Carolin E. Pflueger

A Robust Test for Weak Instruments

We develop a test for weak instruments in linear instrumental variables regression that is robust to heteroscedasticity, autocorrelation, and clustering. Our test statistic is a scaled nonrobust first-stage F statistic. Instruments are considered weak when the two-stage least squares or the limited information maximum likelihood Nagar bias is large relative to a benchmark. We apply our procedures to the estimation of the elasticity of intertemporal substitution, where our test cannot reject the null of weak instruments in a larger number of countries than the test proposed by Stock and Yogo in 2005. Supplementary materials for this article are available online.

Return Predictability in the Treasury Market: Real Rates, Inflation, and Liquidity

This paper decomposes inflation-indexed and nominal government bond excess return predictability into liquidity, real interest rate risk and inflation risk. We estimate a systematic liquidity premium in Treasury Inflation Protected Securities (TIPS) yields relative to nominal yields. The liquidity premium is around 30 bps during normal times but larger during the early years of TIPS and during the financial crisis 2008-2009. We find that time-varying liquidity premia in TIPS and time-varying inflation risk premia in nominal bonds generate return predictability. We find no evidence that shocks to relative issuance generate bond return predictability in the US or UK. Since their first issuance in 1997, inflation-indexed bonds in the U.S. have gained wide acceptance among investors and they now constitute a significant fraction of the stock of U.S. Treasury debt. Yet many academics and Treasury market pundits argue that these bonds, known as Treasury Inflation Protected Securities (TIPS), have a smaller and less liquid market than their nominal counterparts, U.S. Treasury notes and bonds.2 This paper conducts an empirical investigation of the sources and magnitude of illiquidity in the TIPS market. Conditional on a measure of the liquidity discount on TIPS relative to nominal Treasury bonds, it asks to what extent liquidity risk and to what extent time-varying inflation risk and time-varying real interest rate risk generate excess return predictability in government bonds. Understanding the liquidity differential between TIPS and Treasury bonds is important for several reasons. First, it is well-known that the Expectations Hypothesis of the term structure of interest rates does not hold for U.S. nominal government bonds (Campbell and Shiller 1991, Fama and Bliss 1987, Cochrane and Piazzesi 2005). Equivalently, excess returns on U.S. nominal government bonds are predictable. Explanations of return predictability in government bond returns emphasize either a time-varying real interest rate risk premium, or a time-varying inflation risk premium, or a combination of those two (Wachter 2006, Campbell, Sunderam, and Viceira 2010). Pflueger and Viceira (2011) have highlighted that inflation-indexed bonds can be very helpful in disentangling inflation risk and real interest rate risk as the fundamental sources of government bond return predictability. But such an exercise requires identifying price and return differentials between the two bond markets 2For evidence of relatively lower liquidity in TIPS see D’Amico, Kim, and Wei (2008), Campbell, Shiller, and Viceira (2009), Fleckenstein, Longstaff, and Lustig (2010), Fleming and Krishnan (2009), Dudley, Roush, and Steinberg Ezer (2009), Gurkaynak, Sack, and Wright (2010), and Haubrich, Pennacchi, and Ritchken (2011).Estimating the liquidity differential between inflation-indexed and nominal bond yields, we separately test for time-varying real rate risk premia, inflation risk premia, and liquidity premia in U.S. and U.K. bond markets. We find strong, model independent evidence that real rate risk premia and inflation risk premia contribute to nominal bond excess return predictability to quantitatively similar degrees. The estimated liquidity premium between U.S. inflation-indexed and nominal yields is systematic, ranges from 30 bps in 2005 to over 150 bps during 2008-2009, and contributes to return predictability in inflation-indexed bonds. We find no evidence that bond supply shocks generate return predictability.

A Robust Test for Weak Instruments in Stata

We introduce a routine, weakivtest, that implements the test for weak instruments by Montiel Olea and Pflueger (2013, Journal of Business and Economic Statistics 31: 358–369). weakivtest allows for errors that are not conditionally homoskedastic and serially uncorrelated. It extends the Stock and Yogo (2005, Testing for weak instruments in linear IV regression. In Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg, ed. D. W. K. Andrews and J. J. Stock, 80–108. [Cambridge University Press]) weak-instrument tests available in ivreg2 and in the ivregress postestimation command estat firststage. weakivtest tests the null hypothesis that instruments are weak or that the estimator’s Nagar (1959, Econometrica 27: 575–595) bias is large relative to a benchmark for both two-stage least-squares estimation and limited-information maximum likelihood with one endogenous regressor. The routine can accommodate Eicker–Huber–White heteroskedasticity robust estimates, Newey and West (1987, Econometrica 55: 703–708) heteroskedasticity and autocorrelation-consistent estimates, and clustered variance estimates. Copyright 2015 by StataCorp LP.

Precautionary Savings in Stocks and Bonds

We document a strong and robust relationship between the one-year real rate and the valuation of high-volatility stocks, which we contend measures precautionary savings motives. Our novel proxy for precautionary savings explains 41% of the variation in the real rate. In addition, the real rate forecasts returns on the low-minus-high volatility portfolio but has little relation to observable measures of the quantity of risk. These results suggest that precautionary savings motives, and thus the real rate, are driven by time-varying attitudes towards risk. Our findings are difficult to rationalize in models with perfect risk sharing and highlight the role that imperfect diversification plays in determining interest rates. We also explore the implications of our findings for monetary policy, arguing that precautionary savings motives should be included in assessing the natural real rate. ⇤We thank Michael Brennan (discussant), John Campbell, Robert Engle, Xavier Gabaix, Espen Henriksen (discussant), Bryan Kelly, Hanno Lustig (discussant), Thomas Maurer (discussant), Monika Piazzesi, Robert Ready (discussant), Martin Schneider, Andrei Shleifer, Jeremy Stein, Luis Viceira, and seminar participants at the BI-SHoF Conference 2017, CEF 2017, CITE 2017, SITE 2017, FRBSF conference on Advances in Finance Research 2017, London School of Economics, Federal Reserve Board, University of British Columbia, University of Indiana, SFS Cavalcade, and HEC-McGill Winter Finance Workshop for helpful comments. The Online Appendix to the paper can be found here and the Data Appendix can be found here. †Pflueger: University of British Columbia. E-mail: carolin.pflueger@sauder.ubc.ca ‡Siriwardane: Harvard Business School. E-mail: esiriwardane@hbs.edu. §Sunderam: Harvard Business School and NBER. E-mail: asunderam@hbs.edu.