Solving the incomplete markets model with aggregate uncertainty by backward induction

This paper describes a method to solve models with a continuum of agents, incomplete markets and aggregate uncertainty. I use backward induction on a finite grid of points in the aggregate state space. The aggregate state includes a small number of statistics (moments) of the cross-sectional distribution of capital. For any given set of moments, agents use a specific cross-sectional distribution, called “proxy distribution”, to compute the equilibrium. Information from the steady state distribution as well as from simulations can be used to chose a suitable proxy distribution.     

Solving the incomplete market model with aggregate uncertainty using a perturbation method

We use a perturbation method to solve the incomplete markets model with aggregate uncertainty described in den Haan et al. [Computational suite of models with heterogeneous agents: incomplete markets and model uncertainty. Journal of Economic Dynamics & Control, this issue]. To apply that method, we use a “barrier method” to replace the original problem with occasionally binding inequality constraints by one with only equality constraints. We replace the structure with a continuum of agents by a setting in which a single infinitesimal agent faces prices generated by a representative-agent economy. We also solve a model variant with a large (but finite) number of agents. Our perturbation-based method is much simpler and faster than other methods.     

Optimal monetary policy under incomplete markets and aggregate uncertainty: A long-run perspective

This paper examines the role of monetary policy in an environment with aggregate risk and incomplete markets. In a two-period overlapping-generations model with aggregate uncertainty, optimal monetary policy attains the ex-ante Pareto optimal allocation. This policy aims to stabilize the savings rate in the economy by changing real returns of nominal bonds via variation in expected inflation. Optimal expected inflation is procylical and on average higher than without uncertainty. Simple inflation targeting rules closely approximate the optimal monetary policy.     

Solving the incomplete markets model with aggregate uncertainty using the Krusell–Smith algorithm

This paper studies the properties of the solution to the heterogeneous agents model in Den Haan et al. [2009. Computational suite of models with heterogeneous agents: incomplete markets and aggregate uncertainty. Journal of Economic Dynamics and Control, this issue]. To solve for the individual policy rules, we use an Euler-equation method iterating on a grid of pre-specified points. To compute the aggregate law of motion, we use the stochastic-simulation approach of Krusell and Smith [1998. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106, 868–896]. We also compare the stochastic- and non-stochastic-simulation versions of the Krusell–Smith algorithm, and we find that the two versions are similar in terms of their speed and accuracy.     

Consumer surplus analysis under uncertainty: A general equilibrium perspective

This paper derives an exact form of partial equilibrium efficiency measure under uncertainty which is consistent with expected utility maximization in a general equilibrium situation with ex-post spot markets for many goods and asset markets which are in general incomplete.We consider that the good under consideration tends to be negligibly small compared to the entire set of commodity characteristics which is assumed to be a continuum, and look into the limit property of preferences over state-contingent consumption of the good and state-contingent income transfer associated to it. We show that the limit preference exhibits risk neutrality, not only that it exhibits no income effect, meaning that the two conditions are tied together. We also show that the marginal rate of substitution between extra income transfers at different states of the world converges to the ratio between the Lagrange multipliers associated to those states. When the asset markets are complete such ratios are equalized between consumers, but it is not the case in general when the asset markets are incomplete. This means that using the aggregate expected consumer surplus as the welfare measure will be in general inconsistent with individuals’ expected utility maximization in the general equilibrium environment or with ex-ante Pareto efficiency.     

A comparison of two model averaging techniques with an application to growth empirics

Parameter estimation under model uncertainty is a difficult and fundamental issue in econometrics. This paper compares the performance of various model averaging techniques. In particular, it contrasts Bayesian model averaging (BMA) — currently one of the standard methods used in growth empirics — with a new method called weighted-average least squares (WALS). The new method has two major advantages over BMA: its computational burden is trivial and it is based on a transparent definition of prior ignorance. The theory is applied to and sheds new light on growth empirics where a high degree of model uncertainty is typically present.     

Solving the incomplete markets model with aggregate uncertainty using explicit aggregation

We propose a method to solve models with heterogeneous agents and aggregate uncertainty. The law of motion describing aggregate behavior is obtained by explicitly aggregating the individual policy rule. The algorithm is simpler and faster than existing algorithms that rely on parameterization of the cross-sectional distribution and/or a computationally intensive simulation step. Explicit aggregation establishes a link between the individual policy rule and the set of necessary aggregate state variables, an insight that can be helpful in determining what state variables to include in other algorithms as well.     

Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty

This paper describes the first model considered in the computational suite project that compares different numerical algorithms. It is an incomplete markets economy with a continuum of agents and an inequality (borrowing) constraint.     

Core concepts for incomplete market economies

We examine the notion of the core when cooperation takes place in a setting with time and uncertainty. We do so in a two-period general equilibrium setting with incomplete markets. Market incompleteness implies that players cannot make all possible binding commitments regarding their actions at different date-events. We unify various treatments of dynamic core concepts existing in the literature. This results in definitions of the Classical Core, the Segregated Core, the Two-stage Core, the Strong Sequential Core, and the Weak Sequential Core. Except for the Classical Core, all these concepts can be defined by requiring the absence of blocking in period 0 and at any date-event in period 1. The concepts only differ with respect to the notion of blocking in period 0. To evaluate these concepts, we study three market structures in detail: strongly complete markets, incomplete markets in finance economies, and incomplete markets in settings with multiple commodities. Even when markets are strongly complete, the Classical Core is argued not to be an appropriate concept. For the general case of incomplete markets, the Weak Sequential Core is the only concept that does not suffer from major defects.     

Constrained inefficiency in GEI: A geometric argument

In this paper we use global analysis to study the welfare properties of general equilibrium economies with incomplete markets (GEI). Our main result is to show that constrained Pareto optimal equilibria are contained in a submanifold of the equilibrium set. This result is explicitly derived for economies with real assets and fixed aggregate resources, of which real numéraire assets are a special case. As a by product of our analysis, we propose an original global parametrization of the equilibrium set that generalizes to incomplete markets the classical one, first, proposed by Lange [Lange, O., 1942. The foundations of welfare economics. Econometrica 10, 215–228].     

Optimal monetary policy rules,financial amplification,and uncertain business cycles

This paper studies optimal monetary policy in the presence of ‘uncertainty’, time-variation in cross-sectional dispersion of firms׳ productive performance. Using a model with financial market imperfections, the results suggest that (i) optimal policy is to dampen the strength of financial amplification by responding to uncertainty (at the expense of creating mild degree of fluctuations in inflation). (ii) Higher uncertainty makes the welfare-maximizing planner more willing to relax financial constraints. (iii) Credit spreads are a good proxy for uncertainty. Hence, a non-negligible response to credit spreads – together with a strong anti-inflationary policy stance – achieves the highest aggregate welfare possible.     

Aggregate shocks and macroeconomic fluctuations: A bayesian approach

This paper describes Bayesian techniques for analysing the effects of aggregate shocks on macroeconomic time-series. Rather than calculate point estimates of the response of a time-series to an aggregate shock, we calculate the whole probability density function of the response and use Monte-Carlo or Gibbs sampling techniques to evaluate its properties. The proposed techniques impose identification restrictions in a way that includes the uncertainty in these restrictions, and thus are an improvement over traditional approaches that typically use least-squares techniques supplemented by bootstrapping. We apply these techniques in the context of two different models. A key finding is that measures of uncertainty, such as posterior standard deviations, are much larger than are their classical counterparts.     

Sharing risk within and across countries: the role of labor market institutions

This paper studies the effect of labor market institutions on within- and cross-country risk sharing, using a model of international trade in risky assets modified to include a subset of agents, labor-owners who do not access financial markets, and employment security provisions. Labor market, institutions, by promoting within-country risk-shifting arrangements between agents with or without, access to financial markets, reduce the fluctuations of non-tradable labor incomes and amplify the, fluctuations of capital incomes. Capital flows become more volatile across countries, and if the, configuration of labor markets differs across countries, capital-owners bear the burden of systematic, undiversifiable world aggregate uncertainty.     

Can social security be welfare improving when there is demographic uncertainty?

This paper studies the welfare implications of a PAYG pension system in an overlapping generations (OLG) model with demographic uncertainty and incomplete markets. In the absence of public pensions, small cohorts tend to be favoured by the changes in relative prices implied by demographic shocks. PAYG defined-benefit systems can help to share the financial risks created by this type of demographic uncertainty across generations. Our careful quantitative analysis test this possibility with unfavourable results: the overall welfare impact of the public pensions is negative, due to the prominence of the crowding-out effect over the insurance effect.     

Entry and barriers to entry in emerging markets

This note briefly introduces the symposium on entry and entry barriers in emerging markets edited by Nauro Campos and Saul Estrin. The symposium contains four inter-related case studies focusing in depth on the relationship between entry of new firms and institutional arrangements in four major emerging markets: Brazil, China, India and Russia. We find that entry rates are not necessarily low in emerging markets, and that institutional quality is a complex and “fuzzy” notion so that its impact on the entry process is not straightforward.     

Solving the incomplete markets model with aggregate uncertainty using the Krusell–Smith algorithm and non-stochastic simulations

This article describes the approach to computing the version of the stochastic growth model with idiosyncratic and aggregate risk that relies on collapsing the aggregate state space down to a small number of moments used to forecast future prices. One innovation relative to most of the literature is the use of a non-stochastic simulation routine.     

Excess demand function around critical prices in incomplete markets

We show that the aggregate excess demand function in an economy with incomplete real asset markets can be characterized by Walras’ law, homogeneity, and continuity around critical prices that cause one-dimensional drop of the dimension of the budget set.     

Anonymous sequential games with aggregate uncertainty

In this paper we extend a result of Jovanovic and Rosenthal (Anonymous sequential games, Journal of Mathematical Economics 17, 1988) on the existence of equilibrium in Anonymous Sequential Games. Jovanovic and Rosenthal prove existence in the case where the aggregate distribution of agents' characteristics evolves nonstochastically - the case of ‘no aggregate uncertainty’. Here we show how aggregate uncertainty can be introduced into the model (so the aggregate distribution evolves stochastically) and extend the Jovanovic-Rosenthal existence theorem to this case.     

Misspecification Preferred: The Sensitivity of Inefficiency Rankings

Ruggiero (European Journal of Operational Research 115, 555–563. 1999) compared the two popular parametric frontier methods for cross-sectional data—the stochastic frontier and the corrected OLS—in a simulation study. He demonstrated that the inefficiency ranking accuracy of the established stochastic frontier is uniformly inferior to that of the misspecified Corrected OLS (COLS) (which lacks an error term). The reason for his result remains unclear, however. In this paper, a more extensive simulation study is therefore conducted to find out whether the superiority of COLS is simply due to small sample sizes or to poor performance of the inefficiency level estimator.JEL Classification: C1,C2,C5     

Political Economy of City Sizes and Formation

There are two paradigms of city formation and size—the competitive model of large-scale land developers operating in national land markets and the self-organization model of agglomeration. This paper examines the effects of local politics, urban classes, and restrictions in national land markets on city size and formation. It starts by introducing local politics into the two paradigms. Then it turns to a growth situation, where land developers initiate new settlements, but existing cities are either self-organized or governed locally. The paper also examines the politics of local no-growth movements and of governance of specially favored mega-cities.