Recursive Economics - Applications in Economics

Applications in Economics

Some scholars point to Martin Beckmann and Richard Muth as the first application of an explicit recursive equation in economics. However, probably the earliest celebrated economic application of recursive economics was Robert Merton's seminal 1973 article on the intertemporal capital asset pricing model. (See also Merton's portfolio problem). Merton's theoretical model, one in which investors chose between income today and future income or capital gains, is a recursive formulation.

Nancy Stokey, Robert Lucas & Edward Prescott describe stochastic and non-stochastic dynamic programming in considerable detail, giving many examples of how to employ dynamic programming to solve problems in economic theory. This book led to dynamic programming being employed to solve a wide range of theoretical problems in economics, including optimal economic growth, resource extraction, principal–agent problems, public finance, business investment, asset pricing, factor supply, and industrial organization.

The approach gained further notice in Macroeconomics from the extensive exposition in This book describes recursive models applied to theoretical questions in monetary policy, fiscal policy, taxation, economic growth, search theory, and labor economics.

In investment and finance, Avanish Dixit & Robert Pindyck showed the value of the method for thinking about capital budgeting, in particular showing how it was theoretically superior to the standard neoclassical investment rule. Patrick Anderson adapted the method to the valuation of businesses and applied it to the estimation of the aggregate value of privately held businesses in the US.

There are serious computational issues that have hampered the adoption of recursive techniques in practice, many of which originate in the "curse of dimensionality" first identified by Richard Bellman.

Applied recursive methods, and discussion of the underlying theory and the difficulties, are presented in Mario Miranda & Paul Fackler, Meyn 2007 and Dimitri Bertsekas, Dynamic Programming and Optimal Control, Athena Scientific 2005, 2012.