Printer Friendly

Output growth and structural reform in Latin America: have business cycles changed?

I. INTRODUCTION

In recent years. Latin American (LatAm) countries have experienced an unprecedented period of booming asset prices and investment, appreciating real exchange rates, and strong output growth (Izquierdo, Romero, and Talvi 2008: Sosa, Tsounta, and Kim 2013). The improvement in output growth is evident in the statistics for quarterly real gross domestic product (GDP) summarized in Table I for six large LatAm countries (Argentina, Brazil, Chile, Colombia, Mexico, and Peru). For example, during the 1980s, the region's average quarterly real GDP growth rate was 0.43% (almost 2% in annual terms). (1) The region's average growth rate rose to 0.70% in the 1990s and was 1.20% (almost 5% in annual terms) in the 2000s. In addition, we observe a substantial reduction in the volatility of the growth rate of GDP. During the 1980s, the region's average standard deviation of quarterly real GDP growth was 2.85%. There is a reduction to 1.70% in the 1990s, and in the 2000s the standard deviation of the quarterly growth rate was only 1.27%. In sum, over the last 3 decades, LatAm economies have shown a trend toward stronger mean growth and reduced volatility in real GDP.

The empirical literature on LatAm business cycles suggests several explanations for (some of) the changes observed in output growth. For example. Easterly, Loayza, and Montiel (1997) argue that growth in the 1990s was stronger than in previous decades due to the changes in economic policies (structural reforms) implemented in LatAm mainly in the 1980s (Lora 1997. 2012). In contrast, recent research has focused on the role of external conditions. For example. Calderon and Fuentes (2014) argue that the decline in the amplitude of recessions observed in LatAm during what they call the "globalization era" (after 1990) can be partially attributed to structural changes in advanced economies (the Great Moderation). In addition. Osterholm and Zettelmeyer (2007), Izquierdo, Romero, and Talvi (2008), and Camacho and Perez-Quiros (2013) show that favorable external conditions such as abundant international liquidity and a rise in commodity prices can explain a significant share of recent LatAm growth. As summarized in Table I (bottom panel), the average quarterly growth rate of relevant commodity price indexes was negative (-0.31%) in the 1980s and approximately 0% in the 1990s. But after 2003, the average quarterly growth rate of commodity prices rose to 3.75% (approximately 15% in annual terms). That is, the relevant commodity price indexes exhibit a trend similar to the one observed in the mean growth rate and standard deviation of real GDP in LatAm. (2)

Based on these results, in this paper, I ask whether there has been a structural break in LatAm toward stronger growth and more stability. To investigate the nature of the potential structural break in the real GDP growth processes, autoregressive (AR) models with Markov-switching parameters (Kim and Nelson 1999a; Kim, Morley, and Nelson 2004a; Kim, Nelson, and Piger 2004b) that allow for permanent regime shifts are fitted to the quarterly series of the six LatAm countries. Next I ask: If there has been a structural break, has the timing been similar across countries? Finally, I ask: How much of the recent improvement in LatAm's real GDP growth can be attributed to the boom in commodity prices observed in the last decade? To answer this last question, I incorporate the growth rate of commodity prices to the Markov-switching AR models allowing for linear and nonlinear effects on real GDP and compute the average contribution of changes in commodity prices to growth. The approach is similar to the one used in Hamilton (2003, 2011) to model the potentially nonlinear relationship between U.S. real GDP growth and changes in oil prices.

Estimation results suggest important changes in the real GDP processes of the six LatAm countries. First, there is strong evidence of a structural break in real GDP with break dates clustered between the early 1990s and late 1990s. Although there are differences between countries, the break is toward stronger mean growth and a substantial reduction in volatility. Second, the timing of the breaks (around the time of the structural reforms) suggests that the important changes in economic policies of the 1980s and 1990s have been effective in permanently improving economic growth in LatAm. But while the literature has documented mainly an improvement in the mean growth rate of real GDP (e.g., Easterly, Loayza. and Montiel 1997), the results presented here show that the structural reforms also led to important reductions in the volatility of real GDP growth (49% for Argentina. 51% for Brazil, and 67% for Peru). Overall, these changes in the real GDP growth processes have important implications for the characteristics of the business cycle phases in LatAm. As explained in Blanchard and Simon (2001) and Harding and Pagan (2002), these results imply that in the post-break sample recessions are shorter in duration and milder in amplitude. This result is consistent with recent findings of Goncalves and Salles (2008), Aiolfi et al. (2011), and Calderon and Fuentes (2014) who show that the amplitude of recessions has declined in LatAm after 1990.

Finally, I find strong evidence of a positive and linear relationship between the growth rate of real GDP and the growth rate of commodity prices in LatAm. But contrary to Camacho and Perez-Quiros (2013). the hypothesis that commodity price increases have different economic effects from commodity price decreases (i.e., the relationship is nonlinear) is strongly rejected for all countries considered. On average. the effect of commodity prices on real GDP growth in the 1980s and 1990s was small and sometimes negative. In contrast, the effect after 2003 was positive and much larger in magnitude (up to 2% of annual real GDP growth for Peru). As a result, the sustained increase in commodity prices observed in recent years explains an important share of LatAm growth since 2003. But after accounting for the effect of commodity prices, there is even stronger evidence of a structural break in real GDP growth toward an increase in mean growth and a reduction in volatility.

This paper is organized as follows. Section II documents important changes in the real GDP growth processes of the six LatAm countries considered, as well as changes in the evolution of country-specific commodity price indexes. Section III presents model specifications used to investigate the nature of the potential structural break in real GDP growth. Section IV reports estimation results for each country, including a discussion of the timing of the breaks and an estimation of the contribution of commodity prices to real GDP growth. Section V concludes.

II. RECENT CHANGES IN OUTPUT GROWTH

In this Section I document important changes in the output growth processes of six large LatAm countries. Data employed are quarterly real GDP (seasonally adjusted) for Argentina. Brazil. Chile. Colombia, Mexico, and Peru obtained from Cesa-Bianchi et al. (2012) and Rondeau (2012). Quarterly growth rates ([DELTA][y.sub.t]) are computed as l00 x [DELTA] lnn [Y.sub.t] where [Y.sub.t] is quarterly real GDP for a given country. The sample period is 1983Q1-2010Q4 for all countries except Brazil and Colombia. In the case of Brazil, the sample period is 1990Q1-2010Q4, while in the case of Colombia the sample period is 1994Q1-2010Q4. Figure 1 shows the rolling average of quarterly real GDP growth using an 8-year window (solid line) for the six countries. The reported value for quarter t is the average growth rate over quarters t - 31 to t. Figure 1 also shows the estimated linear trends (dashed line) fitted to the rolling averages and the regression [R.sup.2]. Average growth rates have increased over the sample period, that is. the trend coefficient is positive and statistically significant at the 5% level, for all countries except Chile and Mexico. While in the case of Chile the coefficient is negative and statistically significant at the 5% level. Mexico does not show significant changes in average growth.

Figure 2 shows the rolling standard deviation of quarterly real GDP growth using an 8-year window (solid line) for the six countries. The values are computed in the same way as the rolling averages, that is, the reported value for quarter t is the standard deviation of the growth rate over quarters t - 31 to t. Figure 2 also shows the estimated linear trends (dashed line) fitted to the rolling standard deviations and the regression [R.sup.2]. Over the sample period, the volatility of real GDP growth has substantially declined in LatAm. The regressions yield a coefficient on the trend term that is negative and statistically significant at the 5% level for all countries.

The next question is whether these changes in the unconditional moments (mean and variance) of real GDP growth arise from changes in the conditional mean (i.e., changes in the autoregressive coefficients), changes in the conditional variance (i.e., changes in the innovation variance), or both. To answer this question, I test for parameter instability using an autoregressive (AR) model for real GDP growth given by

(1) [DELTA][y.sub.t] = c + [k.summation over of (j=1)] [[phi].sub.j][DELTA][y.sub.t-j] + [[epsilon].sub.t], [[epsilon].sub.t] ~ iidN (0, [[sigma].sup.2.sub.[epsilon]])

where [DELTA][y.sub.t], is quarterly real GDP growth and k = 1. For each country, the models are estimated by ordinary least squares (OLS). using all the available data. Table 2 (top panel) reports parameter estimates and the qLL test of parameter instability of Elliott and Muller (2006). The test statistic for parameter instability in the conditional mean (i.e., c and [phi]) is qL[L.sub.1] and the null hypothesis of joint stability is rejected for small values of the statistic. The results show that we can reject the hypothesis of stability in the conditional mean at the 10% level for Argentina, Mexico, and Peru. To test for instability in the conditional variance, the qLL test is computed for the regression

(2) [square root of [pi]/2] x [absolute value of [[??].sub.t]] = s + [[eta].sub.t],

where [absolute value of [[??].sub.t]] is the absolute value of the OLS residuals in Equation (1) and .v is a constant (a similar approach to McConnell and Perez-Quiros 2000). The test statistic for parameter instability in ,s is [qLL.sub.2] and the results reported in Table 2 (bottom panel) show that we can reject the hypothesis of stability in the conditional variance at the 10% level for all countries except Brazil and Colombia. In sum, based on univariate AR models, there is strong evidence of instability in the conditional moments of real GDP growth.

III. MODEL SPECIFICATION

Based on the results in the previous section, a model for real GDP growth should allow for changes in the conditional mean (the coefficients in the AR model) as well as changes in the conditional variance (the innovation variance) of the time series process. Time variation in the parameters can be incorporated in different ways. The most common approach consists in estimating the AR model allowing for one or more permanent structural breaks in the model parameters. For example, Kim and Nelson (1999a), McConnell and Perez-Quiros (2000), Stock and Watson (2002). Kim. Motley, and Nelson (2004a), and Kim. Nelson, and Piger (2004b) use this approach to analyze the reduction in volatility observed in the U.S. economy in the 1980s known as the Great Moderation. (3) In addition, there is evidence of a positive link between real GDP growth and commodity prices for LatAm countries (Camacho and Perez-Quiros 2013).

As a result, I consider an AR(k) model with Markov-switching parameters and commodity prices given by

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [DELTA][y.sub.t], is quarterly real GDP growth. [DELTA][p.sub.t], is the quarterly growth rate of a relevant commodity price index, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], is an unobserved two-state first-order Markov process with transition probabilities given by

(4) Prob ([S.sub.t] = l | [S.sub.t-1 = 1) = p

(5) Prob ([S.sub.t] = 2 | [S.sub.t-1] = 2) = 1

with 0 < p < 1. This model allows for a one-time permanent structural break in the autoregressive parameters [mu], [phi], and [sigma] (i.e., the second regime is absorbing). Therefore, [[mu].sub.1], [[phi].sub.1], and [[sigma].sub.1] are the parameters of the AR(1) model in the pre-break sample (regime 1) and [[mu].sub.2], [[phi].sub.2], and [[sigma].sub.2] are the parameters of the model in the post-break sample (regime 2). A key component of this model is the term [beta](L)[DELTA][p.sub.t] which captures the contribution of commodity prices to real GDP growth (measured as the optimal one-quarter-ahead forecast). In addition, the term [gamma] (L) [DELTA][p.sup.+.sub.t] allows commodity price increases to have different economic effects from commodity price decreases. (4) These terms imply [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and. as a result, an alternative interpretation of (3) is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], that is, a model with a time-varying and regime-specific mean growth rate. For example, Hamilton (2003, 2011) uses a similar approach to model the potentially nonlinear relationship between U.S. real GDP growth and changes in oil prices. Finally, the unknown break date ([tau]) is treated as a parameter to be estimated as the expected duration of regime I. that is, E([tau])= 1/(1 - p). The model can be estimated by maximum likelihood (ML) following Kim and Nelson (1999b) and Kang et al. (2009).

I consider four competing models based on the following restrictions:

1. Model I: A standard AR(1) without structural breaks or commodity prices.

Restrictions: [[mu].sub.1] = [[mu].sub.2], [[phi]].sub.1] = [[phi]].sub.2], [[sigma].sub.1] = [[sigma].sub.2], and [[beta].sub.1] = [[beta].sub.2] = [[gamma].sub.1] = [[gamma].sub.2] = 0

2. Model II: A MS-AR(1) with one break but no commodity prices.

Restrictions: [[beta].sub.1] = [[beta].sub.2] = [[gamma].sub.1] = [[gamma].sub.2] = 0.

3. Model III: A MS-ARX(1) with one break and linear commodity prices.

Restrictions: [[gamma].sub.1] = [[gamma].sub.2] = 0.

4. Model IV: A MS-ARX(1) with one break and nonlinear commodity prices.

No restrictions.

Model selection is based on the Akaike Information Criterion (AIC) calculated as -ln L + k where In I. denotes the log likelihood and k is the number of parameters in the model. In addition, I investigate the nature of the potential structural break in real GDP growth by testing the following two null hypotheses: (I) No break in the conditional mean ([H.sub.0]: [[mu].sub.1] = [[mu].sub.2] and [[phi].sub.1] = [[phi].sub.2]); (2) No break in the conditional variance ([H.sub.0]: [[sigma].sub.1] = [[sigma].sub.2]). Finally. I investigate the relationship between real GDP growth and the growth rate of commodity prices by testing the following two null hypotheses: (1) No relationship ([H.sub.0]: [[beta].sub.1], [[beta].sub.2] = 0 and [[gamma].sub.1] = [[gamma].sub.2] = 0): (2) A linear relationship ([H.sub.0]: [[gamma].sub.1] = [[gamma].sub.2] = 0). These hypotheses are tested using standard likelihood ratio (LR) tests.

IV. EMPIRICAL RESULTS

In this section. I present empirical results for the four competing models. As before, the sample period is 1983Q1-2010Q4 for all countries except Brazil and Colombia. In the case of Brazil, the sample period is 1990Q1-2010Q4. while in the case of Colombia the sample period is 1994Q1-2010Q4. Country-specific commodity price indexes are from Chen and Lee (2013). (5) Sections 1V.A and IV.B report model selection and estimation results for each country. The results are discussed in more detail in Sections IV.C and IV.D. Finally. Section IV.E reports some robustness results.

A. Model Selection

Table 3 reports the value of the ln L. number of parameters in the model, and AIC for each of the four models considered. For all countries except Argentina, AIC selects a model with a structural break and commodity prices. But contrary to Camacho and Perez-Quiros (2013), models that allow for commodity price increases to have different economic effects from commodity price decreases (i.e.. a nonlinear relationship) are consistently rejected. Only in the case of Argentina AIC selects a model with a break but no commodity prices--a surprising result. Overall, based on the value of the ln L. the improvements in fit relative to the linear AR(1) models with no commodity prices (Model I) can be substantial.

Other model specifications were considered (results not reported). For example, AR models with commodity prices but no breaks, ARX(1), were systematically rejected in favor of models with at least one structural break. Models allowing for two permanent structural breaks, with and without commodity prices, were also rejected in favor of models with one break. Only Argentina shows evidence of a second structural break taking place around 2002Q2. Finally, I considered models with different lag orders, including a [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (L) polynomial of order 2 and a [beta](L) polynomial of order 4. I found that the specification reported above was sufficient to capture the dynamics of real GDP growth in all countries.

B. Estimates

ML estimates of the MS-AR(1) models (Model II). that is. models without commodity prices, are reported in Table 4. Ljung-Box Q-statistics computed for the (centered) generalized residuals (Kim, Morley. and Nelson 2004a: Kim. Nelson, and Piger 2004b: Kang et al. 2009) support that the selected specification was sufficient to capture the dynamics of real GDP growth in all countries as there is no evidence of remaining serial correlation. The first noticeable result is that average quarterly growth rates are larger in regime 2 for all countries except Chile (consistent with the results reported in Figure 1). The changes in mean growth range from modest (Mexico) lo very large (Argentina. Brazil, and Peru). For example, in the case of Peru, pre-break quarterly mean growth is -0.39% while post-break mean growth is 1.33%. The case of Chile is different as quarterly mean growth in the post-break period exhibits a 34% reduction relative to the pre-break average. Similarly, the autoregressive coefficients also exhibit important changes. In this case, however, no clear pattern emerges as some countries exhibit an increase in persistence while others exhibit a reduction. Likelihood ratio tests can be used to determine whether these changes in the conditional mean are statistically significant. The null hypothesis of no break in the conditional mean is [[mu].sub.1] = [[mu].sub.2] and [[phi].sub.1] = [[phi].sub.2] and the test statistic is [L[R.sub.1]. Without commodity prices, we reject the null hypothesis for Argentina. Colombia, and Mexico. We also observe an important reduction in the conditional variance for all countries except Mexico (consistent with the results reported in Figure 2). The post-break estimates of the standard deviation are generally smaller than the pre-break estimates and the reductions range from almost 20% for Colombia to over 67% for Peru. The null hypothesis of no break in the conditional variance is [[sigma].sub.1] = [[sigma].sub.2] and the test statistic is L[R.sub.2]. Without commodity prices, we reject the null hypothesis for all countries except Colombia and Mexico. (6) Point estimates of the break dates are obtained from the expected duration (in quarters) of regime 1 and computed as [??] 1/(1 - [??]). Based on the MS-AR(1) models, the estimated break dates are: 1991Q3 for Argentina, 1992Q1 for Brazil. 1999Q2 for Chile, 2000Q2 for Colombia. 1993Q2 for Mexico, and 1993Q1 for Peru.

Table 5 reports ML estimates of the linear MS-ARX(1) models (Model III), that is. models with a structural break and linear commodity prices. This is the preferred model for all countries except Argentina. As before, Ljung-Box Q-statistics show no evidence of remaining serial correlation. The coefficients on the two lags of commodity prices ([[beta].sub.1], and [[beta].sub.2]) are generally positive and significant. A likelihood ratio test ([LR.sub.3]) can be used to test the null hypothesis that the commodity price coefficients are zero ([[beta].sub.1] = [[beta].sub.2] = 0). Consistent with the model selection results, we reject the null hypothesis of no commodity effects for all countries except Argentina. On the other hand, there is no evidence of commodity price increases having different economic effects from commodity price decreases (non-linearity). (7) In addition, with the inclusion of commodity prices, the shift in mean growth is typically smaller but more accurately estimated. As a result, the null hypothesis of no break in the conditional mean {[LR.sub.1]) is now rejected more often. In this case, the hypothesis is rejected for all countries except Brazil and Mexico. Similarly. the null hypothesis of no break in the conditional variance ([LR.sub.2]) is now rejected for all countries except Colombia. Therefore, with commodity prices in the model, there is stronger evidence of a structural break in real GDP growth toward an increase in mean growth and a reduction in volatility.

Figure 3 plots quarterly real GDP growth rates for each country and the smoothed probabilities of structural break from Model III. The probabilities are computed using Kim's smoothing algorithm (see Kim and Nelson 1999b). The break dates appear to be clustered in the early 1990s (Argentina, Brazil, and Peru) and late 1990s (Chile. Colombia, and Mexico). Break date densities are computed by differencing the smoothed probabilities and plotted in Figure 4. All countries except Brazil and Mexico exhibit very concentrated densities for the break date and the timing of the shift appears to be well identified using models with and without commodities. In the case of Brazil and Mexico, there is more uncertainty about the timing of the break. Overall, these results are consistent with the findings of Calderon and Fuentes (2014) who find that during what they call the "globalization era" (after 1990) recessions in LatAm are shorter in duration and milder in amplitude. As discussed in Blanchard and Simon (2001) and Harding and Pagan (2002). an increase in the mean growth rate combined with a reduction in volatility implies business cycles with fewer and shorter recessions.

C. Discussion: Structural Breaks and Structural Reform

Between the mid 1980s and late 1990s, LatAm countries embarked on a process of structural reform of their economies inspired by the "Washington Consensus." These changes are documented in great detail in Lora (1997. 2012), Morley et al. (1999), and Escaith and Paunovic (2004). While initial reactions suggested disappointment with post-reform growth. Easterly et al. (1997) argue that growth in the region was in fact stronger during the 1990s than the previous decade. In addition, de Carvalho Filho and Chainon (2012) argue that reforms led to large improvements in real household income and a substantial reduction in income inequality. The results presented above provide more evidence in this direction. That is, the important changes in economic policies of the 1980s and 1990s have been effective in permanently improving economic growth in LatAm.

For example. Figure 5 plots the smoothed probabilities of structural break from the MS-AR(1) and MS-ARX(1) models and the (normalized) indexes of structural reform of Lora (2012) and Escaith and Paunovic (2004) for Argentina, Brazil, Mexico, and Peru. (8) Existence of a structural break in real GDP growth around the time of the structural reforms provides strong evidence of the effectiveness of these policy changes in Argentina, Brazil, and Peru. But while Easterly et al. (1997) document only an improvement in the average growth rate of output, the results presented above show that the structural reforms of the 1980s and 1990s also led to very important reductions in the volatility of real GDP growth: 49% for Argentina, 51% for Brazil, and 67% for Peru. For the remaining countries (Chile, Colombia, and Mexico), the data do not cover the period before the structural reforms took place in those countries and. as a result, such calculations are not possible. (9)

In addition to the structural breaks identified in the early 1990s. Chile and Colombia show evidence of a break in 1999 and 2000. respectively. These breaks, however, do not appear to be linked to the structural reforms inspired by the "Washington Consensus" but to the adoption of inflation targeting regimes in these countries. For example, Garcia-Solanes and Torrejon-Flores (2012) argue that the starting date of the inflation targeting regimes corresponds to the moment when the central banks began publishing inflation reports with multi-year targets. These dates are May 2000 in Chile and January 1999 in Colombia, while the estimated break dates are 1999Q2 and 2000Q2. respectively. The reductions in the volatility of GDP growth associated with these breaks are important: 46% for Chile and 20% for Colombia. (10) This result is consistent with the findings of Goncalves and Salles (2008) and Garcia-Solanes and Torrejon-Flores (2012) who show that the adoption of inflation targeting regimes led to lower variability in GDP growth.

D. Discussion: The Effect of Commodity Prices

Recent research by Izquierdo et al. (2008) and Camacho and Perez-Quiros (2013) has shown the existence of a positive link between LatAm output growth and commodity prices. Consistent with this result. I find strong evidence of a positive and linear relationship between the growth rate of real GDP and the growth rate of commodity prices for five of the six LatAm countries considered. As a result, in this Section I ask: How much of the recent improvement in LatAm growth can be attributed to the boom in commodity prices observed during the last decade?

To answer this question. Table 6 reports the average contribution of changes in commodity prices to real GDP growth calculated as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [bar.x], with [bar.x] the average growth rate of commodity prices in the sample. The results are based on the estimates of Model III (Table 5) and reported for three relevant sub-samples. As we can observe, changes in commodity prices had a small and sometimes negative effect on real GDP growth in the 1980s and 1990s. On the other hand, the contribution during the last sub-sample (the period 2003-2010) was positive and larger in magnitude for all countries. For example, during this period the average contributions to real GDP growth range from around 0.5% annual growth (Argentina. Chile, and Colombia) to almost 2% (Peru). As a result, the sustained increase in commodity prices observed in recent years explains an important share of LatAm growth since 2003.

E. Robustness

This section examines the robustness of the results presented above to an alternative index of commodity prices. In this case, instead of using the country-specific indexes of Chen and Lee (2013), the models are estimated using the index of all commodity prices constructed by The Economist. (11) One advantage of using an index of all commodity prices is that potential endogeneity concerns should be mitigated.12 Table 7 reports ML estimates of the linear MS-ARX(1) models (Model III) using this index of all commodity prices. Overall, the results are quite similar to those obtained using country-specific price indexes (Table 5) and. for all countries except Argentina, the results of the tests are unchanged. In the case of Argentina, we now find a stronger and significant effect of commodities on real GDP growth.

V. CONCLUSION

This paper documents strong evidence of a structural break in real GDP of six LatAm countries toward stronger mean growth and a substantial reduction in volatility. The timing of the breaks suggests that the important changes in economic policies of the 1980s and 1990s have been effective in permanently improving economic growth in the region. But while the literature has documented mainly an improvement in the mean growth rate of real GDP (e.g., Easterly et al., 1997), this paper documents substantial reductions in the volatility of real GDP growth (49% for Argentina, 51% for Brazil, and 67% for Peru). These changes in the growth processes imply recessions that are shorter in duration and milder in amplitude, consistent with recent findings of Aiolfi et al. (2011) and Calderon and Fuentes (2014). In addition, there is strong evidence of a positive and linear relationship between the growth rate of real GDP and the growth rate of commodity prices. As a result, the sustained increase in commodity prices observed in recent years explains an important share of LatAm growth since 2003. But after accounting for the effect of commodity prices, there is even stronger evidence of a structural break in real GDP growth toward an increase in mean growth and a reduction in volatility.

doi: 10.1111/coep.12178

ABBREVIATIONS

AIC: Akaike Information Criterion

AR: Autoregressive

GDP: Gross Domestic Product

LatAm: Latin American

LR: Likelihood Ratio

ML: Maximum Likelihood

OLS: Ordinary Least Squares

REFERENCES

Aiolfi, M., L. Catao, and A. Timmermann. "Common Factors in Latin America's Business Cycles." Journal of Development Economics. 95, 2011, 212-28.

Blanchard, O., and J. Simon. "The Long and Large Decline in U.S. Output Volatility." Brookings Papers on Economic Activity, 1, 2001, 135-64.

Calderon, C., and J. R. Fuentes. "Have Business Cycles Changed Over the Last Two Decades? An Empirical Investigation." Journal of Development Economics. 109, 2014, 98-123.

Camacho, M. and G. Perez-Quiros. "Commodity Prices and the Business Cycle in Latin America: Living and Dying by Commodities." Working Paper No. 1304, Madrid: Banco de Espana, 2013.

de Carvalho Filho, L. and M. Chamon. "The Myth of Post-Reform Income Stagnation: Evidence from Brazil and Mexico." Journal of Development Economics, 97, 2012, 368-86.

Cesa-Bianchi, A., M. H. Pesaran. A. Rebucci, and T. Xu, "China's Emergence in the World Economy and Business Cycles in Latin America." Economia, 12, 2012, 1-75.

Chen, Y., and D. Lee. "What Makes a Commodity Currency?" University of Washington Working Paper, 2013.

Easterly, W., N. Loayza, and P. Montiel. "Has Latin America's Post-Reform Growth Been Disappointing?" Journal of International Economics, 43, 1997, 287-311.

Elliott, G., and U. K. Muller. "Efficient Tests for General Persistent Time Variation in Regression Coefficients." Review of Economic Studies. 73, 2006, 907-40.

Escaith, H., and I. Paunovic Reformas estructurales en America Latina y el Caribe en el periodo 1970-2000: Indices y notas metodologicas. Santiago de Chile: Economic Commission for Latin America and the Caribbean, 2004.

Garcia-Solanes, J., and F. Torrejon-Flores. "Inflation Targeting Works Well in Latin America." CEPAL Review, 106, 2012, 37-53.

Goncalves, C. E., and J. M. Salles. "Inflation Targeting in Emerging Economies: What Do the Data Say?" Journal of Development Economics, 85, 2008, 312-18.

Hamilton, J. "What Is an Oil Shock?" Journal of Econometrics, 113, 2003, 363-98.

Hamilton, J. "Nonlinearities and the Macroeconomic Effects of oil Prices." Macroeconomic Dynamics, 15, 2011, 364-78.

Harding, D., and A. Pagan. "Dissecting the Cycle: A Methodological Investigation." Journal of Monetary Economics, 49, 2002, 365-81.

Izquierdo, A., R. Romero, and E. Talvi. "Booms and Busts in Latin America: The Role of External Factors." Working Paper No. 631. Washington, DC: Inter-American Development Bank, 2008.

Kang, K. H., C. J. Kim. and J. Morley. "Changes in U.S. Inflation Persistence." Studies in Nonlinear Dynamics & Econometrics, 13, 2009, 1-21.

Kim, C. J., J. Morley, and C. R. Nelson. "Is There a Positive Relationship between Stock Market Volatility and the Equity Premium?" Journal of Money. Credit and Banking. 36, 2004a, 339-60.

Kim, C. J., and C. R. Nelson. "Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle." Review of Economics and Statistics, 81, 1999a, 608-16.

--. State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. Cambridge, MA: MIT Press. 1999b.

Kim, C. J., C. R. Nelson, and J. Piger. "The Less Volatile U.S. Economy: A Bayesian Investigation of Breadth, and Potential Explanations." Journal of Business & Economics Statistics, 22, 2004b. 80-93.

Lora, E. "A Decade of Structural Reform in Latin America: What Has Been Reformed and How to Measure It." IDB Working Paper No. 348, Washington, DC: Inter-American Development Bank, 1997.

--. "Structural Reforms in Latin America: What Has Been Reformed and How to Measure It (Updated Version)." IDB Working Paper No. 346. Washington. DC: Inter-American Development Bank, 2012.

McConnell, M. M., and G. Perez-Quiros. "Output Fluctuations in the United States: What Has Changed Since the Early 1980's?" American Economic Review, 90, 2000, 1464-76.

Morley, S., R. Machado, and S. Pettinato. Indexes of Structural Reform in Latin America. Santiago de Chile: Economic Commission for Latin America and the Caribbean, 1999.

Osterholm, P., and J. Zettelmeyer. "The Effect of External Conditions on Growth in Latin America." Working Paper No. 07/176. Washington, DC: International Monetary Fund, 2007.

Rondeau, S. "Sources of Fluctuations in Emerging Markets: DSGE Estimation with Mixed Frequency Data." PhD dissertation. Columbia University. 2012.

Sosa, S., E. Tsounta, and H. S. Kim. "Is the Growth Momentum in Latin America Sustainable?" Working Paper No. 13/109. Washington, DC: International Monetary Fund, 2013.

Stock, J. II., and M. W. Watson. "Has the Business Cycle Changed and Why?," in NBER Macroeconomics Annual 2002, edited by M. Gertler and K. Rogoff, 2002, 159-218.

SEBASTIAN FOSSATI, An earlier version of this paper circulated under the name "Output Growth and Commodity Prices in Latin America: What Has Changed?" I would like to thank Ambrogio Cesa-Bianchi. Sebastian Rondeau, and Dongwon Lee for providing part of the data used in this paper. I also thank the editor Brad Humphreys. Cesar M. Rodriguez. Rodrigo Sekkel. and participants at the 2013 Midwest Econometrics Group meeting. 2013 Avances en Economia conference (Universidad de Montevideo). and the 2014 Society for Nonlinear Dynamics and Econometrics symposium for helpful comments.

Fossati: Department of Economics. University of Alberta. Edmonton, AB T6G 2H4. Canada. Phone 780-492-3127. Fax 780-492-3300, E-mail sfossati@ualberta.ca

(1.) LatAm values are a simple average of the corresponding values (mean growth rates, standard deviations) of the six countries considered.

(2.) Country-specific commodity price indexes are defined as the world price of a country's commodity exports and obtained from ('hen and Lee (2013) for the period 1980Q1-2010Q4.

(3.) An alternative approach considered in Blanchard and Simon (2001) consists in estimating AR models with time-varying parameters, that is. models that allow the parameters to change every quarter.

(4.) Consistent estimation of Equation (3) with contemporaneous commodity prices requires the assumption that [[epsilon].sub.t], is uncorrected with [DELTA][p.sub.t] and [DELTA][p.sup.+.sub.t]. I avoid this potential endogeneity problem by including only predetermined variables ([DELTA][p.sub.t-1], [DELTA][p.sub.t-2], [DELTA][p.sup.+.sub.t-1], [DELTA][p.sup.+.sub.t-2]. See. for example. Hamilton (2011).

(5.) Other LatAm countries could not be considered due to data availability issues. See Cesa-Bianchi et al. (2012). Rondeau (2012). and Chen and Lee (2013) for a detailed description of their data sources.

(6.) Mexico exhibits a very deep recession in the middle of the sample which makes the identification of the (potential) structural break date difficult (see Figure 3 below).

(7). L.R tests of (he null hypothesis that [[gamma].sub.1] = [[gamma].sub.2] = 0 are based on Model IV (results not reported).

(8.) If [I.sub.t] is the value of a structural reform index at time t, the normalized index [I.sup.*.sub.t] is calculated as [I.sup.*.sub.t] = [I.sub.t] - min(I)/ max(I)-min<I), with I * [member of] [0,1].

(9.) In Chile, the main policy changes were implemented in the 1970s and in Mexico in the early 1980s. In both cases the data are only available for the period 1983QI -20I0Q4. In the case of Colombia, the data are only for the period 1994Q1-2010Q4.

(10.) In addition, when the model allows for two structural breaks. Peru exhibits a 45% reduction in the volatility of real GDP growth in 200.1Q2. The second break is located about a year after the adoption of inflation targeting (June 2(X)2 according to Garcia-Solanes and Torrejon-Flores 2012). Results not reported.

(11.) Quarterly data were obtained from Global Financial Data (Ticker: CMECALLW).

(12.) In addition to the robustness results reported in this section, generalized method of moments regressions with the lagged commodity prices [DELTA][p.sub.t-1], and [DELTA][p.sub.t-2], as instruments for [DELTA][p.sub.t]), were estimated for the pre- and post-break samples. In the case of Argentina, Chile, Colombia, and Peru, the data appear to support the model specification as all J-tests fail to reject at the 59c level. In the case of Brazil and Mexico, there is some evidence of misspecification in the post-break samples but not before the break.

TABLE 1
Quarterly Summary Statistics

                    ARG     BRA     CHI     COL

Real GDP growth: Mean (%)
  1983Q1-1992Q4    0.37   -0.10    1.60     --
  1993Q1-2002Q4    0.13    0.71    1.16    0.45
  2003Q1-2010Q4    1.87    0.97    1.04    1.14
  Full sample      0.71    0.72    1.28    0.79

Real GDP growth: Standard deviation (%)
  1983Q1-1992Q4    3.30    2.64    1.86     --
  1993Q1-2002Q4    2.28    1.47    1.60    1.28
  2003Q1-2010Q4    1.30    1.54    1.14    0.95
  Full sample      2.58    1.68    1.59    1.18

Commodity price growth: Mean (%)
  1983Q1-1992Q4   -0.06    -0.07    0.67   -1.10
  1993Q1-2002Q4    0.06    -0.09   -0.66    0.29
  2003Q1-2010Q4    2.87     3.72    4.52    3.57
  Full sample      0.82     1.01    1.29    0.73

                   M EX     PER    LatAm

Real GDP growth: Mean (%)
  1983Q1-1992Q4    0.53   -0.25    0.43
  1993Q1-2002Q4    0.67    1.06    0.70
  2003Q1-2010Q4    0.56    1.63    1.20
  Full sample      0.59    0.75    0.81

Real GDP growth: Standard deviation (%)
  1983Q1-1992Q4    1.50    4.97    2.85
  1993Q1-2002Q4    1.78    1.80    1.70
  2003Q1-2010Q4    1.58    1.09    1.27
  Full sample      1.62    3.28    1.99

Commodity price growth: Mean (%)
  1983Q1-1992Q4   -1.18   -0.10   -0.31
  1993Q1-2002Q4    0.80   -0.25    0.02
  2003Q1-2010Q4    3.55    4.27    3.75
  Full sample      0.88    1.09    0.97

Notes: Real GDP growth statistics are computed for the sample period
1983Q1-2010Q4 for all countries except Brazil and Colombia. For
Brazil, the sample period is 1990Q1-2010Q4. For Colombia. the sample
period is 1994Q1-2010Q4. Commodity price mean grow th rates are
computed for the period 1983Q1-2010Q4. LatAm values are a simple
average of the corresponding values (mean growth rates, standard
deviations) of the six countries considered.

TABLE 2
AR(1) OLS Estimates and qLL Tests for Stability

                                 ARG           BRA           CHI

Specification: [DELTA][y.sub.t] = c + [phi] [DELTA][y.sub.t-1] +
[[epsilon].sub.t], [[epsilon].sub.t] ~ iidN
(0, [[sigma.sup.2.sub.[epsilon]])

  c                          0.54 (0.25)   0.56 (0.20)   1.17 (0.20)
  [phi]                      0.24 (0.09)   0.15 (0.11)   0.08 (0.10)
  [[sigma].sub.[epsilon]]       2.53          1.63          1.60
  [qLL.sub.1]                 -14.19 *        -8.27         -9.06

Specification: [square root of [[pi]/2 X [absolute value of
[??].sub.t]] = s + [[eta].sub.t]

  s                          2.35 (0.20)   1.42 (0.16)   1.47 (0.13)
  [[sigma].sub.[eta]]           2.09          1.43          1.34
  [qLL.sub.2]                 -9.06 **        -5.81       -10.58 **

                                 COL           MEX           PKR

Specification: [DELTA][y.sub.t] = c + [phi] [DELTA][y.sub.t-1] +
[[epsilon].sub.t], [[epsilon].sub.t] ~ iidN
(0, [[sigma.sup.2.sub.[epsilon]])

  c                          0.67 (0.18)   0.53 (0.16)   0.54 (0.29)
  [phi]                      0.12 (0.13)   0.13 (0.10)   0.38 (0.09)
  [[sigma].sub.[epsilon]]       1.18          1.61          3.00
  [qLL.sub.1]                  -11.97       -14.58 **     -13.43 *

Specification: [square root of [[pi]/2 X [absolute value of
[??].sub.t]] = s + [[eta].sub.t]

  s                          1.13 (0.11)   1.40 (0.14)   2.54 (0.26)
  [[sigma].sub.[eta]]           0.92          1.43          2.73
  [qLL.sub.2]                   -2.64        -7.36 *      -9.15 **

Notes: [DELTA][y.sub.t] is quarterly real GDP growth.
Standard errors are in parentheses to the right of the OLS
estimates. The sample period is 1983Q1-2010Q4 for all
countries except Brazil and Colombia. For Brazil, the sample
period is 1990Q1-2010Q4. For Colombia, the sample period is
1994Q1-2010Q4. qLL test is described in Elliott and Muller
(2006). [qLL.sub.1] is the test statistic of parameter
stability in c and [phi]. 10% and 5% critical values for the
[qLL.sub.1] test are -12.80 and -14.32. respectively.
[qLL.sub.2] is the test statistic of parameter stability in
s. 10% and 5% critical values for the [qLL.sub.2] test are
-7.14 and -8.36. respectively. * (**) denotes rejection of
the null hypothesis of parameter stability at 10% (5%) level.

TABLE 3
Model Selection

       Model       Breaks   [DELTA][p.sub.t]   [DELTA][p.sup.+.sub.t]

ARG    AR(1)         0             No                    No
       MS-AR(1)      1             No                    No
       MS-ARX(1)     1            Yes                    No
       MS-ARX(1)     1            Yes                   Yes
BRA    AR(1)         0             No                    No
       MS-AR(1)      1             No                    No
       MS-ARX(1)     1            Yes                    No
       MS-ARX(1)     1            Yes                   Yes
CHI    AR(1)         0             No                    No
       MS-AR(1)      1             No                    No
       MS-ARX(1)     1            Yes                    No
       MS-ARX(1)     1            Yes                   Yes
COL    AR(1)         0             No                    No
       MS-AR(1)      1             No                    No
       MS-ARX(1)     1            Yes                    No
       MS-ARX(1)     1            Yes                   Yes
MFX    AR(1)         0             No                    No
       MS-AR(1)      1             No                    No
       MS-ARX(1)     1            Yes                    No
       MS-ARX(1)     1            Yes                   Yes
PER    ARU)          0             No                    No
       MS-AR(1)      1             No                    No
       MS-ARX(1)     1            Yes                    No
       MS-ARX(1)     1            Yes                   Yes

       Model         In L     k        AIC

ARG    AR(1)       -158.45    3     161.45
       MS-AR(1)    -143.74    7     150.74#
       MS-ARX(1)   -142.68    9     151.68
       MS-ARX(1)   -142.31   11     153.31
BRA    AR(1)        -82.02    3      85.02
       MS-AR(1)     -77.11    7      84.11
       MS-ARX(1)    -71.55    9      80.55#
       MS-ARX(1)    -71.29   11      82.29
CHI    AR(1)       -107.22    3     110.22
       MS-AR(1)     -99.49    7     106.49
       MS-ARX(1)    -96.66    9     105.66#
       MS-ARX(1)    -96.05   11     107.05
COL    AR(1)        -42.68    3      45.68
       MS-AR(1)     -39.22    7      46.22
       MS-ARX(1)    -36.62    9      45 62#
       MS-ARX(1)    -35.50   11      46.50
MFX    AR(1)       -108.28    3     111.28
       MS-AR(1)    -105.25    7     112.25
       MS-ARX(1)    -96.39    9     105.39#
       MS-ARX(1)    -94.61   11     105.61
PER    ARU)        -179.78    3     182.78
       MS-AR(1)    -148.02    7     155.02
       MS-ARX(1)   -141.69    9     150.69#
       MS-ARX(1)   -140.35   11     151.35

Notes: The sample period is 1983Q1-2010Q4 for all countries
except Brazil and Colombia. For Brazil, the sample period is
1990Q1-2010Q4. For Colombia, the sample period is 1994Q1-2010Q4.
In L denotes the log likelihood. AIC denotes the Akaike
Information Criterion and is calculated as--In L + k where
k is the number of parameters in the model. Bold values
indicate the best tit for each country.

Note: values indicate the best tit for each country are
indicated with #.

TABLE 4
MS-AR(1) ML Estimates (Model II)

                       ARG            BRA            CHI

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[mu].sub.1]       0.10 (0.59)   -0.77 (1.10)    1.51 (0.23)
[[phi].sub.1]     -0.05 (0.18)   -0.17 (0.56)   -0.01 (0.13)
[[sigma].sub.1]    3.39 (0.42)    2.92 (0.87)    1.84 (0.16)
[[mu].sub.2]       0.96 (0.42)    0.83 (0.19)    0.99 (0.20)
[[phi].sub.2]      0.52 (0.10)    0.14 (0.11)    0.26 (0.13)
[[sigma].sub.2]    1.74 (0.15)    1.44 (0.12)    1.00 (0.11)
p                  0.97 (0.03)    0.86 (0.13)    0.98 (0.02)
ln L                 -143.74         -77.11         -99.49
Q * (1)                0.03           0.05           0.01
Q * (6)                6.97           7.56           2.04
Date                  1991Q3         1992Q1         1999Q2
[LR.sub.1]           8.41 (**)        1.21           4.47
[LR.sub.2]          21.07 (**)     8.36 (**)     12.78 (**)

                       COL            MEX            PER

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[mu].sub.1]       0.41 (0.39)    0.55 (0.18)   -0.39 (1.13)
[[phi].sub.1]      0.36 (0.22)   -0.29 (0.15)    0.37 (0.15)
[[sigma].sub.1]    1.23 (0.19)    1.41 (0.16)    4.53 (0.53)
[[mu].sub.2]       1.00 (0.14)    0.62 (0.28)    1.33 (0.23)
[[phi].sub.2]     -0.20 (0.15)    0.31 (0.12)    0.24 (0.12)
[[sigma].sub.2]    0.99 (0.11)    1.60 (0.14)    1.48 (0.13)
p                  0.96 (0.04)    0.98 (0.02)    0.98 (0.02)
ln L                  -39.22        -105.25        -148.02
Q * (1)                0.05           0.18           0.16
Q * (6)                4.50           6.94           3.71
Date                  2000Q2         1993Q2         1993Q1
[LR.sub.1]         6.75 (**)         5.87 *          3.10
[LR.sub.2]             1.43           0.74         46.27 (**)

Notes: [[DELTA][y.sub.t] is quarterly real GDP growth.
Standard errors are in parentheses to the right of the ML
estimates. The sample period is 1983Q1-201OQ4 for all
countries except Brazil and Colombia. For Brazil, the sample
period is 1990Q1-2010Q4. For Colombia, the sample period is
1994Q1-2010Q4. In ln L denotes the log likelihood and the LR
test statistic are constructed as -2(ln [L.sub.r]-ln
[L.sub.u]) where In [L.sub.r] is the log likelihood of the
restricted model and ln [L.sub.u] is the log likelihood of
the unrestricted model. LR is distributed [chi square](q)
where q is the number of restrictions imposed. [LR.sub.1]
tests [[mu].sub.1] = [[mu].sub.2] and [[phi].sub.1]  =
[[phi].sub.2] [LR.sub.2] tests [[sigma].sub.1] =
[[sigma].sub.2]. Q * (k) is the Ljung-Box statistic for the
(centered) generalized residuals with k the number of lags.
* (**) denotes rejection of the null hypothesis at 10% (5%)
level.

TABLE 5
MS-ARX(1) ML Estimates (Model III)

                       ARC            BRA            CHI

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[mu].sub.1]       0.12 (0.58)    0.57 (0.53)    1.50 (0.22)
[[phi].sub.1]     -0.06 (0.18)    0.14 (0.24)   -0.02 (0.13)
[[sigma].sub.1]    3.42 (0.43)    2.17 (0.34)    1.83 (0.16)
[[mu].sub.2]       0.90 (0.40)    0.62 (0.14)    0.90 (0.17)
[[phi].sub.2]      0.51 (0.10)   -0.20 (0.15)    0.15 10.17)
[[sigma].sub.2]    1.71 (0.15)    1.21 (0.12)    0.94 (0.10)
[[beta].sub.1]     0.03 (0.02)    0.11 (0.03)    0.01 (0.01)
[[beta].sub.2]     0.02 (0.02)   -0.01 (0.02)    0.02 (0.01)
p                  0.97 (0.03)    0.96 (0.04)    0.99 (0.02)
ln L                 -142.68         -71.55         -96.66
Q * (1)                0.02           0.02           0.00
Q * (6)                7.62           7.46           3.35
Date                  1991Q3         1996Q2         1999Q3
[LR.sub.1]           8.10 **          0.63          4.85 *
[LR.sub.2]           22.57 **       9.30 **        15.58 **
[LR.sub.3]             2.12         11.11 **        5.66 *

                       COL            MEX            PER

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[mu].sub.1]       0.38 (0.38)    0.62 (0.23)   -0.29 (1.19)
[[phi].sub.1]      0.33 (0.23)   -0.07 (0.13)    0.41 (0.15)
[[sigma].sub.1]    1.23 (0.19)    1.89 (0.18)    4.57 (0.53)
[[mu].sub.2]       0.94 (0.13)    0.45 (0.19)    1.13 (0.19)
[[phi].sub.2]     -0.21 (0.15)    0.24 (0.13)    0.09 (0.12)
[[sigma].sub.2]    0.93 (0.10)    0.98 (0.10)    1.33 (0.12)
[[beta].sub.1]     0.03 (0.01)    0.05 (0.01)    0.06 (0.02)
[[beta].sub.2]    -0.01 (0.01)    0.02 (0.01)    0.05 (0.02)
p                  0.96 (0.04)    0.98 (0.02)    0.98 (0.02)
ln L                  -36.62         -96.39        -141.69
Q * (1)                0.01           0.03           0.12
Q * (6)                2.01           5.88           2.82
Date                  2000Q1         1998Q1         1993Q2
[LR.sub.1]         6.18 (**)          2.92          4.86 *
[LR.sub.2]             2.12        5.37 (**)     56.22 (**)
[LR.sub.3]            5.20 *      17.73 (**)     12.66 (**)

Notes: [DELTA][y.sub.t] is quarterly real GDP growth and
[DELTA][p.sub.t] is the quarterly growth rate in commodity
prices. Standard errors are in parentheses to the right of
the ML estimates. The sample period is 1983Q1-2010Q4 for all
countries except Brazil and Colombia. For Brazil, the sample
period is 1990Q1-2010Q4. For Colombia, the sample period is
1994Q1-2010Q4. ln L denotes the log likelihood and the LR
test statistic are constructed as -2(ln [L.sub.r]-ln
[L.sub.u]) where In [L.sub.r] is the log likelihood of the
restricted model and ln [L.sub.u] is the log likelihood of
the unrestricted model. LR is distributed [chi square](q)
where q is the number of restrictions imposed. [LR.sub.1]
tests p, = m2 and [[mu].sub.1] = [[mu].sub.2]. [[phi].sub.1]
= [[phi].sub.2]. [LR.sub.2] tests [[beta].sub.1] =
[[beta].sub.2] = 0. Q * {k) is the Ljung-Box statistic for
the (centered) generalized residuals with k the number of
lags. * (**) denotes rejection of the null hypothesis at 10%
(5%) level.

TABLE 6
Commodity Prices and Real GDP Growth

                  ARG      BRA     CHI     COL     MEX     PER

1983Q1-1992Q4    -0.00    -0.01    0.02   -0.02   -0.08   -0.01
1993Q1-2002Q4     0.00    -0.01   -0.02    0.01    0.05   -0.03
2003Q1-2010Q4     0.13     0.38    0.15    0.07    0.23    0.47

Notes: The average contribution of commodity prices to real
GDP growth is computed as ([[??].sub.1] + [[??].sub.2])
[[bar.x].sub.i] for i = 1, 2, 3 with [[bar.x].sub.i] the
average growth rate of commodity prices in the sub-sample i.
The results are based on the estimates of Model III
(Table 5).

TABLE 7
MS-ARX(1) ML Estimates (Model III)-Economist Index

                        ARG             BRA             CHI

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[mu].sub.1]        0.06 (0.59)     0.54 (0.46)     1.50 (0.22)
[[phi].sub.1]      -0. 05 (0.18)    0.13 (0.24)    -0.04 (0.13)
[[sigma].sub.1]     3.42 (0.43)     1.94 (0.29)     1.79 (0.16)
[[mu].sub.2]        0.83 (0.39)     0.66 (0.11)     0.92 (0.19)
[[phi].sub.2]       0.51 (0.10)    -0.33 (0.13)     0.25 (0.15)
[[sigma].sub.2]     1.63 (0.14)     1.04 (0.10)     0.94 (0.10)
[[beta].sub.1]      0.06 (0.03)     0.12 (0.02)    -0.01 (0.02)
[[beta].sub.2]      0.05 (0.03)     0.00 (0.02)     0.05 (0.02)
p                   0.97 (0.03)     0.96 (0.04)     0.99 (0.02)
ln L                  -139.38         -60.93          -94.77
Q * (1)                0.03            0.00            0.00
Q * (6)                6.47            7.03            6.92
Date                  1991Q3          1996Q2          1999Q2
[LR.sub.1]           7.76 (**)         2.74            5.81 *
[LR.sub.2]          23.00 (**)       13.10 (**)      15.09 (**)
[LR.sub.3]           8.71 (**)       32.36 (**)       9.43 (**)

                        COL             MEX             PER

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[mu].sub.1]        0.41 (0.36)     0.46 (0.30)    -0.33 (1.20)
[[phi].sub.1]       0.35 (0.22)     0.10 (0.14)     0.41 (0.15)
[[sigma].sub.1]     1.12 (0.17)     1.89 (0.19)     4.57 (0.53)
[[mu].sub.2]        0.89 (0.12)     0.54 (0.23)     1.18 (0.17)
[[phi].sub.2]      -0.26 (0.14)     0.21 (0.14)     0.02 (0.12)
[[sigma].sub.2]     0.91 (0.10)     1.11 (0.12)     1.33 (0.12)
[[beta].sub.1]      0.05 (0.02)     0.06 (0.02)     0.06 (0.02)
[[beta].sub.2]     -0.00 (0.02)     0.04 (0.02)     0.06 (0.02)
p                   0.96(0.04)      0.98 (0.02)     0.98 (0.02)
ln L                  -33.50          -100.81         -141.26
Q * (1)                0.01            0.13            0.30
Q * (6)                0.71            5.95            2.92
Date                  2000Q1          1997Q3          1993Q1
[LR.sub.1]            5.87 *           0.34           6.61 **
[LR.sub.2]             1.20           5.45 **        53.51 **
[LR.sub.3]           11.45 **         8.88 **        13.53 **

Notes: [DELTA][y.sub.t] is quarterly real GDP growth and
[DELTA][p.sub.t] is the quarterly growth rate in commodity
prices. Standard errors are in parentheses to the right of
the ML estimates. The sample period is 1983Q1-2010Q4 for all
countries except Brazil and Colombia, For Brazil, the sample
period is 1990Q1-2010Q4. For Colombia, the sample period is
1994Q1-2010Q4. ln L denotes the log likelihood and the LR
test statistic are constructed as-2(ln lr-ln [L.sub.u])
where In [L.sub.r] is [he log likelihood of the restricted
model and ln [L.sub.u] is the log likelihood of the
unrestricted model. LR is distributed [chi square](q) where
q is (he number of restrictions imposed. [LR.sub.1] tests =
[[mu].sub.2] and [[mu].sub.2] [[phi].sub.1] = [[phi].sub.2].
tests [[sigma].sub.1] = [[sigma].sub.2] = [LR.sub.3] tests
[[beta].sub.1] = [[beta].sub.2] = 0. Q * (k) is the Ljung-
Box statistic for the (centered) generalized residuals with
k the number of lags. * (**) denotes rejection of the null
hypothesis at 10% (5%) level.
COPYRIGHT 2017 Western Economic Association International
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2017 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Fossati, Sebastian
Publication:Contemporary Economic Policy
Article Type:Report
Geographic Code:0LATI
Date:Jan 1, 2017
Words:8915
Previous Article:A note on the nonlinear effect of minimum wage increases.
Next Article:Voter preferences, institutions, and economic freedom.
Topics:

Terms of use | Privacy policy | Copyright © 2019 Farlex, Inc. | Feedback | For webmasters