Common Factors in Latin America's Business Cycles

Allan Timmermann; Luis Catão; Marco Aiolfi

doi:10.5089/9781451863093.001.A001

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Common Factors in Latin America's Business Cycles

Author: Mr. Allan Timmermann, Mr. Luis Catão, and Mr. Marco Aiolfi

Contributor Notes

Author(s) E-Mail Address: lcatao@imf.org;

Publication Date:: 01 Feb 2006

eISBN:: 9781451863093

Language:: English

Keywords:: WP; real GDP; standard deviation; economic activity; government spending; New World country; business cycle duration; standard deviation estimate; Latin American country

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This paper constructs new business cycle indices for Argentina, Brazil, Chile, and Mexico based on common dynamic factors extracted from a comprehensive set of sectoral output, external data, and fiscal and financial variables spanning over a century. The constructed indices are used to derive a business cycle chronology for these countries and characterize a set of new stylized facts. In particular, we show that all four countries have historically displayed a striking combination of high business cycle and persistence relative to benchmark countries, and that such volatility has been time-varying, with important differences across policy regimes. We also uncover a sizeable common factor across the four economies which has greatly limited scope for regional risk sharing.

Abstract

I. Introduction

Business cycle volatility can arise from a variety of sources and be exacerbated by distinct economic policy regimes, possibly reflecting slowly-evolving institutional factors (Acemoglu, Johnson, Robinson and Thaicharoe, 2003) and different degrees of financial and trade openness (Kose, Prasad, and Terrones 2006). This suggests that important insights into the phenomenon can be gained from long-run data spanning a variety of policy regimes and institutional settings. Yet there is a striking dearth of systematic work along these lines for most countries outside North America and Western Europe.

One region that is particularly under-researched is Latin America. This gap is somewhat surprising not only because the region is deemed as highly volatile and the question of what drives such volatility is of interest in its own right; it is also surprising because the region comprises a large set of sovereign nations which have gone through a number of dramatic changes in policy regimes and institutions over a long period of time and relative to other developing countries in Africa and Asia (many of which only became independent nations in recent decades), thus providing a rich context for assessing business cycle theories. Indeed, Latin America is notoriously absent in the well-known historical business cycle studies by Sheffrin (1988) and Backus and Kehoe (1992), and only Argentina is covered in more recent work along similar lines (Basu and Taylor, 1999). Instead, recent research on Latin American business cycles has been either country-specific and covered only short periods of time (e.g. Kydland and Zarazaga, 1997) or focused on specific transmission mechanisms and limited to post-1980 data (Hoffmaister and Roldos, 1997; Neumeyer and Perri, 2005).² A corollary of this gap in the literature is the absence of any formal attempt to establish a reference cycle dating for these countries similar to those available for others—such as the United States and the Euro area—on the basis of a variety of coincident and leading indicators (Moore, 1983; Gordon, 1986; Artis, Kontolemis, and Osborn, 1997; Stock and Watson, 1999).

This paper seeks to fill some of this lacuna. Unlike previous work, we go back as far as available macroeconomic data permit and jointly focus on four of the largest Latin American economies—Argentina, Brazil, Chile, and Mexico. Together, these countries have accounted for some 70 percent of the region’s GDP over the past half century (Maddison, 2003, pp. 134–140), thus clearly setting the tone for the region’s overall macroeconomic performance. At the same time, data availability for this subset of countries permits us to provide a long-run characterization of the business cycle in these economies similar to that conducted for advanced countries.

The construction of new indices of economic activity and the identification of volatility sources over such long period allows us to address four main questions. First, how volatile has Latin America been relative to other countries? In particular, has economic activity in Latin America been more or less stable in periods of greater trade and financial integration with the world economy, such as during the pre-1930 gold standard and the post-1980s period? Second, how persistent have macroeconomic fluctuations been in those countries? Since the welfare cost of income fluctuations as well as the burden on stabilization policy rise on volatility and persistence,³ these are important questions to ask and document. Third, do we observe similar stylized facts as those documented for other economies that feature in the existing business cycle literature? Finally, is there an identifiable regional business cycle?

As discussed further below, a key requirement for answering these questions is to obtain a measure of economic activity that is expected to be reasonably accurate and consistent over such a long period. We provide this by constructing a new index of economic activity for each of the four countries using a dynamic common factor methodology which, to the best to our knowledge, is for the first time applied to build a business cycle index for this set of countries. This methodology is applied to a uniquely large set of macroeconomic variables compiled from a wide range of historical sources. The data span key sectors such as agriculture, manufacturing, mining and cement production, and include fiscal expenditures and revenues, external variables such as terms of trade, the real exchange rate and import and export volume, as well as a host of financial indicators including interest rates and monetary aggregates. Our index of economic activity is shown to track very closely the existing real GDP data from the full set of national account estimates beginning in the early post-World War II period. Since this index of economic activity is constructed as the common factor that underlies a wide set of macroeconomic and sectorial indicators—thus filtering out idiosyncratic components (including possible measurement errors)—it provides a measure that is germane to the concept of the business cycle as defined in the work of Burns and Mitchell (1946)—which still forms the backbone of the widely used NBER reference cycle indicator for the United States.

The paper’s main findings are as follows. Over the full sample 1870–2004, the average business cycle volatility in all four countries was considerably higher than in the advanced economies-albeit with important differences over sub-periods. Latin American volatility was relatively high in the pre-1930 era, during the formative years of key national institutions. It then dropped sharply during the four decades following the Great Depression—an apparent pay-off of the inward-looking growth and highly interventionist policy regimes at a time when volatility in advanced countries rose to all-time highs. Cyclical instability in Latin America bounced back again in the 1970s and 1980s—when it was more than twice as high as the advanced country average—before declining sharply more recently. Throughout the period, cyclical persistence has been high, with large shocks giving rise to a striking combination of high cyclical volatility and long business cycle durations relative to advanced country standards.

We also find evidence of a number of regularities highlighted in the existing business cycle literature. In particular, external terms of trade have been strongly procyclical, the trade balance counter-cyclical, and fixed investment has been several times more volatile than output. Using the simple gauge proposed in Kaminsky, Reinhart, and Végh (2004), we also find that fiscal policy has been strongly procyclical in these countries. In contrast with evidence more directly supportive of Phillips curve trade-offs among advanced countries, we find that inflation has been historically counter-cyclical in all four Latin American economies. Compared with the more mixed cross-country evidence in other regions, real wages have also been broadly procyclical. Once again, a contrast with advanced economies lies in the strikingly large volatility of these individual variables.

Concordance indices along the lines of Artis et al (1997) and Harding and Pagan (2002) indicate that business cycles in these economies have been reasonably correlated. Pooling data from all four countries, the common factor methodology that we employ permits the identification of a sizeable common regional factor. Since trade linkages between these economies have been small until very recently and capital account linkages remain so to date, global shocks—notably to key foreign interest rates, real income in advanced countries and commodity terms of trade—emerge as key drivers of this common regional business cycle. This result has salient practical implications that have previously been discussed on the basis of distinct methodologies and far more limited data (Calvo, Leiderman, and Reinhart, 1993; Fernandez-Arias, 1994; Agénor et al., 2000; Neumeyer and Perri, 2005).

The remainder of the paper is divided into five sections as follows. Section II lays out the econometric framework and discusses the main estimation issues. Section III reports empirical estimates and provides robustness checks of our methodology, while Section IV presents stylized facts about the business cycle in the Latin American countries. Section V concludes. An appendix contains details of the construction and sources of our data series.

II. Econometric Framework

The idea that a cross-section of economic variables share a common factor structure has a long tradition in economics, dating back at least to the attempt by Burns and Mitchell (1946) to construct an aggregate measure of economic activity. There are two chief motivations for common factor models. First, economic theory suggests strong linkages between economic activity across different sectors due to common productivity, preference and policy shocks. However, since some of these shocks are unobservable, information about them can only be extracted once one has access to a sufficiently large cross-section of economic variables that are at least in part driven by these shocks. Hence, a critical requirement that needs to be met in our analysis is the availability of a broad set of variables that bear sufficiently close relation to aggregate business cycle behavior. Natural candidates include capital formation, government revenue and expenditures, sectorial output series, as well as external trade figures and a host of financial variables. The fact that the Latin American economies have historically been highly dependent on global capital markets and demand from outside trading partners suggests that interest rates and cyclical output in advanced countries also be included in the analysis.

The second motivation for using dynamic factor analysis is related to the presence of measurement errors. Activity levels in many sectors are measured with considerable error. Provided that measurement errors are largely idiosyncratic, cross-sectional information can be used to construct more robust common factors that are not similarly sensitive to the impact of such errors. Here one has to make assumptions on the exposure of such observable variables to common shocks in order to identify the underlying driving factors.

Stock and Watson (1989, 2002) and Forni, Hallin, Lippi and Reichlin (2000) have shown that the application of dynamic common factor models to a sufficiently representative set of macroeconomic and sectorial indicators provides superior forecasting performance for a target variable such as real GDP or indeed any broad index of economic activity. This methodology turns out to be particularly useful when some of the constituent series that add up to a target variable (such as monthly GDP) are lacking, or when such series are suspected to be mismeasured (as commonly deemed to be the case for certain service activities). An important requirement is that such measurement errors are sufficiently idiosyncratic or that the cross-section of available time series be sufficiently large and/or representative. This methodology is clearly suitable when interest lies in reconstructing (backcasting) historical measures of the cycle, as discussed below.

A. Model Specification and Dynamic Factor Estimation

Let X_t be a vector of de-meaned and standardized time-series observations on N economic variables observed over the sample t = 1,…,T. Assuming that X_t admits a dynamic factor representation, we can write

\begin{matrix} Χ_{t} = Λ (L) f_{t} + e_{t} & (1) \end{matrix}

\begin{matrix} = [Λ_{0, \dots . .,} Λ_{s}] [\begin{matrix} f_{t} \\ \dots \\ f_{t - s} \end{matrix}] + e_{t} = Λ F_{t} + e_{t}, & (2) \end{matrix}

where f_t = (f_1t_,…f_qt) is a vector of q common dynamic factors, Λ(L) is an N_xq matrix of filters of length s, e_t is an N x1 vector of idiosyncratic disturbances, $F_{t} = (f_{t}^{'}, \dots, f_{t - s}^{'})$ is an r x1 vector of stacked factors with r = qx(s+1). Notice that while q identifies the number of common shocks, the dimension of F_t depends on the lag structure of the propagation mechanism of those shocks. Similarly, f_t is the vector of q dynamic factors and F_t is the vector of r static factors, while Λ contains the factor loadings. We refer to (1) as the dynamic representation and to (2) static as the static representation.

In practice the factors are typically unobserved and extraction of them from the observables (X_t) requires making identifying econometric assumptions. As is typical in the literature, we assume that the errors e_t are mutually orthogonal with respect to f_t, although they can be correlated across series and through time. In addition the factors are only identified up to an arbitrary rotation—we explain in the empirical section how we choose a particular rotation using the idea that the factors are only identified indirectly via the factor loadings.

The standard estimation method of dynamic factor models involves maximizing the likelihood function by means of the Kalman filter. This technique has been employed for low-dimensional systems by Stock and Watson (1991). When N is large, non-parametric methods such as static principal components (Stock and Watson (2002)), weighted static principal components (Boivin and Ng, 2003) and dynamic generalized principal components (Forni, Hallin, Lippi and Reichlin, 2000) are available for consistent estimation of the factors in approximate dynamic factor models.

Under the assumed orthogonality between the dynamic factors and the idiosyncratic disturbances, we can consider a spectral density matrix or covariance matrix of the X_t decomposition and the common component can be approximated by projecting either on the first r static principal components of the covariance matrix (Stock and Watson, 2002) or on the first q dynamic principal components (Forni, Hallin, Lippi and Reichlin, 2000), possibly after scaling the data by the covariance matrix (Boivin and Ng (2003)). In this paper we consider both approaches and evaluate the robustness of the results to this choice, since there is no clear-cut evidence on which approach is superior.⁴

In Stock and Watson (2002), a principal component estimator of the factors emerges as the solution to the following least squares problem:

\min_{F, Λ} T^{- 1} \sum_{t - 1}^{T} {(Χ_{t} - Λ F_{t})}^{'} (Χ_{t} - Λ F_{t})

subject to the restriction Λ^′Λ=I. The solution to this problem ${\hat{Λ}, {\hat{F}}_{t}}$ takes the form

\begin{matrix} \begin{matrix} \hat{Λ} = v \\ {\hat{F}}_{t}^{S W} = v^{'} Χ_{t}, \end{matrix} & (3) \end{matrix}

where v is an r x1 vector of eigenvectors corresponding to the r largest eigenvalues of the variance-covariance matrix of the X variables, Σ_xx. The resulting estimator of the factors, ${\hat{F}}_{t}^{S W}$ , is the first r static principal components of X_t.

In Forni et al (2000) the dynamic structure in the factors is explored by extracting principal components from the frequency domain. Their approach permits efficient aggregation of variables that may be out of phase, with the common component being estimated by projecting the X -variables on present, past and future dynamic principal components. The factors and their loadings are the solution to the following non-linear least squares problem that weights the idiosyncratic errors by their covariance matrix, $Ω = E [(Χ_{t} - Λ F_{t}) {(Χ_{t} - Λ F_{t})}^{'}]$ :

\min_{F, Λ} T^{- 1} \sum_{t - 1}^{T} {(Χ_{t} - Λ F_{t})}^{'} Ω^{- 1} (Χ_{t} - Λ F_{t}),

again subject to Λ^′Λ=I. As in Forni et al (2003), we adopt a two-step weighted principal component estimation procedure where Ω is estimated as the difference between the sample covariance matrix, ${\hat{Σ}}_{x x}$ , and the dynamic principal components estimator of the spectral density matrix of the common components.⁵

The resulting estimators of the loadings and common factors are

\begin{matrix} \begin{array}{l} \hat{Λ} = v_{g} \\ {\hat{F}}_{t}^{FHLR} = v_{g}^{'} Χ_{t} = v^{'} {\tilde{Χ}}_{t}, \end{array} & (4) \end{matrix}

where v_g are the generalized eigenvectors associated with the largest generalized eigenvalues of the estimated covariance matrices of common and idiosyncratic components and the resulting estimator of the factors is the vector consisting of the first r generalized principal components of X_t. This can be seen as the first r static principal components of the transformed data ${\tilde{Χ}}_{t} = {(\hat{Ω})}^{- 1 / 2} Χ_{t} .$ .

An important requirement when applying these estimators is that all the variables entering the dynamic common factor specification are stationary. With the exception of the inflation rate, real interest rates, and the ratios of export to import value which are stationary by construction, we employ two alternative approaches to ensure stationarity. One is the standard Hodrick-Prescott filter, with a smoothing factor set to 100, as is common practice with annual data (e.g. Backus and Kehoe, 1992; Kose and Reizman, 2001). The second approach to detrending considered here is the symmetric moving average band-pass filter advanced by Baxter and King (1999). Following common practice with annual data, we set the size of the symmetric moving average parameter to three but use a larger-than-usual bandwidth ranging from 2 to 20 years so as to avoid filtering out the longer (12–20 year) prewar cycles first documented by Kuznets (1958) for the United States and found to be present in several advanced countries (Solomou, 1987). As shown below, both detrending methods yield very similar results.

B. Backcasting Historical Activity Measures with Dynamic Factor Models

The common factors derived above, ${\hat{F}}_{t}^{S W}$ or ${\hat{F}}_{t}^{FHLR}$ , are of interest in their own right since they provide broad-based measures of economic activity. However, often particular interest lies in analyzing a particular time-series such as real GDP over long periods of time. However, data on this variable may only be available over a more recent sample. and, even when available, the series may be subject to considerable measurement error.

The common factor approach is ideally suited to handle these problems provided that the variable of interest lends itself to a similar dynamic factor representation as assumed above. Letting the real GDP cycle be represented by the variable γ^t, and under the assumption that γ^t is driven by the common factors f_t = (f_lt,…, f_qt)^′ derived above, we have

\begin{matrix} y_{t} = c + b (L) f_{t} + ε_{t} . & (5) \end{matrix}

Our interest lies in backcasting values to create a new historical time-series of cyclical aggregate output so we estimate the following backcasting equation using contemporaneous factor values:

\begin{matrix} y_{t} = α + β^{'} {\hat{F}}_{t} + ε_{t} . & (6) \end{matrix}

When data of sufficient quality on y_t are only available over a much shorter (recent) sample than data on the variables used to construct estimates of the factors, under the maintained model (5), we can estimate the parameters θ={ α, β} over a (recent) sample period for which quality data are available on output, γ. We can then backcast cyclical output over the longer sample for which estimates of the factors are available. In the following we explain details of how we set up the data and how we deal with estimation issues pertaining to the number of factors and parameter instability.

III. New Business Cycle Indices for Latin America

A full set of national income account data for Argentina, Brazil, Chile and Mexico is only available from the mid-1930s (Argentina) or starting at some point in the 1940s for the other three countries.⁶ Previous researchers have tried to overcome this limitation by constructing proxy measures of economic activity for the earlier period. The quality of these constructs is, however, very uneven due to the lack and/or the very poor quality of output data for broad sectors of the economy. In the case of Argentina and Brazil, for instance, official output data in agriculture, manufacturing, construction, and services only become available from 1900 onwards and, even then, with serious gaps particularly in the case of Brazil (c.f. Haddad, 1978). With regard to Chile and Mexico, sectorial output data stretching back to the 19th century are more readily available but, again, often spanning a small subset of the universe of firms and of questionable quality (see the Appendix). Insofar as previous researchers tried to derive an aggregate measure of economic activity from averages of these production data (resorting to linear interpolation to fill gaps in some discontinuous annual series), the resulting indices are bound to be highly inaccurate. While two other attempts have been made to overcome these problems, they have clear drawbacks. One is that of backcasting Argentine GDP based on a handful of production and trade variables by means of linear OLS regressions (della Paolera, 1989, p.189); the other is the use of static common components to backcast 19th century Brazilian GDP on the basis of foreign trade data (Contador and Haddad, 1975).⁷ Despite this very limited variable span, the latter series has been (misleadingly) compiled by Maddison (1995, 2003) and Mitchell (2003) as a reliable indicator of pre-war Brazilian GDP.

Our paper addresses these data limitations by substantially broadening the number of variables from which one can derive valuable information on the pace of aggregate economic activity. We take into account not only production or foreign trade variables, but also monetary and financial indicators that economic theory suggests should be correlated with the business cycle. As discussed in the Appendix, the data were obtained from an extensive compilation of both primary and secondary data sources. In some cases this resulted in entirely new series being created; once combined with their counterparts from the later 20th century, these series span the entire 1870–2004 period. Still, as one might expect from country-specific idiosyncrasies in data collection (especially before the standardization of national account and balance of payments methodologies), the availability of macroeconomic and financial indicators varies somewhat across countries. For example, for Mexico very few variables were measured prior to 1877, so our business cycle index for that country only starts in 1878. Likewise, it proved impossible to obtain any meaningful series for manufacturing and agriculture output in Brazil before 1900, although we were successful in filling the gap regarding domestic cement consumption (a proxy for construction activity) as well as output in the transportation and communication sectors. A similar gap was filled for pre-1900 Argentina which also benefited from the use of a new proxy indicator of manufacturing activity starting in 1875 and recently compiled by Della Paolera and Taylor (2003).

Overall, we were able to put together a panel of between 20 to 25 time series per country which, as shown below, appears to provide an excellent gauge of the respective national business cycles. The Appendix provides a detailed discussion of measurement issues underlying the various series and the respective data sources. Since we are concerned with real economic aggregates, all variables are measured in real terms deflated by the consumer price index or by the investment or GDP deflators as appropriate—the obvious exceptions being inflation, the ratios of exports to imports, and country spreads (as measured by the difference between the yield on a sovereign foreign-currency denominated bond and the respective U.K. or U.S. yields).⁸

A. Empirical Results

Factors extracted from a dataset comprising information on a variety of variables are not typically straightforward to interpret. Nevertheless, the estimated factor loadings do offer important clues in this respect. While factors are only identified up to an arbitrary rotation, it becomes clear from the individual factor loadings that the first factor bears a strong positive correlation with the GDP cycle during periods for which actual GDP data is available.

Table 1 shows the estimated factor loadings for the first two factors extracted using the Stock and Watson procedure and the HP-detrending since the results using other methods yield very similar estimates, as shown below. We report only the first two factors since the addition of further factors only contributes marginally to the total variance of the panel with the exception of one country (Brazil) for which the third factor is important (more on this below). The first factor (labeled F1) can be interpreted as a broad measure of cyclical activity since it loads positively on indicators that are well-known to be procylical such as sectorial output, fixed capital formation, import quantum and real money, all measured in deviations from their respective long-term trends. The interpretation of the second factor (F2) is less clear-cut. For Argentina, Brazil and Chile, this factor assigns large loadings to money, the domestic interest rate and the real exchange rate (also entered in deviations from trend).

Table 1:

Factor Loadings

The table reports the eigenvectors associated with the first two common factors constructed from the data sample covering the period 1870-2004.

Table 1:

Factor Loadings

The table reports the eigenvectors associated with the first two common factors constructed from the data sample covering the period 1870-2004.

	Argentina		Brazil		Chile		Mexico
	Fl	F2	Fl	F2	Fl	F2	Fl	F2
Agriculture	-	-	-	-	0.03	-0.21	0.25	-0.22
Communication	-	-	0.29	-0.11	-	-	-	-
Manufacturing	-	-	-	-	0.22	0.29	0.19	0.21
Mining	-	-	-	-	0.35	-0.16	0.26	0.05
Cement	0.30	-0.06	0.34	-0.07	-	-	0.21	0.24
Transportation	0.35	-0.05	0.21	-0.26	-	-	0.26	-0.05
Fixed Investment	0.37	-0.09	0.42	0.02	0.34	-0.03	0.30	0.30
Govt. Expenditures	0.30	0.31	0.21	0.36	0.30	0.08	0.24	-0.26
Govt. Revenues	0.31	-0.04	0.31	0.22	0.34	-0.03	0.27	-0.16
Narrow Money	0.19	0.39	0.11	0.18	0.11	0.45	0.34	-0.13
Broad Money	0.30	0.16	0.05	0.18	0.18	0.42	0.33	-0.14
Inflation	-0.08	0.30	-0.10	-0.04	-0.07	0.03	-0.18	-0.03
Domestic Interest Rate	-0.05	-0.37	-0.07	-0.02	-0.00	-0.33	-	-
Mortgage Credit	-	-	-	-	0.05	-0.20	-	-
Terms of Trade	0.17	0.09	0.27	-0.31	0.19	0.06	0.09	0.28
Real Exchange Rate	0.00	-0.43	0.20	-0.19	0.10	-0.43	0.14	0.43
Export Volume	0.04	-0.11	-0.05	0.17	0.31	-0.25	0.21	-0.12
Import Volume	0.36	-0.26	0.43	-0.06	0.39	0.01	0.28	0.38
Trade Balance	-0.25	0.24	-0.30	-0.11	-0.06	-0.16	-0.08	-0.22
External Spread	-	-	0.03	0.27	-	-	-	-
Foreign Capital Inflows	0.23	-0.17	-	-	-	-	-	-
Foreign 3m-Tbill	0.08	-0.11	0.08	0.10	-0.06	0.13	0.17	-0.25
Foreign Output	-0.01	0.11	0.02	-0.43	0.26	-0.00	0.09	0.16
Real wage	0.20	0.25	0.02	0.40	0.29	-0.06	0.25	-0.24
Population	0.09	0.20	-0.10	-0.27	0.01	0.12	0.00	-0.10

Table 1:

Factor Loadings

The table reports the eigenvectors associated with the first two common factors constructed from the data sample covering the period 1870-2004.

	Argentina		Brazil		Chile		Mexico
	Fl	F2	Fl	F2	Fl	F2	Fl	F2
Agriculture	-	-	-	-	0.03	-0.21	0.25	-0.22
Communication	-	-	0.29	-0.11	-	-	-	-
Manufacturing	-	-	-	-	0.22	0.29	0.19	0.21
Mining	-	-	-	-	0.35	-0.16	0.26	0.05
Cement	0.30	-0.06	0.34	-0.07	-	-	0.21	0.24
Transportation	0.35	-0.05	0.21	-0.26	-	-	0.26	-0.05
Fixed Investment	0.37	-0.09	0.42	0.02	0.34	-0.03	0.30	0.30
Govt. Expenditures	0.30	0.31	0.21	0.36	0.30	0.08	0.24	-0.26
Govt. Revenues	0.31	-0.04	0.31	0.22	0.34	-0.03	0.27	-0.16
Narrow Money	0.19	0.39	0.11	0.18	0.11	0.45	0.34	-0.13
Broad Money	0.30	0.16	0.05	0.18	0.18	0.42	0.33	-0.14
Inflation	-0.08	0.30	-0.10	-0.04	-0.07	0.03	-0.18	-0.03
Domestic Interest Rate	-0.05	-0.37	-0.07	-0.02	-0.00	-0.33	-	-
Mortgage Credit	-	-	-	-	0.05	-0.20	-	-
Terms of Trade	0.17	0.09	0.27	-0.31	0.19	0.06	0.09	0.28
Real Exchange Rate	0.00	-0.43	0.20	-0.19	0.10	-0.43	0.14	0.43
Export Volume	0.04	-0.11	-0.05	0.17	0.31	-0.25	0.21	-0.12
Import Volume	0.36	-0.26	0.43	-0.06	0.39	0.01	0.28	0.38
Trade Balance	-0.25	0.24	-0.30	-0.11	-0.06	-0.16	-0.08	-0.22
External Spread	-	-	0.03	0.27	-	-	-	-
Foreign Capital Inflows	0.23	-0.17	-	-	-	-	-	-
Foreign 3m-Tbill	0.08	-0.11	0.08	0.10	-0.06	0.13	0.17	-0.25
Foreign Output	-0.01	0.11	0.02	-0.43	0.26	-0.00	0.09	0.16
Real wage	0.20	0.25	0.02	0.40	0.29	-0.06	0.25	-0.24
Population	0.09	0.20	-0.10	-0.27	0.01	0.12	0.00	-0.10

Thus, it can be broadly interpreted as an index of monetary conditions. In the case of Mexico, the largest loadings are observed on the variables capturing external linkages such as the terms of trade, the real exchange rate or import volume. This is suggestive of an important difference between the economies, possibly indicating that Mexico’s linkage to the U.S. economy is of special relevance—a conjecture that is corroborated by further evidence presented below.

Figure 1 plots the two SW factors for each of the countries using the HP detrending as reported in Table 1. For comparison, we also plot the same factors using band-pass filter detrending. Since the two approaches yield very similar results and given that the HP-detrending has been more extensively used in related studies (Backus and Kehoe, 1992; Kydland and Zarazaga, 1997; Kose and Reizman, 2001; Neumeyer and Perri, 2005), we maintain this detrending method through the remainder of the paper.

While the factors are of interest in their own right, ultimately our interest lies in reconstructing a measure of cyclical activity in the Latin American economies. To this end, Table 2 reports the $\bar{R}$ – value of regressions of de-trended actual GDP on the factors across a range of factor model specifications. The results cover the period 1950–2004, when full national account estimates are available for all four countries. As with the bulk of the series entering the alternative factor specifications, actual GDP is also expressed in deviations from an HP trend—a widely used measure of the output gap. Correlations in Table 2 thus gauge the extent to which the various factor models span the real GDP cycle. To indicate the sensitivity of the results to the adopted econometric methodologies, we present results both for the all-regressor approach—which maximizes the R² by projecting cyclical GDP on all variables—and a range of alternative factor approaches such as the Stock and Watson approach using between one and four common factors and the Forni et al (2000) approach estimated with up to two dynamic factors and up to four static factors. As we shall see later, the high in-sample fit of the all-regressor, “kitchen sink” approach comes at the cost of overfitting the data and producing poor out-of-sample performance.

Table 2:

In-Sample Fit

The table reports the adjusted R-squared for the backcasting equation estimated over the post-war sample (1950-2004). Panel A reports results when the factors are extracted from a panel spanning the period 1870-2004 (1878-2004 for Mexico), while in panel B the factors are extracted from a larger cross-section of variables available during the sample 1900-2004. All-regressors reports results from the backcasting equation that includes all available variables. The remaining backcasting equations estimate the factors using either the Stock and Watson (2002) approach with r static factors (SW(r)) or the Forni et al (2000) dynamic factor approach with q, r dynamic and static factors, respectively (FHLR(q, r)).

Table 2:

In-Sample Fit

Panel A: 1870-2004
	Argentina	Brazil	Chile	Mexico
All regressors	0.89	0.77	0.91	0.92
SW(1)	0.76	0.51	0.72	0.83
SW(2)	0.81	0.52	0.74	0.83
SW(3)	0.81	0.69	0.75	0.86
SW(4)	0.82	0.71	0.78	0.87
FHLR(1,1)	0.79	0.47	0.71	0.75
FHLR(1,2)	0.82	0.67	0.71	0.76
FHLR(1,3)	0.81	0.68	0.71	0.87
FHLR(1,4)	0.81	0.67	0.80	0.86
FHLR(2,1)	0.80	0.46	0.67	0.77
FHLR(2,2)	0.81	0.54	0.74	0.76
FHLR(2,3)	0.80	0.56	0.74	0.84
FHLR(2;4)	0.80	0.68	6:80	0.85

Panel B: 1900-2004
	Argentina	Brazil	Chile	Mexico
All regressors	0.94	0.90	0.91	0.92
SW(1)	0.84	0.65	0.72	0.83
SW(2)	0.88	0.65	0.74	0.83
SW(3)	0.88	0.83	0.75	0.86
SW(4)	0.88	0.84	0.78	0.87
FHLR(1,1)	0.85	0.61	0.71	0.75
FHLR(1,2)	0.87	0.79	0.71	0.76
FHLR(1,3)	0.88	0.80	0.71	0.87
FHLR(1,4)	0.88	0.80	0.80	0.86
FHLR(2,1)	0.86	0.60	0.67	0.77
FHLR(2,2)	0.88	0.66	0.74	0.76
FHLR(2,3)	0.88	0.70	0.74	0.84
FHLR(2,4)	0.88	0.81	0.80	0.85

Table 2:

In-Sample Fit

Panel A: 1870-2004
	Argentina	Brazil	Chile	Mexico
All regressors	0.89	0.77	0.91	0.92
SW(1)	0.76	0.51	0.72	0.83
SW(2)	0.81	0.52	0.74	0.83
SW(3)	0.81	0.69	0.75	0.86
SW(4)	0.82	0.71	0.78	0.87
FHLR(1,1)	0.79	0.47	0.71	0.75
FHLR(1,2)	0.82	0.67	0.71	0.76
FHLR(1,3)	0.81	0.68	0.71	0.87
FHLR(1,4)	0.81	0.67	0.80	0.86
FHLR(2,1)	0.80	0.46	0.67	0.77
FHLR(2,2)	0.81	0.54	0.74	0.76
FHLR(2,3)	0.80	0.56	0.74	0.84
FHLR(2;4)	0.80	0.68	6:80	0.85

Panel B: 1900-2004
	Argentina	Brazil	Chile	Mexico
All regressors	0.94	0.90	0.91	0.92
SW(1)	0.84	0.65	0.72	0.83
SW(2)	0.88	0.65	0.74	0.83
SW(3)	0.88	0.83	0.75	0.86
SW(4)	0.88	0.84	0.78	0.87
FHLR(1,1)	0.85	0.61	0.71	0.75
FHLR(1,2)	0.87	0.79	0.71	0.76
FHLR(1,3)	0.88	0.80	0.71	0.87
FHLR(1,4)	0.88	0.80	0.80	0.86
FHLR(2,1)	0.86	0.60	0.67	0.77
FHLR(2,2)	0.88	0.66	0.74	0.76
FHLR(2,3)	0.88	0.70	0.74	0.84
FHLR(2,4)	0.88	0.81	0.80	0.85

The linear projections of the GDP cycle on the various factors yield a tight fit for Argentina, with ${\bar{R}}^{2}$ − values varying from 0.89 for the all-regressor approach to around 0.80 for the two factor approaches. Correlations are also generally high for Chile and Mexico, with 75–85 percent of the variance of the real GDP cycle explained by the first two factors. The fit for Brazil is relatively worse overall, but by including the series on agricultural and manufacturing output (both of which are only available from 1900 onwards), one can raise it to above 70 percent using the SW and FHLR approaches, c.f. panel B of Table 2.

Further evidence that the various approaches tell a similar story can be gleaned from Figure 2, which show the backcast estimates of cyclical GDP in the four economies. In each case the upper panel plots our estimates and (where available) other estimates of cyclical GDP over the period 1870–1950, while the bottom panel shows the corresponding values for the remaining part of the sample. The close proximity between the fitted and actual values for the post-war period is clear from these plots–visual differences only emerge during rare and extremely large spikes such as in Brazil in 1961–62 and 1980. Overall, however, it is plain that: (i) the estimated values closely track actual cyclical GDP whenever this is available; (ii) the various factor approaches generate quite similar estimates of the cycle and (iii) factor estimates often differ substantially from estimates based on the all-regressor least squares approach which is the furthest away from “actual” values, as judged by the observations from better quality estimates of actuals out-of-sample (as for Argentina over 1935–49, Chile during 1940–49, and Mexico 1925–49).⁹ This strongly cautions against the use of a kitchen sink approach by researchers in the reconstruction of earlier GDP data.

B. Robustness Analysis

It is important to investigate whether our estimates are robust to potential instability of the factor loadings and to changes in the factor specification. The common factor projections were built under the assumption that factor loadings remain constant over time. In the same way that out-of-sample forecasts rely on an implicit assumption that certain relationships between predictor variables and the target variable remain constant over the forecasting period, backcasting economic activity measures without this assumption is infeasible.

An advantage of our approach is that the use of common factors can be expected to be reasonably robust against the structural instability that plagues low-dimensional forecasting regressions. Stock and Watson (2002) provide both theoretical arguments and empirical evidence that principal component factor estimates are consistent even in the presence of temporal instability in the individual time-series used to construct the factors provided that this instability averages out in the construction of the common factors. This occurs if the instability is sufficiently idiosyncratic to the various series.

To evaluate the robustness of our results for the backcasted GDP values, Figure 3 plots the minimum and maximum value across different specifications of the backcasting equation. In particular, we consider:

Two different estimation samples for the backcasting equation, 1915–2004 and 1950–2004 (GDP data for Chile and Mexico are available only after 1940 so for these countries the backcasting equation is estimated only over the sample 1950–2004.)
Six different factor specifications: SW (r), r = 2, 3 (where r is the number of static factors), FHLR (q, r), where the first argument, q, is the number of dynamic factors while the second, r, is the number of static factors. We set (q, r) = (2,1),(3,1),(2,2) and (2,3).
Different samples for factor estimation, where a new sample is adopted if new time series become available (Argentina: 1870–2004, 1875–2004, 1900–2004; Brazil: 1870–2004, 1900–2004; Chile: 1870–2004; Mexico: 1878–2004).
Two different panels of data, one including the external variables while the other excludes these.

The sensitivity analysis produces 72 specifications for Argentina, 36 for Brazil and 12 for Chile and Mexico. With the exceptions of Brazil in 1890–91, 1986 and 1989, Chile in 1929– 32 and Mexico in 1916, the range is very narrow; and even for those outlier observations, all estimates point in the same direction. As it turns out, all indications are that little has changed over time. This congruence would be unlikely to hold if the factor loadings were subject to structural breaks or considerable instability.

In addition, we have also checked for the stability of coefficients in the regression of the factors on the cyclical component of real GDP (equation (5)). This was done by re-estimating the regression (5) for the period 1961–2004 (instead of 1950–2004) and recursively rolling back the estimation to the last point for which reasonably reliable data on real GDP exists.¹⁰ The results plotted in Figure 4 show that the backcasting equation coefficients are reasonably stable over the 1930–60 period (1940–60 for Chile); only in the case of Mexico between 1921 and 1925 is there evidence of some instability. But since the real GDP figures used to compute the recursion over the period in the early post-revolutionary period for Mexico are likely to be marred by measurement problems before the Banco de Mexico centralized the compilation of macroeconomic data in 1925, this should not be surprising.

Overall, the results above make a simple but important point. Even when the common factors are extracted from a dataset containing a limited number of series on output growth, they track the real GDP cycle well. This may not be overly surprising since we selected variables that economic theory suggests should be closely related to cyclical activity. Yet, this evidence underscores the robustness of backcasting inferences on the aggregate output cycle once they are based on a sensible combination of fiscal, financial, sectorial and external variables.

C. Gains from Using Extended Data Set

Although our results do not appear to be sensitive to the particular choice of factor estimation methodology, number of factors or sample period used to estimate the factor loadings or projection coefficients, one might ask what the value-added is of using as wide a set of variables as that adopted here when constructing the common factors. To answer this, we compare in Figure 5 plots of the first common factor constructed using our extensive data set on sectoral output, financial, fiscal and trade variables against that using only sectoral output variables. Common factors based exclusively on sectoral output data are far smoother than those based on the wider set of variables. This shows up in a failure of the more narrowly constructed common factors in fully accounting for the depth of the crises in Argentina in 1918 and 1990, in Brazil and Mexico following World War I and in Chile following the Great Depression. In addition many of the smaller peaks and troughs—such as the cycle around 1900 in Argentina—are entirely missed by the common factor based on sectoral output information.

This limitation of the smaller set is not exclusive to Argentina for which we have only two sectoral variables going back to 1870. Adding industrial output for Argentina (a series that becomes available from 1875) does not overturn this conclusion. Significant gaps also arise for Brazil, Chile, and even Mexico which has a wider sectoral output data coverage back to the 1870s. Discrepancies between the two series are not exclusive to the pre-war period, and hence do not seem entirely attributable to the poorer quality of earlier data; large gaps emerge, for instance, for post-1960 Brazil.

These plots vividly demonstrate the importance to the construction of broad measures of economic activity of using a wide and varied set of economic variables representing not just a few sectoral output series. In other words, fiscal, financial and external trade variables play an important role in filling the gap.

D. Actual vs. Backcasted Series: A Test Based on U.S. data

Skeptical readers might object that we have not, so far, provided any direct evidence that our approach works well in terms of backcasting the cycle. This is true in the sense that the same absence of reliable and broad based historical data on output in Latin America that motivated our analysis also makes it impossible for us to compare our fitted values against realized observations.

To address this concern, we used our approach on the U.S. pre-war cycle. Since the United States has high quality real GDP estimates going back to 1870, we can directly compare model predictions and “actual” values (or, to be precise, reasonably accurate estimates of the “actual” value). For this test to be informative for our analysis, it is important that we use a set of U.S. variables similar to those used for the four Latin American countries, even though much greater data availability for the United States would have allowed us to include many more variables in the estimation of the factor model. With this consideration in mind, we stack the deck against our approach by backcasting the U.S. pre-war cycle based on an even smaller set of variables (18 in total, as described in the Appendix) than those for the four Latin American countries.

Table 3 reports the R² − values of the various estimation methods.¹¹ The fit of the various factor models over the 1950–2004 period is very good, with ${\bar{R}}^{2}$ − values around 0.80. The last column also indicates that our backcasted cycle closely tracks Balke and Gordon’s (1989) revised estimate of U.S. real GDP, which we detrend by an HP filter and plot in Figure 6 together with our estimates.¹² Clearly the fit is not perfect—with the largest discrepancy emerging during the World War II boom; yet, the overwhelming majority of cyclical turning points is consistently picked up by both indices.¹³

Table 3:

In-sample and Out-of-sample Fit for the USA

The table reports the adjusted R-squared for the backcasting equation estimated over the post-war sample (1950-2004) and the pre-war period (1870-1949) with US data. The factors are extracted from a panel spanning the period 1870-2004. For the post-wax sample we report the results using the Balke and Gordon series while for the pre-war period we report results obtained by using the Balke-Gordon, Romer, and Kuznets estimates.

Table 3:

In-sample and Out-of-sample Fit for the USA

	1950-2004	1870-1949
	Balke-Gordon	Balke-Gordon	Romer	Kuznets
All regressors	0.962	0.893	0.894	0.811
SW(1)	0.762	0.725	0.681	0.675
SW(2)	0.758	0.725	0.677	0.730
SW(3)	0.794	0.863	0.832	0.807
SW(4).	0.800	0.874	0.866	0.805
FHLR(1,1)	0.761	0.763	0.716	0.601
FHLR(1,2)	0.761	0.764	0.723	0.723
FHLR(1,3)	0.803	0.847	0.823	0.740
FHLR(1,4)	0.802	0.846	0.822	0.737
FHLR(2,1)	0.816	0.802	0.766	0.727
FHLR(2,2)	0.813	0.809	0.767	0.766
FHLR(2,3)	0.809	0.834	0.804	0.764
FHLR(2,4)	0.819	0.887	0.868	0.790

Table 3:

In-sample and Out-of-sample Fit for the USA

	1950-2004	1870-1949
	Balke-Gordon	Balke-Gordon	Romer	Kuznets
All regressors	0.962	0.893	0.894	0.811
SW(1)	0.762	0.725	0.681	0.675
SW(2)	0.758	0.725	0.677	0.730
SW(3)	0.794	0.863	0.832	0.807
SW(4).	0.800	0.874	0.866	0.805
FHLR(1,1)	0.761	0.763	0.716	0.601
FHLR(1,2)	0.761	0.764	0.723	0.723
FHLR(1,3)	0.803	0.847	0.823	0.740
FHLR(1,4)	0.802	0.846	0.822	0.737
FHLR(2,1)	0.816	0.802	0.766	0.727
FHLR(2,2)	0.813	0.809	0.767	0.766
FHLR(2,3)	0.809	0.834	0.804	0.764
FHLR(2,4)	0.819	0.887	0.868	0.790

This exercise indicates that application of our backcasting methodology to a sufficiently representative set of macroeconomic and sectoral variables can yield a very close proxy of actual cyclical fluctuations in U.S. real GDP. To the extent that the in-sample fit for the post-war period is even higher for some of the Latin American countries shown above—and recalling that the span of variables is larger—this suggests that our approach is very likely to be picking up turning points and cyclical variations in these economies quite accurately.

E. Tracking History

As a final robustness check we ask how well the backcasted series square with qualitative historical evidence on events deemed to be major economic turning points in these countries. Figure 7 relates the two. Starting with pre-war Argentina, the index picks up all economic downturns associated with well-known world events—notably the stock market crashes in Europe and the U.S. in 1873 and the ensuing global economic depression, the 1890 Barings crisis, the 1907 financial panic, the two world wars, and the Great Depression of the 1930s. Likewise, major post-WWII shocks are also conspicuously picked up as turning points in our index, notably the boom and bust in world commodity prices associated with the Korean War in the early 1950s, the oil price shocks of the 1970s, the early 1982–83 debt crisis, as well as the emerging market crises of the 1990s (the 1994–95 “Tequila” crisis and the Asia and Russia crises of 1997–98). A glance at Figure 7 also indicates that such a juxtaposition of cyclical turning points in country indices with major global economic events is broadly corroborated for Brazil, Chile, and Mexico.¹⁴

In addition, the portrait of history provided by our index is consistent with narrative evidence about the macroeconomic repercussions of key country-specific events. In the case of Brazil, the index picks up the mini downturn associated with the 1888 political unrest (end of slavery and the republican transition) as well as the subsequent boom (the “Encilhamento”) stemming from a liberal monetary reform that brought about an unprecedented boom in domestic credit and asset valuations in 1889–90 (see Trinner, 2000). The Brazil index tracks equally well what is deemed to have been one of Brazil’s most protracted recessions which culminated in the country’s first sovereign default and the debt rescheduling arrangements under the auspices of the Rothchilds in 1898 (see Fritsch, 1988).¹⁵ As for Chile, our index highlights the upturn of 1879–82 associated with the “War of the Pacific” (against Peru), the downturn around the country’s exit from the gold standard in 1898 (Llona Rodriguez, 2000), as well as the severity of the 1929–32 depression in Chile due to plummeting terms of trade (Diaz-Alejandro, 1984). Both in Argentina and Chile as well as (to a lesser extent) Brazil, the index identifies clear turning points around the military coups of the 1960s and 1970s.

Finally, the Mexico index yields a picture of economic fluctuations that is remarkably consistent with that depicted by Mexican historiography starting with the 1879–82 upturn that is typically associated with the onset of the new regime headed by General Porfirio Diaz (Cardenas, 1997). Likewise, the subsequent recession, which takes place in the wake of the U.S. economic slowdown of 1883–84, is clearly depicted; its 1885 trough coincides with the well-documented austerity plan imposed by Diaz’s finance minister Manuel Dublan that involved a temporary suspension of payments on domestic public debt (Marichal, 2002). This was followed by an upswing associated with Mexico’s renewed access to international capital markets in the wake of the 1886–87 external debt settlement, which was later brought to a halt by a sharp worldwide fall in silver prices (Mexico’s main export item) coupled with a severe downturn in the United States and sudden stop in capital flows to emerging markets in the early 1890s (c.f. Catão and Solomou, 2005). Finally, our business cycle index also provides a new measure of the severity of the economic downturn associated with the Mexican Revolution of 1911–20 identifying a trough around 1915–16—these were the years when the revolutionary conflict peaked and chaotic monetary conditions triggered a hyperinflation (Cardenas and Manns, 1987).

IV. Stylized Business Cycle Facts

Armed with the business cycle indicators for the four countries, we turn to the task of establishing some stylized facts about the four countries’ business cycles. We start with dating the respective turning points. A classic device to this end, which is also consistent with our definition of the business cycle as output deviations from a stochastic or deterministic trend, is the Bry and Boscham (1971) algorithm.¹⁶ It consists of a sequence of procedures starting with the search for extreme values in order to eliminate (near-) permanent jumps in the series associated with outliers, followed by the use of centered moving averages and the search for local maxima or minima within a chosen window length.¹⁷ To permit the identification of both shorter and longer cycles, Panels A and B of Table 4 report results based on two-year and six-year windows, respectively. As expected, the algorithm identifies peaks and troughs that are broadly consistent with a visual inspection of Figure 7. When the narrow window is used, the average duration of the cycle is shorter overall, more so during the post-war era. This finding is consistent with evidence of the shortening business cycle length among advanced countries (see, e.g., Gordon, 1986). Using a longer window, Panel B indicates that the pre-cycle is dominated by the Kuznets or long swings, with similar turning points as those identified in the literature on Anglo-saxon economies (Solomou, 1987). This evidence is further reinforced by spectral density function estimates of the individual country indices, which point to a dominant cyclical length around 14 to 16 years during the 1870–1930 period (a typical Kuznets-swing length), followed by a 10–12 year cycle in post-war data (Table 5).

Table 4:

Dating the Cycle

The table reports peak and trough dates selected by the Bry-Boschan algorithm.Results in panel A impose a minimum of two years between peaks, while results in Panel B impose a minimum of six years berween peaks.

Table 4:

Dating the Cycle

Panel A
Argentina		Brazil		Chile		Mexico
Peaks	Troughs	Peaks	Troughs	Peaks	Troughs	Peaks	Troughs
1873	1880	1872	1876	1875	1877	1883	1886
1884	1887	1881	1886	1882	1885	1891	1894
1889	1891	1891	1893	1890	1894	1898	1902
1893	1895	1896	1901	1896	1897	1907	1909
1899	1902	1907	1908	1898	1902	1912	1916
1913	1918	1912	1915	1907	1909	1921	1927
1923	1926	1927	1931	1912	1915	1928	1932
1930	1933	1938	1942	1918	1919	1936	1938
1938	1945	1946	1948	1926	1927	1941	1942
1948	1953	1951	1956	1929	1932	1945	1947
1958	1959	1962	1967	1937	1942	1951	1953
1961	1963	1974	1976	1943	1947	1956	1959
1965	1968	1979	1983	1952	1954	1960	1962
1970	1971	1986	1988	1957	1958	1965	1971
1974	1978	1990	1992	1962	1965	1974	1977
1980	1985	1997	1999	1966	1970	1981	1988
1987	1990	2002	-	1972	1975	1994	1995
1994	1995	-	-	1980	1983	2000	2002
1997	2002	-	-	1989	1990	-	-
-	-	-	-	1997	2002	-	-

Panel B
Argentina		Brazil		Chile		Mexico
Peaks	Troughs	Peaks	Troughs	Peaks	Troughs	Peaks	Troughs
1873	1880	1881	1876	1890	1885	1883	1886
1889	1891	1891	1886	1912	1909	1898	1916
1899	1902	1913	1901	1929	1919	1921	1927
1913	1918	1927	1915	1943	1932	1936	1938
1930	1933	1938	1931	1952	1947	1951	1959
1948	1953	1951	1942	1980	1958	1965	1971
1961	1971	1962	1956	1997	1983	1981	1995
1980	1985	1979	1967	-	-	-	-
1997	-	1997	1992	-	-	-	-

Table 4:

Dating the Cycle

Panel A
Argentina		Brazil		Chile		Mexico
Peaks	Troughs	Peaks	Troughs	Peaks	Troughs	Peaks	Troughs
1873	1880	1872	1876	1875	1877	1883	1886
1884	1887	1881	1886	1882	1885	1891	1894
1889	1891	1891	1893	1890	1894	1898	1902
1893	1895	1896	1901	1896	1897	1907	1909
1899	1902	1907	1908	1898	1902	1912	1916
1913	1918	1912	1915	1907	1909	1921	1927
1923	1926	1927	1931	1912	1915	1928	1932
1930	1933	1938	1942	1918	1919	1936	1938
1938	1945	1946	1948	1926	1927	1941	1942
1948	1953	1951	1956	1929	1932	1945	1947
1958	1959	1962	1967	1937	1942	1951	1953
1961	1963	1974	1976	1943	1947	1956	1959
1965	1968	1979	1983	1952	1954	1960	1962
1970	1971	1986	1988	1957	1958	1965	1971
1974	1978	1990	1992	1962	1965	1974	1977
1980	1985	1997	1999	1966	1970	1981	1988
1987	1990	2002	-	1972	1975	1994	1995
1994	1995	-	-	1980	1983	2000	2002
1997	2002	-	-	1989	1990	-	-
-	-	-	-	1997	2002	-	-

Panel B
Argentina		Brazil		Chile		Mexico
Peaks	Troughs	Peaks	Troughs	Peaks	Troughs	Peaks	Troughs
1873	1880	1881	1876	1890	1885	1883	1886
1889	1891	1891	1886	1912	1909	1898	1916
1899	1902	1913	1901	1929	1919	1921	1927
1913	1918	1927	1915	1943	1932	1936	1938
1930	1933	1938	1931	1952	1947	1951	1959
1948	1953	1951	1942	1980	1958	1965	1971
1961	1971	1962	1956	1997	1983	1981	1995
1980	1985	1979	1967	-	-	-	-
1997	-	1997	1992	-	-	-	-

Table 5:

Spectral Density Function Estimates of Cyclical Durations

The table reports business cycle durations (in years) for different sample periods. The estimates refer to the peak value of a Bartlett lag window estimate using a bandwidth set at twice the number of sample observations.

Table 5:

Spectral Density Function Estimates of Cyclical Durations

	1870-1929		1930-1970		1971-2004
	Estimate	T	Estimate	T	Estimate	T
Argentina	4.64 (1.96)	16	3.36 (1.48)	12	2.11 (1.02)	12
Brazil	4.57 (1.92)	16	3.90 (1.72)	12	2.35 (1-13)	12
Chile	2.18 (0.92)	16	2.05 (0.90)	12	3.79 (1.90)	8
Mexico	3.75 (1.59)	14	2.35 (1.04)	8	3.14 (1.52)	12

Table 5:

Spectral Density Function Estimates of Cyclical Durations

	1870-1929		1930-1970		1971-2004
	Estimate	T	Estimate	T	Estimate	T
Argentina	4.64 (1.96)	16	3.36 (1.48)	12	2.11 (1.02)	12
Brazil	4.57 (1.92)	16	3.90 (1.72)	12	2.35 (1-13)	12
Chile	2.18 (0.92)	16	2.05 (0.90)	12	3.79 (1.90)	8
Mexico	3.75 (1.59)	14	2.35 (1.04)	8	3.14 (1.52)	12

In sum, both the Bry and Bosham algorithm and the spectral density function estimates point to a reasonably long average cyclical duration in all four countries. The dominant cyclical pattern was generally longer in the pre-1930 era, but even in the post-World War II period, cycles in Latin America were substantially more protracted than in the United States and other advanced countries.

Against this background, Tables 6 and 7 report a set of descriptive statistics that help characterize other stylized facts about Latin America’s business cycles from a broad cross-country historical perspective. First, standard deviations corroborate the perception that Latin America has been a more cyclically volatile region than both countries deemed advanced by today’s definition as well as countries such as Australia, Canada and Japan that were considered “emerging economies” in the pre-war world. This volatility gap between the two groups has changed over time, however. The four Latin American countries were clearly far more volatile in the early globalization period before the 1930s—characterized as it was by free capital mobility and very limited quantitative restrictions on trade. Conversely, there is evidence that the inward growth policies did succeed in fending these countries off global instability in the 1930–70 sub-period, when global volatility generally rose, partly due to the recovery from the 1929–32 depression and war shocks. This appears reflected in the higher standard deviation of the output gap among advanced countries during the period as well as among a group of other developing economies for which pre-war GDP estimates are available (India, Indonesia, Korea, Malaysia, Sri Lanka, South Africa, Taiwan Province of China, and Turkey). But as output gap volatility came down in advanced countries in the post-1960s period (notwithstanding two oil shocks and dramatic changes in policy regimes), cyclical volatility in Latin America remained relatively high; only in the post-debt crisis period has Latin American cyclical volatility declined markedly compared to earlier levels. Further, Table 7 shows that this decline in cyclical volatility over the past 15 years or so has not been a preserve of Latin America but is also observed in other regions of the developing world—partly reflecting lower real interest rate and output volatility in the United States and other advanced countries (see Table 8). Yet, despite being low relative to its earlier historical record, business cycle volatility in Latin America still remains higher than in advanced countries as well as relative to Asian developing countries. Rolling standard deviations of the output gap in Figure 8 summarize this broad overview of volatility trends in the region by plotting both individual country trends as well as that of the common regional cycle (extracted as discussed below).

Table 6:

Persistence and Volatility of the Cycle

The table reports autocorrelation and standard deviation estimates of the cycle obtained from a static two-factor model. Panel A shows results for the backcasted data while Panel B reports results for actual business cycle measures.

Table 6:

Persistence and Volatility of the Cycle

Panel A: Backcasted Data
	1870-1929				1930-1970
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
AR(1)	0.721	0.706	0.549	0.739	0.593	0.763	0.538	0.573
Std	0.065	0.048	0.063	0.066	0.046	0.032.	0.078	0.029

	1971-1987				1988-2004
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
AR(l)	0.089	0.684	0.614	0.606	0.579	0.402	0.562	0.286
Std	0.029	0.037	0.071	0.039	0.065	0.020	0.020	0.024

Panel B: Actual Data
	1971-1987				1988-2004
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
AR(1)	0.168	0.624	0.590	0.644	0.590	0.622	0.687	0.383
Std	0.034	0.043	0.081	0.039	0.068	0.021	0.033	0.030

Table 6:

Persistence and Volatility of the Cycle

Panel A: Backcasted Data
	1870-1929				1930-1970
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
AR(1)	0.721	0.706	0.549	0.739	0.593	0.763	0.538	0.573
Std	0.065	0.048	0.063	0.066	0.046	0.032.	0.078	0.029

	1971-1987				1988-2004
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
AR(l)	0.089	0.684	0.614	0.606	0.579	0.402	0.562	0.286
Std	0.029	0.037	0.071	0.039	0.065	0.020	0.020	0.024

Panel B: Actual Data
	1971-1987				1988-2004
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
AR(1)	0.168	0.624	0.590	0.644	0.590	0.622	0.687	0.383
Std	0.034	0.043	0.081	0.039	0.068	0.021	0.033	0.030

Table 7:

International Comparisons

The table reports autocorrelation and standard deviation estimates of the business cycle. Panel A shows median regional values for Latin America, LA-4, (Argentina, Brazil, Chile and Mexico), European Countries, EU-4, (France, Germany, Italy and the UK), New World countries, NW-3, (USA, Canada and Australia) and Japan, JP. The estimates of the cycle for Latin America are obtained from a dynamic factor model. Panel B compares median regional values for Latin America, LA-4, (Argentina, Brazil, Chile and Mexico), other developing countries, Other LDCs, (India, Indonesia, Korea, Malaysia, Taiwan, South Africa, and Turkey), Africa (41 countries), Asia (11 countries), and the Middle East (18 countries) based on actual data.

Table 7:

International Comparisons

Panel A: Advanced Countries Data
	1870-1929				1930-1970
	LA-4	EU-4	NW-3	JP	LA-4	EU-4	NW-3	JP
AR(1)	0.719	0.507	0.517	0.031	0.583	0.698	0.731	0.599
Std	0.065	0.051	0.050	0.035	0.039	0.101	0.066	0.128
	1971-1987				1988-2004
	LA-4	EU-4	NW-3	JP	LA-4	EU-4	NW-3	JP
AR(1)	0.610	0.526	0.477	0.683	0.482	0.619	0.501	0.417
Std	0.038	0.017	0.021	0.027	0.022	0.015	0.022	0.018

Panel B: Developing Countries Data
	1930-1950					1950-1970
	LA-4	Other LDCs	Africa	Asia	Middle East	LA-4	Other LDCs	Africa	Asia	Middle East
AR(1)	0.560	0.617	-	-	-	0.273	0.051	0.502	0.416	0.402
Std	0.040	0.078	-	-	-	0.031	0.030	0.038	0.028	0.043
	1971-1987					1988-2004
	LA-4	Other LDCs	Africa	Asia	Middle East	LA-4	Other LDCs	Africa	Asia	Middle East
AR(1)	0.607	0.551	0.563	0.486	0.447	0.606	0.531	0.481	0.547	0.572
Std	0.041	0.038	0.051	0.033	0.031	0.031	0.028	0.035	0.028	0.057

Table 7:

International Comparisons

Panel A: Advanced Countries Data
	1870-1929				1930-1970
	LA-4	EU-4	NW-3	JP	LA-4	EU-4	NW-3	JP
AR(1)	0.719	0.507	0.517	0.031	0.583	0.698	0.731	0.599
Std	0.065	0.051	0.050	0.035	0.039	0.101	0.066	0.128
	1971-1987				1988-2004
	LA-4	EU-4	NW-3	JP	LA-4	EU-4	NW-3	JP
AR(1)	0.610	0.526	0.477	0.683	0.482	0.619	0.501	0.417
Std	0.038	0.017	0.021	0.027	0.022	0.015	0.022	0.018

Panel B: Developing Countries Data
	1930-1950					1950-1970
	LA-4	Other LDCs	Africa	Asia	Middle East	LA-4	Other LDCs	Africa	Asia	Middle East
AR(1)	0.560	0.617	-	-	-	0.273	0.051	0.502	0.416	0.402
Std	0.040	0.078	-	-	-	0.031	0.030	0.038	0.028	0.043
	1971-1987					1988-2004
	LA-4	Other LDCs	Africa	Asia	Middle East	LA-4	Other LDCs	Africa	Asia	Middle East
AR(1)	0.607	0.551	0.563	0.486	0.447	0.606	0.531	0.481	0.547	0.572
Std	0.041	0.038	0.051	0.033	0.031	0.031	0.028	0.035	0.028	0.057

Table 8:

Cyclical Volatility Estimates of Selected Variables

The table reports standard deviations (in percent) for selected variables and different sample periods.

Table 8:

Cyclical Volatility Estimates of Selected Variables

The table reports standard deviations (in percent) for selected variables and different sample periods.

Panel A: 1870-1929
	Argentina	Brazil	Chile	Mexico
Foreign Interest Rate	5.34	5.34	5.34	5.34
Foreign Output	3.46	3.46	3.46	3.46
Domestic Output	6.49	4.84	6.25	7.29
Terms of Trade	14.99	21.79	33.05	29.00
Export Volume	13.20	10.21	17.61	10.34
Fixed Investment	107.80	37.16	76.05	79.00
Government Spending	66.23	47.85	39.33	33.71
Expenditure/Revenue	28.41	20.82	28.83	10.70
Narrow Money	14.94	15.32	16.64	35.07
Broad Money	14.82	14.62	11.39	35.83
Real Wage	12.33	9.14	8.69	32.73

Panel B: 1930-1970
	Argentina	Brazil	Chile	Mexico
Foreign Interest Rate	4.68	4.68	4.68	4.68
Foreign Output	7.08	7.08	7.08	7.08
Domestic Output	4.56	3.25	7.69	2.90
Terms of Trade	12.20	20.27	26,66	29.37
Export Volume	13.59	9.95	16.89	9.52
Fixed Investment	67.96	29.56	64.60	102.36
Government Spending	14.09	13.27	13.69	16.73
Expenditure/Revenue	23.36	16.21	13.83	19.64
Narrow Money	10.20	11.01	19.90	15.43
Broad Money	12.33	10.84	13.46	13.62
Real Wage	6.99	6.54	13.07	18.22

Panel C: 1971-2004
	Argentina	Brazil	Chile	Mexico
Foreign Interest Rate	2.20	2.20	2.20	2.20
Foreign Output	2.97	2.97	2.97	2.97
Domestic Output	5.01	2.94	5.35	3.30
Terms of Trade	27.14	12.24	16.45	22.20
Export Volume	12.94	8.11	6.87	9.61
Fixed Investment	16.39	15.82	16.10	14.93
Government Spending	8.14	66.37	44.21	40.33
Expenditure/Revenue	22.53	9.05	12.15	18.05
Narrow Money	16.84	15.81	21.89	10.48
Broad Money	20.32	22.82	17.31	19.00
Real Wage	12.44	5.72	12.30	15.13

Table 8:

Cyclical Volatility Estimates of Selected Variables

The table reports standard deviations (in percent) for selected variables and different sample periods.

Panel A: 1870-1929
	Argentina	Brazil	Chile	Mexico
Foreign Interest Rate	5.34	5.34	5.34	5.34
Foreign Output	3.46	3.46	3.46	3.46
Domestic Output	6.49	4.84	6.25	7.29
Terms of Trade	14.99	21.79	33.05	29.00
Export Volume	13.20	10.21	17.61	10.34
Fixed Investment	107.80	37.16	76.05	79.00
Government Spending	66.23	47.85	39.33	33.71
Expenditure/Revenue	28.41	20.82	28.83	10.70
Narrow Money	14.94	15.32	16.64	35.07
Broad Money	14.82	14.62	11.39	35.83
Real Wage	12.33	9.14	8.69	32.73

Panel B: 1930-1970
	Argentina	Brazil	Chile	Mexico
Foreign Interest Rate	4.68	4.68	4.68	4.68
Foreign Output	7.08	7.08	7.08	7.08
Domestic Output	4.56	3.25	7.69	2.90
Terms of Trade	12.20	20.27	26,66	29.37
Export Volume	13.59	9.95	16.89	9.52
Fixed Investment	67.96	29.56	64.60	102.36
Government Spending	14.09	13.27	13.69	16.73
Expenditure/Revenue	23.36	16.21	13.83	19.64
Narrow Money	10.20	11.01	19.90	15.43
Broad Money	12.33	10.84	13.46	13.62
Real Wage	6.99	6.54	13.07	18.22

Panel C: 1971-2004
	Argentina	Brazil	Chile	Mexico
Foreign Interest Rate	2.20	2.20	2.20	2.20
Foreign Output	2.97	2.97	2.97	2.97
Domestic Output	5.01	2.94	5.35	3.30
Terms of Trade	27.14	12.24	16.45	22.20
Export Volume	12.94	8.11	6.87	9.61
Fixed Investment	16.39	15.82	16.10	14.93
Government Spending	8.14	66.37	44.21	40.33
Expenditure/Revenue	22.53	9.05	12.15	18.05
Narrow Money	16.84	15.81	21.89	10.48
Broad Money	20.32	22.82	17.31	19.00
Real Wage	12.44	5.72	12.30	15.13

Table 8 focuses on key drivers of aggregate business cycles in the four economies, once again broken down by sub-periods. The table clearly highlights some stylized facts that have been stressed in previous studies (Backus and Kehoe, 1992; Mendoza, 1995; Basu and Taylor, 1999; Agénor et al. 2000). First, cyclical volatility in fixed investment is much higher than that of output. Second, and consistent with the findings of Backus and Kehoe (1992) for advanced countries, government spending volatility is higher than output volatility. For all four countries and across all sub-periods, the magnitude of two simple gauges of government-induced volatility—the real government expenditure cycle and the ratio of public expenditure to revenues—is staggering. Coupled with the positive loadings of the real government expenditure variable on the first (pro-cyclical) factor in Table 1—and with all the caveats about some inevitable endogeneity of this or indeed of any measure of the fiscal stance—this provides a prima facie case that changes in fiscal stances have been important drivers of the business cycle in these countries. This finding squares well with the post-1960 evidence on strong fiscal procyclicality in these countries provided in Kaminsky, Reinhart and Végh (2004) who use the cyclical component of real government spending as their main gauge.

Third, the volatility of monetary aggregates (expressed in real terms) is smaller than that of the fiscal variables with the exception of Argentina and Brazil over the past two decades and Chile in the 1970s reflecting bouts of high- and hyper-inflation in these countries. Interestingly, however, inflation has been broadly counter-cyclical (see Table 1), in stark contrast with the Phillips-curve trade-off which is usually deemed to hold at least among advanced countries. The counter-cyclical behavior of inflation makes the apparent procyclicality of real wages (see Table 1) consistent both with models based on short-run nominal wage stickiness as well as with real business cycle models which emphasize the dominant role of technology shocks in shifting the labor demand schedule over business cycle frequencies. Finally, terms of trade fluctuations are highly procyclical and, consistent with earlier work (Mendoza, 1995), emerge as an important (and more clearly exogenous) source of output volatility. While this may not be particularly surprising given that all four countries have mainly been primary commodity exporters for much of the period (the manufacturing share of Brazil’s and Mexico’s exports only became prominent over the past couple of decades), it is still instructive to observe the sheer magnitude of the phenomenon. To the extent that terms of trade volatility has important welfare implications and is usually associated with poorer long-term growth performance (Blattman, Hwang, and Williamson, 2006), this emerges as an important feature of the data.

A final set of stylized facts that we document can be gleaned from a look at Figure 7, which shows that several major business cycle turning points—such as those of the early 1890s, World War I, the early 1930s and the early 1980s—are common to all or most of the four countries. A formal measure of such synchronicity is the concordance index proposed by Harding and Pagan (2002). It consists of a non-parametric measure of the relative frequency at which countries are jointly undergoing an expansion or a contraction phase gauged by a binary indicator. Table 9 reports the respective statistic which ranges from a minimum of zero (no concordance) to unity (perfect concordance). The results indicate that Latin American business cycles have displayed a reasonably high degree of synchronization through the 1870–2004 period. This is especially striking in light of the fact that there has been very little intra-regional trade between these economies until the past fifteen years or so, and that such synchronization did not decline dramatically during the period from the early 1930s to the early 1970s marked by strong trade restrictions and capital controls. These results indicate the presence of a common regional factor superimposed on the distinct country-specific business cycle drivers. To gauge this hypothesis more formally we use the econometric methodology from Section II to extract common factors from a pooled data set that brings all four countries’ data together.¹⁸ The resulting regional factor jointly loads on the various country specific business cycle indicators. Corroborating the concordance metric of Table 9, the regional factor generates correlation coefficients between 0.6 and 0.75 with the procyclical factor (F1) of the business cycle indices in the four individual countries.¹⁹ This clearly points to a sizeable regional common component. This is consistent with both the importance of external variables in the various countries’ individual factor loadings (see Table 1), as well as with a long and distinguished literature on the roles of foreign interest rates, income shocks in advanced countries, and commodity terms of trade in triggering financial crises and, more generally, driving key macroeconomic aggregates in Latin America (Diaz-Alejandro, 1984; Fishlow, 1989; Calvo, Leiderman, and Reinhart, 1993; Fernandez-Arias, 1994; Neumeyer and Perri, 2005).

Table 9:

Synchronization of the Latin American Cycles

The table reports the Harding-Pagan concordance statistic. Values close to one show evidence of a stronger degree of synchronicity.

Table 9:

Synchronization of the Latin American Cycles

The table reports the Harding-Pagan concordance statistic. Values close to one show evidence of a stronger degree of synchronicity.

	1878-1929				1930-1970
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
Arg	1.00	0.48	0.54	0.62	1.00	0.54	0.54	0.49
Bra	-	1.00	0.79	0.71	-	1.00	0.66	0.46
Chi	-	-	1.00	0.77	-	-	1.00	0.61
Mex	-	-	-	1.00	-	-	-	1.00

	1971-1987				1988-2004
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
Arg	1.00	0.59	0.53	0.76	1.00	0.41	0.82	0.71
Bra	-	1.00	0.71	0.59	-	1.00	0.47	0.47
Chi	-	-	1.00	0.41	-	-	1.00	0.65
Mex	-	-	-	1.00	-	-	-	1.00

Table 9:

Synchronization of the Latin American Cycles

The table reports the Harding-Pagan concordance statistic. Values close to one show evidence of a stronger degree of synchronicity.

	1878-1929				1930-1970
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
Arg	1.00	0.48	0.54	0.62	1.00	0.54	0.54	0.49
Bra	-	1.00	0.79	0.71	-	1.00	0.66	0.46
Chi	-	-	1.00	0.77	-	-	1.00	0.61
Mex	-	-	-	1.00	-	-	-	1.00

	1971-1987				1988-2004
	Arg	Bra	Chi	Mex	Arg	Bra	Chi	Mex
Arg	1.00	0.59	0.53	0.76	1.00	0.41	0.82	0.71
Bra	-	1.00	0.71	0.59	-	1.00	0.47	0.47
Chi	-	-	1.00	0.41	-	-	1.00	0.65
Mex	-	-	-	1.00	-	-	-	1.00

V. Conclusions

This paper has sought to fill some of the lacuna in the international business cycle literature. Taking a century long view of the Latin American business cycle allowed us to characterize a host of stylized facts, compare them with existing evidence for other countries, and identify important differences in business cycle behavior across distinct policy and developmental regimes.

We have shown that Latin America has historically displayed high cyclical volatility compared to advanced country and other relevant benchmarks. Further, this volatility has been time-varying. It was highest during the early globalization era of the late 19th and early 20th century—precisely during the formative years of key national institutions—then declined markedly over the four decades since the great depression. Yet, we have also shown that after bouncing back in the wake of the large global shocks of the 1970s and early 1980s (Bretton Woods abandonment, oil price and interest rate shocks), business cycle volatility in Latin America subsequently declined to near historical lows. Since this coincides with greater trade and financial openness, a prima-facie link between business cycle volatility and openness is unwarranted looking at the period as a whole. Lower external volatility in output and interest rates over the past fifteen years or so is certainly a set of factors at play; more stable fiscal and monetary policies is another, which also helps explain the different volatility performances across countries amidst the general downward trend.

The paper’s other main finding is that such volatility has been strikingly coupled with high business cycle persistence. Since the welfare costs of business cycles are known to rise on both volatility and persistence, the attendant welfare losses have been non-trivial. While it is beyond the scope of our analysis to probe further into the sources of output persistence in the four countries, there is cross-country evidence suggesting that the role of domestic institutions and their constraints on policy making are key (Acemoglu, Johnson, and Robinson, 2006). In addition, to the extent that external developments have themselves been a main source of such persistent shocks via commodity terms of trade and macroeconomic conditions in advanced countries, this has made the task of stabilization policies all the more difficult throughout the region.

We have also shown that several empirical regularities highlighted in the existing business cycle literature readily apply to the four countries. One set of regularities pertains to the countercyclicality of trade balances and the much higher cyclical amplitude of both fixed investment and real government spending relative to output. Indeed, using the simple yardstick of the co-movement between real government expenditures and the output cycle employed elsewhere (Kaminsky, Reinhart and Végh, 2004), we find that fiscal policy has been procylical in all four countries. A comparison between the volatility of external aggregates such as the output gap in advanced countries and external interest rates, and the volatility of domestic aggregates such as public expenditures and revenues as well as, to a lesser extent, real money indicate, if anything, that domestic amplification mechanisms have played a key role. This suggest that these mechanisms deserves close scrutiny by future research on business cycles in these countries.

Finally, our common factor framework also allowed us to identify a sizeable regional common component in Latin American business cycles. Since trade linkages between these economies have been small well into the 1980s, and as capital market linkages remain so to date, this highlights the role of global factors in driving such a regional common cycle. This evidence is consistent with a long literature on the roles of external factors in both triggering financial crises (e.g. Diaz-Alejandro, 1984; Fishlow, 1989) and driving key macroeconomic aggregates in the region (Calvo, Leiderman and Reinhart, 1993; Fernandez-Arias, 1994; Neumeyer and Perri, 2005), as well as with the findings of more general and recent studies emphasizing the role of international factors in individual countries’ business cycles (Kose, Otrok, Whiteman, 2003; Canova 2004). In extending these findings to Latin America based on wider time series evidence, the results presented in this paper further highlight the limited scope that regional risk-sharing has had historically.

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Topics

Countries

Series

About

Resources

Contributor Notes

Abstract

I. Introduction

II. Econometric Framework

A. Model Specification and Dynamic Factor Estimation

B. Backcasting Historical Activity Measures with Dynamic Factor Models

III. New Business Cycle Indices for Latin America

A. Empirical Results

B. Robustness Analysis

C. Gains from Using Extended Data Set

D. Actual vs. Backcasted Series: A Test Based on U.S. data

E. Tracking History

IV. Stylized Business Cycle Facts

V. Conclusions

References