*Reviewed by Chetan G. Shah, CFA*

Nearly 90% of *Recursive Models of Dynamic Linear Economies* was written between 1988 and 1994, and the remaining 10% was completed in 2012, after the authors, Thomas J. Sargent and Lars Peter Hansen, finally abandoned their thought of pursuing many possible improvements before releasing their book. Both authors are Nobel laureates in economics. Thomas J. Sargent was awarded the Nobel prize in 2011 (together with Christopher A. Sims) for empirical research on cause and effect in the macro economy. Lars Peter Hansen (along with Eugene Fama and Robert Shiller) was recognized in 2013 for empirical analysis of asset prices. This book is part of the Gorman Lectures in Economics series.

Recursive statistical models include only unidirectional effects. The next period’s vector of state variables is expressed as a linear function of the current period’s state vector and a vector of random disturbances. The task of dynamics is to study the time paths of the endogenous variables (those variables that are part of the models) associated with alternative possible time paths of the exogenous variables. Developed as useful special cases of the Arrow – Debreu competitive equilibrium model, the theory of recursive competitive equilibriums promises to achieve an easier coexistence with econometric theory than have previous formulations of equilibrium theory.

Hansen and Sargent start with a common set of mathematical tools for dynamic optimization, dynamic estimation, vector representation, and filtering. These tools include linear stochastic difference equations, linear optimal control theory, dynamic equilibrium modeling, statistical analysis of time-series data, and doubling algorithms.

The authors next describe the economy and its components through a set of matrices: consumption goods, intermediate goods, investment in goods, physical capital stock, household capital stock, household labor input, taste or preference shock, technology or endowment shock, and so on. Hansen and Sargent build models to study aspects of competitive equilibriums, including time-series properties of various quantities, spot market prices, asset prices, and rates of return.

Most of the book assumes a common type of household. It can be interpreted as a single household drawn from a population that is homogeneous in all respects. Similarly, the book assumes two firms, Type 1 and Type 2, that encompass the characteristics of the whole industry and yet have no control over prices. Type 1 firms rent capital and labor and buy an endowment, whereas Type 2 firms are in the business of purchasing investment goods and renting capital to Type 1 firms. The final few chapters, however, describe methods for computing equilibriums of economies with consumers who have heterogeneous preferences and endowments; the representative household is an average household that emerges after aggregating the preferences and endowments of a collection of households. Initially, this set satisfies W.M. Gorman’s conditions for aggregation; later, it departs somewhat from Gorman’s framework.

The book tries to display the versatility and tractability of its models. Some applications form versions of several dynamic models and include the markets for housing, cattle, and occupational choice. Versions of a wide range of models from modern capital market theory and asset pricing theory are represented through the book’s framework. The authors provide formulas and algorithms in MATLAB (from MathWorks) for readers’ use in experiments. Competitive equilibriums can be computed easily with these tools. Professionals with a deep background in economics and econometrics could soon be devising their own new models. Readers new to the subject will need the support of additional materials to understand this book.

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