Comparative Static Results Research Articles

Monotone Comparative Statics for Directed Search Models

This note shows how to use monotone methods to derive stronger comparative static results for directed search models. In the context of labor markets, a standard result can be overturned by endogenizing the matching technology. In the context of monetary theory, both the seller-to-buyer ratio and the level of output decrease in the nominal interest rate regardless of the choice of matching function. These results strengthen the predictions of previous research.

Expectations and Stability in the Kaleckian Growth Model

A central element in the canonical Kaleckian growth model is the demand-led output-adjustment stability condition known as the Keynesian stability condition. This condition requires that, all else constant, saving be less responsive to changes in capital capacity utilization than investment. This paper further explores the plausibility of the Keynesian stability condition by enriching the Kaleckian growth model with a more fully developed Keynesian theory of expectations formation. As a result, the responsiveness of investment to changes in capacity utilization is reduced, and through mechanisms that have clear and plausible behavioural underpinnings. It therefore becomes more likely (in principle) that the Keynesian stability condition will hold in practice. The paper also explores the consequences of such re-specification of investment behaviour for certain comparative static results associated with the canonical Kaleckian growth model.

Expectations and Stability in the Kaleckian Growth Model

A central element in the canonical Kaleckian growth model is the demand-led output-adjustment stability condition known as the Keynesian stability condition. This condition requires that, all else constant, saving be more responsive to changes in capital capacity utilization than investment. This paper further explores the plausibility of the Keynesian stability condition by enriching the Kaleckian growth model with a more fully developed Keynesian theory of expectations formation. As a result, the responsiveness of investment to changes in capacity utilization is reduced, and through mechanisms that have clear and plausible behavioural underpinnings. It therefore becomes more likely (in principle) that the Keynesian stability condition will hold in practice. The paper also explores the consequences of such re-specification of investment behaviour for certain comparative static results associated with the canonical Kaleckian growth model.

Price caps, oligopoly, and entry

We extend the analysis of price caps in oligopoly markets to allow for sunk entry costs and endogenous entry. In the case of deterministic demand and constant marginal cost, reducing a price cap yields increased total output, consumer welfare, and total welfare, results consistent with those for oligopoly markets with a fixed number of firms. With deterministic demand and increasing marginal cost, these comparative static results may be fully reversed, and a welfare-improving cap may not exist. Recent results in the literature show that for a fixed number of firms, if demand is stochastic and marginal cost is constant, then lowering a price cap may either increase or decrease output and welfare (locally); however, a welfare-improving price cap does exist. In contrast to these recent results, we show that a welfare-improving cap may not exist if entry is endogenous. However, within this stochastic demand environment we show that certain restrictions on the curvature of demand are sufficient to ensure the existence of a welfare-improving cap when entry is endogenous.

Optimal plans and timing under additive transformations to rewards

The nature and role of additive transformations to rewards are elucidated for a general class of deterministic, nonautonomous, optimal control problems with many state and control variables. Conditions relating to the optimal choice of initial and terminal times and initial and terminal values of state variables are identified such that additive transformations affect optimal plans. General comparative static results are derived and the framework is extended to cover two common classes of stochastic control problems. Three applications are presented: the canonical adjustment cost model of a firm, a stochastic extension of an irreversible pollution accumulation problem with regime-switching, and an extension of a lifecycle model of retirement in which an agent’s retirement wealth evolves stochastically.

Who Obtains Greater Discounts on Automobile Insurance Premiums?

Insurance purchasers obtain varied discounts for insurance. This paper examines what drives these differences, specifically whether the loss probability and the wealth of the insured affect the size of the premium discount in automobile insurance. To describe a bargain between a client and an insurer over premiums and coverage, we first develop a sequential insurance bargaining game where the client has an outside option to bargain with another insurer. We find that the equilibrium involves full coverage and, based on the results of comparative statics, we propose hypotheses regarding the effects of the loss probability and the wealth of the insured on the size of the premium discount. We then use a unique data set of 85,806 observations of Taiwanese automobile liability insurance for property damage to empirically test the predictions. After controlling for underwriting and macroeconomic variables, we find that both (1) the insured with a lower claim probability (as a proxy for the insured with a lower loss probability) and (2) the insured with a higher salvage value car (as a proxy for the wealthier insured) receive a greater premium discount. These results support our theoretical results.

Balancing public goods in agriculture through safe minimum standards

We develop a general framework in which public goods are conflicting (complementary) if an increase in the provision of one public good raises (lowers) the marginal cost of providing another public good. The framework is used to analyse the policy implications of maintaining safe minimum standards (SMSs) for two public goods. The comparative-static results are illustrated using a sector model for Norwegian agriculture in which the SMSs for food security, agrobiodiversity and greenhouse gas emissions are modelled as constraints. The simulations show that even if public goods are conflicting, better-targeted policies can achieve SMSs at lower social costs.

Political Economy in a Changing World

We provide a general framework for the analysis of institutional dynamics in an environment in which payoffs and political powers change stochastically. Assuming that economic and political institutions as well as individual types can be ordered, and preferences and the distribution of political power satisfy natural “single-crossing” (increasing differences) conditions, we prove existence of a pure-strategy Markov voting equilibrium, provide conditions for its uniqueness, and present a number of comparative static results. We then use this framework to study the dynamics of political rights and repression in the presence of threats from extremist groups and the dynamics of collective experimentation.

Structural gravity with dummies only: Constrained ANOVA-type estimation of gravity models

The measurement of trade costs and their effects on outcome is at the heart of a large quantitative literature in international economics. The majority of the recent significant contributions on the matter assumes that trade is log-linear in exporter-specific factors, importer-specific factors, and log trade costs that are additively composed of a parameterized part and a residual part. We demonstrate that, under standard assumptions in the literature, the magnitude of unobservable, residual trade costs is large, and that their ignorance leads to a bias of the importance of observable trade-cost measures as well as of country-specific variables that are either solved implicitly through structural estimation or estimated explicitly as fixed effects. The reason is that, due to general-equilibrium linkages, some country-specific variables are endogenous to residual trade costs, regardless of whether they are captured by iteratively-solved structural terms or by country(-time) fixed effects. As a result, quantifications of effects of trade costs and comparative static results are also biased. Apart from diagnosing this problem, the paper provides remedies for it by proposing theory-consistent approaches including a two-step procedure that permits identifying partial effects of observable gravity variables on total trade costs and trade flows which do not suffer from the unobserved-trade-cost bias.

Status concerns as a motive for crime?

This paper analyzes the implications of potential offenders caring about their relative status. We establish that subjects’ status concerns can result in multiple-equilibrium crime rates and may modify the standard comparative-statics results regarding how the crime rate changes in response to a higher detection probability and higher sanctions. In addition, we argue that the socially optimal level of the detection probability and the sanction will often be higher when potential offenders care about their relative positions. Our analysis can be linked to one of the most important criminological theories of crime, namely strain theory.

Discretionary Disclosures to Risk‐Averse Traders: A Research Note

AbstractVerrecchia (1983) investigates a manager's incentives for costly, discretionary disclosure of his information to risk‐averse traders when the functional form of prices is exogenously specified. We extend Verrecchia (1983) by deriving the endogenously determined functional form of prices that would arise when all traders have constant risk tolerance. We show that these endogenously determined prices are inconsistent with the assumed prices in Verrecchia (1983) when the manager elects to not disclose. We derive the manager's disclosure strategy for our setting and extend the comparative static results in Verrecchia (1990) for risk‐neutral traders to a setting where traders have constant risk tolerance and prices are endogenously derived. Further, in our setting, discretionary disclosure does not affect how traders price risk of different outcomes. Also, we offer a representation of risk‐averse traders' prices using risk‐adjusted distributions. Finally, these results provide implications for empirical‐archival discretionary disclosure studies.

The Impact of Entrepreneurial Risk Aversion on Wages in General Equilibrium

One of the leading theories of entrepreneurship is that less risk averse individuals become entrepreneurs and more risk averse individuals become their employees. Kihlstrom and Laffont (1979) formalized this insight in an elegant and widely taught general equilibrium model. However, their model has not been further developed. A reason may be that their main comparative static result, that an economy-wide increase in risk aversion lowers the equilibrium wage, appeared to require the assumption that all agents had identical risk aversion index, throwing out their motivating insight and indicating that the model is intractable. In this note we prove this comparative static result on risk aversion and wages in general equilibrium, retaining agent heterogeneity in risk aversion and the endogenous division of agents into less risk averse entrepreneurs and more risk averse workers, without adding any assumptions not already in the original paper. Besides the intrinsic value of the result, we hope to increase the usefulness of the Kihlstrom and Laffont (1979) model for other researchers and to facilitate improvement in its exposition for the many graduate courses in which it is taught.

The Mechanics of Dualistic Models: "Comparable" Structures and Comparative Statics Results *

In this paper we present and confront the main comparative static results - effects of labor supply, demand and institutional wage movements - of the (a) basic two-sector model in six different scenarios: free market; partial (one-sector) coverage with perfect intersector mobility; partial (one-sector) coverage with imperfect mobility (Harris-Todaro); multiple (two-sector) coverage with imperfect mobility (Bhagwati-Hamada); partial (one-sector) coverage with affiliation restrictions in the covered sector; partial (one-sector) coverage with limited employment generation ability in the traditional uncovered sector.

A regret theory of capital structure

This paper examines the optimal capital structure of a firm that delegates its financing decision of a risky project to a manager who is both risk averse and regret averse. Regret aversion is characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that the manager optimally opts for zero leverage if risk aversion is relatively more important than regret aversion in representing the manager’s preferences. Otherwise, the optimal capital structure is interior such that the optimal amount of debt increases when regret aversion becomes increasingly more important than risk aversion in representing the manager’s preferences. We further show that the firm’s market leverage ratio is inversely related to the project’s profitability and to the firm’s market-to-book ratio. These comparative static results are consistent with the robust evidence documented in the literature on empirical capital structure.

Impact of Low‐Skilled Immigration on Female Labour Supply

AbstractIn this paper, segmenting the market by educational levels, we investigate which native‐born women are more affected by an increase of low‐skilled immigrants working in the household service sector. We present a model of individual choice with home production and, using a harmonized dataset (the Cross‐National Equivalent File), we estimate its main comparative static results. The results suggest that the share of immigrants working in services is positively associated with an increase of native‐born women's labour supply at the intensive margin, if skilled, and at the extensive margin, if unskilled. Moreover, the results show that these effects are larger in countries with less‐supportive family policies.

Apple Export Competition between the United States and China in the Association of Southeast Asian Nations

We developed a trade model under imperfect competition to analyze the market power of U.S. and Chinese apple producers in the Association of Southeast Asian Nations (ASEAN) market and their domestic markets and the elimination of ASEAN tariffs on U.S. and Chinese apples. We also formulated welfare functions for the United States, China, and ASEAN. Comparative static results are derived to analyze the effect of tariff changes on exports, domestic sales, and welfare. Based on the theoretical model, we derived an econometric specification and used the new empirical industrial organization literature to estimate the market power of U.S. and Chinese apple producers. The econometric model is simulated to quantify the effect of tariff removal on exports and domestic sales.

Fraud and Monitoring in Non-competitive Elections

This article develops a game-theoretic model that reconciles three facts: (1) fraud is pervasive in non-competitive elections, (2) domestic and international monitoring of elections have become nearly universal and (3) incumbent regimes often invite monitoring and still cheat. The incumbent regime commits fraud to manipulate the information generated by a non-competitive election before a political interaction with someaudience. The audience expects fraud, so the incumbent commits fraud because she would appear weak if not doing so. Increasing the visibility of fraud with monitoring is valuable because it lowers the equilibrium level of costly fraud without changing how popular the incumbent appears. The core results hold under multiple extensions, which produce a rich set of comparative static results.

“Little Science” and “Big Science”: The institution of “Open Science” as a cause of scientific and economic inequalities among countries

In this paper we analyse how the science sector's incentive structure strongly contributes to the development of science and of the economy, even if, in the same time, it can cause large disparities in size and productivity of scientific sectors of different countries. In order to show that, we adopt a Schumpeterian growth model where the resources allocated to science are endogenously determined within the economy and science is organised according to the institution of “Open Science”. This latter consists in a self-reinforcing code of conduct, which comprises an incentive scheme based on the priority rule, and on the presence of both real rewards and social rewards. Social rewards take two main forms according to the source concerned: one is the social reward deriving from major innovations; another consists in high reputation enjoyed by researchers who put a high level of effort into their job, and devote themselves to the advancement of science. This set of rules causes the emergence of two locally stable steady-states: a low equilibrium, where the economy is endowed with a small science sector; and a high equilibrium, where the economy has a large science sector with rapid knowledge advancement. The two equilibria can account for the huge differences currently existing between scientific sectors of more developed and less developed countries. Comparative static results further characterise the two equilibria, since monetary and social rewards have different effects according to the type of equilibrium that emerges.

Discretionary Disclosures to Risk-Averse Traders: A Research Note

Verrecchia (1983) investigates a manager’s incentives for costly, discretionary disclosure of his information to risk-averse traders when the functional form of prices is exogenously specified. We extend Verrecchia (1983) by deriving the endogenously determined functional form of prices that would arise when all traders have constant risk tolerance. We show that these endogenously determined prices are inconsistent with the assumed prices in Verrecchia (1983) when the manager elects to not disclose. We derive the manager’s disclosure strategy for our setting and extend the comparative static results in Verrecchia (1990) for risk-neutral traders to a setting where traders have constant risk tolerance and prices are endogenously derived. Further, in our setting, discretionary disclosure does not affect how traders price risk of different outcomes. Also, we offer a representation of risk-averse traders’ prices using risk-adjusted distributions. Finally, these results provide implications for empirical-archival discretionary disclosure studies.

On the optimal target curbside parking occupancy rate

Donald Shoup, following Vickrey, has long advocated cashing out free and underpriced parking. How should this be implemented for curbside parking in practice, considering the stochasticity of curbside parking vacancies? Shoup has proposed adjusting meter rates such that, for each block and time period, a target (average) curbside parking occupancy rate of 85% is achieved. This paper develops a simple structural model of stochastic steady-state curbside parking in an isotropic space, solving for the surplus-maximizing occupancy rate and the corresponding meter rate. By increasing curbside occupancy, a curbside parker imposes a curbside parking externality. The optimal meter rate internalizes this externality. The central comparative static result is that, ceteris paribus, the optimal occupancy and meter rates are higher, the higher is demand relative to curbside parking capacity. This suggests that, in practice, the occupancy rate should be higher in more trafficked locations and at busier times of the day.