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This paper aims to analyze if there is a relationship between economic growth and the volatility of that growth in the Brazilian economy, and, if it exists, to infer if that relationship is positive or negative, since the literature shows evidence for both cases. For that purpose, the econometric strategy used is that of a Generalized Autoregressive Conditional Heteroskedasticity in Mean (GARCH-M) model, using economic growth data compiled by the Central Bank of Brazil, for the period of 1995-2018. The results corroborate the findings of the empirical literature, suggesting a negative relationship between economic growth and its volatility; that is, the hypothesis of the irreversibility of investments prevails. Therefore, the tradeoff between short-term stability and long-term growth for the Brazilian economy in the analyzed period does not seem to occur.

Macroeconomic theory has long addressed the issues associated with long-term economic growth and business cycle fluctuations separately. However, there is reason to believe that growth and volatility may be positively or negatively linked (Fang and Miller [^{1}, then the increase in volatility will lead to a decrease in those investments and, consequently, to lower levels of economic growth. Mirman [

Traditionally, models of economic growth and economic cycles are treated as different frameworks. However, following the paper of Ramey and Ramey [

For the Brazilian economy, Araújo, Carpena and Cunha [

The research problem of this work, then, is to analyze if there is a relationship between economic growth and the volatility of that growth in the Brazilian economy, and, if it exists, to infer if that relationship is positive or negative, since the literature shows evidence for both cases. Thus, the research objective is to investigate the relationship between economic growth and its volatility in the Brazilian economy using monthly data between January 1995 and August 2018, extracted from the Central Bank of Brazil through the econometric methodology Generalized Autoregressive Conditional Heteroskedasticity in Mean (GARCH-M) model.

In addition to this introduction, this paper features four more sections. The literature review is presented next, and section three follows with a discussion on the methodological aspects. The results are analyzed in the fourth section and, lastly, the fifth section presents the concluding remarks.

Several efforts in academic literature have been made in the attempt to identify the relationship between economic growth and growth volatility throughout the years. Ramey and Ramey [

Dawson and Stephenson [

Analyzing European regions and OECD countries, Martin and Rogers [

Fatás [

Kose, Prasad and Terrones [

Fang and Miller [

Lee [

Lin and Kim [

In terms of Brazil, analyzing the country’s business cycles from 1850 to 2000, Araújo, Carpena and Cunha [

Arbache and Sarquis [

This paper uses monthly data, from January 1995 to August 2018, of the GDP series extracted from the Central Bank of Brazil. Firstly, the data were duly deflated using the General Price Index—Internal Availability (ÍndiceGeral de Preços-DisponibilidadeInterna—IGP-DI), which is calculated by the FundaçãoGetúlio Vargas and made available by the Central Bank of Brazil^{2}. Then, we then calculated the GDP real growth rate, which is the variable of interest used in this work.

In order to support the econometric analysis performed here, a preliminary analysis was made of the impact of volatility on long-term growth. The graph below presents a comparison of the growth rates and volatilities of growth for the Brazilian economy in the aforementioned period. It is worth noting that in this preliminary analysis, the standard deviation is used as an indicator of volatility.

One can observe that periods with high volatility presented negative economic growth. Among the periods that seem more relevant, we can highlight January 1999, which features a shift in the Brazilian exchange policy, where the Brazilian Central Bank adopted a floating exchange rate, and triggered an economic crisis and, consequently, a negative growth rate. Another relevant period is January 2001, a year in which the combination of an energy crisis, high interest rates and a strong economic slowdown around the world slowed economic activity.

The beginning of 2003 is also worth mentioning, a period of great economic instability as a result of then President Lula being elected, therefore there was a rise in uncertainty in terms of economic policy. Lula came from the Brazilian Workers Party, which had historically been critical of the orthodox macroeconomic policy which had been practiced in Brazil by the previous government in the eight years prior. The beginning of 2009 was also marked by low economic growth, a period in which Brazil began to suffer the impacts of the 2008 global crisis in a late manner. In 2013 and 2014 the country went through considerable political and economic instability, which culminated in an impeachment process in 2016, where one can observe high volatility and economic recession, which has lingering results in the Brazilian economy (

The analysis of the relationship between volatility and economic growth for the Brazilian economy will occur through the application of the Generalized Autoregressive Conditional Heteroskedasticity model in the mean, or GARCH-M.

The GARCH model, presented by Bollerslev [

ε t = v t h t (1)

where, v t are random variables which are identical and independently distributed with mean zero and variance one, that is, v t ~ ( 0 , 1 ) and h t represents the conditional variance. Thus:

h t = α 0 + ∑ i = 1 s α i ε t − i 2 + ∑ i = 1 r β i h t − i (2)

Equation (2) is known as the Generalized Autoregressive Conditional Heteroscedasticity model of order ( r , s ) , i.e., GARCH ( r , s ) . For some problems, however, a greater refinement of the GARCH model is required. The rate of return of a financial series, for example, depends on the volatility of the process; that is, its conditional variance. To meet this requirement, a new model was developed, called GARCH in the mean (or GARCH-M). A generic GARCH-M (r, s) model is, then, given by:

ε t = v t h t

μ t = β + δ h t (3)

h t = α 0 + ∑ i = 1 s α i ε t − i 2 + ∑ i = 1 r φ i h t − i

where μ t denotes the average return, β and δ are the constants, with δ indicating the risk premium parameter. This model is often used in financial applications where the expected return on an asset is related to its risk. The estimated coefficient on the expected risk is a measure of the risk/return trade-off. In this paper, the trade-off between short-term stability and long-term economic growth is analyzed. Therefore, the use of the GARCH-M model is an adequate strategy. In this context, the model will be used along the lines of Engle, Lilien and Robins [

Y t = X ′ t θ + λ h t + ε t (4)

h t = w + ∑ i = 1 r φ i h t − i + ∑ i = 1 s α i ε t − i 2 + Z ′ t π (5)

In which Y t is the growth rate of the economy, X t is the vector of exogenous variables in the mean equation, and Z t is a vector of exogenous regressors of the conditional variance equation.

The most well-adjusted model is the GARCH-M (2, 2) which includes the growth level lagged in one period ( Y t − 1 ) , in the variance equation. The results are summarized in

Thus, considering the research problem of analyzing the relationship between economic growth in Brazil and its volatility, the results point to a negative and statistically significant relationship; that is, a more stable economic environment can lead to greater economic growth. According to Bernanke [

When analyzing the volatility equation, it can be observed that economic growth has a negative and statistically significant impact on volatility. Evidence along these lines may indicate a rapid process of convergence in economic activity to its steady state.

Mean Equation | Conditional Variance Equation | ||
---|---|---|---|

Variable | Coefficient | Variable | Coefficient |

Const. | 0.68* (0.01) | Const. | 0.57* (0.00) |

GARCH | −0.08** (0.05) | ε t − 1 2 | 0.05* (0.00) |

Y_{t}_{−1 } | −0.15* (0.00) | ε t − 2 2 | −0.16* (0.00) |

Y_{t}_{−2} | −0.10** (0.02) | h_{t}_{−1 } | 0.68* (0.00) |

Y_{t}_{−3} | −0.10* (0.01) | h_{t}_{−2} | 0.33* (0.00) |

Y_{t}_{−4} | −0.21* (0.00) | Y_{t}_{−1} | −0.34* (0.00) |

Y_{t}_{−5} | 0.04 (0.39) | ||

Y_{t}_{−6} | −0.24* (0.00) | ||

Y_{t}_{−7} | −0.07*** (0.09) | ||

Y_{t}_{−8} | −0.06 (0.13) | ||

Y_{t}_{−9} | −0.08*** (0.07) | ||

Y_{t}_{−10} | −0.27* (0.00) | ||

Y_{t}_{−11} | 0.01 (0.65) | ||

Y_{t}_{−12} | 0.54* (0.00) |

1) P-value in parenthesis. 2) *Significant at the 1% level, **Significant at the 5% level and ***Significant at the 1% level 10%.

In order to overcome possible autocorrelation problems, up to 12 economic growth lags were included in the mean equation. To verify the lack of correlation in the residues, we used the autocorrelation (ACF) and partial autocorrelation functions (PACF), described in

It can be observed that, for a level of significance of 5%, both functions are statistically null in all lags. Thus, we do not reject the hypothesis that both functions are zero until lag 24, and therefore we conclude that the residues are not correlated. Also, to verify that the residues are devoid of any ARCH effect, the ACF and PACF of the squared residue series were calculated. The results are shown in

This paper analyzed the relationship between economic growth and its short-term volatility for the Brazilian economy using monthly data between January 1995 and August 2018 and a GARCH-M model.

The results point out a negative relationship between volatility and economic growth. In an environment of political instability, for example, economic growth would be negatively impacted. This evidence has an important implication for macroeconomic policy. In this scenario, it would be interesting for the government to follow clear rules in its economic policies, avoiding abrupt and discretionary measures, in order to produce economic stability and less uncertainty. Thus, the trade-off between short-term stability and long-term growth for the Brazilian economy in the analyzed period does not appear to occur.

Lastly, when analyzing the impact of economic growth on volatility, a negative result is also observed, which can be explained by the acceleration of the speed of convergence. In this scenario, the economy would move faster towards a new steady state, reducing its short-term volatility.

We appreciate the comments of an anonymous reviewer.

The authors declare no conflicts of interest regarding the publication of this paper.

Arruda, E.F., Bastos, F.S., Castelar, P.U.C., Mansilla, F.M. and Brito, A.C. (2019) Growth and Volatility: An Analysis for the Brazilian Economy. Theoretical Economics Letters, 9, 2626-2635. https://doi.org/10.4236/tel.2019.97165