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We use Bayesian time-varying parameters VARs with stochastic volatility to investigate changes in the marginal predictive content of the yield spread for output growth in the United States and the United Kingdom, since the Gold Standard era, and in the Eurozone, Canada, and Australia over the post-WWII period. Overall, our evidence does not provide much support for either of the two dominant explanations why the yield spread may contain predictive power for output growth, the monetary policy-based one, and Harvey's [1988. The real term structure and output growth. Journal of Financial Economics 22, 305–333] ‘real yield curve’ one. Instead, we offer a new conjecture.

Since the end of the 1980s, a large literature has investigated the predictive content of the long–short nominal yield spread for both inflation, and for the rates of growth of GDP and individual expenditure components.1While the spread's predictive content for inflation, once having controlled for lagged inflation, has almost uniformly been found to be low or non-existent, several papers have documented how, both in the United States, and in other OECD countries, the yield spread appears to have contained information on future output growth independent of that contained in other macroeconomic aggregates, thus allowing forecasting improvements upon models including standard predictors like indices of leading indicators, inflation measures, etc. 2 Especially intriguing is the finding, documented by Estrella and Hardouvelis (1991) and Plosser and Rouwenhorst (1994), that the informational content of the spread appears to have been independent of both nominal and real short-term interest rates, thus providing prima facie evidence that the spread's information may be (at least partly) independent of monetary policy actions. 3 Interestingly, as first documented by Dotsey (1998) and Estrella et al. (2003), in the United States the marginal predictive content of the spread for output growth appears to have largely disappeared in recent years. 4 Although the predictive content of the spread for output growth has now been systematically documented for almost two decades, such finding is still to be regarded essentially as a stylised fact in search of a theory. Currently, there are two main explanations why the nominal yield spread may contain information on future output growth, one dealing with the workings of monetary policy, the other with the interaction between intertemporal consumption smoothing, on the one hand, and the stochastic properties of inflation, as determined by the underlying monetary regime, on the other. A simple, ‘introductory macro’ description of the first explanation runs as follows. A temporary monetary tightening can be expected to produce two results: first, a recession; and second, a fall in inflation, and therefore in inflation expectations. To the extent that the tightening – i.e., the increase in the short rate – is temporary, the fall in inflation expectations automatically guarantees that long rates increase less than short rates, thus causing a flattening of the yield curve. By the same token, a symmetrical argument explains why a monetary expansion causes both a steepening of the yield curve and an economic expansion. An important point to stress is that, according to this explanation, the predictive content of the spread for future output growth is entirely spurious, in the sense that fluctuations in both the spread and future output growth are caused by a third variable, monetary policy actions. According to the second explanation,5 on the other hand, the informational content of the spread for output growth is not spurious, but rather intrinsic – to put it differently, it finds its origin in the workings of the deep structure of the economy, rather than in monetary policy actions. According to such a view, first clearly articulated by Harvey (1988), based on standard intertemporal consumption smoothing arguments, the predictive content of the spread pertains to the real term structure, rather than to the nominal one. The fact that the predictive content intrinsic to the real term structure translates, or does not translate, to the nominal term structure then crucially depends on the stochastic properties of inflation – in particular, inflation persistence – and therefore, ultimately, upon the nature of the underlying monetary regime. If inflation is, in the limiting case, a pure random walk, so that innovations are entirely permanent, a shock to inflation today shifts expected inflation at all horizons by an identical amount, thus leaving the nominal yield curve, for a given real yield curve, unaffected. In this case the predictive content of the spread intrinsic to the real yield curve translates one-to-one to the nominal yield curve. If, on the other hand, inflation has little persistence – as it was the case under metallic standards, and currently is the case for several inflation-targeting countries 6 – a shock to inflation uniquely increases short-term inflation expectations, leaving instead long-term expectations unaffected, and therefore, for a given real yield curve, by increasing short rates and leaving long rates unchanged, it twists the nominal yield curve, thus ‘blurring’ the informational content of the real curve. Which, if either, of the two explanations is correct? Or might it be the case that they are both wrong? As stressed by Bordo and Haubrich (2004, p. 3), [w]hether the yield curve's ability to predict [output growth] emerges as a general property of the American business cycle or depends sensitively on the structure of the economy, financial markets, and monetary policy seems an obvious question. Particularly since a subtext of the yield curve's predictive ability has been the instability of its relationship with output growth, looking at a long time series seems warranted. A broader historical perspective may also shed some light on the reasons behind the yield curve’s ability to predict future output – for example, one simply cannot ascribe twists in the yield curve during the 1880s to an FOMC ratcheting up short-term rates. (emphasis added) Bordo and Haubrich hit upon a crucial point: if one wants to discriminate between the two previously discussed theories, (s)he has to examine sample periods during which the two theories are not observationally equivalent, and, as a simple matter of logic, the chance of finding such periods increases (1) with the length of the sample period considered; and (2) with the variety of monetary arrangements examined, for the simple reason that, in both explanations, monetary policy plays, either directly or indirectly, a crucial role. Under this respect, both the recent experience of inflation targeting countries, and the U.S. and U.K. experience under metallic standards, should be regarded as potentially valuable, as they should provide sufficient variation in the monetary policy rule to discriminate between the two rival explanations. It is, therefore, quite surprising that – with the single exception of Kessel (1965) – Bordo and Haubrich (2004) is the only paper to have ever attempted a systematic investigation of (changes over time in) the predictive content of the spread based on long spans of data. Although conceptually pathbreaking, the work of Bordo and Haubrich (2004) suffers; however, in our opinion, from a crucial drawback, in that it only investigates whether the yield spread contains information beyond that already encoded in lagged output growth, being therefore by definition silent on the crucial issue of whether the spread contains information which is not already encoded in other macroeconomic variables, first and foremost measures of the monetary policy stance such as short-term interest rates. Such a problem is unfortunately quite common in the literature, with several papers only having one regressor, the spread, 7 and another group of papers having, like Bordo and Haubrich (2004), only one additional regressor beyond the spread, the lagged dependent variable. 8 1.1. Issues addressed in the present work Based on data for the United States and the United Kingdom, since the Gold Standard era, and the Eurozone, Canada, and Australia over the post-WWII period (Fig. 1, Fig. 2 and Fig. 3 show the raw data used in this paper), in this paper we use Bayesian time-varying parameters VARs with stochastic volatility along the lines of Cogley and Sargent (2005), first, to re-examine the crucial issue in this literature: • Once controlling for the information contained in other regressors – in particular, in measures of the monetary policy stance, such as the short rate – Does the yield spread still contain information useful for predicting output growth?Although, in principle, a proper attempt to provide an answer to this question would require an examination of every available macroeconomic indicator, in this paper we limit ourselves to inflation, output growth, and a short rate. There are two reasons for this. First, as a matter of practicality: the time-varying Bayesian methodology used herein is extremely computer intensive, to the point that expanding the benchmark data set beyond four variables would become prohibitively cumbersome.9 Second, it can reasonably be argued that these three variables provide a sufficiently exhaustive statistical summary of the properties of any advanced economy,10 so that they should provide a reasonably robust benchmark against which to measure the informational content of the spread. We then tackle three additional issues: • Has the marginal predictive content of the spread remained broadly unchanged over time, or has it exhibited significant time-variation? • In case it has changed over time, do such changes bear any clear relationship with changes in the underlying monetary regime? • Does our evidence clearly falsify/reject either of the two explanations we previously discussed in Section 1.1? 1.2. Key results Based on Stock and Watson's classical time-varying parameters (henceforth, TVPMUB) methodology, we detect strong evidence of random-walk time-variation, against the null of time-invariance, in output growth regressions for all countries, with comparatively large median-unbiased estimates of the overall extent of parameter drift. These results provide strong prima facie evidence – but, it is important to stress, only prima facie evidence – that both output growth's overall extent of predictability, and the marginal predictive power of individual regressors for output growth, may have changed over time. A proper assessment of both issues necessarily calls, however, for multivariate methods, as it requires a (time-varying) estimate of the entire spectral density matrix of the data. Moving to a multivariate context, overall our evidence does not provide full support for either of the two previously discussed explanations why the yield spread may contain predictive power for output growth. On the one hand, the ‘real yield curve’ explanation is contradicted by the fact that in both the United States, the United Kingdom, and Canada over the post-WWII era, the broad decrease in inflation persistence we identify for all the three countries over the second part of the sample was not accompanied by a corresponding decrease in the marginal predictive content of the spread compared to the information already encoded in past output growth. The monetary policy-based explanation, on the other hand, appears incompatible with the fact that, for example, results for the United States during both the interwar and the post-WWII periods clearly point towards several periods during which the spread exhibited predictive power for output growth over and above that already encoded in the short rate. In particular, during both the Volcker recession, and the 2000–2001 one, the spread clearly appears to have possessed additional information compared with that contained in the simplest measure of the monetary policy stance. The paper is organised as follows. The next section presents preliminary evidence on the presence of (random-walk) time-variation in univariate regressions for output growth, based on the Stock–Watson time-varying parameters median-unbiased estimation methodology. Section 3 describes the Bayesian methodology we use to estimate time-varying parameters VARs with stochastic volatility, while Section 4 discusses the methodology we use to compute, at each point in time, measures of overall and marginal predictability at the various horizons. Section 5 presents the empirical evidence. Section 6 discusses the implications of our findings for the two explanations discussed in the Introduction, and proposes yet another conjecture. Section 7 concludes.

In this paper we have used Bayesian time-varying parameters VARs with stochastic volatility to investigate changes in the marginal predictive content of the yield spread for output growth in the United States and the United Kingdom, since the Gold Standard era, and in the Eurozone, Canada, and Australia over the post-WWII period. Overall, our evidence has not provided full support for any of the two dominant explanations for why the yield spread may contain predictive power for output growth, the monetary policy-based one, and Harvey's (1988) ‘real yield curve’ one.