## Extension of Probit Model II Contagion Effect

A spate of recent financial crises, the international crisis of Mexico in 1995, the still unfolding effects of the Asian crisis and the more recent financial crisis in Russia have been accompanied by episodes of financial market contagion in which financial markets of many countries have experienced increases in volatility. Using a panel data set with annual information for 30 countries during the period from 1975 to 1996, Esquivel and Larrain

(1998) find that the contagion effects in currency crises among countries in the same regions are both economically and statistically significant. Theoretically, economists have identified two main explanations for contagion effects. The first one focuses on trade linkages and in the loss of competitiveness associated with devaluation by a main trading partner, which in turn leaves the domestic currency in particular and the domestic financial market in general more vulnerable to a speculative attack (Gerlach and Smets, 1995). The second is related to multiple equilibrium of the economy, and suggests that a crisis in one country may raise the odds of a crisis elsewhere by signalling that currency devaluation or a financial trouble is more likely as a result of the initial crisis. The signal may then lead to a self-fulfilling speculative attack (Mason, 1998).

The following is a partial list of economic factors that can contribute to the contagion effect or cross-correlations among countries:

• trading interdependence; this can be measured by the ratio of crosscountry trade to regional trade, or to the total trade of a country;

• cross-border capital flows for portfolio and direct investment purposes;

• cross-labour flows (Mexican-American labour sending earnings back);

• membership in regional economic organizations (for example, NAFTA (North American Free Trade Agreement) and APEC (Asia-Pacific Economic Cooperation)); and

• direct and reverse direct investment.

The contagion effect among countries has many important implications for investments and risk management. For instance, financial contagion implies high correlation between some financial markets during bad times. Therefore, portfolio diversification across financial regions that have different contagion patterns is of great importance.

Because financial contagion is important, it should be incorporated in country risk models. Balkan's (1995) probit model assumes the independence of default risk between countries. That is, the default or financial crisis in one country does not provide any information about the financial status of other countries. This is inconsistent with our observation on financial contagion.

In this section, we incorporate the contagion effect into the probit model. Define a random variable y¡ for country i such that ytt = 1 if a default occurs in country i at time t and zero otherwise. Using Balkan's notation, we can write:

and yU = 1 I X = Xit if a + Pi • X„ + ett > 0, where Xit is the vector of economic and political indicators observed at time t for country i and eit is an i.i.d. normal variable associated with country i (i = 1,2,.. ., n).

To allow for financial contagion among countries, we assume that the error term eit is determined by a factor model such that:

eit = li1u1t + . . . + 1 imumt + eit, where in,..., iim are constant coefficients and u1t,..., umt are standard normal variables that are i.i.d. over t. The residual term eit is assumed to be i.i.d. over t, be independent of u1t,..., umt, and be independent of eJtfor allj + i. For simplicity, we can assume that factors u1t,. .., umt, are mutually independent.3

The factors u1t, . . ., umt have quite a few economic interpretations. The simplest case is a one-factor model where m = 1. In this case, a common factor can affect the whole world economy. A factor can also be interpreted as a regional economic variable that affects countries in a particular economic region or countries sharing certain common financial characteristics. In this case, we may impose some restrictions on i;1, . . ., iim. For instance, if u1t is a regional factor for Asian countries, we can set ii1 = 0 for all non-Asian countries.

By assumption, the vector of eit, = [eit\ni=1, has the following joint normal distribution:

$t ~ N(0,2). The (i, j) cell of matrix 2 is given by m

The above probit model can be estimated by employing the standard maximum likelihood econometric methodology. The likelihood function is

where * denotes the Hadamard product,4

The expression F[x; O] denotes the cumulative distribution function of A[0, O].

Exhibit 13.9 shows a summary of the full model we are proposing.

### Exhibit 13.9 Summary of proposed country risk model

Based on previous research results and our analysis, we believe that the following adjusted probit model is a more comprehensive model of country risk. The points marked with an asterisk (*) are added by the authors of this chapter.

• Economic Indicators: Debt Service Capacity

• Reserves/imports

• Amortization rate

• Interest/exports

• Debt outstanding/ GNP

• Export growth

• Current account deficit/exports

• Domestic saving/GNP

• OECD growth rate

* Economic Indicators: Currency/Financial Crisis Index

• Seigniorage

• Real exchange rate misalignment

• Soundness of banking system

• Conditional volatility and/or jump probability in exchange rates

The last variable is related to other economic variables. The conditional volatility of exchange rates can be estimated by using ARCH or GARCH type models. The probability of jump in exchange rates can be estimated by using historical jump frequency in exchange rates or by compiling a subjective index.

• Political Indicators

• Democracy index

• Political instability variables

Contagion Effect The contagion effect can be incorporated in a probit model as discussed in the previous section.

In short, we propose a new probit model that is based on Balkan's (1995) original work and takes two additional important factors, currency risk and contagion effect, into account. Mathematically, the model can be summarized as shown in Exhibit 13.10. We let yit = 1 if default occurs in country i at time t, and zero otherwise.

Exhibit 13.10 The extension of the probit model of country risk

The Probit Model yit = 0 I X=XU if a + p,xu + SU < 0

and yu = 1 I X = Xu if a + Pi• Xu + eu> 0, where Xit is the vector of economic and political indicators listed above.

Adjustment for Jump Risk and Currency Risk Exchange rate following the jump-diffusion process dE

The estimates of the parameters in the above jump-diffusion process are used as input variables (Xit) in the probit model.

### Adjustment for Contagion Effect

The contagion effect is incorporated in the probit model by letting the residual terms eit be correlated and be governed by a factor model e. = 7,u,( +... +'v. u , + e..

The residual term eit is assumed to be i.i.d over t, be independent of u1t,. . . , umt, and be independent of ett for all j + i.

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