## The Political Economy of Sovereign Default

|# 2. Empirics

## Texte intégral

1This section tests the predictions of Section 1 empirically. I first describe the data. Then I present the methodology used in my estimation and my results.

# 2.1. Data

## 2.1.1. Political variables

2My main variables of interest are institutional. Since the concepts of Winning Coalition and Selectorate are not widely used even in political science, not to mention economics, their relation to the real world needs clarification. I proceed in three steps. First, I describe which configurations of Winning Coalition and Selectorate sizes correspond to different types of political regimes. Second, I discuss how the variables are measured in practice. Finally, I use examples to show how these variables evolve for individual countries over time.

*s* and *w* for archetypical political regimes21

- 21 Bueno de Mesquita et al. (2003), p. 79-87.

3**large ****s**** large ****w****: Democracy.** Democracies tend to grant a large subset of their residents a say in the choice of government. In modern democracies, *S* comprises essentially the entire adult population, with differing provisions on foreigners, convicts and so forth. Likewise, *W* tends to be large, although distinctions are possible, depending on the type of democracy. In presidential systems, leaders usually require *w* ≈ *s*/2 to be elected. In first past the post parliamentary systems, where a prime minister forming a government needs one half of the votes of the elected representatives in parliament, each of whom require one half of the votes of their constituents to be elected, governments can get by with as little as *w* = *s*/4. In proportional representation systems, the necessary Winning Coalition might be even smaller.

- 22 Bueno de Mesquita et al. (2003), p. 80.

4**small ****s**** small ****w****: Monarchy.** In monarchies, membership in the Selectorate is restricted by birth, typically to the aristocracy. This means the group of people with a potential say in choosing the government is small. In hereditary monarchies, *w*/*s* is usually assumed to equal 1/2.22

5**small ****s**** small ****w****: Military Junta.** A different way of restricting membership in the Selectorate is practised in military juntas. Here, the group of those with a say in electing the military dictator is extremely small, usually a small group of senior military officers, who command most of the men and weapons. The eventual leader usually needs less than half of *S* to sustain himself in power. Consequently, military juntas have some of the most concentrated and privileged Winning Coalitions.

- 23 The Bolsheviks held one of the first elections under universal suffrage in 1917, Bueno de Mesquita (...)

6**large ****s**** small ****w****: Electoral Autocracy.** Leaders supported by small Winning Coalitions drawn from a large Selectorate exemplify the case of rigged election autocracies. Here, membership the Selectorate is not overly restricted. A large group of people has a nominal say in choosing the leader. Entry into *W*, however, is usually only granted on the basis of special characteristics, such as membership in the Communist Party, as in Soviet Russia, or religious authority, as in today’s Iran. Both of these regimes permit elections23, but the outcome is a foregone conclusion. Nevertheless, any member of the Selectorate can theoretically accede to membership in *W*, unlike in monarchies or military juntas, where birth or military rank alone are the key to access.

### Measuring *s* and *w*

7Bueno de Mesquita et al. (2003) and (2010) have assembled data on Selectorate and Winning Coalition size. *s* and *w* are attractive as measures of institutions for two reasons. First, they allow comparisons across different types of categories of political regimes. Second, they provide a continuous means to parsimoniously describe the institutions shaping resource allocation. Changes within a polity over time can be captured by changes in *w* and *s*, and cross-country comparisons are facilitated by the fact that all types of regimes can potentially be placed somewhere along the two-dimensional continuum defined by these two variables.

- 24 Bueno de Mesquita et al. (2003), p. 211.
- 25 The table summarizes Bueno de Mesquita et al. (2003), p. 211-216. Notation:
*S*=_{i,t}*s*in country*i*(...)

8In practice, the measurement of *w* and *s*, is, as the authors admit,24 a long way from yielding an exact, continuous yardstick of politics. Instead, *w* and *s* are constructed as a weighted index of different components of commonly used *categorical* political variables. The two sources are the *Polity IV* database and Arthur Banks’s *Cross National Time Series Data Archive*. Table 1 summarizes the construction.25

9The authors argue that for *W** _{i,t}* no single variable alone is sufficient to guarantee a large

*w*. Nevertheless, the variables used to construct the index all relate to dependence of leaders on larger or smaller groups of people for political support. Therefore, countries that check more of the boxes necessary for a large

*w*are more likely to have larger Winning Coalitions than countries that check fewer boxes.

10Still, the construction of the institutional variables is a crude simplification. The upshot is that variables conceived as a continuous departure from categorical regime types in theory are in reality categorical themselves. As Tables 2 and 3 show, *W** _{i,t}* takes on only 5 distinct values and

*S*

*only 3 distinct values.*

_{i,t}11As is readily apparent from the frequency distributions, most countries at most times have large Selectorates (coded with a 1). This means that their legislators are selected by popular elections. A small group of countries through time have either a Selectorate value of .5 (meaning legislators are selected less openly, usually by the executive, ascriptive or heredity) or 0 (meaning no legislature exists). For the Winning Coalition, the picture is more heterogeneous. A large group of countries have values of 1 or .75, making them broadly democratic. A smaller group of countries have smaller values of .25 or even zero, meaning recruitment into and competition for executive positions are severely restricted. Data are available for 185 countries and around 43 years.

*s* and *w* in the real world

12A few examples will illustrate how the institutional variables are reflected in the historical experience for individual countries. I begin with case of a democracy. Figure 2 plots *s* and *w* for the United States from the period from 1945 until 2007. For the entire period, *s* is at is maximum value of 1, indicating the large Selectorate of popular elections. Similarly, *w* equals 1 for the entire sample period, stemming from the fact that the democratically elected executive relies on large Winning Coalitions.

- 26 Background on Chile: http://www.state.gov/r/pa/ei/bgn/1981.htm

background on Peru: http://www.state(...)

13Second, consider military juntas.26 Figures 3 and 4 plot the institutional variables over the same period for Chile and Peru respectively. For Chile, the period of the Pinochet-regime 1973-1990 shows up in the graph as a period during which *s* = *w* = 0. The same is the case for Peru under General Alvarado 1968-1975 and his successor Bermúdez, who ruled until 1980. As discussed, military regimes both severely restrict the access to the Selectorate and produce leaders reliant on extremely small Coalitions. Note that the indicators closely match the historical record, with Selectorate and Winning Coalition size increasing in both countries before the juntas were officially replaced. Pinochet’s lost referendum of 1988 and Peru’s new constitution of 1979 drive up the variables in both countries, reflecting the transition to more open elections and democratic governance.

- 27 Background on Saudi-Arabia: http://www.state.gov/r/pa/ei/bgn/3584.htm

14For the case of a monarchy, Figure 5 plots *w* and *s* for Saudi-Arabia27 for the relevant period. The Gulf Kingdom’s political system is an absolute monarchy, with membership in the Winning Coalition likely restricted to the Saudi royal family. Consequently, *W* is small, but not as concentrated as in the case of a military junta, where power lies in the hands of a few generals. Similarly, *S* is small, but has increased in size in the early 1990s. This is due to the creation of Saudi “Basic Law”, a charter defining the principles of governance in accordance with Shari’a law and the “Consultative Council”, a quasi-legislative body of King-appointed members with limited power, established shortly thereafter.

15The graph for Saudi Arabia also illustrates an important general point about the data. For the period until 1993, *W* is larger than *S*. This is of course impossible in the theory, which defines the former as a subset of the latter. Consequently, the data for *s* and *w* as they stand now should be understood only ordinally: large values mean that a given group is made up of a larger fraction of a country’s residents.

- 28 Background on Gabon: http://www.state.gov/r/pa/ei/bgn/2826.htm
- 29 African Elections Database, http://africanelections.tripod.com/ga.html
- 30 Polity IV country report for Gabon, http://systemicpeace.org/polity/polity06.htm

16As a final example, consider the case of Gabon, a rigged-election autocracy. Figure 6 plots *w* and *s* since 1960. Gabon28 is a multiparty republic, that, since 1990, has held legislative and presidential elections at roughly 3 to 5 year intervals.29 Single party elections were held when Gabon existed as a one-party state from 1968 to 1990 under President Ali Bongo Ondimba and as a multiparty presidential republic since then. Thus *s* = 1 for the entire period. At the same time, elections were invariably won by the incumbent, pointing to small Coalitions. Note that despite the transition to multiparty elections in 1990, *w* actually declined. This is because elections under the new constitution of 1990 were once again rigged and produced the same winner as before.30

## 2.1.2. Economic Variables

### Independent variables

17Whether a country defaults and/or is viewed as credit-worthy by investors depends first and foremost not on institutions, but on whether its finances are “in order” – that is whether the country is seen as capable of debt-repayment in purely economic terms.

- 31 For my regressions, I use the natural logarithm of GDP per capita. I decided against using the PPP (...)

18One determinant of credit worthiness is income level. Richer countries were seen historically as more credit-worthy (although that might change in the coming years). I thus collected data on GDP per capita.31 Further, countries that are growing more quickly reduce their relative debt burden and allow their governments to generate revenues with which to repay debt. Countries that try to inflate away their debt might be seen as not trustworthy. At the same time, high inflation is indicative of macroeconomic instability, and can also be interpreted as a proxy for other factors contributing to an increased likelihood of default. I thus collected data on GDP growth and inflation. For external debt, it might also matter whether a country is a net exporter or net importer. I therefore collected data on Current Account balances, a large part of which are trade balances. These data come from the World Bank’s World Development Indicators (WDI) and cover around 180 countries up to 2009 going back on average until around 1980 although country coverage becomes much thinner beyond that date.

- 32 I will not take debt composition into account in my baseline regressions, but discuss it in a sepa (...)
- 33 Panizza (2008), p. 4.

19The most important variable in assessing whether a country’s debt is “sustainable” is its debt-to-GDP ratio. I collected these data from Abbas et al. (2010), a newly created IMF database covering 173 countries up to 2009, with time-coverage similar to the WDI data. The identity of the creditor might also matter32 since default on foreign-owned debt entails not making net transfers to foreigners, whereas defaults on domestically-held debt means the effect stays “in the country”. In fact, as Panizza (2007) discusses, good data on creditor-identity are hard or impossible to come by. He therefore suggests jurisdiction of issuance of debt as an alternative measure. Accordingly, *external debt is debt issued in foreign countries and under the jurisdiction of a foreign court*.33 I thus collected data on domestic and foreign debt as a share of total sovereign debt. These data come from an updated version of Panizza (2007) and cover 123 countries for around 30 years on average.

### Dependent variables

20The phenomena I seek to explain are defaults, interest rates, spreads, and sovereign ratings.

- 34 Again, external debt is defined as debt issued under foreign jurisdiction.

21Patterns of default are the “most direct” phenomenon, with interest rates, spreads, and ratings presumably dependent on the risk of default. The problem is that outright default episodes are very rare and might not lend themselves to produce precise estimates. Nevertheless, I collected data on domestic and external34 sovereign debt crises from a database assembled by Reinhart and Rogoff (2010). These data are available for 70 countries until 2010. While their series extend until the 19^{th} century for some countries, I used the data from 1940. I also produced an aggregate dummy from these two variables, which takes a value of one if country *i* is in an either a domestic or an external debt crises at time *t* and zero otherwise.

22A potentially more fruitful avenue for testing my hypothesis are interest rates on longterm government bonds. Short-term rates are policy-rates and thus likely negatively correlated with default risk: governments or central banks might lower rates to prop up the economy during a recession when the risk of default is high. Long-term bonds, on the other hand, are traded for a longer period and their interest rates should therefore more accurately reflect market perceptions of default risk. I thus collected data on longterm interest rates on government bonds from the IMF’s International Financial Statistics. These data cover 68 countries for a period of on average 31 years.

- 35 I am greatly indebted to Ugo Panizza, who kindly agreed to share the data.
- 36 See J.P. Morgan (1999) for details.

23While better than short term rates, long term interest rates may reflect more things than simply the risk of lending to a sovereign. For this reason, I follow McGillivray and Smith (2003) and collected data on JPM’s Emerging Market Bond Index spreads.35 The EMBI covers bonds issued by sovereign and quasi-sovereign entities denominated in $U.S. Only issues with a face value outstanding of 500 millions $U.S. or more are included. Spreads are over the theoretical zero coupon yield on U.S. treasury securities.36 Data are limited, covering 45 countries for a period of on average a little over 9 years.

- 37 http://www2.standardandpoors.com/spf/pdf/fixedincome/SP_CreditRatingsGuide.pdf
- 38 http://www.moodys.com/researchdocumentcontentpage.aspx?docid=PBC 109490
- 39 http://www.fitchratings.com/creditdesk/public/ratings defintions/index.cfm

24As a final way of testing my theory, I explored sovereign ratings. Ratings reflect the *ability and willingness of an issuer to repay in full and on time* (S&P’s ratings)37, *credit risk as a function of country economic resiliency and government financial robustness* (Moody’s ratings)38, or *the likelihood of repayment* (Fitch ratings).39 They are thus an excellent market-based measure of sovereign risk. I thus obtained data on sovereign ratings from these three major rating agencies, and produced a simple arithmetic mean of the three ratings. Country coverage is better than for defaults and interest rates with around 140 countries, but the series are much shorter with only 17 and 13 years until 2010 on average for foreign and local currency ratings respectively.

25Figure 7 shows histograms for my different dependent variables. Clearly, cases of low interest rates and spreads dominate the sample. There are many more instances of countries not in default than in default. Finally, more countries at most times have good ratings, although the picture is less skewed than for the other variables. All of these facts point to some degree of sample selection. More data are available for rich countries, who default less often, pay lower interest rates and enjoy higher ratings.

# 2.2. Baseline specifications

26I work with the following vector of regressors for all baseline specifications

27Also for all baseline specifications, *β* is the vector of true coefficients associated with the vector of regressors.

### Debt crises

28The first two left-hand-side variables I examine are *domestic_debt_cris* and *external_debt_cris*. I estimate the binary response for a model with individual country-effect *⍺*_{i}

29I first specify *F* (.) as a linear probability model with country fixed effects. That is I have

30where the *⍺** _{i}* are allowed to be correlated with the regressors and

*∊*

*is assumed*

_{i,t}*i.i.d.*uncorrelated with

*⍺*

*or the regressors. Second, I specify*

_{i}*F*(.) as a Probit and estimate it under the assumption that the

*⍺*

*are uncorrelated with the regressors, using random effects. That is I have*

_{i}- 40 The fixed effects transformation is available for the logistic distribution for functional form re (...)

31Finally, I specify *F*(.) as a Logit and estimate it using both random and fixed effects, the latter allowing for the correlation between the *⍺** _{i}* and the regressors.40 This gives

### Long terms interest rates and spreads

32As alternative right-hand-side variables, I examine long-term-interest rates and EMBI spreads. Since these are continuous variables, I use conventional panel-data models. I estimate

33using (1) pooled OLS, (2) random effects, and (3) fixed effects. In the pooled OLS case, a common intercept is assumed for all countries, that is *⍺** _{i}* =

*⍺*∀

*i*, whereas individual country specific effects are possible for (2) and (3). For (2), it must be assumed that

*E*[

**x**

_{i,t}^{T}

*⍺*

*] = 0, whereas in the fixed effects case, individual country specific heterogeneity can be correlated with the regressors.*

_{i}### Ratings

34Finally, I investigate the relationship between ratings on the left-hand-side and the institutional variables on the right-hand-side, controlling again for economic variables in **x**** _{i,t}**, using (1) pooled OLS, (2) random effects, and (3) fixed effects. Specifically, I estimate the following two models three times each

- 41 Technically, my ratings variables are not continuous, as they are averages constructed from catego (...)

35where *FCR* stands for foreign currency rating and *LCR* for local currency rating. The same comments apply for these specifications as for interest rates and spreads.41

# 2.3. Baseline results

### Debt crises

36The results for debt crises are in Tables 4-6. As it is likely that time invariant idiosyncratic disturbances are correlated with the institutional variables, fixed effects is the most sensible estimation method. Results are mixed. Beginning with Table 4, where I use an aggregate dummy taking a value of 1 if country *i* is in either a domestic or foreign debt crisis in year *t* and 0 otherwise as the left-hand-side variable, I find that the economic controls are correctly signed and significant.

Table 4: Results for all debt crises

*t* statistics in parentheses^{∗}*p* < 0.05, ^{∗∗}*p* < 0.01, ^{∗∗∗}*p* < 0.001

- 42 Countries
*could*try to offset the reversal of their Capital Account by using foreign currency rese (...) - 43 The coefficient is significant at the 5 percent level for the random effects Probit and the fixed (...)

37Countries that are richer and that are growing more quickly experience fewer debt crises. Higher inflation and larger debt-to-GDP ratios are associated with a higher incidence of debt crises. A puzzling result is that positive Current Account balances are associated with higher incidences of defaults. This likely reflects reverse causality. Since my crisis-dummy takes a value of 1 for the entire duration of the episode, the covariance between the incidence of crises and the size of the coefficients is driven by the economic conditions in the country not only at the start of the crises, but by those prevailing for their entire duration. Countries in external debt crises must run Current Account surpluses to compensate for the Capital Account deficits as foreign investors withdraw their funds.42 This would be one way to explain why debt crises seem associated with Current Account surpluses: countries initially in deficit as the crisis hits experience sharp reversals of their Current Accounts into surplus, leading to a positive coefficient estimate. For my institutional variables of interest, I find increases in Selectorate size to be positively and significantly43 associated with the incidence of debt crises for three of the four specifications, including the fixed effects Logit specification in column (4). The coefficient on the size of the Winning Coalition has the wrong sign (increases in the size of *W* are associated with higher incidence of debt crises as opposed to my theory’s predictions), but is insignificant at conventional levels.

Table 5: Results for domestic debt crises

*t* statistics in parentheses^{∗}*p* < 0.05, ^{∗∗}*p* < 0.01, ^{∗∗∗}*p* < 0.001

- 44 Although Winning Coalition size is significant at the ten percent level.

38Looking only at domestic debt crises (Table 5), the coefficients on the economic controls once again have the correct signs. Inflation is no longer significant, however. One way to explain this would be that if debt issued under domestic jurisdiction is mostly domestic currency debt and debt issued under foreign jurisdiction is mostly foreign currency debt, bouts of inflation increase the value of foreign debt in domestic currency, as they are likely to lead to a depreciation of the domestic currency. For domestic debt crises this effect is absent, and so inflation is insignificant. The discussion of the effect of debt crises on the Current Account above suggests that this effect should be absent for domestic debt crises. This is the case. Less encouraging is the fact that the coefficients on the institutional variables are all insignificant at the five percent level44 and have the wrong sign: increases in Selectorate size are associated with lower incidence of domestic debt crises and increases in Winning Coalition size are associated with higher incidence.

39For external debt crises (Table 6), *S* has the correct sign: increases in Selectorate size are associated with higher incidence of default. Further, this effect is statistically significant at the one percent level for all three non-linear probability models. *W* is again insignificant here. The economic controls again have the correct sign, although growth is now insignificant.

Table 6: Results for external debt crises

*t* statistics in parentheses^{∗}*p* < 0.05, ^{∗∗}*p* < 0.01, ^{∗∗∗}*p* < 0.001

### Long term interest rates and EMBI

- 45 p = 0.088 for Selectorate size.

40Turning to long-term interest rates and the EMBI (results in Table 7), I once again find the controls to be correctly signed. Richer countries pay lower interest rates and have lower EMBI spreads. Inflation strongly predicts higher interest rates, but seems to play no role for the EMBI. Interestingly, higher debt burdens are a good predictor for higher spreads, but do not seem to significantly affect long term interest rates. This likely reflects the ability of heavily indebted (non-emerging-market) industrial countries such as Japan to borrow cheaply. For the institutional variables, the evidence seems to mostly reject my hypothesis. For long term interest rates, the coefficients have the correct sign and are relatively close to being significant in the fixed effects specification.45 Spreads, on the other hand, do not fit the predictions of my model at all: Increases in the size of the Winning Coalition are strongly associated with increases in spreads, whereas Selectorate size is insignificant.

Table 7: Results for LT interest rates and EMBI

*t* statistics based on robust Standard Errors in parentheses^{∗}*p* < 0.05, ^{∗∗}*p* < 0.01, ^{∗∗∗}*p* < 0.001

### Sovereign ratings

41Looking finally at sovereign ratings (Table 8), I find that for economic controls, larger debt-to-GDP ratios as well as higher inflation are associated significantly with lower ratings.

Table 8: Results for sovereign ratings

*t* statistics based on robust Standard Errors in parentheses^{∗}*p* < 0.05, ^{∗∗}*p* < 0.01, ^{∗∗∗}*p* < 0.001

42Richer countries tend to have higher ratings, although growth doesn’t seem to matter. Curiously, Current Account surpluses are a significant (5 percent level) predictor of lower local currency ratings. One possible explanation is simultaneity: countries more susceptible to debt crises receive lower ratings. They must then generate Current Account surpluses to offset Capital Account deficits as investors flee the country. This effect should be more pronounced for foreign currency ratings, but in fact the Current Account balance is insignificant here. For the institutional variables, Winning Coalition size is significant at the one percent level with the correct sign for both foreign and local currency ratings in the pooled OLS specification. For fixed effects, only local currency ratings seem to be significantly influenced by the institutional variables, albeit with the wrong signs: Larger Selectorates are a highly significant (.1 percent level) predictor of better ratings, whereas increases in the size of the Winning Coalition are associated (5 percent level) with lower ratings.

### Conclusions from the baseline

- 46 When I examine the effect of creditor identity later however, I do not find evidence to support th (...)

43Overall, the results for debt crises point to an effect of the institutional environment on the likelihood of default that is driven by Selectorate size. Increases in the size of the Selectorate mean that current members of the Winning Coalition are more likely to be excluded from future Winning Coalitions and the benefits attached to membership, should they decide to topple the current government. Therefore, since governments are less likely to be sanctioned by more loyal Winning Coalitions, they will be more likely to default. Note however, that this effect is only present for external debt crises. One way to interpret this effect would be that the mechanism driving my model disregards the pressure that powerful domestic creditors – likely members of the Selectorate and perhaps the Winning Coalition – are able to bring to bear directly on the government to prevent it from violating their interests. External creditors, who cannot influence the government directly, must rely on the punishment mechanisms underlying my model. Therefore, the effect of Selectorate size is only observed for external debt crises.46 For a rough quantitative idea of the effects, I only consider the results from the fixed effects Logit specification, since this allows to consider within-country changes in institutions, while accounting for country-specific unobservables. Thus for individual countries, increases in Selectorate size by two within-country standard deviations (an increase of .54) increase the probability of a country experiencing any debt crisis by 75% and the probability of experiencing an external debt crisis by 94%. The political change involved corresponds roughly to implementing Gabon-style rigged elections in societies where small Winning Coalitions coexisted previously with limited political participation.

44For long term interest rates, results are in line with the theory for the fixed effects specification in that the coefficients on the institutional variables are correctly signed. They are, however, too imprecisely estimated to allow me to be very confident about this. The rest of the empirical evidence does not support my model. For the Winning Coalition, the expected effect is missing. This is compounded by significant coefficient estimates contradicting my model’s predictions for spreads and local currency ratings, while foreign currency ratings seem to be largely unaffected by changes in institutions.

# 2.4. Splitting the sample

45The relationship between economic fundamentals and institutions on the one hand and countries’ vulnerability to default on the other may not be adequately captured by a model assuming a single coefficient vector for all countries. Estimation using fixed effects allows for country specific heterogeneity in the constant term, but still imposes homogeneous slopes for all countries.

## 2.4.1. Panel Threshold Regression

- 47 Hansen considers only balanced panels. I have written code that allows estimating threshold models (...)

46One way of tackling structural breaks in the underlying data generating process is the Panel Threshold Regression (PTR) model proposed by Hansen (1999). The setup is as follows. Observed data are from a panel47{*y** _{i,t}*,

*q*

*,*

_{i,t}**x**

**: 1 ≤**

_{i,t}*i*≤

*n*, 1 ≤

*t*≤

*T*

*}, with*

_{i}*t*indexing time and

*i*indexing individuals.

*y*is the dependent variable,

*q*is the threshold variable and

**x**is the vector of regressors, including the threshold variable. The structural equation is

47which can be more compactly written by letting *β* = [*β*** _{1}**,

*β*

**] as**

_{2}48*∊** _{i,t}* (γ) is assumed

*iid*across time, individuals and regimes, with mean zero and finite variance

*σ*

^{2}. The sample is split and observations are assigned to one of two regimes depending on whether a particular realization of the threshold variable

*q*

*lies above or below the threshold γ. Letting*

_{i,t}49and

50as well as

51where **I**(.) is an indicator function, the model can be written in deviations from individual specific means as:

52Now let

53as well as

54The slope vector *β* can be estimated for a given γ using least squares on the demeaned data, i.e.

55which yields different vectors of slopes *β*** _{1}** and

*β*

**above and below the threshold. The regression residuals are**

_{2}56and the sum of squarred residuals is

57which is simply the sum of the two SSRs above and below the threshold. γ is estimated by minimizing the concentrated sum of squared residuals using least squares, that is

58Hansen recommends implementing the minimization numerically using a grid search over a grid of quantiles of *q** _{i,t}*. The model is estimated once for each grid point and the combined SSR above and below the threshold is recorded.

*γ*ˆ is the value of

*q*

*corresponding to the grid point yielding the lowest combined SSR.*

_{i,t}59Given *γ*ˆ, the slope estimate is *β*ˆ (*γ*ˆ) and the residual variance is computed as

### Testing for a threshold

60The significance of the threshold-effect is tested against *H*_{0 }: no structural break in the slope. This corresponds to

61*H*_{0 }: *β*** _{1}** =

*β*

**.**

_{2}62Since γ is not identified under *H*_{0}, a bootstrap must be used to simulate the asymptotic distribution of the test statistic. The implementation works as follows. Under *H*_{0}, the model can be written as

63Taking deviations from individual specific means gives

64Once the actual statistic is computed, the bootstrap is implemented by drawing a sample of size *n* with replacement from the residuals ⍲*∊* (*γ*). This draw is used to create a bootstrap sample under *H** _{0}* using a homogeneous slope-vector. Since

*F*

*does not depend on*

_{1}*β*

_{1}, any slope vector can be used. With the bootstrap sample, the model is estimated under

*H*

*and*

_{0}*H*

*(the threshold model) and the bootstrap*

_{1}*F*

*statistic is computed. Repeating this procedure a large number of times, the percentage of draws for which the boostrap*

_{1}*F*

*statistic exceeds the actual*

_{1}*F*

*statistic is the asymptotic*

_{1}*p*-value for

*F*

*under*

_{1}*H*

*.*

_{0}## 2.4.2. Monte Carlo trials

65Since the PTR estimator is not implemented for standard software packages, I coded it in* R*. To assess the performance of my program, I ran a Monte Carlo simulation using artificial data. I began by drawing *n* = 100 times *T* = 30 observations from a jointly distributed normal random vector [*x*_{1;}* _{i,t}*,

*x*

_{2;}

*,*

_{i,t}*∊*

*] with the mean vector for each individual*

_{i,t }66and covariance matrix for all individuals

67I then used these data to generate observations for the left-hand-side variable under *H*_{0 }: no threshold as

68The setup for *⍺** _{i}* was chosen to generate individual specific effects correlated with one of the explanatory variables. For

*H*

_{1}, I used the same raw data to generate two different sets of left-hand-side variables. The first set was generated according to

69For the second set I generated

70I picked two different slope vectors above the threshold, since I wanted to investigate how precisely my estimator would estimate small versus large structural breaks. To get a feel for the artificial data under *H*_{0} and *H*_{1}, consider Figure 8, which plots **x**** _{2}** against

**y**together with a linear regression line.

71Clearly, the linear model is misspecified under *H*_{1}. For my simulation I generated 250 datasets under *H*_{0} and the first *H*_{1} and 250 under *H*_{0} and the second *H*_{1}. I then deleted 20% of the observations at random in each to create the unbalanced panels, which I fed to my estimator. I used a grid of quantiles: {5%, 5.25%, 5.5%, …, 94.75%, 95%}, which contains 361 grid points for *x*_{2}, and 300 replications for the bootstrap. The estimator performed decently for the case of the small structural break and well for the large structural break. Tables 9 and 10 present summary statistics for the two simulations.

Table 9: Summary statistics for Monte Carlo simulation: *β*_{2}^{below γ} = 10, *β*_{2}^{above γ} = 11, 250 trials, n = 100, T = 30

Table 10: Summary statistics for Monte Carlo simulation: *β*_{2}^{below }^{γ} = 10, *β*_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30

72Figures 9-14 show kernel density plots of the different statistics, with the vertical lines indicating true values. Note that for the large threshold case with *β*_{2} = 20 no kernel density for the *F*_{1} statistic is displayed, since the bootstrap *F*_{1} statistic never exceeded the actual statistic in any of the 300 bootstrap replications for the 250 datasets. Given the results of this exercise, I am reasonably confident in the estimator’s ability to pick up structural breaks. Coefficient estimates are consistent for both large and small breaks, but thresholds are only estimated consistently for larger breaks. A doubling of the coefficient associated with one of the regressors after the threshold lets me estimate the threshold with great precision and confidence. For a 10% increase in slope on the other hand, the distribution of the threshold estimate has most of the observations around the true value, but the distribution is not centred on it, as it is for the larger threshold.

Figure 9: Kernel density plots of the threshold estimate under *H*_{0} and *H*_{1}with *β*_{2}^{below }^{γ} = 10, *β*_{2}^{above }^{γ} = 11, 250 trials, n = 100, T = 30

Figure 10: Kernel density plots of bootstrap *F*_{1} statistic of the threshold estimate under *H*_{0} and *H*_{1}with *β*_{2}^{below }^{γ} = 10, *β*_{2}^{above }^{γ} = 11, 250 trials, n = 100, T = 30

Figure 11: Kernel density plots of coefficient estimates under *H*_{0} and *H*_{1}with *β*_{2}^{below }^{γ} = 10, *β*_{2}^{above }^{γ} = 11, 250 trials, n = 100, T = 30

Figure 12: Kernel density plots of the threshold estimate under *H*_{0} and *H*_{1}with *β*_{2}^{below }^{γ} = 10, *β*_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30

Figure 13: Kernel density plots of bootstrap *F*_{1}statistic of the threshold estimate under *H*_{0} and *H*_{1}with *β*_{2}^{below }^{γ} = 10, *β*_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30

Figure 14: Kernel density plots of coefficient estimates under *H*_{0} and *H*_{1}with *β*_{2}^{below }^{γ} = 10, *β*_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30

## 2.4.3. Applying PTR – debt thresholds

73My story so far has emphasized the willingness of governments to repay as shaped by political constraints as an important determinant of sovereign debt defaults. Default risk, however, is likely non-linear. For high values of debt-to-GDP, further increases in debt are likely to make investors lose confidence in a country’s ability to repay, even if defaults will lead to the government’s ouster. To investigate the presence of a structural break in the relationship between default risk and my institutional variables depending on countries’ debt levels, I implement the PTR estimator for long-term interest rates as dependent variable and debt-to-GDP as threshold variable. Specifically I have

- 48 Given that the validity of bootstrap inference for the significance of the threshold is not guaran (...)

74where the vector of regressors **x**** _{i,t}** is defined as in the baseline specifications. The estimated debt threshold is at 60.954% of GDP. However an asymptotic

*p*-value for the

*F*

_{1}statistic of .61 suggests that this structural break is not significant and a linear model with fixed effects is the better specification.48

Table 11: PTR estimates for debt threshold and long term interest rates

*t* statistics based on robust Standard Errors in parentheses^{∗}*p* < 0.05, ^{∗∗}*p* < 0.01, ^{∗∗∗}*p* < 0.001

- 49 Growth is now significant at the 1% level, whereas it was insignificant in the baseline.

75Table 11 presents the estimates based on the split sample, with column (1) replicating column (3) of Table 7 for comparison. Consider first column (3). Here my variables of interest have the “wrong” sign: increases in *s* are associated with lower interest rates and increases in *w* with higher rates. More strikingly however, not only are the coefficients on the institutional variables insignificant, but all economic controls except inflation have become insignificant as well. This suggests that for countries above a certain threshold of debt, investor perceptions of creditworthiness and therefore borrowing costs are not straightforwardly related to fundamentals. Turning to column (2), the economic controls are once again significant and have the correct signs: richer countries and countries growing more quickly49 pay lower interest rates, whereas countries with higher inflation pay more. Debt-to-GDP ratio and Current Account balance remain insignificant, as in the baseline. The important difference concerns the coefficients on the institutional variables. Both are now significant and have the right sign. Increases in the size of the Winning Coalition are associated with lower borrowing costs and increases in Selectorate size are associated with higher borrowing costs. Specifically, for countries below the debt threshold of 61%, an increase in Winning Coalition size of .5, corresponding roughly to the difference in Winning Coalition size that, for example, Poland has seen in its transition from communism to democracy, is associated with a 3.7% lower interest rate on long-term government obligations. Likewise, an increase in Selectorate size of .5 is associated with a 2.7% increase in the rate. This result fits my model’s predictions well. For countries below a critical threshold of overall government debt to GDP, governments have more discretion in their default decisions. To what extent they use this discretion depends on the institutional constraints they face.

## 2.4.4. Applying PTR – share of external debt thresholds

- 50 As discussed, I do not have data on creditor identity. I wil use the data on juridiction of debet (...)

76Creditor identity does not play a part in my model. However, governments might be more inclined to violate the property rights of foreign creditors, who do not wield direct political influence domestically. If influential members of the Winning Coalition are simultaneously important creditors to the government, the government might try harder to repay debt than if most creditors sit abroad and only have the threat of capital market exclusion to enforce repayment. To examine this possibility, I will introduce the share of country’s debt that is external as an additional regressor50 and use the PTR estimator to check for threshold effects. Accordingly, my vector of regressors changes from the baseline to

77I again use long-term interest rates as my left-hand side variable and use the following specification to implement PTR with share of external debt as threshold variable

78The estimated threshold for share of external debt is 0.649. Contrary to the debt-to-GDP threshold examined above, this threshold is significant, if not highly so (*p* = 0.0725).

Table 12: PTR estimates for threshold of share of external debt and long term interest rates

*t* statistics based on robust Standard Errors in parentheses^{∗}*p* < 0.05, ^{∗∗}*p* < 0.01, ^{∗∗∗}*p* < 0.001

- 51 One possibility is that, since countries with a larger share of external debt are predominantly de (...)
- 52 Compare this to column (1) of Table 11, where debt-to-GDP was insignificant.

79Table 12 presents the results. First note that introducing the extra regressor severely cuts down the number of usable observations, which may account for the imprecise estimates. For the economic controls, inflation is significant with the correct sign for the whole sample as well as for the two subsamples above and below the threshold. Richer countries pay significantly lower interest rates only for countries below the threshold of external debt. Growth is significant only for countries above the threshold, albeit with the incorrect sign.51 Note also that the debt-to-GDP ratio a significant predictor of higher rates for all countries, once the share of external debt is accounted for52 and even more so for the subsample of countries with 65% and more of external debt. This probably reflects the fact that richer countries, who usually have a large market for government domestic debt, pay lower interest rates even though they generally able to shoulder heavier debt burdens. Looking only at countries with higher external shares then captures poorer countries, where debt accumulation is seen as detrimental to repayment prospects by investors and therefore penalised with higher interest rates. Current Account balances are insignificant for the whole sample, as well as, somewhat surprisingly, for the subsample with a larger share of external debt. The institutional variables have the correct signs in all three specifications, but only come close to significance (*p*≈ .12 for both *s* and *w*) for the subsample of countries with a lower share of external debt. Thus if anything, institutions affect long-term interest rates more in the expected fashion when more debt is issued under domestic jurisdiction. While I do not attach too much importance to this result, it suggests that creditor identity does not matter greatly for the way *s* and *w* influence perceived credit risk.

## Notes

21 Bueno de Mesquita et al. (2003), p. 79-87.

22 Bueno de Mesquita et al. (2003), p. 80.

23 The Bolsheviks held one of the first elections under universal suffrage in 1917, Bueno de Mesquita et al. (2003), p. 7; Iran held its last presidential election in 2009.

24 Bueno de Mesquita et al. (2003), p. 211.

25 The table summarizes Bueno de Mesquita et al. (2003), p. 211-216. Notation: *S** _{i,t}* =

*s*in country

*i*at time

*t*& similarlr for

*W*

*.*

_{i,t}26 Background on Chile: http://www.state.gov/r/pa/ei/bgn/1981.htm

background on Peru: http://www.state.gov/r/pa/ei/bgn/35762.htm

27 Background on Saudi-Arabia: http://www.state.gov/r/pa/ei/bgn/3584.htm

28 Background on Gabon: http://www.state.gov/r/pa/ei/bgn/2826.htm

29 African Elections Database, http://africanelections.tripod.com/ga.html

30 Polity IV country report for Gabon, http://systemicpeace.org/polity/polity06.htm

31 For my regressions, I use the natural logarithm of GDP per capita. I decided against using the PPP correction, since especially for the repayment of foreign debt, what matters is not domestic purchasing power of goods and services produced domestically, but their value on Dollars.

32 I will not take debt composition into account in my baseline regressions, but discuss it in a separate section.

33 Panizza (2008), p. 4.

34 Again, external debt is defined as debt issued under foreign jurisdiction.

35 I am greatly indebted to Ugo Panizza, who kindly agreed to share the data.

36 See J.P. Morgan (1999) for details.

37 http://www2.standardandpoors.com/spf/pdf/fixedincome/SP_CreditRatingsGuide.pdf

38 http://www.moodys.com/researchdocumentcontentpage.aspx?docid=PBC 109490

39 http://www.fitchratings.com/creditdesk/public/ratings defintions/index.cfm

40 The fixed effects transformation is available for the logistic distribution for functional form reasons, but not for the Probit model, see Cameron ans Triveli (2005), p. 796.

41 Technically, my ratings variables are not continuous, as they are averages constructed from categorical country ratings. I nevertheless treat them as continuous.

42 Countries *could* try to offset the reversal of their Capital Account by using foreign currency reserves. This, however, would make the country vulnerable to a speculative attack, thereby making a sharp adjustment in the Current Account inevitable eventually. See Calvo (1998).

43 The coefficient is significant at the 5 percent level for the random effects Probit and the fixed effects Logit specifications and significant at the 1 percent level for the random effects Logit specification.

44 Although Winning Coalition size is significant at the ten percent level.

45 p = 0.088 for Selectorate size.

46 When I examine the effect of creditor identity later however, I do not find evidence to support this argument.

47 Hansen considers only balanced panels. I have written code that allows estimating threshold models using unbalanced panels, but it is unknow whether the asymptotic arguments establishing the validity of inference about the threshold in Hansen (1999) extend to the unbalanced case.

48 Given that the validity of bootstrap inference for the significance of the threshold is not guaranteed for unbalanced panels, this should not be viewed as definitive evidence against structural breaks. Drukker et al. (2005), who implement PTR for the unbalanced case, suggest using a Bayesian Information Criterion (BIC) akin to the procedure used in Time Series Econometrics for model selection. See Gonzalo and Pitarakis (2002) for a discussion of this approach.

49 Growth is now significant at the 1% level, whereas it was insignificant in the baseline.

50 As discussed, I do not have data on creditor identity. I wil use the data on juridiction of debet issuance instead.

51 One possibility is that, since countries with a larger share of external debt are predominantly developing and emerging countries, the significance of the growth rate reflects growth factored into the interest rate, rather than credit risk.

52 Compare this to column (1) of Table 11, where debt-to-GDP was insignificant.

## Table des illustrations

Titre | Table 1: Construction of institutional variables |
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URL | http://books.openedition.org/iheid/docannexe/image/518/img-1.png |

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Titre | Table 2: Frequency table for W_{i,t} |

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Titre | Table 3: Frequency table for S_{i,t} |

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Titre | Figure 2: s and w for the USA, 1945-2007 |

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Titre | Figure 3: s and w for Chile, 1945-2007 |

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Titre | Figure 4: s and w for Peru, 1945-2007 |

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Titre | Figure 5: s and w for Saudi Arabia, 1945-2007 |

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Titre | Figure 6: s and w for Gabon, 1960-2007 |

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Titre | Figure 7: Histograms of the dependent variables |

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Titre | Table 4: Results for all debt crises |

Légende | t statistics in parentheses^{∗}p < 0.05, ^{∗∗}p < 0.01, ^{∗∗∗}p < 0.001 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-17.png |

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Titre | Table 5: Results for domestic debt crises |

Légende | t statistics in parentheses^{∗}p < 0.05, ^{∗∗}p < 0.01, ^{∗∗∗}p < 0.001 |

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Titre | Table 6: Results for external debt crises |

Légende | t statistics in parentheses^{∗}p < 0.05, ^{∗∗}p < 0.01, ^{∗∗∗}p < 0.001 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-19.png |

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Titre | Table 7: Results for LT interest rates and EMBI |

Légende | t statistics based on robust Standard Errors in parentheses^{∗}p < 0.05, ^{∗∗}p < 0.01, ^{∗∗∗}p < 0.001 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-20.png |

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Titre | Table 8: Results for sovereign ratings |

Légende | t statistics based on robust Standard Errors in parentheses^{∗}p < 0.05, ^{∗∗}p < 0.01, ^{∗∗∗}p < 0.001 |

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Titre | Figure 8: Simulated data with and without a threshold effect |

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Titre | Table 9: Summary statistics for Monte Carlo simulation: β_{2}^{below γ} = 10, β_{2}^{above γ} = 11, 250 trials, n = 100, T = 30 |

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Titre | Table 10: Summary statistics for Monte Carlo simulation: β_{2}^{below }^{γ} = 10, β_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-45.png |

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Titre | Figure 9: Kernel density plots of the threshold estimate under H_{0} and H_{1}with β_{2}^{below }^{γ} = 10, β_{2}^{above }^{γ} = 11, 250 trials, n = 100, T = 30 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-46.png |

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Titre | Figure 10: Kernel density plots of bootstrap F_{1} statistic of the threshold estimate under H_{0} and H_{1}with β_{2}^{below }^{γ} = 10, β_{2}^{above }^{γ} = 11, 250 trials, n = 100, T = 30 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-47.png |

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Titre | Figure 11: Kernel density plots of coefficient estimates under H_{0} and H_{1}with β_{2}^{below }^{γ} = 10, β_{2}^{above }^{γ} = 11, 250 trials, n = 100, T = 30 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-48.png |

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Titre | Figure 12: Kernel density plots of the threshold estimate under H_{0} and H_{1}with β_{2}^{below }^{γ} = 10, β_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-49.png |

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Titre | Figure 13: Kernel density plots of bootstrap F_{1}statistic of the threshold estimate under H_{0} and H_{1}with β_{2}^{below }^{γ} = 10, β_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-50.png |

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Titre | Figure 14: Kernel density plots of coefficient estimates under H_{0} and H_{1}with β_{2}^{below }^{γ} = 10, β_{2}^{above }^{γ} = 20, 250 trials, n = 100, T = 30 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-51.png |

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Titre | Table 11: PTR estimates for debt threshold and long term interest rates |

Légende | t statistics based on robust Standard Errors in parentheses^{∗}p < 0.05, ^{∗∗}p < 0.01, ^{∗∗∗}p < 0.001 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-53.png |

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Titre | Table 12: PTR estimates for threshold of share of external debt and long term interest rates |

Légende | t statistics based on robust Standard Errors in parentheses^{∗}p < 0.05, ^{∗∗}p < 0.01, ^{∗∗∗}p < 0.001 |

URL | http://books.openedition.org/iheid/docannexe/image/518/img-56.png |

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© Graduate Institute Publications, 2012