Instability tests in cointegration relationships. An application to the term structure of interest rates

This paper tries to review, from a practitioner's point of view, the recent strand of literature on cointegration tests allowing for structural changes or parameter instability. Thus, we apply several tests using as an example the expectations model of the term structure of interest rates. The results are consistent with the existence of cointegration between the long and the short run Spanish interest rates, with a vector (1,−1), as predicted by the theory. However, there is also evidence of structural instability, mainly at the beginning of 1994, that can be attributed to the financial changes that occurred in Spain as a result of its external commitments in the process of the European Monetary Union.     

Real interest rates: nonlinearity and structural breaks

Real interest rate is a crucial variable that determines the consumption, investment and saving behavior of individuals and thereby acts as a key policy tool that the central banks use to control the economy. Although many important theoretical models require the real interest rates to be stationary, the empirical evidence accumulated so far has not been able to provide conclusive evidence on the mean reverting dynamics of this variable. To resolve this puzzle we re-investigate the stochastic nature of the real interest rates by developing unit root tests for nonlinear heterogeneous panels where the alternative hypothesis allows for a smooth transition between deterministic linear trends around which stationary asymmetric adjustment may occur. When the newly developed panel unit root tests are applied to the real interest rates of the 17 OECD countries, we were able to uncover overwhelming empirical support in favor of mean reversion in the short-run and long-run real interest rates. Therefore, these results show that the conclusions drawn from a miss-specified test that ignores the presence of either nonlinearity, structural breaks or cross sectional dependence can give quite misleading results about the stochastic behavior of the real interest rates.     

Loss aversion and the term structure of interest rates

This article studies how the loss averse behaviour affects the term structure of real interest rates. Since the pro-cyclical conditional expected marginal rate of substitution, implied from the US consumption data, is consistent with the proposition of loss aversion, we incorporate the loss averse behaviour of prospect theory into the consumption-based asset pricing model. Motivated by the similarity between habit formation and the prospect theory utility, habit formation is exploited to determine endogenously the reference point of this behavioural finance utility. The highly curved characteristic of the term structure of real interest rates can thus be captured by the additional consideration of loss aversion. This model also fits the downward sloping volatility of the real yield curve in the data of US Treasury Inflation-Protection Securities (TIPS). Moreover, depending on the effective risk attitude of the representative agent with the loss averse behaviour of prospect theory, our model is capable of generating a normal or an inverted yield curve.     

Risk-aversion and the term structure of real interest rates

The term structure of real interest rates is studied in the context of a consumption-based general-equilibrium model. It is shown that the expectations hypothesis is approximately satisfied for low interest rate volatility. Otherwise the term premia are generally positive.     

Financial integration and the term structure of interest rates

This paper presents a model of the term structure for an open economy. A flexible VAR approach is used to model macroeconomic growth, inflation, short rate and the yield spread. Then the term structure is built given restrictions implied by the no-arbitrage condition. Contrary to previously proposed macrofinance models of the term structure, the model suggested here explicitly accounts for financial and real spillovers between economies. As documented in the paper, foreign macroeconomic factors contain a lot of information about the domestic term structure of yields. Put to data, the model explains the dynamics of yields very well. It provides better out-of-sample forecasting results than the closed economy models. Openness induces more variability in the estimated term premia of yields with shorter maturities.     

The expectations hypothesis, term premia, and the Canadian term structure of interest rates

In this paper monthly data are used over the period 1960:7 to 1995:12 to examine the determinants of term premia implicit in the Canadian T-bill term structure of interest rates. In sharp contrast to U.S. evidence, the conditional variances of Canadian macroeconomic variables are found to be insignificant predictors of term premia in the Canadian T-bill term structure. The conditional variances of U.S. macroeconomic variables, however, are found to be important determinants of Canadian term premia. JEL Classification: E43, G1
L'hypothese des anticipations, les primes de temps et la structure temporelle des taux d'intérêt canadiens. Ce mémoire utilise des données mensuelles de juillet 1960 à décembre 1995 pour examiner les déterminants des primes de temps implicites dans la structure des taux d'intérêt pour les bons du trésor canadiens. Contrairement à ce que l'on trouve aux Etats-Unis, il semble que les variances conditionnelles des variables macroéconomiques canadiennes ne sont pas des prédicteurs utiles de ces primes. Cependant, il appert que les variances conditonnelles des variables macroéconomiques des Etats-Unis sont des déterminants importants de ces primes.     

Markov-switching models,rational expectations and the term structure of interest rates

In order to evaluate the efficiency of the monetary transmission mechanism, we develop the formulas for testing rational expectations theory in the term structure of interest rates with VAR models of stochastically switching regimes in which all the parameters are regime dependent. These formulas are obtained for the strict version of rational expectations as well as for the case where measurement errors are assumed in the expectations relationship. They are extensible to other contexts that involve variables linked by rational-expectations behaviours. The testing procedure is implemented on interest rates of the Spanish inter-bank money market. Measurement errors must be assumed to find signs favourable to the theory.     

Incomplete markets,liquidation risk,and the term structure of interest rates

We analyse the term structure of interest rates in a general equilibrium model with incomplete markets, borrowing constraint, and positive net supply of government bonds. Uninsured idiosyncratic shocks generate bond trades, while aggregate shocks cause fluctuations in the trading price of bonds. Long bonds command a “liquidation risk premium” over short bonds, because they may have to be liquidated before maturity – following a bad idiosyncratic shock – precisely when their resale value is low – due to the simultaneous occurrence of a bad aggregate shock. Our framework endogenously generates limited cross-sectional wealth heterogeneity among the agents (despite the presence of uninsured idiosyncratic shocks), which allows us to characterise analytically the shape of the entire yield curve, including the yields on bonds of arbitrarily long maturities. Agents? desire to hedge the idiosyncratic risk together with their fear of having to liquidate long bonds at unfavourable terms implies that a greater bond supply raises the level of the yield curve, while an increase in the relative supply of long bonds raises its slope.     

The term structure of interest rates and the Mexican economy

Can the yield spread, which has been found to predict with surprising accuracy the movement of key macroeconomic variables of developed countries, also predict such variables for a developing country experiencing economic turmoil? This article presents empirical results that suggest significant forecasting ability for the yield spread for segments of the Mexican economy during the 1995–1997 period of economic volatility. The actual and predicted variable changes sometimes conflict with those experienced by developed countries in part because of the unusually close relationship between the Mexican Treasury and the Banco de México. Consequently, analysts and policy officials may exploit the forecast potential of the yield spread, but only in the context of evolving institutional considerations.     

Regime shifts in the Danish term structure of interest rates

Within a bivariate VAR model allowing for two-state Markov regime switching we test and evaluate the Expectations Theory (ET) of the term structure using Danish 1- and 3-months interest rates covering the period 1976–1997. A regime-shift approach is used in order to account for the change in monetary policy and the 1992–93 exchange rate crises that occured during this period. The basic findings are that these episodes did change the term structure, and, although we do find departures from the ET, several of the implications of the theory are consistent with the data, especially in the later part of the sample. First version received: June 1997/Final version received: March 1998     

Fractional cointegration and the term structure

According to the expectations theory of the term structure of interest rates, the yield spread between long-term and short-term interest rates is an optimal predictor of future changes in short rates over the long-run. Results concerning the empirical validity of this hypothesis are not unanimous. These contradictions may be due to the fact that the traditional concept of cointegration is too restrictive. We refer here to the concept of fractional cointegration introduced by Granger (1986). We study the expectations theory by testing for the existence of a (fractional) cointegration relationship between short-term and long-term interest rates. There is evidence of fractional cointegration between interest rates for the G7 countries, with the exception of Germany.First version received: July 2002 / Final version received: July 2003We thank two anonymous referees for very helpful and detailed comments.     

An empirical note on Euro market interest rates,domestic interest rates and the expectations theory of the term structure

An empirical analysis of recent monthly data for 8 currencies indicates that the performance of the expectations theory to explain the short term maturity spectrum of Euro interest rates is rather good in most cases and that it is not related to the degree of integration of Euro and domestic markets.     

Nonstationary term premia and cointegration of the term structure

This paper proposes a model of the term structure with nonstationary term premia which exhibit a factor structure. This explains the common empirical finding of a cointegrating rank smaller than the one predicted by the rational expectations hypothesis of the term structure. An application to German interest rate data yields easily interpretable results.     

The information content of the term structure of interest rates

The profitability of chartist trading rules on foreign exchange markets is still under debate. Since simple technical trading rules may not adequately capture the complex phenomenon of chartist trading, this study focuses on the prominent head-and-shoulder pattern as a representative trading rule which incorporates various ‘technical’ ideas such as smoothed trends, trend reversal, resistance levels, and volatility clustering. For various combinations of the building blocks of head-and-shoulder definitions the result is generally negative: Returns to head-and-shoulder trading rules are not significantly positive - and if there is any evidence for non-zero returns at all, then it is evidence for negative returns.     

Time-series model forecasts and structural breaks: evidence from Spanish pre-EMU interest rates

Analysis of the future behaviour of economic variables can be biased if structural breaks are not considered. When these structural breaks are present, the in-sample fit of a model gives us a poor guide to ex ante forecast performance. This problem is true for both univariate and multivariate analysis and can be extremely important when co-integration relationships are analysed. The main goal of this article is to analyse the impact of structural breaks on forecast accuracy evaluation. We focus on forecasting several interest rates from the Spanish interbank money market. In order to carry out the analysis, we perform two forecasting exercises: (a) without structural breaks and (b) when structural breaks are explicitly considered. We use new sequential methods in order to estimate change-points in an endogenous way. This method allows us to detect structural breaks in all four rates in May 1993. However, the effects of these breaks are not very strong, since we found scarce gains in forecasting accuracy when the structural breaks are included in the models.     

Bayesian estimation of cointegrating thresholds in the term structure of interest rates

Threshold Error Correction Models are used to analyse the term structure of interest Rates. The paper develops and uses a generalisation of existing models that encompasses both the Band and Equilibrium threshold models of [Balke and Fomby ((1997) Threshold cointegration. Int Econ Rev 38(3):627–645)] and estimates this model using a Bayesian approach. Evidence is found for threshold effects in pairs of longer rates but not in pairs of short rates. The Band threshold model is supported in preference to the Equilibrium model.

Imports and exports in 50 countries: Tests of cointegration and structural breaks

This paper provides new evidence on the long-run convergence between imports and exports in 50 countries over the quarterly period 1973:2 to 1998:1. Cointegration analyses are based on the Johansen [Johansen, S. (1995). Likelihood-based inference in cointegrating vector autoregressive models. New York: Oxford University Press.] and the Stock and Watson [J. Am. Stat. Assoc. 83 (1988) 1097.] system approaches. Evidence of stability of the cointegration space is examined using the SupF test developed by Hansen [J. Bus. Econ. Stat. 10 (1992) 321]. Based on the Johansen technique, we find evidence in favor of cointegration in 35 of the 50 countries. In addition, cointegration is confirmed for all countries (except Mexico) using the Stock and Watson test. This finding indicates that macroeconomic policies have been effective in the long-run and suggests that these countries are largely not in violation of their international budget constraint. We find evidence that in most of the countries where the slope coefficient on the export variable is positive, the cointegrating coefficient is also unity. The cointegration space appears stable for most of the countries. Nonetheless, the results suggest that countries in the regions of the Middle East, Latin America, and Europe have cointegrating relations that are more unstable than those in other regions.