ESTIMATING STRUCTURAL PARAMETERS IN REGRESSION MODELS WITH ADAPTIVE LEARNING
研究了在有限理性代理人使用自适应学习规则形成预期的简单宏观经济模型中，普通最小二乘估计量对结构参数的估计性质，推导了两种学习算法下估计量的渐近分布，发现估计量一致但推断可能非标准。
This paper examines the ordinary least squares (OLS) estimator of the structural parameters in a simple macroeconomic model in which agents are boundedly rational and use an adaptive learning rule to form expectations of the endogenous variable. The popularity of learning models has recently increased amongst applied economists and policy makers who seek to estimate them empirically. Yet the econometrics of learning models is largely uncharted territory. We consider two prominent learning algorithms, namely constant gain and decreasing gain learning. For each of the two learning rules, our analysis proceeds in two stages. First, the paper derives the asymptotic properties of agents’ expectations. At the second stage, the paper derives the asymptotics of OLS in the structural model, taking the first stage learning dynamics as given. In the case of constant gain learning, the structural model effectively amounts to a stationary, cointegrating, or co-explosiveness regression. With decreasing gain learning, the regressors are asymptotically collinear such that OLS does not satisfy, in general, the Grenander conditions for consistent estimability. Nevertheless, this paper shows that the OLS estimator remains consistent in all models considered. It also shows, however, that its asymptotic distribution, and hence any inference based upon it, may be nonstandard.