A compendium to information theory in economics and econometrics.

*(English)*Zbl 0769.62003Summary: An extensive synthesis is provided of the concepts, measures and techniques of Information Theory (IT). After an axiomatic description of the basic definitions of “information functions”, “entropy” or uncertainty, and the maximum entropy principle, the paper demonstrates the power of IT as both an interpretive and technically productive tool. It is argued that this power and universality is primarily due to the common need for (i) measures of distance and discrimination and, (ii) appropriate partitioning-aggregation properties. IT offers a very suggestive unification for a bewildering and arbitrary set of approaches that have evolved in different disciplines.

Applications are discussed or indicated. These applications have relevance to economics, finance, industrial organization, marketing, statistical inference and model selection, political science and communication. A main focus of the discussion is the generative power of IT measures in statistical examinations of unknown distributions and random phenomena. Measures of concentration and inequality, aggregation functions and index numbers, tests of nested and non-nested hypotheses, and measures of volatility, mobility and divergence are presented. Estimation of unknown regression functions, densities and score functions is examined based on the maximum entropy principle. Some empirical examples are cited.

Applications are discussed or indicated. These applications have relevance to economics, finance, industrial organization, marketing, statistical inference and model selection, political science and communication. A main focus of the discussion is the generative power of IT measures in statistical examinations of unknown distributions and random phenomena. Measures of concentration and inequality, aggregation functions and index numbers, tests of nested and non-nested hypotheses, and measures of volatility, mobility and divergence are presented. Estimation of unknown regression functions, densities and score functions is examined based on the maximum entropy principle. Some empirical examples are cited.

##### MSC:

62B10 | Statistical aspects of information-theoretic topics |

62P20 | Applications of statistics to economics |

94A15 | Information theory (general) |

94A17 | Measures of information, entropy |