**Mathematical Economics, Statistics, and Econometrics**

Methods Of Mathematical Economics, Mathematics and Economics

Before we consider the development of econometrics, it is worthwhile to briefly consider the distinctions among mathematical economics, statistics, and econometrics. They are often grouped together, even though they should not be.

The term mathematical economics refers only to the application of mathematical techniques to the formulation of hypotheses. It is formal, abstract analysis used to develop hypotheses and clarify their implications. The term statistics refers to a collection of numerical observations, and statistical analysis refers to the use of statistical tests derived from probability theory to gain insight into those numerical observations. Econometrics combines mathematical economics, which is used to formulate hypotheses, and statistical analysis, which is used to formally test hypotheses. The combination is not symmetrical; one can do mathematical economics without doing econometrics, but one cannot do econometrics without first doing mathematical economics. Only mathematical economics gives one a theory specific enough to be tested formally.

The separation of mathematical economics from statistics can be seen in history. In the late nineteenth century, the economists who most strongly opposed the mathematical formalization of economic thinking were the German historical school and the forerunners of the U.S. institutionalist school. These groups included some strong advocates of data collecting and statistical analysis—they argued that one had to know what real-world phenomena one was talking about before it made any sense to talk about theoretical generalizations. On the other hand, many formal theorists during that time were hesitant about using statistical analysis. For example, both Marshall and Edgeworth were hesitant about the ability to statistically measure a demand curve, believing that the ceteris paribus assumptions used to analytically derive the curves made them difficult to quantify. Edgeworth wrote in his discussion of demand curves in Palgraves (1910 edition): "It may be doubted whether Jevons's hope of constructing demand curves by statistics is capable of realization."

What economists hoped to gain from mathematical economics was a precision of hypothesis testing that would make it possible to reduce the ambiguity of tests. For example, instead of relying on common sense and a general heuristic understanding that demand curves slope downward, they wanted to be able to prove empirically that demand curves slope downward. Prior to the mathematical formalization of economic theory, economists employed words to state economic theories and hypotheses. Testing of general hypotheses was done in relation to current circumstances or in relation to historical events, but in either case the use of statistics was minimal. This essentially heuristic approach did not permit hypotheses to be tested in a manner acceptable to formal economists.

The 1960s and 1970s saw enormous advances in formal statistical testing and in an understanding of econometric methods. Advances in computer technology made it possible to conduct extremely complicated empirical work. Statistical tests that earlier would have taken days now could be done in seconds. During that period the hopes for econometrics were high. Some believed that econometrics would make economics a science in which all theories could be tested. During this time, logical positivism and Popperian falsificationism were the reigning methodologies, and it was believed that the errors of the past—formulating theories in such a way as to render them untestable—could be avoided. Most of these initial hopes have not been realized