经济学核心 15 模型 · 交互精读Fifteen Core Models in Economics — an interactive reader

Consumer theory appears to be a pile of separate functions — Marshallian demand, compensated demand, indirect utility, expenditure — but they are four projections of a single optimisation problem. Once you see which is which, comparative statics, welfare analysis and the whole of production theory turn out to be the same mathematics wearing different clothes.

Production theory is almost a mirror of consumer theory: isoquants for indifference curves, RTS for MRS, cost function for expenditure function, and Shephard's lemma working on both sides. Only one genuinely new object appears — the elasticity of substitution σ — and it arranges every familiar production function along a continuous spectrum.

Partial equilibrium pretends that what happens in one market leaves the others alone. General equilibrium makes no such assumption: all prices are determined together and all markets clear together. Its two welfare theorems are the strongest normative results in economics and the benchmark against which every policy argument is measured.

Perfect competition and monopoly are the two extremes. The ground between them — oligopoly — cannot be handled with price-taking, because each firm's decision shifts every other firm's best choice. Nash equilibrium is the solution concept that makes this interdependence consistent, and it is the shared language of modern industrial organisation, auction theory, contract theory and macroeconomic coordination-failure models.

The first four models all assume symmetric information. Relax that assumption and the result is not a modest efficiency loss but the possible collapse of the market altogether — with everyone rational, everyone honest, and gains from trade plainly available. This one strand underpins the analysis of insurance, labour markets, credit, used cars and health care.

What makes Solow's model great is that it demonstrates its own insufficiency: under diminishing returns, however high the saving rate, it can raise the level of income but not the long-run growth rate, which is set entirely by exogenous technical progress g. That residual is what forced the endogenous growth literature into existence (Model 8).

Because Solow's saving rate is exogenous, the model cannot answer how much saving is right. Ramsey has households maximise discounted utility over an infinite horizon, which makes the saving rate an outcome. The price is that dynamic optimisation must now be handled: Euler equations, phase diagrams, saddle paths, transversality conditions. That toolkit is the common language of modern macroeconomics — RBC, DSGE and New Keynesian alike.

By attributing long-run growth to an exogenous g, Solow effectively conceded that growth theory could not explain growth. Endogenous growth makes g an outcome of economic decisions. The Schumpeterian branch (Aghion–Howitt) is the most interesting of them: the value of an innovation is destroyed by future innovations, a self-undermining mechanism that is at once the engine of growth and its brake. The 2025 Nobel Prize went to Aghion, Howitt and Mokyr for exactly this line of work.

What made RBC provocative is that a model with no frictions, no money and no unemployment reproduces most of the second moments of post-war US output. Whether or not one accepts the conclusion, it set the methodological standard of modern macroeconomics: write down microfoundations, calibrate, simulate, compare moments with the data. Every DSGE model in use today descends from it.

In RBC money is neutral and policy is powerless. Add the single friction that prices cannot be reset every period and the conclusions reverse: demand shocks generate real fluctuations, and monetary policy both can and should respond. The three-equation model is the minimum shared language of virtually every monetary policy discussion today.

Almost every empirical paper says it controls for X. The FWL theorem states precisely what that means: a coefficient in a multiple regression equals the coefficient from a simple regression of one residual on another, once the other regressors have been partialled out of both. Grasp it and omitted variable bias, fixed effects, detrending and partially linear models all turn out to be the same operation.

When x is correlated with the error — omitted variables, measurement error, reverse causation — OLS cannot be salvaged. IV takes another route: use not all the variation in x but only the part driven by an exogenous instrument z. This is the central technique of the credibility revolution, and the one most easily abused.

DID is the most widely used design in applied microeconomics, and Card and Krueger's minimum wage study pushed it into the mainstream. Since 2018, however, a series of papers has shown that when treatment timing is staggered and effects vary over time, the standard two-way fixed effects estimator can return an answer with the wrong sign. This is the most important methodological correction in econometrics of the past decade, and not knowing it means reaching for the wrong tool.

RD makes the weakest and most credible identifying assumption of any quasi-experimental design: everything other than treatment must be continuous at the cutoff. The price is very narrow external validity — what is estimated is the effect for those near the threshold and no one else. It is now used heavily in education, health insurance, elections and financial regulation.

GMM unifies OLS, IV, 2SLS and maximum likelihood into a single framework — drive the sample moments to zero — and is the common grammar of modern econometrics. In time series, stationarity is the premise of all asymptotic theory: regressing non-stationary series on one another produces spurious regressions, with a high R² and large t-statistics and conclusions that are entirely false.