Software prints about forty numbers. Roughly six of them matter. Here’s what every number in a regression table actually means — coefficients, standard errors, t-stats, p-values, R², F-stat — with annotated output from R, Stata and Excel, plus the six questions to ask any result.
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Compound Interest Formula: Simple vs Compound vs Continuous Compounding with Worked Examples
Einstein probably never called compound interest the eighth wonder of the world — but the mathematics is remarkable enough without the quote. A complete guide to simple interest, compound interest, compounding frequency, the number e, continuous compounding, the Rule of 72, and effective annual rates, with worked examples and exam technique for AP and Cambridge A-Level.
Lagrange Multipliers in Economics: Shadow Prices, the Envelope Theorem, and Kuhn-Tucker Conditions
Every proposition in microeconomics is the solution to the same problem: optimise subject to a constraint. A complete guide to Lagrange multipliers, the envelope theorem, why λ is a shadow price, Kuhn-Tucker conditions, and the duality between utility maximisation and cost minimisation.
The Solow Growth Model: Steady State, the Golden Rule, and Why Saving Doesn’t Cause Growth
Solow’s model proves that capital accumulation cannot generate sustained growth in living standards — and then declares that the thing which can is exogenous. A complete guide to the steady state, the Golden Rule, growth accounting, conditional convergence, and the East Asian growth debate.
Quantitative Easing and the Zero Lower Bound: What Fifteen Years of Evidence Actually Shows
Central banks expanded their balance sheets by trillions and inflation did not appear — until it did, for reasons that had little to do with QE. A complete guide to the zero lower bound, QE’s transmission channels, the Japanese experiment, and why almost every 2009 prediction was wrong.
Ordinary Least Squares (OLS): Derivation, Assumptions, and Why Omitted Variable Bias Ruins Everything
OLS is a covariance-to-variance ratio. Everything else in econometrics is machinery to make one untestable assumption believable. A complete guide: the derivation, the Gauss-Markov assumptions, omitted variable bias, heteroskedasticity, clustering, and the credibility revolution.
The Efficient Market Hypothesis: Theory, Anomalies, and Why Fama and Shiller Both Won the Nobel
Fama and Shiller shared a Nobel Prize for contradicting each other. A complete guide to the Efficient Market Hypothesis: the three forms, the anomalies (momentum, excess volatility, value), the joint hypothesis problem, the limits of arbitrage, and the Grossman-Stiglitz paradox.
Asymmetric Information in Healthcare: Adverse Selection, Moral Hazard and Why Health Markets Fail
Why does the healthcare market fail? Arrow’s 1963 analysis, Akerlof’s lemons model, adverse selection versus moral hazard, and the evidence from the RAND and Oregon insurance experiments — with the NHS, QALYs and NICE thresholds as case studies.
Carbon Pricing and the Social Cost of Carbon: Nordhaus, Stern, and What the Evidence Shows
Why do Nordhaus and Stern disagree by an order of magnitude about climate policy? A complete guide to carbon pricing: Pigouvian taxes, Weitzman’s prices-vs-quantities rule, the social cost of carbon, and case studies from Sweden, the EU ETS and British Columbia.
Minimum Wage and Monopsony: Why the Competitive Model Gets Labour Markets Wrong
Does the minimum wage destroy jobs? The competitive model says yes; the monopsony model says it depends. A complete guide to both, with Card and Krueger’s New Jersey experiment, the modern bunching evidence, and what three decades of research actually established.
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