题目：Nonlinear but “Nice” Engel Curves

　　主讲人：Prof. Robert G.Chambers, University of Maryland

　　时间：2020年11月24日（星期二） 北京时间 上午 8:00-10:00

　　形式：线上会议，将于23日统一发送包含会议链接的邮件

　　请扫描以下二维码以完成本场讲座注册，如需技术支持请联系：liuxingshuo@pku.edu.cn

　　Prof. Robert G. Chambers is a chair Professor of Department of Agricultural and Resource Economics, University of Maryland, College Park, USA and Honorary Professor, School of Economics, University of Queensland, Australia. He is also the fellow of Agricultural and Applied Economics Association, the editor for Journal of Productivity Analysis, and an adviser to OECD Trade and Agricultural Directorate for Environmental Adjusted Agricultural TFP Measurement. His research interests cover agricultural economics, decision making under uncertainty, production economics, microeconomic theory, public economics and agricultural and natural resource policy. Over the past four decades, he has made a great achievement in the field of decision making under uncertainty, agricultural economics and productivity analysis and published more than 100 articles in reputable international refereed journals including American Economic Review, Economic Journal, Econometrica, Review of Economic Studies, American Journal of Agricultural Economics etc. His recent research work on analyzing the climate effects on U.S. Total Agricultural Productivity has also been published in world top scientific journal “Proceedings of the National Academy of Sciences (PNAS)”.

　　【讲座介绍】

　　在生产和消费理论中，如何使用性状良好的偏好推导非线性的恩格尔曲线始终是人们无法解决的难题。有鉴于此，线性和拟线性的恩格尔曲线通常被用来作为对现实中非线性的消费-收入关系的一种近似。虽然许多经济学家（包括诺贝尔经济学奖获得者Engles Deaton在内）对此开展了大量的理论和实证研究，并试图通过发展了包括AIDS和Trans-log方程在内的一系列新的需求函数提升线性恩格尔曲线对同质性偏好的近似程度，但是上述理论矛盾始终未能得到彻底解决。

　　基于距离函数（distancefunction）的相关文献，Chambers教授最近证明存在一组特定的偏好可以用来推导“性状良好”的非线性的恩格尔曲线，并首次使用几何双曲线描述非线性的消费-收入关系。在此“性状良好”是指用新的恩格尔曲线所描述的非线性消费-收入关系既能满足单调递增的条件又能保有线性的恩格尔曲线所具有的同质性偏好的特征。这一发现借鉴了“效率”分析的理论，并与包括Blackorbery and Donaldson (1980)和 Luenberger(1992)在内的讨论保持了高度一致。这一研究不仅极大地推进了微观经济理论的发展，从本质上解决了良好性状偏好与非线性恩格尔曲线间不一致的问题，而且也为证明社会需求背后代表性消费（或生产者）的存在性提供了理论依据。

　　在本次讲座中，Chambers教授将系统阐述上述理论发展的背景、趋势及其对微观经济学未来发展的影响，以及该理论在现实中的应用。正如Gorman所说“(the frameworkallows) economists to immerse themselves in their data… and then to choseforms which seem capable of handling this information…”。通过本次讲座，我们也希望鼓励北大及相关领域学者积极参与相关的实证研究。

　　The conventional preference classes that do not exhibit a non-linear Engel curve has widely been regarded as a paradox in the consumption and production theory. Consequently, the widely used homothetic and quasi-homothetic preferences (representing the linear and affine Engel curve) could not reflect the consumption and production behavior that one may expect rational agents to exhibit as they expand across indifference curves or isoquants. For decades, many studies including Barten (1969), Solari (1971), Park (1971), Powell (1974) and Deaton (1975, 1978) have attempted to resolve the puzzle through developing better demand functions, i.e. the quadratic demand function by Christensen, Jorgenson and Lau (1975) and the almost ideal demand system, AIDS, by (Deaton and Muellbauer 1980). However, the puzzle remains.

　　This paper by Chambers (2020) investigates a preference class that possesses nonlinear but “nice” Engel curves, which helps to shorten the gap in literature. By “nice”, it means that the derived Engel curves based on this new preference class are positively sloped, whose behavior, like homothetic and quasi-homothetic preferences, is characterized by reference indifference sets. The attempt was inspired by efficiency measures derived by Chambers and Miller (2014) and follows the distance function literature, i.e. Blackorby and Donaldson (1980), Luenberger (1992). It helps to create a homeomorphism, and is more aptly compared to how hyperbolic geometry adjusts the parallel postulate to accommodate non-linear structure. While calling this preference class path homothetic is not truly precise, it is evocative as a feature and exhibits behavior similar to homotheticity for an appropriate transformation of commodity space, and that similarity ensures slopes of indifference surfaces are constant along monotone paths.

　　Contributing to the literature, the class of preference facilitates measurement of welfare and prices, and it rationalizes the existence of a representative agents so as to convey both analytic and empirical tractability. As such, the proposed approach here is to renormalize commodity units to obtain tractable models that do not require implausible behavior. In addition, the assumption of a representative agent comes back alive. In the words of Gorman, the attempt frame a method that allows “… economists to immerse themselves in their data … and then to choose forms which seem capable of handling this information. More empirical studies should be conducted to test the theoretical results based on the proposed framework, although econometricians have already do this along with the line to estimate nonlinear Engel curves.