Given Greg's comment a couple weeks ago and the comments from my students before their first intermediate macro exam last week, I've had to explain why economics relies heavily on math a number of times recently. I see two major reasons:
1) Size matters. Economists know more than anyone that there are no
easy decisions--there are only trade-offs. Using equations allows one to
estimate the sizes of these effects. We should be careful that our
estimates are only that, estimates, and that model specification
matters (Here's Russ Roberts with some appropriate sarcasm). But still, it is often helpful to quantify effects.
2) Clarity matters. Most of the complaints I hear regarding math in economics are not in regard to estimating numbers, but in the way we fit an economic problem into a system of equations (and this gets into the structural vs. reduced form econometrics argument). While it might be difficult to correctly model economic phenomena, I think the benefits outweigh the costs. The costs are a few years learning some mathematical concepts and some more thought to model economic questions. The benefits are twofold. First, math is a very clear language. Using math puts in plain sight the assumptions that lie behind a model and the mechanisms at work in the model. Second, math provides a common language for economic thought. Unlike in other disciplines, a degree in economics gives you the skill set to read a paper in any field of economics and the ability to understand it. This is not true of other disciplines, especially those in the social sciences (e.g. a political scientist who studied comparative politics would likely not be able to read a paper in formal theory).
To the extent that one is a theorist, one thinks 2) is more important and may believe that we shouldn't pretend to put precise numbers on our models. And vice versa- those in applied micro, who live and die by running regressions, think little of 2). As someone who sees value in structural econometrics, I see both 1) and 2) as strong reasons for economics to rely heavily on math. Bryan Caplan make these two points very well in section 4 of his essay "Why I am Not an Austrian Economist".
Although I'll admit that I might have taken this too far: Much of the work I did in graduate school applied tools from macro economics to questions in political economy. This has perhaps gone over the head of many departments where I've applied for positions in both macro and public. Only knowing the titles of the papers I've worked on (e.g. "Flip-flopping: Ideological Adjustment Costs in the United States Senate") you might believe that I only have an understanding of a tiny area in public economics, but reading further, any macroeconomist will see clearly what's going on, because the math is the same (e.g. the model of senators is just like the model of firms in the literature on firm dynamics). I thought extending a literature and creatively applying my tools was a good idea, but it may have backfired- I have a strong background in macro, but have gotten little attention from those positions because of the titles of some of my work.
2) Clarity matters. Most of the complaints I hear regarding math in economics are not in regard to estimating numbers, but in the way we fit an economic problem into a system of equations (and this gets into the structural vs. reduced form econometrics argument). While it might be difficult to correctly model economic phenomena, I think the benefits outweigh the costs. The costs are a few years learning some mathematical concepts and some more thought to model economic questions. The benefits are twofold. First, math is a very clear language. Using math puts in plain sight the assumptions that lie behind a model and the mechanisms at work in the model. Second, math provides a common language for economic thought. Unlike in other disciplines, a degree in economics gives you the skill set to read a paper in any field of economics and the ability to understand it. This is not true of other disciplines, especially those in the social sciences (e.g. a political scientist who studied comparative politics would likely not be able to read a paper in formal theory).
To the extent that one is a theorist, one thinks 2) is more important and may believe that we shouldn't pretend to put precise numbers on our models. And vice versa- those in applied micro, who live and die by running regressions, think little of 2). As someone who sees value in structural econometrics, I see both 1) and 2) as strong reasons for economics to rely heavily on math. Bryan Caplan make these two points very well in section 4 of his essay "Why I am Not an Austrian Economist".
Although I'll admit that I might have taken this too far: Much of the work I did in graduate school applied tools from macro economics to questions in political economy. This has perhaps gone over the head of many departments where I've applied for positions in both macro and public. Only knowing the titles of the papers I've worked on (e.g. "Flip-flopping: Ideological Adjustment Costs in the United States Senate") you might believe that I only have an understanding of a tiny area in public economics, but reading further, any macroeconomist will see clearly what's going on, because the math is the same (e.g. the model of senators is just like the model of firms in the literature on firm dynamics). I thought extending a literature and creatively applying my tools was a good idea, but it may have backfired- I have a strong background in macro, but have gotten little attention from those positions because of the titles of some of my work.
