Method Of Comparative Statics Research Articles

Comparative Static Analysis on the Agricultural Mechanization Development Levels in China’s Provincial Areas

The foundation of the national economy is agriculture, agricultural modernization is the symbol of national modernization and agricultural mechanization is an important symbol of agricultural modernization. In this paper, the authors conducted an analysis of the agricultural mechanization levels of 31 provincial areas in China. In order to assess the agricultural mechanization levels of the provincial areas in China as accurately as possible, the authors adopted indicators in the year 2005, the year 2010 and the year 2015, and used the comparative static analysis method to observe the dynamic changes in the data over the three years. Eight items, including total agricultural mechanization power/grain output (10 million watts/10 k tons), number of large and medium-sized tractors/grain output (pcs/10 k tons), tractor plowing area/grain output (k hectares/10 k tons), total input of agricultural mechanization business operation/grain output (million yuan/10 k tons), total income of agricultural mechanization business operation/grain output (million yuan/10 k tons), and fuel consumption for agricultural production/grain output (hundred tons/10 k tons), were used as assessment indicators. With the gray weighted cluster assessment instrument, 31 provincial areas of China were classified into five gray categories at high development level, relatively high development level, medium development level, medium to low development level and low development level. An objective, scientific and comprehensive assessment of the cluster results was conducted in an effort to better provide references for the authorities to draft relevant policies and measures.

Index-wise comparative statics

This paper identifies a necessary and sufficient condition for index-wise comparative statics, which can: (i) establish comparative statics of a single decision without solving the entire model and (ii) enable analysis in settings where substitutability among variables otherwise precludes the use of current comparative statics methods. We prove this result with an extended version of lattice theory. By means of an example, we highlight the advantages as well as disadvantages offered by index-wise comparative statics.

Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set

Motivated by the asymmetrical attitudes of investors towards downside losses and upside gains, this paper proposes a robust multi-period portfolio selection model based on downside risk with asymmetrically distributed uncertainty set, in which the downside losses of a portfolio are controlled by the lower partial moment (LPM). A computationally tractable approximation approach based on second-order cone optimization is used for solving the proposed model. We show in theory that the optimal solution of the robust model can generate a given probability guarantee for individual and joint stochastic constraints. The effect of the asymmetrically distributed uncertainty set on performance of the optimal solution is analyzed by the usual comparative static method. Comprehensive numerical comparisons with real market data are reported and indicate that the proposed model can obtain the smaller standard deviation and turnover ratios which reduce the Sharpe ratios of optimal portfolio, compared with some well-known models in the literature.

Analytical Model for the Change of Travel Time Savings With Waiting Time and Service Level

An extended classical time allocation model with travel time reliability constraint is proposed in this study. The valuation function of travel time savings is deduced, and the relationship between the value of travel time savings and other social environment variables, especially the waiting time and service level, is revealed. Meanwhile, the change of the value of travel time savings with the waiting time and the service level is investigated through a comparative static analysis method. Analytical results show that the change of the value of travel time savings with the service level is dependent on the inverse of the cumulative distribution function. By contrast, the value of travel time savings tends to decrease with the increase in waiting time. The findings further imply that adopting the optimal head start can relieve the waiting time of urban commuters, thereby minimizing their generalized travel cost. Moreover, the values of service headway and reliability are analyzed, which can improve the quality of service toward either frequency or reliability improvements to reduce the cost for the society.

The Comparative Statics of Sorting

We create a general and tractable theory of increasing sorting in pairwise matching models with transferable utility — one that subsumes Becker (1973) as the extreme cases with most and least sorting. We first prove that the positive quadrant dependence order smartly measures increasing sorting, e.g. it rises in the correlation of matched partners. Our theory centers on synergy — the cross partial difference or derivative of match production. Notably, if synergy everywhere increases, sorting need not rise, but cannot fall. To rescue increasing sorting, we posit often met cross-sectional restrictions on match synergy. Our theory illuminates top economics sorting papers, affording quick proofs of their results and new insights. Synergy reflects basic economic forces, such as diminishing returns, moral hazard, insurance, and learning dynamics. Our proof develops and exploits new monotone comparative statics methods. The main proof proceeds by induction with finitely many types, and secures the continum type results by taking limits. Classification- C6, D2, D5, J1

Index-Wise Comparative Statics

This paper identifies a necessary and sufficient condition for index-wise comparative statics, which can: (i) establish comparative statics of a single decision without solving the entire model and (ii) enable analysis in settings where substitutability among variables otherwise precludes the use of current comparative statics methods. We prove this result with an extended version of lattice theory. By means of an example, we highlight the advantages as well as disadvantages offered by index-wise comparative statics.

Inverse Functions and Existence Principles

Each one of six general existence principles of compactness (the extreme value theorem), completeness (the Newton method or the modified Newton method), topology (Brouwer’s fixed point theorem), homotopy (on contractions of a sphere to its center), variational analysis (Ekeland’s principle), and monotonicity (the Minty–Browder theorem)) is shown to lead to the inverse function theorem, each one giving some novel insight. There are differences in assumptions and algorithmic properties; some of the propositions have been constructed specially for this paper. Simple proofs of the last two principles are included. The proof by compactness is shorter and simpler than the shortest and simplest known proof, that by completion. This gives a very short self-contained proof of the Lagrange multiplier rule, which depends only on optimization methods. The proofs are of independent interest and are intended as well to be useful in the context of the ongoing efforts to obtain new variants of methods that are based on the inverse function theorem, such as comparative statics methods.

How to do comparative dynamics on the back of an envelope for open‐loop Nash equilibria in differential game theory

SummaryThe primal‐dual comparative statics method of Samuelson (1965) and Silberberg (1974) is extended to cover the class of non‐autonomous, finite horizon differential games in which a locally differentiable open‐loop Nash equilibrium exists. In doing so, not only is a one‐line proof of an envelope theorem provided but also the heretofore unknown intrinrsic comparative dynamics of open‐loop Nash equilibria are uncovered. The intrinsic comparative dynamics are shown to be contained in a symmetric and negative semidefinite matrix that is subject to constraint. The results are applied to a canonical differential game in capital theory, and the resulting comparative dynamics are given an economic interpretation. Copyright © 2016 John Wiley & Sons, Ltd.

Book Reviews

Benjamin Williams of George Washington University reviews “Structural Econometric Models”, by Eugene Choo and Matthew Shum. The Econlit abstract of this book begins: “Twelve papers explore recent developments in the use of structural econometric models in empirical economics. Papers discuss Euler equations for the estimation of dynamic discrete choice structural models; approximating high-dimensional dynamic models—sieve value function iteration; identifying dynamic games with serially correlated unobservables; partial identification in two-sided matching models; identification of matching complementarities—a geometric viewpoint; comparative static and computational methods for an empirical one-to-one transferable utility matching model; a test for monotone comparative statics; estimating supermodular games using rationalizable strategies; estimation of the loan spread equation with endogenous bank-firm matching; the collective marriage matching model— identification, estimation, and testing; deflation in durable goods markets—an empirical model of the Tokyo condominium market; and a dynamic analysis of the U.S. cigarette market and antismoking policies. Choo is with the Department of Economics at the University of Calgary. Shum is with the Division of Humanities and Social Sciences at the California Institute of Technology.”

Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application

A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by an attempt to analyze the problems of functioning of low competitive macroeconomic structures. The model is formalized in the form of a Bellman equation, for which a closed-form solution is found. The stochastic process of product stock variations is proved to be ergodic and its final probability distribution is found. Expressions for the average production load and the average product stock are found by analyzing the stochastic process. A system of model equations relating the model variables to official statistical parameters is derived. The model is identified using data from the Fiat and KAMAZ companies. The influence of the credit interest rate on the firm market value assessment and the production load level are analyzed using comparative statics methods.

Extreme IPO underpricing

Purpose – The purpose of this paper is to model the Chinese unique regulation changes with the supply-and-demand analytical framework and structure the relationship between initial public offerings (IPO) underpricing and institutional changes with the comparative static method. A well-functioning stock market is crucial to the transition into a market economy, but the Chinese stock market is somehow twisted with frequent government interventions, particularly the IPO market. Can the underpricing issue be mitigated in the changing institutional settings? Can the market-orientated incremental reform of regulations succeed in the Chinese stock market? Design/methodology/approach – The theoretical analysis confirms that IPO underpricing becomes relatively better with dynamic changes of relaxation of the approval and pricing systems. Collecting and examining the data of newly listed firms from 1993 to 2010, the influence of institutional changes on IPO underpricing with regressions, such as ordinary least square (OLS), bootstrap and two stage least square (2SLS) estimation methods was further empirically examined. Findings – The magnitude of the Chinese IPO underpricing during the past two decades is as high as 181.6 per cent on the average. The sizes of IPO underpricing significantly reduce with an increase in the issuing sizes and the ratios of price-earnings ratios. The dummy variables of government-approved regulations are negatively associated with IPO underpricing. The dummy variables of pricing regulations are positively related to IPO underpricing and the coefficients become smaller with newer regulations. Generally, the magnitude of the Chinese IPO underpricing decreases over time. Originality/value – This paper enriches the IPO literature by dynamically examining the effect of institutional changes on IPO underpricing in Chinese primary markets. We argue that institutional changes characterized by incremental marketization can help to alleviate extreme IPO underpricing and to promote financial development. The Chinese transition from the planning system to the market system in the IPO market will be a long and strenuous process, but it works.

Analyzing the effect of advanced agriculture development policy

This paper broadens the scope of current theoretical studies, divides rural agriculture into two sectors—advanced and traditional, and takes into consideration the land factor and the urban informal sector. Under the assumption that wages in the advanced agricultural sector are higher than in the traditional agricultural sector, this paper analyzes the effect of policies to promote advanced agricultural development with the comparative static method. The main conclusions of this paper are: wage subsidization of the advanced agricultural sector, in addition to having the same economic impact as interest subsidies on the advanced agricultural sector, could also increase the land employment in the advanced agricultural sector and reduce that in the traditional agricultural sector. Therefore, the effect of wage subsidizing policies is stronger than that of interest subsidies, while land rent subsidies for the advanced agricultural sector have the same economic effect as wage subsidies.

Sensitivity Analysis for Newsvendor Model with General Advertisement-Sensitive Demand

Advertising is a very important measure to induce consumer demand and make more profit for a firm. The newsvendor problem with advertising decision provides an important means to examine how operational problems interacts with marketing issues to influence decision-making at the firm level. In this paper, we explore the changes of optimal decisions about the system parameters for newsvendor model under general additive-multiplicative advertising-dependent demand distribution through comparative statics method.

Impact of Technological Progress on Energy Resources Intertemporal Extraction Sequence

Technological progress is an important and complex factor which affects extraction sequence of energy resources. Based on the resources intertemporal extraction model, by means of comparative static analysis methods, we analyze the impact of technological progress on extraction sequence of energy resources. The results show that technological advance influences extraction sequence of energy resources in multiple ways, such as the stock of energy resources, energy consumption pattern, and marginal cost of mining. Different technological advance has different influence of intensity and direction. Technological progress adverse to restrain consumption may accelerate the resources depletion, but energy substitution is the effective way to achieve the sustainable utilization of energy resources.

The Neglect of Monotone Comparative Statics Methods

Monotone methods enable comparative static analysis without the restrictive assumptions of the implicit-function theorem. Ease of use and flexibility in solving comparative static and game-theory problems have made monotone methods popular in the economics literature and in graduate courses, but they are still absent from undergraduate mathematical economics courses and textbooks. In this article, the authors illustrate the generality of monotone comparative statics relative to the implicit function approach. For example, to sign the effect of a discrete policy shift on a choice variable, the marginal returns will increase with the policy parameter. They also apply monotone methods in game theory settings. As mathematical economics courses and majors gain popularity, incorporating monotone methods into curriculum and textbooks would provide a modern treatment of comparative static analysis.

THE MODEL OF TAX EVASION, ITS COHERENCE TO THE PRACTICAL TAX ADMINISTRATION

In this paper, a theoretical model of tax evasion, proposed by Allingham and Sandmo, is briefly presented. This model tries to explain the taxpayer’s decision to reveal only part of the taxable income and to evade taxes in this way. The main parameters of the model are personal income, the rates of tax and penalty, probability of the tax audit. By the method of comparative statics it is possible, at least partially, to evaluate the influence of changes of the model’s parameters on a person’s decision to evade tax.As some of the assumptions of the Allingam–Sandmo model differ from taxation rules in practice or the model’s conclusions do not match the actual taxpayers’ behaviour, in this paper some criticism and improvements of the proposed model are reviewed. A comparison of the model’s assumptions and actual aspects of the tax administration in Lithuania is also provided.This article contains also a model of tax evasion with regard for the peculiarities of tax administration in Lithuania and the possible corrections of tax audit probability function.

The Neglect of Monotone Comparative Static Methods

Monotone methods enable comparative static analysis without the restrictive assumptions of the implicit function theorem. Ease of use and flexibility in solving comparative static and game theory problems have made monotone methods popular in the economics literature and in graduate courses, but they are still absent from undergraduate mathematical economics courses and textbooks. We illustrate the generality of monotone comparative statics relative to the implicit function approach. For example, to sign the effect of a discrete policy shift on an optimal control or choice variable, one need only check that marginal returns increase with the policy parameter. We also apply monotone methods in game theory settings. As mathematical economics courses and majors gain popularity, incorporating monotone methods into curriculum and textbooks would provide a modern treatment of comparative static analysis.

Comparative statics of the generalized maximum entropy estimator of the general linear model

The generalized maximum entropy method of information recovery requires that an analyst provides prior information in the form of finite bounds on the permissible values of the regression coefficients and error values for its implementation. Using a new development in the method of comparative statics, the sensitivity of the resulting coefficient and error estimates to the prior information is investigated. A negative semidefinite matrix reminiscent of the Slutsky-matrix of neoclassical microeconomic theory is shown to characterize the said sensitivity, and an upper bound for the rank of the matrix is derived.

Higher-order generalizations of Arrow–Pratt and Ross risk aversion: A comparative statics approach

We analyze comparative risk aversion in a new way, through a comparative statics problem in which, for a cost, agents can shift from an initial probability distribution toward a preferred distribution. The Ross characterization arises when the original distribution is riskier than the preferred distribution and the cost is monetary, and the Arrow–Pratt characterization arises when the original distribution differs from the preferred distribution by a simple mean-preserving spread and the cost is a utility cost. Higher-order increases in risk lead to higher-order generalizations, and the comparative statics method yields a unified approach to the problem of comparative risk attitudes.

Monotone Comparative Statics for Models of Politics

We elucidate a powerful yet simple method for deriving comparative statics conclusions for a wide variety of models: Monotone Comparative Statics (Milgrom and Shannon 1994). Monotone comparative static methods allow researchers to extract robust, substantive empirical implications from formal models that can be tested using ordinal data and simple nonparametric tests. When these methods apply, they can replace a diverse range of more technically difficult mathematics (facilitating richer, more realistic models), assumptions that are hard to understand or justify substantively (highlighting the political intuitions underlying a model's results), and a complicated set of methods for extracting implications from models. We present an accessible introduction to the central monotone comparative statics results and a series of practical tools for using these techniques in applied models (with reference to original sources, when relevant). Throughout we demonstrate the techniques with examples drawn from political science.