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## Algorithms for solving nonlinear dynamic decision models

### Annals of Operations Research (1993-06-01) 44: 115-142 , June 01, 1993

In this paper we discuss two Newton-type algorithms for solving economic models. The models are preprocessed by reordering the equations in order to minimize the dimension of the simultaneous block. The solution algorithms are then applied to this block. The algorithms evaluate numerically, as required, selected columns of the Jacobian of the simultaneous part. Provisions also exist for similar systems to be solved, if possible, without actually reinitialising the Jacobian. One of the algorithms also uses the Broyden update to improve the Jacobian. Global convergence is maintained by an Armijo-type stepsize strategy.

The global and local convergence of the quasi-Newton algorithm is discussed. A novel result is established for convergence under relaxed descent directions and relating the achievement of unit stepsizes to the accuracy of the Jacobian approximation. Furthermore, a simple derivation of the Dennis-Moré characterisation of the Q-superlinear convergence rate is given.

The model equation reordering algorithm is also described. The model is reordered to define heart and loop variables. This is also applied recursively to the subgraph formed by the loop variables to reduce the total number of above diagonal elements in the Jacobian of the complete system. The extension of the solution algorithms to consistent expectations are discussed. The algorithms are compared with Gauss-Seidel SOR algorithms using the USA and Spanish models of the OECD Interlink system.

## The relative efficiency of stock versus mutual S&Ls: A stochastic cost frontier approach

### Journal of Financial Services Research (1993-06-01) 7: 151-170 , June 01, 1993

From an agency theory perspective, recent conversion activity of savings and loan associations (S&Ls) from mutual to stock organizations should improve the overall performance of the thrift industry. We employ a two-step approach to examine this issue using a sample of 559 S&Ls in the Atlanta Federal Home Loan Bank District in 1988. In the first step, we estimate inefficiency scores for individual S&Ls using a stochastic cost frontier methodology. In a second step Tobit model we use these inefficiency scores to examine the relationship between firm inefficiency and organizational form. We find three important results: (1) that the mutual and stock S&Ls in our sample have similar cost structures, allowing the pooling of S&L data; (2) that S&Ls have a wide range of inefficiency scores, with a mean score of 16 percent indicating that the average S&L could produce its output with only 84 percent of the inputs actually used; and (3) that operating inefficiency was not significantly related to form of ownership.

## The underpricing of initial public offerings: A theoretical and empirical reconsideration of the adverse selection hypothesis

### Review of Quantitative Finance and Accounting (1993-06-01) 3: 221-239 , June 01, 1993

In this paper we generalize Rock's theory regarding the underpricing of IPOs. In Rock's model, informed investors have a firm-specific informational advantage pertaining to a firm's cash flow. We derive the new results that the level of beta and the size of the market risk premium positively affect underpricing. These implications extend the adverse selection theory and further distinguish this theory from the current state of signalling theories of underpricing. The results put the “hot and cold” issue markets phenomenon in a theoretical context. Empirical results are consistent with the theoretical propositions and provide support for Rock's theory of underpricing.

## Comments on Pan-European GSM signal modulation

### Telecommunication Systems (1993-12-01) 2: 399-403 , December 01, 1993

Recent results relating the channel bit rate to the variability of received signal strength at a moving antenna in dense scatterers stimulated a renewed critical interest in the modulation specified for the Pan-European GSM cellular radio link. Cogent questions arise concerning link performance at the extremes of vehicle speed and delay spread.

## Die ökonomische Analyse des Rechts

### Zeitschrift für die gesamte Versicherungswissenschaft (1993-03-01) 82: 57-70 , March 01, 1993

## Mathematical programming and the sensitivity of multi-criteria decisions

### Annals of Operations Research (1993-02-01) 43: 109-122 , February 01, 1993

We report on the current state of a project whose aim is to implement a framework for sensitivity analysis in Multi-Criteria Decision Making (MCDM). The framework is largely based on mathematical programming. Due to the potentially large number and nature of the mathematical programmes, it is far from trivial to provide solutions to all of them in acceptable computing times. The challenge is even greater when we recognize that much decision analysis is performed in the context of decision conferences where any sensitivity analysis needs to be conducted in near real time (preferably) on a PC. We present a parallel processing approach to this challenge and point to some of the difficulties still to be resolved. Preliminary results obtained on a network of transputers are discussed.

## Framing effects in the evaluation of multiple risk reduction

### Journal of Risk and Uncertainty (1993-04-01) 6: 145-159 , April 01, 1993

We studied how evaluation of changes in low-probability risks are affected by reference points and framing effects. Subjects considered hypothetical situations with one or two low-probability risks. Different frames were used to describe changes in risk levels. In the first experiment, subjects chose between risk-reduction options that achieved the same overall risk reduction: large reduction of one risk vs. equal (smaller) reduction of two risks. When the risks were described as losses relative to the no-risk ideal, more subjects were indifferent between the options than when the same options were described as gains relative to the status quo. In the latter case subjects preferred equal reduction of both risks, unless one risk could be reduced to zero. In a related experiment, subjects were less willing to pay any price for a commodity that carried small increases in two risks than for a commodity carrying a comparable large increase in one risk. In other experiments, subjects evaluated single changes in risks rather than comparing or evaluating pairs of changes. Subjects again placed particularly high value on reducing any risks to zero, and they were even more inclined to do so when some other risk would also be reduced to zero. In a final experiment, elimination of risk was found to be less highly valued if its source was not fully eliminated, and a status-quo effect was found. The findings are interpreted in terms of reference theories of choice.

## Insurer ambiguity and market failure

### Journal of Risk and Uncertainty (1993-08-01) 7: 71-87 , August 01, 1993

A series of studies investigate the decision processes of actuaries, underwriters, and reinsurers in setting premiums for ambiguous and uncertain risks. Survey data on prices reveal that all three types of these insurance decision makers are risk averse and ambiguity averse. In addition, groups appear to be influenced in their premium-setting decisions by specific reference points such as expected loss and the concern with insolvency. This behavior is consistent with a growing analytical and empirical literature in economics and decision processes that investigates the role that uncertainty plays on managerial choices. Improved risk-assessment procedures and government involvement in providing protection against catastrophic losses may induce insurers to reduce premiums and broaden available coverage.

## A theory of optimal denominations for government liabilities

### Economic Theory (1993-12-01) 3: 597-623 , December 01, 1993

### Summary

The design and implementation of monetary arrangements has important implications for the welfare and determinacy properties of equilibria that arise under competitive monetary exchange. In this paper we consider one particular feature of a monetary arrangement. We ask whether a government should issue its liabilities so that they are imperfectly divisible and whether they should at the same time regulate private intermediation. We argue that the answer is affirmative. We then consider the optimal minimum denomination for government liabilities given that the social planner would like to implement a particular equilibrium. We show that generically the steady state equilibria supported by minimum denominations that result in Pareto optimal allocations are indeterminate. We then pose the question, what is the best (in a Pareto sense) stationary equilibrium that can be supported, subject to the constraint that the equilibrium display certain minimal determinacy properties? The existence of an optimum in this sense is established. Such equilibria are supported by having the government issue indivisible liabilities with appropriately chosen minimum denominations.

## Welfare payments and migration in a nonlinear, extended input-output model with an application to Scotland

### Papers in Regional Science (1993-04-01) 72: 177-199 , April 01, 1993

This paper examines an extended input-output model that includes a migration mechanism and a locally funded welfare benefit regime. The model is developed to include two regions. Two different solution methods of the model are discussed, one involving the introduction of nonlinearities into the input-output framework. The results of the two solutions are compared using test data for a one-region formulation, and data for a two-region division of Scotland. The regional impacts of varying unemployment benefits differentially are assessed, and a range of impacts of economic and demographic regional injections presented.