Constrained-efficient Allocation Research Articles

Equilibrium underemployment

This paper develops a model of human capital investment in a frictional labor market with two-sided heterogeneity and liquidity constraints. The model generates underemployment in equilibrium: workers are employed in jobs for which they are over-qualified. Subsidizing education can decrease the returns to human capital investment, increase the underemployment rate, and decrease the unemployment rate. I calibrate the model to the U.S. economy and find the aggregate supply of human capital and underemployment rate are inefficiently low. The constrained-efficient allocation is implemented by increasing unemployment benefits and subsidizing both the creation of high-skill jobs and human capital investment.

Optimal taxation in asset markets with adverse selection

Constrained efficiency is characterized in an asset market, subject to search frictions, where sellers are privately informed about the type of their asset. The type determines the opportunity cost of the asset for sellers and the quality of the asset for buyers. The constrained-efficient allocation is implemented using a sales tax schedule. The optimal schedule has a single-crossing property, requiring the trading of low-quality assets to be subsidized and trading of high-quality assets to be taxed. Surprisingly, the optimal schedule could be non-monotonic in the quality or price of assets even when buyers and sellers agree on the ranking of assets. This result implies that using a linear tax schedule, as typically assumed in the literature, could significantly limit the benefits of taxation. The role of traditional search frictions, and the effects of higher measure of distressed sellers, higher quality of assets and more efficient matching technology on the optimal schedule are also studied.

Risk Premium Shocks Can Create Inefficient Recessions

Abstract We develop a simple flexible-price model of business cycles driven by spikes in risk premiums. Aggregate shocks increase firms’ uninsurable idiosyncratic risk and raise risk premiums. We show that risk shocks can create quantitatively plausible recessions, with contractions in employment, consumption, and investment. Business cycles are inefficient—output, employment, and consumption fall too much during recessions, compared to the constrained-efficient allocation. Optimal policy involves stimulating employment and consumption during recessions.

Constrained-Efficient Capital Reallocation

We analyze the constrained-efficient allocation in an equilibrium model of investment and capital reallocation with heterogeneous firms facing collateral constraints. The model features two types of pecuniary externalities: collateral externalities, because the resale price of capital affects firms’ ability to borrow, and distributive externalities, because buyers of old capital are more financially constrained than sellers, consistent with empirical evidence. We show analytically and quantitatively that the equilibrium price of old capital is inefficiently high in general, because the distributive pecuniary externality exceeds the collateral externality, by a factor of two in the calibrated model. New investment generates a positive aggregate externality by reducing the future price of old capital, fostering reallocation toward more constrained firms. The constrained-efficient allocation induces a consumption-equivalent welfare gain of 5% compared to the competitive equilibrium, and can be implemented with subsidies on new capital and taxes on old capital. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Externalities as Arbitrage

Regulations on financial intermediaries can create apparent arbitrage opportunities. Intermediaries are unable to fully exploit these opportunities due to regulation, and other agents are unable to exploit them at all due to limited participation. Does the existence of arbitrage opportunities imply that regulations are sub-optimal? No. I develop of general equilibrium model, with financial intermediaries and limited participation by other agents, in which a constrained-efficient allocation can be implemented with asset prices featuring arbitrage opportunities. Absent regulation, there would be no arbitrage; however, allocations would be constrained-inefficient, due to pecuniary externalities and limited market participation. Optimal policy creates arbitrage opportunities whose pattern across states of the world reflects these externalities. From financial data alone, we can construct perceived externalities that would rationalize the pattern of arbitrage observed in the data. By examining these perceived externalities, and comparing them to the stated goals of regulators, as embodied in the scenarios of the stress tests, we can ask whether regulations are having their intended effect. The answer, in recent data, is no.

Efficient Risk Sharing with Limited Commitment and Storage

We extend the model of risk sharing with limited commitment (Kocherlakota, 1996 )b y introducing both a public and a private (non-contractible and/or non-observable) storage technology. Positive public storage relaxes future participation constraints and may hence improve risk sharing, contrary to the case where hidden income or effort is the deep friction. The characteristics of constrained-efficient allocations crucially depend on the storage technology’s return. In the long run, if the return on storage is (i) moderately high, both assets and the consumption distribution may remain time-varying; (ii) sufficiently high, assets converge almost surely to a constant and the consumption distribution is time-invariant; (iii) equal to agents’ discount rate, perfect risk sharing is self-enforcing. Agents never have an incentive to use their private storage technology, i.e., Euler inequalities are always satisfied, at the constrained-efficient allocation of our model, while this is not the case without optimal public asset accumulation.

Optimal credit fluctuations

Under which conditions are extrinsic credit fluctuations socially optimal? In order to answer this question we characterize constrained-efficient allocations in an infinite horizon, two-good economy with limited commitment for two market structures, random pairwise meetings and centralized meetings. If agents meet bilaterally, then constrained-efficient allocations specify the highest stationary output level that is incentive feasible, and it is implemented with take-it-or-leave-it offers and “not-too-tight” solvency constraints. If agents meet in a centralized location, constrained-efficient allocations can be non-stationary, in which case they feature a credit boom followed by stagnation due to “too-tight” solvency constraints. We also characterize constrained-efficient allocations under partial commitment by the planner. If commitment is low, the economy experiences rare but pronounced credit crunches. If commitment is high, the economy experiences infrequent but large credit booms.

Decentralizing constrained-efficient allocations in the Lagos–Wright pure currency economy

This paper offers two ways to decentralize the constrained-efficient allocation of the Lagos–Wright (2005) pure currency economy. The first way has divisible money, take-it-or-leave-it offers by buyers, and a transfer scheme financed by money creation. If agents are sufficiently patient, the first best is achieved for finite money growth rates. If agents are impatient, the equilibrium allocation approaches the constrained-efficient allocation asymptotically as the money growth rate tends to infinity. The second way has indivisible money, take-it-or-leave-it offers by buyers, and no government intervention. We discuss the strict implementation of constrained-efficient allocations and the applicability of our scheme to economies with Lucas trees, endogenous participation, match-specific heterogeneity, and sequential competitive markets.

Optimal Intermediary Rents

This paper studies a dynamic production economy with financial intermediation. It is assumed that claims held on intermediaries cannot be fully enforced such that intermediation is subject to intermediary equity requirements. It is shown that competitive equilibria are not constrained efficient whenever the aggregate amount of intermediary equity in the economy is low enough to limit production. Specifically, a constrained social planner can achieve a Pareto improvement by creating long-term rents for intermediaries, which immediately reduces intermediary equity requirements. The constrained-efficient allocation can be implemented by a positive tax on future intermediary activity. (JEL D21, D82, D86, G21, G28)

Controlling a Distribution of Heterogeneous Agents

This paper analyzes the problem of a benevolent planner wishing to control a population of heterogeneous agents subject to idiosyncratic shocks. This is equivalent to a deterministic control problem in which the state variable is the cross-sectional distribution. We show how, in continuous time, this problem can be broken down into a dynamic programming equation plus the law of motion of the distribution, and we introduce a new numerical algorithm to solve it. As an application, we analyze the constrained-efficient allocation of an Aiyagari economy with a fat-tailed wealth distribution. We find that the constrained-efficient allocation features more wealth inequality than the competitive equilibrium.

Optimal Intermediary Rents

This paper studies a dynamic production economy with financial intermediation. It is assumed that claims held on intermediaries cannot be fully enforced such that intermediation is subject to intermediary equity requirements. It is shown that competitive equilibria are not constrained efficient whenever the aggregate amount of intermediary equity in the economy is low enough to limit production. Specifically, a constrained social planner can achieve a Pareto improvement by creating long-term rents for intermediaries which immediately reduces intermediary equity requirements. The constrained-efficient allocation can be implemented by a positive tax on future intermediary activity.

Fraud deterrence in dynamic Mirrleesian economies

Insurance schemes rely on legal consequences to deter fraud and tax evasion. This observation guides us to introduce random state verification in a dynamic economy with private information. With some probability, an agent's skill becomes known to the planner who prescribes punishments to misreporting agents. Deferring consumption can ease the provision of incentives creating a motive for subsidizing savings. In an infinite horizon economy, the constrained-efficient allocation converges to high consumption, full insurance, and no labor distortions for any positive probability of state verification.

Imperfect interbank markets and the lender of last resort

This paper presents a monetary model in which interbank markets have limited commitment to contracts. Limited commitment reduces the proportion of assets that can be used as collateral, and thus banks with high liquidity demands face borrowing constraints in interbank markets. These constraints can be relieved by the central bank (a lender of last resort) through the provision of liquidity loans. I show that the constrained-efficient allocation can be decentralized by controlling only the money growth rate if commitment to interbank contracts is not limited. Otherwise, a proper combination of central bank loans and monetary policy is needed to bring the market equilibrium into a state of constrained efficiency.

The Cost of Inflation: A Mechanism Design Approach

I apply mechanism design to quantify the cost of inflation that can be attributed to monetary frictions alone. In an environment with pairwise meetings, the money demand that is consistent with a constrained-efficient allocation takes the form of a continuous correspondence that can fit the data over the period 1900–2006. For such parameterizations, the cost of moderate inflation is zero. This result is robust to different assumptions regarding the observability of money holdings, the introduction of match-specific heterogeneity, and endogeneous participation decisions.

Optimal Labor-Market Policy in Recessions

The authors examine the optimal labor market-policy mix over the business cycle. In a search and matching model with risk-averse workers, endogenous hiring and separation, and unobservable search effort they first show how to decentralize the constrained-efficient allocation. This can be achieved by a combination of a production tax and three labor-market policy instruments, namely, a vacancy subsidy, a layoff tax and unemployment benefits. The authors derive analytical expressions for the optimal setting of each of these for the steady state and for the business cycle. Their propositions suggest that hiring subsidies, layoff taxes and the replacement rate of unemployment insurance should all rise in recessions. The authors find this confirmed in a calibration targeted to the U.S. economy.

Optimal Labor-Market Policy in Recessions

Within a search and matching model with risk-averse workers, endogenous hiring and separation, and unobservable search effort, we show how to decentralize the constrained-efficient allocation by a combination of a production tax and three labor-market policy instruments: vacancy subsidies, layoff taxes, and unemployment benefits. We derive analytical expressions for the optimal mix of these over the business cycle. Calibrating the model to the US economy under the assumption that wages are rigid, we find that hiring subsidies and layoff taxes should rise considerably and persistently in recessions. The optimal variation in unemployment benefits, in contrast, is quantitatively small and short-lived. (JEL E24, E32, J24, J63, J64, J65)

On the Coexistence of Money and Higher-Return Assets and its Social Role

This paper adopts mechanism design to tackle the central issue in monetary theory, namely, the coexistence of money and higher-return assets. I describe an economy with pairwise meetings, where fiat money and risk-free capital compete as means of payment. Whenever fiat money has an essential role, any constrained-efficient allocation is such that capital commands a higher rate of return than fiat money.

Revisiting Overborrowing and its Policy Implications

This paper analyzes quantitatively the extent to which there is overborrowing (i.e., inefficient borrowing) in a business cycle model for emerging market economies with production and an occasionally binding credit constraint. The main finding of the analysis is that overborrowing is not a robust feature of this class of model economies: it depends on the structure of the economy and its parametrization. Specifically, underborrowing in a production economy is found with the baseline calibration, but overborrowing with more impatient agents and more volatile shocks. Endowment economies display overborrowing regardless of parameter values, but they do not allow for policy intervention when the constraint binds (in crisis times). Quantitatively, the welfare gains from implementing the constrained-efficient allocation are always larger near crisis times than in normal ones. In production economies, they are one order of magnitude larger than in endowment economies both in crisis and normal times. This suggests that the scope for economy-wide macro-prudential policy interventions (e.g., prudential taxation of capital flows and capital controls) is weak in this class of models.

Fraud Deterrence in Dynamic Mirrleesian Economies

Social and private insurance schemes rely on legal action to deter fraud and tax evasion. This observation guides the authors to introduce a random state verification technology in a dynamic economy with private information. With some probability, an agent's skill level becomes known to the planner, who prescribes a punishment if the agent is caught misreporting. The authors show how deferring consumption can ease the provision of incentives. As a result, the marginal benefit may be below the marginal cost of investment in the constrained-efficient allocation, suggesting a subsidy on savings. They characterize conditions such that the intertemporal wedge is negative in finite horizon economies. In an infinite horizon economy, the authors find that the constrained-efficient allocation converges to a high level of consumption, full insurance, and no labor distortions for any probability of state verification.

Specialization and efficiency with labor-market matching

This paper constructs a labor-market matching model with heterogeneous workers. Due to matching frictions, there may be a mismatch of talents within a production team, forcing a worker to specialize in a task at which she is not talented. We consider a partnership model where production takes place in teams consisting of two workers. We characterize the steady-state of the matching equilibrium. The constrained efficiency of the matching equilibrium depends on the distribution of talents. The constrained-efficient allocation can always be implemented by a type-specific tax. We also examine an alternative model with Diamond–Mortensen–Pissarides type matching between firms and workers.