraction and expansion phases have been classified according to various criteria,7 in order to not only identify those policies needed for sound growth, but also those policies needed to deal with various contingencies.
14. A by-product of estimating the characteristics of business cycles is the ability to identify the excess demand, or output gap, in any given time period. The output gap measures the difference between actual and potential output, both in log terms. In this manner, the rate of long-term sustainable growth, consistent with the availability of technological and productive factors, can be estimated. The existence of an output gap, either positive or negative, implies an allocation of resources that is not efficient and can generate market distortions.
15. Burns and Mitchell argued that there is a deterministic decomposition of GDP, with which certain indicators of GDP can be identified. This analysis gave rise to the one of the most commonly used techniques for forecasting economic cycles—the study of leading indicators. However, the work of Nelson and Plosser (1982) showed the advantage of examining stochastic trends in time series to identify their characteristics. Consequently, much research has been aimed at establishing techniques that rely on the consistency between the theoretically predicted economic properties of time series and the time series properties obtained through a stochastic decomposition.8
16. Given that the business cycle can behave in a myriad of ways, including exhibiting high volatility, it is difficult to formulate techniques that identify adequately all of its characteristics and, at the same time, satisfy the conditions of a stochastic decomposition. However, since the properties of the permanent component of a time series tend to be more homogeneous, most techniques focus on identifying the trend component and obtain the cyclical component as a residual.
17. Traditionally, two types of models have been used to estimate potential GDP. One type defines potential output as the level of production that would be observed if the economy were at its natural rate of unemployment.9 Potential output is then usually determined on the basis of estimates of production functions.
18. The second type of model is based on the assumption that the behavior of the permanent component of GDP is influenced primarily by exogenous shocks that affect aggregate supply and thus determine the magnitude of the deviation between potential and observed GDP. In this model, the business cycle is not necessarily due to changes in aggregate demand or to the path of certain variables that could affect the productive capacity of the economy. Instead, the business cycle is a function of the decisions taken by economic agents regarding the optimal allocation of resources each time there is an unexpected productivity shock.
19. The latter type of model identifies potential output as synonymous with trend output, which is estimated based on the observed GDP time series. The key challenge is to formulate techniques that permit the identification of temporary versus permanent shocks.
20. In practice, few procedures can be classified as falling solely under one or the other of the above strands of models, but instead have elements of both. Deficiencies in the satisfactory identification of the components, as well as the sensitivity of the results to the estimation technique, have motivated a number of hybrid experiments. These experiments, to a greater or lesser degree, incorporate certain restrictions implied by the economic models. In the remainder of this section, the qualitative characteristics of the main procedures found in the literature are described.
The Hodrick-Prescott filter
21. The HP filter10 (Hodrick and Prescott, 1997) is a technique for smoothing time series that identifies the permanent component of a series through the solution of the following procedure:11
{y*t} = argmin Σ (yt-y*t)2+λ Σ [(y*t+1-y*t)-(y*t-y*t-1)]2
where λ determines the degree of smoothing of the permanent component, and yt and y*t represent current and potential output, respectively.12 Hodrick and Prescott propose values for λ of 100, 1600, and 14400 for data with annual, quarterly, and monthly frequencies.
22. The HP filter is linear in two stages. In the first stage, the series is differenced, and in the second stage it is smoothed. The technique uses information related to the behavior of those fluctuations lasting between 6 and 32 quarters, which are consistent with the definition of the business cycle proposed by Burns and Mitchell.
23. One shortcoming of the HP filter is that the choice of the parameter λ often is not well related to the characteristics of the time series to be decomposed.13 Another shortcoming of the HP filter is related to the distortions in the filter at the endpoints of the sample. Owing to the initial and ending conditions imposed by the filtering process, the HP filter tends to dampen the endpoints in the series being detrended and not capture the full effects of permanent shocks resulting from recent structural reforms (such as the implementation of NAFTA beginning in 1994).
24. Finally, some authors have argued against the use of an HP filter because it does a poor job of replicating the properties of an ideal filter in small samples. It should also be noted that even if the HP were to perform as an ideal filter does, if the characteristics of the series’ spectrum are similar to those identified by Granger (1966), then the behavior of any filter (high-pass or band-pass) is technically poor.
The method of nonobservable components
25. This method attempts to measure nonobservable components, such as potential output or the NAIRU (non-accelerating inflation rate of unemployment), based on a set of observable variables and the implied relationships that help to identify the former components. The representation used to designate dynamic processes, known as “state-space,” allows for very general, but explicit specifications to model a wide variety of such processes.
26. A popular decomposition process that relies on nonobservable components techniques is that proposed by Beveridge and Nelson (1981). This specification assumes that potential output is a nonobservable variable that can be characterized by a pair of components. The first component has a random walk with drift, intended to capture the long-run trend of GDP. The second component is characterized by a stationary autoregressive process, and provides information about the persistence of short-run fluctuations of GDP.
27. The characteristics of the decomposition proposed by Beveridge and Nelson depend, to a large extent, on the goodness of fit the ARIMA can obtain. In GDP series, which are usually integrated of order one, the ARIMA specification has minimal capacity to forecast output fluctuations. This is because of the use of partial information (only past growth rates of GDP are considered) to characterize fluctuations. The ARIMA specification tends to indicate relatively small magnitude business cycles, which are very sensitive to the addition of new information.
28. Watson (1986) and Quah (1992), among others, have criticized the use of the above decomposition, because it imposes characteristics on the cyclical and permanent components that are not corroborated under other specifications, or that are not in concordance with the theoretical implications of the real business-cycle literature.
29. Univariate nonobservable components techniques exist which yield a decomposition that allows for the independence between the cyclical and permanent components.14 This allows the identification of distinct shocks that might affect only one of the components, which is not possible in the BN model.
30. The use of multivariate nonobservable components techniques has made it easier to estimate simultaneous economic relationships (Rotemberg and Woodford, 1996).15 A specific example of the use of such a technique is the estimation of potential output and the NAIRU through a system of simultaneous equations that defines the relationship between Okun’s Law and the Phillips Curve.
Structural vector autoregressions
31. This method has its theoretical groundings in a synthesis of Keynesian and neoclassical models presented at the outset of this chapter. Blanchard and Quah (1989) associate supply shocks with permanent effects on trend GDP, while demand shocks are associated with temporary deviations from trend.
32. Vector autoregressions (VARs) are used to estimate the components of series. VARs, introduced by Sims (1980), have been described as atheoretical since they do not impose any theoretical restriction on the estimation process. However, Blanchard and Quah suggest a structure for VARs that depends on long-term restrictions in the variance-covariance matrix. These restrictions assume limits on the extent of shocks and their effects on each of the variables in the vector. For instance, the estimation presented in this paper assumes that shocks related to demand have only a short-term effect, so that the covariance between output and money errors is zero if they are further than six quarters away from each other.
33. DeSerres, Guay and St. Amant (1995) have estimated the permanent component of GDP for Mexico. This study explicitly identifies the effects of changes in the money supply and oil prices on potential output, and also finds that the variability of oil prices is an important source of changes in the long-run trend of potential output.
34. The DGS study assumes that real GDP growth (Δy), changes in the price of oil (Δo), and changes in the monetary base (Δm), are all stationary stochastic processes that respond to three types of contemporary orthogonal innovations: supply shocks (εs), oil price shocks (ε0), and demand shocks (εd). The moving average representation of the model is:
where εt = [εs εo εd]’ and Δxt = [ΔytΔotΔmt]’
35. In order to estimate the structural model, first the reduced form of the VAR is estimated. The residuals depend on the innovations in equation (1) as follows:
et = A0εt
which implies the following:
E(ete’t) = A0E(εtε’t)A0’
and permits setting the long-run restrictions that each of the innovations in the variance-covariance matrix must meet.
36. The main problem encountered when using the above methodology is the identification of those shocks, which because of their nature, have simultaneous effects on the short- and long-run structure of the model.
Production functions
37. In general, this methodology is based on a production function with two factors, capital and labor. Traditionally, production functions have relied on the Cobb-Douglas specification, even though other specifications, such as CES and TRANSLOG, can often provide richer results.16
38. In order to estimate potential GDP, total factor productivity is assumed to be decomposable into two parts: 1) trend growth that represents the deterministic (non-stochastic) growth of productivity; and 2) a stochastic component that describes the variations of output from trend.
39. In contrast to the other methodologies, production functions allow for an explicit identification of the determinants of potential output. However, the main disadvantages stem from the oversimplification of the production technology, and the statistical deficiencies that may exist in supporting estimates. In particular, reliable series on the stock of capital or the NAIRU for the Mexican economy do not exist. Therefore, this methodology will not be used in this chapter.
C. Estimates of Potential GDP and the Output Gap
Annual estimates
40. Annual data on real GDP for Mexico are available starting in 1900. However, because of the Revolutionary War, the series is missing almost a decade’s worth of data. Thus, a usable sample starts in 1921. Furthermore, the System of National Accounts has kept a record of only a limited number of economic variables for an extended period of time. This has impeded the use of econometric techniques that rely on information about prices, demand, and production-related variables before 1980. This lack of data limits the techniques that can be used—in this chapter, only the HP filter is applied to the annual data.
41. Figures 1 and 2 show observed and potential GDP (log levels and percentage change) from 1921 to 2001.17
Mexico: Observed and Potential GDP
(Log valus of GDP in billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(Log valus of GDP in billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(Log valus of GDP in billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(Percentage change)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(Percentage change)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(Percentage change)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
42. Three distinct growth episodes can be identified. Period 1, 1921-35, shows a low annual average growth rate for potential output of 0.7 percent. Period 2, 1936-81, represents a stage of relatively high growth rates, with potential GDP growth averaging 5.7 percent a year. Period 3, 1982-2000, including the debt-crisis of the early 1980s and the most recent economic and financial crisis of 1994-95, shows an average annual growth of potential GDP of only 2.8 percent.
43. Structural breaks in the production capacity of the economy were found at the beginning of periods 2 and 3 (1936-81 and 1982-2000). GDP log differences were run against an ARIMA process and dummy variables for those periods. An econometric specification was obtained that maximizes the likelihood function and yields independent and normal errors. The limitations of structural break tests applied to series such as the ones used in this paper are discussed in the concluding section.
44. The output gap is shown in Figure 3. During 1936-81, actual GDP fluctuated around its potential within a range of+/- 4 percent, except in the early 1980s, when the gap averaged 8.5 percent. Such a large gap was not sustainable, and ultimately led to a reduction in potential GDP. This is an indication that excessively large or long-lasting gaps can ultimately derail economic stability.
Mexico: Ouptul GDP
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Ouptul GDP
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Ouptul GDP
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Quarterly estimates
45. The permanent component of Mexican GDP, obtained using the HP filter, and the implicit output gap, are shown in Figures 4 and 5.
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Output Gap
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Output Gap
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Output Gap
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
46. The estimated annual growth rate of potential GDP, after extending the sample,18 is 2.7 percent in the 1980-2000 period. Two episodes of continuous growth can be observed. The first one runs from 1980QI to 1982QII, with a positive output gap (actual output exceeding potential output) of 4.2 percent, on average. During this period, Mexico attained its highest level of investment in the last 20 years (26.7 percent of GDP) (Table 1). The external current account deficit averaged 4.7 percent of GDP over the same period. These data indicate the level of physical investment and financial resources that are required to sustain an output gap of that magnitude.
Mexico: Potential GDP and Related Indicators, 1980–82
Mexico: Potential GDP and Related Indicators, 1980–82
| Q1-Q2 | ||||
|---|---|---|---|---|
| Indicator | 1980 | 1981 | 1982 | Average |
| GDP growth | 8.8 | 8.5 | 1.8 | 6.4 |
| Potential GDP growth | 5.6 | 5.0 | 3.5 | 4.7 |
| Output gap | 2.5 | 5.7 | 4.4 | 4.2 |
| Inflation | 29.8 | 28.7 | 49.5 | 36.0 |
| Current account balance (in percent of GDP) | -5.0 | -6.1 | -2.9 | -4.7 |
| Investment (in percent of GDP) | 26.5 | 28.5 | 25.0 | 26.7 |
Mexico: Potential GDP and Related Indicators, 1980–82
| Q1-Q2 | ||||
|---|---|---|---|---|
| Indicator | 1980 | 1981 | 1982 | Average |
| GDP growth | 8.8 | 8.5 | 1.8 | 6.4 |
| Potential GDP growth | 5.6 | 5.0 | 3.5 | 4.7 |
| Output gap | 2.5 | 5.7 | 4.4 | 4.2 |
| Inflation | 29.8 | 28.7 | 49.5 | 36.0 |
| Current account balance (in percent of GDP) | -5.0 | -6.1 | -2.9 | -4.7 |
| Investment (in percent of GDP) | 26.5 | 28.5 | 25.0 | 26.7 |
47. In the second period of continuous expansion, 1991QI-1994Q4, the average gap was 2.0 percent. Investment was kept at a relatively moderate level (21.1 percent of GDP). Nevertheless, foreign financing (opposite sign to the current account balance) reached a historical high of 7.0 percent of GDP for 1994 and averaged 6.0 percent of GDP for the four-year period. Related indicators are shown in Table 2.
Mexico: Potential GDP and Related Indicators, 1991–94
Mexico: Potential GDP and Related Indicators, 1991–94
| Indicator | 1991 | 1992 | 1993 | 1994 | Average |
|---|---|---|---|---|---|
| GDP growth | 4.2 | 3.5 | 1.9 | 4.5 | 3.5 |
| Potential GDP growth | 3.4 | 3.1 | 2.3 | 2.6 | 2.8 |
| Output gap | 1.4 | 1.9 | 1.2 | 3.3 | 2.0 |
| Inflation | 18.8 | 11.9 | 8.0 | 7.1 | 11.5 |
| Current account balance (in percent of GDP) | -4.6 | -6.7 | -5.8 | -7.0 | -6.0 |
| Investment (in percent of (GDP) | 19.8 | 21.6 | 21.0 | 22.2 | 21.1 |
Mexico: Potential GDP and Related Indicators, 1991–94
| Indicator | 1991 | 1992 | 1993 | 1994 | Average |
|---|---|---|---|---|---|
| GDP growth | 4.2 | 3.5 | 1.9 | 4.5 | 3.5 |
| Potential GDP growth | 3.4 | 3.1 | 2.3 | 2.6 | 2.8 |
| Output gap | 1.4 | 1.9 | 1.2 | 3.3 | 2.0 |
| Inflation | 18.8 | 11.9 | 8.0 | 7.1 | 11.5 |
| Current account balance (in percent of GDP) | -4.6 | -6.7 | -5.8 | -7.0 | -6.0 |
| Investment (in percent of (GDP) | 19.8 | 21.6 | 21.0 | 22.2 | 21.1 |
The Beveridge-Nelson Decomposition
48. Figure 6 shows the results of performing a BN decomposition on the GDP series. Since the BN methodology suffers from technical problems (as discussed above), the confidence level is minimal and, therefore, there are few meaningful implications for the design of economic policies. Indeed, note that the lines for observed and potential GDP in the figure below are almost indistinguishable, indicating the low capacity of the BN methodology to estimate the Mexican output gap.
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Structural VARs
49. The permanent and cyclical components of GDP obtained by employing the structural VAR specification described by DeSerres, Guay, and St. Amant for Mexico are shown in Figures 7 and 8. In contrast to the DGS study that uses the index of industrial production as a proxy for GDP and the price of West Texas Intermediate oil, in this chapter, GDP and the price of the Mexican oil export mix are used.
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Observed and Potential GDP
(In billions of 1993 pesos)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
50. The HP and DGS techniques show similar results when identifying the permanent and cyclical components. The magnitude of the output gap is very similar for the whole sample, especially during the two periods of expansion already mentioned, and for the contemporary period.
Mexico: Output Gap
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Output Gap
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
Mexico: Output Gap
(In percent of potential output)
Citation: IMF Staff Country Reports 2001, 191; 10.5089/9781451825572.002.A001
51. The annual average growth of potential GDP during 1980QI-2000QI is 2.7 percent. The gap during 1980QI–1982QII was estimated to be 4.6 percent. During the second expansion period (1991QI-1994Q4), the average gap was 1.9 percent. Although the structural VAR and HP methodologies indicate similar maxima for the gap, the estimated variance of the gap increases under the VAR specification compared with the HP filter.
D. Conclusion
52. The procedures outlined in this chapter were formulated during the last 20 years in order to meet the theoretical and empirical need for a better understanding of the determinants of long-run growth and fluctuations around its long-term trend. They also served to help design policy instruments that would minimize the effects of recessions and, in so doing, contribute to taking full advantage of the economy’s growth potential.
53. The wide variety of procedures reviewed demonstrates the difficulty of identifying, with a reasonable degree of confidence, the permanent and cyclical components of the business cycle. Different techniques can point to the economy being at varied stages of the business cycle, despite being based on the same information set. This complicates the design of optimal policies.19
54. The specific characteristics of the Mexican economy also pose a challenge for the design of procedures to identify the time series components of GDP. The effects of the shocks experienced in the 1980s on the permanent and cyclical components have received little attention in the literature. Therefore, sufficiently powerful techniques to discern such effects on potential GDP have yet to be developed. Special attention should be focused on structural break tests for the potential output.20
55. The expansion periods indicated by the HP filter and those of the structural VAR preceded the most important crises experienced by Mexico in the last 20 years. During the expansion phase of 1980QI-1982QII, average annual GDP growth exceeded potential by 1.7 percentage points. During the subsequent expansion phase of 1991QI—1994QI, the difference was three-fourths of a percentage point. In both cases, these rates of growth fostered a positive output gap that ultimately contributed to destabilizing economic imbalances. With hindsight, this is not surprising since overheating involves an intensive use of resources, which often requires excessive external financing. This was not sustainable and ultimately was a factor leading to abrupt economic contractions. Thus, in those circumstances, the benefits for Mexico from high rates of growth proved to be largely illusionary.
56. The following table presents estimates of the current output gap and some related indicators:
57. The results shown in Table 3, derived using an HP filter, indicate that potential GDP growth averaged 4.5 percent during 1997QI-2000Q4. Similarly, considering only the period 2000QI-2000Q4, potential GDP growth is estimated to be 4.9 percent.
Mexico: Potential GDP and Related Indicators, 1997–2001
Not including 2001:Q1.
Mexico: Potential GDP and Related Indicators, 1997–2001
| Q1 | ||||||
|---|---|---|---|---|---|---|
| Indicator | 1997 | 1998 | 1999 | 2000 | 2001 | Average 1/ |
| GDP growth | 6.8 | 4.9 | 3.8 | 6.9 | 1.9 | 5.6 |
| Potential GDP growth | 3.8 | 4.3 | 4.7 | 4.9 | 4.4 | 4.5 |
| Output gap | 0.7 | 1.6 | 0.0 | 2.0 | 0.6 | 1.0 |
| Inflation | 15.7 | 18.6 | 12.3 | 9.0 | 7.2 | 13.9 |
| Current account balance (in percent of GDP) | -1.8 | -3.8 | -3.0 | -3.1 | -0.7 | 2.9 |
| Investment (in percent of GDP) | 21.5 | 22.6 | 22.7 | 23.2 | 23.4 | 22.5 |
Not including 2001:Q1.
Mexico: Potential GDP and Related Indicators, 1997–2001
| Q1 | ||||||
|---|---|---|---|---|---|---|
| Indicator | 1997 | 1998 | 1999 | 2000 | 2001 | Average 1/ |
| GDP growth | 6.8 | 4.9 | 3.8 | 6.9 | 1.9 | 5.6 |
| Potential GDP growth | 3.8 | 4.3 | 4.7 | 4.9 | 4.4 | 4.5 |
| Output gap | 0.7 | 1.6 | 0.0 | 2.0 | 0.6 | 1.0 |
| Inflation | 15.7 | 18.6 | 12.3 | 9.0 | 7.2 | 13.9 |
| Current account balance (in percent of GDP) | -1.8 | -3.8 | -3.0 | -3.1 | -0.7 | 2.9 |
| Investment (in percent of GDP) | 21.5 | 22.6 | 22.7 | 23.2 | 23.4 | 22.5 |
Not including 2001:Q1.
58. Estimates derived from the structural VAR technique indicate potential GDP growth during 1997Q1-2000Q4 to be 4.6 percent a year on average, and during 2000Q1-2000Q4 to be 5 percent a year. These results are similar to those obtained applying the HP filter.
59. The estimates of potential GDP growth presented in this chapter should be seen as indicative of the potential growth rate to which the Mexican economy can strive over the long run. They indicate at what pace the Mexican economy can grow without overheating, for a given set of structural and other conditions (such as the quality of capital and labor, integration into global markets, as well as access to public services). This paper has not examined the underlying factors affecting potential GDP growth in detail, leaving this to future research.
60. Following a period of substantial growth during 1936-81, with the debt crisis of 1982, the economy entered a phase of relatively slow growth during the 1980s. Partly reflecting the impending approval of NAFTA, as well as a number of ongoing structural changes in the economy, growth accelerated in the 1990s, until it was interrupted by the economic and financial crisis of 1994-95. The quick return to macroeconomic stability following the crisis and a deepening of earlier structural reforms has contributed to a recovery of economic activity and has placed the economy on the path to sustainable, strong output growth. To the extent that macroeconomic stability is maintained and structural conditions continue to improve, the potential rate of GDP growth can be raised, without causing overheating. This is the key challenge facing Mexican policymakers today.
APPENDIX
I. Beveridge-Nelson Decomposition Analysis of GDP Series (logs) Quarterly Data From 1980:1 to 2001:1 ARIMA Model: (0,1,2)×(0,1,1)
I. Beveridge-Nelson Decomposition Analysis of GDP Series (logs) Quarterly Data From 1980:1 to 2001:1 ARIMA Model: (0,1,2)×(0,1,1)
| Summary statistics: | |
|---|---|
| R Bar**2 | 0.984544 |
| Standard error of dependent variable | 0.151452 |
| Standard error of estimate | 0.018828 |
| Sum of squared residuals | 0.026589 |
| Durbin-Watson statistic | 1.886761 |
| Q(20-2) | 9.250304 |
| Significance level of Q | 0.953659 |
I. Beveridge-Nelson Decomposition Analysis of GDP Series (logs) Quarterly Data From 1980:1 to 2001:1 ARIMA Model: (0,1,2)×(0,1,1)
| Summary statistics: | |
|---|---|
| R Bar**2 | 0.984544 |
| Standard error of dependent variable | 0.151452 |
| Standard error of estimate | 0.018828 |
| Sum of squared residuals | 0.026589 |
| Durbin-Watson statistic | 1.886761 |
| Q(20-2) | 9.250304 |
| Significance level of Q | 0.953659 |
| Variable | Coefficient | Standard error | T-stat | P-value |
|---|---|---|---|---|
| MA{2} | 0.474252011 | 0.115268947 | 4.11431 | 0.00009858 |
| SMA{4} | -0.528720375 | 0.112501110 | -4.69969 | 0.00001157 |
| DUM951 | -0.023449331 | 0.012743882 | -1.84005 | 0.06971787 |
| DUM952 | -0.060968999 | 0.013726677 | -4.44164 | 0.00003028 |
| DUM972 | 0.061573385 | 0.013962351 | 4.40996 | 0.00003401 |
| Variable | Coefficient | Standard error | T-stat | P-value |
|---|---|---|---|---|
| MA{2} | 0.474252011 | 0.115268947 | 4.11431 | 0.00009858 |
| SMA{4} | -0.528720375 | 0.112501110 | -4.69969 | 0.00001157 |
| DUM951 | -0.023449331 | 0.012743882 | -1.84005 | 0.06971787 |
| DUM952 | -0.060968999 | 0.013726677 | -4.44164 | 0.00003028 |
| DUM972 | 0.061573385 | 0.013962351 | 4.40996 | 0.00003401 |
II. Structural VAR Estimation Sample (adjusted): 1980:1 to 2001:1 Restrictions in Variance-Covariance Matrix of Innovations: 3
(Standard errors and T-statistics in parentheses)
II. Structural VAR Estimation Sample (adjusted): 1980:1 to 2001:1 Restrictions in Variance-Covariance Matrix of Innovations: 3
(Standard errors and T-statistics in parentheses)
| Y | O | M | |
|---|---|---|---|
| Y(-l) | 0.508628 | -0.543105 | 0.241446 |
| (0.27461) | (0.42894) | (0.43821) | |
| (1.85219) | (-1.26615) | (0.55098) | |
| Y(-2) | 0.427595 | 1.039839 | -0.330109 |
| (0.32260) | (0.50390) | (0.51479) | |
| (1.32546) | (2.06356) | (-0.64125) | |
| Y(-3) | -0.687960 | -0.890261 | -0.857700 |
| (0.34170) | (0.53373) | (0.54526) | |
| (-2.01336) | (-1.66800) | (-1.57300) | |
| Y(-4) | 0.144980 | -0.140424 | 0.359975 |
| (0.28811) | (0.45002) | (0.45975) | |
| (0.50322) | (-0.31204) | (0.78298) | |
| O(-1) | 0.225357 | 0.981250 | 0.222068 |
| (0.12749) | (0.19914) | (0.20344) | |
| (1.76762) | (4.92739) | (1.09154) | |
| O(-2) | -0.155242 | -0.134621 | -0.032309 |
| (0.15801) | (0.24682) | (0.25215) | |
| (-0.98247) | (-0.54543) | (-0.12814) | |
| O(-3) | 0.186859 | 0.137281 | 0.186644 |
| (0.15768) | (0.24630) | (0.25162) | |
| (1.1 8506) | (0.55738) | (0.74178) | |
| O(-4) | 0.172263 | -0.161425 | -0.066811 |
| (0.13114) | (0.20485) | (0.20927) | |
| (-1.31355) | (-0.78803) | (-0.31925) | |
| M(-1) | 0.052770 | 0.120418 | 0.491866 |
| (0.14088) | (0.22006) | (0.22481) | |
| (0.37457) | (0.54722) | (2.18792) | |
| M(-2) | 0.066361 | 0.305920 | 0.333047 |
| (0.15397) | (0.24050) | (0.24569) | |
| (-0.43101) | -1.27203) | (1.35554) | |
| M(-3) | 0.059696 | 0.51663 | 0.106570 |
| (0.14970) | (0.23383) | (0.23888) | |
| (0.39878) | (0.22095) | (0.44612) | |
| M(-4) | 0.073389 | 0.265847 | -0.195446 |
| (0.13265) | (0.20720) | (0.21167) | |
| (0.55326) | (1.28307) | (-0.92334) | |
| C | 0.007686 | 0.015758 | 0.011488 |
| (0.00355) | (0.00554) | (0.00566) | |
| (2.16666) | (2.84369) | (2.02928) | |
| R-squared | 0.708168 | 0.686236 | 0.697109 |
| Adj. R-squared | 0.653450 | 0.627405 | 0.640317 |
| Sum sq. resides | 0.032795 | 0.080016 | 0.083511 |
| S.E. equation | 0.022637 | 0.035359 | 0.036123 |
| Log likelihood | 189.5506 | 155.2111 | 153.5650 |
| Akaike AIC | 189.8883 | 155.5487 | 153.9026 |
| Schwarz SC | 190.2840 | 155.9444 | 154.2983 |
| Mean dependent | 0.024454 | 0.036964 | 0.031954 |
| S.D. dependent | 0.038453 | 0.057927 | 0.060231 |
| Determinant residual covariance | 5.03E-11 | ||
| Log likelihood | 585.1801 | ||
| Akaike information criteria | 586.1931 | ||
| Schwarz criteria | 587.3802 | ||
II. Structural VAR Estimation Sample (adjusted): 1980:1 to 2001:1 Restrictions in Variance-Covariance Matrix of Innovations: 3
(Standard errors and T-statistics in parentheses)
| Y | O | M | |
|---|---|---|---|
| Y(-l) | 0.508628 | -0.543105 | 0.241446 |
| (0.27461) | (0.42894) | (0.43821) | |
| (1.85219) | (-1.26615) | (0.55098) | |
| Y(-2) | 0.427595 | 1.039839 | -0.330109 |
| (0.32260) | (0.50390) | (0.51479) | |
| (1.32546) | (2.06356) | (-0.64125) | |
| Y(-3) | -0.687960 | -0.890261 | -0.857700 |
| (0.34170) | (0.53373) | (0.54526) | |
| (-2.01336) | (-1.66800) | (-1.57300) | |
| Y(-4) | 0.144980 | -0.140424 | 0.359975 |
| (0.28811) | (0.45002) | (0.45975) | |
| (0.50322) | (-0.31204) | (0.78298) | |
| O(-1) | 0.225357 | 0.981250 | 0.222068 |
| (0.12749) | (0.19914) | (0.20344) | |
| (1.76762) | (4.92739) | (1.09154) | |
| O(-2) | -0.155242 | -0.134621 | -0.032309 |
| (0.15801) | (0.24682) | (0.25215) | |
| (-0.98247) | (-0.54543) | (-0.12814) | |
| O(-3) | 0.186859 | 0.137281 | 0.186644 |
| (0.15768) | (0.24630) | (0.25162) | |
| (1.1 8506) | (0.55738) | (0.74178) | |
| O(-4) | 0.172263 | -0.161425 | -0.066811 |
| (0.13114) | (0.20485) | (0.20927) | |
| (-1.31355) | (-0.78803) | (-0.31925) | |
| M(-1) | 0.052770 | 0.120418 | 0.491866 |
| (0.14088) | (0.22006) | (0.22481) | |
| (0.37457) | (0.54722) | (2.18792) | |
| M(-2) | 0.066361 | 0.305920 | 0.333047 |
| (0.15397) | (0.24050) | (0.24569) | |
| (-0.43101) | -1.27203) | (1.35554) | |
| M(-3) | 0.059696 | 0.51663 | 0.106570 |
| (0.14970) | (0.23383) | (0.23888) | |
| (0.39878) | (0.22095) | (0.44612) | |
| M(-4) | 0.073389 | 0.265847 | -0.195446 |
| (0.13265) | (0.20720) | (0.21167) | |
| (0.55326) | (1.28307) | (-0.92334) | |
| C | 0.007686 | 0.015758 | 0.011488 |
| (0.00355) | (0.00554) | (0.00566) | |
| (2.16666) | (2.84369) | (2.02928) | |
| R-squared | 0.708168 | 0.686236 | 0.697109 |
| Adj. R-squared | 0.653450 | 0.627405 | 0.640317 |
| Sum sq. resides | 0.032795 | 0.080016 | 0.083511 |
| S.E. equation | 0.022637 | 0.035359 | 0.036123 |
| Log likelihood | 189.5506 | 155.2111 | 153.5650 |
| Akaike AIC | 189.8883 | 155.5487 | 153.9026 |
| Schwarz SC | 190.2840 | 155.9444 | 154.2983 |
| Mean dependent | 0.024454 | 0.036964 | 0.031954 |
| S.D. dependent | 0.038453 | 0.057927 | 0.060231 |
| Determinant residual covariance | 5.03E-11 | ||
| Log likelihood | 585.1801 | ||
| Akaike information criteria | 586.1931 | ||
| Schwarz criteria | 587.3802 | ||
Where DUMxxx are dummies for the year (first two digits) and quarter (last digit) indicated. Analysis of the residuals:
The Ljung-Box Chi-Squared test for serial correlation
Test statistic: 13.0912 Significance level: 0.90540
The F-test for autoregressive conditional heteroskedasticity
Test statistic: 0.4035 Significance level: 0.98563
The Jarque-Bera normality test, ChiSqr (2)
Test statistic: 0.0202 Significance level: 0.98993
List of References
Baxter, M., and R.G. King, 1995, “Measuring Business-Cycles: Approximate Band Pass Filters for Economic Time Series,” NBER Working Paper 5022, National Bureau of Economic Research.
Beveridge, S., and C. R. Nelson, 1981, “A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the Business Cycle,” Journal of Monetary Economics, Vol. 7, pp. 151–74.
Blanchard, O. J., and D. Quah, 1989, “The Dynamic Effect of Aggregate Demand and Aggregate Supply,” American Economic Review, Vol. 79, pp. 655–73.
Bosworth, Barry, 1998, “Productivity Growth in Mexico,” Background paper prepared for a World Bank project on Productivity Growth in Mexico, Mexico: Enhancing Factor Productivity Growth, Report No. 17392-ME, Country Economic Memorandum, August 31, 1998.
Burns, A. F., and W. A. Mitchell, 1946, Measuring Business Cycles, National Bureau of Economic Research.
Cogley, T., and J. Nason, 1995, “Effects of the Hodrick-Prescott Filter on Trend and Difference Stationary Time Series: Implications for Business-Cycle Research,” Journal of Economic Dynamics and Control, 19, pp. 253–78.
DeSerres, A., A. Guay, and P. St-Amant, 1995, “Estimating and Projecting Potential Output using Structural VAR Methodology: The Case of the Mexican Economy,” Working Paper 95–2, Bank of Canada.
Granger, C.W.J., 1966, “The Typical Spectral Shape of an Economic Variable,” Econometrica, 37, pp. 424–511.
Guay, A., and Pierre St-Amant, 1996, “Do Mechanical Filters Provide a Good Approximation of Business-Cycles?,” Technical Report 78, Bank of Canada.
Hamilton, J. D., 1989, “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle,” Econometrica, 57, pp.357–84.
Hodrick, R. J., and E. C. Prescott, 1997, “Post-war U.S. Business-Cycles: An Empirical Investigation,” Journal of Money, Credit and Banking, 29, pp. 1–16.
King, R. G., and M. Watson, 1996, “Money, Prices, Interest Rates and the Business-Cycle,” Review of Economics and Statistics, 78, pp. 35–53.
Lucas, R E., 1994, “Review of Milton Friedman and Anna J. Schwartz‘s’A Monetary History of the United States: 1876-1960,” Journal of Monetary Economics, 34, pp. 5–16.
Nelson, C. R., and C. Plosser, 1982, “Trends and Random Walks in Macroeconomic Time Series,” Journal of Monetary Economics, Vol. 10, pp. 139–67.
Prescott. E. C, 1986, “Theory Ahead of Business Cycle Measurement,” Quarterly Review, Federal Reserve Bank of Minneapolis.
Quah, D., 1992, “The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds,” Econometrica, 60, pp 107–118.
Rotemberg, J., 1999, “A Heuristic Method for Extracting Smooth Trends from Economic Time Series,” NBER Working Paper 7439, National Bureau of Economic Research.
Rotemberg, J., and M. Woodford, 1996, “Real Business-Cycle Models and the Forecastable Movements in Output, Hours and Consumption,” American Economic Review, Vol. 86, pp. 71–89.
Sims, C. A., 1980, “Macroeconomics and Reality,” Econometrica, 48, p. 1 –48.
Stock, J. H., and M. W. Watson, 1991, “A Probability Model of the Coincident and Leading Indicators,” in K. Lahiri, and G. H. Moore, eds., Leading Economic Indicators: New Approaches and Forecasting Records, pp. 63–85. NY: Cambridge University Press.
Stock, J. H., 1993, “A Procedure for Predicting Recessions with Leading Indicators: Econometric Issues and Recent Experience,” in J. H. Stock, and M. W. Watson, eds., Business Cycles, Indicators and Forecasting, pp. 95–156. Chicago: University of Chicago Press.
Watson, M. W., 1986, “Univariate Detrending Methods with Stochastic Trends,” Journal of Monetary Economics, Vol. 18, pp. 49–75.
This chapter was prepared by staff of the Mexican Secretariat of Finance and Public Credit (Ernesto Acevedo, Marlon Aguilar, and Andrés Conesa) and of the IMF (Philip Young). The opinions expressed in this paper by the staff of the Mexican Secretariat of Finance and Public Credit do not necessarily reflect the official views of the Secretariat.
Plosser coined the term “real business-cycle theory” to designate those models that attached a relatively greater weight to changes in total factor productivity as the main determinants of output fluctuations.
Although real business-cycle theory argues for the design of policies that reduce the volatility of total factor productivity, financial crises have imposed a different sort of challenge in that the necessary correction to counteract any financial disequilibrium needs to be effective almost immediately, while the suggested policies from the above-mentioned models take longer to be effective.
Although Prescott concluded that monetary policy didn’t affect real business cycles, Lucas (1994) disagreed. He argued that the success of real business cycle theory in explaining economic fluctuations should be “interpreted as evidence that postwar monetary policy has resulted in near-efficient behavior, not as evidence that money doesn’t matter.”
Barry Bosworth (1998) found a notable decline in trend productivity growth in Mexico during the 1980s.
GDP throughout this chapter refers to real GDP.
The factors that cause fluctuations in aggregate demand and supply are classified in three categories: 1) domestic factors, such as trend changes in employment or inflation; 2) external factors, such as sudden changes in the nominal exchange rate or the terms of trade; and 3) structural factors such as technological changes or productivity shocks.
Such a decomposition is nontrivial considering, for example, that time series which are co-integrated of order one can have an infinite number of cyclical/trend decompositions.
The rate of unemployment at which there is no upward pressure on the price level.
The HP filter is a procedure that removes low frequencies (high-pass) from a time series. Filters that remove low and high frequencies (band-pass), such as that proposed by Baxter and King (1995) have properties similar to those of the HP filter. For this reason, they are not discussed in detail in this chapter.
A number of analytic frameworks permit the identification of the specific characteristics of an economic time series. Traditionally, emphasis is given to properties of a time series such as its mean and variance. However, time series have other characteristics that can be better seen using alternative perspectives or domains. The frequency domain allows the identification of qualitative indicators of the time series, related directly to its components, such as the amplitude, length of cycle, and frequency. Another alternative is the state-space domain. Under this domain it is quite straightforward to identify characteristics of a time series, hence its growing popularity in the analysis of stochastic processes. The solution to the procedure expressed here is obtained through state-space domain optimization techniques.
Although the terms “filter” and “smoother” are often used interchangeably, technically they are different. Filters recreate a series by filtering the observations one by one. A smoother takes into account the full information set before smoothing the series. Under this definition, the HP filter behaves more like a smoother than a filter.
The values suggested by Hodrick and Prescott for λ correspond to the ratio of the variance of the cyclical component to the variance of the permanent component. These values are very sensitive to the characteristics of the series to be decomposed. For that reason, the appropriate use of the HP filter requires the estimation of λ in the specific case of Mexico’s GDP series. Rotemberg (1999) has proposed a two-stage procedure that yields, first, an optimal λ, and second, the corresponding permanent component of the series.
The benefits of this property are specific to the model. In some models of business cycles, it would be inconsistent to assume independence between the cyclical and permanent components.
Assuming the existence of a group of economic variables that move together during a business cycle. This formulation has encouraged the use of techniques that extract common cyclical and permanent components (Stock and Watson, 1991 and 1993), and with asymmetric rates of growth (Hamilton, 1989), frequently used in the theory of leading economic indicators.
In general, the production technology is assumed to have constant returns to scale, and the factor markets are assumed to be characterized by perfect competition.
The final year is projected.
The sample was extended for three years on both ends to control for the end-point distortions that typically occur when using an HP filter. The series was extended backwards by interpolating the annual average growth rate of 1977-79 to the quarters corresponding to those years. The series was extended three years ahead by applying the average of GDP forecasts reported by consulting firms.
In an effort to reduce the number of relevant techniques to choose from in studying the components of a time series, King and Watson (1996) have proposed several estimators that show the robustness of the permanent and cyclical components through the moments obtained in the analysis of the series spectrum.
Popular techniques for the identification of structural breaks cannot be used in this type of analysis. Given that the HP filter technique does not yield any error term, it is not possible to identify structural breaks nor to apply recursive residual analysis. In the case of the VAR specification, structural breaks are difficult to identify because the restrictions imposed would distort the meaningfulness of any statistical tests.
