بررسی مجدد قابلیت پیش بینی فعالیت های اقتصادی با استفاده از میزان بازده: یک رویکرد غیر خطی

This paper examines the feasibility of using the term structure of nominal interest rates in empirical predictive relationships with future real activity growth serving as the dependent variable. In particular, we will focus on the strength and stability of the spread–output relationship. We employ smooth transition nonlinear models that can accommodate (a) regime switching type nonlinear behaviour and (b) time-varying parameters. We verify that the link exhibits strong threshold effects with respect to near past spread values implying that the relation is sufficiently strong in economic terms if past spread values did not exceed a positive threshold value. Furthermore, we are able to explicitly model time-variation in the preceding effects reaching the conclusion that the importance of the spread as an output predictor has been significantly diminished if not eradicated during recent years. The timing of the change in the information content of the spread appears to be related to a turn in certain monetary policy practices, in particular, the turn towards stronger inflation targeting practices.

Numerous authors have documented that the yield spread, the difference in yields between long-term and short-term interest-bearing-securities, is a consistent predictor of real activity. A significantly positive relationship has been reported employing data for many different economies and for a variety of time periods in the post-war period (see, e.g., Estrella & Hardouvelis, 1991, Estrella & Mishkin, 1997, Plosser & Rouwenhorst, 1994 and Stock & Watson, 1996). The predictive content of the term structure also appears robust to the inclusion of other financial variables such as real interest rates, central bank rates, real money supply or stock prices. Cozier and Tkacz (1994) also confirm that the predictive power of the spread is not simply a cyclical phenomenon that is endogenous to the business cycle since the spread predicts real GDP changes even when the output “gap” is introduced as an additional explanatory variable. One notable feature of the results is that the predictive content of the spread is more important in some countries than others. In two recent papers, Estrella (1998) and Hamilton and Kim (2001) address the theoretical question of why the yield should forecast real activity. Hamilton and Kim show that the contribution of the spread can be decomposed into the effect of expected future changes in short rates and the effect of the term premium where the respective contributions differ. Estrella derives the reduced form relationship between changes in real output and the spread from a simple linear structural model of the economy. This model is of the type specified by Fuhrer and Moore (1995). The core of the model consists of five structural equations: (1) an “accelerationist” Phillips curve, (2) an IS curve relating real output to the long-term real interest rate, (3) a monetary policy reaction function relating the short-term interest rate to deviations of the rate of inflation from target, deviations of output from trend, and the lagged short-term interest rate to capture inertia, (4) the Fisher equation linking the long-term nominal interest rate to the real long-term rate and expected inflation, and (5) the expectations form of the term structure linking the long-term rate to a weighted average of the current short-term rate and rationally formed expectations of future short rates. Estrella (1998) demonstrates the key finding that the coefficient linking changes in real output to the spread derived from this model is dependent upon the coefficients in the monetary reaction function. In particular, the more averse the policy maker is to deviations of inflation from target the smaller the coefficient linking the spread to future output changes. Intuitively, if the policy maker is solely concerned with stabilizing inflation, then inflation and expected inflation will equal target inflation so that from the Phillips curve expected changes in inflation will be zero. Consequently, the spread has no predictive power for future changes in inflation and, in the Estrella model, no predictive content for future changes in real output. This result has the obvious but interesting empirical implication that shifts in the relationship between real output changes, and the spread will occur when shifts in policy regimes occur and that the strength of the relationship between the spread and output change will depend in part on the monetary regime in operation. One feature of previous empirical work is that the relationship between output change and the spread has typically been modelled in a linear framework without investigating the possibility of asymmetric effects or structural shifts. In a recent paper, Galbraith and Tkacz (2000) report empirical evidence that is suggestive that the empirical relationship between the spread and output change may indeed be nonlinear. They test for asymmetry in the predictive content of the spread in the form of a threshold effect. Their study finds evidence, for the United States and Canada, of the presence of an asymmetric impact on the conditional expectation of output growth depending on the position (above or below the threshold) of past spread values, though the reduced form they estimate includes other variables such as changes in government expenditures. Tkacz (2001) employs neural network models1 and documents the improved forecast accuracy (in terms of lower forecasting errors) that can be achieved using nonlinear models to link the yield spread to economic activity. The purpose in the present paper is to examine the yield spread–output link in the United States, Canada and UK by addressing the following two issues: (a) the strength of the link from the spread to real GDP and (b) the stability of the link. Regarding the first issue, we will generalize the analysis of Galbraith and Tkacz (2000) by considering smooth transition nonlinear models. Smooth transition models (STR) have been found to be useful in univariate modelling of many economic time series. Particularly relevant from our perspective is that measures of real activity such as real output or industrial production have been parsimoniously modelled using the STR model (e.g., Ocal & Osborn, 2000 and Terasvirta & Anderson, 1992). STR nonlinear models are less restrictive than their threshold counterparts since they nest two or three threshold models when the transition speed between regimes is too high. Smooth transition between extreme regimes is also an attractive parameterization because it is locally linear and allows easy interpretation. It allows for a continuum of states between the two extremes thus it permits adjustment through intermediate states where the probability of being in each state is determined by the transition function. The “modelling cycle” of STR models, from preliminary nonlinearity testing to final model specification, has been well documented (see, for example, Granger & Terasvirta, 1993 and Terasvirta, 1998). STR models also have the empirical advantages that they are straightforward to estimate through the application of nonlinear least squares (NLS) are empirically tractable and the application of the Newey and West (1987) method of obtaining robust standard errors is not prohibited. Regarding the second issue, research has been limited. Cozier and Tkacz (1994) conduct recursive Chow tests on Canadian output–spread relationships and conclude that at almost every possible sample split we must reject the null hypothesis of parameter stability at the 1% level. Although the authors attributed such instability to the “constant term” pointing to changes in productivity (slow down) commencing in the 1970s, the null hypothesis was still rejected at 1% level around 1983–1984 even though the constant term had been adjusted for a structural break. Haubrich and Dombrosky (1996) and Dotsey (1998) using US data demonstrate that the predictive content of the term spread for economic activity has diminished since 1985 but conclude that the spread still contains significant information pertaining to future real growth. These conclusions were based on linear models. The model of Estrella points to how changes in regime will impact on the relationship between output changes and the spread. In this regard, we can think of discrete changes in regime —such as might occur after the move to an independent Central Bank—as well as changes in the relationship due to the authorities following a nonregime invariant monetary rule. In the latter context, it is interesting that Bec, Ben Salem, and Collard (2000) found that the empirical description of monetary policy by linear Taylor rules could be improved by employing a STR form.2 Due to all the above reasons, there are good a priori grounds for testing for stability of the output spread relationship. To test for this, we will employ the time-varying smooth transition regression (TV-STR) models that can simultaneously test for regime switching and time varying parameters. These models are presented in Lundbergh, Terasvirta, and Van Dijk (2000) and given their general structure they can nest and model in isolation either nonlinearity or parameter nonconstancy or both. The remainder of the paper is structured as follows. Section 2 is a brief presentation and discussion of the nonlinear models we will consider. In Section 3.2, we confirm the significance of the spread as a predictor of output change in a linear relationship and extend the analysis to consider switching regime nonlinearities with respect to different past levels of the spread. Section 3.3 examines the stability of the link between real activity and spread. We first estimate a restricted version of the TV-STR model based on the presence of at least one structural break in the predictive ability of the spread. Then, we estimate the full TV-STR models that provide an integrated picture on the presence of threshold effects and time-varying parameters. Our results support both threshold effects and time-variation in the economic significance of the spread as a leading indicator uncovering the complex nature of the celebrated relationship. Finally, Section 4 is our conclusion.

We have examined the strength of the link between the spread and real activity as well as the stability of the link using US, Canada, and UK data covering at least the last 40 years. Our analysis is based on nonlinear models that allow regime-switching nonlinearity (a feature of the link recently uncovered by Galbraith & Tkacz, 2000) in conjunction with parameter time-variation. We confirm that threshold effects exist for a number of forecasting horizons affecting the power of the spread as a leading indicator while linear or nonlinear specifications are not free of parameter time-variation. Apparently, we are able to establish the presence of a structural break (without arguing that it is the only one) for all three countries which seems to coincide with a lagged recognition of a change in monetary policy attitude towards inflation. Such a claim finds theoretical support by the recent work of Estrella (1998). Although applied analysts may employ sophisticated forecasting models, univariate regressions could be employed as a rule-of-thumb or as a tool providing a first impression on future activity. Our results suggest that applied analysts should be careful with the implementation of linear leading indicator models and our research can be readily extended to other leading indicators as well as to multivariate models. The possibility of false alarms (positive or negative) due to the inadequacy of linear models cannot be ruled out and researchers should always be cautious on the stability of relations across time.