Agents for Economics

complexity, expectations, control and explanations

Colin Rowat
colinian.rowat@rakuten.com

Rakuten Institute of Technology

June 9, 2026

Table of contents

  1. ABM in economics and finance
  2. Three models of discrimination
  3. Will the world run out of natural resources?
  4. How do markets work?
  5. Can we trade off inflation & unemployment?
  6. How to break heterogeneity (if you must)
  7. How should taxes balance equity & efficiency?
  8. MIT researchers with SOTA computers, II
  9. Conclusions?
  10. Tutorial
  11. Some stray quotes

ABM in economics and finance

What is ABM in economics and finance?

a class of computational techniques … to represent individual behavior for purposes of studying social phenomena. Models of this type feature a population of objects called agents, which are typically heterogeneous and situated in an economic or social environment. The individual agents are given explicit rules of behavior, which can be quite general — as in ‘seek greater utility’ — or very specific (e.g., ‘lower prices by 5% if inventory exceeds target levels’). The agents interact directly with one another through social, spatial, or physical networks that are either exogenously specified or endogenously generated. Such models may produce conventional agent-level equilibria (e.g., Nash equilibria), or can yield perpetual dynamics at the micro-level as agents constantly adjust their behaviors. Importantly, the aggregate level is not explicitly pre-specified. Rather it emerges from the myriad interactions of the agents. … We see ABM as a complement rather than a substitute for conventional economic modeling. (Axtell and Farmer 2025)

On misnomers:

  • post-WWII microeconomics has focussed on agents: e.g. “An abstract economy, then, may be characterized as a generalization of a game in which the choice of an action by one agent affects both the pay-off and the domain of actions of other agents.” (Arrow and Debreu 1954)
  • rationality means complete and transitive preferences:
    • complete: for any \(x, y \in X\) either \(x \succ y, y \succ x\) or \(x \sim y\)
    • transitive: \(x \succ y\) and \(y \succ z \Rightarrow x \succ z\)

Should models be realistic?

Where’s ‘realistic’?

An abstraction’s value may derive from the closeness with which it approximates reality. … What keeps economists from moving from [neoclassical abstractions] to [increased realism] are a variety of conceptual, mathematical and econometric difficulties that can make richer models intractable. (§1.2 Axtell and Farmer 2025)

in general, the more significant the theory, the more unrealistic the assumptions … A hypothesis is important if it ‘explains’ much by little, that is, if it abstracts the common and crucial elements from the mass of complex and detailed circumstances surrounding the phenomena to be explained and permits valid predictions on the basis of them alone. To be important, therefore, a hypothesis must be descriptively false in its assumptions. (Friedman 1953)

Three models of discrimination

Schelling (1971): bottom-up discrimination

An agent with at least the minimum number of neighbours to be happy stays; otherwise, it moves to a random empty cell where it would be happy.


0
  • easy to understand: just look!
  • does this surprise us?
  • what takeaways do we take from this?
  • do we care about 'comparative statics'?
  • policy: people should be less discriminatory?

Phelps (1972) : exogenous group differences

  • worker belongs to one of two observable groups, \(j \in \left\{ R, B \right\}\).

  • worker’s unobservable skill is \(q \sim N \left( \mu_j, \sigma^2_j \right)\)

  • firm does observe a noisy signal, \(\theta = q + \varepsilon, \quad \varepsilon \sim N \left( 0, \sigma^2_{\varepsilon_j} \right)\)

  • firms pay workers their (conditional) productivity

    \[w = E \left\{ q \mid \theta \right\} = \frac{1}{\sigma^2_j + \sigma^2_{\varepsilon_j}} \left[ \sigma^2_j \theta + \sigma^2_{\varepsilon_j} \mu_j \right]\]

    1. noisy signal (\(\sigma^2_{\varepsilon_j}\) large): wage reflects group average, \(w \approx \mu_j\)
    2. precise signal (\(\sigma^2_{\varepsilon_j}\) small): wage reflect individual performance signal, \(w \approx \theta\)

  • takeaways

    1. workers with the same observed productivity may be treated differently
    2. identifies variables that drive discrimination, which can focus policy: make signals more precise

(our presentation of Phelps (1972), Arrow (1973) drawn from Fang and Moro (2011))

Arrow (1973) : endogenous discrimination by self-fulfilling prophecies

  • again, firms observe worker’s \(j \in \left\{ R, B \right\}\)
  • firms have a production function, \(f \left( L_U, L_S \right)\), with \(L_U\) unskilled labour and \(L_S\) skilled
  • any worker can supply \(L_U\), and receive \(w_U = f_U \left( L_U, L_S \right)\)
  • to supply \(L_S\), a worker must invest \(c \sim G \left( \cdot \right)\), whose CDF is independent of \(j\)
  • a worker assigned to supply \(L_S\) is paid \(w_S = w_j\) if tested as skilled, and \(w_S = 0\) otherwise
  • firms pay \(r\) to test a worker
  • in equilibrium, \(w_B = \frac{\pi_R}{\pi_B} w_R + \left( 1 - \frac{\pi_R}{\pi_B} \right) f_S \left( L_S, L_U \right)\) so that \(\pi_R < \pi_B \Rightarrow w_R < w_B\)
  • asymmetric equilibria in which \(w_R < w_B\) may exist for self-fulfilling reasons:
    • if \(\pi_R\) is low, firms assume that \(R\)’s have high cost \(\Rightarrow\) low \(w_R\)
    • low \(w_R\) leads to fewer \(R\) being willing to pay \(c\) given the lower wage premium that it earns
    • which leads to low \(\pi_R\) …
  • takeaway: discrimination can exist even without Schelling’s bias/animus or Phelps’ group differences
  • policy: can self-fulfilling expectations be broken on their own, or do you need to e.g. subsidise \(c\) for \(R\)’s?’

Will the world run out of natural resources?

MIT researchers with SOTA computers (Meadows et al. 1992)

Four paths forward for humanity (Meadows et al. (1992))
  • World3 computer model built over two years by 17 researchers in the System Dynamics Group of MIT’s Sloan School of Management
  • “originally programmed in DYNAMO, a simulation language developed at [MIT] specifically for analyzing system dynamics models”, running on IBM 360/370 mainframes

we use World3 to calculate the interactions among all its 225 variables. The computer calculates a new value for each variable every six months in simulated time from the year 1900 to the year 2100. The model thus produces more than 90,000 numbers for every scenario.

Are we reaching peak humanity? (Meadows et al. 1992)

Population and material standard of living under Beyond the Limits simulations (Meadows et al. (1992))

[T]he model system, and by implication the “real world” system, has a strong tendency to overshoot and collapse. In fact, in the thousands of model runs we have tried over the years, overshoot and collapse has been by far the most frequent outcome.

Opening Big Blue’s box (Nordhaus 1992)

Alternative growth paths and output and sensitivity to specification

[The LTG model is] a system of nonlinear difference equations, most of them being first-order. The system can be written succinctly as \[ Y_t = F \left( Y_{t-1}, Z_t, \beta \right) \] where … \(Y_t\) is the set of endogenous variables, approximately 150 in number …; \(Z_t\) represents the exogenous variables; and \(\beta\) represents the system’s parameters. (Nordhaus 1992)

  • hard to reason about such a complicated model
  • ‘distills’ an LTG model that can generate similar dynamics
  • finds four ‘lethal’ conditions, each leading to decline; LTG has all four
  • LTG’s “sensitivity runs” do not address any of the lethal conditions
  • policy: distilled model identifies critical parameter values

Fill in the blanks: replicating Nordhaus’ Figure 1

\(\theta_1\) \(\theta_2\) \(\xi_1\) \(\xi_2\) \(L_0\) \(Y_0\)
Case \(\theta_1\) \(\theta_2\) \(\xi_1\) \(\xi_2\) \(L_0\) \(Y_0\)
A \(1.04\) \(0.00\)
B \(3.50\) \(3.50\)
C \(4.00\) \(4.10\)

Three equation illustrative model:

  1. diminishing returns to labour, \(Y_t = \theta_1 L_{t-1} - \theta_2 L_{t-1}^2\)
  2. Malthusian population growth, \(B_t = \xi_1 + \xi_2 Y_t\)
  3. births become labour, \(L_t = B_{t-1}\)

How do markets work?

Trading posts (Shapley and Shubik 1977)

Decentralised trade

  • \(n\) traders, endowed with \(m\) goods, and money, \(a^i = \left( a^i_1, \ldots, a^i_m, a^i_{m+1} \right)\)

  • \(m\) trading posts, post \(k\) exchanges good \(k\)

  • each trader \(i\) submits to post \(k\):

    • \(b_{ik}\), money offered to buy good \(k\)
    • \(q_{ik}\), units of good \(k\) offered for sale

  • price at post \(k\) emerges from aggregate flows:

    \[p_k = \frac{\sum_i b_{ik}}{\sum_i q_{ik}}\]

  • takeaway: prices are an emergent property of decentralised strategic interaction

Theorem 1 (Shapley and Shubik 1977)

For each trader, \(i = 1, \ldots, n\) let \(u_i\) be continuous, concave, and nondecreasing. For each good, \(j = 1, \ldots, m\), let there be at least two traders with positive initial endowments of good \(m + 1\) whose utility for good \(j\) is strictly increasing. Then a noncooperative equilibrium exists.

Theorem 2 (Shapley and Shubik 1977)

Assume that for infinitely many values of \(k\) the market has a symmetric, interior Nash equilibrium, and let \(\hat{p}^{(k)}\) be the corresponding \(m\)-vector of prices. Let \(\tilde{p}\) be any limit point of the \(\hat{p}^{(k)}\), and define \(\tilde{p}_{m+1} = 1\). Then the \(m + 1\) prices \(\tilde{p}_i, \ldots, \tilde{p}_m, \tilde{p}_{m+1}\) will be competitive for the market (for any value of \(k\)); that is, an allocation \(x\) will exist for which \(\bar{\tilde{x}} = \bar{a}\) and, for each \(s\) and \(t\), \(\tilde{x}^{ts}\) maximizes \(u^t (x^{ts})\) subject to \(x^{ts} >\) 0 and \[ \sum_{j=1}^{m+1} \tilde{p}_j \left( x_j^{ts} - a_j^{ts} \right) = 0. \]

Gode and Sunder (1993): zero-intelligence traders (via LeBaron (2016))


  • 500 buyers, each with \(v_b \sim U[0, 200]\)
  • 500 sellers, each with \(c_s \sim U[0, 200]\)
  • each \(t\): randomly chosen trader submits random quote for one unit
  • quote trades against the best quote on the other side, becomes the new best quote if it improves on it, or fails
  • after crossing, both matched traders drop out
  • stop at \(t=\) 50,000
  • takeaway: don’t need profit-maximising traders or a market maker:
    • realises \(\approx 95\%\) of market surplus
    • 10-trade average price \(\rightarrow\) CE price
    • 10-trade price variance \(\rightarrow 0\)
  • is this surprising, given that extreme traders match early?
  • focus on allocative efficiency obscures huge inefficiencies in hit rate

Can we trade off inflation & unemployment?

Phillips’ curve: an exploitable trade off between inflation and unemployment

US unemployment vs. inflation, 1960–1969
  • Phillips (1958): low unemployment \(\Leftrightarrow\) high wage growth stable for a century in the UK
  • Samuelson and Solow (1960) extend it to prices: lower unemployment \(\Leftrightarrow\) higher inflation
  • takeaway
    1. clear theory: low unemployment makes workers scarcer \(\Rightarrow\) higher wages, prices
    2. clear empirics: three different specifications all show a negative relationship
  • policy
    1. use fiscal/monetary policy to reach your preferred \(\left( u, \pi \right)\) pair
    2. e.g. print money \(\Rightarrow\) high inflation \(\Rightarrow\) lower unemployment

The trouble with normal… (Cockburn 1983)

The Phillips loop, 1960–1984
  • in practice
    • increased US government spending, oil shocks and end of gold standard \(\Rightarrow\) higher inflationary expectations
    • expecting inflation, people increased their prices/wages, creating inflation
  • in theory
    • Lucas (1976) critique: when policy changes, agents change their behaviour: estimated relationships are not structural (q.v. Goodhart’s Law)
    • curves fit to data are not structural: Phillips’ trade-off changes with expectations
  • takeaway: a model that fits is not necessarily a model you can use for policy
  • policy: Volcker recession

Economic agents form (forward-looking) expectations

Expectations-augmented Phillips curves (\(\pi^e = \bar{\pi}\), the sample mean)
  • Friedman (1968), Phelps (1968): bargain over real wages, using expected inflation \(\pi^e\)
  • naïve Phillips curve: \(\pi = \beta_0 - \beta_1 u\)
  • expectations augmented (Blanchard 2017): \(\pi =\) \(\pi^e\) \(-\, \beta (u -\) \(u^\ast\) \()\)
  • policy
    • higher \(\pi\) to fight \(u\) may increase \(\pi^e\)
    • \(\pi^e = \pi \Rightarrow u = u^\ast\), no long-run policy trade-off
  • takeaways
    1. rational expectations agents are as intelligent as we are
    2. fixed points, rather than just simultaneous equations (Fair 2015; Sargent 2022)
    3. latent/structural variables: \(\pi^e, u^\ast\)

Learning to control a macroeconomy with explore = 0

actual: \(\left( u, \pi \right) \approx \left( 6.125, 5.279 \right)\)

  • four equation vector autogression (Sims 1980)
  • fitted values at \(t\) solved given actual \(t-1\) data
  • policy: Taylor rule extracted from VAR \(i_t = 0.3944 + 0.0205 \pi^{core}_t - 0.0504 u_t + 0.9746 i_{t-1}\)

counterfactual: \(\left( u, \pi \right) \approx \left( 6.134, 5.110 \right)\)

  • policy maker observes 5 months of real data
  • each subsequent month
    1. uses actual Taylor rule to respond
    2. fits VAR with OLS to counterfactual data

How to break heterogeneity (if you must)

Geanakoplos et al. (2012)

  • 2012: 55 mn mortgages in the US
  • in almost all, the borrower has option to prepay: “Prepayments radically change the cash flows and valuation of the mortgages to the holder”
  • “tremendous heterogeneity, and a small number of transactions per month”
  • Kidder Peabody/Ellington “model began as a conventional aggregate model and evolved into an agent-based model, even before detailed loan level information became available”
  • conventional aggregate approach \[\text{prepay} \left( t \right) = f \left( \text{age} \left( t \right), \text{seasonality} \left( t \right), \text{old rate} - \text{new rate} \left( t \right), \text{burnout} \left( t \right), \boldsymbol{\theta} \right)\]

In sample: 1986-96; out-of-sample 1996-99

With a relatively small number of parameters one can closely fit thousands of data points, including all coupons issued either by Fannie or Freddie each year since 1986.

  • ABM, each mortgage-holder
    • has cost of prepayment, \(\boldsymbol{c}\); alertness parameter, \(\boldsymbol{a}\)
    • knows its \(\boldsymbol{c}, \boldsymbol{a}\), chooses prepayment optimally given “expectations implied by the derivatives market”
    • unlike in conventional approach, burnout emerges automatically
    • smart factor: \(\downarrow \boldsymbol{c}, \uparrow \boldsymbol{a}\) “as prepayment behavior becomes more rational”
    • contagion parameters: “as prepayments increase, alertness rises in subsequent months”

How should taxes balance equity & efficiency?

Optimum income taxes balance equity and efficiency (Mirrlees 1971)

  • government wants ‘first best’ non-distortionary taxes, redistributing from able to less able
  • asymmetric information: government can’t see ability, \(a\), only income, \(a \times l\), where \(l\) is labour
  • thus, must use distortionary taxes on income: high \(a\) workers can act as if they are lower \(a\) by working less
  • agent solves \[\max_{l \in [0, 1)]} u \left( c, l \right) \text{ s.t. } c = a \times l - \tau \left( a \times l \right)\] where \(c\) is consumption and \(\tau \left( \cdot \right)\) a tax schedule
    • \(\frac{\partial u}{\partial c} > 0, \frac{\partial u}{\partial l} < 0\) and other technical conditions…
  • government knows the density, \(f \left( a \right)\), so solves \[\max_{\tau \left( \cdot \right)} \int G \left( u \left( c, l \right) \right) f \left( a \right) da \quad \text{ s.t. } \begin{align*} \int \tau \left( a \times l \right) f \left( a \right) da \ge E, \\ a \left( 1 - \tau' \right) u_c + u_l = 0 \end{align*}\] for some increasing, concave function \(G \left( \cdot \right)\) and revenue requirement \(E\)
  • policy: tax rate \(\tau' \left( \cdot \right) \in \left[ 0, 1 \right]\), no one will work at \(> 100\%\) marginal tax rate

Minecraft disguised as two-level reinforcement learning (Zheng et al. 2022)

  • multi-dimensionality heterogeneity: build-skill, proximity to resources
  • tax revenue is evenly returned to the agents
  • reinforcement learning
    1. agents learn to move, trade, earn coins, build
    2. government learns tax policy
  • parameters calibrated (not 1:1!) to US data
  • \(>\) 1bn training steps for \(n \le 10\) agents
  • robust to Lucas critique: parties learn optimal policies, not just curve fitting
  • higher welfare than benchmarks
  • weird tax schedule: how robust to misspecification?
  • policy: “it is not possible to provide an intuitive explanation of these AI tax schedules”
  • takeaways: RL can play more than just Atari?

MIT researchers with SOTA computers, II

Large population models (Chopra 2025)

Many of society’s most pressing challenges … emerge from the collective behavior of millions of individuals making decisions over time. [LPMs] offer an approach to understand these complex systems by simulating entire populations with realistic behaviors and interactions at unprecedented scale.

  • \(N\) agents, each with state \(\boldsymbol{s}_i \left( t \right)\) and environment \(e \left( t \right)\)
  • \(m_{ij} \left( t \right)\) is the message that \(i\) receives from \(j\) at time \(t\)
  • \(l \left( \cdot \mid \boldsymbol{s}_i \left( t \right) \right)\) is agent \(i\)’s behaviour at time \(t\); function addresses Lucas critique
  • \(\boldsymbol{\theta}\) denotes model parameters
  • at time \(t\), state and environment update according to \[ s_i \left( t+1 \right) = f \left( \boldsymbol{s}_i \left( t \right), \bigotimes_{j \in \boldsymbol{N}_i \left( t \right)} m_{ij} \left( t \right), l \left( \cdot \mid \boldsymbol{s}_i \left( t \right) \right), e \left( t; \boldsymbol{\theta} \right) \right), \quad e \left( t+1 \right) = g \left( \boldsymbol{s} \left( t \right), e \left( t \right), \boldsymbol{\theta} \right) \]
  • aggregate outcomes, \(\boldsymbol{x}_t = h \left( \boldsymbol{s} \left( t \right) \right) \Rightarrow\) simulation, \(\boldsymbol{x} = F \left( \boldsymbol{\theta}, \boldsymbol{s} \left( 0 \right), \boldsymbol{e} \left( 0 \right) \right)\)
  • calibration: find \(\hat{\boldsymbol{\theta}}\) so that simulation outputs are consistent with observed data
  • analysis: “understand system dynamics, explore counterfactuals, and inform decision-making”

COVID-19 in NYC: “What if we give stimulus checks?” (Chopra 2025)

Modeling 8.4mn agents over 90 steps for US$500
  • \(N = 8.4\)mn
  • “recreational and workplace mobility parameterized using Google Mobility trends” > NYC health officials received diverse data streams—clinical reports from hospitals, mobility patterns from cell phones, economic indicators from government agencies, and survey data on compliance behaviors—each with different granularity, reliability, and privacy constraints.
  • representative agent archetypes to overcome scale problem with LLM prompts; probabilistic sampling introduces further heterogeneity
  • assertion: “LPMs enable more accurate predictions, more efficient policy evaluation, and more seamless integration with real-world systems.”
  • policy: ???

Measuring skills exposure in the AI economy (Chopra et al. 2025)

Built on MIT’s Large Population Models, and powered by Oak Ridge National Laboratory’s Frontier supercomputer, Iceberg turns trillions of workforce data points into scenario-planning capability.

  • inputs
    1. 150,000 attributes \(\times\) 151 mn US workers
    2. 13,000+ AI workforce
    3. 2.5 bn human-AI interactions
  • outputs
    1. Surface Index: tech sector exposure
    2. Iceberg Index: white-collar exposure
  • validation
    1. skill-based: similarity scores of O*NET occupational profiles embeddings achieve 85% recall predicting actual career transitions
    2. adoption: compare Surface Index exposure to Anthropic Economic Index usage
    • “validation is correlational rather than causal”

Conclusions?

Discussion: what do we conclude from this?

  • ice breakers?
    1. degrees of freedom, overfitting, regularisation (Andrews et al. 2025)?
    2. robustness, misspecification, incentive compatibility, Stiglitz (1996)
    3. computational power v mathematical skill \(\approx\) propositional logic v HOL?

Each realization of an ABM is a sufficiency theorem (Newell and Simon 1972): IF agents start with certain initial states, \(S\), and engage in specific behaviors, \(B\), THEN after some number of interactions, \(N\), they will have definite new states, \(S' = B(S, N)\); \((S, B, N)\) are sufficient to produce \(S'\). … Theorems of this type have limited generality, but by making many runs of a specific model and allowing random seeds or other stochastic elements to vary … the generality of the model results can be assessed and distribtional properties of agent states characterized. (Axtell and Farmer 2025)

  • loose ends
    1. better illustration of fixed point (existence, uniqueness) v iterative
    2. arbitrage opportunities against naive agents?
    3. systemic risk: what does ABM (e.g. §2.2.4, Axtell and Farmer (2025)) do that e.g. Shin (2010) doesn’t?

Tutorial

Replicating the Iceberg Index’ adoption validation

AEI usage
leading emerging aspiring
II exposure leading \(8\) \(9\)
emerging \(18\)
aspiring \(6\) \(9\)
  1. how hard is it to replicate this pattern
    1. as \(3 \times 3\) matrix?
    2. as full ranking?
  2. what should the alignment of usage and exposure be?
state AEI usage
leading (AEI: leading) Washington, DC \(4.30\)
Massachusetts \(1.60\)
Washington \(1.58\)
New York \(1.57\)
California \(1.55\)
Colorado \(1.49\)
Virginia \(1.29\)
Utah \(1.26\)
Wyoming \(1.16\)
Maryland \(1.06\)
Hawaii \(1.05\)
Oregon \(1.05\)
Connecticut \(1.03\)
- —————- ——–
emerging (AEI: upper/lower middle) Vermont \(1.02\)
New Hampshire \(1.00\)
Rhode Island \(1.00\)
Illinois \(0.97\)
Georgia \(0.96\)
New Jersey \(0.96\)
North Carolina \(0.94\)
Florida \(0.91\)
Pennsylvania \(0.91\)
Texas \(0.87\)
Arizona \(0.86\)
Delaware \(0.81\)
Nevada \(0.83\)
Minnesota \(0.81\)
Idaho \(0.68\)
Michigan \(0.68\)
Tennessee \(0.68\)
Indiana \(0.66\)
Ohio \(0.66\)
Nebraska \(0.66\)
Maine \(0.65\)
Kansas \(0.64\)
Missouri \(0.64\)
Wisconsin \(0.64\)
Montana \(0.52\)
Iowa \(0.47\)
- —————- ——–
aspiring (AEI: emerging) Alaska \(0.51\)
Oklahoma \(0.50\)
Alabama \(0.49\)
South Carolina \(0.48\)
Louisiana \(0.47\)
New Mexico \(0.46\)
Kentucky \(0.42\)
Arkansas \(0.41\)
South Dakota \(0.39\)
North Dakota \(0.37\)
Mississippi \(0.28\)
West Virginia \(0.28\)

etc.

  1. has this sparked any thoughts? Can we explore those?
  2. replicate Nordhaus Figure 1
  3. is Schelling implementation right?
  4. is my explore = 0 slide right?

References

References

Andrews, Isaiah, Drew Fudenberg, Lihua Lei, Annie Liang, and Chaofeng Wu. 2025. The Transfer Performance of Economic Models. https://arxiv.org/abs/2202.04796.
Arrow, Kenneth J. 1973. “The Theory of Discrimination.” In Discrimination in Labor Markets, edited by Orley Ashenfelter and Albert Rees. Princeton University Press.
Arrow, Kenneth J., and Gerard Debreu. 1954. “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 (3): 265–90.
Athey, Susan. 2013. Interview with Susan Athey: Stanford Economist on Optimal Auctions, Better Models and the Future of Big Data. Interview, The Region, Federal Reserve Bank of Minneapolis. https://www.minneapolisfed.org/article/2013/interview-with-susan-athey.
Axtell, Robert L., and J. Doyne Farmer. 2025. “Agent-Based Modeling in Economics and Finance: Past, Present, and Future.” Journal of Economic Literature 63 (1): 197–287.
Baumol, William J. 1984. “On My Attitudes: Sociopolitical and Methodological.” The American Economist 28 (1): 5–9.
Blanchard, Olivier. 2017. Macroeconomics. 7th Global Edition. Pearson Education.
Chopra, Ayush. 2025. “Large Population Models.” arXiv Preprint arXiv:2507.09901.
Chopra, Ayush, Santanu Bhattacharya, DeAndrea Salvador, et al. 2025. “The Iceberg Index: Measuring Skills-Centered Exposure in the AI Economy.” arXiv Preprint arXiv:2510.25137, November.
Cockburn, Bruce. 1983. The Trouble with Normal. True North Records.
Fair, Ray C. 2015. “Reflections on Macroeconometric Modeling.” The B.E. Journal of Macroeconomics 15 (1): 445–66.
Fang, Hanming, and Andrea Moro. 2011. “Theories of Statistical Discrimination and Affirmative Action: A Survey.” Handbook of Social Economics 1: 133–200.
Friedman, Milton. 1953. “The Methodology of Positive Economics.” Chap. 1 in Essays in Positive Economics. University of Chicago Press.
Friedman, Milton. 1968. “The Role of Monetary Policy.” American Economic Review 58 (1): 1–17.
Geanakoplos, John, Robert Axtell, J. Doyne Farmer, et al. 2012. “Getting at Systemic Risk via an Agent-Based Model of the Housing Market.” American Economic Review 102 (3): 53--58.
Gilboa, Itzhak, Andrew Postlewaite, Larry Samuelson, and David Schmeidler. 2014. “Economic Models as Analogies.” The Economic Journal 124 (578): F513–33.
Gode, Dhananjay K., and Shyam Sunder. 1993. “Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality.” Journal of Political Economy 101 (1): 119–37.
Kreps, David M. 1997. “Economics: The Current Position.” Daedalus 126 (1): 59–85.
LeBaron, Blake. 2016. “Zero Intelligence Traders: Gode and Sunder (1993).” Brandeis University. https://people.brandeis.edu/~blebaron/classes/agentfin/GodeSunder.html.
Lucas, Jr., Robert E. 1976. “Econometric Policy Evaluation: A Critique.” In The Phillips Curve and Labor Markets, edited by Karl Brunner and Allan H. Meltzer, vol. 1. Carnegie-Rochester Conference Series on Public Policy. North-Holland.
Meadows, Donella H., Dennis L. Meadows, and Jørgen Randers. 1992. Beyond the Limits: Global Collapse or a Sustainable Future. Chelsea Green Publishing.
Mirrlees, James A. 1971. “An Exploration in the Theory of Optimum Income Taxation.” The Review of Economic Studies 38 (2): 175–208.
Newell, Allen, and Herbert A. Simon. 1972. Human Problem Solving. Prentice-Hall.
Nordhaus, William D. 1992. “Lethal Model 2: The Limits to Growth Revisited.” Brookings Papers on Economic Activity, no. 2: 1–43.
Phelps, Edmund S. 1968. “Money-Wage Dynamics and Labor-Market Equilibrium.” Journal of Political Economy 76 (4, Part 2): 678–711.
Phelps, Edmund S. 1972. “The Statistical Theory of Racism and Sexism.” The American Economic Review 62 (4): 659–61.
Phillips, A. W. 1958. “The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957.” Economica 25 (100): 283–99.
Samuelson, Paul A. 1967. “Prudent Investment, I.” Newsweek, July 24, 67.
Samuelson, Paul A., and Robert M. Solow. 1960. “Analytical Aspects of Anti-Inflation Policy.” American Economic Review 50 (2): 177–94.
Sargent, Thomas J. 2022. “Learning from Lucas.” Journal of Economic Methodology 29 (1): 17–29.
Schelling, Thomas C. 1971. “Dynamic Models of Segregation.” Journal of Mathematical Sociology 1 (2): 143–86.
Shapley, Lloyd, and Martin Shubik. 1977. “Trade Using One Commodity as a Means of Payment.” Journal of Political Economy 85 (5): 937–68.
Shin, Hyun Song. 2010. Risk and Liquidity. Clarendon Lectures. Oxford University Press.
Sims, Christopher A. 1980. “Macroeconomics and Reality.” Econometrica 48 (1): 1–48.
Stigler, George J. 1950. “The Development of Utility Theory. II.” Journal of Political Economy 58 (5): 373–96.
Stiglitz, Joseph E. 1996. Whither Socialism? MIT press.
Zheng, Stephan, Alexander Trott, Sunil Srinivasa, David C. Parkes, and Richard Socher. 2022. “The AI Economist: Taxation Policy Design via Two-Level Deep Multiagent Reinforcement Learning.” Science Advances 8 (18): eabk2607.

Some stray quotes

Anecdotes do not constitute social science. (Samuelson 1967)

It is always easy and usually sterile to introduce a new variable into a system, which then becomes more general. (Stigler 1950)

the need for theory is in some ways magnified by having large amounts of data. When you have a small amount of data, you can just look at the data and build your intuition from it. When you have very large amounts of data, just taking an average can cost thousands of dollars of computer time. So you’d better have an idea of what you’re doing and why before you go out to take those averages. (Athey 2013)

In the fall of 1970, I wrote a four-page note on testing the accelerationist hypothesis about the Phillips curve. I gave a copy to Ed Prescott who had an office two doors down the hall. Ed returned to my office the next day, set the paper on my desk, and said “there are two definitions of rational expectations, yours and Lucas’s”. Then he walked back to his office. That was a long conversation for Ed. I had no idea about what Ed meant, and having little confidence in myself technically, I took it to mean that Ed thought that what I had written was mistaken and that I should learn more before trying to write something. Fair enough. Years later, while jogging, I suddenly understood what Ed had told me: Lucas had defined a rational expectations equilibrium as a fixed point in a space of functions of Markov state vectors, while I had defined it as a fixed point in a space of stochastic processes (i.e. random sequences indexed by time). Both perspectives are useful. Ed saw that immediately and had not meant to insult me, or at least that is what I now think. (Sargent 2022)

  1. THE CRITERION OF GENERALITY: The successful theory was always more general than the theory it supplanted.
  2. THE CRITERION OF MANAGEABILITY: ... Economists long delayed in accepting the generalized utility function because of the complications in its mathematical analysis, although no one ... questioned its realism. ... economists tacitly agreed that it is better to have a poor, useful theory than a rich, useless one. ... Manageability should mean the ability to bring the theory to bear on specific economic problems, not ease of manipulation.
  3. THE CRITERION OF CONGRUENCE WITH REALITY: ... It was required of a new theory that it systematize and 'explain' a portion of the empirical knowledge of the times. ... Not only were such specific implications not sought and tested, but there was a tendency, when there appeared to be the threat of an empirical test, to reformulate the theory to make the test ineffective.

(Stigler 1950)

economics, at least as practiced by mainstream economists, is a field that values tradition. If phenomenon \(X\) can be explained within the standard canon, such an explanation is usually preferred to another explanation that ventures outside the canon because, given our relative paucity of data, adherence to canonical assumptions provides us with a measure of discipline. (Kreps 1997)

A well-designed model is, after all, a judiciously chosen set of lies, or perhaps more accurately put, partial truths about reality, which have been chosen so as to permit us to reason more effectively about some issue than we otherwise could. The model must be an oversimplification if it is to be tractable analytically. Optimality in model construction must be based on the trade-off between these two desiderata – accuracy of representation of reality and usability in analysis. Two conclusions follow from these observations. First, increased realism is not necessarily a virtue. Indeed, if it complicates the model to a degree that effectively precludes its use in analysis, it deserves to be treated as a mortal sin. The second conclusion that follows is that a particular model can neither be judged good nor bad in the abstract. Only when related to the issue for whose analysis it is meant to be used can one judge its quality. A model which is admirably suited for the analysis of one such issue may be ill-adapted to another. (Baumol 1984)

People often wonder why economists analyse models whose assumptions are known to be false, while economists feel that they learn a lot from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyse models that are ‘theoretical cases’, which help understand economic problems by drawing analogies between the model and the problem. Thus, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice and why economists prefer simple cases. (Gilboa et al. 2014)

Rule-based reasoning has several advantages over case-based reasoning. First, a rule is a concise description of a regularity, compared with a large and ever-growing database of cases that conform to this regularity. Second, formulating a small set of general rules gives people a feeling of understanding and explaining a phenomenon in a way that a database of cases does not. Thus, even if the two methods perform equally well in terms of prediction, there is a preference for rule-based approaches, and one is often willing to sacrifice some accuracy of prediction in return for the compactness of rules. (Gilboa et al. 2014)

  • generative versus discriminative: “Rule-based reasoning is akin to learning a distribution function, whereas case-based reasoning is related to data-based methods such as kernel estimation and nearest-neighbour approaches.” (Gilboa et al. 2014)