TY  - JOUR
AU  - Ludvigson,Sydney
AU  - Paxson,Christina H.
TI  - Approximation Bias in Linearized Euler Equations
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 236
PY  - 1999
Y2  - March 1999
UR  - http://www.nber.org/papers/t0236
L1  - http://www.nber.org/papers/t0236.pdf
N1  - Author contact info:
Sydney C. Ludvigson
Department of Economics
New York University
19 W. 4th Street, 6th Floor
New York, NY  10002
Tel: 212/998-8927
Fax: 212/995-4186
E-Mail: sydney.ludvigson@nyu.edu

Christina Paxson
424 Robertson Hall
Princeton University
Princeton, NJ 08544-1022
Tel: 609/258-6474
Fax: 609/258-5974
E-Mail: cpaxson@princeton.edu
AB  - A wide range of empirical applications rely on linear approximations to dynamic Euler equations.  Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence.  Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence.  This literature has produced puzzling results: Estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low.  Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation.  We also present Monte Carlo evidence that shows that the instrumental variables methods commonly used to estimate the parameters correct some, but not all, of the approximation bias.
ER  -