A new archive

1What economics studies

Economics studies a small set of things in the economy.

• Agents decide: households, firms, banks, governments, central banks, other countries.
• Markets are where agents meet and something is exchanged: goods, labor, money, capital, foreign exchange, and the land and air that have no market until one is made.
• Institutions set the rules they meet under: property, contracts, regulation, taxes, the rules of policy, and the networks that decide who can reach whom.
• Flows run between them: spending and goods, work and wages, saving and lending, taxes and government purchases, exports and their payments, emissions. Totals such as output and employment are sums of these flows.

It reads them with a small set of methods: optimization, equilibrium, strategic interaction, measurement, computation and history. Methods are of another kind. They are not in the economy. They are the tools a model uses to say how the rest moves.

Arrange agents, markets and institutions as the rings of one wheel, the circular flow that Frank Knight drew in 1933 as a “wheel of wealth”, with the methods as its hub. The agents stand on the rim, where everything that circulates starts and ends, and the flows run between the rings. Markets ring the institutions, and the methods are the hub, the tools every other ring is read with. Part 1 built this wheel one stage at a time, and five of its stages added a tool to the hub: optimization in Stage 2, strategy in Stage 4, equilibrium in Stage 5, measurement in Stage 7 and history in Stage 8. The plan below is the wheel cut open and laid flat. Each row is one ring.

Folded, the view steps back from the plan, and the wheel is built ring by ring beside the page. The agents come first, then the markets, through which goods, work and money start to circulate, then the institutions, and last the methods at the hub. It is the wheel the folded pages of Parts 1 and 2 lie on. Each cell holds what one course knows about one thing, and its name is a door to that course.

The economy is one wheel, and every figure in a textbook is drawn on part of it. The methods at the hub are not part of what is studied. They are how it is studied.

2What a model is

No textbook figure draws the whole wheel. A model picks part of it and works out how that part moves. On the wheel, a model gives every cell one of three states.

• Moving: what the model solves for. In Figure 1.1, the goods market, with its buyers, its sellers and the price.
• Held still: what it takes as given, at a value. In Figure 1.1, income, held at 1, and with it the households and firms behind the two curves.
• Left out: what it does not contain. Figure 1.1 has no banks, no government and no other countries.

Two more things complete a model: the method at the hub that moves its moving parts, and the assumptions it makes about the agents in them (section 4).

Part 1 named under every figure what the figure holds fixed, and folding the page raised that quantity as a third dimension. In twenty-two of its thirty figures the hidden axis is the value of a held cell: income in Figure 1.1, the interest rate in Figure 2.3, the price level in Figure 6.2. In four it is what the method climbs, read as contour lines: utility in Figures 2.1 and 5.1, profit in 4.1, the central bank’s loss in 6.4. Alfred Marshall described the method of holding in his Principles of Economics (1890): the causes that would disturb a question are set aside “in a pound called Ceteris Paribus”. On the wheel, that pound is the hatched cells.

The two models differ in what they move, and so in what they hold. IS–LM moves goods and money at once and holds the price level, which is the quantity Figure 1.1 solved for in its one market. Folded, the wheel beside the page takes the state of each model in turn. The routes through a held cell stop, with their parcels where they were, and the cells left out empty to their outline. Opening a held cell sets its routes moving again.

A model is a choice of what moves, what is held and what is left out. Most hidden axes in Part 1 are the value of what a model holds.

3How models are related

Part 1 wrote beside every figure what it builds on and where it returns, and Part 2 wrote what each section relaxes. Each of these is a change in the state of the wheel, and there are five kinds.

A course is a sequence of such changes. The classical sequence of Part 1 starts with one market moving and the rest held or left out. Each stage opens, adds, relaxes or measures one thing, until every cell but two moves.

Stage 1 moves the goods market and holds the households and firms behind its curves. Stages 2 and 3 open them. Stage 4 opens no agent or market; it relaxes an assumption, and strategy arrives at the hub. Stage 5 opens income, the last held cell, so that every market moves at once. Stages 6 and 8 add what was left out, and Stage 7 measures what the moving wheel produces. Two cells never move: networks and computation. Part 2 is where they are built. Folded, the wheel takes the state of each stage in turn, and the route of Part 1 is drawn through it figure by figure.

The core is the shortest sequence that sets every market moving at once, with money, the state and measurement. A field course goes one change beyond it.

4The assumptions

A model’s assumptions are claims about the agents in its moving cells: how many of them stand for their kind, who can reach whom, whether they can move the price, what they know. Eight run through Part 1. Figure 3.4 marks where each is made and where it is relaxed.

Six of the eight are relaxed inside the classical sequence. Price-taking gives way in Stage 4, full information in Figure 5.3, complete markets in Figure 5.2 and two field courses, consistent choice in Figure 8.9, equilibrium at once in Figure 6.3, and the claim that data show relationships in Stage 7. Two are never relaxed head-on. The representative agent lets one household or one firm stand for all of its kind. It is touched once, in Figure 8.10, where missing credit makes the distribution of wealth decide investment. The assumption of no connections lets anyone trade with anyone. These are the two halves of the assumption that Part 1’s last section names, and their opposites are the title of Part 2: unlike and connected.

Folded, the assumptions show on the agents of the wheel. Drawn as a representative agent assumes, every firm is the same size. Relaxed, the firms are as unequal as Zipf’s law says, and households differ in income. Drawn without connections, any household buys from any firm through the market. Relaxed, each is tied to a few, and what moves travels along the ties.

Part 2 is not a separate economics. It relaxes the two assumptions the classical sequence keeps to the end.

5What holding still requires

Every figure of Parts 1 and 2 holds something still, and folded, the held value rose as the figure’s hidden axis. This section takes that axis seriously. A model sends what it holds to what it moves: in Figure 1.1 the equilibrium price is a function of income, p*(I). “Other things equal, a higher income raises the price” is a claim about the slope of that function. The claim means something only if four things are true. An equilibrium exists at every held value. Near each there is only one. It moves without breaks as the held value moves. And the economy reaches it. Each is a property of a surface, and each is guaranteed by a theorem: existence by the fixed-point theorems of Brouwer and Kakutani, local uniqueness and the slope by the implicit function theorem, continuity by Berge’s maximum theorem, and stability by the conditions Paul Samuelson (1947) tied to comparative statics. This is why economists learn topology.

Folded, income rises as an axis and the three lines lie at their incomes. Between them a sheet fills in, and the sheet crosses the floor of zero along a single line: at every income there is one equilibrium, and it moves without a break. The slope of that line, five units of price for one of income, is what “other things equal” means here. Off the line the sheet pushes the price back toward it, so the equilibrium is also stable.

The four properties can fail, and not because anyone is irrational. Hugo Sonnenschein (1972), Rolf Mantel (1974) and Gérard Debreu (1974) showed that the excess demands of households who are each rational can add up to almost any shape. Figure 3.6 takes one that the theorem allows.

Folded, the sheet folds over itself, and its crossing of zero becomes an S. Between ω = 1/6 and 5/6 there are three equilibria. In the middle one the sheet slopes the wrong way, so a price near it runs away. Raise ω slowly and the price follows the low branch until the branch ends at ω = 5/6, then leaps from 3.5 to 8. Lower it again and the price stays high until ω = 1/6, where it falls to 2. A small change in what is held moves the economy a long way, and where it ends up depends on where it came from.

The textbook’s single crossing is bought by the representative agent. Relax it, as Part 2 does, and the theorems that made “other things equal” safe have to be checked again.

A held value matters for evidence as well. A scatter of two variables is the shadow of every other value that moved while they were recorded (Figure 7.1). Figure 3.7 draws one such shadow from data.

Flat, the cloud seems to refute the Phillips curve. Folded, each year rises to the inflation households expected, and the years lie close to one plane: with the third axis, inflation’s variation is 87 percent accounted for. Seen along the plane, the cloud is a line. The plane then rejects something in its turn. It is steep in expectations and nearly flat in unemployment, so since 1978 the short-run trade-off of Figure 6.3 has been small.

The rescue is fair only because the axis was named before the test and measured apart from it. When a prediction fails, what is refuted is the theory together with everything it held, as Pierre Duhem (1906) and W. V. O. Quine (1951) argued. An axis chosen after the test can rescue any cloud. Survey expectations also move with recent inflation, so part of the plane is inflation explaining itself, and separating the two takes a research design.

Name what is held before the test, with its value, and measure it apart. Then “other things equal” leaves a model refutable.

6Two hands, and what the core must hold

Economists are teased for answering “on the one hand … on the other.” The habit has a structure. When a held value changes, the moved value responds through more than one channel, and the channels can push in opposite directions. The slope of section 5’s surface is then a sum whose sign theory alone does not fix. The two hands are the two channels. The economist’s work is to name them, to state the condition under which each wins, and to measure that condition.

Folded, the employer’s power rises as an axis and the two lines become the edges of one surface. On it the effect of a higher floor changes sign along two lines. Above what the employer would pay and below the competitive wage, a higher floor adds jobs; past the competitive wage it costs jobs at any μ. Which region a real market is in is a question for a research design, such as David Card and Alan Krueger’s (1994) comparison of fast-food employment in New Jersey, which raised its minimum wage, and neighboring Pennsylvania, which did not.

The same surface shows what a core can safely leave out. A textbook core leaves cells out to stay short. If a left-out cell can reverse one of the core’s conclusions, the core is not short but wrong where that cell matters. The archive therefore keeps a reversal rule: the core is the shortest sequence, except that any cell or assumption whose addition reverses a core conclusion comes into the core, and every core conclusion names what would reverse it.

Folded, the closed economy’s multiplier is a single level across every degree of capital mobility, the core’s answer. Adding the foreign cell splits it. Under a floating rate, spending raises the interest rate, capital flows in, the currency appreciates and exports fall, so with mobile capital the multiplier approaches zero, whatever the import share. Under a fixed rate the central bank must buy the inflow, money expands, and the multiplier rises above the closed value, less so the more the economy imports. Ethan Ilzetzki, Enrique Mendoza and Carlos Végh (2013) found multipliers near zero under flexible exchange rates and larger under fixed ones. For a floating, open economy such as Korea’s, the closed answer is reversed, so by the rule the foreign cell belongs in the core.

A conclusion of the core is a corner of a larger surface. The core is trustworthy when it names the cells that would move the corner.

7A unit of the textbook

If what a textbook teaches is models, a unit of the textbook is one model, and it can be written down in the same nine fields every time. Part 1 already writes most of them beside each figure.

Five rules arrange the units into a textbook.

1. A unit makes one change: it opens one cell, adds one, relaxes one assumption, measures what the moving cells produce, or returns a structure in another cell.
2. A unit comes after the units it builds on. A cell must be built before it can be opened, and moving before it can be relaxed.
3. The core is the shortest sequence that sets every market moving at once under the classical assumptions, with money, the state and measurement. In Part 1 it is Stages 1 to 7.
4. A field course is one step beyond the core: it adds one thing or relaxes one assumption, as each course of Stage 8 does.
5. A modern field is a step along an assumption, and can leave the core at any stage. Part 2 is made of such steps.

Folded, the wheel shows the card one field at a time: the cell the unit moves, the cells it holds at their values, the cell it opens, the agents as it assumes them, and the tool at the hub.

Written in the same nine fields, units can be put in a different order without losing what each one assumes.

8Five ways through

Each path below enters the wheel somewhere else and visits the cells it needs in its own order. A question, an agent or a market enters at a cell. An assumption follows a property of the agents from cell to cell, and a method starts at the hub.

The paths by question, agent and market follow cells. The path by an assumption follows what Part 2 relaxes: it starts where Figure 1.1 makes the assumption of no connections and ends where a loss travels between banks. The path by a method stays at one tool of the hub while it moves around the rim, from the household to the firm, the central bank and the investor.

A course is one path among several. The archive keeps the classical sequence as one of them, without making it the only way in.

9The textbooks

The archive needs textbooks written to it. In them each chapter is a unit: one model, with what it holds fixed, the mathematics its conclusion rests on, the data that could refute it, and a page for the reader to write. The plan has twenty-two books and 301 chapters. Ten make the core and eleven are field books. The last one, read after the field books, asks again what economics has known and how. Five of the twenty-two are new to the archive: Economic reasoning, a second volume of mathematics, Probability and statistics, Computational economics, and Methods and philosophy.

The books are not ordered by semester or year. They are ordered by eight works, each a thing the reader has to do and hand in. A work is done when what it hands in passes three tests on a case the books do not contain, however long that takes, and a book or a work may take more than a year. Reading can run ahead of the order. Only what is handed in follows it.

After Work 2 the order splits in two. One line proves, then builds the whole economy (Works 3 and 4); the other measures (Work 5). Neither waits for the other. Computing waits for both lines, and the field books wait for the economy and for measurement. Three books are read across two works, because some of their chapters wait for chapters of another book. Intermediate microeconomics reads general equilibrium only after the fixed-point theorem of Mathematics II; Game theory reads the choice among several equilibria only after their stability.

The order can be checked against the chapters themselves. Of the 960 places where one chapter refers to another, 28 point to a work not yet done. Ten of them state a theorem that a later work proves, which is why Work 2 asks the reader to check a theorem’s assumptions and not to prove it. The other eighteen hand a case where a result fails on to a later book. A first draft had one more: the first chapter of Mathematics II used the definition of convergence in probability from chapter 5 of Probability and statistics, which sat in Work 5. Chapters 5 and 6 of that book were moved to Work 2.

Each of the six methods at the hub now has a book that teaches it: optimization in Mathematics I, equilibrium in Mathematics II, strategy in Game theory, measurement in Probability and statistics and Econometrics, computation in Computational economics, and history in Economic history. Computation is one of the two cells Part 1 never moves, and no course taught it. Seventeen of the books are the archive’s existing courses, and their names open the course pages, which describe each course as it is taught now. The five new books have no page yet.

The order of the books is the order of what a reader must be able to do, and it can be checked chapter by chapter.

The archive is a proposal, not a finished machine. Its cells are the courses that already exist, read through the models they teach. What it adds is the wheel that shows what each model moves, holds and leaves out, and how the models connect.