This paper reviews the development of agent-based (computational) economics (ACE) from an econometrics viewpoint. The review comprises three stages, characterizing the past, the present, and the future of this development. The first two stages can be interpreted as an attempt to build the econometric foundation of ACE, and, through that, enrich its empirical content. The second stage may then invoke a reverse reflection on the possible agent-based foundation of econometrics. While ACE modeling has been applied to different branches of economics, the one, and probably the only one, which is able to provide evidence of this three-stage development is finance or financial economics. We will, therefore, focus our review only on the literature of agent-based computational finance, or, more specifically, the agent-based modeling of financial markets. 188of those stylized facts based on the literature. Section 3.2 then analyzes how these stylized facts are successfully explained or replicated by various classes of ACF models.The same style of analysis is carried over in addressing the second stage of the development. At this stage, we ask what makes an ACE model econometrically tractable. Alternatively put, what are the necessary restrictions or assumptions that need to be imposed before an ACE model can be estimated? However, we will soon realize that the answer cannot be independent of the estimation method involved. This leads us to distinguish three main estimation methods, namely, maximum likelihood (MLE), least squares (LS), and the method of moments, as well as variations of the three. Generally speaking, the complexity of the objective function associated with the number of the parameters to be estimated will determine which of the estimation methods will be used. As a result, ACE models can also be categorized by the appropriate estimation method, which makes them econometrically tractable.The questions addressed in the third stage are very different from those asked in the first two. The issue is not the empirical relevance or empirical validation of the built ACE models, but concerns using the ACE models as a tool to address the aggregation problem or the analogy principle, which has been extensively discussed in the literature (Blinder, 1983; Barker & Pesaran, 1990;Forni & Lippi, 1997;Gallegati et al., 2006). In light of the Debreu-Mantel-Sonnenschein theorem, there are no grounds to expect macro behavior to be in any way similar or analogous to the behavior of individual agents. ACE models can help us to see how dissimilar the macro and micro behavior can be.With the above description, the rest of the chapter is organized as follows. A taxonomy of ACE models is given in Section 2. The three-stage development of the literature is described in Section 3, Section 4, and Section 5. Concluding remarks are given in Section 6.Agent-based economic models and econometrics

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After a brief review of natural computationalism, this introductory chapter presents a new skeleton of computational economics and finance (CEF) along with an overview of the handbook. It begins with a conventional pursuit focusing on the algorithmic or numerical aspect of CEF such as computational efforts devoted to rational expectations, (dynamic) general equilibrium, and volatility. It then moves toward an automata- or organism-based perspective of CEF, involving nature-inspired intelligence, algorithmic trading, automated markets, network- and agent-based computing, and neural computing. As an alternative way to introduce this novel skeleton, the chapter starts with a view of computation or computing, addressing what computational economics intends to compute and what kinds of economics make computation so hard, and then it turns to a view of computing systems in which the Walrasian kind of computational economics is replaced by the Wolframian kind due to computational irreducibility.