Comparative Statics Exercises Research Articles

Search, unemployment, and the Beveridge curve: Experimental evidence

We report on a laboratory experiment testing the predictions of the Diamond–Mortensen–Pissarides (DMP) search-and-matching model, which is a workhorse, decentralized model of unemployment and the labor market. We focus on the job vacancy posting problem that firms face in the DMP model. We explore the model’s comparative statics predictions concerning variations in the separation rate, the vacancy posting cost, and the firm’s surplus earned per employee. Across all treatments, we find strong evidence for an inverse relationship between vacancies and unemployment, consistent with the Beveridge curve. We also find that the results of our various comparative statics exercises are in-line with the predictions of the theory.

Stochastic Ordering of Stationary Distributions of Linear Recurrences: Further Results and Economic Applications

We investigate pairwise stochastic comparisons of stationary solutions to the linear recurrence Xt+1=AtXt+Bt, where At and Bt are non-negative random variables. We establish novel order-preserving properties, which enable us to obtain comparison theorems about well-known measures of conditional size, tail variability and skewness across probability distributions. While useful in studies of ergodic wealth accumulation processes and the persistence of inequality, our results can fruitfully be exploited to conduct comparative statics exercises in structural models entailing Kesten-type reduced-form representations. An application of our analysis to a dynamic asset accumulation model uncovers the qualitatively similar effects of capital income and earnings taxation on expected wealth concentration over higher quantiles as well as on conditional upper tail dispersion of wealth holdings, qualifying previous results that solely rely on the determination of Pareto exponents.

Robots, Trade, and Luddism: A Sufficient Statistic Approach to Optimal Technology Regulation

Abstract Technological change, from the advent of robots to expanded trade opportunities, creates winners and losers. How should government policy respond? We provide a general theory of optimal technology regulation in a second-best world, with rich heterogeneity across households, linear taxes on the subset of firms affected by technological change, and a non-linear tax on labour income. Our first set of results consists of optimal tax formulas, with minimal structural assumptions, involving sufficient statistics that can be implemented using evidence on the distributional impact of new technologies, such as robots and trade. Our final results are comparative static exercises illustrating, among other things, that while distributional concerns create a rationale for non-zero taxes on robots and trade, the magnitude of these taxes may decrease as the process of automation and globalization deepens and inequality increases.

Heterogeneous effects and spillovers of macroprudential policy in an agent-based model of the UK housing market

AbstractWe develop an agent-based model of the UK housing market to study the impact of macroprudential policy experiments on key housing market indicators. The heterogeneous nature of this model enables us to assess the effects of such experiments on the housing, rental, and mortgage markets not only in the aggregate, but also at the level of individual households and sub-segments, such as first-time buyers, homeowners, buy-to-let (BTL) investors, and renters. This approach can, therefore, offer a broad picture of the disaggregated effects of financial stability policies. The model is calibrated using a large selection of micro-data, including data from a leading UK real-estate online search engine as well as loan-level regulatory data. With a series of comparative static exercises, we investigate the impact of (i) a hard loan-to-value limit and (ii) a soft loan-to-income limit, allowing for a limited share of unconstrained new mortgages. We find that, first, these experiments tend to mitigate the house price cycle by reducing credit availability and therefore leverage. Second, an experiment targeting a specific risk measure may also affect other risk metrics, thus necessitating a careful calibration of the policy to achieve a given reduction in risk. Third, experiments targeting the owner-occupier housing market can spill over to the rental sector, as a compositional shift in home ownership from owner-occupiers to BTL investors affects both the supply of and the demand for rental properties.

A Game Theoretic Approach to Peer Review of Grant Proposals

Abstract This paper studies the grant peer review process employed by the Turkish regional development agencies, which is adapted from a review procedure of the Education, Audiovisual and Culture Executive Agency of the European Union. To model this process, we consider a Bayesian strategic-form game played by three reviewers who observe both a common and a private score signal about an evaluated project and assign their scores to minimize the sum of their disutilities from the false acceptance and false rejection of the project. We numerically compute the Bayesian Nash equilibria of this game and conduct several comparative statics exercises, after calibrating the model parameters accordingly. We also introduce two simpler review processes and compare their performances to that of the calibrated process in terms of outcome statistics, involving pass and fail rates of the evaluated projects, and manipulation statistics, involving the reviewers’ manipulation rate and size of scores.

Policy shocks, current account and the macroeconomy in a developing country

Purpose This is a theoretical paper in the field of international macroeconomics. The purpose of this paper is to focus on a dynamic interaction between current account imbalance and unemployment in response to some policy-induced shocks for a small open economy under a flexible exchange rate. Design/methodology/approach The paper uses a two-sector framework: one sector is traded and another is the non-traded sector that is subject to an effective demand constraint. The current account imbalance arises due to the discrepancy between production of traded goods, household consumption of traded goods and government purchases of importables. The authors keep the asset structure simple by considering only domestic currency and foreign bonds that are imperfect substitutes. The paper considers a standard methodology of dynamic adjustment process involving change in foreign exchange reserves and exchange rate under perfect foresight. The saddle path properties of the equilibrium are also examined. Findings The results of comparative static exercises depend on a set of structural features of a developing country, which include asset substitutability, wage price rigidity and sectoral asymmetries. The paper shows that expansionary monetary policy, balanced budget fiscal expansion and financial liberalization have an ambiguous effect on the current account balance, foreign exchange reserves, non-traded sector and the level of employment. Originality/value The existence of Keynesian unemployment with fixed prices is the key ingredient of this paper. The paper introduces the problem of effective demand to analyze the dynamics of current account balance and exchange rate, which, in turn, determine the sectoral composition of output and level of employment.

Optimal consumption decisions of family networks with similar felicity functions

Family networks have increased at an accelerated pace through social networking through social networking services, online platforms, and social media clubs. This paper develops a model of an economy populated by networks of families with similar preferences (the same functional form of the felicity or utility function) but family members differ in their deep parameters (compulsion for consumption and risk tolerance), which, in turn, leads to some kind o heterogeneity among the families. In this context, the problem of felicity (utility) maximization of the average family in the network is solved. The optimal path of consumption is obtained for the average family and graphical comparative static exercises are performed. Finally, the economic welfare of the typical family in a network is calculated and comparative static experiments are carried out. This approach improves the understanding of the consumption decision making of families interacting in social networking services.

Globalization, Agro-Based Industry and Unemployment: A Three-Sector General Equilibrium Model

This paper explains how different interconnected measures of globalization, namely, tariff reform, labour market reform and capital account liberalization influence different sectors of the economy, unemployment and flexible wage of unskilled labour in the informal sector. In so doing we depart from the conventional Harris-Todaro type of model of open urban unemployment. The different comparative static exercises performed in a three-sector general equilibrium clearly indicate that globalization is not a panacea for the multitude of problems of an emerging market economy.JEL Classification- E26, F16

Two‐Aggregate Games: Demonstration Using a Production–Appropriation Model

AbstractWe expand the scope of the two‐aggregate method by applying it to a situation in which many heterogeneous players are free to contribute to both aggregates. Such situations naturally arise in various resource allocation problems. Hence, our method is useful in many applications. A production–appropriation model is employed to illustrate how the problem of establishing the Nash equilibrium can be reduced from solving n>2 best‐response functions in n unknowns to solving two consistency conditions in two unknowns. We then conduct a comparative static exercise that the conventional approach could not handle easily, if at all, to demonstrate the power of our method.

Capital Accumulation, Asset Price Dynamics and the Macroeconomy

This article develops a dependent economy model of determination of employment and asset prices that integrates the roles of relative prices, expectations and dynamics of capital accumulation. In this model, money wage is rigid which leads to persistence of unemployment. Labour and capital are used as factors of production in the traded sector while the non-traded sector uses labour and imported intermediate inputs. The article examines macroeconomic implications of selective economic reforms for asset price dynamics, growth and employment. The discussion of comparative static exercises shows that not only the effects of different policies are ambiguous but also the short-run and the long-run effects are qualitatively different. For example, tariff liberalization causes the short-run expansions of both traded and non-traded sectors but overtime it may depress the capital stock leading to contraction of both the sectors and an increase in unemployment. The broad message of this article is that the design of macroeconomic policy should not be purely based on considerations of the short-run effects of policy changes. JEL: E22, F13, F41

How do people choose their commuting mode? An evolutionary approach to travel choices

A considerable amount of studies in the transport literature is aimed at understanding the behavioural processes underlying travel choices, like mode and destination choices. In the present work, we propose the use of evolutionary game theory as a framework to study commuter mode choice. Evolutionary game models work under the assumptions that agents are boundedly rational and imitate others’ behaviour. We examine the possible dynamics that can emerge in a homogeneous urban population where commuters can choose between two modes, private car or public transport. 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 society towards more sustainable transportation patterns.

Coordination on Networks

We study a coordination game among agents on a network, who choose whether or not to take an action in an uncertain environment that yields value increasing in the actions of neighbors. We develop an algorithm that fully characterizes the equilibrium partitions (coordination sets) and thresholds using the primitives of the model. We show that there is a single coordination set if and only if the network is balanced, i.e., the average degree of each subnetwork is no larger than the average degree of the network. Comparative statics exercises as well as welfare properties are investigated. In particular, we show that contagion is localized within coordination sets. Compared to the perfect information case, both the equilibrium selection, the comparative statics properties as well as the policy implications are different.

Regularity of a general equilibrium in a model with infinite past and future

We develop easy-to-verify conditions to assure that a comparative statics exercise in a dynamic general equilibrium model is feasible, i.e., the implicit function theorem is applicable. Consider an equilibrium equation, ϒ(k,E)=k of a model where an equilibrium variable (k) is a continuous bounded function of time, real line, and the policy parameter (E) is a locally integrable function of time. The key conditions are time invariance of ϒ and the requirement that the Fourier transform of the derivative of ϒ with respect to k does not return unity. Further, in a general constant-returns-to-scale production and homogeneous life-time-utility overlapping generations model we show that the first condition is satisfied at a balanced growth equilibrium and the second condition is satisfied for “almost all” policies that give rise to such equilibria.

Illicit activity and money laundering from an economic growth perspective: A model and an application to Colombia

This paper contributes to the economic analysis of illicit activities and money laundering. First, it presents a theoretical model of long-run growth that explicitly considers illicit workers, activities, and income, alongside a licit private sector and a functioning government. Second, it generates estimates of the size of illicit income and provides simulated and econometric estimates of the volume of laundered assets in the Colombian economy. In the model, the licit sector operates in a perfectly competitive environment and produces a good through a standard neoclassical production function. The illicit sector operates in an imperfectly competitive environment and is composed of two different activities: The first activity produces an illicit good that nonetheless is valuable in the market (for example illegal drugs); the second does not add value to the economy but only redistributes wealth (for example robbery, kidnapping, and fraud). The paper provides a series of comparative statics exercises to assess the effects of changes in government efficiency, licit sector productivity, and the demand for illegal drugs. From the model, the analysis derives a set of estimable macroeconometric equations to measure the size of laundered assets in the Colombian economy in the period 1985–2013. The paper assembles a dataset whose key components are estimates of illicit income from drug trafficking and common crime. Illicit incomes increased drastically until 2001, reaching a peak of nearly 12% of gross domestic product and then decreasing to less than 2% by 2013. The decline not only overlaps with a period of high economic growth but also occurs after the implementation of Plan Colombia. The dataset is used to estimate the volume of laundered assets in the economy by applying the Kalman filter for the estimation of unobserved dynamic variables onto the derived macroeconometric equations from the model. The findings show that the volume of laundered assets increased from about 8% of gross domestic product in the mid-1980s to a peak of 14% by 2002, and declined to 8% in 2013.

Huggett economies with multiple stationary equilibria

I obtain a closed-form solution to a Huggett economy with constant absolute risk aversion (CARA) utility when the vector of individual state variables follows a VAR(1) process with an arbitrary shock distribution. The stationary equilibrium is unique if the income process is AR(1), but not necessarily so otherwise. With Gaussian shocks, I provide general sufficient conditions for the existence of at least three equilibria when the income process is either ARMA(1,1), AR(2), or has a persistent-transitory (PT) representation with negatively correlated shocks. The possibility of multiple equilibria calls for caution in comparative statics exercises and policy analyses using heterogeneous-agent models. As an illustration I provide an example in which the welfare implication of changing the income risk goes in opposite directions depending on the choice of equilibrium.

Huggett Economies with Multiple Stationary Equilibria

I obtain a closed-form solution to a Huggett economy with constant absolute risk aversion (CARA) utility when the vector of individual state variables follows a VAR(1) process with an arbitrary shock distribution. The stationary equilibrium is unique if the income process is AR(1), but not necessarily so otherwise. With Gaussian shocks, I provide general sufficient conditions for the existence of at least three equilibria when the income process is either ARMA(1,1), AR(2), or has a persistent-transitory (PT) representation with negatively correlated shocks. The possibility of multiple equilibria calls for caution in comparative statics exercises and policy analyses using heterogeneous-agent models. As an illustration I provide an example in which the welfare implication of changing the income risk goes in opposite directions depending on the choice of equilibrium.

Heterogeneite de la Transmission de la Politique Monetaire et Evaluation Interne du Risque de Credit : Analyse en Equilibre Partiel

This article presents a partial equilibrium model of the credit market, with banking duopoly subject to a regulatory capital. The results of the model reveal a heterogeneity of monetary policy transmission, due to the disparity of internal rating based methods used by banks to calculate risk-weighted assets and capital requirement. The comparative statics exercise shows a weakening of the credit channel because of risk estimation bias and internal rating methods variability. Thus, the article highlights the strategic issue of the “laissez-faire” given to banks in determining their regulatory capital and calls for a reconciliation between micro-prudential regulation and macroeconomic policy making so as to establish macro-prudential regulation.

The MBR intertemporal choice criterion and Rawls’ just savings principle

This paper provides general theorems about the control that maximizes the mixed Bentham–Rawls (MBR) criterion for intergenerational justice, which was introduced in Alvarez-Cuadrado and Long (2009). We establish sufficient concavity conditions for a candidate trajectory to be optimal and unique. We show that the state variable is monotonic under rather weak conditions. We also prove that inequality among generations, captured by the gap between the poorest and the richest generations, is lower when optimization is performed under the MBR criterion rather than under the discounted utilitarian criterion. A quadratic example is also used to perform comparative static exercises: it turns out, in particular, that the larger the weight attributed to the maximin part of the MBR criterion, the better-off the less fortunate generations. All those properties are discussed and compared with those of the discounted utilitarian (DU, Koopmans 1960) and the rank-discounted utilitarian (RDU, Zuber and Asheim, 2012) criteria. We contend they are in line with some aspects of the rawlsian just savings principle.

Macroprudential Policy in an Agent-Based Model of the UK Housing Market

This paper develops an agent-based model of the UK housing market to study the impact of macroprudential policies on key housing market indicators. This approach enables us to tackle the heterogeneity in this market by modelling the individual behaviour and interactions of first-time buyers, home owners, buy-to-let investors, and renters from the bottom up, and observe the resulting aggregate dynamics in the property and credit markets. The model is calibrated using a large selection of micro-data, mostly from household surveys and housing market data sources. We perform a series of comparative statics exercises to investigate the impact of the size of the rental/buy-to-let sector and different types of buy-to-let investors on housing booms and busts. The results suggest that an increase in the size of the buy-to-let sector may amplify house price cycles and increase house price volatility.Furthermore, in order to illustrate the effects of macroprudential policies on several housing market indicators, we implement a loan-to-income portfolio limit. We find that this policy attenuates the house price cycle.

Integrating Collective Codels and the Marriage Market: An Illustration

In this paper, I show how the ITU framework developed recently by Galichon, Kominers and Weber (2016) can be used to integrate collective models to the marriage market. I set up a simple model with Cobb-Douglas utility functions, and show how it can be embedded in their matching framework. I show how important concepts such as the Pareto weights or the sharing rule are connected to this setting. Finally, I provide several numerical examples as well as comparative statics exercises to illustrate the properties of the model.