Mathematical Economics

What is Mathematical Economics?

Mathematical economics is a method of economics that utilizes math principles and tools to create economic theories and to investigate economic quandaries. Mathematics permits economists to construct precisely defined models from which exact conclusions can be derived with mathematical logic, which can then be tested using statistical data and used to make quantifiable predictions about future economic activity.

The marriage of statistical methods, mathematics, and economic principles enabled the development of econometrics. Advancements in computing power, big data techniques, and other advanced mathematics applications have played a large part in making quantitative methods a standard element of economics.

Understanding Mathematical Economics

Mathematical economics relies on defining all the relevant assumptions, conditions, and causal structures of economic theories in mathematical terms. There are two main benefits from doing this. First, it allows economic theorists to use mathematical tools such as algebra and calculus to describe economic phenomena and draw precise inferences from their basic assumptions and definitions. Second, it allows economists to operationalize these theories and inferences so that they can be tested empirically using quantitative data and, if validated, used to produce quantitative predictions about economic matters for the benefit of businesses, investors, and policymakers.

Prior to the late 19th century, economics relied heavily on verbal, logical argument, situational explanations, and inference based on anecdotal evidence to attempt to make sense of economic phenomenon. Economists often wrestled with competing models capable of explaining the same recurring relationship called an empirical regularity, but could not definitively quantify the size of the association between central economic variables.

At that time, mathematical economics was a departure in the sense that it proposed formulas to quantify changes in the economy. This bled back into economics as a whole, and now most economic theories feature some type of mathematical proof.

From Main Street to Wall Street to Washington, decision-makers have become accustomed to hard, quantitative predictions about the economy due to the influence of mathematical economics. When setting monetary policy, for example, central bankers want to know the likely impact of changes in official interest rates on inflation and the growth rate of the economy. It is in cases like this that economists turn to econometrics and mathematical economics.

Econometrics

Econometrics attempts to translate abstract economic theories into useful tools for everyday economic policymaking by combining mathematical economics with statistical methods. The objective of econometrics as a whole is to convert qualitative statements — such as “the relationship between two or more variables is positive” — into quantitative statements — such as “consumption expenditure increases by 95 cents for every one dollar increase in disposable income.”

Econometrics is particularly useful in solving optimization problems where a policymaker, for example, is looking for the best tweak out of a range of tweaks to affect a specific outcome.

As we're flooded with ever more information, econometric methods have become ubiquitous in economics. As Stock and Watson's Introduction to Econometrics put it, “econometric methods are used in many branches of economics, including finance, labor economics, macroeconomics, microeconomics, and economic policy.”

Economic policy decisions are rarely made without econometric modeling to assess their impact and empirical economics papers are rarely published without some econometric content in them.

Criticism of Mathematical Economics

Critics caution that mathematical economics may obscure rather than clarify economic theory and create a false air of precision, certainty to both theoretical and empirical economics. Formulating statements about economic theories in mathematical terms must always depend on a painstakingly precise definition of the terms that are being treated as quantities in a mathematical model.

Unfortunately, due to the inescapable fact that economic phenomena always involve subjective and unobservable elements that take place within the human minds of the economic agents under study, such a precise definition is never entirely possible in economics. This inevitably leads to ambiguities of interpretation and the fudging of factors that can't be readily fit into a mathematical or econometric model.

Such ambiguity and fudging is exactly what the practice of mathematical economic purports to avoid in its quest to provide hard, precise answers to the questions of decision-makers and policymakers. At best, this sharply limits the level of certainty that can be placed on the conclusions thereby generated and, at worst, sophisticated mathematics can be used to cloak fundamentally misleading results and conclusions.

As a result, economists, and those who rely on them as experts and authorities, tend to gloss over these issues in the interest of confidence and certitude in pushing their preferred economic explanations and policy prescriptions.