Investment and liquidation in renegotiation-proof contracts with moral hazard

In a long-term contract with moral hazard, the liquidation of the firm can arise as the outcome of the optimal contract. However, if the future production capability or market opportunities remain unchanged, liquidation may not be free from renegotiation. Will the firm ever be liquidated if we allow for renegotiation? This paper shows that the firm can still be liquidated even though liquidation is not free from renegotiation in the long-term contract. In addition to liquidation, the renegotiation-proof contract generates important features of the investment behavior and dynamics of firms observed in the data.     

Precautionary saving and partially observed income

I propose an intertemporal precautionary saving model in which the agent's labor income is subject to (possibly correlated) shocks with different degrees of persistence and volatility. However, he only observes his total income, not individual components. I show that partial observability of individual components of income gives rise to additional precautionary saving due to estimation risk, the error associated with estimating individual components of income. This additional precautionary saving is higher, when estimation risk is greater. Compared with a precautionary agent who is otherwise identical, but ignores estimation risk, the rational agent consumes less at the beginning of his life, but consumes more later, because of larger wealth accumulated from savings for estimation risk. The utility cost of ignoring estimation risk is also quantified in closed form.     

Consumption and risk sharing over the life cycle

A striking feature of U.S. data on income and consumption is that inequality increases with age. This paper asks if individual-specific earnings risk can provide a coherent explanation. We find that it can. We construct an overlapping generations general equilibrium model in which households face uninsurable earnings shocks over the course of their lifetimes. Earnings inequality is exogenous and is calibrated to match data from the U.S. Panel Study on Income Dynamics. Consumption inequality is endogenous and matches well data from the U.S. Consumer Expenditure Survey. The total risk households face is decomposed into that realized before entering the labor market and that realized throughout the working years. In welfare terms, the latter is found to be more important than the former.     

Geographical segmentation of US capital markets

Demographic variation in savings behavior can be exploited to provide evidence on segmentation in US bank loan markets. Cities with a large fraction of seniors have higher volumes of bank deposits. Since many banks rely heavily on deposit financing, this affects local loan supply and economic activity. I show a positive effect of local deposit supply on local outcomes, including the number of firms, the number of manufacturing firms, and the number of new firms started. The effect is stronger in industries that are heavily dependent on external finance. The deregulation of intrastate branching reduced the effect of local deposit supply by approximately a third.     

Insurance and opportunities: A welfare analysis of labor market risk

Using a model with constant relative risk-aversion preferences, endogenous labor supply and partial insurance against idiosyncratic wage risk, this paper provides an analytical characterization of three welfare effects: (a) the welfare effect of a rise in wage dispersion, (b) the welfare gain from completing markets, and (c) the welfare effect from eliminating risk. The analysis reveals an important trade-off for these welfare calculations. On the one hand, higher wage uncertainty increases the cost associated with missing insurance markets. On the other hand, greater wage dispersion presents opportunities to raise aggregate productivity by concentrating market work among more productive workers. Welfare effects can be expressed in terms of the underlying parameters defining preferences and wage risk or, alternatively, in terms of changes in observable second moments of the joint distribution over individual wages, consumption and hours.     

Business credit information sharing and default risk of private firms

We investigate whether and how business credit information sharing helps to better assess the default risk of private firms. Private firms represent an ideal testing ground because they are smaller, more informationally opaque, riskier, and more dependent on trade credit and bank loans than public firms. Based on a representative panel dataset that comprises private firms from all major industries, we find that business credit information sharing substantially improves the quality of default predictions. The improvement is stronger for older firms and those with limited liability, and depends on the sharing of firms’ payment history and the number of firms covered by the local credit bureau office. The value of soft business credit information is higher the smaller the firms and the lower their distance from the local credit bureau office. Furthermore, in spatial and industry analyses we show that the higher the value of business credit information the lower the realized default rates. Our study highlights the channel through which business credit information sharing adds value and the factors that influence its strength.     

Saving-based asset-pricing

This paper explores the implications of a novel class of preferences for the behavior of asset prices. Following a suggestion by Marshall (1920), we entertain the possibility that people derive utility not only from consumption, but also from the very act of saving. These “saving-based” preferences are related to models of habit formation and the spirit of capitalism, but incorporate the feature that people have anticipatory habits because they care about the future accumulation of wealth. We derive the Euler equations for these preferences and estimate them with GMM. Our estimates suggest that the preference for saving is economically significant.     

Stress testing credit risk: The Great Depression scenario

By employing Moody’s corporate default and rating transition data spanning the last 90 years we explore how much capital banks should hold against their corporate loan portfolios to withstand historical stress scenarios. Specifically, we will focus on the worst case scenario over the observation period, the Great Depression. We find that migration risk and the length of the investment horizon are critical factors when determining bank capital needs in a crisis. We show that capital may need to rise more than three times when the horizon is increased from 1 year, as required by current and future regulation, to 3 years. Increases are still important but of a lower magnitude when migration risk is introduced in the analysis. Further, we find that the new bank capital requirements under the so-called Basel 3 agreement would enable banks to absorb Great Depression-style losses. But, such losses would dent regulatory capital considerably and far beyond the capital buffers that have been proposed to ensure that banks survive crisis periods without government support.     

Optimal smooth consumption and annuity design

We propose an optimization criterion that yields extraordinary consumption smoothing compared to the well known results of the life-cycle model. Under this criterion we solve the related consumption and investment optimization problem faced by individuals with preferences for intertemporal stability in consumption. We find that the consumption and investment patterns demanded under the optimization criterion is in general offered as annuity benefits from products in the class of ‘Formula Based Smoothed Investment-Linked Annuities’.     

Dynamic risk management

Both financing and risk management involve promises to pay that need to be collateralized, resulting in a financing versus risk management trade-off. We study this trade-off in a dynamic model of commodity price risk management and show that risk management is limited and that more financially constrained firms hedge less or not at all. We show that these predictions are consistent with the evidence using panel data for fuel price risk management by airlines. More constrained airlines hedge less both in the cross section and within airlines over time. Risk management drops substantially as airlines approach distress and recovers only slowly after airlines enter distress.     

Credit risk transfer and contagion

Some have argued that recent increases in credit risk transfer are desirable because they improve the diversification of risk. Others have suggested that they may be undesirable if they increase the risk of financial crises. Using a model with banking and insurance sectors, we show that credit risk transfer can be beneficial when banks face uniform demand for liquidity. However, when they face idiosyncratic liquidity risk and hedge this risk in an interbank market, credit risk transfer can be detrimental to welfare. It can lead to contagion between the two sectors and increase the risk of crises.     

Financing constraints, irreversibility, and investment dynamics

We develop a model of an industry with many heterogeneous firms that face both financing constraints and irreversibility constraints. We use this model to examine the cyclical behavior of aggregate fixed investment, variable capital investment, and output in the presence of persistent idiosyncratic and aggregate shocks. Our model yields three main results. First, the effect of the irreversibility constraint on fixed capital investment is reinforced by the financing constraint. Second, the effect of the financing constraint on variable capital investment is reinforced by the irreversibility constraint. Finally, the interaction between the two constraints is key for explaining why input inventories and material deliveries of US manufacturing firms are so volatile and procyclical, and also why they are highly asymmetrical over the business cycle.     

Portfolio choice and mortality-contingent claims: The general HARA case

We solve a portfolio choice problem that includes mortality-contingent claims and labor income under general HARA preferences. Our contribution beyond existing literature is to (i) focus on the covariance between shocks to human capital and financial capital, to (ii) model the utility of a family with basic needs and (iii) include life insurance and pension annuity claims in one unified life-cycle model. Our solution employs a “similarity reduction” mapping which reduces the two-dimensional HJB equation into one dimension. This allows for the implementation of a quick numerical scheme. And, when shocks to human capital and financial capital are perfectly correlated, a closed-form expression is obtained as a special case.     

Optimal life insurance purchase and consumption/investment under uncertain lifetime

In this paper, we consider optimal insurance and consumption rules for a wage earner whose lifetime is random. The wage earner is endowed with an initial wealth, and he also receives an income continuously, but this may be terminated by the wage earner’s premature death. We use dynamic programming to analyze this problem and derive the optimal insurance and consumption rules. Explicit solutions are found for the family of CRRA utilities, and the demand for life insurance is studied by examining our solutions and doing numerical experiments.     

Time diversification: Definitions and some closed-form solutions

We establish general conditions under which younger investors should invest a larger proportion of their wealth in risky assets than older ones. In the finite horizon dynamic setting, we show that such phenomenon, known as ‘‘time diversification,” can occur in the presence of human wealth, guaranteed consumption, or mean-reverting stock returns. We formalize two alternative notions of time diversification commonly confounded in the literature. Analytic solutions are provided for both time-series and cross-sectional forms of time diversification. To our best knowledge, this paper is the first to solve in closed-form the hedging demand for a CARA investor with inter-temporal consumption and a finite horizon, facing mean-reverting expected returns. Our results indicate that horizon can have a significant effect on the portfolio demand of a CARA investor due to inter-temporal hedging.     

An equilibrium model of wealth distribution

I present an explicitly solved equilibrium model for the distribution of wealth and income in an incomplete-markets economy. I first propose a self-insurance model with an inter-temporally dependent preference [Uzawa, H. 1968. Time preference, the consumption function, and optimal asset holdings. In: Wolfe, J.N. (Ed.), Value, Capital, and Growth: Papers in Honour of Sir John Hicks. Edinburgh University Press, Edinburgh, pp. 485-504]. I then derive an analytical consumption rule which captures stochastic precautionary saving motive and generates stationary wealth accumulation. Finally, I provide a complete characterization for the equilibrium cross-sectional distribution of wealth and income in closed form by developing a recursive formulation for the moments of the distribution of wealth and income. Using this recursive formulation, I show that income persistence and the degree of wealth mean reversion are the main determinants of wealth-income correlation and relative dispersions of wealth to income, such as skewness and kurtosis ratios between wealth and income.     

Heterogeneous life-cycle profiles, income risk and consumption inequality

Was the increase in income inequality in the US due to permanent shocks or merely to an increase in the variance of transitory shocks? The implications for consumption and welfare depend crucially on the answer to this question. We use Consumer Expenditure Survey (CEX) repeated cross-section data on consumption and income to decompose idiosyncratic changes in income into predictable life-cycle changes, transitory and permanent shocks and estimate the contribution of each to total inequality. Our model fits the joint evolution of consumption and income inequality well and delivers two main results. First, we find that permanent changes in income explain all of the increase in inequality in the 1980s and 1990s. Second, we reconcile this finding with the fact that consumption inequality did not increase much over this period. Our results support the view that many permanent changes in income are predictable for consumers, even if they look unpredictable to the econometrician, consistent with models of heterogeneous income profiles.