Experimental MathematicsJeff Kline · Interactive

Economics Nobel 2026 · Explored with AI

Stabilizing the economy through expectations

Published · Updated · Version 1.6

A central bank can help stabilize the economy through expectations. Even when today’s interest rate can’t go any lower, a promise about what the bank will do later can raise spending now, if people believe it. That is a result of the models behind this year’s Nobel Prize in economics, awarded to Robert E. Hall and Michael Woodford: households and firms plan ahead, so what they expect about the future shapes what they spend today.

Much of today’s news is about expectations, from AI’s impact on work to tariffs and oil supply shocks, which makes this work feel especially relevant.

I don’t have a background in economics, and it wasn’t obvious to me how expectations connect to policy, so I built this page to make that connection clear, at least in a small way, and to sharpen my own thinking. I directed the work and edited the prose heavily, collaborating with AI on research, code and drafting. The charts are computed from two small models, a household planner and a three-equation model of the economy, whose math and code are written out below; the original sources are at the end. I welcome corrections from people who know this field.

Here is the case I started with: a recession is bad enough that the central bank has already cut its rate to zero, the floor in this model. It can’t cut any further, so it promises to keep the rate at zero for a while after the slump ends. The chart below compares three versions of this case.

No extra time at zeroNo extra time at zero

In all three: the same 18-month slump, with the rate at zero throughout.

Illustrative model results. Models like this one make promises too powerful, and the size of the effect depends on assumptions I chose. See the limits.

What this has to do with the Nobel Prize

Robert E. Hall and Michael Woodford won for connecting the decisions of households and firms to central-bank policy. Hall showed how to test whether households respond to news about their income the way a careful planner would. Woodford built models that combine households’ spending with firms’ pricing, and used them to ask what a central bank should do.

The explanation starts with a single household deciding what to spend. This textbook example follows one thread of that work, forward guidance: changing spending today by changing what people expect the bank to do later. The prize covers much more. The Academy’s introduction tells the wider story.

The result depends on people believing what the bank will do later. The Academy’s scientific background notes that the model presumes an independent central bank, or at least one able to commit to a rule, though the analysis itself does not require independence. The older argument for independence comes from Kydland and Prescott’s work on why commitments are hard to keep, which won the 2004 prize.

A raise you know is coming

Suppose that at 35 you learn your pay will rise by $10,000 a year starting at 40. Would you spend more now, or wait for the money?

A simple way to see the idea behind Hall’s test is a planner who spreads what they expect to earn evenly over the rest of their life. For that planner, spending moves as soon as the news arrives, years before the paycheck changes. A pay cut would work the same way in reverse, though people seem to respond to cuts and raises differently; what the model leaves out covers that research.

The chart below shows this for someone who, without the change, earns $50,000 a year from 25 to 64 and then $20,000 through 85. Each line is a change from that original plan: red for the planner’s spending, blue for income. Someone who spends each paycheck as it arrives would follow the blue line.

An income gain

change in the planner’s yearly spending

Change in planned spendingChange in income

Model predictions. Zero means no change from the original plan.

Spending can move before income because the planner has savings. Before a known raise, the planner saves less. Someone without savings or credit may have to wait for the raise before spending more. Over a lifetime, each household in this example spends exactly what it earns.

What Hall tested

Friedman and Modigliani developed the idea of spreading income over a lifetime in the 1950s. Hall’s 1978 paper gave it a test: under his simplifying assumptions, information people already have should not predict their next change in spending. Only news can change the plan.

Hall and Mishkin’s 1982 study fitted a model to families’ food spending. In their estimate, about 80% of that spending followed lifetime income and the rest tracked current income. That is an estimate from their model and sample, not a fixed split in the population. Living paycheck to paycheck can reflect a lack of savings or credit.

As a separate illustration, suppose 80% of households follow the planner’s rule and 20% spend each paycheck as it arrives. Then an unexpected one-time $10,000 gain at 40 raises average spending that year by about $2,200. That number is a model calculation, not their empirical result.

Steering through a slump

Woodford’s model puts planners like the one above into a whole economy, along with firms that change their prices only now and then. Below are five scenarios for the same slump as the opening experiment, each with a different policy. From scenario 2 on, a dashed line shows another scenario for comparison, and the legend names it. Output is everything the economy produces; zero means its normal level.

Scenario 1 of 5

A slump begins

Something makes households cautious, and they spend less. For 18 months, the interest rate that would keep spending at its normal level, called the neutral rate, falls from its usual 1% to −5%. It is a real rate, so it already allows for inflation. Everyone in this example knows when the slump will end.

Suppose the bank leaves its rate at its normal 3%. In these conditions saving pays too well and borrowing costs too much. Spending falls, firms sell less, and at its worst output is 9.5% below normal. Inflation falls below the 2% target.

This is a slump in demand. An energy shortage or another supply problem would need a different example.

Illustrative model results. The chart scales stay fixed across all five scenarios.

The general model: set your own policy

Here is the general model, with more settings to change and test: the size of the slump, the bank’s rate during it, how long the promise lasts, and whether people believe it. One goal of a central bank is holding inflation steady; other goals can also drive its policy. The dashed line is always the slump you chose, with the bank holding its rate at 3%.

Your policyHolding the rate at 3%

Size of the slump: the drop in the neutral real rate, in percentage points, for 18 months.

Rate during the slump: the quoted annual rate. 3% is normal; zero is the floor here.

Promise to hold it: extra quarters at that rate after the slump ends.

If people don’t believe the promise from the start, they expect normal policy after the slump. When the bank keeps its rate low anyway, they believe the rest of the promise.

Illustrative model results. The axes stay fixed, so every setting is drawn on the same scale.

What the model leaves out

The model

This is the three-equation New Keynesian model as written in the Academy’s scientific background, with time measured in quarters. Here y is the output gap in percent, π inflation, i the policy rate and rn the neutral rate, all as departures from normal in percentage points per quarter. The charts show rates per year: four times the quarterly departure, plus the normal level. Et marks what people expect in quarter t about the next quarter. When a promise is believed, that is what happens; when people doubt it, the two differ until it takes effect.

yt=Etyt+1−1σ(it−Etπt+1−rtn)
πt=βEtπt+1+κyt
it=ϕππt+ϕyyt

I use σ = 1, β = 0.99 and κ = 0.01. σ sets how strongly spending responds to the real interest rate (a larger σ means a weaker response), β is how much people discount the next quarter, and κ is how strongly inflation responds to output. The usual textbook β and the 1% normal real rate are separate illustrative choices, not a calibrated pair. The third equation is the bank’s usual rule, the Taylor rule: ϕπ = 1.5 is how much the rate rises for each point of inflation above target, and ϕy = 0.5 for each point of output above normal, both stated on annual rates. During the slump and any promise, the rule is replaced by the chosen rate. The rule never goes below the floor. Once the slump starts, everyone knows how long it will last. I solve the 60-quarter path as one linear system, with the economy back to normal at the end, and recheck which quarters the floor binds until the answer stops changing. A promise people doubt until it takes effect is solved twice: first with people expecting the usual rule after the slump, then again from the end of the slump, when the bank keeps its promise and people believe the rest of it. The output shortfall adds up the quarters below normal, as a share of a normal year’s output; a later boom does not offset it.

Read the JavaScript solver

The model runs locally in plain JavaScript. The code below is the same engine used by every experiment on this page. It solves the spending and inflation equations together, subject to the chosen policy and the interest-rate floor.

How this page was checked

Before publishing, I had separate AI reviewers check the work. One rebuilt the solver independently and compared it with this page at all 2,704 slider settings; another checked the text against the cited papers. They found eight corrections, which are applied here. These were AI reviews, not review by an economist, and they check that the page computes its stated model, not that the model describes a real economy. A public standard for this work describes how I check AI-assisted work.

I directed this work, using AI to read the background papers, build the models and draft text. I rejected early versions, asked for major changes, and edited the writing for accuracy and voice. This is an attempt to understand existing work, not new research. Where a summary here and a source below disagree, trust the source.

Further reading

  1. Royal Swedish Academy of Sciences, Microfoundations deliver macro insights, popular science background, October 2026. The best short account of the prize.
  2. Royal Swedish Academy of Sciences, Microeconomic foundations of macroeconomic stabilization, scientific background, October 2026. The three equations above, and the forward guidance puzzle.
  3. F. E. Kydland and E. C. Prescott, Rules rather than discretion: the inconsistency of optimal plans, Journal of Political Economy 85(3) (1977), 473–491. doi:10.1086/260580. Why a policymaker’s promises can be hard to keep.
  4. R. E. Hall, Stochastic implications of the life cycle–permanent income hypothesis: theory and evidence, Journal of Political Economy 86(6) (1978), 971–987. doi:10.1086/260724. A test of whether spending changes can be predicted under the model’s assumptions.
  5. R. E. Hall and F. S. Mishkin, The sensitivity of consumption to transitory income: estimates from panel data on households, Econometrica 50(2) (1982), 461–481. doi:10.2307/1912638. Evidence on food spending and responses to temporary and lasting income changes.
  6. M. Woodford, Interest and prices: foundations of a theory of monetary policy, Princeton University Press (2003). The full model and its case for rules and communication.
  7. G. B. Eggertsson and M. Woodford, The zero bound on interest rates and optimal monetary policy, Brookings Papers on Economic Activity 2003(1). How a credible promise of later low rates can help when the current rate is at its floor.
  8. M. Del Negro, M. P. Giannoni and C. Patterson, The forward guidance puzzle, Journal of Political Economy Macroeconomics 1(1) (2023), 43–79. Why the basic model makes promises too powerful.
  9. J. Galí, Monetary policy, inflation, and the business cycle, 2nd edition, Princeton University Press (2015). A textbook treatment of the same model.
  10. A. Fuster, G. Kaplan and B. Zafar, What would you do with $500? Spending responses to gains, losses, news, and loans, Review of Economic Studies 88(4) (2021), 1760–1795. doi:10.1093/restud/rdaa076. Survey evidence on different responses to good and bad news.
  11. A. McKay, E. Nakamura and J. Steinsson, The power of forward guidance revisited, American Economic Review 106(10) (2016), 3133–3158. doi:10.1257/aer.20150063. How borrowing limits and income risk weaken promises about the distant future.
  12. R. S. Gürkaynak, B. Sack and E. T. Swanson, Do actions speak louder than words? The response of asset prices to monetary policy actions and statements, International Journal of Central Banking 1(1) (2005), 55–93. Evidence that the Federal Reserve’s statements about future policy move long-term rates.
  13. O. Coibion, D. Georgarakos, Y. Gorodnichenko and M. Weber, Forward guidance and household expectations, Journal of the European Economic Association 21(5) (2023), 2131–2171. doi:10.1093/jeea/jvad003. A survey experiment on how households respond to information about future rates.
  14. I. A. Duca, G. Kenny and A. Reuter, Inflation expectations, consumption and the lower bound: micro evidence from a large euro area survey, ECB Working Paper 2196 (2018). Survey evidence that people who expect higher inflation are more likely to make major purchases, especially when rates are at the floor.
  15. N. Bloom, S. Bond and J. Van Reenen, Uncertainty and investment dynamics, Review of Economic Studies 74(2) (2007), 391–415. doi:10.1111/j.1467-937X.2007.00426.x. Why uncertainty can make firms wait.
  16. K. Handley and N. Limão, Trade and investment under policy uncertainty: theory and firm evidence, American Economic Journal: Economic Policy 7(4) (2015), 189–222. How credible commitments about future trade policy affect firms.