Vector autoregressions and reduced form representations of DSGE models

The performance of dynamic stochastic general equilibrium models is often tested against estimated VARs. This requires that the data-generating process consistent with the DSGE theoretical model has a finite order VAR representation. This paper discusses the assumptions needed for a finite order VAR(p) representation of a DSGE model to exist. When a VAR(p) is only an approximation to the exact infinite order VAR, the truncated VAR(p) may return largely incorrect estimates of the impulse response function. The results do not hinge on small-sample bias or on incorrect identification assumptions. But the bias introduced by truncation can lead to bias in the identification of the structural shocks. Identification strategies that work in the exact VAR representation perform poorly in the truncated VAR.     

NEW EVIDENCE CONCERNING THE EXPECTATIONS THEORY FOR THE SHORT END OF THE MATURITY SPECTRUM

This paper re-examines the evidence rejecting the expectations theory of the term structure. Weekly, monthly, and quarterly data on three- and six-month interest rates are employed for five subperiods—1910–1914, 1919–1933, 1934–1959, 1959–1978, and 1979–1989. Econometric techniques are used to correct standard errors for overlapping data and for heteroscedasticity. Findings indicate that the weekly and monthly data are consistent with a weak form of the expectations hypothesis in which the yield curve has substantial predictive power for short rates for each subperiod except 1934–1959 and 1979–1989. Results for the period before the founding of the Federal Reserve indicate that a strong version of the expectations hypothesis cannot be rejected in which the joint hypothesis of rational expectations and expectations theory is hypothesized. The use of cointegration tests and an error-correction model framework to determine whether short and long rates have a common stochastic trend indicates that long and short rates are cointegrated.     

THE EXPECTATIONS HYPOTHESIS OF THE TERM STRUCTURE IN EUROCURRENCY MARKETS

This paper uses daily eurocurrency deposit rates for six currencies to extend previous research on the expectations hypothesis of the term structure. The reported results confirm earlier findings that the behavior of long term interest rates is perverse. For example, it is shown that in the case of five-year eurocurrency deposits denominated in US dollars, German marks and Swiss francs, the coefficient relating the excess holding period return to the yield spread between long and short term securities exceeds one, implying that long term rates tend to move in a direction opposite to the prediction of the expectations hypothesis. This study also employs a variety of techniques to examine the temporal stability of the coefficient in both the long and short maturity regressions used in testing the expectations hypothesis. While we do find instability, the nature of the parameter variation is markedly different from that found in foreign exchange markets when similar tests are employed.     

New Hope for the Expectations Hypothesis of the Term Structure of Interest Rates

Survey data on interest rate expectations permit separate testing of the two alternative hypotheses in traditional term structure tests: that the expectations hypothesis fails, and that expected future interest rates are ex post inefficient forecasts. We find that the source of the spread's poor predictions of future interest rates varies with maturity. At short maturities the expectations hypothesis fails. At long maturities, however, changes in the yield curve reflect changes in expected future rates one-for-one, an implication of the expectations hypothesis. This result confirms earlier findings that long rates underreact to short rates, but now it cannot be attributed to term premia.     

DIVERGENCE OF OPINION AND LONG‐TERM PERFORMANCE OF INITIAL PUBLIC OFFERINGS

Miller's hypothesis posits that divergence of opinion can lead to asset overvaluation and subsequent long‐term underperformance in markets (such as initial public offerings [IPOs]) with restricted short‐selling. Consistent with this hypothesis, we find that early‐market return volatility, a proxy for divergence of opinion, is negatively related to subsequent IPO long‐term abnormal returns. This relation holds after accounting for other factors that previous studies suggest affect long‐term abnormal returns for IPOs (including another proxy for divergence of opinion). Moreover, we find that this relation is stronger in IPO markets than in non‐IPO markets (where short‐selling restrictions are less stringent), again consistent with Miller's hypothesis.     

Predicting Long‐Term Financial Returns: VAR versus DSGE Model—A Horse Race

This paper considers a U.S. institutional investor who is implementing a long‐term portfolio allocation using forecasts of financial returns. We compare the predictive performance of two competing macrofinance models—an unrestricted vector autoRegression (VAR) and a fully‐structural dynamic stochastic general equilibrium (DSGE) model—for horizons up to 15 years. Although the performances are similar for short horizons, the DSGE model outperforms the VAR at forecasting financial returns in the long term. This model also generates substantially higher Sharpe ratios. Although it contains fewer unknown parameters, it benefits from economically grounded restrictions that help anchor financial returns in the long term.     

Domestic variance and international comovement bonds tests of interest rates

This article demonstrates that long rates exhibit both domestic excess variance and international excess comovement compared to fundamental yields derived from short rates under the rational expectations theory of term structure. The results are consistent for all countries sampled: the US, UK, Canada, Germany, and Japan. Probing deeper, long rates are found to “overreact” to domestic expected future inflation and/or short real rates both of which are the underlying components of the short nominal rate according to the Fisher hypothesis. Since inflation rates as well as short real rates are highly correlated between countries, the excess volatility in long rates translates into excess covariance (“co-overreact”) internationally.     

Testing the expectations hypothesis when interest rates are near integrated

Nominal interest rates are unlikely to be generated by unit-root processes. Using data on short and long interest rates from eight developed and six emerging economies, we test the expectations hypothesis using cointegration methods under the assumption that interest rates are near integrated. If the null hypothesis of no cointegration is rejected, we then test whether the estimated cointegrating vector is consistent with that suggested by the expectations hypothesis. The results show support for cointegration in 10 of the 14 countries we consider, and the cointegrating vector is similar across countries. However, the parameters differ from those suggested by theory. We relate our findings to existing literature on the failure of the expectations hypothesis and to the role of term premia.     

The skinny on the 2008 naked short-sale restrictions

On July 15, 2008, the US Securities and Exchange Commission announced temporary restrictions on naked short sales of the stocks of 19 financial firms. The restrictions offer a unique empirical setting to test Miller’s (1977) conjecture that short-sale constraints result in overpriced securities and low subsequent returns. Consistent with Miller’s overpricing hypothesis, we find evidence of a positive (negative) market reaction to the announcement (expiration) of the short-sale restrictions. Announcement returns are higher for firms that appear to be subject to more naked short selling in the days immediately preceding the announcement of the restrictions. The restrictions are successful in eliminating naked short sales for the restricted stocks, but naked short sales increase dramatically for a closely matched sample of financial firms during the restricted period. We also find that the restrictions negatively impact various measures of liquidity, including bid-ask spreads and trading volume. From a public policy perspective, our findings suggest that, at a minimum, policymakers should pause when considering further short sale restrictions.     

What does a technology shock do? A VAR analysis with model-based sign restrictions

This paper estimates the effects of technology shocks in VAR models of the U.S., identified by imposing restrictions on the sign of impulse responses. These restrictions are consistent with the implications of a popular class of DSGE models, with both real and nominal frictions, and with sufficiently wide ranges for their parameters. This identification strategy thus substitutes theoretically motivated restrictions for the atheoretical assumptions on the time-series properties of the data that are key to long-run restrictions. Stochastic technology improvements persistently increase real wages, consumption, investment and output in the data; hours worked are very likely to increase, displaying a hump-shaped pattern. Contrary to most of the related VAR evidence, results are not sensitive to a number of specification assumptions, including those on the stationarity properties of variables.     

Structural breaks, parameter uncertainty, and term structure puzzles

We show that uncertainty about parameters of the short rate model can account for the rejections of the expectations hypothesis for the term structure of interest rates. We assume that agents employ Bayes rule to learn parameter values in the context of a model that is subject to stochastic structural breaks. We show that parameter uncertainty also implies that the verdict on the expectations hypothesis varies systematically with the term of the long bond and the particular test employed, in the same way that is found in empirical tests.     

Incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions

This article extends Merton's (1987) asset-pricing model under incomplete information to consider the situation when investors' beliefs are divergent and short selling is restricted. The article finds that the diversity of beliefs increases the mean variance inefficiency of the market portfolio and the shadow cost of information. However, the inefficiency of the market portfolio due to divergent beliefs is mitigated by short-sale restrictions. The article also finds that the effect of firm size is intertwined with the residual return variance risk. Consistent with the findings of Levy (1978) and Carroll and Wei (1988), the residual return variance plays an important role in determining the risk and risk premium of each security. Finally, the shadow cost of information is larger and the equilibrium security return is higher when expectations are more diverse. And the effects of divergent beliefs on both information cost and required rates of returns are negatively related to the relative size of investor base for a particular security.     

Cash-flow or return predictability at long horizons? The case of earnings yield

We examine the predictive ability of the aggregate earnings yield for both market returns and earnings growth by estimating variance decompositions at multiple horizons. Based on weighted long-horizon regressions, we find that most of the variation in the earnings yield is due to return predictability, with earnings growth predictability assuming a minor role. However, by using implied estimates from a first-order restricted VAR, we find an opposite predictability mix. The inconsistency in results stems from a misspecification of the restricted VAR. Using an unrestricted first-order VAR estimated by OLS, or alternatively, estimating the restricted VAR by the Projection Minimum Distance method, produces long-run variance decompositions that are substantially more similar to the decomposition obtained under the direct method. Hence, earnings yield is not fundamentally different from the dividend yield. These results suggest that the practice of analyzing long-run return and cash-flow predictability from a restricted VAR can be quite misleading.     

Further analysis of the expectations hypothesis using very short-term rates

Longstaff [Longstaff, F., 2000. The term structure of very short-term rates: new evidence for the expectations hypothesis. Journal of Financial Economics 58, 397–415] finds support for the expectations hypothesis at the very short end of the repurchase agreement (repo) term structure while other studies find calendar-time-based regularities cause rejection of the expectations hypothesis. Using Longstaff’s methods on a sample of repo rates that pre-dates Longstaff’s sample, we reject the expectations hypothesis for every maturity. The pre-Longstaff-sample repo data comes from a time period where the behavior of short-term interest rates is similar to the long-run average behavior of short-term interest rates. Our results imply that expectations hold when rates are less volatile and/or that we may be entering a period of lower volatility.     

Stock Market Returns and Economic Fundamentals in an Emerging Market: The Case of Korea

This paper investigates the feedback relationship between stock market returnsand economic fundamentals in an emerging market. Starting from an intertemporalconsumption-based CAPM (CCAPM), we obtain a restricted VAR model for stockreturns and macroeconomic variables. We then apply this model to Korea and findstatistically significant departures from the restrictions implied by CCAPM.Consequently, an unrestricted VAR model is used to analyze the variations of expectedand unexpected returns in the Korean stock market. It is shown that the expectedmarket returns vary with a set of macroeconomic variables, and that thepredictable component is substantial. Reflecting richer dynamics in the data,relative to the usual single equation modeling in the literature, the estimatedVAR model shows considerable predictive ability for both real economic activityand real returns. Using the model for a variance decomposition of unexpectedreturns, we find that, although we cannot directly observe the market's revisionof expected future dividend growth, we can estimate a large part of therevision with the news in the expected industry output growth from our VAR model.Finally, we also find that economic fundamentals can explain only a smallportion of the variation in unexpected returns in the Korean stock market.     

Consumption risk and the cross-section of government bond returns

In this paper we provide a consumption-based explanation of risk in nominal US Treasury bond portfolios. We use a consumption-CAPM with Epstein–Zin–Weil recursive preferences. Our model introduces two sources of risk: uncertainty about current consumption (reflected in contemporaneous consumption growth) and uncertainty about prospects of consumption in a long run (reflected in innovations to expectations about future consumption growth). We use a novel approach to estimate pricing factors in our model: we employ a factor-augmented VAR model with common factors, extracted from a large panel of macroeconomic and financial data, as state variables. We find that the important source of risk in US bonds is related to uncertainty in prospects in future consumption and it induces a positive and significant risk premium. We find as well that covariance risk related to innovations in expectations about future consumption growth is greater for long term bond portfolios than for short term bond portfolios, which is consistent with a duration measure of risk and justifies why long term bonds require greater premium than short term bonds. Our model explains well the cross-sectional variation in average excess returns of bonds with different maturities over the period 1975–2011 and compares favorably with competing models.     

Expectations Models of Asset Prices: A Survey of Theory

This paper identifies restrictions on preferences under which various classes of “expectations” theories of asset prices—i.e., uncertainty models of asset prices which coincide with the corresponding certainty theory except that expected future prices replace actual future prices—are valid. Major classes of expectations models surveyed are martingale models, the expectations hypothesis of the term structure of interest rates, and models of exhaustible resources and futures markets. In each case the required restriction is related to the assumptiono f risk—neutrality, but the precise nature of the required restriction is shown to differ significantly among the various classes of expectations theories.     

Expectations Hypothesis and Term Structure of Interest Rates: An Evidence from Emerging Market

The integration of emerging economies with developed economies has changed the behaviour of interest rates and exchange rate fluctuation. The current study tries to analyse the implication of expectation hypothesis (EH) and term structures of interest rates between India and US. Using vector auto regressive estimates, the study tries to test the dynamic interdependence of interest rates on exchange rate fluctuation. Further, the study estimates Granger causality tests and Impulse Response Functions to test the behaviour of interest rate movements for a period of nineteen years ranging from June 1996 to June 2015.The empirical results of the study show evidence in line with the existence of EH in the case of emerging market. Nevertheless, in the case of advanced economies we do not find any evidence for EH. The findings revealed that the spread between long and short rate of India is influenced by short-term interest rates and past values of Indian spread. This implies that the fluctuations in the long rate over the short rate evidenced the strong presence of EH as far as emerging economy is concerned.To the best of our knowledge, this is the first study in Indian market, which tests the role of EH in interest rate fluctuations along with exchange rate. Since majority of the studies on term structure of interest rates focus on developed markets, the present study is an attempt to test the causal relationship between developed and developing economies.     

Lattice Models for Pricing American Interest Rate Claims

This article establishes efficient lattice algorithms for pricing American interest-sensitive claims in the Heath, Jarrow, and Morton paradigm, under the assumption that the volatility structure of forward rates is restricted to a class that permits a Markovian representation of the term structure. The class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility. The algorithm exploits the Markovian property of the term structure and permits the efficient computation of all types of interest rate claims. Specific examples are provided.