Abstract
Using annual data from two panels, one of 11 Eurozone countries and another of 31 OECD countries, we estimate a tworegime loglinear as well as a nonlinear model for the spread as a function of macroeconomic and qualityofinstitutions variables. The two regimes, a highspread and a lowspread regime, are distinguished by using a threshold, in accordance with the perceived “fair” value of the spread as a reference point. Our results suggest that governmentbond spreads are regimedependent, as most of the regression coefficients of the determinants of the spread are larger (in absolute value) in the highspread regime than in the lowspread regime. That is, an improvement in the macroeconomic environment (e.g., lower unemployment, lower inflation, lower growth of the debttoGDP ratio, less macroeconomic uncertainty, higher growth of real GDP), and/or an improvement in the quality of institutions (e.g., less corruption) reduce the spread facing a country (by enhancing its creditworthiness) to a greater extent in highspread situations than in lowspread situations. A possible explanation is that the demand for and the supply of loans are inelastic at higher than “fair” interest rates and elastic at lower rates.
1 Introduction
In recent years, the deterioration of macroeconomic indicators (fiscal imbalances, government indebtedness, unemployment, etc.), in both developed and less developed countries, and the governments’ borrowing strategies have given rise to concerns about the risks posed for individual countries as well as for the global financial system. Some studies question the notion that spreads can be explained only by macroeconomic indicators in one state of the world, however, suggesting that other factors might be affecting spreads, such as the perception of sovereign risk at various spread levels (e.g., GomezBengoechea and Arahuetes 2019; Haugh, Ollivaud, and Turner 2009). Furthermore, when assessing risk, it appears that some variables, which determine a country’s creditworthiness, e.g., macroeconomic and quality of institutions indicators, are more important in periods of high risk exposure (hence high spreads), and less important in periods of low risk exposure (low spreads).
This paper is an empirical analysis that aims to provide new insights about the link between macroeconomic indicators and sovereign bond yield spreads, assuming two states of the world. We consider a decision maker in charge of financing his/her government’s spending program by borrowing from the markets, which charge him/her an interest rate in accordance with the prevailing macroeconomic conditions and the quality of institutions, serving as indicators of the borrower’s credibility. We assume that he/she believes that the country’s financial condition is sufficient for a loan of a specified amount at a “fair” interest rate, known to both parties. We then ask: How would the borrower respond if the markets offered him/her an interest rate (r) that is (i) higher than the subjective “fair” rate, a state of affairs which we call highspread regime, or (ii) lower than or equal to the “fair” rate, a state we call lowspread regime?
Here, we are contemplating the possibility that the borrower’s demand for loans is inelastic at higher than “fair” interest rates and elastic at lower rates. Such behavior can be described by the loginverse model, L = exp(β_{0} + β_{1}/r), where L is the quantity of loan demanded and β_{1} > 0. The interest elasticity of demand in this case is −β_{1}/r < 0. As a consequence, a given increase in the demand for loans raises the spread by more at the highspread regime than at the lowspread regime. This is our “thresholdvalue hypothesis,” the novelty of the paper, in which the “reference point” is assumed to be the “threshold” that separates the two regimes.
We make this hypothesis operational by defining a dummy variable, I, and its complement, 1 – I; multiplying each with the determinants of the spread, thus creating interaction variables that will allow the effect of each determinant to differ from regime to regime; and testing the hypothesis of equality of the coefficients of the corresponding interaction variables in our regressions for the spread. If the coefficients of these interaction variables in the highspread regime turn out to be larger (in absolute value) than their counterparts in the lowspread regime, this will lend support to our hypothesis, as providing evidence that a given change in a determinant of the spread that shifts the demand for loans, thus leading to a new equilibrium in the loan market, influences the spread by more in the highspread regime than it does in the lowspread regime.
To illustrate this nonlinearity, consider Figure 1, which is consistent with the loginverse model for the demand for loans given above. Assume that initially our decision maker borrows an amount L_{0} at an interest rate r_{0}, but then an increase in his/her demand for loans occurs, say, because unemployment (a shift variable hidden in the intercept, β_{0}) has increased, and he/she needs funds to implement a “lean against the wind” policy. Thus, at the initial interest rate (r_{0}), which prevailed when quantity demanded was L_{0}, his/her quantity demanded increases from L_{0} to L_{1} and there occurs an excess demand for loans, which pushes the interest rate up. After all, during periods of high unemployment, the country’s economy is weaker and the markets require an additional premium to compensate for their risk exposure. Now, a large increase in the interest rate (the highspread regime), e.g., Δr^{i} = r_{1}^{i} – r_{0}, is associated with an inelastic demand of the decision maker, whereas a small increase (the lowspread regime), e.g., Δr^{e} = r_{1}^{e} – r_{0}, where Δr^{i} > Δr^{e}, is associated with an elastic demand. (The superscripts i and e stand for “inelastic” and “elastic” demand, respectively.)
Figure 1:
The above argument can be reinforced by assuming that the supply of loans is also inelastic at higher than “fair” interest rates and elastic at lower rates. Figure 2 shows the case of an initial and a new equilibrium (after a shift in demand) that occur at low rates, where both demand and supply are highly elastic.^{[1]} The figure shows an initial equilibrium at point A, where the interest rate is r_{0}, and then an increase in the demand for loans, say, because of an increase in the rate of unemployment, so equilibrium moves to point B. Because the supply and demand curves are assumed to be highly elastic at low interest rates, a small increase in the interest rate, say, from r_{0} to r_{1}, suffices to restore equilibrium after a large increase in demand.
Figure 2:
Using annual data from two panels, one of 11 Eurozone countries and another of 31 OECD countries, we estimate a tworegime threshold model in accordance with Hansen (1999) ^{[2]} and Cassou, Shadmani, and Vázquez (2017). This simple model serves our purpose satisfactorily, which is to test our “thresholdvalue hypothesis” via the interaction variables defined above, so we did not pursue more sophisticated approaches, such as a Markov switching model, a “panel smooth transition regression model” (González et al. 2017; Hmiden and Cheikh 2016), or a model that relates the threshold more directly to fundamentals, such as public debt (HadziVaskov and Ricci 2019).
We employ a loglinear as well as a nonlinear spread equation. The basic model is derived in Feder and Just (1977a, 1977b), Edwards (1984), and elsewhere, and considers the spread as a function of the probability of default, which is itself a function of a set of macroeconomic and other variables. In accordance with the literature, this set includes the growth rate of GDP, the unemployment rate, the inflation rate, the primary budget surplus, the growth rate of debt to GDP, an uncertainty index, the real exchange rate, a riskfree interest rate, a United States (US) longterm interest rate, private investment, public investment, government effectiveness, control of corruption, and political stability (Afonso 2003; Afonso and Jalles 2019; Cantor and Packer 1996; HadziVaskov and Ricci 2019; Hmiden and Cheikh 2016).
We use two empirical definitions of the “fair” value of the spread, denoted as M and R, which are described in detail in Section 2. Briefly, according to definition M, there is only one “fair” value of the spread for all the countries in the sample in year t, and that is the average spread in year t; whereas, according to definition R, there are as many “fair” values as rating classes, and the “fair” value for each country is the average spread of the associated rating class that the country belongs to in year t. In both definitions, we use the simple (instead of a weighted) average, since there is no substantial variation across countries. We also use two estimation methods, least squares and the generalized method of moments (GMM). With two functional forms, two panels of data, two definitions of the “fair” spread, and two estimation methods, we end up estimating 16 regressions. To confirm or reject our assertions and to judge the reliability of the 16 regressions, we use a battery of tests.
Our results broadly support our “thresholdvalue hypothesis,” as most of the coefficients of the interaction variables defined earlier are larger (in absolute value) in the highspread regime than their counterparts in the lowspread regime. More specifically, we find that macroeconomic variables (e.g., unemployment rate, inflation rate, growth rate of real GDP, growth rate of the debttoGDP ratio, and an uncertainty index), as well as some quality of institutions indices (e.g., a corruption index), all of which are important determinants of a country’s creditworthiness, have a greater effect on the spread in highspread situations than in lowspread situations. Incorporating this hypothesis into our model and testing it aims at providing the policy maker with a more adequate explanation of the mechanism that determines the spread.
Section 2 specifies the model, Section 3 describes the data and discusses their stochastic properties, Section 4 estimates and tests the 16 regressions and discusses the results, and Section 5 concludes.
2 The model
According to Feder and Just (1977b), Eaton and Gersovitz (1981), and Sachs (1983), among others, the spread over LIBOR charged on Eurodollar loans taken by a country reflects its probability of default, p. Thus, following Feder and Just (1977b), Edwards (1984), Bassat and Gottlieb (1992), and Ozdemir (2004), we assume that
where γ = 1 + r^{*}, and r^{*} is a riskfree interest rate. Edwards (1984) derives Eq. (1) by assuming perfectly competitive financial markets and riskneutral lenders. The lender is indifferent between gaining the return 1 + r with probability 1 – p and the riskfree return 1 + r^{*} with certainty. Equilibrium requires that the following condition hold:
Solving this equation for r, subtracting r^{*} from both sides of the resulting equation, and setting s = r – r^{*} and γ = 1 + r^{*} yields Eq. (1).
The (subjective) probability p is not observable, but can be estimated by assuming that it is a function of variables collected in a vector x, say, p(x) (Feder and Just 1977b). Since p(x) must be bounded between zero and one for all choices of x, the most widely used functional form for p(x) is the logistic form (Cox 1970), which gives
Combining (1) and (3) yields the following nonlinear equation for the spread:
Taking logarithms in (4); adjusting the notation for panel data; and assuming that γ is a timevarying variable whose value in year t applies to all the countries in the sample, whereas β_{0} is constant across time and countries; yields the loglinear equation
Thus, denoting the threshold value as s_{ t }^{*}, the tworegime loglinear model is
where all coefficients are allowed to vary from regime to regime.
Again, we use two definitions of the “fair” spread. First, for a given year t, we take the spreads facing all the countries in the sample and calculate their mean, denoted as s_{ t }^{ * }, which is the same for all the countries in the sample. This is the definition used in Eq. (6); in what follows, it is denoted by M.
Second, we sort the countries into rating classes, depending on their credit rating (provided by Moody’s), and measure the “fair” spread facing country i in year t by the average spread of the associated rating class that country i belongs to in year t. This “fair” value, denoted as s_{ it }^{ * }, is indexed by i, because in a given year t, the various countries in the sample belong to different rating classes. For example, if country i is rated AAA in year t, then s_{ it }^{ * } is the average spread of all the countries rated AAA in year t, but in the same year countries in other rating classes will be faced with a different “fair” spread.^{[3]} In what follows, this ratingbased definition is indicated by R.
An advantage of using definition R is that country ratings are taken into account. There are two problems with this definition, however. First, in terms of Figure 1, it implies that the demand functions for funds of two countries that belong to different rating classes exhibit the same curvature. Thus, for example, if these two countries end up paying the same spread (say, because the better rated country experiences negative shocks for a period of time), their demand functions for funds may falsely exhibit the same nonlinearity. Second, it introduces an endogeneity problem noted by Hansen (1999, pp. 346 and 356), as the threshold becomes an endogenous variable. For if there is a negative shock in country i that raises its spread, the average spread in its rating class will rise, especially if the number of countries in that class is small, and this may cause some of the other countries in that class to be placed in a wrong regime. Thus, as will be seen shortly, this problem renders all of the explanatory variables used in our regressions endogenous. In contrast, when we use definition M, this problem is expected to be much less severe, as an increase in country i’s spread will not affect noticeably the average spread of the entire panel in year t.^{[4]}
A threshold regression emerges by combining the two regimes in Eq. (6), using the dummy variable I_{ it }, where I_{ it } = 1 if s_{ it } > s_{ t }^{ * } and I_{ it } = 0 if s_{ it } ≤ s_{ t }^{*}, and the country dummies D_{1}, …, D_{N1}, to capture fixed countryspecific effects (ignoring time effects for the moment), and by adding an error term, ε_{ it }, which reflects both supply and demand shocks, since Eq. (1) is derived from the equilibrium condition (2). The result is
The logarithmic transformation could potentially destroy the consistency of the estimates, however,^{[5]} so we also estimate the nonlinear model, Eq. (4), the threshold version of which can be written as
When Eq. (8) was estimated, there was evidence of serial correlation, which could be interpreted as a sign of model misspecification, so we modify Eq. (8) to incorporate the partial adjustment mechanism. Let s_{
it
}^{
d
} denote the desired level of the spread, which is not directly observable, and assume that if there is a shock to it, a complete adjustment of the actual spread (s_{
it
}) to its desired level may not be achieved in a single period, because of technological constraints, institutional rigidities, lags in the publication of data, etc., but only a fraction δ of the ratio
Replacing s_{it} with s_{it}^{d} on the lefthand side of (8), substituting the result into (9) for s_{it}^{d}, and adding an error term, we obtain
Note that in six out of the eight cases where we estimate Eq. (10) the serial correlation problem has disappeared (see Regressions 5, 6, and 13–16 in Tables 4 and 6). Note also that for δ_{1} = δ_{2} = 1 (immediate adjustment), Eq. (10) reduces to (8).
3 The data
We use annual data from two unbalanced panels. The first, Panel 1, considers 11 Eurozone countries over the time period 1997–2014, namely Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, and Spain. This group of countries has been used in various papers, such as Barrios et al. (2009). Its selection is based on data reliability and availability limitations, mainly for the Baltic countries, which joined the Eurozone only recently. The macroeconomic data for this group of countries were collected from the Eurostat Database.
As a robustness check, we also use another panel of 31 OECD countries, Panel 2, over the time period 1996–2014. In addition to the above 11 Eurozone countries, Panel 2 includes Australia, Canada, Chile, Czech Republic, Denmark, Hungary, Iceland, Israel, Japan, Korea, Mexico, New Zealand, Norway, Poland, Slovak Republic, Slovenia, Sweden, Switzerland, United Kingdom, and the United States.
The variables used in our analysis are as follows: (1) the spread facing country i, which is measured as the difference between its 10year governmentbond yield and the Libor; (2) GAMMA = 1 + r^{*} and LGAMMA = log(1 + r^{*}), where r^{*} is assumed to capture shocks that occur in international markets; (3) the inflation rate (INFL); (4) the growth rate of the debttoGDP ratio (DEBTGRO);^{[6]} (5) the growth rate of real GDP (GDPGRO); (6) the primary budget surplus (PRIMBS); (7) the unemployment rate (UR); (8) public investment (PUBINV); (9) a volatility index (VIX), which serves as an indicator of uncertainty; (10) the real exchange rate (REER_WB), an increase in which means real depreciation of the home currency; (11) the 10year US government bond yield (LONG_US); and (12) several indices of quality of institutions, like control of corruption (CORRU), political stability (POLSTAB), government effectiveness (GOVEFFECT), etc. Higher values of these indices imply higher quality of institutions. To facilitate the interpretation of the regression coefficients reported in Tables 3–6, we report the sample means of these variables in Table 1.
Table 1:
Panel 1: 11 Eurozone countries  Panel 2: 31 OECD countries  

(1997–2014)  (1996–2014)  
Variable  Mean  Variable  Mean  Variable  Mean  Variable  Mean 
LIBOR  0.0177  LONG_US  4.1400  LIBOR  0.01920  LONG_US  4.2611 
LSLIBOR  −4.2648  REER_WB  99.7458  LSLIBOR  −4.0558  REER_WB  99.4160 
GAMMA  1.0346  CORRU  1.5976  GAMMA  1.0359  CORRU  1.3583 
LGAMMA  0.0340  POLSTAB  1.0385  LGAMMA  0.0351  POLSTAB  0.7878 
INFL  0.0201  RLAW  1.5453  INFL  0.0288  RLAW  – 
UR  0.0819  PRINV  132.7896  UR  0.0750  PRINV  – 
GDPGRO  0.0166  PUBINV  22.4448  GDPGRO  0.0242  PUBINV  30.5815 
DEBTGRO  0.01705  GOVEFFECT  1.6005  DEBTGRO  0.0212  GOVEFFECT  1.3943 
PRIMBS  −0.0301  DUMMYM  0.5278  PRIMBS  −0.0212  DUMMYM  0.6197 
VIX  21.4689  DUMMYR  0.5966  VIX  21.2042  DUMMYR  0.4720 
We also construct interaction terms after defining the dummy variable I1 as I1_{ it } = 1 – I_{ it }, e.g., IUR = I × UR, I1UR = I1 × UR, ICORRU = I × CORRU, I1CORRU = I1 × CORRU, etc. From these definitions, it is obvious that, to the extent that the dummy variables I_{ it } and I1_{ it } are endogenous (see our discussion on the definitions M and R for the “fair” spread in Section 2) so are these interaction variables; and that is true even for variables that can be taken as exogenous in this paper, such as CORRU. This problem exacerbates the already existing endogeneity problem, since the macroeconomic determinants of the spread are inherently endogenous. Consider, for example, the rate of growth of the debttoGDP ratio (DEBTGRO). A positive shock in Eq. (7), ε_{ it } > 0, which causes the spread to rise, it also causes DEBTGRO to rise, so DEBTGRO is expected to be correlated with ε_{ it }. Thus, GMM estimates (see Tables 5 and 6) should be considered more reliable than the leastsquares ones (Tables 3 and 4). This discussion implies that if we use the above variables (IUR, I1UR, ICORRU, etc.) as instruments, we should lag them at least by one time period.
The sources of the data are as follows: The 10year government bond yields, the Libor rate over Euro, and the volatility index were obtained from the Federal Reserve Bank of St. Louis. The riskfree rate (r^{*}), proxied by Germany’s longrun interest rate, was obtained from the European Central Bank (ECB Monthly Bulletin 2014). The quality of institutions indicators and the real exchange rate were obtained from the World Bank, whereas the remaining series from the Eurostat.
Next, we perform the following unitroot tests: (1) Levin, Lin, and Chu (2002) (LLC); (2) Breitung (2000); (3) Im, Pesaran, and Shin (2003) (IPS); (4) Fishertype Augmented DickeyFuller (ADF) test; and (5) Fishertype PhillipsPerron (PP) test (Maddala and Wu 1999, and Baltagi 2001, pp. 240–241). The results are reported in Table 2. Note, first, that the LLC and Breitung tests require “stronglybalanced” panels, so these two tests do not provide any results for the variables that do not satisfy this requirement. Second, for each variable, stationarity is supported by at least two tests, so we take all the variables used in our regressions to be I(0). Third, depending on the deterministic components included in the testing regression, each test produces several statistics; we take the one that most strongly supports stationarity. Fourth, as we noted earlier, the tests suggest that the debttoGDP ratio and its logarithm are I(1), so we do not use these variables. Finally, the tests suggest that the first differences are I(0).
Table 2:
Test  LLC  Breitung  IPS  FisherADF  FisherPP  I(0) or I(1)? 

Variable  
LIBOR  –  –  −6.6^{***}  173.2^{***} (c)  155.8^{***} (c)  I(0) 
LSLIBOR  –  –  –  92.5^{***} (c)  177.2^{***} (c)  I(0) 
GAMMA  0.4  −6.1^{***}  −8.7^{***}  37.2  145.5^{***}  I(0) 
LGAMMA  0.7  −6.0^{***}  −8.5^{***}  33.1  137.9^{***}  I(0) 
INFL  −5.8^{***} (c)  −3.8^{***}  −8.0^{***}  192.2^{***} (c)  296.3^{***} (c)  I(0) 
UR  −8.4^{***}  −2.0^{**} (c)  −1.5^{*}  153.3^{***}  76.5 (c)  I(0) 
GDPGRO  −8.5^{***} (c)  −9.1^{***} (c)  −9.3^{***}  186.3^{***} (c)  231.4^{***} (c)  I(0) 
DEBTGDP  –  –  0.6  74.5^{*} (c)  62.3 (c)  I(1) 
LDEBTGDP  –  –  0.1  70.3 (c)  70.4 (c)  I(1) 
DEBTGRO  –  –  −10.9^{***}  140.2^{***}  715.3^{***} (c)  I(0) 
PRIMBS  –  –  −5.3^{***}  141.5^{***} (c)  114.4^{***} (c)  I(0) 
VIX  −11.4^{***} (c)  −7.9^{***}  −3.8^{***}  209.4^{***} (c)  99.1^{***} (c)  I(0) 
LONG_US  −10.9^{***}  −6.7^{***}  −7.4^{***}  158.9^{***}  108.1^{***}  I(0) 
REER_WB  −3.4^{***} (c)  −1.2 (c)  −4.3^{***}  103.0^{***} (c)  103.7^{***} (c)  I(0) 
CORRU  –  –  −3.5^{***}  56.8  162.9^{***}  I(0) 
POLSTAB  –  –  −5.5^{***}  102.9^{***} (c)  175.3^{***}  I(0) 
RLAW  –  –  −7.3^{***}  88.2^{***}  79.7^{***} (c)  I(0) 
PRINV  −5.0^{***} (c)  −0.5  −2.8 ^{***}  111.2^{***} (c)  77.1^{***} (c)  I(0) 
PUBINV  −5.1^{***} (c)  −2.7^{***} (c)  −4.3^{***}  109.7^{***} (c)  94.0^{***} (c)  I(0) 
GOVEFFECT  −9.4^{***}  −2.5^{***} (c)  −5.0^{***}  189.0^{***}  158.0^{***}  I(0) 
DUMMYM  −7.7^{***}  −8.3^{***} (c)  −7.9^{***}  150.9^{***} (c)  196.0^{***} (c)  I(0) 
DUMMYR  –  –  −7.6^{***}  234.5^{***} (c)  267.1^{***} (c)  I(0) 

(1) ^{***}, ^{**}, and ^{*} indicate statistical significance at the 1, 5, and 10percent level, respectively, assuming onesided alternatives; (2) the indication (c) next to the value of a test statistic means that only a constant was included in the deterministic components of the regression, but not a trend; whereas no indication at all means that both a constant and trend were included; (3) the reported statistic for the Fishertype Augmented DickeyFuller (ADF) and PhillipsPerron (PP) tests is inverse chisquared (denoted by P), whereas that for the IPS test is the “Zttildebar” test; (4) blank spaces occur because the LLC and Breitung tests require strongly balanced panels, and some of our variables do not satisfy this requirement; (5) in each cell of the table, we report the figure that most strongly supports the stationarity hypothesis; (6) for a given variable, if at least two tests support stationarity, the variable is taken to be I(0); otherwise it is deemed I(1); (7) the figures reported in this table have been derived by the econometric program STATA.
4 Empirical results
Tables 3–6 report our empirical results for the two Equations, (7) and (10), two panels of data, Eurozone and OECD, two estimation methods, least squares (with robust standard errors to heteroscedasticity and to serial correlation) and GMM, and two definitions for the “fair” spread, M and R, 16 regressions altogether. The loglinear regressions (1–4 and 9–12) include both country and time dummies (to allow for the possibility that the years from 2008 onward might have had a special impact on the spread, because of the financial crisis), whereas the nonlinear ones (5–8 and 13–16) include only country dummies, to avoid convergence problems.
Table 3:
Explanatory variables & tests  Panel 1: 11 Eurozone countries  Panel 2: 31 OECD countries  

Regr. 1 (M)  Regr. 2 (R)  Regr. 3 (M)  Regr. 4 (R)  
Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  
I  −4.51^{***} (−25.9)  −5.19^{***} (−21.0)  −0.03 (−0.2)  −0.60 (−1.1) 
ILGAMMA  −32.79^{***} (−9.1)  −12.67^{***} (−2.9)  −11.82^{***} (−5.2)  −13.26^{***} (−5.0) 
IINFL  12.18^{***} (6.4)  15.00^{***} (5.9)  1.28 (0.4)  2.49 (1.1) 
IDEBTGRO  1.05^{***} (4.0)  1.46^{***} (5.1)  −0.29 (−0.9)  −0.09 (−0.4) 
IUR  6.16^{***} (9.4)  8.05^{***} (8.8)  5.17^{***} (4.8)  5.02^{***} (4.3) 
IVIX  0.04^{***} (5.1)  0.02^{***} (2.6)  −0.001 (−0.2)  −0.00 (−0.2) 
IGDPGRO  −4.93^{***} (−4.6)  −8.65^{***} (−6.3)  −8.70^{***} (−4.3)  −7.08^{***} (−4.0) 
IPRIMBS  0.72 (1.5)  −0.37 (−0.6)  −1.98^{***} (−2.4)  −2.24^{**} (−1.8) 
IREER_WB  0.09 (1.9)  −0.00 (−0.2)  −0.005^{**} (−1.7)  −0.004^{**} (−1.6) 
IPUBINV  −0.001 (−0.7)  −0.004^{***} (−3.5)  −0.009^{***} (−7.1)  −0.010^{***} (−9.1) 
IPRINV  0.00 (0.0)  0.00 (0.8)  –  – 
IPOLSTAB  0.04 (0.4)  0.22 (1.1)  0.13 (0.9)  0.04 (0.5) 
I1  −3.10^{***} (−3.7)  −4.20^{***} (−20.5)  −0.15 (−0.8)  −0.58 (−0.7) 
I1LGAMMA  −3.57 (−0.8)  1.05 (0.1)  −13.09^{***} (−3.9)  −2.00 (−1.0) 
I1INFL  1.34 (0.3)  −2.55 (−0.6)  −2.91 (−0.8)  −3.03 (−1.0) 
I1DEBTGRO  −1.62 (−1.5)  −0.50 (−0.4)  0.20 (0.8)  0.20 (0.5) 
I1UR  1.53 (0.8)  1.74 (0.9)  3.93^{***} (2.7)  4.61^{***} (3.2) 
I1VIX  0.01^{***} (2.3)  0.02^{**} (1.9)  0.02^{***} (2.8)  0.00 (0.2) 
I1GDPGRO  −9.31^{***} (−5.0)  −7.88^{***} (−4.4)  −4.74^{***} (−3.5)  −9.22^{***} (−4.0) 
I1PRIMBS  −5.55^{***} (−3.4)  −5.95^{***} (−4.5)  −2.84^{***} (−2.6)  −1.83^{**} (−1.9) 
I1REER_WB  −0.01^{**} (−1.7)  0.00 (0.2)  −0.01^{***} (−3.3)  −0.01^{***} (−4.1) 
I1PUBINV  −0.002 (0.5)  −0.001 (−0.4)  −0.009^{***} (−10.5)  −0.008^{***} (−10.4) 
I1PRINV  −0.00^{*} (−1.6)  −0.00 (−0.4)  –  – 
I1POLSTAB  −0.38^{***} (−4.1)  −0.59^{***} (−5.5)  −0.04 (−0.3)  −0.06 (−0.7) 
Usable obs. (n)  113  111  476  471 
Centered R^{2}  0.95  0.93  0.64  0.66 
H_{0}: One regime 




RESET

0.0 (0.50)  0.02 (0.89)  0.4 (0.54)  0.5 (0.50) 
DWH 




H_{0}: no serial corr.  t_{54} = 0.8 (0.40)  t_{55} = 3.1^{***} (0.00)  t_{390} = 6.9^{***} (0.00)  t_{385} = 5.4^{***} (0.00) 
H_{0}: no break in 2008 









(1) A line separates the two regimes; (2) the numbers in parentheses next to the coefficient estimates are tstatistics; those next to the test statistics are pvalues; (3) the routine LINREG of WinRATS 9.1 was used with the option EickerWhite standard errors; (4) shaded coefficients refer to variables that were dropped, as insignificant; (5) A dash in a cell means that no estimate is available due to insufficient data on that variable; (6) Note (1) to Table 2 applies here, too.
Table 4:
Explanatory variables & tests  Panel 1: 11 Eurozone countries  Panel 2: 31 OECD countries  

Regr. 5 (M)  Regr. 6 (R)  Regr. 7 (M)  Regr. 8 (R)  
Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  
I  −7.22^{***} (−6.6)  −6.57^{***} (−16.0)  −3.18^{***} (−10.2)  −2.76^{***} (−13.0) 
IINFL  28.94^{***} (3.6)  26.26^{***} (2.7)  13.14^{***} (2.9)  13.22^{***} (3.1) 
IDEBTGRO  1.33^{***} (3.3)  1.06^{***} (4.6)  0.90^{**} (2.1)  1.06^{***} (6.4) 
IUR  12.92^{***} (11.5)  9.69^{***} (13.3)  −5.57 (−1.5)  −24.10 (−1.4) 
IVIX  0.11^{**} (2.2)  0.13^{***} (4.3)  0.04^{*} (1.4)  0.30 (1.2) 
IGDPGRO  −11.86^{***} (−3.6)  −8.11^{***} (−3.9)  −16.13^{***} (−7.3)  −14.62^{***} (−7.5) 
IPRIMBS  49.42 (0.7)  −1.18 (−0.7)  17.84 (1.4)  −21.40 (−1.1) 
IPUBINV  0.001 (0.3)  −0.010 (−0.7)  −0.002^{***} (−2.9)  −0.002^{***} (−8.0) 
IPOLSTAB  −0.47^{**} (−1.8)  −7.48 (−0.9)  −0.33^{***} (−5.0)  −0.28^{***} (−6.0) 
ILONG_US  −0.01 (−0.1)  −0.38^{***} (−5.3)  −0.24^{***} (−2.9)  −0.15^{***} (−3.1) 
ICORRU  0.31 (0.7)  3.06 (0.9)  −0.05 (−0.1)  −0.71 (−0.6) 

0.51^{***} (3.2)  0.50^{***} (8.3)  0.37^{***} (4.9)  0.48^{***} (5.9) 
I1  −5.53^{***} (−24.5)  −6.81^{***} (−4.7)  2.31 (0.3)  −104.15 (−0.6) 
I1INFL  16.26^{***} (2.4)  103.01 (0.7)  252.12 (0.4)  −9.62 (−0.1) 
I1DEBTGRO  −4.52 (−1.0)  10.23 (0.9)  27.84 (0.4)  8.93 (0.9) 
I1UR  5.52^{**} (2.2)  6.82 (1.2)  20.93 (0.4)  69.84 (0.8) 
I1VIX  0.01 (0.5)  0.10^{*} (1.4)  −0.90 (−0.5)  −0.38 (−1.2) 
I1GDPGRO  −6.23 (−0.9)  −20.32^{**} (−1.9)  −213.85 (−0.5)  134.90 (0.9) 
I1PRIMBS  −17.20^{***} (−4.1)  −19.07^{***} (−2.7)  −14.54 (−0.2)  29.89 (0.4) 
I1PUBINV  0.00 (0.5)  0.02 (0.5)  0.03 (0.3)  0.01 (0.7) 
I1POLSTAB  −0.11 (−0.5)  2.63 (0.9)  −0.69^{**} (−2.2)  −1.88^{***} (−3.3) 
I1LONG_US  −2.6 (−1.0)  −0.2 (−1.2)  −1.37^{***} (−7.4)  −0.85^{***} (−4.5) 
I1CORRU  0.03 (0.3)  −1.91 (−0.9)  −0.46^{**} (−1.7)  −0.80^{**} (−2.1) 

0.71^{***} (3.1)  0.30^{***} (2.7)  0.13^{***} (7.9)  0.13^{***} (4.7) 
Usable obs. (n)  113  149  360  359 
H_{0}: One regime 




H_{0}: no serial corr.  t_{61} = −0.6 (0.53)  t_{124} = −0.6 (0.58)  t_{246} = 3.7^{***} (0.00)  t_{246} = 5.1^{***} (0.00) 
H_{0}: no break in 2008  F_{7,90} = 5.5^{***} (0.00)  F_{6,130} = 2.7^{**} (0.02)  F_{4,330} = 5.9^{***} (0.00)  F_{3,330} = 2.1^{*} (0.09) 
F_{11,86} = 6.2^{***} (0.00)  F_{9,127} = 2.1^{**} (0.03)  F_{8,326} = 5.7^{***} (0.00)  F_{7,326} = 3.1^{***} (0.00) 

(1) The routine NLLS of WinRATS 9.1 was used with the option lwindow = panel to obtain robust standard errors; (2) see also the Notes to Table 3.
Table 5:
Explanatory variables & tests  Panel 1: 11 Eurozone countries  Panel 2: 31 OECD countries  

Regr. 9 (M)  Regr. 10 (R)  Regr. 11 (M)  Regr. 12 (R)  
Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  
I  −6.27^{***} (−13.8)  −4.44^{***} (−18.0)  −3.67^{***} (−16.2)  −3.94^{***} (−16.8) 
ILGAMMA  −38.60^{***} (−7.3)  −28.40^{***} (−5.0)  −3.34 (−0.3)  3.60 (0.6) 
IINFL  15.55^{***} (6.2)  14.16^{***} (3.6)  10.40^{**} (1.7)  18.02^{***} (3.3) 
IDEBTGRO  0.31 (0.8)  1.90^{*} (1.6)  0.92 (0.4)  2.92^{**} (1.9) 
IUR  10.46^{***} (5.4)  9.16^{***} (6.0)  7.73^{***} (6.3)  6.91^{***} (3.8) 
IGDPGRO  −7.56^{***} (−4.5)  −6.21^{**} (−1.9)  −10.69^{***} (−3.5)  0.23 (0.0) 
IPRIMBS  −0.34 (−0.5)  2.10 (1.0)  −2.80 (−0.4)  1.12 (0.3) 
IVIX  0.11^{***} (8.8)  0.02 (0.8)  0.02 (0.6)  −0.03 (−0.7) 
IPUBINV  −0.00 (−0.6)  −0.01^{***} (−2.7)  −0.002^{**} (−2.1)  −0.002^{***} (−2.9) 
IPOLSTAB  0.38 (1.1)  −0.30 (−0.7)  −0.41^{***} (−5.7)  −0.36^{***} (−4.8) 
ICORRU  0.14 (1.0)  0.24 (0.8)  −0.12 (−0.5)  −0.01 (−0.0) 
IGOVEFFECT  0.10 (0.4)  −0.01 (−0.0)  −0.16 (−0.6)  0.01 (0.0) 
I1  −5.95^{***} (−19.8)  −3.61^{***} (−7.6)  −2.67^{***} (−9.3)  −3.11^{***} (−9.1) 
I1LGAMMA  −18.78^{***} (−5.1)  −12.66 (−1.2)  30.61 (0.8)  22.37 (1.1) 
I1INFL  6.53^{*} (1.3)  11.40 (0.9)  4.36 (0.2)  2.18 (0.2) 
I1DEBTGRO  −1.35 (−1.3)  1.91 (1.0)  2.85^{*} (1.6)  −4.21 (−1.3) 
I1UR  8.67^{***} (3.2)  4.79^{*} (1.3)  −2.85 (−0.3)  4.62^{*} (1.4) 
I1GDPGRO  −5.54^{***} (−2.7)  −6.81^{**} (−1.7)  −10.97 (−0.8)  −14.28^{***} (−2.6) 
I1PRIMBS  −6.14^{***} (−3.6)  −7.23^{***} (−2.7)  0.38 (0.0)  6.53 (0.9) 
I1VIX  0.07^{***} (8.7)  −0.02 (−0.6)  0.01 (0.2)  −0.05 (−1.5) 
I1PUBINV  0.00 (0.5)  0.01 (0.6)  −0.001^{**} (−1.7)  −0.001^{**} (−2.0) 
I1POLSTAB  −0.09 (−0.6)  0.29 (0.6)  −0.01 (−0.1)  −0.11 (−0.5) 
I1CORRU  −0.01 (−0.1)  −0.46^{**} (−1.7)  −0.87^{***} (−5.7)  −0.60^{***} (−3.6) 
I1GOVEFFECT  −0.13 (−0.9)  −0.75^{**} (−1.8)  −0.01 (−0.1)  0.51 (0.4) 
Usable obs. (n)  82  87  296  292 
H_{0}: one regime 




pvalue of J (d.f.)  0.09 (27)  0.58 (8)  0.19 (6)  0.74 (7) 
H_{0}: no serial corr. 




H_{0}: no break in 2008 









(1) In Regressions 9 and 10, the option “Jrobust = Distribution” is used, which produces a Jagannathan and Wang (1996) type weighting matrix, and the limiting distribution of the statistic J is nonstandard, whereas in Regressions 11 and 12 no such option is used, so the limiting distribution of J is chisquared; (2) the number in parentheses next to the pvalue of J is the number of overidentifying restrictions; (3) see also the Notes to Table 3.
Table 6:
Explanatory variables & tests  Panel 1: 11 Eurozone countries  Panel 2: 31 OECD countries  

Regr. 13 (M)  Regr. 14 (R)  Regr. 15 (M)  Regr. 16 (R)  
Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  Coeff. (tstat)  
I  −10.46^{***} (−7.2)  −9.85^{***} (−4.2)  −7.16^{***} (−2.9)  −2.95^{***} (−29.3) 
IINFL  17.33^{**} (2.3)  11.82^{**} (1.8)  0.06 (0.0)  4.91 (0.9) 
IDEBTGRO  1.87^{***} (5.0)  1.30^{***} (3.9)  1.87 (0.6)  1.09^{**} (1.8) 
IGDPGRO  −8.24^{***} (−2.4)  −9.82^{**} (−2.6)  −9.59^{**} (−2.0)  −8.48^{***} (−3.9) 
IPRIMBS  0.49 (0.2)  −2.34 (−1.1)  −10.69^{***} (−3.1)  −2.56^{**} (−1.8) 
IUR  13.39^{***} (5.4)  13.81^{***} (3.8)  0.27 (0.1)  −6.90 (−1.2) 
IVIX  0.24^{***} (3.7)  0.21^{***} (2.4)  0.19^{*} (1.6)  0.02 (0.8) 
ICORRU  3.77 (0.3)  0.28 (0.7)  −0.33^{**} (−1.7)  −0.37^{***} (−5.8) 

0.44^{***} (3.6)  0.54^{***} (3.3)  0.34^{**} (2.1)  0.79^{***} (4.4) 
I1  −7.73 (−0.4)  −3.44 (−1.1)  −1.24 (−0.2)  −1.70 (−0.3) 
I1INFL  −159.24 (−0.9)  84.92 (0.8)  8.96 (0.6)  18.43 (0.8) 
I1DEBTGRO  3.75 (0.2)  7.16 (0.1)  −0.78 (−0.5)  8.53 (1.1) 
I1GDPGRO  2.00 (0.0)  −104.13 (−0.6)  −1.60 (−0.1)  −67.17 (−0.4) 
I1PRIMBS  −196.48 (−0.2)  −70.61 (−1.2)  −1.40 (−0.2)  −14.13 (−0.8) 
I1UR  −13.51 (−0.6)  5.50 (0.4)  0.13 (0.0)  6.71 (0.8) 
I1VIX  −0.07 (−0.5)  −0.40 (−0.7)  −0.1 (−0.4)  0.62 (0.4) 
I1CORRU  −2.80 (−0.2)  0.22 (0.1)  0.22 (0.7)  4.06 (0.2) 

0.05 (0.2)  0.10 (0.7)  −1.93 (−0.8)  0.04 (0.2) 
Usable obs. (n)  77  80  318  306 
H_{0}: one regime 




pvalue of J (d.f.)  0.10 (21)  0.39 (21)  0.12 (7)  0.15 (16) 
H_{0}: no serial corr. 




H_{0}: no break in 2008 








Before we discuss the results, the following comments are in order. First, the top (bottom) part of each table contains the coefficients for the high (low) spread regime. To get an idea of how “informed” each part is, note that for the Eurozone panel (respectively, for the OECD panel), when the definition M is used, on average, 33.8 (61.9) percent of the sample observations fit in the highspread regime and 66.2 (38.1) percent in the lowspread regime; whereas in the case of the definition R, these percentages are 59.1 (41.8) and 40.9 (58.2), respectively.
Second, each regression has been estimated in accordance with the “generaltospecific” approach. That is, we begin with a long list of possible determinants of the spread; construct the interaction variables, e.g., IUR, I1UR, etc., so the initial list of variables doubles; and drop (normally, one at a time) the insignificant ones. We select the variables to be included in a regression based on economic as well as on empirical identification, i.e., correct signs and statistically significant coefficients at the 10 percent level or lower (Johansen and Juselius 1994, p. 8). This procedure is not straightforward, however. A variable that may appear to be statistically insignificant in one configuration of variables it may appear to be significant in a different configuration, where some previously “significant” variables may appear to be insignificant, perhaps because of multicollinearity.
Third, if a particular variable is dropped from a regression as insignificant, we report its coefficient and its tstatistic (obtained at a previous stage) in a shaded cell of Tables 3–6. Fourth, in the spirit of achieving both economic and empirical identification, when reporting the statistical significance of a coefficient, we view the alternative hypothesis as onesided, in accordance with the expected sign of that coefficient. Thus, for example, in Regression 1 the sign of the coefficient of IREER_WB was expected to be negative, so the positive value of its tstatistic, t = 1.9, which would be viewed as significant at the 10percent level if the alternative hypothesis was considered to be twosided, it is now viewed as falling in the nonrejection region of the tdistribution, and IREER_WB is thus dropped. Fifth, a dash (−) in a cell implies that no estimate is available for that coefficient because of insufficient data on the corresponding variable (see Regressions 3 and 4 in Table 3).
We begin our discussion of the empirical results by considering Regression 1, which uses the data from Panel 1 and definition M for the “fair” spread to estimate Eq. (7) by least squares. Analogous comments apply to the other regressions, so they will be limited to comparisons amongst regressions only.
First, consider the signs and magnitudes of the coefficients of Regression 1. The estimate of β_{0} is −4.51, which does not seem to be unreasonable, since the sample mean of the logarithm of the spread in Panel 1 is −4.2648 (see Table 1). The signs of the other coefficients are as expected: (1) negative for LGAMMA, since, by definition, the riskfree rate (r^{*}) negatively influences the spread (s = r – r^{*}); (2) positive for the inflation rate (the Fisher effect); (3) positive for the rate of growth of the debttoGDP ratio, higher values of which erode the country’s creditworthiness and raise the spread; (4) positive for the unemployment rate, as recessions reduce creditworthiness; (5) negative for the growth rate of real GDP (by the same token); (6) positive for the uncertainty index, as uncertainty raises the risk of default; (7) negative for the primary budget surplus, as a higher primary surplus improves a country’s ability to service its debt; (8) negative for the real exchange rate, as a real depreciation of the home currency raises the country’s competitiveness in international markets, thus strengthening its economy; (9) negative for private investment, which also strengthens the economy; and (10) negative for the qualityofinstitutions indicators, such as the index for political stability, higher values of which indicate better quality of institutions, hence higher credibility and lower spread.
Note that the coefficients are semielasticities. Thus, for example, in Regression 1, a ceterisparibus increase in the inflation rate (INFL) by one percentage point, e.g., from 0.04 to 0.05 is expected to raise the spread by 12.18 percent in the highspread regime, e.g., from 0.03 to 0.033654, but leave it intact in the lowspread regime, as the coefficient of I1NFL, 1.34 (t = 0.30), is taken to be zero, hence I1NFL was dropped from the regression. As another example, since the coefficients of IVIX and I1VIX in Regression 1 are 0.04 and 0.01, respectively, a ceterisparibus increase in the uncertainty index by one unit, say, from 20 to 21, is expected to raise the spread by 4 percent in the highspread regime, e.g., from 0.03 to 0.0312, and by 1 percent in the lowspread regime, e.g., from 0.03 to 0.0303.
Second, the evidence supports the tworegime “thresholdvalue hypothesis,” as in most cases the coefficient of an explanatory variable is larger (in absolute value) in the highspread than in the lowspread regime, suggesting that its impact on the spread is larger in the highspread regime. In each regression, we formally test the oneregime hypothesis, that the corresponding coefficients in the lowspread and in the highspread regime are equal. In the context of Eq. (7), this amounts to testing the following restrictions on the coefficients: β_{0} = β_{0}′, β_{ j } = β_{ j }′, α = α′, j = 1, …, k. Note, if a coefficient, say, β_{ j }′, turns out to be statistically insignificant, we set β_{ j }′ = 0, so the restriction tested in this case is β_{ j } = 0. The oneregime hypothesis is strongly rejected in every regression of Tables 3–6, as the pvalue of the test is always zero. In addition, in 94 out of 128 pairs of coefficients (β_{0}, β_{0}′), (β_{ j }, β_{ j }′), and (α, α′) reported as statistically significant in Regressions 1–16, the unprimed coefficient is larger than its counterpart primed one (in absolute value). This is consistent with the hypothesis that the demand for loans is less elastic at high than at low spreads (see Section 1). Using a quantile regression, GomezBengoechea and Arahuetes (2019) find a similar result, namely the impact of some macroeconomic variables (e.g., public debt and the unemployment rate) on the spread is larger at higher than at lower spreads.
Third, we now turn to the evaluation of Regression 1 using several diagnostic tests. Based on the RESET, which essentially tests for nonlinearities, the results can be considered reliable, as the pvalue of the squared fitted value included as an additional regressor in (7) is 0.50, so the null hypothesis of a loglinear model cannot be rejected. In addition, the coefficient of determination (R^{2}) is high (0.95). Regression 1 also passes the serial correlation test (pvalue = 0.40). This test is based on a GaussNewton regression (GNR) described in MacKinnon (1992, Section 2, pp. 110–112) and in Davidson and MacKinnon (1993, pp. 357–358). Regression 1 fails, however, the structural stability test. The null hypothesis in this case is that the regression coefficients remained stable after 2008, when the financial and economic crisis took effect.^{[7]} This test is also based on a GNR; see MacKinnon (1992, Section 3, p. 114) and Davidson and MacKinnon (1993, pp. 377–381). Finally, there is evidence that the endogeneity problem discussed in Sections 2 and 3 is serious. In particular, the DurbinWuHausman (DWH) test strongly rejects the null hypothesis that the least squares estimates of Regression 1 are consistent (Davidson and MacKinnon 1993, pp. 237–242). The same is true for Regressions 2–4. Note that the DWH test is implemented in Regressions 1–4 by employing the instrumental variables (IVs) used in the estimation of Regressions 9–12, respectively; and since it strongly rejects the null hypothesis in Regressions 1–4, we consider the latter unreliable.
Next, assuming no time effects, we estimate the nonlinear model, Eq. (10), by nonlinear least squares (NLLS) with robust standard errors and report the results in Table 4. Qualitatively, these results do not differ from those of the loglinear model. In particular, note that the evidence supports again the “thresholdvalue hypothesis.” It also supports the hypothesis of partial adjustment, as the estimates of δ_{1} and δ_{2} are between zero and one and are highly significant. It is worth noting that in Regressions 6–8 the estimate of δ_{1} is larger than that of δ_{2}, which suggests that adjustment occurs faster in the highspread regime, in that governmentbond yield spreads are affected more quickly by information on government creditworthiness and financial health in the highspread regime than in the lowspread regime. Note that Regressions 5–6 pass the serialcorrelation test, but are subject to the endogeneity problem discussed earlier. In addition, all of the Regressions of Table 4 fail the structural stability test at the 5percent level. It should be noted, however, that if the whole set of regression coefficients (including those of the dummies for the fixed effects) is tested for stability after 2008, only Regressions 15 and 16 pass the test, perhaps because they are parsimonious.^{[8]} Thus, in Regressions 1–14, we can only opt for testing the stability of only a subset of coefficients, especially those of the macroeconomic variables.
As a reaction to the endogeneity problem addressed earlier, we now estimate Eqs. (7) and (10) by GMM with robust standard errors and report the results in Tables 5 and 6. In Regressions 9 and 10, the efficient GMM estimator, which uses the “optimal” weighting matrix suggested by Hansen and Singleton (1982), fails, apparently because of the relatively small sample size (Hayashi 2000, p. 215), so we use a weighting matrix in line with Jagannathan and Wang (1996). As a consequence, the limiting distribution of the wellknown J statistic for testing the overidentifying restrictions is not chisquared, but nonstandard (RATS User’s Guide 2014, p. 140). In Regressions 11 and 12, however, where the sample size is larger, the “optimal” weighting matrix works well.
Note, first, that in an effort to produce statistically significant estimates, we use a different instrument set in each of the eight regressions of Tables 5 and 6. Second, the sizes (but not the signs) of the estimated coefficients differ across models and data. Third, in most cases, the “thresholdvalue hypothesis” is supported again, most sharply by Regressions 9 and 13–16, especially by the last four, where all coefficients in the lowspread regime are not statistically different from zero (see Table 6). Figure 2 provides a possible explanation for this phenomenon: if the supply curve of loans is almost perfectly elastic at low interest rates, only a negligible increase in the interest rate is required to restore equilibrium after a large increase in demand (see Section 1). Fourth, on the basis of the J statistic, these results can be considered reliable at the 5percent level. Fifth, all of the regressions of Tables 5 and 6 pass the serial correlation test. Sixth, Regressions 9–12 and 15–16 pass the structural stability test, at least for the subset of coefficients of the macroeconomic variables. Thus, since these regressions are estimated by GMM and are thus not expected to suffer from the endogeneity problem discussed in Section 2, they can be considered fairly reliable, and hence usable. Finally, note that in Regressions 15 and 16, which are estimated with data from the wider OECD area, the coefficient of the primary surplus is consistent with our “thresholdvalue hypothesis,” since it has the expected sign and is significant at the highspread regime, but is zero at the lowspread regime. This result, which also emerges in Regression 4, is at variance, however, with that obtained in seven of our regressions (1–3, 5–6, and 9–10), six of which use the data from the 11 Eurozone countries. In these six regressions (1–2, 5–6, and 9–10), contrary to our intuition, the primary surplus, on which the wellknown financial institutions focus their attention, matters only in the lowspread regime. Taken at face value, this finding means that, for the Eurozone countries that suffer from high spreads, the insistence on achieving primary surpluses in order to reduce the debttoGDP ratio may not be an appropriate policy, as pursuing such targets may further deteriorate the economy and increase the probability of default. Cantor and Packer (1996) report a similar result.
5 Summary and conclusions
Broadly speaking, our results support the following conclusions. First, our estimates support the “thresholdvalue hypothesis,” as in most cases the coefficient of a given explanatory variable is larger (in absolute value) in the highspread regime than in the lowspread regime. In particular, based on our preferred regressions (9, 15, and 16), we conclude that an improvement in the macroeconomic environment, e.g., lower unemployment, lower inflation, lower growth of the debttoGDP ratio, less macroeconomic uncertainty, and higher growth of real GDP reduce the spread facing a country (by enhancing its creditworthiness) to a greater extent in highspread situations than in lowspread situations. Regressions 15 and 16 take this to the extreme, since they imply that the spread reacts noticeably to changes in the above variables, as well as in the primary surplus, only in the highspread regime. In terms of Figures 1 and 2, this can happen if the demand for and supply of loans have relatively low elasticities at high rates, and the supply curve is almost perfectly elastic at low rates. This scenario may not be unreasonable in longrun competitive equilibrium, where at relatively low levels of output the constantcost industry assumption holds approximately, but at higher levels of output costs are increasing, thus giving rise to an upwardsloping supply curve.
Second, an improvement in the quality of institutions (e.g., less corruption) lowers the spread to a greater extent in highspread situations than in lowspread situations. We interpret this to imply that quality of institutions is particularly important for countries facing multidimensional problems (e.g., high unemployment), which put them among the highspread countries.^{[9]}
Third, the signs (but not the sizes) of the coefficients are fairly robust to substantial changes in the following: (1) the functional form of the model (loglinear vs. nonlinear); (2) the sample (Panel 1 vs. Panel 2); (3) the method of estimation (NLLS vs. GMM); and (4) the definition of the “fair” value of the spread (mean spread vs. ratingbased spread).
Fourth, the evidence presented in Tables 3–6 suggests that the economic and financial crisis of 2008 caused at least some of the regression coefficients to change.
Fifth, because of the endogeneity problem discussed in Sections 2 and 3, we consider the GMM estimates to be more reliable than the leastsquares ones.
Sixth, the definition of the “fair” spread in year t as the average spread facing all the countries in the panel in that year seems to be more consistent with the rest of the paper, because it introduces less endogeneity and is more supportive of our “thresholdvalue hypothesis,” as Regression 9 demonstrates.
Finally, based on Regressions 13–16, especially the last two, the only two regressions that remained stable as a whole after 2008; and also recalling our caution that the log transformation might not be innocuous after all (see Section 2); we tend to conclude that for the problem at hand the nonlinear model that embodies the partial adjustment hypothesis may be considered preferable to the loglinear one. Nevertheless, the loglinear Regression 9 is also one of our preferred regressions, as it does not seem to suffer from any problems, and is supportive of our “thresholdvalue hypothesis.”
Acknowledgment
The paper is an extensively revised version of the doctoral dissertation of the second author, completed in 2017 at the University of Ioannina, Department of Economics. We thank Professors Angelos A. Antzoulatos and Athanasios G. Noulas for their valuable comments and suggestions. We are also grateful to two anonymous referees of this Journal for their constructive comments, which improved the paper significantly. The usual disclaimer applies.

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

Research funding: None declared.

Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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