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VAR-based estimation of Euler equations with an application to New Keynesian pricing

机译：基于VAR的欧拉方程估计及其在新凯恩斯定价中的应用

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VAR-based estimation of Euler equations exploits cross-equation restrictions that the theory imposes on a vector-autoregressive (VAR) process for market expectations. This paper shows that Sargent's (1979. A note on maximum likelihood estimation of the rational expectations model of the term structure. Journal of Monetary Economics 5, 133-143.) original approach of imposing these restrictions on the endogenous variable of the Euler equation (i.e. computing the rational expectations solution) implies multiple solutions and is therefore impracticable. The paper shows that this identification problem can be circumvented by reverse-engineering the cross-equation restrictions on the forcing variable of the Euler equation. The proposed reverse-engineering approach contrasts with the conventional approach in the literature that avoids the identification problem by constraining the system formed by the Euler equation and the VAR process to yield a unique stable rational expectations equilibrium. This uniqueness condition makes little economic sense because the VAR process is just a reduced-form approximation of true market expectations, and a simulation experiment shows that imposing uniqueness can lead to severe misspecification bias. The severity of this misspecification bias is illustrated in practice with an application to Gali and Gertler's (1999. Inflation dynamics: a structural econometric analysis. Journal of Monetary Economics 44, 195-222.) hybrid New Keynesian Phillips Curve.
机译：基于VAR的Euler方程估计利用了交叉方程约束，该约束施加在理论上的矢量自回归（VAR）过程中，以实现市场期望。本文显示了萨金特（1979.关于期限结构的合理期望模型的最大似然估计的注解。货币经济学期刊5，133-143。）的原始方法是将这些限制强加于Euler方程的内生变量（也就是说，计算合理的期望值解决方案意味着多个解决方案，因此是不切实际的。本文表明，可以通过逆向工程对Euler方程强制变量的交叉方程式限制来解决此识别问题。所提出的逆向工程方法与文献中的常规方法形成对比，后者通过约束由Euler方程和VAR过程形成的系统以产生唯一的稳定有理期望均衡来避免识别问题。这种唯一性条件在经济上几乎没有意义，因为VAR过程只是真实市场预期的简化形式，并且模拟实验表明，施加唯一性会导致严重的错误指定偏差。在实践中可以通过应用Gali和Gertler（1999年，《通货膨胀动力学：结构计量经济分析》，《货币经济学期刊》，第195-222页）混合New Keynesian Phillips曲线说明这种错误指定偏差的严重性。

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