Comparative Statics Exercises Research Articles

Decisiones de consumo y portafolio con Utilidad Diferencial Recursiva Estocástica (UDRE): Modelos alternativos

The intertemporal elasticity of substitution and the risk aversion coefficient are regularly obtained from models for the valuation of assets based on consumption as in Merton (1973), Lucas (1978), Breeden (1979) and Maenhout (2004). However, this approach is criticized for two reasons: the first is related to the empirical issue, since in practical research the models do not fit the data, and the second one does not distinguish between intertemporal elasticity of substitution and risk aversion coefficient due the functional form of utility assumed in this approach. Evidently, these two concepts are useful in the economic theory, since they are related to different relevant aspects of consumer preferences. This research focuses on the second problem, being the goal of this paper to use the concept of Recursive Stochastic Differential Utility to obtain the parameters in question, separately, but in the same model. Under this framework, several continuous-time decision making models of a rational consumer having access to different assets are developed, this allows a better interpretation and explanation of the mentioned parameters. Finally, comparative static exercises are performed to explain the dynamics of the decision variable to changes in the independent variables with Mexican data.

Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset

This paper analyzes a noncooperative and symmetric dynamic game where players have free access to a productive asset whose evolution is a diffusion process with Brownian uncertainty. A Euler–Lagrange equation is found and used to provide necessary and sufficient conditions for the existence and uniqueness of a smooth Markov Perfect Nash Equilibrium. The Euler–Lagrange equation also provides a stochastic Keynes–Ramsey rule, which has the form of a forward–backward stochastic differential equation. It is used to study the properties of the equilibrium and to make some comparative statics exercises.

Unemployment Insurance in the Presence of an Informal Sector

We study the effect of UI bene?ts in a typical developing country where the informal sector is sizeable and persistent. In a partial equilibrium environment, ruling out the macroeconomic consequences of UI benefits, we characterize the stationary equilibrium of an economy where policyholders may be employed in the formal sector, short-run unemployed receiving UI benefits or long-run unemployed without UI benefits. We perform comparative static exercises to understand how UI benefits affect unemployed workers'effort to secure a formal job and their labor supply in the informal sector. Our model reveals that an increase in UI benefits generates two opposing effects for the short-run unemployed. First, since search efforts cannot be monitored it generates moral hazard behaviours that lower effort. Second, it generates an income effect as it reduces the marginal cost of searching for a formal job and increases effort. Even though in general it is ambiguous which effect dominates, we show that for short durations UI benefits increase unemployed worker's effort to secure a formal-sector job and decreases informal-sector work.

How Do People Choose Their Commuting Mode? An Evolutionary Approach to Transport Choices

The issue of transportation is of primary importance in our societies. A large share of greenhouse gases is generated by the transport sector, and road casualties are one among the most common causes of death. In the present work, we study commuter choice between alternative transport modes using an evolutionary- game model, wherein commuters can choose between using their private car or taking the bus. We examine the possible dynamics that can emerge in a homogeneous urban population, where agents are boundedly rational and imitate the others. We obtain a different number of equilibria depending on the values of the parameters of the model. We carry out comparative-static exercises and examine possible policy measures that can be implemented in order to modify the agents’ payoff, and consequently the equilibria of the system, leading the society towards more sustainable transportation patterns.

Dynamic matching and bargaining with heterogeneous deadlines

This paper analyzes bargaining outcomes when agents do not have stationary time preferences (as represented by a constant discount factor) but are pressed by firm deadlines. We consider a dynamic model where traders with heterogeneous deadlines are matched randomly into pairs who then bargain about the division of a fixed surplus. A trader leaves the market when an agreement has been reached or when his deadline expires. Our analysis encompasses both the case of perfect and imperfect information about the partner’s deadline. We define, characterize and show the existence of a stationary equilibrium configuration. We characterize when delay occurs and when deadlines are missed in equilibrium and show that the payoffs of traders are strictly increasing and concave in own deadline, unless bargaining takes place under imperfect information and no delay occurs, in which case all pairs immediately agree on an almost even split. We provide comparative statics exercises and illustrate our results by some examples.

Identification and counterfactuals in dynamic models of market entry and exit

This paper addresses a fundamental identification problem in the structural estimation of dynamic oligopoly models of market entry and exit. Using the standard datasets in existing empirical applications, three components of a firm’s profit function are not separately identified: the fixed cost of an incumbent firm, the entry cost of a new entrant, and the scrap value of an exiting firm. We study the implications of this result on the power of this class of models to identify the effects of different comparative static exercises and counterfactual public policies. First, we derive a closed-form relationship between the three unknown structural functions and the two functions that are identified from the data. We use this relationship to provide the correct interpretation of the estimated objects that are obtained under the ‘normalization assumptions’ considered in most applications. Second, we characterize a class of counterfactual experiments that are identified using the estimated model, despite the non-separate identification of the three primitives. Third, we show that there is a general class of counterfactual experiments of economic relevance that are not identified. We present a numerical example that illustrates how ignoring the non-identification of these counterfactuals (i.e., making a ‘normalization assumption’ on some of the three primitives) generates sizable biases that can modify even the sign of the estimated effects. Finally, we discuss possible solutions to address these identification problems.

Identification and Counterfactuals in Dynamic Models of Market Entry and Exit

This paper deals with a fundamental identification problem in the structural estimation of dynamic oligopoly models of market entry and exit. Using the standard datasets in existing empirical applications, there are three key components of a firm's profit function that are not separately identified: the fixed cost of an incumbent firm, the entry cost of a new entrant, and the scrap-value of an exiting firm. We study the implications of this result on the power of this class of models to identify the effects of comparative static exercises or public policies involving changes in these structural functions. First, we derive a closed-form relationship between the three unknown structural functions and two functions that are identified from the data. We use this relationship to provide the correct interpretation of the estimated objects that are obtained under the 'normalization assumptions' considered in most applications. Second, we characterize a class of counterfactual experiments that are identified using the estimated model, despite the non-separate identification of the three primitives. Third, we show that there is a general class of counterfactual experiments of economic relevance that are not identified. We present numerical examples that illustrate how ignoring the non-identification of these counterfactuals (i.e., making a 'normalization assumption' on some of the three primitives) generates sizable biases that can modify even the sign of the estimated effects. Finally, we discuss possible solutions to deal with these identification problems.

Altruistically unbalanced kidney exchange

Although a pilot national live-donor kidney exchange program was recently launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange framework that has both compatible and incompatible pairs, and patients are indifferent over compatible pairs. Only two-way exchanges are permitted because of institutional constraints. We explore the structure of Pareto-efficient matchings in this framework. We show that under Pareto-efficient matchings, the same number of patients receive transplants, and it is possible to construct Pareto-efficient matchings that match the same incompatible pairs while matching the least number of compatible pairs. We extend the celebrated Gallai–Edmonds Decomposition in the combinatorial optimization literature to our new framework. We also conduct comparative static exercises on how this decomposition changes as new compatible pairs join the pool.

Estimating the cost of future global energy supply

Abstract This study produces an attempt to estimate the cost of future global energy supplies. The approach chosen to address this concern relies on a comparative static exercise of estimating the cost of three energy scenarios representing different energy futures. The first scenario, the business as usual scenario, predicts the future energy-mix based on the energy plans held by major countries. The second scenario is the renewable energy scenario, where as much of the primary energy supply as possible is replaced by renewable energy by 2050. The cost of the renewable energy generating technologies and their theoretical potential are taken into account in order to create a plausible scenario. The third scenario, the nuclear case, is based on the use of nuclear and renewable energy to replace fossil-fuels by 2050. Endogenous learning rates for each technology are modeled using an innovative approach where learning rates are diminishing overtime. It results from the analysis that going fully renewable would cost between −0.4 and 1.5% of the global cumulated GDP over the period 2009–2050 compared to a business as usual strategy. An extensive use of nuclear power can greatly reduce this gap in costs.

On the moral hazard problem without the first-order approach

We study the moral hazard problem without the first-order approach or other common structure. We present sufficient conditions under which the shadow value of simultaneously tightening the minimum payment and individual rationality constraints has a simple and intuitive expression. We then show how this expression can be used to perform comparative statics exercises in which we study (i) the effect of a change in the agentʼs wealth on the well-being of the principal; and (ii) the effects of the outside option and minimum payment on the effort level optimally implemented.

Disclosure of information in matching markets with non-transferable utility

We present a model of two-sided matching where utility is non-transferable and information about individualsʼ skills is private, utilities are strictly increasing in the partnerʼs skill and satisfy increasing differences. Skills can be either revealed or kept hidden, but while agents on one side have verifiable skills, agents on the other side have skills that are unverifiable unless certified, and certification is costly. Agents who have revealed their skill enter a standard matching market, while others are matched randomly. We find that in equilibrium only agents with skills above a cutoff reveal, and then they match assortatively. We show that an equilibrium always exists, and we discuss multiplicity. Increasing differences play an important role to shape equilibria, and we remark that this is unusual in matching models with non-transferable utility. We close the paper with some comparative statics exercises where we show the existence of non-trivial externalities and welfare implications.

Unemployment Insurance in the Presence of an Informal Sector

We study the effect of UI benefits in a typical developing country where the informal sector is sizeable and persistent. In a partial equilibrium environment we characterize the stationary equilibrium of an economy where policyholders may be employed in the formal sector, short-run unemployed receiving UI benefits and long-run unemployed without UI benefits. We perform comparative static exercises to understand how UI benefits affect unemployed workers’ effort to secure a formal job, their labor supply in the informal sector and leisure time. Our model reveals that an increase in UI benefits generates two opposing effects for the short-run unemployed. First, since search efforts cannot be monitored it generates moral hazard behaviours that lower effort. Second, it generates an income effect as it reduces the marginal cost of searching for a formal job and increases effort. The overall effect is ambiguous and depends on the relative strength of these two effects. Additionally, we show that an increase in UI benefits increases the efforts of long-run unemployed workers. Using data from Brazil to calibrate the parameters of the model we provide a simple simulation exercise which suggests that the income effect pointed out is not necessarily of second-order importance in comparison with moral hazard strength: An increase in UI benefits may increase unemployed workers efforts to secure a job in the formal sector, instead of increasing informal-sector work. This result softens the widespread opinion that the presence of dual labor markets is an obstacle to providing UI in developing countries.

Contests with group-specific public goods and complementarities in efforts

This paper starts from the observation that in public-goods group contests, group impact can in general not be additively decomposed into some sum (of functions) of individual efforts. We use a CES-impact function to identify the main channels of influence of the elasticity of substitution on the behavior in and the outcome of such a contest. We characterize the Nash equilibria of this game and carry out comparative-static exercises with respect to the elasticity of substitution among group members’ efforts. If groups are homogeneous (i.e. all group members have the same valuation and efficiency within the group), the elasticity of substitution has no effect on the equilibrium. For heterogeneous groups, the higher the complementarity of efforts of that group, the lower the divergence of efforts among group members and the lower the winning probability of that group. This contradicts the common intuition that groups can improve their performance by solving the free-rider problem via higher degrees of complementarity of efforts.

Estimating the Cost of Future Global Energy Supply

This study produces an attempt to estimate the cost of future global energy supplies. The approach chosen to address this concern relies on a comparative static exercise of estimating the cost of three energy scenarios representing different energy futures. The first scenario, the business as usual scenario predicts the future energy-mix based on the energy plans held by major countries. The second scenario is the renewable energy scenario, where as much of the primary energy supply as possible is replaced by renewable energy by 2050. The cost of the renewable energy generating technologies and their theoretical potential are taken into account in order to create a plausible scenario. The third scenario, the nuclear case, is based on the use of nuclear and renewable energy to replace fossil-fuels by 2050. Endogenous learning rates for each technology were modeled using an innovative approach where the learning rate of a traditional experience curve is diminishing overtime. It results from the analysis that going fully renewable would cost about 10-40% extra compared to a business as usual case. Extensively using nuclear power can greatly this gap in costs.

Skill-Biased Labor Market Reforms and International Competitiveness

AbstractThis paper proposes a multi-industry trade model with integrated capital and goods markets. Labor market imperfections in line with Mortensen and Pissarides (Job Creation and Job Destruction in the Theory of Unemployment, 1994) give rise to unemployment and a channel for the government to influence markets through institutional changes. Labor market interventions feedback into the product market through changes in a country’s competitiveness. Moreover, the distinction between high- and low-skill workers facilitates the analysis of skillbiased institutional changes that have stronger impact on certain skill groups. The comparative static exercise in this paper shows that high-skilled benefit from low-skill biased labor market reforms through higher wages. Lower labor costs reduce unemployment of the low-skilled and increases the reforming country’s competitiveness. One-sided labor market interventions have feedback effects through adjustments at the extensive margin, which affect all workers at home and abroad irrespective of their level of skill. Governments in the non-reforming countries may react to this loss in competitiveness by initiating cooperative labor market reforms instead.

Macroeconomic consequences of increased productivity in less developed economies

This paper examines the impact of improvements in productivity on prices, output, the real wage rate and the balance of payments. Within the context of the model used in this paper, an improvement in productivity can take two alternative forms: (1) a cost saving for a given output and (2) an increase in production without a direct decrease in employment. The results presented are based on a simple model of a small open economy that includes some key features of less developed economies. It is shown that, in the presence of monetary and fiscal restraints, an improvement in productivity leads to increases in output, employment and the real wage and the effect on the balance of payments, in the short and the medium runs, is also positive. We find that whether or not improvement in productivity is import saving plays a crucial role in both comparative static and simulation exercises.

Altruistically Unbalanced Kidney Exchange

Although a pilot national live-donor kidney exchange program was recently launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange framework that has both compatible and incompatible pairs, and patients are indifferent over compatible pairs. Only two-way exchanges are permitted due to institutional constraints. We explore the structure of Pareto-efficient matchings in this framework. The mathematical structure of this model turns out to be quite novel. We show that under Pareto-efficient matchings, the same number of patients receive transplants, and it is possible to construct Pareto-efficient matchings that match the same incompatible pairs while matching the least number of compatible pairs. We extend the celebrated Gallai-Edmonds Decomposition in the combinatorial optimization literature to our new framework. We also conduct comparative static exercises on how this decomposition changes as new compatible pairs join the pool.

Equilibrium Simulation with Microeconometric Models: A New Procedure with an Application to Income Support Policies

Many microeconometric models of discrete labour supply include alternative-specific constants meant to account for (possibly besides other factors) the density or accessibility of particular types of jobs (e.g. part-time jobs vs. full-time jobs). The most common use of these models is the simulation of tax-transfer reforms. The simulation is usually interpreted as a comparative statics exercise, i.e. the comparison of different equilibria induced by different policy regimes. The simulation procedure, however, typically keeps fixed the estimated alternative-specific constants. In this note we argue that this procedure is not consistent with the comparative statics interpretation. Since the constants reflect the number of jobs and since the number of people willing to work changes as a response to the change in tax-transfer regime, the new equilibrium induced by the reform implies that the constants should also change. A structural interpretation of the alternative-specific constants leads to the development of a simulation procedure consistent with the comparative statics interpretation. The procedure is illustrated with a simulation of alternative reforms of the income support policies in Italy.

A new equilibrium simulation procedure with discrete choice models

Many microeconometric models of discrete choice include alternative-specific constants meant to account for (possibly besides other factors) the density or accessibility of particular types of alternatives. A notable area of application is labour supply, where for example part-time jobs vs. full-time jobs might be more or less accessible. The most common use of these models is the simulation of tax-transfer reforms. The simulation is usually interpreted as a comparative statics exercise, i.e. the comparison of different equilibria induced by different policy regimes. The simulation procedure, however, typically keeps fixed the estimated alternative- specific constants. In this note we argue that this procedure is not consistent with the comparative statics interpretation. Since the constants reflect the number of jobs and since the number of people willing to work changes as a response to the change in tax-transfer regime, the new equilibrium induced by the reform implies that the constants should also change. A structural interpretation of the alternative-specific constants leads to the development of a simulation procedure consistent with the comparative statics interpretation. The procedure is illustrated with a simulation of alternative reforms of the income support policies in Italy.

Firm R&D Games With Differing Manufacturing Costs

The paper considers an industry where competition is characterized as a two-stage game between the two firms in which the product reliabilities are determined before the (Coumot) quantities. Reliability is determined by R&D expenditure. The focus is on how competitive conditions in terms of manufacturing costs affect tile firms' decision about optimal reliability. The main result of the paper is that the firm with lower manufacturing cost produces a more reliable product. However a reduction in a given. firm 's manufacturing cost only causes it to produce a more reliable product when the difference in costs between firms is low. Comparative static exercises suggest that reliability generally increases when customers have a higher reservation price for the product and a lower customer cost of product failure.