Panel multi-predictor test procedures with an application to emerging market sovereign risk

doi:10.1016/j.ememar.2016.06.003

Emerging Markets Review

Volume 28, September 2016, Pages 44-60

https://doi.org/10.1016/j.ememar.2016.06.003 Get rights and content

Highlights

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This paper develops a block bootstrap-based panel predictability.
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The procedure accommodates multiple predictors.
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Empirical application covers 20 emerging markets.
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Predictability of sovereign risk is dominated by global predictor variables.

Abstract

As a response to the inefficient practices and possibly misleading inferences resulting from the unit-by-unit application mostly found in the literature, the current paper develops a block bootstrap based panel predictability test procedure that accommodates multiple predictors. As an empirical illustration we consider emerging market sovereign risk where data are usually available across multiple countries, and local and global predictors. The results, which are in agreement with the existing literature on the determinants of sovereign risk, suggest that the global predictors are best and that the predictive ability of the local predictors is limited, at best.

Introduction

Consider a panel data variable, y_i,t, observable for t = 1,…,T time series and i = 1,…,N cross-sectional units. Recent years have witnessed an immense proliferation of research asking whether y_i,t can be predicted using the one-period lagged of some other variable, x_i,t −1 say. The conventional way in which earlier studies have been trying to test the predictability hypothesis is to first run a time series regression of y_i,t onto a constant and x_i,t −1, and then to apply a conventional t-test to test the exclusion restriction of x_i,t −1 (see, for example, Ang and Bekaert, 2007, Driesprong et al., 2008, Polk et al., 2006, Rapach et al., 2013). This test is then repeated for each unit in the sample, each time using only the sample information for that particular unit. This practice has recently led to the development of panel tests that make use not only of the time series variation in the data, but also the information coming from the cross-sectional variation (see Hjalmarsson, 2010, Kauppi, 2001, Westerlund and Narayan, 2015, Westerlund and Smeekes, 2015). However, while potentially more powerful, the pooling along the cross-section is at the same time the source of the greatest weakness of the panel tests. Specifically, while the null hypothesis is typically taken to be that all series in the panel are unpredictable, the alternative hypothesis is formulated as that at least some series are predictable. As Pesaran (2012) points out (in the context of unit root testing), this leaves a rejection of the null somewhat uninformative, because it does not indicate how many predictable series there are. The unit-by-unit and panel approaches therefore have their own strengths and weaknesses. One of the aims of the present paper is to device testing procedures that explore the panel information without for that matter sacrificing accuracy of inference.

The second aim of the paper is related to the first in that it involves exploring yet another source of information that is typically ignored in the literature. In particular, while most empirical work involves multiple predictors, the way that existing tests are constructed (as t-ratios) requires that the predictors are fitted one at a time. This is important for several reasons. First, given the plethora of plausible predictors that typically exists, tests of this type are bound to suffer from omitted variables bias. Second, single-predictor tests ignore the information contained in the correlation between predictors. The purpose of the current paper is therefore to device tests that can be used to flexibly test for predictability in a panel multi-predictor setting. In so doing, we build on the recent work of Westerlund and Smeekes (2015), who develop block bootstrap-based t-tests for predictability in the single predictor setting. The main reason for this is that the block bootstrap is very general and allows, for example, heterogeneous predictive slopes, persistent predictors, and complex error dynamics, including cross-unit endogeneity. In fact, except for some mild regulatory conditions, there are virtually no restrictions on the forms of serial and cross-sectional dependence that can be permitted. Two block bootstrap-based test procedures are considered; one is appropriate when testing the abovementioned hypothesis of full panel unpredictability versus at least some predictability, while the other can be used to sequentially determine the units for which predictability holds. These procedures therefore allow one to explore the strength of both the time series (unit-by-unit) and panel approaches.

The third aim of this paper is related to understanding the nature of predictability with respect to sovereign credit risk and the role of local and global risk factors. In the benchmark model of Longstaff and Schwartz (1995) there are two such determinants, namely, an asset factor represented by the stock price index and an interest rate factor represented by a short rate. Hence, in this literature even the simplest model involves multiple predictors, and subsequent research has established even more predictor candidates (see, for example, Collin-Dufresne et al., 2001, Longstaff et al., 2011). The state-of-the-art model has two types of determinants, local and global, where the former is unit-specific while the latter is common. The purpose of the empirical part of the paper is to formally test for the first time the predictive ability of both types of determinants when modeling the sovereign credit default swap (CDS) spread in a panel data framework in emerging market settings.

For this empirical exercise we focus on emerging markets given their sensitivity to sovereign events. The choice of the countries within emerging market group is dictated by objective criterion of covering as many number of countries with respect different emerging market regions subject to CDS data availability for the chosen sample period. We found 20 emerging markets meeting the sample criteria with a spread of countries. We ensured adequate coverage of different emerging market regions subject to data availability. Specifically, we cover 10 European Union (EU) countries with four being part of the European Monetary Union (EMU) (Slovakia, Cyprus, Portugal and Greece) and six non-EMU countries (Czech Republic, Poland, Bulgaria, Croatia, Hungary and Rumania). Latin America is a highly indebted region with sizable contribution to emerging market sovereign risk due to its heavy international borrowing. We cover five key Latin American countries in this sample (Chile, Brazil, Mexico, Colombia and Argentina). We also cover the African region with Morocco, Tunisia and South Africa being part of our sample. For Asia, we only cover Thailand due to data availability.

The balance of the paper is organized as follows. In Section 2, we describe the econometric model that we have in mind and explain how it related to existing models in the literature. Section 3 presents the two test procedures, whose asymptotic and finite sample properties are studied in 4 Asymptotic distributions, 5 Monte Carlo simulations, respectively. Section 6 contains the empirical results. Section 7 concludes.

Section snippets

The model

Consider the panel data variables y_i,t and x_i,t, where y_i,t is a scalar and x_i,t is r × 1. The data generating process of these variables is given by $y_{i, t} = α_{i} + β_{i}^{'} x_{i, t - 1} + v_{i, t},$ $x_{i, t} = δ_{i} (1 - ρ_{i}) + ρ_{i} x_{i, t - 1} + w_{i, t},$ where x_i,0 = 0_r ×1, a r × 1 vector of zeros, β_i = (β_1,i,…,β_r,i)′ and ρ_i = diag(ρ_1,i,…,ρ_r,i), with δ_i having a similar diagonal structure. This is a multi-predictor panel extension of the prototypical predictive regression model that has been widely used in the time series literature, in which x_i,t is a

The test procedures

In this section we develop tests that are appropriate when wanting to test if y_i,t can be predicted using all or a subset of the predictors contained in x_i,t −1. Let us therefore denote by R an r₀ × r matrix of zeroes and ones selecting the r₀ predictors to be tested. For example, if the hypothesis of interest is that β_1,i = 0 (with β_2,i,…,β_r,i unrestricted), then r₀ = 1 and $R = (1, 0_{1 \times (r_{0} - 1)})$ . Denote by p the number of units for which y_i,t can be predicted using these predictors, that is, p is the

Asymptotic distributions

We begin by reporting the asymptotic distributions of the test statistics when applied to the sample data. The results are summarized in Theorem 1. Here Φ is a symmetric Nr × Nr matrix with typical r × r block Φ_ij = [Φ]_ij = −ω_vv,ijΩ_ww,ij/(c_i + c_j), where Ω_ww,ij = [Ω_ww]_ij is the typical r × r block of Ω_ww and ω_vv,ij = [Ω_vv]_ij. The diagonal r × r blocks of Φ and Ω_ww are denoted $Φ_{i} = {[Φ]}_{i i} = - ω_{v v, i}^{2} Ω_{w w, i} / (2 c_{i})$ and Ω_ww,i = [Ω_ww]_ii, respectively.

Theorem 1

Suppose that Assumptions ERR, 2 The model, Assumption BW hold. Then the

Monte Carlo simulations

In this section we investigate very briefly the performance of the proposed panel tests in small samples. The data generating process used for this purpose is given by a restricted version of Eqs. (1) and (2) that sets r = 1, and α_i = δ_i = 0 and c_i = c for all i. Also, by setting m = T^1/10, we obtain ρ_i = ρ = 1 + T^−9/10c and β_i = T^−9/10b_i, where b_i ∼ U(b_l,b_u). Endogeneity and cross-section correlation are allowed via $v_{i, t} = λ_{i} f_{t} + γ w_{i, t} + ε_{i, t},$ where λ_i ∼ N(1,1) independently of (f_t,w_i,t,ε_i,t)′∼ N(0_3 ×1,I₃). The values

Motivation

In the model of Longstaff and Schwartz (1995) the corporate credit spread, which is the yield difference between the risky bond and the risk free benchmark, is determined by two factors; (i) an asset factor, represented by the stock market index capturing the default risk, and (ii) an interest rate factor, represented by the short rate capturing the interest rate risk. This two-factor model leads to the prediction that the asset and interest rate factors should be negatively related to changes

Conclusion

The difficulty of predicting financial variables using time series data alone has recently motivated researchers to consider panel data as a means to increase the power of conventional (time series) tests. However, the few panel data tests that do exist are not only based on restrictive assumptions, but are also rather uninformative in the sense that they cannot be used to identify the units for which returns can be predicted. Moreover, although data on multiple predictors are typically

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^*: The first author would like to thank the Knut and Alice Wallenberg Foundationfor financial support through a Wallenberg Academy Fellowship, and the Jan Wallander and Tom Hedelius Foundation for financial support under research grant number P2014–0112:1.

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Panel multi-predictor test procedures with an application to emerging market sovereign risk*

Highlights

Abstract

Introduction

Section snippets

The model

The test procedures

Asymptotic distributions

Monte Carlo simulations

Motivation

Conclusion

Econ. Model.

Emerg. Mark. Rev.

J. Financ. Econ.

Emerg. Mark. Rev.

Emerg. Mark. Rev.

J. Financ. Econ.

J. Financ. Econ.

J. Bank. Financ.

Econ. Model.

J. Econ.

J. Econ.

Econ. Lett.

J. Financ. Econ.

Emerg. Mark. Rev.

J. Asian Econ.

J. Bank. Financ.

Stock return predictability: is it there?

Rev. Financ. Stud.