[We use Monte Carlo simulations and real data to assess the performance of methods dealing with measurement error in investment equations. Our experiments show that fixed effects, error heteroscedasticity, and flata skewness severely affect the performance and reliability of methods found in the literature. Estimators that use higher-order moments return biased coefficients for (both) mismeasured and perfectly measured regressors. These estimators are also very inefficient. Instrumental-variable-type estimators are more robust and efficient, although they require restrictive assumptions. We estimate empirical investment models using alternative methods. Real-world investment data contain firm-fixed effects and heteroscedasticity, causing high-order moments estimators to deliver coefficients that are unstable and not economically meaningful. Instrumental variables methods yield estimates that are robust and conform to theoretical priors. Our analysis provides guidance for dealing with measurement errors under circumstances researchers are likely to find in practice.]

This paper develops a dynamic model of rational behavior under uncertainty, in which the agent maximizes the stream of future τ ‐quantile utilities, for τ ∈ (0,1). That is, the agent has a quantile utility preference instead of the standard expected utility. Quantile preferences have useful advantages, including the ability to capture heterogeneity and allowing the separation between risk aversion and elasticity of intertemporal substitution. Although quantiles do not share some of the helpful properties of expectations, such as linearity and the law of iterated expectations, we are able to establish all the standard results in dynamic models. Namely, we show that the quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, via a fixed point argument, this value function is concave and differentiable, and the principle of optimality holds. Additionally, we derive the corresponding Euler equation, which is well suited for using well‐known quantile regression methods for estimating and testing the economic model. In this way, the parameters of the model can be interpreted as structural objects. Therefore, the proposed methods provide microeconomic foundations for quantile regression methods. To illustrate the developments, we construct an intertemporal consumption model and estimate the discount factor and elasticity of intertemporal substitution parameters across the quantiles. The results provide evidence of heterogeneity in these parameters.

We use Monte Carlo simulations and real data to assess the performance of methods dealing with measurement error in investment equations. Our experiments show that fixed effects, error heteroscedasticity, and data skewness severely affect the performance and reliability of methods found in the literature. Estimators that use higher-order moments return biased coefficients for (both) mismeasured and perfectly measured regressors. These estimators are also very inefficient. Instrumental-variable-type estimators are more robust and efficient, although they require restrictive assumptions. We estimate empirical investment models using alternative methods. Real-world investment data contain firm-fixed effects and heteroscedasticity, causing high-order moments estimators to deliver coefficients that are unstable and not economically meaningful. Instrumental variables methods yield estimates that are robust and conform to theoretical priors. Our analysis provides guidance for dealing with measurement errors under circumstances researchers are likely to find in practice. The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: [email protected]., Oxford University Press.