Shorter Papers and Comments: The Risk Premium on Italian Government Debt, 1976–88

The behavior of the yield differential between government and nongovernment bonds in Italy between 1976 and 198S is considered. The trend increase of the differential in this period was significantly influenced by the deterioration of public finances, as reflected both by an increase in the supply of government paper relative to nongovernment paper and by a worsening of selected default-risk indicators. The effect of relative supply factors, in turn, was found to be statistically more robust and quantitatively more important than that of risk indicators in explaining movements in yield differentials.

Abstract

The behavior of the yield differential between government and nongovernment bonds in Italy between 1976 and 198S is considered. The trend increase of the differential in this period was significantly influenced by the deterioration of public finances, as reflected both by an increase in the supply of government paper relative to nongovernment paper and by a worsening of selected default-risk indicators. The effect of relative supply factors, in turn, was found to be statistically more robust and quantitatively more important than that of risk indicators in explaining movements in yield differentials.

IN many countries government liabilities are considered the archetypal risk-free asset. Financial market studies therefore use the yield on government paper as a benchmark to measure against the yield of private bonds, pointing to the existence of default risks on private bonds as the reason for the frequently observed yield differential. Under conditions of high and persistent imbalances in public sector finances, however, this assumption requires some revision. As public debt increases, the market may start wondering how the intertemporal budget constraint of the government will be respected, and the possibility of government “default” may be explicitly considered.

A case in point is provided by the Italian experience between 1976 and 1988. From the mid-1970s to the end of the 1980s public debt in relation to gross domestic product (GDP) rose from 50 percent to 100 percent. With the burden of interest payments becoming progressively heavier (reaching 80 percent of the deficit in 1989), several questions have arisen about the existence of a “debt problem” and the possible use of extraordinary measures to solve it, including forms of partial repudiation. Has the risk of default, a term which we define here as also including milder forms of repudiation, already been discounted by the market? Is that risk partially responsible for the current high level of real rates on Italian government paper? Is it perceived as being related to the size of the deficit or the debt or both?

Despite the importance of the issue, indications of the existence of a default-risk premium on the Italian Government’s debt are almost exclusively anecdotal. Although increasing deficits have been shown to have a positive effect on the level of real rates (see Modigliani and Jappelli (1988)), this is not proof of an increase in issuer-specific risk premium, since rising deficits may affect real rates without affecting the risk premium.1

An increasing risk premium on government paper should be signaled by a rise in the yield differential between government and nongovernment assets that are comparable in terms of currency denomination, maturity, and liquidity. In order to assess the existence of a default-risk premium, we analyze the yield differential between fixed-coupon, medium-term paper (BTPs) issued by the government and by Special Credit Institutions (SCIs), the major nongovernment issuer of bonds in Italy.2 The value of this differential, computed on bonds of equal maturity, turned from negative to positive between the 1970s and 1980s. This finding alone does not necessarily imply an increasing risk premium, however, since changes in relative supply can explain changes in the yield differential between assets that are imperfect substitutes.3 Therefore, an interpretation of the observed change in the yield differential requires a comprehensive econometric analysis allowing for separate effects of default-risk indicators, of relative supply effects, and of institutional constraints.

I. Theoretical Underpinnings and Stylized Facts

The empirical model for the yield differential considered in this paper can be derived from the mean-variance approach to portfolio choice. Under simplifying assumptions (most notably on the separability of portfolio decisions), and allowing for different propensities to accept the risk of banks and of the nonbank public, the expected yield differential between BTPs and SCI bonds can be expressed as follows (see Cottarelli and Mecagni (1990)):

δe=ϕ0+ϕ1qg+ϕ2h+ϕ3P*BP*Pb.(1)

In equation (1) the differential is a function of the supply of BTPs relative to the total supply of BTPs and SCI bonds (qg),4 the bond distribution between the nonbank public and banks (h), and a measure of the constraint imposed on portfolio choices by the 1973–86 investment requirement forcing banks to purchase SCI bonds, (P*/B)(P*/Pp).5 In principle, even under the assumption of time-invariant preferences, the model parameters ϕ0, ϕ1, and ϕ2 should change over time, since they depend on the variance-covariance matrix of yields (which changes in time if default risks change) and on the strength of the portfolio constraints. Indeed, it can be shown that the coefficients tend to increase, in absolute value, the more binding is the portfolio constraint.6

In the presence of default risk, the expected yields on the two assets can be expressed as the sum of expected yields in the absence of default (rgNe and rgNe) minus the expected cost of default:

E(rg)=rgNepgtgE(rp)=rpNepptp,(2)

where pg and pp are the probabilities of default, and tg and tp are the costs of default, respectively, for BTPs and SCI bonds. Recalling that δe = E(rg)- E(rp), and by substituting equation (2) into equation (1), we obtain

δ=ϕ0+ϕ1qg+ϕ2h+ϕ3P*BP*Pb+pgtgpptp.(3)

Equation (3) shows that δ, the yield differential computed under the hypothesis of no default (δ=rgNerpNe), is a function of the expected differential cost of default (pgtg-pptp). The default probabilitiespg and pp are not observed; while we assume that pp was constant in the period under consideration,7 we correlate the probability of default on BTPs to a set of indicators of fiscal performance that could trigger confidence crises. Recent research (Alesina, Prati, and Tabellini (1989) and Giavazzi and Pagano (1989)) has suggested two variables that in the past may have significantly affected investors’ confidence in Italian Government paper: the maturity of the debt, and the amount of debt that comes to maturity in each period.8 It is plausible to add to these variables two fiscal policy indicators on which public opinion usually focuses: the ratio of the deficit to GDP and the ratio of the debt to GDP. We therefore assume that

pg=λ0+λ1m+λ2MAD+λ3DFY+λ4DYλ1<0,λ2>0,λ3>0,λ4>0,(4)

where m is the average maturity of government debt, MA is the amount of debt coming to maturity in the period, DF is the deficit, Y is GDP, and D is the stock of public debt. By substituting equation (4) into (3), we obtain an equation relating the yield differential to the distribution of bonds between households and banks, to the relative supply of government paper, to the investment requirement, and to default-risk indicators9

δ=ϕ0+ϕ1qg+ϕ2h+ϕ3P*BP*Pb+ϕ4m+ϕ5MAD+ϕ6DFY+ϕ7DY,(5)

where

ϕ0=ϕ0+tgλ0pptpϕ4=tgλ1ϕ5=tgλ2ϕ6=tgλ3ϕ7=tgλ4.

The sign of the coefficients is expected to be positive for ϕ13 ϕ5, ϕ6, and ϕ7, and negative for ϕ4 the sign of ϕ2 is not determined a priori, depending on the relative propensity of households and banks to purchase government paper (that is, on their relative risk aversion).

The evidence depicted in Figure 1 is consistent with the model. As the net value of tax differential between the average yield of the outstanding stock of BTPs and SCI bonds turned from negative to positive between the 1970s and the 1980s (top panel, solid line), the relative supply of BTPs rose rapidly (central panel), and the above-mentioned risk indicators, especially the public debt and deficit ratios, deteriorated. The differential dropped in 1987–88, following the removal of the above-mentioned investment requirement (bottom panel). This decline proved to be temporary, and the differential rose again, reaching 50 basis points in the first quarter of 1990.

II. Econometric Estimates

Because changes in the average maturity of BTPs and SCI bonds may have heavily influenced the movements of the average yield differentials, the econometric analysis presented in this section was based on differentials measured on bonds of the same residual maturity.10 Our sample covers 49 quarters (from 1976:4 to 1988:4), with a total of 457 observations, The annual averages of these observations are plotted in Figure 1 (top panel, dashed line); the data adjusted for maturity differences confirm the trend increase observed on unadjusted data.

Figure 1.
Figure 1.

Interest Rate Differentials, Relative Supply of BTPs, and Portfolio Investment Requirement on SCI Bonds, 1970–90

(Annual average)

Citation: IMF Staff Papers 1990, 004; 10.5089/9781451930788.024.A007

Source: Bank of Italy, Bolletino Statistico (various issues).a Yield to maturity differential between BTPs and Special Credit Institutions (SCI) bonds (industrial credit). The dashed line refers to the average differential computed on bonds of equal maturity; the figure for 1990 refers to the first quarter.bRatio of the stock of BTPs to the stock of total nonindexed bonds.cThe solid line refers to the minimum investment requirement in SCI bonds over total SCI bonds held by banks. The dashed line refers to the minimum investment requirement in SCI bonds over total SCI bonds and BTPs held by the market.

The individual observations on the yield differential, adjusted for expected inflation, were then regressed on the variables on the right-hand side of equation (5), and on the maturity of each differential. The estimated equation was

δnt=XtΦ+ϕ9fnt+ηnt,(6)

where the subscript nt refers to the differential computed on the n th BTP (that is, a certain BTP issue) observed at time t; Xt is the matrix containing, together with the constant, the seven time-varying regressors included in equation (5); ϕ is the vector of coefficients on these regressors; fnt, is the residual maturity (in months) of each BTP issue at time t; and ηnt is a stochastic error term. Note that ϕ9 cannot be signed a priori and will depend on the relative slope of the term structure of the two different types of bonds.

The estimate of equation (6) was based on a set of simplifying assumptions: first, all parameters were assumed to be time invariant, although the analysis of Section I suggested that they might be time dependent. Second, zero correlation was assumed between the error term and the regressors.11 Finally, it was assumed that

E(ηnt)=0E(ηnt2)=σjt2=σit2E(ηit,ηjt)=0forij(7)
E(ηnt2)E(ηns2)forst.(8)
Table 1.

Panel Data Estimates of the Equation of the Real Yield Differential

article image
Note: Estimated by GLS; 1976:4 to 1988:4; 457 observations. The figures in parentheses are (-statistics, and R2 is the adjusted coefficient of determination.

The portfolio constraint index is introduced in the equations with a three-quarter lag (see Cottarelli and Mecagni (1990)).

Largest percentage change of coefficients between the ninth and tenth iteration (in absolute terms). All equations (except equation (I)) include three seasonal dummies and a dummy on one BTP issue between the first quarter of 1981 and the second quarter of 1982; equation (1) includes only a seasonal dummy (in the second quarter) and the 1981–82 dummy.

These equations imply that the variance of the error term is allowed to vary over time but is assumed to be the same for all observations in the same quarter; in addition, the covariance between disturbances related to different observations is assumed to be equal to zero.

Due to the heteroscedastic nature of its stochastic term, equation (6) was estimated by generalized least squares (GLS).12 The results presented in equation (A) of Table 1 are broadly consistent with the theoretical model of Section II, with only one coefficient (on the average maturity of the debt) having the wrong sign,13 However, the estimates tend to converge rather slowly; as shown in the last row of the table, after ten iterations, at least one coefficient still changes by more than 16 percent, To overcome this problem, which is likely due to high collinearity among regressors, in equation (B), the two variables with lowest t-statistics (that is, the bond distribution and the deficit ratio) are omitted; the convergence indicator improves, but convergence is still not obtained after ten iterations.

Convergence is achieved in specifications (C) and (D). In specification (C) the ratio of debt to GDP is omitted without loss in terms of goodness of fit; however, the sign of the coefficient of the debt maturity is still positive. The debt-to-GDP ratio is reintroduced in specification (D), and the debt maturity is excluded, with a small decline in the adjusted R2 and a slight improvement in the standard error of the equation. Clearly, there are no statistical grounds for preferring specification (D) over specification (C); however, the signs of the coefficients of the former are consistent with the theoretical model, and the magnitude of the coefficients also appears more plausible (see below). No improvement is obtained by reintroducing the deficit ratio (specification (E)) and the bond distribution (specification (F)): in specification (E) the deficit ratio is now significant but has the wrong sign; and specification (F) does not achieve convergence. Starting again from (D), specifications (G) and (H) were estimated to evaluate the relative importance of relative supply vis-à-vis risk indicators, by removing them in turn. Both factors seem relevant, since both equations (G) and (F) are worse in terms of goodness of fit with respect to equation (D). However, the deterioration is more evident when supply factors are removed; indeed, the specification without risk factors, although having a lower adjusted R2 than equation (D), has the lowest standard error of all the specifications and converges rapidly. Finally, in equation (I) the statistically nonsignificant seasonal dummies included in equation (D) are removed without relevant changes in the results.

Given the characteristics of the incomplete panel data used for the regressions, the usual diagnostic tests, particularly those on residual autocorrelation, cannot be applied to the regressions presented in Table 1.14 To circumvent this obstacle, and also as a check on the results discussed so far, equation (I) was re-estimated on aggregate data obtained by averaging the cross-sectional observations for each time period. Consistent with the specification of the error term in equation (8), the aggregate data equation was also estimated by GLS, weighting the observations with an estimate of the (time-varying) variance of the disturbances computed from the residuals of the corresponding panel data estimates. The GLS estimates (Table 2, first column) are remarkably similar to those obtained from the panel data, the main difference being the loss of significance on the coefficient on the BTP maturity; the high level of the adjusted R2 and the inspection of actual and fitted values (Figure 2, top panel) confirm that the model is able to reproduce the main movements of the differential. However, the Durbin-Watson (DW) test signals the presence of serial autocorrelation, which may be indicative of some misspecification.15 As a first check, the equation was re-estimated with the Cochrane-Orcutt technique (second column); after this correction, the coefficients on the risk factors collapse, while the opposite occurs to the coefficient of relative supply.

Table 2.

Aggregate Data Estimates of the Equation of the Real Yield Differential

(1976:4–1988:4)

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Note: Figures in parentheses are t-statistics; R2 is the adjusted coefficient of determination.

Adjusted for first-order residual correlation with the Cochrane-Orcutt technique.

The portfolio constraint is introduced in the equations with a three-quarter lag (see Cottarelli and Mecagni (1990)).

Figure 2.
Figure 2.

Estimated Equations for Real Yield Differential Between BTPs and SCI Bonds, 1977:1 to 1988:4

Citation: IMF Staff Papers 1990, 004; 10.5089/9781451930788.024.A007

aGLS aggregate data estimates not adjusted for serial correlation.bGLS aggregate data estimates adjusted for serial correlation.

On account of these results, equation (H) (which excludes the risk factors) was also estimated on aggregate data. The new estimates (Table 2, third column) show that, since the DW statistic remains low, the presence of risk factors was not the reason for the serial correlation. The adjustment for serial correlation (Table 2, last column) reduces the value and the significance of the coefficient on the BTP maturity but does not substantially alter the other coefficients, which remain close to those of the corresponding panel data estimates; actual and fitted values for this equation are plotted in Figure 2 (lower panel).

The presence of serial correlation in the OLS and GLS aggregate estimates, and possibly also in the corresponding panel data estimates, may be due to several reasons. The first is the static nature of the estimated regressions. The relevance of this factor was confirmed by computing the common factor test for equation (H) of Table 2. The value of the test statistics was 3.20 against a critical value of 9.49 of the χ2 -distribution at the 5 percent probability level. Thus, the hypothesis that the correction for autocorrelation is, in our empirical model, a convenient simplification for a more complex dynamic process cannot be rejected.

An additional reason for autocorrelated residuals may be the imposition of time-invariant parameters on a data-generating process characterized by coefficients varying over time, a concrete possibility, given the discussion in Section I. The stability of the coefficients in the disaggregated equations (I) and (H) in Table 1 was, therefore, checked by recursive GLS. Mixed indications were obtained: while both point and interval estimates for the entire sample and their profiles during the recursions remained approximately within the initial confidence intervals in most cases, for some parameters the assumption of invariance over time appeared questionable.16 Formal Chow tests for the equality of parameters in the two subsamples 1976:4–1983:3 and 1983:2–1988:4 rejected the null of parameter invariance for both specifications. Although indicative, these results should be considered with caution, since the Chow-test distribution is known to be sensitive to the restrictive assumptions of nonstochastic regressors, and of normality and independence of the disturbances. The recursive estimation procedure was therefore also applied to equation (H) on aggregate data, for which the corrections for heteroscedasticity and first-order serial correlation make more appropriate the application of Chow tests. In this case, the hypothesis of parameter constancy was always accepted at the 5 percent level. Even in this instance, however, the addition of the most recent information was accompanied by an increasing value and significance of the relative supply parameter.17

In conclusion, the available empirical evidence seems to confirm the relevance of supply effects, risk indicators, and institutional constraints in explaining the movements in the yield differential between government and SCI bonds, while the relevance of the bond distribution between banks and the nonbank public is not confirmed. The evidence also suggests that supply factors were more important than risk indicators; indeed, the simple specification (H) of Tables 1 and 2, which excludes risk indicators, seems to describe adequately the behavior of the yield differential and passes the statistical diagnostic tests.

As to the multipliers implicit in the point estimates, the effect on the differential of a change in the public debt of Lit 10 trillion at the end of 1988 (around 1 percent of total debt and also of GDP), one third of which was financed by the issuance of BTPs, was computed from equations (I) and (H) of Tables 1 and 2. Although the various specifications differ in the split of the total effect between risk and supply factors, the overall effect appears to be close to 20 basis points in all specifications. Note also that the specifications in which risk factors are present indicate that 80 percent of the overall effect is due to a change in the relative supply of assets.18

III. Conclusions

This paper presented econometric evidence on determinants of the movements of the real yield differential between government and nongovernment paper in Italy, We showed that the increase in the differential observed between the middle of the 1970s and the end of the 1980s was heavily influenced by the deterioration of public finances. This deterioration affected the differential in two ways: first, through an increase in the relative supply of government bonds with respect to SCI bonds, in the context of imperfect substitutability between the two assets; and second, through an increase in the default-risk premium, reflected by changes in selected default-risk indicators (specifically, the ratio of debt to GDP and the share of maturing debt over total debt). However, relative supply factors were also found to be statistically more robust and quantitatively more important than risk indicators in explaining the trend increase in the differential. These conclusions appeared to be robust with respect to changes in the specification of the estimated equation, use of aggregate versus panel data, and different estimation techniques. Some caveats are nonetheless required: the analysis allowed only partially for time dependence of parameters—a likely occurrence in light of the theoretical discussion. Moreover, during the period considered in this paper, market behavior was distorted by an investment requirement on bank portfolios; since the constraint reduced the elasticity of portfolio shares to changes in the interest rate differentials in the sample period, the absolute values of the parameters reflecting the effect of supply and risk factors on the differential were probably overestimated.

REFERENCES

  • Alesina, Alberto, Alessandro Prati, and Guido Tabellini, “Public Confidence and Debt Management: A Model and a Case Study of Italy,” NBER Working Paper 3135 (Cambridge, Massachusetts: National Bureau of Economic Research, October 1989).

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  • Cottarelli, Carlo, and Mauro Mecagni, “The Risk Premium on Italian Government Debt, 1976–88,” IMF Working Paper 90/38 (Washington: International Monetary Fund, April 1990).

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  • Giavazzi, Francesco, and Marco Pagano, “Confidence Crises and Public Debt Management,” CEPR Discussion Paper 318 (London: Centre for Economic Policy Research, May 1989).

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  • Modigliani, F., and T. Jappelli, “The Determinants of Interest Rates in the Italian Economy,” paper presented at the Conference on “Debito pubblico, struttura produttiva e disoccupazione” (Rome: Consiglio Nazionale delie Ricerche, June 1988).

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Carlo Cottarelli is an Economist in the Southern European Division of the European Department. He is a graduate of the University of Siena and holds a graduate degree from the London School of Economics and Political Science. Mauro Mecagni, an Economist in the Southern European Division of the European Department, is a graduate of Bocconi University in Milan. He received his doctorate from the University of Pennsylvania. The authors are grateful to Pierluigi Ciocca, Giampaolo Galli, Giampiero Gallo, Manuel Guitián, Lazaros Molho, Alessandro Penati, William Perraudin, Erich Spitäller, and Ignazio Visco for helpful comments. The reader is referred to Cottarelli and Mecagni (1990) for a detailed discussion of theoretical and empirical issues related to this paper.

1

Indeed, if Ricardian equivalence does not hold, an increase in the deficit (and/or the debt) will tend to increase aggregate demand and the real interest rate for given resources and/or money. In addition, increasing deficits and debt could affect real rates by increasing the “currency-specific” risk premium; an accumulation of debt may increase the likelihood of future monetization and inflation and may push up interest rates on all assets (public and private) denominated in the risky currency.

2

SCIs are financial intermediaries specializing in long-term credit for industrial and real estate investment. Although many of these institutions are public entities, they are largely independent from the government and have their own capital endowment and legal status; their assets are represented mainly by loans to the private sector, and their bonds are rated independently of those of the government.

3

The hypothesis that BTPs and SCI bonds behaved as imperfect substitutes during the period under consideration is sustained here by three arguments. First, during most of the period, a portfolio investment requirement forced banks to purchase SCI bonds, thus reducing their yield and, possibly, their yield variance. Second, although the relative default risk may not have changed in the period, a constant difference in the level of risk is in itself sufficient to induce imperfect substitutability. Third, and most important, the imperfections of Italian bond markets are likely to have deeply influenced the relative liquidity of the two assets and the variance-covariance matrix of their returns, particularly their yield correlation.

4

The expected yield differential δe required by the market increases with qg. This increase will henceforth be referred to as “relative supply effect,” although, in a mean-variance context it should be interpreted as a risk premium, since it corresponds to the increase in the expected yield differential required to move investors away from the minimum-variance portfolio—that is, to accept a higher risk; indeed, δe is zero only when the relative market supply of the two assets corresponds to the minimum-variance portfolio.

5

The regulation on the investment requirement changed over time and became progressively less relevant. In equation (1) the effect of the constraint is considered to be larger, the larger is the investment requirement in relation to the total demand of SCI bonds by banks (P*/Pb) and in relation to the size of the bond market (P*/B).

6

Intuitively, the increase in the coefficients occurs because the demand curves for BTPs and SCI bonds become less elastic to changes in the yield differential; consequently, a larger change in the differential is required to accommodate a shift in supply composition.

7

This is a reasonable assumption, since the profitability and capital adequacy of SCIs remained satisfactory throughout the period.

8

In this context, the probability of a “confidence crisis” is higher when the maturity of the debt is short and when a larger amount of debt comes to maturity in each period.

9

We have already observed that what we call “relative supply effect” could be seen as a component of the risk premium; strictly speaking, what we call “risk factors” should be seen as factors affecting the expected return of government bonds, not the variance (that is, the portfolio risk).

10

Although the term “maturity” will be used here for brevity, the average residual life was considered to allow for different amortization plans of BTPs and SCI bonds. The following procedure was used to derive the maturity-adjusted yield differentials: the yield of individual SCI bonds and BTPs was first collected on a quarterly basis from 1976 to 1988. A linear interpolation of SCI bond yields was then computed for each quarter. This interpolation served two purposes: first, it provided an estimate or SCI bond yields for maturities for which no SCI issue was outstanding; second, it helped to remove the high “noise” in individual SCI bond yields probably connected to market imperfections and to the small outstanding amount of each SCI bond issue. The differentials between the yield on each BTP issue and the corresponding interpolated yield were computed: thus, for each quarter, the number of available observations on the yield differential is equal to the number of outstanding BTP issues.

11

In this respect, the main reason for the inclusion of an error term in equation (6) is associated with the existence of a random disturbance in the demand for Government bonds. Therefore, unless the relative supply of government bonds (qg) is independent of demand conditions, qg in equation (6) is likely to be correlated with ηnt. Since qg = G/(P + G), even if we assume that G (the supply of BTPs) is exogenous, P (the supply of SCI bonds) is likely to be affected by the level of interest rates; finally, when the portfolio model of Section I is included in a macroeconomic model of the economy, it is clear that the interest rate levels, the yield differential, and P (and hence, qg) are determined simultaneously, and that qg is therefore likely to be correlated with ηnt. In what follows, however, we assume that at the quarterly level considered here, the composition of supply is not affected by the level of interest rates and that a random shock in the demand for government bonds is therefore entirely reflected in changes in the yield differential. This assumption is sustained by the long lags characterizing the supply response of SCI bonds to changes in the level of interest rates, due to the lagged response of investments and lengthy administrative procedures in the issue of SCI bonds.

12

To improve efficiency in finite samples, an iterative estimation procedure was implemented. The variance-covariance matrix, initially obtained from ordinary-least-square s (OLS) residuals, was re-estimated based on the GLS estimates, producing residuals then used in a second GLS estimate; all results in Table 1 refer to the tenth iteration. Seasonal dummies were included because of the seasonality of some regressors, A dummy on the differential on one BTP issue between 1981:1 and 1982:2 was also included. The coefficient on this dummy turned out to be very high (between 200 and 300 basis points in all specifications) and was probably due to a measurement error, which was removed in the third quarter of 1982.

13

As mentioned above, the coefficient onfnt (the maturity of the BTP on which the differential is computed) cannot be signed a priori; the fact that this coefficient is always negative in the estimates implies that the term of structure of interest rates, in the sample average, rises more steeply (or declines more gradually) for SCI bonds than for BTPs. This feature may be connected to differences in the relative supply of BTPs and SCI bonds along the maturity axis. Indeed, the supply of BTPs was always relatively larger on shorter maturities.

14

There are n, residuals for each period, but it is not clear what should be considered the lagged value of each residual: the residual on an interest rate differential of the same maturity in the previous period would be economically meaningful but is almost never observed, while the use of the residual on the same BTP issue observed in the previous period (that is, on the residual on the BTP characterized by a specific serial number) could hardly be explained in economic terms.

15

In order to check for the possibility that the autocorrelation of the residuals could be a symptom of spurious regression among nonstationary variables, Phillips-Perron unit root tests were applied to the variables used in the GLS estimation procedures. For all weighted time series, the presence of a unit root was always decisively rejected.

16

In equation (I) the response parameter of the real interest rate differential to the debt-to-GDP ratio was not statistically different from zero in samples until approximately the end of 1983; with the addition of the most recent information, the parameter increased in value and precision. Similarly, in equation (H), the increasing sample size coincided with a gradual increase in value of the relative supply parameter.

17

To allow, at least partially, for time dependence of the parameters, equation (I) was re-estimated on aggregate data by entering the debt ratio in a nonlinear fashion. Indeed, the perception of risk may be connected nonlinearly to public imbalance indicators: increases in the debt-to-GDP ratio may be considered irrelevant when the ratio is low but may attract attention when the ratio is already high. In order to explore this possibility, the response parameter of the debt-to-GDP ratio was allowed to vary according to a logistic function of the level of the ratio itself. The results did not improve upon those presented in Table 2. The significance of relative supply and of the portfolio constraint was confirmed, but the estimates for the debt ratio parameter and for the parameters of the logistic curve were statistically insignificant and nonrobust to selected starting values in sensitivity analysis. Although informative, this attempt to model nonlinearities is by no means conclusive; more attention will have to be dedicated in future research to alternative estimation methods involving switching regimes.

18

The estimate of the effect of changes in the relative supply may appear large and would imply low substitutability between BTPs and SCI bonds of the same maturity. However, as already mentioned, the estimates presented in this paper reflect the dominance in the sample of the portfolio constraint that reduced the substitutability between the two types of bonds; as a consequence, the estimates presented here tend to overestimate the effect on the yield differential of changes in relative supply (and indeed of risk factors as well) in the absence of a portfolio constraint. For a better appreciation of the relative importance of relative supply and risk factors in explaining the movements in the yield differential, the decomposition of the change in the differential between the beginning and the end of the sample period was also computed. Again, all specifications agreed that the overall effect of supply and risk factors was close to 400 basis points; when risk factors were present, they were estimated to account for one third of the overall effect, mainly as a consequence of the increase in the debt ratio. The effect on the yield differential of supply and risk factors was largely offset by the removal of the portfolio constraint, which allowed a decline in the yield differential of over 300 basis points.

IMF Staff papers: Volume 37 No. 4
Author: International Monetary Fund. Research Dept.