The EMBI in Latin America: Fractional Integration, Non-Linearities and Breaks

This paper analyses the main statistical properties of the Emerging Market Bond Index (EMBI), namely long-range dependence or persistence, non-linearities, and structural breaks, in four Latin American countries (Argentina, Brazil, Mexico, Venezuela). For this purpose it uses a fractional integration framework and both parametric and semi-parametric methods. The evidence based on the former is sensitive to the specification for the error terms, whilst the results from the latter are more conclusive in ruling out mean reversion. Further, non-linearities do not appear to be present. Both recursive and rolling window methods identify a number of breaks. Overall, the evidence of long-range dependence as well as breaks suggests that active policies might be necessary for achieving financial and economic stability in these countries.


Introduction
The EMBI (Emerging Market Bond Index) is an index constructed by JP Morgan for dollar-denominated sovereign bonds issued by a selection of emerging countries. In addition to being useful for measuring the performance of this asset class, it is the most widely used and comprehensive benchmark for emerging sovereign debt markets, and it also helps increase their visibility.
The EMBI is based on the interest differential between dollar-denominated bonds issued by developing countries and US Treasury bonds respectively, the latter traditionally being considered to be risk-free. This differential, also known as spread or swap, is expressed in basis points (bp). A spread of 100 bp means that the yield on bonds issued by the government in question is one percent (1%) higher than that on the risk-free US Treasury Bills: riskier bonds (with a higher default probability) pay higher interest. An increase in sovereign bond yields tends to drive up long-term interest rates in the rest of an economy, affecting both investment and consumption decisions. On the fiscal side, higher government bond yields imply higher debt-servicing costs and can significantly raise funding costs. This could also lead to an increase in rollover risk, as debt might have to be refinanced at unusually high cost or, in extreme cases, it might not be possible any longer to roll it over (Gómez-Puig and Mari del Cristo, 2014). Large increases in government funding costs can therefore have real effects in addition to the purely financial effects of higher interest rates (see Caceres et al., 2010).
This paper analyses the statistical properties of the EMBI in four Latin American countries, namely Argentina, Brazil, Mexico and Venezuela. Specifically, we examine long-range dependence or persistence, non-linearities and structural breaks.
The rest of the paper is structured as follows. Section 2 briefly reviews the existing literature on the EMBI in Latin America. Section 3 outlines the empirical 3 methodology used for the analysis. Section 4 describes the data and the main empirical results, while Section 5 offers some concluding remarks.

Literature Review
There are very few studies on the EMBI in Latin American countries. Fracasso (2007) examines the case of Brazil, and shows that foreign investors' appetite for risk impacts substantially on EMBI spreads. Nogués and Grandes (2001) argue that in Argentina country risk is mainly determined by macroeconomic variables such as the external debt-to-exports ratio and growth expectations rather than the devaluation risk. Vargas et al. (2012)

Methodology
The methods used here are based on the concept of fractional integration, which is more general than the standard approaches based on integer degrees of differentiation that simply consider the cases of stationarity I(0) and nonstationarity I(1).
For the present purposes, we define an I(0) process as a covariance-stationary one for which the infinite sum of the autocovariances is finite. This includes the white noise case, but also weakly dependent (stationary) ARMA-type processes. Instead a process is said to be fractionally integrated of order d (and denoted by I(d)) if it requires d-differences to make it stationary I(0). In other words, a process {x t , t = 0, ±1, …} is said to be I(d) if it can be represented as: Note, however that x t can be the errors in a regression model such as where z t is a set of deterministic terms that might include an intercept and/or a time trend, and f can also be of a non-linear form.
First we consider a linear model, where z t contains an intercept and linear time trend, such that (2) and (1) under the assumptions of white noise and autocorrelated errors in turn. We estimate the differencing parameter d using a Whittle parametric function in the frequency domain (Dahlhaus, 1989); other maximum likelihood methods (Sowell, 1992;Beran, 1995) produced essentially the same results (not reported). We also apply semi-parametric methods; in particular, we use a "local" Whittle approach introduced by Robinson 5 (1995) and later developed by Abadir et al. (2007) and others. Further, the possibility of non-linear structures in the presence of fractional integration is examined taking the approach of Cuestas and Gil-Alana (2015), who use Chebyshev's polynomials in time as an alternative to linear trends. Such polynomials, defined as offer various advantages. First, the fact that they are orthogonal means that one avoids the problem of near collinearity in the regressors matrix that typically occurs in the case of standard time polynomials; second, this specification makes it possible to approximate highly non-linear trends with rather low-degree polynomials (Bierens, 1997); third, their shape is ideally suited for modeling cyclical behaviour. We also investigate stability using recursive and rolling-window methods for the estimation of the fractional differencing parameter. Finally, a model combining fractional integration and structural breaks at unknown points in time (Gil-Alana, 2008) is estimated.

Data and Empirical Results
The EMBI series analysed are monthly and cover the period from January 1997 to June 2015. The data source in each case is the Central Bank of the corresponding country.  As a first step we consider the linear model given by equation (3) and estimate the fractional differencing parameter for the three standard cases found in the literature, i.e., those of no deterministic terms, (β 0 = β 1 = 0 in (3)), an intercept (β 0 unknown and β 1 = 0) and an intercept with a linear time trend (β 0 and β 1 unknown). The results are displayed in Table 1 for uncorrelated (white noise) and autocorrelated errors (as in Bloomfield, 1973) respectively, the latter being a non-parametric approach that produces errors decaying exponentially as in the ARMA case.
[Insert Table 1 about here] It can be seen that under the white noise specification the unit root null hypothesis is rejected in favour of orders of integration higher than 1 in the case of Argentina, Brazil and Mexico. For Venezuela the estimated value of d is also above 1 but the unit root null (i.e. d = 1) cannot be rejected. When using the exponential model of Bloomfield (1973), all the estimated parameters are below 1, and the unit root cannot be rejected for Brazil and Venezuela, but it is rejected in favour of mean reversion (i.e., d < 1) in the case of Argentina and Mexico.
[Insert Table 2 and Figure 2 about here] Because of the differences in the results depending on the specification of the error term, we also apply a semi-parametric method that does not require modelling assumptions about the error term. The results reported in Table 2 are  The possibility of non-linear behaviour is then examined using the approach developed by Cuestas and Gil-Alana (2015). The model specification is the following: where m = 2 to allow for a certain degree of non-linearity. Next we investigate if the fractional differencing parameter changes over time.
The stability analysis is based on the results displayed in the lower panel of Table 1, i.e.
those for the Bloomfield specification with an intercept, which is chosen using a battery of diagnostics tests on the residuals. Two different approaches are taken: a recursive one, starting with a sample of 60 observations corresponding to the first five years (1997 -2001), and then adding six more observations at a time, and a rolling one with a window of 60 observations. [Insert Table 4

about here]
Finally, we test for breaks in the context of an I(d) model as in Gil-Alana (2008).
The detected breaks coincide with those identified with the Bai and Perron (2003) method in the case of Argentina (2001M12 and2005M7). For Brazil the break date is found to be two months before (2004M6); for Mexico, the dates coincide for the first break (1999M12) but not for the second one, now estimated to occur in 2008M3; finally for Venezuela a single break is now found in 2008M9. Venezuelaa unit root is found in the first subsample, and an order of integration significantly higher than 1 after the break at 2008M9.

[Insert Tables 5 and 6 about here]
When allowing for autocorrelated errors, the break dates coincide with those

Conclusions
The EMBI is a key benchmark for emerging sovereign debt markets. However, very limited empirical evidence is available concerning its behaviour in Latin America. The present study fills this gap by examining it in four countries belonging to this region (Argentina, Brazil, Chile and Mexico), and investigating in particular long-range dependence or persistence, as well as possible non-linearities and structural breaks.
Moreover, it uses a fractional integration framework which is more general than the standard approach based on the I(0)/I(1) dichotomy.
Both parametric and semi-parametric methods are applied. The evidence based on the former is sensitive to the specification for the error terms, whilst the results from the latter are more conclusive in ruling out mean reversion. Further, non-linearities do 10 not appear to be present. Both recursive and rolling window methods identify a number of breaks, which can be plausibly be interpreted in terms of some well-known political and economic developments in the countries of interest. Overall, the evidence of longrange dependence as well as breaks suggests that active policies might be necessary for achieving financial and economic stability in these countries.    The values in the parenthesis are in the second column, the 95% confident intervals, and in the remaining columns they are their corresponding t-values.