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Yuzhe Zhang

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Mohamad L . Hammour

Pierre-Olivier Gourinchas

University of California, Berkeley

Carleton University

Carleton University

Syarif Hidayatullah State Islamic University, Jakarta

University of Graz

Michele Boldrin

Washington University in St. Louis

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Papers by Yuzhe Zhang

China's Housing Bubble, Infrastructure Investment, and Economic Growth

International Economic Review, 2021

China's housing prices have been growing rapidly over the past few decades, despite low growth in... more China's housing prices have been growing rapidly over the past few decades, despite low growth in rents. We study the impact of housing bubbles on China's economy, based on the understanding that local governments use land-sale revenue to fuel infrastructure investment. We calibrate our model to the Chinese data over the period 2003-2013 and find that our calibrated model can match the declining capital return and GDP growth, the average housing price growth, and the rising infrastructure to GDP ratio in the data. We conduct two counterfactual experiments to estimate the impact of a bubble collapse and a property tax.

Wealth Effects with Endogenous Retirement

Economic Quarterly, 2019

n this article, we discuss the so-called wealth e¤ects: the response of aggregate consumption to ... more n this article, we discuss the so-called wealth e¤ects: the response of aggregate consumption to exogenous movements in wealth. Wealth e¤ects are of interest to market participants and policymakers, as they can be informative about expected GDP growth given observed movements in asset prices. Estimated in a standard way, the wealth e¤ect in aggregate data amounts to about 2.4 cents on the dollar. From the point of view of the simple permanent income theory, as in Friedman (1957), Bewley (1977), or Hall (1978), these estimates are surprisingly low. With changes in asset prices unpredictable, an exogenous increase in wealth of $1 increases the agent's permanent income by r dollars, where r is the riskless rate of interest or the agent's rate of time preference. With the standard estimate of r = 5 percent, permanent income theory predicts the wealth e¤ect of 5 cents on the dollar, which is about twice the e¤ect we observe in the data. 1 Poterba (2000) reviews the main explanations of weak wealth effects that have been proposed in the literature. At the aggregate level, the response of consumption to wealth changes may be low because wealth concentration is high and consumption of high net worth households may be relatively inelastic. Cagetti and De Nardi (2008) and Saez and Zucman (2016) document a recent further increase in wealth The authors thank Caroline Davis, Felipe Schwartzman, Bruno Sultanum, and John Weinberg for their helpful comments and Emma Yeager for excellent research assistance. The views expressed in this article are those of the authors and not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System.

Stochastic optimal growth with a non-compact state space

Journal of Mathematical Economics, 2007

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and M... more This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [J. Econ. Theory 4 (1972)] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with noncompact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.

Dynamic contracting with persistent shocks

Journal of Economic Theory, 2009

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in... more In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound-immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.

Optimal Contracts with Reflection

In this paper, we show that whenever the agent's outside option is nonzero, the optimal contr... more In this paper, we show that whenever the agent's outside option is nonzero, the optimal contract in the continuous-time principal-agent model of Sannikov (2008) is reflective at the lower bound. This means the agent is never terminated or retired after poor performance. Instead, the agent is asked to put zero effort temporarily, which brings his continuation value up. The agent is then asked to resume effort, and the contract continues. We show that a nonzero agent's outside option arises endogenously if the agent is allowed to quit and find a new firm (after a random search time of finite expected duration). In addition, we find new dynamics of the reflection at the lower bound. In the baseline model, the dynamics of the reflection are slow, as in Zhu (2013), i.e., the zero-action is used often. However, if the agent's disutility from the first unit of effort is zero, which is a standard Inada condition, or if his utility of consumption is unbounded below, the reflectio...

A Duality Approach to Continuous-Time Contracting Problems with Limited Commitment,” Working paper

We propose a duality approach to solving contracting models with either one-sided or two-sided li... more We propose a duality approach to solving contracting models with either one-sided or two-sided limited commitment in continuous time. We establish weak and strong duality theorems and provide a dynamic programming characterization of the dual problem. The dual problem gives a linear Hamilton-Jacobi-Bellman equation with a known state space subject to free-boundary conditions, making analysis much more tractable than the primal problem. We provide two explicitly solved examples of a consumption insurance problem. We characterize the optimal consumption allocation in terms of the marginal utility ratio. We find that neither autarky nor full risk sharing can be an optimal contract with two-sided limited commitment, unlike in discrete-time models. We also derive an explicit solution for the unique long-run stationary distribution of consumption relative to income. JEL Classification: C61, D86, D91, E21

A Characterization of Optimal Contracts with One-Sided Limited Commitment

In this paper I provide an analytic solution to a large class of contracting models with one-side... more

Unemployment insurance: payments, overpayments and unclaimed benefits

The Regional Economist, 2012

In the U.S. unemployment insurance program, most of the overpayments due to fraud arise from indi... more

Optimal Infant Industry Protection

We consider a dynamic model in which a domestic firm has a positive marginal cost of production a... more We consider a dynamic model in which a domestic firm has a positive marginal cost of production and a foreign firm has zero marginal cost. With free trade the foreign firm would serve the entire domestic market and the domestic firm would not produce. We assume that there is a social benefit for the domestic nation if the domestic firm produces. This could be, for example, because there is learning by doing at the firm level that spills over to other domestic firms. We also assume that the domestic firm can stochastically improve its technology and produce at zero cost. This probability is increasing in domestic production. However, whether the domestic firm has transitioned to zero cost or not is private information. We use a mechanism design approach to deliver optimal protection in the presence of such persistent private information. Our incentive-compatible protection policy induces the domestic firm to reveal its true cost. Our results are as follows. First, the import quota i....

Optimal liquidity policy with shadow banking

Economic Theory, 2019

We study the impact of shadow banking on optimal liquidity regulation in a Diamond–Dybvig maturit... more We study the impact of shadow banking on optimal liquidity regulation in a Diamond–Dybvig maturity-mismatch environment. In this economy, a pecuniary externality arising out of the banks’ access to private retrade renders competitive equilibrium inefficient. A tax on illiquid assets and a subsidy to the liquid asset similar to the payment of interest on reserves (IOR) constitute an optimal liquidity regulation policy. Shadow banking gives banks an outside option allowing them to escape regulation at the cost of forgoing access to the government safety net. We derive two implications of shadow banking for optimal liquidity regulation policy. First, optimal policy must implement a macroprudential cap on illiquid-asset prices that binds only when the return on illiquid assets is high. Second, optimal policy must implement a fire sale of illiquid assets when high demand for liquidity is anticipated. We show how these features can be implemented by adjusting the IOR rate and the illiquid-asset tax rate.

Market-based incentives

In this article, we study market-induced, external incentives similar to career concerns jointly ... more In this article, we study market-induced, external incentives similar to career concerns jointly with standard, contractual incentives linking compensation to performance. We consider a dynamic principal–agent problem in which the agent’s outside option is determined endogenously in a competitive labor market. In equilibrium, strong performance increases the agent’s market value. When this value becomes sufficiently high, the threat of the agent quitting forces the principal to increase the agent’s compensation. The prospect of obtaining this raise gives the agent an incentive to exert effort, which reduces the need for standard incentives. In fact, whenever the agent’s option to quit is sufficiently close to being “in the money,” the market-induced incentive eliminates the need for standard incentives altogether: Compensation becomes completely insensitive to current performance.

Shared Patent Rights and Technological Progress

International Economic Review, 2015

We study how to reward innovators who build on one another. Rewards come in the form of patents. ... more We study how to reward innovators who build on one another. Rewards come in the form of patents. Because patent rights are scarce, the optimal allocation involves sharing: More than one innovator's patent is in force at a given time. We interpret such allocations as patents that infringe one another as licensing through an ever growing patent pool and as randomization through litigation. We contrast the rate of technological progress under the optimal allocation with the outcome if sharing is prohibitively costly. Avoiding sharing initially slows progress and leads to a more variable rate of technological progress.

Optimal investment taxes and efficient market provision of liquidity in the Diamond-Dybvig model

We study taxation as an alternative to intermediation in a Diamond-Dybvig economy with a private ... more We study taxation as an alternative to intermediation in a Diamond-Dybvig economy with a private ex post retrade market and with private ex ante investment. The possibility of private investment imposes an additional constraint on the social planner beyond resource feasibility and incentive compatibility. With this constraint, the simple asset market equilibrium is efficient. If access to private investment is costly, i.e., the private return on the illiquid investment is smaller than the publicly observable return on illiquid investment, then an asset market equilibrium is efficient with investment taxes. An optimal tax system consists of a proportional subsidy to liquid investment and a proportional tax on illiquid investment. In either case, efficiency is attained without intermediation.

Unemployment Benefits: How Much Money Goes Unclaimed?

Economic Synopses

Unemployment Insurance Fraud

Economic Synopses

Dynamic Contracting, Persistent Shocks and Optimal Taxation

In this paper I develop continuous-time methods for solving dynamic principal-agent problems in w... more In this paper I develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. I characterize the optimal contract as the solution to a system of ordinary differential equations, and show that, under this contract, the agent's utility converges to its lower bound-immiseration occurs. I also show that, unlike in environments with i.i.d. shocks, the principal would like to renegotiate with the agent when the agent's productivity is low-it is not renegotiation-proof. I apply the theoretical methods I have developed and numerically solve this (Mirrleesian) dynamic taxation model. I find that it is optimal to allow a wedge between the marginal rate of transformation and individuals' marginal rate of substitution between consumption and leisure. This wedge is significantly higher than what is found in the i.i.d. case. Thus, using the i.i.d. assumption is not a good approximation quantitatively when there is persistence in productivity shocks.

Market-Based Incentives

International Economic Review

Dynamic Contracts, Persistent Shocks, and Optimal Taxation,” Federal Reserve Bank of Minneapolis working paper

Foreign Aid, Public Spending, Optimal Fiscal and Monetary Policies, and Long-Run Growth

Cema Working Papers, 2008

This paper presents a group of models showing the strikingly different implications of foreign ai... more This paper presents a group of models showing the strikingly different implications of foreign aid to the private sector and public sector. In the first model, with decentralized decision-making and without optimal choices of fiscal policies on behalf of the government, foreign aid to the private sector has no effect on the long-run capital accumulation and it raises private consumption one to one; whereas foreign aid to the government leads to more public spending and higher private capital accumulation. In another model with optimal choices of both fiscal and monetary policies, foreign aid to the private sector gives rise to higher inflation and income taxation. Although aid to the private sector raises private money holdings and consumption, it reduces capital accumulation. However, when foreign aid is provided to the public sector, the government cuts both the inflation rate and the income tax rate, raises public spending, and provides more incentives for private capital accumulation and money holdings. In the long run, aid to the public sector leads to more private capital accumulation, consumption, money holdings, and welfare.

Optimal Unemployment Insurance with Hidden Trade

This paper studies the optimal design of unemployment insurance in an environment where the insur... more This paper studies the optimal design of unemployment insurance in an environment where the insurance agency could monitor neither the searching efforts nor the asset holding of an unemployed worker. Previous results with no hidden trade violate the Euler equation of a worker and thus can not be implementable if he has private access to asset market. We abandon the traditional first-order approach and solve the incentive problem directly. With CARA utility functions, we obtain the optimal contract in closed form. We find that, counter-intuitively, an unemployed worker's consumption will decline faster than that implied by Hopenhayn and Nicolini (1997).

China's Housing Bubble, Infrastructure Investment, and Economic Growth

International Economic Review, 2021

China's housing prices have been growing rapidly over the past few decades, despite low growth in... more China's housing prices have been growing rapidly over the past few decades, despite low growth in rents. We study the impact of housing bubbles on China's economy, based on the understanding that local governments use land-sale revenue to fuel infrastructure investment. We calibrate our model to the Chinese data over the period 2003-2013 and find that our calibrated model can match the declining capital return and GDP growth, the average housing price growth, and the rising infrastructure to GDP ratio in the data. We conduct two counterfactual experiments to estimate the impact of a bubble collapse and a property tax.

Wealth Effects with Endogenous Retirement

Economic Quarterly, 2019

n this article, we discuss the so-called wealth e¤ects: the response of aggregate consumption to ... more n this article, we discuss the so-called wealth e¤ects: the response of aggregate consumption to exogenous movements in wealth. Wealth e¤ects are of interest to market participants and policymakers, as they can be informative about expected GDP growth given observed movements in asset prices. Estimated in a standard way, the wealth e¤ect in aggregate data amounts to about 2.4 cents on the dollar. From the point of view of the simple permanent income theory, as in Friedman (1957), Bewley (1977), or Hall (1978), these estimates are surprisingly low. With changes in asset prices unpredictable, an exogenous increase in wealth of $1 increases the agent's permanent income by r dollars, where r is the riskless rate of interest or the agent's rate of time preference. With the standard estimate of r = 5 percent, permanent income theory predicts the wealth e¤ect of 5 cents on the dollar, which is about twice the e¤ect we observe in the data. 1 Poterba (2000) reviews the main explanations of weak wealth effects that have been proposed in the literature. At the aggregate level, the response of consumption to wealth changes may be low because wealth concentration is high and consumption of high net worth households may be relatively inelastic. Cagetti and De Nardi (2008) and Saez and Zucman (2016) document a recent further increase in wealth The authors thank Caroline Davis, Felipe Schwartzman, Bruno Sultanum, and John Weinberg for their helpful comments and Emma Yeager for excellent research assistance. The views expressed in this article are those of the authors and not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System.

Stochastic optimal growth with a non-compact state space

Journal of Mathematical Economics, 2007

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and M... more This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [J. Econ. Theory 4 (1972)] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with noncompact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.

Dynamic contracting with persistent shocks

Journal of Economic Theory, 2009

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in... more In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound-immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.

Optimal Contracts with Reflection

In this paper, we show that whenever the agent's outside option is nonzero, the optimal contr... more In this paper, we show that whenever the agent's outside option is nonzero, the optimal contract in the continuous-time principal-agent model of Sannikov (2008) is reflective at the lower bound. This means the agent is never terminated or retired after poor performance. Instead, the agent is asked to put zero effort temporarily, which brings his continuation value up. The agent is then asked to resume effort, and the contract continues. We show that a nonzero agent's outside option arises endogenously if the agent is allowed to quit and find a new firm (after a random search time of finite expected duration). In addition, we find new dynamics of the reflection at the lower bound. In the baseline model, the dynamics of the reflection are slow, as in Zhu (2013), i.e., the zero-action is used often. However, if the agent's disutility from the first unit of effort is zero, which is a standard Inada condition, or if his utility of consumption is unbounded below, the reflectio...

A Duality Approach to Continuous-Time Contracting Problems with Limited Commitment,” Working paper

We propose a duality approach to solving contracting models with either one-sided or two-sided li... more We propose a duality approach to solving contracting models with either one-sided or two-sided limited commitment in continuous time. We establish weak and strong duality theorems and provide a dynamic programming characterization of the dual problem. The dual problem gives a linear Hamilton-Jacobi-Bellman equation with a known state space subject to free-boundary conditions, making analysis much more tractable than the primal problem. We provide two explicitly solved examples of a consumption insurance problem. We characterize the optimal consumption allocation in terms of the marginal utility ratio. We find that neither autarky nor full risk sharing can be an optimal contract with two-sided limited commitment, unlike in discrete-time models. We also derive an explicit solution for the unique long-run stationary distribution of consumption relative to income. JEL Classification: C61, D86, D91, E21

A Characterization of Optimal Contracts with One-Sided Limited Commitment

In this paper I provide an analytic solution to a large class of contracting models with one-side... more

Unemployment insurance: payments, overpayments and unclaimed benefits

The Regional Economist, 2012

In the U.S. unemployment insurance program, most of the overpayments due to fraud arise from indi... more

Optimal Infant Industry Protection

We consider a dynamic model in which a domestic firm has a positive marginal cost of production a... more We consider a dynamic model in which a domestic firm has a positive marginal cost of production and a foreign firm has zero marginal cost. With free trade the foreign firm would serve the entire domestic market and the domestic firm would not produce. We assume that there is a social benefit for the domestic nation if the domestic firm produces. This could be, for example, because there is learning by doing at the firm level that spills over to other domestic firms. We also assume that the domestic firm can stochastically improve its technology and produce at zero cost. This probability is increasing in domestic production. However, whether the domestic firm has transitioned to zero cost or not is private information. We use a mechanism design approach to deliver optimal protection in the presence of such persistent private information. Our incentive-compatible protection policy induces the domestic firm to reveal its true cost. Our results are as follows. First, the import quota i....

Optimal liquidity policy with shadow banking

Economic Theory, 2019

We study the impact of shadow banking on optimal liquidity regulation in a Diamond–Dybvig maturit... more We study the impact of shadow banking on optimal liquidity regulation in a Diamond–Dybvig maturity-mismatch environment. In this economy, a pecuniary externality arising out of the banks’ access to private retrade renders competitive equilibrium inefficient. A tax on illiquid assets and a subsidy to the liquid asset similar to the payment of interest on reserves (IOR) constitute an optimal liquidity regulation policy. Shadow banking gives banks an outside option allowing them to escape regulation at the cost of forgoing access to the government safety net. We derive two implications of shadow banking for optimal liquidity regulation policy. First, optimal policy must implement a macroprudential cap on illiquid-asset prices that binds only when the return on illiquid assets is high. Second, optimal policy must implement a fire sale of illiquid assets when high demand for liquidity is anticipated. We show how these features can be implemented by adjusting the IOR rate and the illiquid-asset tax rate.

Market-based incentives

In this article, we study market-induced, external incentives similar to career concerns jointly ... more In this article, we study market-induced, external incentives similar to career concerns jointly with standard, contractual incentives linking compensation to performance. We consider a dynamic principal–agent problem in which the agent’s outside option is determined endogenously in a competitive labor market. In equilibrium, strong performance increases the agent’s market value. When this value becomes sufficiently high, the threat of the agent quitting forces the principal to increase the agent’s compensation. The prospect of obtaining this raise gives the agent an incentive to exert effort, which reduces the need for standard incentives. In fact, whenever the agent’s option to quit is sufficiently close to being “in the money,” the market-induced incentive eliminates the need for standard incentives altogether: Compensation becomes completely insensitive to current performance.

Shared Patent Rights and Technological Progress

International Economic Review, 2015

We study how to reward innovators who build on one another. Rewards come in the form of patents. ... more We study how to reward innovators who build on one another. Rewards come in the form of patents. Because patent rights are scarce, the optimal allocation involves sharing: More than one innovator's patent is in force at a given time. We interpret such allocations as patents that infringe one another as licensing through an ever growing patent pool and as randomization through litigation. We contrast the rate of technological progress under the optimal allocation with the outcome if sharing is prohibitively costly. Avoiding sharing initially slows progress and leads to a more variable rate of technological progress.

Optimal investment taxes and efficient market provision of liquidity in the Diamond-Dybvig model

We study taxation as an alternative to intermediation in a Diamond-Dybvig economy with a private ... more We study taxation as an alternative to intermediation in a Diamond-Dybvig economy with a private ex post retrade market and with private ex ante investment. The possibility of private investment imposes an additional constraint on the social planner beyond resource feasibility and incentive compatibility. With this constraint, the simple asset market equilibrium is efficient. If access to private investment is costly, i.e., the private return on the illiquid investment is smaller than the publicly observable return on illiquid investment, then an asset market equilibrium is efficient with investment taxes. An optimal tax system consists of a proportional subsidy to liquid investment and a proportional tax on illiquid investment. In either case, efficiency is attained without intermediation.

Unemployment Benefits: How Much Money Goes Unclaimed?

Economic Synopses

Unemployment Insurance Fraud

Economic Synopses

Dynamic Contracting, Persistent Shocks and Optimal Taxation

In this paper I develop continuous-time methods for solving dynamic principal-agent problems in w... more In this paper I develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. I characterize the optimal contract as the solution to a system of ordinary differential equations, and show that, under this contract, the agent's utility converges to its lower bound-immiseration occurs. I also show that, unlike in environments with i.i.d. shocks, the principal would like to renegotiate with the agent when the agent's productivity is low-it is not renegotiation-proof. I apply the theoretical methods I have developed and numerically solve this (Mirrleesian) dynamic taxation model. I find that it is optimal to allow a wedge between the marginal rate of transformation and individuals' marginal rate of substitution between consumption and leisure. This wedge is significantly higher than what is found in the i.i.d. case. Thus, using the i.i.d. assumption is not a good approximation quantitatively when there is persistence in productivity shocks.

Market-Based Incentives

International Economic Review

Dynamic Contracts, Persistent Shocks, and Optimal Taxation,” Federal Reserve Bank of Minneapolis working paper

Foreign Aid, Public Spending, Optimal Fiscal and Monetary Policies, and Long-Run Growth

Cema Working Papers, 2008

This paper presents a group of models showing the strikingly different implications of foreign ai... more This paper presents a group of models showing the strikingly different implications of foreign aid to the private sector and public sector. In the first model, with decentralized decision-making and without optimal choices of fiscal policies on behalf of the government, foreign aid to the private sector has no effect on the long-run capital accumulation and it raises private consumption one to one; whereas foreign aid to the government leads to more public spending and higher private capital accumulation. In another model with optimal choices of both fiscal and monetary policies, foreign aid to the private sector gives rise to higher inflation and income taxation. Although aid to the private sector raises private money holdings and consumption, it reduces capital accumulation. However, when foreign aid is provided to the public sector, the government cuts both the inflation rate and the income tax rate, raises public spending, and provides more incentives for private capital accumulation and money holdings. In the long run, aid to the public sector leads to more private capital accumulation, consumption, money holdings, and welfare.

Optimal Unemployment Insurance with Hidden Trade

This paper studies the optimal design of unemployment insurance in an environment where the insur... more This paper studies the optimal design of unemployment insurance in an environment where the insurance agency could monitor neither the searching efforts nor the asset holding of an unemployed worker. Previous results with no hidden trade violate the Euler equation of a worker and thus can not be implementable if he has private access to asset market. We abandon the traditional first-order approach and solve the incentive problem directly. With CARA utility functions, we obtain the optimal contract in closed form. We find that, counter-intuitively, an unemployed worker's consumption will decline faster than that implied by Hopenhayn and Nicolini (1997).