Equilibrium Policy Research Articles

An Ergodic Measure for Active Learning From Equilibrium

This article develops KL-ergodic exploration from equilibrium (KL-E3), a method for robotic systems to integrate stability into actively generating informative measurements through ergodic exploration. Ergodic exploration enables robotic systems to indirectly sample from informative spatial distributions globally, avoiding local optima, and without the need to evaluate the derivatives of the distribution against the robot dynamics. Using a hybrid systems theory, we derive a controller that allows a robot to exploit equilibrium policies (i.e., policies that solve a task) while allowing the robot to explore and generate informative data using an ergodic measure that can extend to high-dimensional states. We show that our method is able to maintain Lyapunov attractiveness with respect to the equilibrium task while actively generating data for learning tasks such, as Bayesian optimization, model learning, and off-policy reinforcement learning. In each example, we show that our proposed method is capable of generating an informative distribution of data while synthesizing smooth control signals. We illustrate these examples using simulated systems and provide simplification of our method for real-time online learning in robotic systems. Note to Practitioners —Robotic systems need to adapt to sensor measurements and learn to exploit an understanding of the world around them such that they can truly begin to experiment in the real world. Standard learning methods do not have any restrictions on how the robot can explore and learn, making the robot dynamically volatile. Those that do are often too restrictive in terms of the stability of the robot, resulting in a lack of improved learning due to poor data collection. Applying our method would allow robotic systems to be able to adapt online without the need for human intervention. We show that considering both the dynamics of the robot and the statistics of where the robot has been, we are able to naturally encode where the robot needs to explore and collect measurements for efficient learning that is dynamically safe. With our method, we are able to effectively learn while being energetically efficient compared with state-of-the-art active learning methods. Our approach accomplishes such tasks in a single execution of the robotic system, i.e., the robot does not need human intervention to reset it. Future work will consider multiagent robotic systems that actively learn and explore in a team of collaborative robots.

Rational Expectations Models with Higher-Order Beliefs

This paper develops a general method of solving rational expectations models with higher order beliefs. Higher order beliefs are crucial in an environment with dispersed information and strategic complementarity, and the equilibrium policy depends on infinite higher order beliefs. It is generally believed that solving this type of equilibrium policy requires an infinite number of state variables (Townsend, 1983). This paper proves that the equilibrium policy rule can always be represented by a finite number of state variables if the signals observed by agents follow an ARMA process, in which case we obtain a general solution formula. We also prove that when the signals contain endogenous variables, a finite-state-variable representation of the equilibrium may not exist. For this case, we develop a tractable algorithm that can approximate the solution arbitrarily well. The key innovation in our method is to use the factorization identity and Wiener filter to solve signal extraction problems conditional on infinite observables. This method can be used in a wide range of applications. We demonstrate its strong practicability by solving several classical models featuring higher order beliefs, and also a full-blown business cycle model that is driven by confidence shocks.

State and Local Economic Policy in Equilibrium

State and Local Economic Policy in Equilibrium

Saving the American Dream? Education Policies in Spatial General Equilibrium

Saving the American Dream? Education Policies in Spatial General Equilibrium

Decentralized Congestion Policies: Pricing Versus (Grandfathered) Slots in Airport Networks

This dissertation consists of four related studies on the assessment of decentralized welfare-maximizing airport congestion policies involving (grandfathered) slot policy and pricing policy. Different demand structures and airport networks are considered in the presence of origin-destination passengers. These studies capture that local and non-local origin-destination passengers may have one or two destinations to choose from, in which the two destinations may or may not be considered as substitutes. This dissertation shows that even a small variation can fundamentally change the analysis and the assessment of the congestion policies. The first study considers networks with two or three airports. The results show that equilibrium policies involve slots when airport profits do not matter and pricing policies when airport profits matter. The main results show that in the presence of congestion effects, equilibrium slot policies will lead to too high and equilibrium pricing policies to too low passenger quantities relative to the first best outcome that maximizes the welfare of all airport regions. The second study considers a stylized airport network with two airports designed to clearly identify the role of local and non-local passengers. The analysis shows that the local welfare-maximizing slot quantity can coincide with the first-best outcome whereas this is impossible in the case of pricing policy. Whether the outcomes coincide in the case of slot policy depends on the shares of inframarginal and marginal local and non-local passengers. The results provide clear insights on the reasons why slot quantities are found to be excessive in the three-airport network considered in the first study. The third study is an extension of the analysis of the three-airport network considered in the first study. This extension involves a variation of the demand structure in the sense that the air services offered at the congested airports are considered as imperfect substitutes whereas they are not considered as substitutes in the first study. The analysis shows that the presence of substitute air services is a necessary condition for equilibrium slot quantities to reach the first-best outcome. The results derived from the second study help understand the reasons why equilibrium slot quantities can lead to first-best outcome. Whereas equilibrium pricing levels will always be too high relative to the first-best prices independent of the presence or absence of substitute air services. By contrast with the third study, the fourth study proceeds with the consideration of substitute air services for non-local passengers in a three-airport network to concentrate on the role of airport competition. The results show that airport competition will lead to too low equilibrium slot quantities in the case of slot policies, or too low equilibrium prices in the case of pricing policies, to maximize the total welfare of the two congested airports. The results further show that slot policies can lead to first-best outcome that maximizes the total welfare of three airport regions. Whereas pricing policies are too strict with too high equilibrium prices relative to the first-best outcome.

Leaping into the Dark: A Model of Policy Gambles with Self-Fulfilling Features

We examine why rational voters support risky “policy gambles”, even when detrimental to welfare, over maintaining a safe status quo. We present a model of electoral competition with two groups of agents. Elites own the means of production and choose how much future output they require as compensation for investing in risky projects. Voters are residual claimants of output. The output depends on the future government’s policy. When investments are made, the incumbent cannot pre-commit to retain the status quo. Instead, future policy is determined by political parties vying to win the election. Voters can increase their expected output share by supporting policy gambles. Our analysis highlights how uncertainty about future policy shapes equilibrium policy choices and provides a mechanism where income inequality is a driver for abandoning the status quo. Institutions that support consensus between political parties can improve welfare by eliminating the gamble equilibrium.

Examining the Impact of Electoral Competition and Endogenous Lobby Formation on Equilibrium Policy Platforms

Abstract This paper formulates a mathematical model that combines the dynamics of interest group formation with electoral politics, involving office-seeking and corrupt political candidates and voting population with well-defined policy as well as ideological preferences. The analysis provides several interesting insights into the factors affecting lobby membership, free-riding incentives of citizen-voters and aggregate monetary donations garnered by lobby groups. Besides this, the paper also explores the impact of the formation of distinct lobby groups, the presence of swing voters and the corrupt practices or financial embezzlement on the equilibrium policy choice of electoral contenders. The findings reveal that more honest spending of campaign donations by electoral contenders reduces both the size of the lobby (or membership) as well as aggregate campaign contributions in equilibrium. In contrast, a rise in the fixed cost of organization is found to augment lobby membership along with the total amount of campaign contributions. In addition, a reduction in the level of electoral uncertainty as well as a rise in the ideological or swing voter density is found to increase the effectiveness of campaign contributions in raising an electoral candidate’s perceived popularity and, therefore, a smaller lobby group with lower aggregate donations is deemed as sufficient in influencing electoral outcomes. Moreover, the results indicate that a lower utility difference derived by the citizen-voters when comparing the two electoral candidate’s policy choices translates into smaller dispersion of the voters’ ideological bias, and consequently results in an increase in the size of lobby groups and their corresponding aggregate donations. As regards the choice of equilibrium policy, evidence of full policy convergence is not found in the case when citizen-voters of the two groups have separable preferences. In addition, policy equilibrium for a more realistic case in which the two policy platforms exhibit strategic interaction by reacting to each other has also been estimated with the help of simulations. Finally, this paper helps in categorically deciphering the influence of the median voter effect (or the centripetal force) and the distinct centrifugal forces in the form of lobbying effect, swing voter effect and the financial embezzlement effect on the equilibrium policy choice by employing different parametric specifications of the model.

Distributive politics with other‐regarding preferences

AbstractThis paper analyzes a nonsmooth model of probabilistic voting with two parties and a broad family of other‐regarding behavior, including fairness and quasi‐maximin preferences, income‐dependent altruism, and inequity aversion. The paper provides conditions for equilibrium existence and uniqueness. It also characterizes the Nash equilibrium in pure strategies when parties hold either symmetric payoffs, or minor forms of asymmetries. The characterization shows that the two parties converge to an equilibrium policy that maximizes a mixture of a “self‐regarding utilitarian” social welfare function and an aggregate of society's other‐regarding preferences. These results are shown to be applicable to other nonsmooth frameworks, such as probabilistic voting with loss averse voters. The characterization also shows that the direction and the size of the inefficiencies emerging from electoral competition depend in a subtle way on the nature of the other‐regarding preferences (and resp., loss aversion).

Believers vs. deniers: Climate change and environmental policy polarization

This paper theoretically studies the consequences of partisanship with an application to environmental policy. We model an election between a right-wing and a left-wing candidate who strategically propose environmental policies to gain the support of an electorate divided based on their climate change beliefs and productive assets. While environmental regulations imply a trade-off between a more sustainable environment and higher incomes for all voters, climate change believers have a higher belief in human activity-induced climate change, which translates into greater expected environmental benefits from policy, and high-asset voters care relatively more about mitigating economic costs. Voters view the left-wing candidate as more effective in addressing environmental challenges, whereas her right-wing opponent is the better candidate to deliver relief from the economic burden of regulations. In equilibrium, there exists policy divergence and the right-wing candidate always proposes the more pro-industry policy. We find that higher asset inequality moves equilibrium policies in a pro-industry direction as long as high-asset voters are ideologically more homogeneous than low-asset ones. Equilibrium policies become further polarized with greater partisanship as those voters with the same climate change belief hold similar ideologies.

Distributed Reinforcement Learning for Cyber-Physical System With Multiple Remote State Estimation Under DoS Attacker

In this paper, we consider cyber-physical system (CPS) with multiple remote state estimation under denial-of-service (DoS) attack in infinite time-horizon. The sensors monitor the system and send their local state estimate to remote estimators by choosing the local channels in “State 0” or “State 1”. The aim of sensors is to find policies for choosing local channel in a specific state to transmit message to minimize the total estimation error covariance on account of energy-saving in an infinite time-horizon. The DoS attacker aims to achieve the opposite goal by choosing channels to attack or not. The games between sensors and DoS attacker under two different structures of public information are investigated, that is the open-loop case (where sensors and attacker cannot observe others' behaviors) and the closed-loop case (where sensors and attacker can observe the others' behaviors causally). For the open-loop case with assumption that the DoS attacker can get the information from the remote estimators to the sensors, the distributed reinforcement learning algorithms for sensors and attacker based on local information are proposed to find their Nash equilibrium policies, respectively. Further, we consider in closed loop case that the DoS attacker cannot get the information from the remote estimators to the sensors which leads to asymmetric information between the sensors and attacker. To derive Nash equilibrium policies for sensors and attacker, we convert the original game into a belief-based continuous-state stochastic game. The convergence of distributed reinforcement learning method is proved. Some simulations are presented to demonstrate its effectiveness.

Optimal emissions tax rates under habit formation and social comparisons

The existing climate models ignore the behavioral anomalies of households and conclude that the optimal environmental tax rate should comove with business cycles. However, this assumption has received extensive criticism recently. To this end, this paper studies the optimal emissions tax rate when households are bounded rational. In particular, we calculate the optimal climate policy in a dynamic stochastic general equilibrium (DSGE) model that features households with habit formation (internal habits) and social comparisons (external habits). Compared to the benchmark model without consumption externality, the social comparisons model amplifies consumption volatility but produces a similar response of pollutant emissions in the presence of the three types of economic shocks considered. In contrast, the habit formation model decreases the volatility of both consumption and pollutant emissions. In contrast to the previous result that the optimal emissions tax rate should be procyclical, we find that the social comparisons model largely mitigates the procyclicality of optimal emissions tax rates, and the optimal emissions tax rates under the habit formation model remain constant in response to all the economic shocks considered.

Empirical Models of Lobbying

This article offers a review of the recent empirical literature on lobbying within political economy. In surveying extant research, we emphasize quid pro quo and informational issues in special interest politics and highlight crucial open questions in both. The two main unresolved methodological issues remain ( a) how to account for the impact of lobbying on which equilibrium policies are chosen and advanced and ( b) how distorted those equilibrium policies are relative to the social optimum. Of the principal open questions within political economy, a comprehensive, quantitative assessment of the welfare effects of lobbying remains one of the most elusive.

Price and Quality Management with Strategic Consumers: Whether to Introduce a High or Low Product Variant

We consider a firm that sells a product to strategic consumers sensitive to both price and quality over two periods. The firm can change its product quality and must determine its prices in both periods as well as whether and how to change product quality in the second period. In equilibrium, the firm would choose one strategy from the following four: simultaneous markdown and downgrade, markdown only, simultaneous markup and upgrade, and simultaneous markdown and upgrade. Such a policy structure holds irrespective of whether the firm is patient. However, the policy set shrinks when the marginal cost changes from quadratic to linear in quality and expands when customer types are uncertain in the sense that the firm is not certain about the upper bound of the support of the customer type. In the latter, the equilibrium policy is same when the uncertainty is the highest as when uncertainty is absent.

A Multistage Sustainable Production–Inventory Model with Carbon Emission Reduction and Price-Dependent Demand under Stackelberg Game

This paper investigated a multistage sustainable production–inventory model for deteriorating items (i.e., raw materials and finished goods) with price-dependent demand and collaborative carbon reduction technology investment under carbon tax regulation. The model was developed by first defining the total profit of the supply chain members under carbon tax regulation and, second, considering a manufacturer (leader)–retailer (follower) Stackelberg game. The optimal equilibrium solutions that maximize the manufacturer’s and retailer’s total profits were determined through the method analysis. An algorithm complemented the model to determine the optimal equilibrium solutions, which were then treated with sensitivity analyses for the major parameters. Based on the numerical analysis, (a) carbon tax policies help reduce carbon emissions for both the manufacturer and retailer; (b) most carbon emissions from supply chain operations negatively impact the total profits of both members; (c) the retailer may increase the optimal equilibrium selling price to respond to an increase in carbon emissions from supply chain operations or carbon tax; and (d) autonomous consumption positively affects both members’ optimal equilibrium policies and total profits, whereas induced consumption does the opposite. These findings are very managerial and instructive for companies seeking profits and fulfilling environmental responsibility and governments.

Supermajority Politics: Equilibrium Range, Diversity, and Compromise

Do legislative voting rules affect the diversity of policies observed across structurally similar political economies, and if so, to what extent? To what degree do these voting rules affect legislative compromise and the stability of the social optimum? Using a spatial model of political competition with single-peaked preferences, we examine these questions in settings where changing incumbent or proposed policies requires supermajority consensus. We develop three findings pertaining to equilibrium policies that are immune to change by any supermajority coalition. First, we prove that at least one equilibrium policy exists and then find the maximum number of equilibrium policies that exist as a function of the supermajority's size. Policy diversity increases, in a nontrivial manner, in the size of the supermajority coalition needed to change the status quo, and the Median Voter Theorem is a particular case of the result with minimal policy diversity. Second, we find the optimal level of compromise needed by a leader to ensure that her proposed policy is not defeated and establish that compromise decreases in the supermajority's size. Third, we identify the minimal supermajority rule that ensures the stability of the social optimum. The robustness of these findings and their theoretical and policy implications are further investigated in the paper.

Better Policies from Policy-Selective Aid?

Abstract The increased policy selectivity of aid allocations observed in recent years provides aid-recipient countries with an incentive to improve policies. The paper estimates that a change in the World Bank’s Country Policy and Institutional Assessment policy index from 1.5 to 2 for a recipient is associated with an increase of about 13 percent in aid. The analysis also finds a modest but statistically significant positive relationship between the global level of policy-selective aid and policy, suggesting that policy-selective aid improves policies in aid-recipient countries. This effect is properly identified, as the level of policy-selective aid in the global aid budget is exogenous to a recipient country’s policy choice. Furthermore, the paper provides a game-theoretic model that establishes the link between the policy selectivity of the global budget and better recipient-country policies in equilibrium.

Microfoundations and macroeconomics: 20 years

This paper summarizes Horwitz’s contributions in Microfoundations and Macroeconomics: An Austrian Perspective and evaluates its connection with recent contributions in Austrian macroeconomics. The paper emphasizes the connection between relative price, monetary equilibrium, and monetary policy. The paper pays particular attention to the implications of Horwitz’s denomination of capital theory as a “missing link” in economic theory.

Two candidate competition on differentiated policy sets

In the classical spatial model of two candidate competition, an equilibrium exists only if the distribution of voter ideal points is such that every median hyperplane passes through a single policy. The necessity of this condition crucially depends upon both candidates being able to propose any policy in a Euclidean space. We assume that each candidate is affiliated with a party which restricts the policies that its candidate can propose and that voters have Euclidean spatial preferences. We show that if the candidates can only make proposals from disjoint sets of policies, then an equilibrium exists if each median hyperplane passes through a region with a nonempty interior that contains the equilibrium policy. An equilibrium, if it exists, is generically robust to perturbations of the voters' ideal points.

Carbon Tariff vs. Emission Cap of North–South Countries in Response to Manufacturer’s Production

Economy prosperity has concurrently caused severe emission damages worldwide, which calls for strong abatement efforts from both nations and manufacturers. In this paper, we establish a two-stage game to investigate the policy selections of a foreign developed country (North) and a domestic developing country (South), and the response of a Southern manufacturer. The welfare-maximizing governments in the two countries participate in an announcement game of environmental policies where the South decides on whether or not to enforce an emission cap and the North chooses either a carbon tariff or no policy, after which the profit-seeking manufacturer reacts to make production strategies and distribute differentiated products to the two countries. Our analysis shows that under an emission cap, the manufacturer shrinks product quantities in both markets, cuts emissions, and suffers profit losses. A carbon tariff has similar impacts on the manufacturer except for unaffected domestic sales. In addition, equilibrium policy selections for the two governments depend on the degree of emission damage in the South: A moderate level of damage generates an equilibrium in the scenario of the unilateral tariff policy where the Northern welfare peaks and the Southern well-being is not the worst; a severe damage leads to a prisoner’s dilemma, since the two governments would arrive at an equilibrium in the bilateral-policy scenario, but it is dominated by a no-policy scheme. What is more, we find that a negotiation between the two governments is able to help them out of the dilemma and achieve a Pareto-improving outcome.

A Single-Judge Solution to Beauty Contests

We show that the equilibrium policy rule in beauty contest models is equivalent to that of a single agent’s forecast of the economic fundamental. This forecast is conditional on a modified information process, which simply discounts the precision of idiosyncratic shocks by the degree of strategic complementarity. The result holds for any linear Gaussian signal process (static or persistent, stationary or nonstationary, exogenous or endogenous), and also extends to network games. Theoretically, this result provides a sharp characterization of the equilibrium and its properties under dynamic information. Practically, it provides a straightforward method to solve models with complicated information structures. (JEL C72, D82, D83, D84)