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Identifying Sovereign Bond Risks Peter Benczur Magyar Nemzeti Bank and Central European Universityy February 2007 Abstract This paper links sovereign bond spreads and actual repayment behavior. Its instrumental variables method tests whether the explanatory power of fundamentals in a spread equation is attributable to their predictive power for observed risk realizations. Using historical data on foreign-currency denominated bonds from developing countries, I …nd that bond spreads can be described as expected values consistent with realizations: the reduced form explanatory power of fundamentals can be attributed to their in‡ uence on default and illiquidity risk predictions. There is, however, strong evidence that during currency crises, bond spreads increase more than do risk probabilities. JEL Classi…cation Numbers: C31, F30, F34, G12, G14, G15 Keywords: sovereign bond spreads, default risk, market liquidity, rational expectations, currency crisis. I am grateful for seminar participants at the MIT Macro Lunch, International Breakfast, the National Bank of Hungary, a Global Development Network workshop in Prague, a workshop on Liquidity of Financial Markets at Central European University, a seminar at Central European University, the EEA Annual Meeting, the Econometric Society European Winter Meeting, for their suggestions and comments. I have also bene…ted from comments of and discussions with Daron Acemoglu, Ricardo Caballero, Rudiger Dornbusch, László Mátyás, Dirk Niepelt, András Simon, Ádám Szeidl and János Vincze. I thank Nagyné Gajdácsi Márta for editing assistance. All the remaining errors are mine. y email: benczurp@mnb.hu 1 1 Introduction It is a standard notion to view bond yield di¤erentials as the market’ assessment of the relative s riskiness of the issuers. This immediately raises three important questions: What risks (expected losses or gains) are involved in such comparisons? Are there certain times when the spread changes more than implied by changes in these risks? Do market participants perceive the expected values of these risks correctly? There is a growing, mostly empirical literature on the …rst two questions, with a particular focus on testing whether default risk is the only determinant of bond spreads, or there is a role for risk premia, market liquidity or limited arbitrage.1 The third question has a long empirical history, dating back to the appearance of rational expectations in econometrics.2 These issues, however, are necessarily interrelated: without looking at the right risks, one cannot test if their perceived probabilities are close to observed probabilities, or whether spreads deviate from a probability-based pricing equation. On the other hand, it is impossible to identify the risks involved in bond prices and potential deviations unless we have some picture of how such probabilities are formed. A main determinant of spreads should be default risk, but bonds may also be subject to further risks, like changes in the short-term rate, or exchange rate movements. When attempting to separate these factors empirically, a major obstacle is that the conditional expectations of various losses are not directly observable. Various solutions have been proposed to this problem. One is to assume that there is only one source of risk (default), postulate a relationship between fundamentals and the risk probability, and then another between the probability and the spread. Substituting one into the other yields a reduced-form equation connecting the spread and fundamentals. This approach is adopted by (among others) Edwards (1986), Stone (1991) and Ozler (1993). A di¤erent solution is to …nd acceptable proxies for the probabilities, like credit ratings (Cantor and Packer, 1996, Elton et al, 2001, Kamin and von Kleist, 1999). Cumby and Pastine (2001) use multiple issues of the same borrower, and assume a common value of the expected default loss. This paper o¤ers an alternative approach, which essentially adopts the rational expectations macro-econometrics approach to bond pricing: the idea is to use data on the realizations of the risk events (losses). This poses an identi…cation problem, since actual realizations are correlated with prediction errors. The solution is to recognize that any information available at the time of pricing can serve as valid instruments. A reinterpretation of this procedure is that it tries 1 Examples include: Amihud and Mendelson (1991), Bradely (1991), Broner and Lorenzoni (2000), Cumby and Pastine (2001), Eichengreen and Mody (1998), Elton et al (2001), Hirtle (1988), Kamin and von Kleist (1999), Kim et al (1993), Pástor and Stambaugh (2003), Redding (1999). 2 Mishkin (1983), Att…eld, Demery and Duck (1985), or Wickens (1982). 2 to attribute the reduced form e¤ect of certain fundamentals to their predictive power for risks. Overidenti…cation then receives a central role: it tests whether information only enters through risk probabilities, or there are some additional channels. Applying this approach to a moderate-sized historical sample of sovereign bond spreads and default behavior of several developing countries, the paper addresses the following speci…c issues. The …rst is whether sovereign bond price di¤erentials can be attributed entirely to di¤erences in expected returns, consistent with expected values (probabilities) predicted from realizations. Second, what risks are involved in the calculation of expected returns, and what their relative importance is. In particular, whether default risk alone, or default and illiquidity risk – about which much less is known3 – together can explain bond spreads. Third, whether market conditions occasionally have an extra impact. This means estimating an arbitrage-based pricing equation for bonds, and testing for a role of imperfections in certain distressed periods. Let me brie‡ summarize the main …ndings. The in‡ y uence of fundamentals on bond spreads can be attributed to their e¤ect through predicted risks: When including a repayment trouble indicator, the benchmark interest rate, and country dummies, the overidenti…cation test accepts. Including a currency crisis indicator as extra instrument leads to a rejection, which indicates that during crises, spreads increase more than the change in default risk. Overidenti…cation is restored either by including the crisis dummy on the right hand side –default risk and market conditions explain the spread – or a term representing future (expected) illiquidity. Although , the crisis indicator is not vital for overidenti…cation in this latter case, its coe¢ cient still stays large and signi…cant when including both a crisis and a future illiquidity indicator. This full speci…cation yields a strong and robust causal description of the spread: it re‡ ects predicted default and illiquidity risk, but market conditions cause deviations during currency crises. The paper is organized as follows. The next section describes the basic empirical speci…cation, the estimation strategy, and my data sources. Section 3 contains the main …ndings: the …rst part tries to explain bond spreads only by default risk, while the second part introduces a role for market conditions and illiquidity risk. This approach yields a successful description of bond spreads, the robustness of which is tested in Section 4. The last section concludes and points to some possible future directions. Some skipped details are then presented in the Appendix. There are some theoretical papers, like Grossman and Miller (1988); and empirical contributions, but the latter mostly concentrate on U.S. Treasuries. For example, Redding (1999), Amihud and Mendelson (1991), Bradley (1991) and Hirtle (1988). See Benczur (2005) for a more detailed discussion. Pástor and Stambaugh (2003) analyze stock returns, by incorporating a market-level illiquidity risk into their analysis. 3 3 2 2.1 The setup of the empirical analysis Main speci…cation Each data point j means a bond spread observation, corresponding to country i(j) in year t(j). For some observations, a more precise date is available, but this information is often missing. Moreover, a full set of country fundamentals is rarely available at a higher-than-annual frequency, so I cannot go beyond the annual level. In order to limit the list of potential risks, I will focus on spreads of sovereign bonds of developing countries over government bonds of industrial countries (mostly the United States, Germany, and Japan), denominated in the same currency, and similar in maturity. By using developing country bonds denominated in the same currency as the benchmark, these spreads should contain no “pure” exchange rate component. They allow, however, a spillover e¤ect of large exchange rate movements (current liquidity or market conditions). Working with spreads relative to similar maturity benchmarks, I can reduce the interest rate risk: this spread should be largely independent from interest rate movements. This still leaves us with default risk, and potentially, current liquidity and future illiquidity risk. Starting with default risk, let pj = E[di(j)t(j) jZi(j)t(j) ; Ri(j)t(j) ] denote the conditional probability that, as of information available at the time of pricing (Zi(j)t(j) and Ri(j)t(j) ), country i(j) does not fully repay its outstanding bonds in the future (neglecting the possibility of a selective default), which is event di(j)t(j) Then my basic speci…cation for the spread is as follows: sj = rj Ri(j)t(j) = + Ri(j)t(j) + pj + "1j : (1) Here Rj = Ri(j)t(j) is a similar maturity and currency-denominated “riskless”bond rate at time t(j): a developed-country government bond yield; for example, U.S. Treasuries for dollar bonds. The linear term p can be derived from risk-neutrality and pro…t maximization, under the assumption that there is a partial default on the principal but not on the interest: (1 implies r R = p(1 x): (2) p)(1 + r) + p(x + r) = 1 + R Thus, one calculates the spread and tries to explain it with predicted default probabilities. For a more complex default case, the link between the spread and the probability of default becomes less tractable. For simplicity, I will concentrate on this simple, convenient and standard case. It serves to capture a positive relationship between predicted probabilities and spreads. 4 The main speci…cation will allow for a second risk term E[li(j)t(j) jZi(j)t(j) ; Rj ] (expected loss from time-varying future market conditions –“liquidity black holes” as put by Persaud (2001) , and Morris and Shin (2004) – a role for current market conditions (currency crises, cj = ci(j)t(j) ), , and country-speci…c …xed e¤ects hi(j) :4 sj = + Rj + def E[di(j)t(j) jZi(j)t(j) ; Rj ] + liq E[li(j)t(j) jZi(j)t(j) ; Rj ] + cri cj + hi(j) + "1j : (3) 2.2 The estimation strategy: a structural asset pricing regression The core problem is that conditional probabilities and expectations are not directly observable. As a remedy, some studies5 assume that there is only default risk, and its probability is some function of fundamentals, the form of which is known to the market. Then this relationship is substituted into the spread equation, which leads to a reduced-form speci…cation describing the spread itself as some function of fundamentals. From a forecasting or descriptive viewpoint, this speci…cation would be su¢ cient to learn how fundamentals of a borrower and observable market conditions in‡ uence the spread it pays on its bond issues. A major shortcoming is that we necessarily attribute all variation in spreads to changes in the underlying risk (default) probability. Whenever a fundamental changes, it will change the spread entirely through its e¤ect on the unobserved probability. Such an approach cannot succeed when there is more than one determinant of the spread. More importantly, it is unable to determine why a speci…c fundamental or market indicator has such an e¤ect, how much the results would depend on the choice of fundamentals, and whether a certain e¤ect of a fundamental is consistent with the way that fundamental in‡ uences actual payo¤ behavior of the asset. Finally, it hinges on two functional form assumptions: the relation between fundamentals and the risk probability, and also the risk probability and the spread. One potential solution is to …nd acceptable proxies for the probabilities themselves: credit rating, for example, might represent default risk. One can then estimate a relation between spreads and credit ratings, and test whether credit ratings are su¢ cient statistics of available information (Cantor and Packer (1996), Elton et al (2001) and Kamin and von Kleist (1999) follow such an approach). This method, however, still cannot determine what risks are represented by credit ratings, and whether the information is used correctly. Cumby and Pastine (2001) use data on di¤erent issues of the same borrower to test for a common underlying default probability. They …nd evidence that di¤erent issues imply di¤erent In principle, one could try to explore the panel nature of my data. Time-speci…c …xed e¤ects are then represented by the Rt(j) term: the speci…cs of a given year should be captured by the bond-speci…c benchmark rate. However, my data is a very unbalanced and sparse panel. For this reason, I did not attempt to go beyond the eleven country dummies. 5 For example: Edwards (1986), Stone (1991), Ozler (1993). 4 5 probabilities. Their approach, however, cannot identify more than one source of risk, or test for a systematic extra e¤ect of fundamentals or events. As an alternative, I use data on the risk events themselves. Given realizations of the random variables constituting the source of risk, one can estimate their conditional distribution. Assume that the conditional expectation (probability) that country i defaults over the lifetime of a bond being priced at time t (dit ) is some function g of available information Rit and Zit , then dit = E[dit jRit ; Zit ] + "2it = g(Rit ; Zit ) + "2it : (4) Here Zit is a set of country- and world-level economic indicators, available at the beginning of year t. Thus, they usually correspond to data from year t choice of these variables will be discussed later on. Though g is unknown in general, the prediction error "2it is by de…nition orthogonal to Rit and Zit . The spread equation for bond j can be rewritten as sj = + Rj + g(Ri(j)t(j) ; Zi(j)t(j) ) + "1j = + Rj + di(j)t(j) + "1j "2i(j)t(j) : (5) 1 and earlier. The particular Here dit is, of course, not orthogonal to the error terms: de…nitely not to "2it , and from the simultaneity setup, not even to "1j . Nevertheless, any subset of Zit can serve as valid instruments for the problem: by assumption and de…nition, they are uncorrelated with the error terms, but they are correlated with the event indicator, since they enter the prediction equation. This even overidenti…es the interest rate equation, and eliminates the dependence on any functional form assumption, omitted variable problems or selection bias6 in the default prediction equation: I do not have to specify or estimate the probability model, it is enough just to know that some fundamental variables are correlated with the risk event, thus they are valid instruments in the interest rate equation. Using only a subset of available information (fundamentals) will not lead to inconsistent estimates, it would only in‡ uence e¢ ciency. Moreover, one can then test this overidenti…cation, and check if there are any variables which have a direct e¤ect (above their in‡ uence on predicted probabilities) on the spread. Though such an e¤ect might come from various sources,7 my strategy is to attribute them to some extra factor (market conditions, bargaining terms etc.) which has an e¤ect on the spread not only 6 From the second half of the time period of my data set, I mostly have new issues, while the …rst half contains both secondary market quotes and new issues. It is clear that the ability of a country to issue a new bond is correlated with its riskiness, thus the default prediction equation may be subject to selection bias. Such a problem, however, is less severe in the pricing equation: once we have the default probability, the ability to issue a new bond should not contain substantial extra information. 7 For example, if the true event the market “fears” di¤erent from the one I am using, then some of the is instruments might be absorbing the di¤erences of the probability predictions. A rejection might as well be due to problems with the rational expectations and risk-neutrality approach used in deriving the interest rate equations. 6 through increased risk, but more directly, too. As I will show, default and illiquidity risk, a role for current market conditions (currency crises) and country e¤ects together (which is equation 3), do o¤er an acceptable and robust speci…cation, without a need for risk-aversion or market irrationality. The approach is reminiscent of well-known practices for testing rational expectations (e.g. Mishkin (1983), Att…eld, Demery and Duck, 1985). Wickens (1982) also proposed using past information as instruments, but in a somewhat more restrictive setting. The Appendix draws a detailed parallel, and explains the mechanics of the overidenti…cation test and identi…cation. As an important, alternative interpretation of the method described so far, one can start from the reduced form of the asset pricing equation. Certain variables (Zit , Rit ) have explanatory power in an asset pricing (bond spread) equation: sj = + Rj + Zi(j)t(j) + "j : (6) In order to understand where these relationships are coming from, one needs a structural framework. Assume that the spread re‡ ects the expected value of some uncertainty (the “risk” a of certain event eit , which might be a zero-one, or a continuous variable): sj = 0 + 0 E[ei(j)t(j) jRj ; Zi(j)t(j) ] + "0 : j Use a rational expectations (linear) prediction of that event (denoted by eit ): eit = 00 + 00 Rit + 00 Zit + "it : To estimate the original speci…cation, replace the latent expectation term with its best linear prediction; or, as a more robust interpretation, use the realization itself and do instrumental variables: sj = 0 0 00 00 00 + + Rj + Zi(j)t(j) + "000 = j 0 + 0 This means that one tries to attribute the …t and explanatory power of R and Z to their predictive power for (correlation with) the event e. Again, the overidenti…cation test is the right tool to determine whether the reduced form is captured by the structural form. In case of a rejection, one can include additional factors (like liquidity risk, market conditions and country e¤ects, as in equation 3) and see whether they are su¢ cient for the overidenti…cation test to pass. The argument shows that the only linearity I need is in the pricing equation (3), but the prediction equation (4) does not have to be linear. This generality makes the method readily applicable in many other asset pricing frameworks: for example, one can estimate an uncov7 ei(j)t(j) + "j : e ered interest parity condition as in Benczur (2002); or it can be applied to understand the determinants of bank loan spreads (Benczur and Ilut, 2005). 2.3 Data sources There are three main sources of my data. International Financial Statistics, World Development Indicators and the Federal Reserve’ data site provide all major economic variables for countries s and the world, and also world interest rates (long- and short-term government bond yields for the major lending currencies), and exchange rates. Though I have all the necessary annual variables whenever I have data on bond yields, the sample size would be fatally reduced with quarterly data. Arrears, reschedulings and debt relief agreements are from the World Bank’ World Debt s Tables. A debt relief refers to an event when the debt stock is reduced due to debt forgiveness or such a rescheduling which actually lowers the present discounted value of debt obligations. These relief agreements are restricted to the period starting in 1985. The major bottleneck is the need for a su¢ ciently long bond yield (price) data set, which is necessary to be able to use default predictions (i.e., instrument realized events with predetermined predictors). Current databases rarely cover more than the nineties, so I had to go further back to pre-electronic sources. Bond prices are from three sources. One is Moody’ Bond Record, which gives the coupon s and the current price of all sovereign bonds traded in the United States. I have entered the data from its January issues, from 1975 to 1997. Unfortunately, it switches to reporting only the coupons of current issues around 1990 – since the earlier observations of new issues show that coupons are usually chosen right at issue, the issue prices are well approximated by 100%. The other source is Euromoney (1975 to 1988), which reports each month the currently issued Eurobonds, with their nominal yield and issue price. Again, they stop giving this information around 1987. The last source is Moody’ International Manual (1975 to 1988), which reports – s beside many other information –sovereign bond issues: not for all countries; and sometimes the issue price is given, sometimes not (again, it is usually very close to 100%). The common data structure of my three sources was coupons, maturities and price quotes. To keep yields comparable, and to use the most of my scarce price data, I adopt the following simple spread calculation. Given maturity, coupon and price, the approximate yield is r + 100 T and the spread is r + 100 p T p , RT . A missing maturity was replaced by the sample average, and a missing issue price was approximated by 100 (full). For the benchmark rate, I used the longterm (10-year) government bond yield of the lending currency for all observations with at least 3 years to maturity; and the 1-year rate otherwise. Apart from missing data, this calculation can err in two major ways: its …rst-order approx8 imation may become imprecise for large interest rates or secondary market prices well below 100%; and the benchmark yield curve is in general more complicated than the distinction between short and long-term rates. For the second some data might exist, but it is not very accessible. To reduce this problem, I worked only with at least 3-year maturity bonds, where it makes relatively little di¤erence to work with 5- or 7-year rates. The approximation problem should lead to a systematic downward bias of yields: whenever benchmark rates increase, the approximation error becomes larger, thus the calculated yield increases less than it should. This will lead to a too low benchmark rate coe¢ cient (both in the reduced form (6) and the structural form (3))– which is exactly what I have found (signi…cantly below one). Unfortunately, any more precise attempt to calculate yields is likely to amplify preexisting data problems: an explicit discounting of future coupon payments, for example, is very sensitive to assumptions about the benchmark yield curve. Moreover, it also reduces the number of observations, since the exact maturity is crucial for such calculations. Nevertheless, when I tried to calculate the present value of future payments and obtain spreads from those results, the course benchmark rate (1- versus 10-year maturity) coe¢ cient indeed became one. Using the approximated yield curve for the benchmark rate as well (a linear scheme …tted on the 1- and 10-year values), however, produced even smaller interest rate coe¢ cients. This I take as an indication that the too low interest rate coe¢ cient is a result of yield calculation problems, but I still stick to the less precise, but at least more robust, method, and discuss this alternative only as a robustness test. These three sources give me approximately 350 observations, from around 100 country-year cells, overwhelmingly in dollar denomination. For the main speci…cation, I keep only the longterm bonds (of at least three years to maturity). I also discard those bonds which were already in default and then were extended. This gives me a sample size of 266, from 11 countries,8 with an average spread of 123 basis points over the benchmark yield. 3 3.1 Main results Only default risk First I present the reduced form estimates of (3): it means estimating sj = 8 4 + 4 Rj + 4 Zi(j)t(j) + 4 Hi(j)t(j) + "4j ; The countries are (number of observations in parentheses): Algeria (4), Argentina (22), Brazil (28), Hungary (19), Malaysia (20), Mexico (74), Philippines (6), Thailand (3), Turkey (23), Uruguay (4), Venezuela (56). 9 where Hit denotes country dummies and a currency crisis indicator (a large depreciation of the currency, abandoning a …xed exchange rate for a ‡ oat, or a managed ‡ oat for a free ‡ oat). Z contains the …rst lags of the following standard variables (at an annual frequency): reserves to imports, exports to GDP, external debt to GDP, current account balance to GDP (positive if in surplus), GDP growth (in percentage), GDP per capita (in 1000 dollars), an indicator of total past repayment troubles (arrears, relief and rescheduling agreements since 1970), and the percentage of countries in the region with arrears (a special form of regional e¤ects, being surprisingly powerful in diagnostic regressions). These regressions simply try to explain the interest surcharge faced by a country. The results are contained in the …rst four columns of Table 1. The overall …t is an R2 of 0.2 (around 0.1 without the 11 country dummies). This is not extremely strong, but we see that these variables do have reasonable explanatory power.9 It also means that though spreads are responsive to fundamentals, their reaction is moderate. On average, fundamentals still explain a reasonable portion of spreads. Given the annual frequency of fundamentals, these …ndings are not surprising: yearly fundamentals have relatively little variation, so they cannot account for all the variation of spreads. In general, I would not read any strong stories from these descriptive results: …rst, some multicollinearity might be present even within the …rst lags of the variables; and second, the speci…cation is probably subject to omitted variable and selection problems. I still point out two results: the …rst is the signi…cant positive e¤ect of the currency crisis dummy. The other is the surprising negative coe¢ cient of the benchmark interest rate. Although it is statistically signi…cant, the con…dence intervals “almost” contain zero. My interpretation is that the true coe¢ cient is close to zero, but the approximate yield calculation gives a systematic negative error when long-term rates are high. In the robustness test section, I also used a more precise formula for calculating yields, but it did not resolve the problem. Mechanically, the future results will be a re…nement of these reduced forms: when replacing the right hand side with + 4R + R + p, I impose the parameter restriction 4Z 4 + + 4H = + R+ ( 2 + 2R + 2Z + 2 H) + H: The overidenti…cation test will reject exactly when this interpretation of the reduced form is not acceptable. Before actually switching to the structural form, I need to discuss brie‡ the …rst stages of y One reason for the low R2 is that many observations correspond to multiple data in the same country-year cell, and the within-cell variation cannot be captured by the explanatory variables. If one regressed the average values on the same right hand side (which means 71 observations and 11-21 explanatory variables), the …t would improve signi…cantly (to 0.2-0.4). The point estimates would be mostly similar, which supports the initial hypothesis that the within-cell variations are orthogonal to the right hand side variables. 9 10 all structural form estimations: the linear probability equations (columns 5 and 6 of Table 1) – which in fact measure the correlation of the instruments and the right hand side events. For a discussion about the choice and average values of these event variables, see section 3.2. The results suggest that default and variance can be predicted quite well, even without the country dummies, which means that the instruments are highly correlated with this event variable. This would apply much less to crisis indicators: even with country dummies, the R2 would stay below 0.35. It is hardly surprising, since crises are usually poorly predictable. The good …t, however, conveys an unrealistic picture: in order to interpret the high R2 as high correlation of the instruments and the events, I kept the same multiple country-year cells, which arti…cially increases the …t. Using country-year averages produces very similar estimates, and an even higher R2 for both variables. Though the small sample also raises concerns about the …t, one can still conclude that the selected fundamentals have good predicting power for default, and they are su¢ ciently correlated with future variance. Section 4.2 discusses the consequences of choosing a smaller or larger set of instruments. Having checked our instruments in terms of being correlated with dit and lit , we can now turn to estimating (3). Table 2 reports the scenario with a single event, a repayment problems indicator on the right hand side. In column 1, the choice of the default indicator is the ratio of debt forgiven (in the next 5 years) to current debt stock; in 2, it is an indicator of debt relief, rescheduling or arrears in the next 5 years; …nally, 3, 4 and 5 considers only relief and rescheduling agreements (see section 3.2 for further details). The …rst two choices give insigni…cant results, and though the overidenti…cation hypothesis is accepted in column 2, it also corresponds to a very weak …t. The coe¢ cients in columns 3-5, on the other hand, are meaningful, signi…cant and stable: a 10 percentage point increase in predicted relief or rescheduling adds 8.4-8.8 basis points to the spread. Increasing the predicted value of future default from its sample median (0.58) to the 90th percentile (1.08), the spread increases by around 40 basis points. This is in fact similar to the average e¤ect, as the sample average of the default indicator is around 0.5. Compared to the 123 basis-point average of the spread, these numbers are economically signi…cant.10 Another feature of the results is the surprisingly stable (-0.1) and signi…cant coe¢ cient of the benchmark interest rate. This conclusion is found also in Eichengreen and Mody (1999), Benczur and Ilut (2005) and Uribe and Yue (2006).This coe¢ cient is practically the same as in the reduced form: since the benchmark rate was not signi…cant in the default prediction equation, default probabilities do not change the interest rate coe¢ cient. This reinforces my earlier interpretation of attributing this negative term to approximation and calculation errors In equation (2), it means x 0:99. With the narrow interpretation of default in (2), bondholders do not seem to expect large losses in case of default. 10 11 in bond yields. The most important result concerns the overidenti…cation test: with a set of country dummies on the right hand side (thus also as instruments), the structural form is accepted, but it is rejected in all other cases. This …nding describes bond spreads by default risk, the benchmark yield and country-speci…c e¤ects. This still means that one has to be careful when inferring di¤erences in predicted risk by comparing spreads of di¤ erent countries. As we shall see, however, even the acceptance result is not yet robust; some further elements will also play a role. 3.2 3.2.1 Illiquidity risk and market conditions Choice of the event indicators Uncertain returns lead to bond price di¤erentials even with risk-neutral investors, since no arbitrage implies that the expected return, including all sources of randomness, is equalized across bonds, but not necessarily the face value. Market conditions, however, may occasionally deviate from the benchmark setting of no arbitrage: limited participation, …nancial constraints, “market sentiment” informational problems – in general: variations in the “risk appetite” , of investors – imply that demand is not always horizontal (limited arbitrage). This is usually referred to as the liquidity of the market. If market conditions are constant in time, then this liquidity is a …xed characteristic of the bond (or the entire bond market), and not a separate source of randomness. Market conditions may, however, ‡ uctuate in time: there are normal times when a sudden transaction means very little loss (almost horizontal demand), and there are distressed times when almost nobody is willing to buy on the market (upward-sloping demand).11 So if investors face a chance of early sale, then the expected loss from such a transaction may be incorporated into bond prices. This introduces a second expected loss component into the spread, which I label as illiquidity risk (in contrast to liquidity itself, which is not an expected, but a current event). In the case of foreign-currency denominated sovereign bonds, a currency crisis can be the source of such distress.12 An expected or realized devaluation leads to heavy losses in the localcurrency denominated bond market. The markets for a country’ local- and foreign-currency des nominated bonds usually have many common investors, which implies that the liquidity squeeze of the market that was actually hit by a fundamental shock will lead to transactions on the other market as well. If participation is limited and investors face some credit constraints, then potential buyers will lack the necessary funds, so prices on the second market will have to drop more than implied by changes, if any, in default risk. Of course, this is only one potential mechanism for an overall decrease in the risk-bearing ability, or willingness, of investors. 11 12 Persaud (2001) and Morris and Shin (2004) label such events as ” liquidity black holes” . This illustrative argument builds on Broner and Lorenzoni (2000). 12 Consequently, my two major risk choices are a repayment di¢ culty (“default” variable, and ) an illiquidity indicator. Once I have both of these probabilities incorporated into the interest rate equation, I can check whether one or the other is enough to explain why fundamentals in‡ uence spreads in the way the reduced form shows; and to test if, during crises, spreads increase more than implied by risk movements. With default realizations for bonds, the choice is not obvious: hardly any sovereign bond defaults have happened in my data sample (from the mid-seventies to the mid-nineties), and even less in foreign-currency denominated bonds (as documented in Standard and Poor’ CreditWeek, s 1998). As the recent Argentine experience suggests, one should still not conclude that there is no default risk in such bonds. For this reason, I will use an indicator of repayment problems on any form of sovereign borrowing. Such repayment di¢ culties were frequent among developing countries, but they remained systematically restricted to bank lending: arrears, reschedulings or even defaults (usually, in the form of debt relief agreements) on syndicated loans. As the previous subsection shows, the indicator of debt relief or rescheduling in the next 5 years is a successful choice. The sample average of this binary variable is 0:5. Since it is an indicator of at least one relief or rescheduling event in the next …ve years, it is reasonable that its value is this large in a developing country sample. To support this choice, I would argue that this privileged repayment discipline on bonds was not, or even could not have been foreseen by market participants during most of my sample period. Thus, repayment problems on bank loans are also the realizations of the default risk on bonds. Another argument could be that whenever loan defaults become more likely, bond default probabilities also increase (or: expected recovery rates decrease), thus predicted loan defaults can proxy predicted losses from bond defaults. The overidenti…cation test shows that this event is useful for describing bond spreads, moreover, its size and signi…cance is robust to many alternative speci…cations. This con…rms the use of this event as a proxy for default. For the currency crisis indicator, I use a dummy for an at least 50% devaluation in the given year, abandoning a pegged exchange rate regime for a ‡ oat, or moving from managed to free ‡ oat. Although these episodes might not fully coincide with crises, the results indicate that bond prices indeed behave systematically during these periods. The sample average of this variable is 0:1. Some further choices are discussed in the robustness test section. Finally, what can describe a future “illiquidity event” First of all, if illiquid episodes are ? driven by currency crises, then an indicator of such crises in the future is an immediate choice. Unfortunately, this variable is neither signi…cant nor relevant for overidenti…cation, since crises are particularly hard to predict. A debt crisis can also trigger illiquidity episodes: the future repayment problem indicator may as well represent future depressed markets. This would also 13 imply that a current repayment problem should increase spreads, which is not supported by the data (see section 4.3). Another, more general candidate for measuring liquidity is the observed behavior of the market itself. Although it would be less clear to see what causes liquidity to ‡ uctuate, it does not restrict depressed periods to currency crises. Moreover, a more general event might turn out to be more predictable. Such measures can be obtained from trade quantities, bid-ask spreads, or prices themselves. Pástor and Stambaugh (2003) use market-level trade intensity to capture illiquidity risk in the stock market. For bonds, however, quantities or bid-ask spreads are hard to get – particularly for a long time horizon and broad cross-section, which would be essential for predictability. So the only feasible option is to extract a liquidity measure from prices, but then this variable will be hard to distinguish from default risk. One proxy could be an indicator when the current value of r R r or r R increases substan- tially, by more than what could be attributed to changes in default risk (like it is hypothesized during crises). However, the change in risk can only be estimated, and recycling such an estimation is problematic. One can also assume that large spread movements always have some components above default risk (for long-term bonds, even a debt crisis is unlikely to put repayment at immediate danger), so a large spread increase re‡ ects a case when the market for these bonds “dries out” I experimented with a number of choices for such an indicator. In general, . it has the wrong sign, and it is often insigni…cant (it cannot disentangle illiquidity from default risk).13 So, instead, I adopted a di¤erent choice: the sample variance of future spreads, taking all bonds of a country into account. The best performing choice is the 5-year variance, which is reasonably signi…cant, moreover, it is very in‡ uential in the overidenti…cation test. Such a variance variable also tries to quantify volatile episodes of the market: again, if volatility is not caused exclusively by changes in default risk, then more volatility indicates a bigger role for market conditions.14 The sample average of this term is 3:08. 3.2.2 Results This subsection tests whether illiquidity risk and market conditions (in particular: currency crises) also play a role in the determination of bond spreads. The results are reported in Table 3, where speci…cations include a repayment problem indicator, di¤erent liquidity indicators, the benchmark bond rate, a crisis indicator and country dummies (or a subset of these variables) on the right hand side. The former …nding can be explained by a mechanical link: if spreads will increase substantially in the near future, then they are likely to be below average now, so the probability of a future spread increase might get a negative coe¢ cient in current spreads. 14 See Benczur (2005) for a more direct liquidity interpretation of such a variable and further discussion. 13 14 Before interpreting the various liquidity and market condition results, let me point out two common and robust features of all estimates. The coe¢ cient of the benchmark interest rate is always signi…cantly negative, its value is between 0:1 and 0:3. The remarkable stability of this negative coe¢ cient rea¢ rms that this phenomenon is due to measurement of bond yields, which is unrelated to fundamentals, default risk and currency crises. As discussed earlier, the variance term is also in‡ uenced by these miscalculations, which shows up as a signi…cantly more negative interest rate coe¢ cient in columns 4-6. The other unchanging result is the signi…cant positive coe¢ cient of default risk, being between 0:65 and 1:29. Column 1 repeats the regression from column 3 of Table 2, with using a currency crisis dummy as an extra instrument. The coe¢ cients stay the same, but overidenti…cation is rejected at the 10% level. The positive sign of the crisis indicator in the reduced form thus cannot be fully attributed to higher default risk during such episodes. We see in column 2 that including the crisis dummy on the right hand side re-establishes overidenti…cation; the variable gets a coe¢ cient of 0.75, highly signi…cant. These results imply that during currency crises, bond spreads increase more than changes in default risk predictions. There are three potential explanations for such an extra e¤ect: one is that there are some other risk factors in‡ uencing spreads, and the crisis dummy captures the increase of this other risk. A second is a based on rational but constrained investors: limited participation or a systematic decrease in the “risk-bearing ability” willingness of investors during or crises. A variant of this argument is that the “true” expected loss from bond default increases more than the probability of overall repayment problems. A third explanation, empirically hardly distinguishable from the second, is that market participants systematically overestimate default risk around crises, at least relative to observed (future) default behavior. The …rst explanation implies that the e¤ect of crises should be eliminated by including an appropriate extra risk term; while the other two mean that there is an extra crisis term above any risk probabilities.15 Columns 3-6 try to confront each explanation with the data. The …rst step is to look for risks which could replace the direct crisis e¤ect. I experimented with many crisis or market condition indicators (future price collapses, spread variance, IMF agreements, various exchange rate regime changes). With the exception of the variance term, all speci…cations has led to noisy estimates, were heavily in‡ uenced by the exclusion of country dummies, or by perturbing the set of instruments (even overidenti…cation failed occasionally). The limited success of the variance term (as shown in column 4) indicates that expected future market conditions are incorporated into the spread, in a more general sense than purely 15 Explanation two would also imply that there should be an additional risk factor in spreads: if investors are aware of implied losses during crises, then a future crisis risk should be incorporated into the spreads. Such a term would be missing under explanation three. Crises, however, are usually hard to predict, making the proposed distinction of these two explanations hard to test. This is con…rmed by column 3 of the table. 15 crises (column 3). Column 4 shows that its coe¢ cient is signi…cantly positive, large, and it can take over the crisis e¤ect: overidenti…cation is accepted without a direct crisis term (the same applies for the speci…cation without country dummies). Accepting overidenti…cation does not mean that the direct crisis e¤ect becomes zero: in column 5, which includes both the variance term and the crisis dummy, the latter stays around 0.7, highly signi…cant (the same holds if one drops the country dummies), but the variance coe¢ cient stays similar. As this speci…cation captures all three aspects I was looking for (default and illiquidity risk, plus market conditions), I view this as my benchmark case. Assessing the size of each determinant, an increase from predicted default risk from its sample median (0.41) to its 90th percentile (1.11) increases the spread by around 0.65*60 39 basis points. Increasing the value of predicted future variance from its sample median (2.39) to its 90th percentile (7.44), the spread increases by 0.24*505 121 basis points. Switching the currency crisis indicator from zero to one increases the spread by 79 basis points. Compared to the sample average of the spread (123 basis points), these e¤ects are economically signi…cant. A common feature of columns 4 and 5 is the further decrease of the interest rate coe¢ cient. This is due to the variance term: in the …rst stage regression of variance, the benchmark rate has a large and signi…cant coe¢ cient. This means that a positive structural coe¢ cient of variance must imply a decrease in the structural estimate of the interest rate coe¢ cient. From the e¤ect of interest rates on variance, I attributed a large part to measurement problems with bond yields. This means that a “true variance” would be less responsive to interest rates. Column 6 makes an adjustment into this direction: it uses a modi…ed variance term, which is obtained by subtracting 2:06 from variance in years 1980-1985 (periods with unusually high benchmark rates). The interest rate coe¢ cient indeed moves slightly closer to zero, and the variance coe¢ cient increases. One could use further adjusted variance measures, which would also lead to higher variance, interest rate and, occasionally, even higher default coe¢ cients. In any case, one could not reject that all the interest rate coe¢ cients are equal to each other. The evidence thus indicates that there is an extra risk included in bond spreads (explanation one), but crisis periods imply an even bigger increase in spreads than the total increase in risks (explanations two and three –but due to noisy crisis predictions, the data cannot tell these two explanations apart). This extra risk re‡ ects distressed future market conditions: partly because of future crises, but it appears to be a more general notion of market conditions. To get a sense about the average contribution of the two risk factors and the extra e¤ect of crises, I plug in sample averages into the speci…cation of column 5. This purely illustrative 16 exercise yields d \ spread = 0:65 def + 0:24 variance + 0:79 {z ccrisis + 2:37 0:28 {z benchm : {z } | } } |{z} | | {z } | {z } | price variation crisis adjustments country e ects 1:23 default risk {z } | {z } | {z } | {z } | 0:33 0:74 0:079 0:08 The equation suggests that the benchmark rate adjustments and the country e¤ects are sizable determinants of spreads, since both are more than twice the average (measured) spread. The benchmark rate e¤ect is likely to re‡ yield calculation problems. It is not clear, however, ect why country e¤ects are this large: though there can be some country-speci…c …xed fundamentals, but then those fundamentals must have a large e¤ect above risk probabilities. Section 4.4 o¤ers some further re…nements. The remainder of the spread is a time-and country-varying component, above changes in benchmark interest rates and country …xed e¤ects: it can be interpreted as an adjusted spread. From its average value of 1.15, default risk is responsible for 29%, price variance constitutes an additional 64%, and the remaining 7% is the crisis term.16 How large is this additive crisis e¤ect, relative to increases in risk predictions during crises? Since the crisis dummy is included on the right hand side of the regression, the same average decomposition can be applied to the crisis and the non-crisis sub-samples. Then one can compare the changes in each average during crises: d spread = 0:65 def + 0:24 | {z } | {z } | 0:84 default risk: 0:11 price variation: 0:5 The change in the “adjusted spread” 0:84 + 0:56 = 1:4, from which 0:11 (7.8%) can be is \ variance + 0:79 {z ccrisis + | 0:16 {z } | } crisis: 0:79 total: 0:28 {z 0:56 benchm : } attributed to increased default risk, 0:5 (35.7%) comes from higher variance (future volatility), but the major e¤ect (56.5%) is the extra additive increase. Notice that both of the risk predictions increase during crises: the di¤erence between crisis and non-crisis averages is 0:16 for default (compared to the 0:5 unconditional average), and 2:08 for variance (compared to 3:08). So what happens during crises is that default predictions increase, but near-future volatility increases even more. Thus, though the additive crisis e¤ect can also be attributed to a nonlinear relationship between spreads and risk probabilities, default risk is unlikely to be the only source of the crisis e¤ect. Based on all the results presented, the reduced form …t can be attributed to default risk, some form of illiquidity risk, the benchmark interest rate and country …xed e¤ects. There is, The average value of this adjusted spread is 0:46 in column 2 (with default risk and crisis), and 1:08 in column 4 (default and illiquidity risk). From the unreasonably low 0:46 of column 2, 0:38 (83%) is default risk; this number is 0:34 (31%) in column 4. The absolute contribution of default risk is highest in column 3, where the default coe¢ cient is 1:29: there the value is 0:65 (65 basis points). In all cases, default predictions are substantial, but not the only determinants of spreads. 16 17 however, an extra increase during currency crises, above changes in risks and adjustments. 4 Robustness checks of the results In this section, I brie‡ comment on estimates from numerous modi…cations of the benchmark y speci…cation (column 5 of Table 3).Giving away the lessons from these robustness checks in advance, I conclude that my benchmark speci…cation passed all the tests reasonably well. The standard errors increased in many cases, but the parameter estimates moved only little. 4.1 Di¤erent left hand side variable p Instead of the linear formula for yield calculation (r R+ 100 T ), I also tried to …t an approximate yield curve to the short- and long-term benchmark rates, and use the implied future rates to accumulate the payo¤ ‡ of sovereign bonds (thus assuming that coupon payments are ow reinvested in benchmark bonds). Using this terminal payo¤ and the current price level, I can calculate the implied annual rate of return, and then subtract the corresponding benchmark rate (using the approximate yield curve again). In principle, this procedure should eliminate the approximation error from the linear formula. Following it completely (using the appropriate maturity approximated benchmark rate on the right hand side as well), the interest rate coe¢ cient moved further away from zero, while other estimates changed little. When, however, I used the long-term benchmark rate on the right hand side of regressions (and the approximate yield curve only for calculating the left hand side), its coe¢ cient indeed became very close to zero. Altogether, this suggests that there is some systematic calculation error when I use the linear approximation, but in the absence of …ne information on the benchmark yield curve, coupon payment frequencies and dates, etc., one cannot eliminate this problem. The estimations show that it is mostly the benchmark rate coe¢ cient that goes wrong and changes with di¤erent choices of the spread, so this coe¢ cient seems to capture most of the mismeasurement, and the other results are relatively immune to the problem. 4.2 Di¤erent instruments First I estimated the benchmark speci…cation with OLS –thus neglecting the endogeneity issue – then I varied the set of instruments, between the two extremes: a just-identi…ed speci…cation , (two instruments), and a large set of instruments. None of these speci…cations led to any major changes in the estimates. The results showed the following pattern: the OLS estimates were smaller than with any IV; and the large instrument set estimates were close to OLS. The …rst observation is consistent 18 with the standard measurement error speci…cation: the nonorthogonal right hand side variable has a negative covariance with the error term, so OLS produces too small estimates. The second observation matches the pattern that IV estimates are biased towards OLS in small samples (see Angrist, Imbens and Krueger (1999) for further discussion). On the whole, I consider the benchmark set of instruments as a reasonable tradeo¤ between less bias (just identi…ed) and more precision (large set of instruments). The just-identi…ed results showed some sensitivity to the choice of the two instruments, but they were quite imprecise. When using many instruments (further fundamentals, like gross investment growth, credit to private sector etc.; or various time e¤ects), overidenti…cation was accepted in all cases – but with many instruments and a relatively small sample, its power becomes questionable. 4.3 Varying the event indicators Table 3 already contained some variations of the repayment problem indicator. Here, instead of varying the classi…cation itself, I reran the results with di¤erent time windows. With a realization within three instead of …ve years, there are hardly any changes. With ten years, the vast majority of the observations will have an actual default value of one, so the speci…cation is uninformative. The same applies to the ill-performing “depressed future prices” indicator: even when I changed the cuto¤ level or the time window, the variable had the wrong sign, it was not in‡ uential for the overidenti…cation test, and it was often insigni…cant. I also experimented with di¤erent choices for the price variance term: I worked with the 3-year variance, the “full forward variance” (up to the most recent observation available), the adjusted versions of these terms, and dummies for the 5-year variance being in the upper 25th or 10th percentile of its sample distribution. None of these changes had any signi…cant impact on other variables or overidenti…cation, though the coe¢ cients became somewhat smaller in general. Finally, I considered some alternative measures of current and future crisis. First I added a current default dummy: it corresponded to a completed relief or renegotiation, thus it was exogenous as of time t. This variable was completely insigni…cant, refuting the interpretation that repayment trouble is also a source of market distress, and its predicted probability is in fact an illiquidity prediction. Then I introduced detailed measures of currency regime changes, for example, from free ‡ to managed ‡ oat oat. These variables, either current or future, did not show anything di¤erent from the large devaluation indicator. 19 4.4 Re…ning country e¤ects I checked whether the e¤ect of country dummies can be described with long-term debtor history of the countries, using data from Lindert and Morton (1989). This history includes bond defaults in the 19th-early 20th century (up to the 1930s), default in the thirties, the number of years in default (in some cases, default episodes spanned many years), and an indicator of a new sovereign (independence or entering the Eastern block after World War II), hence a new debtor. From these variables, only the indicator of default in the 1930s was signi…cant, and it also led to accepting the overidenti…cation with country dummies only as instruments, thus replacing the direct in‡ uence of country e¤ects. This result, however, is driven entirely by Argentina. If one checks whether some of the country dummies alone are su¢ cient for overidenti…cation, this is the case for Argentina or Brazil. This implies that the e¤ect of country dummies above default and illiquidity predictions is mostly a treatment di¤erential for Argentina (all other things being equal, a smaller spread), and Brazil (a higher spread). One interpretation of such a di¤erence is that my default observations (or risks in general) are “downgraded” the market for Argentina, by and upgraded for Brazil. 5 Summary and conclusions The objective of this paper was to test if one can describe sovereign bond spreads by predicted risk probabilities (default and illiquidity risk), and whether there are certain episodes (in particular: currency crises) when spreads increase more than risk probabilities do, indicating limits of arbitrage. In other words, I attributed the in‡ uence of fundamentals to movements in predicted probabilities (conditional expectations) of observed risk realizations. This yields a structural approach: risk probabilities are predicted by fundamentals, then bond spreads are determined by predicted probabilities. Spreads are still in‡ uenced by fundamentals, but we have a clear sense of why: because they predict risk probabilities. I …nd that the structural form captures the reduced form …t: including a default indicator, benchmark rates, country dummies and a currency crisis indicator, overidenti…cation passes; also with a default indicator, an illiquidity term (future, pre-maturity price volatility), benchmark rates and country dummies. These speci…cations are tight in the sense that overidenti…cation is rejected if any of the explanatory variables is excluded. Even in the second case, the currency crisis dummy stayed large and signi…cant, although not vital for overidenti…cation. These …ndings depict sovereign bond spreads as being determined by default risk, illiquidity risk, an extra increase during currency crises, plus adjustments (the benchmark rate and country e¤ects). In general, the marginal and the average e¤ect of risk probabilities is economically signi…cant, though not huge. I see a couple of major open issues here. One is to get a precise picture of these risk events, 20 which would require higher frequency fundamentals, more detailed information on countryspeci…c events, and detailed panel data on individual bonds. Another task is to further investigate why the market shrinks so heavily for these bonds at certain times, and why there are no investors coming to arbitrage on this opportunity, thus mollifying the collapse. Potential explanations could also be related to the acceleration of information revelation in these crisis periods, thus an increased volatility of near-future prices;17 or investor-speci…c liquidity shocks. Finally, one could use the same structural framework to study the pricing of other assets: for example, local-currency denominated bonds, where exchange rate ‡ uctuations constitute an additional risk. In that setup, one can handle the otherwise latent expected exchange rate movement by the same instrumental variables method, thus structurally estimate a risk-adjusted uncovered interest parity equation. References [1] Amihud, Yakov, and Haim Mendelson, 1991, Liquidity, Maturity and the Yields on U.S. Treasury Securities, The Journal of Finance, Vol. XLVI. (4), 1411-1425 [2] Angrist, Joshua D., Guido W. Imbens, and Alan B. Krueger, 1999, Jackknife Instrumental Variables Estimation, Journal of Applied Econometrics, Vol. 14(1), 56-67 [3] Att…eld, Cli¤ L. F., David Demery, and Nigel W. Duck, 1985. Rational Expectations in Macroeconomics, Chapter 6 (Basil Blackwell). [4] Benczur, Peter, 2002, Bond spreads, exchange rate movements and risks, mimeo, National Bank of Hungary and Central European University [5] Benczur, Peter, 2005, Information revelation, liquidity shocks, the volatility and the level of bond spreads, Economica, Vol. 72, pp. 95-119 [6] Benczur, Peter, and Cosmin Ilut, 2005, Determinants of Spreads on Sovereign Bank Loans: The Role of Credit History, CEU-Economics WP 3/2005 [7] Bradley, Finbarr, 1991, Neglected Factors in the Market Pricing of Eurodollar Bonds, Journal of Portfolio Management, 62-73 [8] Broner, Fernando, and Guido Lorenzoni, 2000, Supply of Funds, Maturity, and Spreads on Emerging Market Sovereign Bonds, in Fernando Broner: Essays on Balance of Payment Crises (MIT Thesis). 17 This argument is elaborated in Benczur (2005). 21 [9] Cantor, Richard, and Frank Packer, 1996, Determinants and Impact of Sovereign Credit Ratings, Federal Reserve Bank of New York Economic Policy Review, Vol. 2(2) [10] Cumby, Robert E., and Tuvana Pastine, 2001, Emerging Market Debt: Measuring Credit Quality and Examining Relative Pricing, Journal of International Money and Finance, 591609 [11] Edwards, Sebastian, 1986, The Pricing of Bonds and Bank Loans in International Markets, European Economic Review, Vol. 30, 565-589 [12] Eichengreen, Barry and Ashoka Mody, 1998, Lending Booms, Reserves and the Sustainability of Short - Term Debt: Inferences from the Pricing of Syndicated Bank Loans, NBER Working Paper no. 7113. [13] Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann, 2001, Explaining the Rate Spread on Corporate Bonds, The Journal of Finance, Vol. LVI. (1), 247-277 [14] Grossman, Sanford J., and Merton H. Miller, 1988, Liquidity and Market Structure, The Journal of Finance, Vol. XLIII. (3), 617-637 [15] Hirtle, Beverly, 1988, Default and Liquidity Risk in the Junk Bond Market, Federal Reserve Bank of New York Research Paper No. 8816. [16] Kamin, Steven B., and Kartsen von Kleist, 1999, The Evolution and Determinants of Emerging Market Credit Spreads in the 1990s, International Finance Discussion Papers No. 653, Board of Governors of the Federal Reserve System [17] Kim Joon, Krishna Ramaswamy, and Suresh Sundaresan, 1993, Does Default Risk in Coupons A¤ect the Valuation of Corporate Bonds?: A Contingent Claims Model, Financial Management, 117-131 [18] Lindert, Peter H., and Peter J. Morton, 1989, How Sovereign Debt has Worked, in Je¤rey Sachs, ed.: Developing Country Debt and Economic Performance, Volume I: The International Financial System ( University of Chicago Press) [19] Mishkin, Frederic S., 1983, A Rational Expectations Approach to Macroeconometrics (The University of Chicago Press). [20] Morris, Stephen, and Hyun Song Shin, 2004, Liquidity Black Holes, Review of Finance, Vol. 8 (1), 1-18 22 [21] Ozler, Sule, 1993, Have Commercial Banks Ignored History?, American Economic Review, Vol. 83 (3), 608-620 [22] Pástor, Lubos, and Robert F. Stambaugh, 2003, Liquidity Risk and Expected Stock Returns, Journal of Political Economy, Vol. 111, 642– 685 [23] Persaud, Avinash, 2001 Liquidity Black Holes, Working Paper, State Street Bank. [24] Redding, Lee S., 1999, Negative Nominal Interest Rates and the Liquidity Premium, Economic Letters, Vol. 62 (2), 213-16 [25] Sovereign Defaults Continue To Decline In 1998, in: Standard and Poor’ CreditWeek, s 1998, August 12, 1-11 [26] Stone, Mark R., 1991, Are Sovereign Debt Secondary Market Returns Sensitive to Macroeconomic Fundamentals? Evidence from the Contemporary and Interwar Markets, Journal of International Money and Finance, Vol. 10, 100-122 [27] Uribe, Martín and Vivian Z. Yue, 2006, Country Spreads and Emerging Countries: Who Drives Whom?, Journal of International Economics, Vol. 69, 6-36. [28] Wickens, Michael R., 1982, The E¢ cient Estimation of Econometric Models with Rational Expectations, Review of Economic Studies, Vol. XLIX., 55-67 Appendix The estimation framework in a general setting A variable X depends on the predicted value of a (potentially vector) variable Y: Xt = + E[Yt jZt ] + t; (7) where Zt is the information available for predicting Yt . One then speci…es a prediction (conditional expectation) equation Yt = g(Zt ) + "t ; and rewrites (7) as Xt = + g(Zt ) + t: (8) (9) With assumptions on the form of g, equations (8) and (9) can be estimated by some full information and in general nonlinear method (GMM). The reduced form of (7) is Xt = f (Zt ) + 23 t: (10) It describes how Xt is predicted by past information (Zt ), without implying any causality. Suppose that some theory suggests that the in‡ uence of Zt should come through the predicted value of E[Yt jZt ] –as in (7). Then the structural form (9) rewrites the reduced form (10) as f (Zt ) = + g(Zt ): (11) This gives a straightforward test of whether the structural form is really a good reinterpretation of the reduced from: estimating (8) and (10) simultaneously, and then testing the restriction f (Zt ) = + g(Zt ). My approach is similar but importantly di¤erent: instead of using any speci…c functional form for g, then estimating the two equations simultaneously (full information), and testing a nonlinear overidenti…cation hypothesis, I estimate Xt = directly. Here the error term is et = by using Zt as instruments. + + Yt + et (7B) + "t , which is not orthogonal to t (g(Zt ) Yt ) = t Yt = g(Zt ) + "t , but orthogonal to Zt . Moreover, Yt is correlated with Zt , so I can estimate (7B) Deriving identi…cation for the two event case The three equations are (skipping the error terms for convenience) d= l= s= + + 2R 3R 2 3 + + 2Z 3Z + + ll 2H 3H (12) (13) (14) + R+ dd + + H: The …rst two are already in reduced form, and the third becomes s=( + | + l 3) + ( d 2 {z 1 } | + d 2 {z 1 + l 3) R } +( | d 2 + {z 1 l 3) Z } +( + | d 2 {z 1 + l 3 ) H: } (15) 24 This means that estimating (12), (13) and (15) immediately gives us 3, 2; 2; 2; 2, 3; 3; 3, plus the following conditions: = = = + + d 2i 1 1 1i 1 d 2 d 2 + + l 3 l 3 + l 3i = + d 2 + l 3: If the dimension of Z is at least two (in general: we have at least as many excluded exogenous variables from (14) as endogenous variables, i.e., events), then the l, equation gives us d and even overidentifying those two parameters, and then ; and can be obtained from the appropriate equations. This shows that (14) is identi…ed. The overidenti…cation test Here the overidenti…cation test means checking if the residuals Xt b bYt are orthogonal to b Yt Yt ? Zt . Zt : Under the null (all instruments are valid), the estimates are consistent, so the residuals + + E[Yt jZt ] b bYt = b+ + (E[Yt jZt ] ! 0, t t t Yt ) should be orthogonal to Zt , since b The last term suggests that it is crucial that the market uses the right (rational) expectation: without that assumption, the prediction error E[Yt jZt ] Yt is in general non-orthogonal to the ! 0, b ? Zt , and E[Yt jZt ] predictors, and overidenti…cation fails. It also fails if the endogenous right hand side variable Yt is not the true event or not the only event the market was using. The previous nonlinear test of (11) would become identical to this simple test if one restricts the functions f and g to be linear. Then I would get a linear reduced form: Xt = Yt = 00 0 + + 0 00 Zt + t (10B) (8B) Zt + t ; and the structural form would impose the restrictions 0 = + 00 and 0 = 00 : (11B) However, as the argument shows, testing the orthogonality of the residuals and the instruments is a valid overidenti…cation test even in a nonlinear setup: the only linearity I need is in the pricing equation (7), but the prediction equation (8) does not have to be linear. 25 Table 1: Reduced form resultsa r (1) Reserves to imports Exports to GDP Debt to GDP Current account to GDP GDP growth GDP per capita ($1000) Past repayment problems Arrears in region Currency crisis Benchmark yield Constant Country dummies R2 d (2) -1.00 (3.26)* -0.01 (2.55)* 0.46 (1.09) -2.99 (1.59) -2.33 (1.31) 0.17 (1.50) -0.03 (0.95) 0.76 (1.08) 0.55 (2.70)* Left hand side variable R Defaultb (3) (4) (5) 0.35 (0.23) 0.05 (2.14)* 1.84 (1.53) -5.56 (3.94)* -0.73 (0.28) 0.7 (2.58)* -0.03 (1.23) -1.62 (0.79) 0.71 (4.40)* -0.16 (2.66)* -0.17 (2.61)* 0.09 (0.05) 0.04 (1.82) 1.54 (1.24) -5.35 (3.80)* -0.57 (0.21) 0.7 (2.49)* -0.06 (1.82) -0.64 (0.31) -0.61 (2.32)* -0.01 (4.36)* 0.93 (5.53)* 0.73 (1.65) 1.28 (1.00) 0.1 (1.45) 0.01 (1.45) 0.67 (1.37) -0.10 (1.43) 0.03 (1.26) -1.55 (1.02) yes 0.22 yes 0.20 no e Variancec (6) -4.77 (2.41)* 0.00 -1.19 (4.27)* -0.02 (2.68)* 0.44 (1.03) -3.24 (1.64) -2.05 (0.99) 0.18 (1.58) -0.05 (1.41) 1.17 (1.59) (0.04) -2.64 (1.31) -1.65 (0.44) -5.54 (1.15) 0.53 (2.52)* -0.31 (2.85)* 7.37 (1.75) -0.45 (1.66) 0.49 (5.17)* 4.41 (0.82) noe 0.66 -0.13 (2.83)* 4.19 (1.82) no 0.10 -0.12 (2.78)* 4.45 (2.15)* no 0.11 0.56 a All equations are estimated by OLS. The sample size is 266 in columns 1-5, and 259 in column 6. All variables are annual. T statistics are in parentheses. They are robust to clustering at the country level. * denotes signi…cance at the 95% level. b Default is an indicator of debt relief or rescheduling in the next 5 years (including the current one). c Variance is the 5-year empirical variance of all bond spreads of the country starting from the given year. d The benchmark yield is the yield on long-term (10-year) government bonds of the appropriate currency. e Including the 11 country dummies would make the estimates of the economic fundamentals very imprecise, thus insigni…cant. The R2 would become 0.75 and 0.83, respectively. 26 Table 2: Regression results: only default risk considereda Left hand side variable: r relative size (1) Default indicator Benchmark yield Constant Country dummies F stat: value included F(1,10) 2.27 0.16 d c R Choice of the default indicatorb with arrears (2) -7.37 (0.88) -0.09 (1.51) (3) 0.86 (5.61)* -0.13 (2.94)* without arrears (4) 0.88 (5.25)* -0.10 (3.49)* 1.60 (10.93)* included F(1,10) 0.79 0.39 0.62 included F(1,10) 31.56 0.00 0.28 instruments F(2,10) 13.86 0.00 0.00 (5) 0.84 (2.63)* -0.10 (2.96)* 1.61 (12.17)* – F(2,10) 4.57 0.03 0.06 10.89 (1.56) -0.08 (1.50) 8 > deg. of fr. < > : p value p value of overid test 0.04 a All estimations are IV, using as instruments the …rst lag of reserves to imports, exports to GDP, debt to GDP, current account balance to GDP, GDP growth, GDP per capita, past repayment troubles, arrears in region and benchmark bond yields. The sample size is 266. All variables are annual. T statistics are in parentheses. They are robust to clustering at the country level. * denotes signi…cance at the 95% level. b In column 1, the indicator is the sum of the relief to debt stock ratios in the next …ve years (including the current one). In column 2, it is an indicator of debt relief, rescheduling or arrears in the next 5 years (including the current one). Columns 3-5 is similar to 2, but without arrears. c The benchmark yield is the yield on long-term (10-year) government bonds of the appropriate currency. d The overidenti…cation test regresses the residuals on the exogenous right hand side variables and instruments. 27 Table 3: Main resultsa Left hand side variable: r (1) Default indicator Future crisis Variance d c b R (5) 0.65 (7.90)* (6) 0.68 (8.54)* (2) 0.77 (4.35)* (3) 1.29 (3.68)* -1.71 (1.36) (4) 0.69 (5.36)* 0.79 (5.34)* 0.24 (2.21)* e 0.24 (2.20)* 0.79 (3.35)* 0.30 (2.20)* 0.77 (2.97)* -0.24 (3.79)* F(3,10) 28.30 0.00 0.93 259 Current crisis 0.75 (3.10)* f 0.24 (0.49) -0.19 (2.82)* F(3,10) 31.06 0.00 0.78 259 -0.27 (3.29)* F(2,10) 15.97 0.00 0.63 259 Benchmark yield -0.13 (2.86)* F(1,10) 28.52 0.00 g -0.14 (2.88)* F(2,10) 11.51 0.08 0.31 266 -0.28 (3.34)* F(3,10) 33.58 0.00 0.92 259 F stat: 8 > deg. of fr. < > : value p value p value of overid test Number of obs. 0.09 266 a All estimations are IV, using as instruments …rst lags of reserves to imports, exports to GDP, debt to GDP, current account balance to GDP, GDP growth, GDP per capita, past repayment troubles, arrears in region, a current crisis dummy and benchmark bond yields. The 11 country dummies are used as extra right hand side variables. All variables are annual. T statistics are in parentheses. They are robust to clustering at the country level. * denotes signi…cance at the 95% level. b Default is an indicator of debt relief or rescheduling in the next 5 years (including the current one). c Future crisis is an indicator of a currency crisis next year. d Variance is the 5-year empirical variance of all bond spreads of the country starting from the given year. e An indicator for a large devaluation or abandoning a …xed or limited ‡ regime. oat f The benchmark bond yield is the yield on long-term (10-year) government bonds of the appropriate currency. g The overidenti…cation test regresses the residuals on the exogenous right hand side variables and instruments. 28

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posted: | 12/15/2009 |

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