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A lot, including a few things you may not expect. Previous studies find that the term spread forecasts GDP but these regressions are unconstrained and do not model regressor endogeneity. We build a dynamic model for GDP growth and yields that completely characterizes expectations of GDP. The model does not permit arbitrage. Contrary to previous findings, we predict that the short rate has more predictive power than any term spread. We confirm this finding by forecasting GDP out-of-sample. The model also recommends the use of lagged GDP and the longest maturity yield to measure slope. Greater efficiency enables the yield-curve model to produce superior out-of-sample GDP forecasts than unconstrained OLS regressions at all horizons.

The behavior of the yield curve changes across the business cycle. In recessions, premia on long-term bonds tend to be high and yields on short bonds tend to be low. Recessions, therefore, have upward sloping yield curves. Premia on long bonds are countercyclical because investors do not like to take on risk in bad times. In contrast, yields on short bonds tend to be procyclical because the Federal Reserve lowers short yields in recessions in an effort to stimulate economic activity. For example, for every 2 percentage point decline in GDP growth, the Fed should lower the nominal yield by 1 percentage point according to the Taylor (1993) rule. Inevitably, recessions are followed by expansions. During recessions, upward sloping yield curves not only indicate bad times today, but better times tomorrow. Guided from this intuition, many papers predict GDP growth in OLS regressions with the slope of the yield curve, usually measured as the difference between the longest yield in the dataset and the shortest maturity yield.1 The higher the slope or term spread, the larger GDP growth is expected to be in the future. Related work by Fama (1990) and Mishkin, 1990a and Mishkin, 1990b shows that the same measure of slope predicts real rates. The slope is also successful at predicting recessions with discrete choice models, where a recession is coded as a one and other times are coded as zeros (see Estrella and Hardouvelis, 1991 and Estrella and Mishkin, 1998). The term spread is also an important variable in the construction of Stock and Watson (1989)'s leading business cycle indicator index. Despite some evidence that parameter instability may weaken the performance of the yield curve in the future (see comments by Stock and Watson, 2001), it has been amazingly successful in these applications so far. For example, every recession after the mid-1960s was predicted by a negative slope—an inverted yield curve—within 6 quarters of the impending recession. Moreover, there has been only one “false positive” (an instance of an inverted yield curve that was not followed by a recession) during this time period. Hence, the yield curve tells us something about future economic activity. We argue there is much more to learn from the yield curve when we explicitly model its joint dynamics with GDP growth. Our dynamic model also rules out arbitrage possibilities between bonds of different maturities and thus imposes more structure than the unrestricted OLS regression framework previously used in the literature. While OLS regressions show that the slope has predictive power for GDP, it is only an incomplete picture of the yield curve and GDP. For example, we would expect that the entire yield curve, not just the arbitrary maturity used in the construction of the term spread, would have predictive power. Using information across the whole yield curve, rather than just the long maturity segment, may lead to more efficient and more accurate forecasts of GDP. In an OLS framework, since yields of different maturities are highly cross-correlated, it is difficult to use multiple yields as regressors because of collinearity problems. This collinearity suggests that we may be able to condense the information contained in many yields down to a parsimonious number of variables. We would also like a consistent way to characterize the forecasts of GDP across different horizons to different parts of the yield curve. With OLS, this can only be done with many sets of different regressions. These regressions are clearly related to each other, but there is no obvious way in an OLS framework to impose cross-equation restrictions to gain power and efficiency. Our approach in this paper is to impose the absence of arbitrage in bond markets to model the dynamics of yields jointly with GDP growth. The assumption is reasonable in a world of hedge funds and large investment banks. Traders in these institutions take large bond positions that eliminate arbitrage opportunities arising from bond prices that are inconsistent with each other in the cross-section and with their expected movements over time. Based on the assumption of no-arbitrage, we build a model of the yield curve in which a few yields and GDP growth are observable state variables. This helps us to reduce the dimensionality of a large set of yields down to a few state variables. The dynamics of these state variables are estimated in a vector autoregression (VAR). Bond premia are linear in these variables and are thus cyclical, consistent with findings in Cochrane and Piazzesi (2002). Our yield-curve model leads to closed-form solutions for yields of any maturity which belong to the affine class of Duffie and Kan (1996). We address two main issues regarding the predictability of GDP in the no-arbitrage framework. We first demonstrate that the yield-curve model can capture the same amount of conditional predictability that is picked up by simple OLS regressions. However, OLS approaches and the forecasts implied by our model yield different predictions. Using the term structure model, we attribute the predictive power of the yield curve to risk premium and expectations hypothesis components and show how the model can generate the OLS coefficient patterns observed in data in small samples. The second question we investigate is how well GDP growth can be predicted out-of-sample using term structure information, where the coefficients in the prediction function are either estimated directly by OLS, or indirectly, by transforming the parameter estimates of our yield-curve model. We find that our yield-curve model has several main advantages over unrestricted OLS specifications. First, the theoretical framework advocates using long-horizon forecasts implied by VARs. While some authors, like Dotsey (1998) and Stock and Watson (2001), use several lags of various instruments to predict GDP, to our knowledge the efficiency gains from long-horizon VAR forecasts have not previously been considered by the literature. Second, the estimated yield-curve model guides us in choosing the maturity of the yields that should be most informative about future GDP growth. Our results show that if we are to choose a single yield spread, the model recommends the use of the longest yield to measure the slope, regardless of the forecasting horizon. This result requires the framework of the term structure model to determine, in closed form, the predictive ability of any combination of yields of any maturity. Third, the model predicts that the nominal short rate contains more information about GDP growth than any yield spread. This finding stands in contrast to unconstrained OLS regressions which find the slope to be more important. This prediction of the model is confirmed by forecasting GDP growth out-of-sample. Finally, our model is a better out-of-sample predictor of GDP than unrestricted OLS. This finding is independent of the forecasting horizon and of the choice of term structure regressor variables. The better out-of-sample performance from our yield-curve model is driven by the gain in estimation efficiency due to the reduction in dimensionality and imposing the cross-equation restrictions from the term structure model. The rest of this paper is organized as follows. Section 2 documents the relationship between the yield curve, GDP growth and recessions. Section 3 describes the yield-curve model and the estimation method. Section 4 presents the empirical results. We begin by discussing the parameter estimates, perform specification tests, and then show how the model characterizes the GDP predictive regressions. We also present a series of small sample simulation experiments to help interpret the results of the model. We show that the model leads to better out-of-sample forecasts of GDP than unconstrained OLS regressions in Section 5. Section 6 concludes. We relegate all technical issues to Appendix A.

We present a model of yields and GDP growth for forecasting GDP. Our approach is motivated from term structure approaches for pricing bonds in a no-arbitrage framework. The model is easily estimated and gives us a number of advantages to forecasting future economic growth. First, the model advocates using a select number of factors to summarize the information in the whole yield curve. These factors follow a VAR, and long-term forecasts for these factors and GDP are simply long-horizon forecasts implied by the VAR. Second, the yield-curve model guides us in choosing the right spread maturity in forecasting GDP growth. We find that the maximal maturity difference is the best measure of slope in this context. Third, the nominal short rate dominates the slope of the yield curve in forecasting GDP growth both in- and out-of-sample. We find that the factor structure is largely responsible for most of the efficiency gains resulting in better out-of-sample forecasts. In contrast, our term structure approach allows us to show that risk premia not captured by the factor dynamics matter less in forecasting GDP. However, an unanswered question is whether we can improve on these yield curve forecasts by combining both term structure information and other macro variables. Furthermore, a better out-of-sample test than just using U.S. data is to use international data to test the efficiency gains of factor approaches implied by a term structure model.