When is market incompleteness irrelevant for the price of aggregate risk (and when is it not)?

In a standard incomplete markets model with a continuum of households that have constant relative risk aversion (CRRA) preferences, the absence of insurance markets for idiosyncratic labor income risk has no effect on the premium for aggregate risk if the distribution of idiosyncratic risk is independent of aggregate shocks and aggregate consumption growth is independent over time. In equilibrium, households only use the stock market to smooth consumption; the bond market is inoperative. Furthermore, the cross-sectional distributions of wealth and consumption are not affected by aggregate shocks. These results hold regardless of the persistence of idiosyncratic shocks, even when households face tight solvency constraints. A weaker irrelevance result survives when we allow for predictability in aggregate consumption growth.     

Public debt and welfare in a quantitative Schumpeterian growth model with incomplete markets

This paper quantifies the welfare effects of counterfactual public debt policies using an endogenous growth model with incomplete markets. The economy features public debt, Schumpeterian growth, infinitely-lived agents, uninsurable income risk, and discount factor heterogeneity. Two versions of the model are specified, one with households holding equity in the group of innovating firms. The model is calibrated to the U.S. economy to match the degree of wealth inequality, the share of R&D expenditure in GDP, the firms’ exit rate, the average growth rate, and other standard long-run targets. When comparing balanced growth paths, I find large welfare gains in equilibria characterized by governments accumulating public wealth. The result is robust to the mechanism used to generate a highly concentrated wealth (i.e., preference heterogeneity or “superstar” income shocks). Welfare effects decompositions show that level effects and growth effects reinforce each other. The responses of both the intermediate goods and their market conditions are key in explaining the large level effects. The version of the model without equity is computationally easier to solve, allowing to consider transitional dynamics. Taking into account the dynamic adjustment to the new long-run equilibrium, I show that the transitional welfare costs are not large enough to change the sign of the welfare effects stemming from a change in public debt. I find that eliminating public debt would lead to a 0.8% increase in welfare, while moving to a debt/GDP ratio of 100% would entail a welfare loss of 0.5%. A decomposition analysis shows that growth accounts for approximately 50% of the overall welfare effects.     

IDIOSYNCRATIC AND AGGREGATE RISKS,INEQUALITY AND GROWTH

The paper disaggregates productivity shocks at a firm level into idiosyncratic and aggregate risks, and studies their impacts on inequality, growth and welfare. It develops a growth model with human capital and incomplete insurance and credit markets that provides a closed‐form solution for income inequality dynamics. We find that uninsured idiosyncratic risks are the most important determinants of inequality, growth and welfare. They are the source of nondegenerate wealth distribution. A lower weight of these shocks leads to lower steady‐state inequality, higher growth and welfare. A redistribution of income that serves as social insurance against such risks increases welfare and decreases inequality. But, it also decreases growth by distorting individual consumption and saving decisions.     

New financial markets: who gains and who loses

Summary. We evaluate the effects of new financial markets in a two-period incomplete markets model with heterogenous agents. For analytical tractability, we focus on the special case where utility is exponential and risks are normally distributed. We provide a complete characterization of life-cycle consumption and portfolio choice. The effect of new financial markets on individual welfare equals the sum of what we call the portfolio effect and the price effect. The portfolio effect is proportional to the square of the difference between the average exposure to the new asset in the economy and an individual investors exposure adjusted for risk aversion. The portfolio effect is always positive and measures the improved ability of investors to transfer consumption across states. The price effect captures the effect on individual welfare of changes in asset prices. We show that new financial markets drive down the prices of all assets which raises the interest rate and thus affects the ability of investors to transfer consumption across time. The price effect is positive for net savers but can be negative for net borrowers. For net borrower households, the price effect can wipe out the portfolio effect and lead to welfare reductions.Received: 24 July 2003, Revised: 22 March 2004, JEL Classification Numbers: D31, D52, G11, G12.Paul Willen: Thanks to Viral Acharaya, Alberto Bisin, Steve Davis, John Geanakoplos and a thoughtful anonymous referee for helpful comments and suggestions. Thanks also to seminar audiences at Stanford, Berkeley and at the 2001 Stony Brook workshop on incomplete markets for comments and suggestions. I gratefully acknowledge research support from the Graduate School of Business at the University of Chicago.     

International Risk Sharing and the Transmission of Productivity Shocks

This paper shows that standard international business cycle models can be reconciled with the empirical evidence on the lack of consumption risk sharing. First, we show analytically that with incomplete asset markets productivity disturbances can have large uninsurable effects on wealth, depending on the value of the trade elasticity and shock persistence. Second, we investigate these findings quantitatively in a model calibrated to the U.S. economy. With the low trade elasticity estimated via a method of moments procedure, the consumption risk of productivity shocks is magnified by high terms of trade and real exchange rate (RER) volatility. Strong wealth effects in response to shocks raise the demand for domestic goods above supply, crowding out external demand and appreciating the terms of trade and the RER. Building upon the literature on incomplete markets, we then show that similar results are obtained when productivity shocks are nearly permanent, provided the trade elasticity is set equal to the high values consistent with micro-estimates. Under both approaches the model accounts for the low and negative correlation between the RER and relative (domestic to foreign) consumption in the data—the "Backus–Smith puzzle".     

Capital Controls,Global Liquidity Traps,and the International Policy Trilemma*

The zero bound on interest rates introduces a new dimension to the trilemma in international policy. The openness of the international financial market might render monetary policy ineffective, even within a system of fully flexible exchange rates, because shocks that lead to a liquidity trap in one country are propagated through financial markets to other countries. However, the effectiveness of monetary policy can be restored by the imposition of capital controls. We derive the optimal response of monetary policy to a global liquidity trap in the presence of capital controls. We show that, even though capital controls might facilitate effective monetary policy, capital controls are not generally desirable in terms of welfare.     

Imperfect Competition, Capital Shortages and Unemployment Persistence

We construct a model integrating the traditions of imperfect competition macroeconomics and real business cycles. For this we study a dynamic economy with optimizing households, firms and trade unions subject to stochastic shocks. We can derive closed form solutions for the behaviour of all agents. It is found that the combination of capital shortages and imperfect competition in labor markets can give rise to unemployment, and that this unemployment is quite persistent, even when the underlying shocks are not.     

Redistributive innovation policy,inequality, and efficiency

We examine the efficiency and distributional effects of regressive and progressive public R&D policies that target high‐tech and low‐tech sectors using a heterogenous‐agent growth model with in‐house R&D and incomplete capital markets. We find that such policies have important implications for efficiency and inequality. A regressive public R&D investment financed by income tax could boost growth and welfare via a positive effect on individual savings and effort. It could, however, also lower growth and welfare via its effect on the efficiency–inequality trade‐off. Thus, the relationship between public R&D spending and welfare is hump‐shaped, admitting an optimal degree of regressivity in public R&D spending. Using our baseline model, and the US state‐level GDP data, we derive the degree of regressiveness of public R&D investment in US states. We find that US states are more regressive in their R&D investment than the optimal regressiveness implied by our growth model.     

On the empirics of risk-sharing across MENA countries

In this article, we compute the potential welfare gains and the realized gains from risk-sharing among Middle East and North African (MENA) countries, including the oil-rich Gulf region and the resource-scarce economies. We find that the overall potential welfare gains across MENA countries are positive for all countries under the assumption of full risk-sharing. The potential welfare gains among the six Gulf Cooperation Council (GCC) countries are positive even though the magnitudes are smaller compared to those of the rest of the MENA region. We also quantify the extent of risk-sharing for the MENA region and show that it is significant for the MENA region and its subgroups; however, we could not find any sign of inter-temporal smoothing across the same groups. Decomposing the aggregate output shocks shows that the extent of risk-sharing is significant when only positive output shocks exist across the resource-scarce MENA economies. However, we observe that GCC countries share output risks with each other even under negative output shocks.     

Imperfect credibility,sticky wages,and welfare

This paper studies optimal monetary policy under imperfect credibility in a New Keynesian model with staggered price and wage setting. In our imperfect credibility framework, the central bank commits to a policy plan but occasionally reneges on past promises with a given common knowledge probability. We find that the welfare gains from increasing credibility are approximately linear on the initial credibility level. We also find that the output-inflation stabilisation trade-off is nonmonotonic as higher credibility does not always reduce output volatility. The variance decomposition shows that wage markup shocks are the main driver of economic fluctuations and that these shocks are better contained, even in relative terms, when credibility is high. We then show that the degree of credibility impacts the effect of wage flexibility on welfare. When credibility is low, monetary policy is less potent and the economy can experience a feedback loop between wage volatility and price volatility. We show, though, that once wage markup shocks are taken into account, wage flexibility is usually welfare improving.     

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

Equity home bias,incomplete financial markets,and nominal rigidities

Abstract This paper analyzes optimal portfolio decisions in a monetary open‐economy framework. It is found that market completeness and the specific form of nominal rigidities, namely, nominal price vs. nominal wage rigidities, matter for justifying the observed structure of equity holdings. When markets are complete, sticky prices generate a negative correlation between the non‐diversifiable labour income and the profit of domestic firms with respect to the productivity shocks, which explains why households invest little abroad. In contrast, when markets are incomplete, rigidities in goods prices result in a counterfactual ‘super home bias’, because domestic equities provide a good hedge against not only the labour income risk but also the relative price risk. Wage rigidities, however, have the opposite effect. Therefore, nominal rigidities in both goods prices and wage rates are needed to address the empirical composition of gross equity positions under incomplete markets.     

Consumption,welfare, and stochastic population dynamics when technology shocks are (Un)tied

The impact of uncertainty on consumption and welfare seems obvious; because of the precautionary saving motive, higher uncertainty reduces consumption, and subsequently, deteriorates welfare. Recent several studies, however, find that this intuitive narrative is not necessarily true. This paper provides the analytical underpinnings for this. In the absence of technological progress, I find that the larger demographic shocks always reduce consumption, but improve the welfare of households. Moreover, when demographic shocks are negatively tied to technology shocks, there emerges an inverted-U relationship between the size of two shocks and consumption, and a U-shaped relationship between the size of two shocks and household welfare. These results are all characterized analytically in the framework of the stochastic two-sector growth model featuring the correlated Brownian motion process. The findings suggest that demographic policies should not be implemented with no reference to the state of technology.     

Strategic R&D Commitment and the Gains from Trade

This paper examines how trade liberalization affects innovation, profits and welfare in a model of reciprocal markets when firms pre‐commit to research and development (R&D). We establish that the equilibrium is not always unique and show that, with trade, R&D commitment leads to higher levels of innovation, lower profits, higher consumer surplus and higher welfare than when R&D is chosen simultaneously to output levels. Furthermore, if the effectiveness of R&D is sufficiently high, trade always yields higher welfare than autarky, implying that R&D commitment may significantly enhance the welfare gains from trade liberalization.     

Common Currencies vs. Monetary Independence

We study the optimal monetary policy in a two-country open-economy model under two monetary arrangements: (a) multiple currencies controlled by independent policy makers; (b) common currencies with a centralized policy maker.
Our findings suggest that: (i) monetary policy competition leads to higher long-term inflation and interest rates with large welfare losses; (ii) the inflation bias and the consequent losses are larger when countries are unable to commit to future policies; (iii) the welfare losses from higher long-term inflation dominates the welfare costs of losing the ability to react optimally to shocks.     

Optimal research and development and the cost of business cycles

While research and development (R&D) investment has been procyclical in the post-war period, recent literature suggests that the optimal path for R&D is countercyclical, and that the economy would be better off by subsidizing R&D in recessions. The objective of this paper is to analyze the welfare effects of distortions in the intertemporal allocation of R&D resources and to compare diverse policy interventions so as to improve social welfare. To this end, we introduce a calibrated dynamic stochastic general equilibrium model with Schumpeterian endogenous growth that is capable of explaining the observed procyclicality of R&D. Our results show that the cost of business cycles is lower in the decentralized economy with procyclical R&D than in the efficient allocation with countercyclical R&D. This is because the suboptimal propagation of shocks in the decentralized equilibrium offsets some of the existing steady-state distortions. In this second-best context, countercyclical R&D subsidies have no positive effect on welfare. In contrast, fiscal policies aimed at restoring the optimal steady-state produce large welfare gains.     

Monetary union: A welfare based approach

This article attempts to shed light on the consequences of the transition to EMU for individual welfare following specific shocks. To this end, we develop a two country intertemporal general equilibrium model that extends the Obstfeld and Rogoff (Journal of Political Economy 103 (3) (1995) 624) specification to nominal rigidities through price adjustment costs and pricing-to-market behavior.We show that, when facing a positive asymmetric permanent shock to either technology or government expenditures occurring in one country, implementing a monetary union is beneficial to the households living in this economy. Conversely, it is detrimental to foreigners. Further, a sensitivity analysis shows that if the gains/losses to implementing monetary union are qualitatively robust when facing changes in the degree of nominal rigidities and the elasticity of substitution between foreign and domestic goods, they are quite sensitive to the degree of pricing-to-market in the economy.     

Incomplete cost pass-through under deep habits

A number of empirical studies document that marginal cost shocks are not fully passed through to prices at the firm level and that prices are substantially less volatile than costs. We show that in the relative-deep-habits model of Ravn, Schmitt-Grohé, and Uribe [Ravn, M., Schmitt-Grohé, S., Uribe, M., 2006. Deep habits. Review of Economic Studies 73, 195–218], firm-specific marginal cost shocks are not fully passed through to product prices. That is, in response to a firm-specific increase in marginal costs, prices rise, but by less than marginal costs leading to a decline in the firm-specific markup of prices over marginal costs. Pass-through is predicted to be even lower when shocks to marginal costs are anticipated by firms. In our model unanticipated firm-specific cost shocks lead to incomplete pass-through (or a decline in markups) of about 20 percent and anticipated cost shocks are associated with incomplete pass-through of about 50 percent. The model predicts that cost pass-through is increasing in the persistence of marginal cost shocks and U-shaped in the strength of habits. The relative-deep-habits model implies that conditional on marginal cost disturbances, prices are less volatile than marginal costs.     

Learning in asymmetric duopoly markets: competition in information and market correlation

This paper explores experimentation and learning in asymmetric duopoly markets with product differentiation and demand uncertainty. We define the concepts of strategic substitutability and strategic complementarity in information and we show how both the mode of information competition and the transmission of information across markets affect duopoly experimentation. We relate information competition with market competition and we find that, when goods are substitutes and the correlation between market shocks is negative, firms will have a higher incentive to experiment in asymmetric markets than in symmetric ones. The opposite result follows when such correlation is positive. Also, when goods are complements the above findings are reversed.JEL Classification: D83, C72The authors thank partial financial support from the Spanish Ministry of Science and Technology under project B2000-1429, from the Spanish Ministry of Education and Science under project SEJ2004-07554 and from the “Generalitat Valénciana” under project GRUPOS04/13.     

Portfolio allocation and international risk sharing

Abstract We show that recent explanations of the consumption‐real exchange rate anomaly that rely on goods and financial market frictions are not robust to introducing just one additional international asset. When portfolios are selected optimally, international trade in two nominal bonds implies a consumption‐real exchange rate correlation that is too high compared with the data even when there are many shocks. Monetary policy specification plays a potentially important role for the degree of risk sharing provided by nominal bonds, both in the benchmark model with only tradable and non‐tradable sector supply shocks and also in the model that allows for news.