Stochastic Equilibrium Model Research Articles

Consistent formulation of network equilibrium with stochastic flows

Traffic flows in real-life transportation systems vary on a daily basis. According to traffic flow theory, such variability should induce a similar variability in travel times, but this “internal consistency” is generally not captured by existing network equilibrium models. We present an internally-consistent network equilibrium approach, which considers two potential sources of flow variability: (i) daily variation in route choice and (ii) daily variation in origin–destination demand. We particularly aspire to a flexible formulation that permits alternative statistical assumptions, which allows the best fit to be made to observed variability data in particular applications. Joint probability distributions of route—and therefore link—flows are derived under several assumptions concerning stochastic driver behavior. A stochastic network equilibrium model with stochastic demands and route choices is formulated as a fixed point problem. We explore limiting cases which allow an equivalent convex optimization problem to be defined, and finally apply this method to a real-life network of Kanazawa City, Japan.

Bayesian forecasting with small and medium scale factor-augmented vector autoregressive DSGE models

Advanced Bayesian methods are employed in estimating dynamic stochastic general equilibrium (DSGE) models. Although policymakers and practitioners are particularly interested in DSGE models, these ...

A SAA nonlinear regularization method for a stochastic extended vertical linear complementarity problem

In this paper we propose a new stochastic equilibrium model, a stochastic extended vertical linear complementarity problem, which arises in the stochastic generalized bimatrix games and includes stochastic linear complementarity problem as its special case. Based on the log-exponential function, a sample average approximation (SAA) regularization method is proposed for solving this problem. The analysis of this regularization method is carried out in two steps: first, under some mild conditions, the existence and convergence results to the proposed method are provided. Second, under conditions on row representative of matrices, the exponential convergence rate of this method is established. At last, the regularization method proposed is applied to finding a generalized Nash equilibrium pair for a stochastic generalized bimatrix game.

Envy, guilt, and the Phillips curve

We incorporate inequality aversion into an otherwise standard New Keynesian dynamic stochastic equilibrium model with Calvo wage contracts and positive inflation. Workers with relatively low incomes experience envy, whereas those with relatively high incomes experience guilt. The former seek to raise their income and the latter seek to reduce it. The greater the inflation rate, the greater the degree of wage dispersion under Calvo wage contracts, and thus the greater the degree of envy and guilt experienced by the workers. Since the envy effect is stronger than the guilt effect, according to the available empirical evidence, a rise in the inflation rate leads workers to supply more labor over the contract period, generating a significant positive long-run relation between inflation and output (and employment), for low inflation rates. Provided that wage adjustments are costly, this tradeoff remains significant even once the degree of wage stickiness adjusts to the inflation rate. This Phillips curve relation, together with an inefficient zero-inflation steady state, provides a rationale for a positive long-run inflation rate. Given standard calibrations, optimal monetary policy is associated with a long-run inflation rate around 2%.

Combining International Cap-and-Trade with National Carbon Taxes

This paper examines the effects of combining an international cap-and-trade scheme with national carbon taxes. We consider a two-country stochastic partial equilibrium model with log-normally distributed uncertainty. The situation is analogous to the situation where European countries impose national carbon taxes in addition to the EU emissions trading. The allowance price in the joint cap-and-trade scheme depends on the tax rate, the relative size of countries and abatement options, the magnitude of uncertainty, and correlation of abatement costs. In most cases, the additional tax will not lead to additional production of the public good beyond the fixed targets. The additional tax results in higher costs of abatement to the country introducing the additional tax, and higher costs overall.

Sampling average approximation method for a class of stochastic Nash equilibrium problems

We consider a class of stochastic Nash equilibrium problems (SNEP). Under some mild conditions, we reformulate the SNEP as a stochastic mixed complementarity problem (SMCP). We apply the well-known sample average approximation (SAA) method to solve the SMCP. We further introduce a semismooth Newton method to solve the SAA problems. The comprehensive convergence analysis is given as well. In addition, we demonstrate the proposed approach on a stochastic Nash equilibrium model in the wholesale gas–oil markets.

The optimal shape of compensation contracts with earnings management

The research question of why earnings management occurs is decomposed into two questions in this article: Which component of executive compensation generates incentives for earnings management? and Why is the compensation structured that way in the first place? We first use as a dynamic stochastic equilibrium model to show that ‘big bath’ and earning overstatement can co-exist as equilibrium financial reporting strategies when thresholds are used in compensation contracts. In order to understand the use of performance thresholds as a prevailing compensation strategy in practice, we then derive the optimal compensation contract when the manager is privately informed about economic earnings and his expertise in managing earnings. Equilibria exist in which the inactive region below a threshold in compensation should be economically significant.

Transportation serviceability analysis for metropolitan commuting corridors based on modal choice modeling

Major commuting corridors in metropolitan areas generally comprise multiple transportation modes for commuters, such as transit (subways or buses), private vehicles, or park-and-ride combinations. During the morning peak hour, the commuters would choose one of the available transportation modes to travel through the corridors from rural/suburban living areas to urban working areas. This paper introduces a concept of transportation serviceability to evaluate a transportation mode’s service status in a specific link, route, road, or network during a certain period. The serviceability can be measured by the possibility that travelers choose a specific type of transportation service at a certain travel cost. The commuters’ modal-choice possibilities are calculated using a stochastic equilibrium model based on general travel cost. The modeling results illustrate how transportation serviceability is influenced by background traffic flow in a corridor, value of comfort for railway mode, and parking fee distribution.

Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems

We take advantage of the interpretation of stochastic capacity expansion problems as stochastic equilibrium models for assessing the risk exposure of new equipment in a competitive electricity economy. We develop our analysis on a standard multistage generation capacity expansion problem. We focus on the formulation with nonanticipativity constraints and show that their dual variables can be interpreted as the net margin accruing to plants in the different states of the world. We then propose a procedure to estimate the distribution of the Lagrange multipliers of the nonanticipativity constraints associated with first stage decisions; this gives us the distribution of the discounted cash flow of profitable plants in that stage.

The Impact of Uncertainty on the European Energy Market: A Scenario Aggregation Approach

We present a simple approach to transform a deterministic numerical model, where several agents simultaneously make decisions, into a stochastic model. This approach, which builds on scenario aggregation, a numerical method developed to solve decision problems under uncertainty, is used to build a large stochastic numerical equilibrium model of the Western European energy markets. We use the stochastic model to analyze the impact of economic and political uncertainty on the Western European energy markets. We demonstrate that the equilibria under uncertainty differ significantly from the deterministic outcomes.

Reference-Dependent Stochastic User Equilibrium with Endogenous Reference Points

We consider the application of reference-dependent consumer choice theory to traffic assignment on transportation networks. Route choice is modelled based on random utility maximisation with systematic utility embodying loss aversion for the travel time and money expenditure attributes. Stochastic user equilibrium models found in the literature have considered exogenously given reference points. The paper proposes a model where reference points are determined consistently with the equilibrium flows and travel times. The referencedependent stochastic user equilibrium (RDSUE) is defined as the condition where (i) no user can improve her utility by unilaterally changing path, (ii) each user has as reference point the current travel time and the money expenditure of one of the available paths, and (iii) if each user updates the reference point to her current path the observed path flows do not change. These conditions are formally equivalent to a multi-class stochastic equilibrium where each class is associated with a path and has as reference point the current state on the path, and the number of users in each class equals the current flow on the path. The RDSUE is formulated as a fixed point problem in the path flows. Existence of RDSUE is guaranteed under usual assumptions. A heuristic algorithm based on the method of successive averages is proposed to solve the problem. The model is illustrated by two numerical examples, one relates to a two-link network and another to the Nguyen-Dupuit network. A reference-dependent route choice model calibrated on stated preference data is used. The second example serves also to demonstrate the algorithm. The impact on the equilibrium of different assumptions on the degree of loss aversion with respect to the travel time attribute are investigated.

Unemployment and Endogenous Reallocation Over the Business Cycle

We build an analytically and computationally tractable stochastic equilibrium model of unemployment in heterogeneous labor markets. Facing search frictions within markets and reallocation frictions between markets, workers endogenously separate from employment and endogenously reallocate between markets, in response to changing aggregate and local conditions. Empirically, using the 1986-2008 SIPP panels, we document the occupational mobility patterns of the unemployed, finding notably that occupational change of unemployed workers is procyclical. The heterogeneous-market model yields highly volatile countercyclical unemployment, and is simultaneously consistent with procyclical reallocation, countercyclical separations and a negatively-sloped Beveridge curve. Moreover, the model exhibits unemployment duration dependence, which (when calibrated to long-term averages) responds realistically to the business cycle, creating substantial longer-term unemployment in downturns. Finally, the model is also consistent with different employment and reallocation outcomes as workers gain experience in the labor market, on average and over the business cycle.

Unemployment and Endogenous Reallocation Over the Business Cycle

We build an analytically and computationally tractable stochastic equilibrium model of unemployment in heterogeneous labor markets. Facing search frictions within markets and reallocation frictions between markets, workers endogenously separate from employment and endogenously reallocate between markets, in response to changing aggregate and local conditions. Empirically, using the 1986-2008 SIPP panels, we document the occupational mobility patterns of the unemployed, finding notably that occupational change of unemployed workers is procyclical. The heterogeneous-market model yields highly volatile countercyclical unemployment, and is simultaneously consistent with procyclical reallocation, countercyclical separations and a negatively-sloped Beveridge curve. Moreover, the model exhibits unemployment duration dependence, which (when calibrated to long-term averages) responds realistically to the business cycle, creating substantial longer-term unemployment in downturns. Finally, the model is also consistent with different employment and reallocation outcomes as workers gain experience in the labor market, on average and over the business cycle.

La modélisation en équilibre général dynamique et stochastique des cycles économiques en Afrique Sub-saharienne : une revue de la littérature

Cet article propose une revue de la litterature sur les modeles d'equilibre general dynamique et stochastique appliques aux pays d'Afrique Sub-saharienne. Cette litterature a pour double objectif (i) d'identifier les facteurs specifiques a ces economies susceptibles d'expliquer leur tres forte instabilite et (ii) d'evaluer les politiques monetaires et fiscales adequates face a ces facteurs. Nous presentons les avancees de cette litterature a l'aune de ces deux objectifs et en soulignons les limites.

Why the Housing Sector Leads the Whole Economy: The Importance of Collateral Constraints and News Shocks

This paper establishes a dynamic stochastic partial equilibrium model for explaining residential investment dynamics in the United States, focusing on the distinctive cyclical features of residential investment in that it leads the whole economy. This paper is different from the existing literature by adding three new features to the model: news shocks, collateral constraints and agent heterogeneity. The partial equilibrium analysis where interest rates are exogenously fixed shows that these assumptions are essential to generating the dynamic pattern in which residential investment leads consumption and GDP.

Serviceability Based Park and Ride Choice Behaviors Influenced by Road Toll Policy for Metropolitan Commuting Corridors

Existing park and ride (P&R) facilities may enhance the serviceability of the transportation systems by redistributing travelers from vehicles mode to mass transit. As a tool in transportation demand management, road tolling policy will have an influence on the transportation system with P&R facilities. In this paper, impact of various road tolling policies on modal choice behaviors within context of commuting corridors with P&R services are investigated from the perspective of serviceability. The related road tolling schemes contains first-best toll, distance-based toll and cordon-based toll. The probability of commuters’ modal-choice is estimated using a stochastic equilibrium model. Innovatively, the serviceability concept is adopted to evaluate performances of different travel modes. Model results illustrate how transportation system performance is influenced by the different types of road tolling policies. Some of the results are concordant with empirical findings in the literature.

Stochastic Traffic Equilibrium Based on Travel Time Robust Reliability

An assumption that pervades the current reliable traffic equilibrium problem is that probability distributions of the origin-destination (O-D) demand or/and link capacities are known explicitly. However, these distributions are difficult to be accurately obtained. This paper relaxes this assumption. It only needs to know the first m moments of travel demand (where m is a positive integer associated with the formulation of link cost function), and then applies two worse-case Value-at-Risk (WVaR) and Conditional value-at-risk (CVaR) risk measures to define robust percentile travel time (RPTT) and robust mean-excess travel time (RMETT) and prove that this two kinds travel time is equal under general distribution. By incorporating the defined travel time and travelers' perception error, the robust percentile stochastic user equilibrium (RPSUE) or robust mean-excess stochastic traffic equilibrium model (RMESTE) is proposed, which is formulated as an equivalent route-based variational inequality. Conditions are established guaranteeing existence of this equilibrium. A heuristic solution problem is introduced to solve the variational inequalities problem. A numerical example is used to illustrate the applications of the proposed model and the solution algorithm.

C-logit stochastic user equilibrium model: formulations and solution algorithm

This article considers the stochastic user equilibrium (SUE) problem with the route choice model based on the C-logit function. The C-logit model has a simple closed-form analytical probability expression and requires relatively lower calibration efforts and represents a more realistic route choice behaviour compared with the multinomial logit model. This article proposes two versions of the C-logit SUE model that captures the route similarity using different attributes in the commonality factors. The two versions differ with respect to the independence assumption between cost and flow. The corresponding stochastic traffic equilibrium models are called the length-based and congestion-based C-logit SUE models, respectively. To formulate the length-based C-logit SUE model, an equivalent mathematical programming formulation is proposed. For the congestion-based C-logit SUE model, we provide two equivalent variational inequality formulations. To solve the proposed formulations, a new self-adaptive gradient projection algorithm is developed. The proposed formulations and new solution algorithm are tested in two well-known networks. Numerical results demonstrate the validity of the formulations and solution algorithm.

Generation Capacity Expansion in a Risky Environment: A Stochastic Equilibrium Analysis

We cast models of the generation capacity expansion type formally developed for the monopoly regime into equilibrium models better adapted for a competitive environment. We focus on some of the risks faced today by investors in generation capacity and thus pose the problem as a stochastic equilibrium model. We illustrate the approach on the problem of the incentive to invest. Agents can be risk neutral or risk averse. We model risk aversion through the CVaR of plants' profit. The CVaR induces risk-adjusted probabilities according to which investors value their plants. The model is formulated as a complementarity problem (including the CVaR valuation of investments). An illustration is provided on a small problem that captures several features of today's electricity world: a choice often restricted to coal and gas units, a peaky load curve because of wind penetration, uncertain fuel prices, and an evolving carbon market. We assess the potential of the approach by comparing energy-only and capacity market organizations in this risky environment. Our results can be summarized as follows: a deterministic analysis overlooks some changes of capacity structure induced by risk, whether in the capacity market or energy-only organizations. The risk-neutral analysis also misses a shift towards less capital-intensive technologies that may result from risk aversion. Last, risk aversion also increases the shortage of capacity compared to the risk-neutral view in the energy-only market when the price cap is low. This may have a dramatic impact on the bill to the final consumer. The approach relies on mathematical programming techniques and can be extended to full-size problems. The results are illustrative and may deserve more investigation.

Policy analysis : tool applied to colombian needs: patacon model description

En este articulo describimos los fundamentos microeconomicos de un modelo de equilibrio general dinamico y estocastico llamado “herramienta para el analisis de la politica aplicada a las necesidades de Colombia” (Patacon, por su sigla en ingles); una herramienta predictiva que se utiliza como guia para el diseno de las politicas economicas de Colombia. En documentos complementarios describimos aspectos adicionales de este modelo, incluyendo el calculo de los parametros que afectan las funciones de dinamica y de impulso-respuesta.