題目：Nonlinear but “Nice” Engel Curves

　　主講人：Prof. Robert G.Chambers, University of Maryland

　　時(shí)間：2020年11月24日（星期二） 北京時(shí)間 上午 8:00-10:00

　　形式：線(xiàn)上會(huì)議，將于23日統(tǒng)一發(fā)送包含會(huì)議鏈接的郵件

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　　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)”.

　　【講座介紹】

　　在生產(chǎn)和消費(fèi)理論中，如何使用性狀良好的偏好推導(dǎo)非線(xiàn)性的恩格爾曲線(xiàn)始終是人們無(wú)法解決的難題。有鑒于此，線(xiàn)性和擬線(xiàn)性的恩格爾曲線(xiàn)通常被用來(lái)作為對(duì)現(xiàn)實(shí)中非線(xiàn)性的消費(fèi)-收入關(guān)系的一種近似。雖然許多經(jīng)濟(jì)學(xué)家（包括諾貝爾經(jīng)濟(jì)學(xué)獎(jiǎng)獲得者Engles Deaton在內(nèi)）對(duì)此開(kāi)展了大量的理論和實(shí)證研究，并試圖通過(guò)發(fā)展了包括AIDS和Trans-log方程在內(nèi)的一系列新的需求函數(shù)提升線(xiàn)性恩格爾曲線(xiàn)對(duì)同質(zhì)性偏好的近似程度，但是上述理論矛盾始終未能得到徹底解決。

　　基于距離函數(shù)（distancefunction）的相關(guān)文獻(xiàn)，Chambers教授最近證明存在一組特定的偏好可以用來(lái)推導(dǎo)“性狀良好”的非線(xiàn)性的恩格爾曲線(xiàn)，并首次使用幾何雙曲線(xiàn)描述非線(xiàn)性的消費(fèi)-收入關(guān)系。在此“性狀良好”是指用新的恩格爾曲線(xiàn)所描述的非線(xiàn)性消費(fèi)-收入關(guān)系既能滿(mǎn)足單調(diào)遞增的條件又能保有線(xiàn)性的恩格爾曲線(xiàn)所具有的同質(zhì)性偏好的特征。這一發(fā)現(xiàn)借鑒了“效率”分析的理論，并與包括Blackorbery and Donaldson (1980)和 Luenberger(1992)在內(nèi)的討論保持了高度一致。這一研究不僅極大地推進(jìn)了微觀經(jīng)濟(jì)理論的發(fā)展，從本質(zhì)上解決了良好性狀偏好與非線(xiàn)性恩格爾曲線(xiàn)間不一致的問(wèn)題，而且也為證明社會(huì)需求背后代表性消費(fèi)（或生產(chǎn)者）的存在性提供了理論依據(jù)。

　　在本次講座中，Chambers教授將系統(tǒng)闡述上述理論發(fā)展的背景、趨勢(shì)及其對(duì)微觀經(jīng)濟(jì)學(xué)未來(lái)發(fā)展的影響，以及該理論在現(xiàn)實(shí)中的應(yīng)用。正如Gorman所說(shuō)“(the frameworkallows) economists to immerse themselves in their data… and then to choseforms which seem capable of handling this information…”。通過(guò)本次講座，我們也希望鼓勵(lì)北大及相關(guān)領(lǐng)域?qū)W者積極參與相關(guān)的實(shí)證研究。

　　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.