There are whole Reddit threads devoted to a shared hatred of calculus – math majors included, engineers especially. Poetry has been penned contra calculus. Major American publications have argued against its inclusion on high school curricula. In the 5th century B.C., somewhere off the coast of southern Italy, the cult of Pythagoras drowned a member for suggesting the possibility of irrational numbers: a theorem which Isaac Newton and Gottfried Leibniz would use to develop “the calculus” 2,500 later. (It would take another 120 years for the world to accept it.)
So an almost biological aversion toward calculus is perhaps understandable. But for economics, it’s the lingua franca. (Its Latin translation: small pebble used for counting.) In this Ohio State course, Professor Fowler exhumes calculus from theory’s stuffy casket and places it in the context of application: how does this stuff work in the real world? For instance, how fast will a wobbly ladder slide down a building? And, how can you build a better ladder? Once we learn how to solve these questions mathematically, we can move on to questions like, why were all the ladders at Home Depot sold out? And, how did Home Depot get so good at selling ladders in the first place? But first, baby steps. Fowler’s course – which covers functions and limits, differentiation and anti-differentiaion, derivatives, and more – is straightforward, engaging, and surprisingly fun. Even if you’re well-versed, it’s worth revisiting.
- Pythagoras and the Pythagoreans: This history of the Pythagoreans and their tradition starts with its founder through to Johannes Kepler, the 17th century luminary and leader of the scientific revolution.
- The Calculus Wars: A thrilling account on Newton, Leibniz, and the “greatest mathematical clash of all time.”
A Tour of the Calculus: In what the New York Times Book Review calls an “an odd and tantalizing book,” we get an overview of the everyday uses of calculus, from the mundane to the extraordinary.
Principles of Microeconomics
Once we’ve got our math squared, we can move on to the proper study of economic theory, which is generally divided between micro and macroeconomics. Microeconomics, which concerns the relationship between individual decision-makers – manifest in supply and demand – typically comes first, probably because it was discovered first. (A useful history is available at Invostepedia.) Its chief theorist is, of course, Adam Smith: still history’s most influential, controversial economist; in his own way, responsible for Hegel, Marx, Hayek, Keynes, Friedman, and the Founding Fathers, all of whom were forced to respond to his free market concepts. (To label Smith an “economist” is admittedly reductive; he was also a political theorist, moral philosopher, and leading figure of the Scottish Enlightenment, alongside his friend, David Hume.) Margaret Thatcher is said to have carried his The Wealth of Nations in her handbag.
All that said: Professor José Vázquez-Cognet’s course, through the University of Illinois at Urbana-Champaign, is a consciously practical, real-world-driven review of microeconomics as thought about and practiced today: supply and demand, market efficiency and government policy, elasticity, production and costs; but also, the environment, love and marriage, education, crime, sports, and labor markets. Vázquez-Cognet wants “to shatter” the common perception that economics is exclusively the study of money – and, therefore, exclusively the study of specialists. To wax populist, he takes the copy of The Wealth of Nations out of Thatcher’s handbag, adds a few updates and revisions, and mass-distributes it among us common folk. As one reviewer puts it: “clear, accessible, rich, and necessary.”
- The Wealth of Nations: The book that put Adam Smith and his groundbreaking ideas on the map.
- Microeconomics: A Very Short Introduction: From a Professor of Economics Emeritus at Princeton University, this handy guide was a 2014 Financial Times Best Book.
Principles of Macroeconomics
Macroeconomic theory was developed in the 20th century, initially by John Maynard Keynes against Adam Smith’s classical and rational market ideas. What Keynes saw were not distinct, individual forces at work, nor any kind of beneficent invisible hand guiding the market toward prosperity; instead, Keynes found aggregate supply and demand and larger business cycles, most of which was out of individuals’ control (and which would lead to the Great Depression). Following World War II, the Chicago School of Economics – and, most famously, Milton Friedman – tried to synthesize Smith and Keynes, with supporters and detractors.
In our lifetimes, these macroeconomic practices have shared the limelight, while splitting political proponents. What UC Irvine’s Dr. Peter Navarro manages to accomplish is both to frame the debate and explain the principles underlying it. For anyone with a passing interest in contemporary economic policy, it’s fascinating; for our purposes, it’s indispensable. Among the topics discussed include the Federal Reserve and monetary policy; unemployment, inflation, and stagflation; economic growth and prosperity; budget deficits and public debt; international business, and more. Particularly for Navarro’s insistence on historical context, this is an excellent introduction.
- Keynes Hayek: The story of how two Depression-era economists, polar opposites in every regard, came to define the liberal and conservative theories of modern economics.
- Capitalism and Freedom: The codex of Chicago School, Milton Friedman’s imminently readable case for free markets made the Times Literary Supplement‘s list for the hundred most influential books since World War II.
Data Analysis for Social Scientists
The study of “the collection, analysis, interpretation, presentation, and organization of masses of data” first appeared among the Ancient Greeks: in History of the Peloponnesian War, Thucydides has the Athenians using it to approximate the number of bricks in a wall. Still, modern statistics doesn’t surface until the 18th century. (If you’re noticing a pattern, good. The Enlightenment was important.) Now, you can find statistical analyses from sports to fantasy sports, Bach and Chopin, Jackson Pollock, and zebras.
MIT professors Esther Duflo and Sara Fisher Ellison stick to more – for our purposes – relevant application, and discuss probability, applied probability, Bayesian and frequentist statistical inference, statistics with R, hypothesis testing, confidence intervals, data visualization, and other skills and concepts: all of which (rest assured) will be extremely helpful when we get to econometrics.
- The Signal and the Noise: This bestselling book from the country’s most famous statistician, Nate Silver, explores how the advent of predictive big data has serious draws and drawbacks alike.
- Moneyball: Another household-bestseller-turned-Oscar-contender, Michael Lewis’s fascinating account of how the Oakland Athletics revolutionized baseball through small-budget math is a cross-genre classic.
- The Misbehavior of Markets: Dismissed in his own time as an eccentric mathematician, Benoit Mandelbrot’s application of fractal geometry to irrational markets has gained particular attention since the Great Recession.
Intermediate Microeconomic Theory
Sergei Izmalkov’s course in intermediate economic theory takes Swift‘s observation as its premise: “Where I am not understood, it shall be concluded that something very useful and profound is couched underneath.” It’s a silly presumption for Swift, arch satirist, and Professor Izmalkov seems to agree. Yes, we have advanced from introductory economics, but the fundamentals still apply; no need to shrink in intimidation.
Through MIT’s OpenCourseWare, studies are divided into five units: Consumer Theory, Producer Theory, Markets, Market Failure, and Asymmetric Information, touching on a wide range of topics. Izmalkov also keeps us in the loop on present-day concerns, drawing on research from Daniel Kahneman and Amos Tversky, Faruk Gul and Wolfgang Pesendorfer, Jean Tirole, and John Nash (best known as the subject of A Beautiful Mind.) For his part, Professor Izmalkov is a recognized leader in economic theory and mechanism design, with work published in the Journal of Economic Theory, American Economic Journal, and Games and Economic Behavior. He shared the Nobel Prize for Economics in 2007 for research in economic mechanisms.
Intermediate Macroeconomic Theory
Next, back to macro: this time carrying the principles we first learned – namely, Keynes vs. Friedman – and performing a deep dive. Some questions posed in Professor Angeletos’s course:
- What drives economic growth, and what’s the role of policy in economic growth (if any)?
- Why does unemployment exist? Can government protect against and/or mitigate unemployment?
- Should the government try to stabilize the economy against business-cycle fluctuations – how? Or is it better to let market forces play out naturally?
- What causes financial recessions, depressions, and panics?
Many of these issues pre-date even Adam Smith; we’ll continue to wrestle with them. Among the economists we consider include Robert Solow, Robert Hall, Robert Barro, and other non-Roberts. At MIT, Professor Angeletos is the recipient of a Sloan Fellowship and won the Bodossaki Foundation Prize in Social Sciences in 2008.
Developed by Norwegian economist Ragnar Frisch in the 1920s (among others), econometrics is the “use of mathematics and sophisticated statistical modeling to test economic or financial theories, as well as forecast the effects of changes in economic or financial factors under various scenarios,” as defined by the Financial Times. Dumbed down, it’s how we measure economic theories – hence, metrics.
The Erasmus School of Economics has divided the course into six units: simple regression, multiple regression, model specification, endogeneity, binary choice, and time series, all geared toward practical, real-world usage. (A case study is available.) For instance, we might use econometrics to study the income effect, which proposes that an individual’s demands increase as their income does, i.e., the more we make, the more we spend. It certainly sounds right. Econometrics allows us to determine empirically a) the validity of the theory and b) predict future income-demand patterns. Or, as the International Monetary Fund puts it, “if economic theory is to be a useful tool for policymaking, it must be quantifiable.”
No one knows where money came from. This seems true enough: since its introduction, coin has been tough to track. Some historians have proposed it replaced bartering – I’ll give you five spears for that heifer – but there’s only so much evidence. Aristotle offered a fairly practical, economic explanation: “When the inhabitants of one country became more dependent on those of another, and they imported what they needed, and exported what they had too much of, money necessarily came into use.”
All that said, if you know how money works, you’ve got a better shot at keeping it. In a post-Great Recession world, that rule is particularly true and the starting point of Prof. Perry G. Mehrling’s Economics of Money and Banking course at Columbia University, produced and sponsored by the Institute for New Economic Thinking. Mehrling argues that over the last three to four decades, the modern monetary system has undergone significant changes, while our basic approach to it has remained static. In short, those changes are threefold:
- 1) Capital markets and money markets became intertwined
- 2) Globalization created a new international monetary order
- 3) Money and finance became inseparable, which lead to derivative contracts
Each of these factors directly contributed to the financial crisis, but the average person is still financially illiterate. Covering balance sheet basics, money markets, funding liquidity, market liquidity, the international monetary system, and more, Columbia’s money and banking course is (disregarding its elective status) required.
- The Ascent of Money: Niall Ferguson’s sweeping financial history of the world argues that the development of money and banking – and credit and debt – created civilization as we know it.
- The Wheels of Commerce: The second volume in Fernand Braudel’s monumental Civilization & Capitalism is a masterpiece in financial scholarship, here focusing on the banking and trading systems of 15th-18th centuries.
- The End of Alchemy: “Something is wrong with our banking system.” So goes the premise of this timely, enlightening book on money, banking, and the future of the global economy.
What we haven’t adequately accounted for – and what’s perhaps most overlooked among all the economic graphs, equations, and policy theories – is human behavior. Humans don’t make consistently rational decisions; in fact, quite the contrary. How, then, do our suboptimal actions affect the marketplace?
Professor Dilip Soman, of the University of Toronto, addresses this problem through three introductory modules. In the first, we examine the principles underlying decision-making and the emergence of “nudge theory”, as popularized by economist Richard Thaler. From there, students learn how to to critique, design, and interpret behavioral research experiments, including the three basic types of experimental designs, analysis of variance, and regression techniques (here, our statistics knowledge will come in handy again). Finally, we will design “nudges” and other tools that encourage people to make better decisions, from saving money to eating healthier foods. (Yes, the latter is both an economic and dietary decision.) In addition to lectures from Soman, this practical, “in action” course includes guest lessons from Professor Sendhil Mullainathan (Harvard University), Professor John Lynch (University of Colorado), Rory Sutherland (Ogilvy Group), Owain Service (Behavioural Insights Team), Shankar Vedantam (NPR columnist), and more.
- Thinking Fast and Slow: From Nobel Prize-winning economist Daniel Kahneman, this international bestseller is among the most important contributions to economics and human psychology in recent memory.
- Nudge: Improving Decisions About Health, Wealth, and Happiness: Cass Sunstein and Richard Thaler’s book is about “choices—how we make them and how we can make better ones.” Championed by the likes of Malcolm Gladwell, Steven Levitt, and Michael Lewis.
- The Theory of Moral Sentiments: The father of economics was also the father of behavioral economics. In this lesser-known tract, Adam Smith lays out the psychological principles that affect our economic decisions, predating even the Utilitarian ideas of Mill and Bentham.
In April 1519, Cortés found himself in a pickle. Charged with conquering the Aztec Empire, he landed on the shores of present-day Veracruz, well-armed but vastly outmanned. If he wanted to turn around, he couldn’t: the governor in Cuba would have his head. (Given his nature, fleeing was probably never a serious consideration.) So, Cortés sunk his ships (or burned them, depending on your source). This was quite clever: on the one hand, he eliminated the possibility of retreat, forcing his soldiers to fight as if their lives depended on it (they did); better still, he made sure the Aztecs saw him commit this apparently wild, hyper-confident act of self-sabotage. Who would sink his own ships? the Aztecs wondered. Only someone who thought victory was a foregone conclusion. For their part, the Aztecs were less sure and retreated into the peninsula.
Four-hundred years later, John von Neumann and Oskar Morgenstern provided a mathematical basis to Cortez’s maneuver called Game Theory – today, used in politics, sports, war, movies, philosophy, and, with major consequence, economics. It’s not possible to summarize sufficiently here, but Professor Ben Polak does an admirable job in his Open Yale Course, which is among the most comprehensive on the internet, with twenty-four lectures on dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling, among other concepts.
- Theory of Games and Economic Behavior: Morgenstern and von Neumann’s original treatise remains an excellent resource. (Edition includes intro, afterword, and contemporary reviews.)
- A Beautiful Mind: Adapated into an Academy Award-winning film, this remarkable biography of the polymathic John Nash is at once profoundly moving and re-enchanting.