Estimates of agents’ risk aversion differ between market studies and experimental studies. We demonstrate that these estimates can be reconciled through consistent treatment of agents’ propensity for narrow framing.
We analyze two firms’ choice between merging, allying, and trading assets. We consider a setting in which firms have assets, skills, and core capabilities; skills are the component of organizational capital that increases in the course of joint operations, core capabilities the component that does not. We find that the two firms trade assets for them to operate separately in case the two firms have high initial skills; the two firms merge in case they have similar core capabilities; they ally where there is little equilibrium double moral hazard. We compare the times to dissolution in the alliance with those to divesture or post-merger integration in the merger; for all but the last jointly operated asset, we find that joint operations cease earlier in the alliance than in the merger.
It is standard in economics to assume that assets are normal goods and demand is downward sloping in price. This view has its theoretical foundation in the classic single period model of Arrow with one risky asset and one risk free asset, where both are assumed to be held long. However when short selling is allowed, we show that the risk free asset can not only fail to be a normal good but can in fact be a Gi¤en good even for widely popular members of the hyperbolic absolute risk aversion (HARA) class of utility functions. Distinct regions in the price-income space are identi?ed in which the risk free asset exhibits normal, inferior and Gi¤en behavior. Moreover for uility functions with decreasing relative risk aversion, such as the weighted average constant relative risk aversion (WACRRA) class introduced in this paper, the risk free asset can become a Gi¤en good only when it is held long. Examples are provided in which Gi¤en behavior occurs over multiple ranges of income. The analysis is also extended to a two period setting.
We present a flexible and scalable method to compute global solutions of high-dimensional non-smooth dynamic models. Within a time-iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximal problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of MPI and OpenMP. This parallelization enables us to efficiently use modern high-performance computing architectures. Our time iteration algorithm scales up nicely to more than one thousand parallel processes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.
The demand for commodities in standard applications typically is increasing in in- come, whereas the demand for the risk free asset in the classic portfolio problem often decreases with income. The latter is shown to occur if and only if the consumer is uncertainty preferences over assets satisfy the condition that the risk free asset is more readily substituted for the risky asset as the quantity of the risky asset increases. In this case, the risky asset is said to be "urgently needed" following the terminology of Johnson in his classic 1913 certainty analysis [19]. The asset and certainty settings differ in critical ways which result in a much greater likelihood for the urgently needed preference property to be satisfied in the portfolio problem. We provide several sufficient conditions for when the risky asset will be urgently needed and a surprisingly simple, complete characterization for widely popular members of the HARA (hyperbolic absolute risk aversion) class. For more general preferences, two examples are given where it is possible to fully describe the region of asset space in which the risky asset is urgently needed. Finally, using a standard representative agent model we show that the risky asset being urgently needed is equivalent to the equilibrium (relative) price of the risky asset increasing with its own supply.
