What is Mathematical Economics?
Mathematical economics is a model of economics that utilizes math principles and methods to create economic theories and to investigate economic quandaries. Mathematics permits economists to conduct quantifiable tests and create models to predict future economic activity.
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. These elements are all backed by scientific methods advancing the study of economics.
The marriage of statistical methods, mathematics and economic principles has created an entirely new branch of economics called econometrics. Mathematical economics is a specialization with the branch of econometrics.
Understanding Mathematical Economics
Mathematical economics relies on statistical observations to prove, disprove, and predict economic behavior. Although the discipline of economics is heavily influenced by the bias of the researcher, mathematics allows economists to explain observable phenomenon and provides the backbone for theoretical interpretation. There was a time when economics relied heavily on anecdotal evidence or situational explanations to attempt to make sense of economic phenomenon. 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.
Economists often wrestle with competing models capable of explaining the same recurring relationship called an empirical regularity, but few models provide definitive clues to the size of the association between central economic variables. From Main Street to Wall Street to Washington, this is what matters most to policymakers. 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.
The Impact of Mathematical Economics
Mathematical economics opened the door for true economic modeling. Through the language of mathematics, theoretical economic models have turned into useful tools for everyday economic policymaking. 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”). Mathematical economics 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, it's something of an understatement to say the blending of qualitative and quantitative methods are a substantial improvement on traditional economic techniques. As Stock and Watson (2007) 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 mathematical modeling to assess their impact and new economics papers are rarely published without some mathematics in them.