A Lanczos Method for Approximating Composite Functions

We seek to approximate a composite function h(x) = g(f(x)) with a global polynomial. The standard approach chooses points x in the domain of f and computes h(x) at each point, which requires an evaluation of f and an evaluation of g. We present a Lanczos-based procedure that implicitly approximates g with a polynomial of f. By constructing a quadrature rule for the density function of f, we can approximate h(x) using many fewer evaluations of g. The savings is particularly dramatic when g is much more expensive than f or the dimension of x is large. We demonstrate this procedure with two numerical examples: (i) an exponential function composed with a rational function and (ii) a Navier-Stokes model of fluid flow with a scalar input parameter that depends on multiple physical quantities

The Disutility of International Debt: Analytical Results and Methodological Implications

In dealing with the problematic relationship of morality to rational choice theory, neoclassical economists since Lionel Robbins have often argued that they can incorporate moral values into consumer theory by putting those values into the utility function. This paper tests the viability of such an approach in the context of international finance. The moral value at stake is autonomy, which may be lost when borrowers must submit to the edicts of international financial institutions. When such a value is inserted into the utility function of a small economy, the growth rate of consumption and the level of investment change. Furthermore, potential borrowers may lose their ability to credibly commit to paying back loans, resulting in a complete absence of borrowing where it might otherwise take place. The author argues that while this model illustrates the possibility of analyzing a noneconomic value (sovereignty) through rational choice theory, it also shows that standard methods of empirical inference, policy evaluation, and welfare analysis may fail in such a situation. To answer questions that mix morality and economics, economists must seek tools other than conventional rational choice theory.: Values, Lionel Robbins, international debt, methodology

"The Disutility of International Debt: Analytical Results and Methodological Implications"

In dealing with the problematic relationship of morality to rational choice theory, neoclassical economists since Lionel Robbins have often argued that they can incorporate moral values into consumer theory by putting those values into the utility function. This paper tests the viability of such an approach in the context of international finance. The moral value at stake is autonomy, which may be lost when borrowers must submit to the edicts of international financial institutions. When such a value is inserted into the utility function of a small economy, the growth rate of consumption and the level of investment change. Furthermore, potential borrowers may lose their ability to credibly commit to paying back loans, resulting in a complete absence of borrowing where it might otherwise take place. The author argues that while this model illustrates the possibility of analyzing a noneconomic value (sovereignty) through rational choice theory, it also shows that standard methods of empirical inference, policy evaluation, and welfare analysis may fail in such a situation. To answer questions that mix morality and economics, economists must seek tools other than conventional rational choice theory.