The effects of foreign shocks when interest rates are at zero

In a two‐country DSGE model, the effects of foreign demand shocks on the home country are greatly amplified if the home economy is constrained by the zero lower bound on policy interest rates. This result applies even to countries that are relatively closed to trade such as the United States. Departing from many of the existing closed‐economy models, the duration of the liquidity trap is determined endogenously. Adverse foreign shocks can extend the duration of the trap, implying more contractionary effects for the home country. The home economy is more vulnerable to adverse foreign shocks if the neutral rate is low—consistent with “secular stagnation”—and trade openness is high.     

Dividends, safety and liquidation when liabilities are long-term and stochastic

This paper investigates the optimal management of a firm faced with a long-term liability that occurs at a random date. Three issues are analysed: The optimal dividend policy; optimal expenditure on safety to delay the occurrence of the liability; and the optimal liquidation date of the firm. An owner faced with dynamic unlimited liability never liquidates and therefore accumulates capital to the golden rule level. For long-term liabilities, dividend payments and safety expenditure are non-decreasing over time. The owner protected by limited liability may liquidate the firm in finite time in order to avoid paying the liability. If this is the case, then it accumulates less capital than the dynamic unlimited liability owner; and may decrease dividend payments and safety expenditure over time. The paper shows that a finite liquidation date is more likely to be optimal when the arrival rate of the liability occurrence increases over time.     

Long-term investment with stochastic interest and inflation rates: The need for inflation-indexed bonds

We examine the long term investment problem, under stochastic interest and inflation rates and within financial market incompleteness. Four basic financial assets are available on the financial market: a money market account (the cash), a real consumption good, a financial stock index and a bond with constant maturity. In this incomplete framework, we provide the general solution of the expected utility maximization. We compute the monetary loss from not having access to an inflation-indexed bond, in order to be hedged against the inflation risk. We show that this latter one usually reaches high levels (more than 1% per year). Thus, the magnitude of such costs reaches those of management fees or transaction costs. They highlight the significant value of introducing inflation-indexed bonds in the financial markets.     

Constancy of equilibrium interest rates for power utility functions and stochastic constant returns to scale technologies

Metron (1969, 1971) examined, inter alia the consumption and portfolio rules in a partial equilibrium context wherein the preferences are represented by a time additive power utility function. In these papers he exogenously assumed a constant instantaneously risk free rate of interest. In this paper we naturally embellish the results of Merton in a closed production economy where there are a number of stochastic constant returns to scale technologies with correlated outputs and show that the endogenously determined interest rate is a constant. While this result is recognized by researchers, explicit analytical characterization of equilibrium interest rate obtained in this paper is a new result. This paper establishes the internal consistency of the assumptions found in Metron (1969, 1971).     

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.     

Portfolio choice,consumption and welfare when rates of return are related to prices of consumer goods

This paper generalizes the two period model of portfolio selection under uncertainty by decomposing the aggregate consumption in each period into several goods, the prices of some of which are positively related to rates of return on some assets. The effect of these relations on the choice of portfolio is analyzed. The effects on the chosen portfolio of a lateral translation and of a mean preserving increase in the risk of the distributions of the random variables are analyzed. A generalization of the Hicks compensation to the case where the prices of consumer goods are positively related to rates of return on assets is offered and welfare implications are drawn.