Walras’ Road to Objectivity

Economists often cite US President Truman’s famous adage: “Give me a one-handed economist! All my economists say ‘on the one hand… [and then] on the other.’”? To many in the profession, President Truman’s critique exemplifies economists’ virtues: Economists, like no other social scientists, recognize trade-offs. The trouble is that the public often doubts economists’ objectivity. After the Brexit vote in the UK, a YouGov survey found that only 21% of respondents believed economists’ comments were based on “mainly verifiable data and analysis”. A plurality thought their interventions reflected “personal opinions” or “political opinions or affiliations.” Take note: the issue isn’t the opinions economists hold, but whether they are grounded in verifiable data and analysis or driven by sentiment.

To see where sentiment can lead, consider this: According to a recent AEA survey of US-based economists, 77.7% disagreed with the statement, ‘The distribution of income and wealth has little, if any, impact on economic stability and growth.’ This is a reasonable stance, supported by research linking wealth or talent distribution to labour supply and consumption behaviour. For instance, a study of Swedish lottery winners reveals that labour supply decreases as wealth rises, while (in line with heterogeneous agent models) the propensity to consume is highest among lower-wealth households. Unfortunately, the same survey found that 56.8% of respondents also agreed with the statement, ‘Macro models based on the assumption of a “representative, rational agent” yield generally useful and reasonably accurate predictions.’ These two beliefs are difficult to reconcile. If the wealth distribution affects growth rates, then models relying on averages are inaccurate. Agreeing with both positions suggests incoherence. Worse, the overlap in responses implies that at least a third of the profession (0.777 + 0.568 – 1 = 0.345) may be guilty of contradictory thinking.

In recent years, economic theorists have increasingly explored models that incorporate misspecified beliefs (see work by Paul Heidhues, Botond Kőszegi, Philipp Strack) and false narratives (see work by Kfir Eliaz and Ran Spiegler). These models suggest that agents interpret economic data—such as inflation or labor supply—through faulty or oversimplified causal models, leading to incorrect predictions even with abundant data. While I remain optimistic that, over time, people will overcome these errors, what if they do not? Many of my colleagues take these models extremely seriously. The notion that decision-makers are biased is widely held. If true, professional economists can be no exception to this rule. In that case, identifying economists with more accurate beliefs becomes paramount, particularly for soliciting policy advice.

Others have made this point before me. My colleagues tell me that the Queen was appalled when she visited the LSE after the financial crisis. She asked: ‘How could no one have anticipated the financial crisis?’ The common response among economists is: ‘Some did.’ To which I would retort: ‘What are we doing to elevate the voices of those who predicted it correctly? And are we giving less credence to the voices of those who were wrong? ‘ There is no system that raises or lowers reputations in line with predictive accuracy, unlike how personal wealth rises and falls in the investment market.

One possible solution is to establish a prediction market that directly links economists’ reputations to their success at predicting economic events.

Let me outline the key components of this idea. First, this prediction market would not exist for individual economists to profit, nor would it simply aggregate information. Existing prediction markets already do that. Rather, it would allow the public to identify economists whose beliefs about the economy are most accurate. Importantly, we would need to consider how to incentivize economists to participate—how to ensure that they are motivated to spend time making predictions and sharing those predictions publicly (rather than playing online chess).

Here’s how I would structure it:

Subscription Fee and Currency: Each user pays a modest yearly subscription fee of $2.71 (chosen in honour of Euler’s constant). Subscribers then receive a daily allotment of 74 (Hayek, who I venture would like the idea of prices revealing information in prediction markets, was awarded the Nobel Prize in 1974) virtual currency—“ndows”—which they can use to place bets on economic events. Unused ndows depreciate over time to encourage activity. Throughout the year, users can cash out their ndows at a fixed exchange rate: 100 ndwos are worth $0.01.

Betting on Economic Events: The core activity would involve making bets on binary events, like whether Germany will experience two consecutive recessions. These bets are modeled after Arrow-Debreu securities, which allow economists to “go long” (betting the event will happen) or “short” (betting the event won’t happen) at any given time.

Sharpe Ratio as a Betting Score: To measure predictive accuracy, we could use a metric similar to the Sharpe ratio, which is commonly used in finance to measure the return of an investment relative to its risk. In this context, it would help assess an economist’s accuracy in predictions—higher scores indicating more accurate forecasts, while lower scores suggest errors in judgment.

Will this market design restore economists’ reputation? Over time, yes. The improvement of policy advice will be even more crucial. Let me be specific: some economists sit on the monetary policy committee to decide whether to raise nominal interest rates; others serve as arbiters in decisions about VAT on private schools or increasing employer social security contributions; still others use game theory to advise on national security matters. These are serious questions. With prediction markets stepping in, I believe it’s less likely that such critical decisions will be left to the whims of some “defunct economists.” And if they are, prediction markets can help shorten their tenure.

A few afterthoughts: Yes, I’ve tasted my own medicine. If there was ever a year to test one’s crystal ball, this was it—mine even predicted the Republican vice-presidential pick correctly. That said, I want to make clear that I’m not encouraging gambling. What I’m advocating for is this: while gambling can be ruinous, making well-calibrated bets on behalf of the public is a virtue of public office. The key is getting advice from the right people, and that means looking for a track record. Now if someone could build the prediction market as outlined below, that would be quite something.

Technical Appendix: Prediction Market Design

1. Purpose of the Prediction Market

The primary goal of the proposed prediction market is to create a system that allows economists’ reputations to rise or fall based on their predictive accuracy. This is intended to provide a clearer, more objective mechanism for evaluating the beliefs of economists in the public domain, particularly those whose predictions influence policy decisions.

2. Market Design Overview

The market operates on a virtual currency called “ndows,” which can be used to place bets on various economic events. The betting is structured around binary events, such as whether a specific country will experience a recession or whether inflation will exceed a certain threshold.

  • Subscription and Currency Distribution:
    • Each user will pay a nominal yearly subscription fee of $2.71 (approximately Euler’s constant).
    • Subscribers receive a fixed daily allotment of 74 ndows (chosen in honour of Hayek’s 1974 Nobel Prize).
    • Unused ndows depreciate by 1% per day to encourage active participation.
    • At the end of the year, ndows can be cashed out at a fixed exchange rate: 100 ndows = $0.01.
  • Types of Bets:
    • Participants can place bets on binary economic events, such as:
      • Whether a country will experience two consecutive recessions.
      • Whether inflation will exceed a certain percentage in a given year.
      • Whether private school enrolment will drop below a certain threshold.
    • These bets are modeled on Arrow-Debreu securities, where participants can buy (long) or sell (short) bets based on their predictions of future events.

3. How Bets Work

In practice, trading will take place via limit-orders. This ensures that the platform never incurs any inventory risk. Buy orders specify a maximum bid price and sell orders a minimum ask price. We denote the strike price, i.e., the price at which trading takes place, P. Then 1/P is the current belief of the median market participant regarding the probability of the event occurring.

  • Long and Short Bets:
    • If an economist buys a long position at price P at time t, they are betting that the event will occur. If the event happens, they earn P – 1 in ndows; if the event does not happen, they lose 1.
    • Conversely, if an economist sells a short position at price P, they are betting that the event will not happen. If the event does not happen, they earn 1 in ndows; if the event happens, they lose P – 1.
  • Bet Adjustment and Cashing Out:
    • Bets can only be cashed out if the future inflow of ndows will cover the bettor’s liabilities with certainty.

4. Calculating Predictive Accuracy: The Sharpe Ratio

To evaluate economists’ predictive abilities, we will use a metric similar to the Sharpe ratio. In finance, the Sharpe ratio measures the performance of an investment by comparing its return to its volatility. Here, the Sharpe ratio will be used to measure how well an economist’s predictions have matched reality over time.

  • Sharpe Ratio Formula for Prediction Markets:
    The Sharpe ratio for an economist at time t is defined as:
\text{Sharpe ratio} = \frac{R_t}{\sigma_t}

Where:

  • R  is the weighted average return of the economist’s bets at time t.
  • σ​ is the weighted standard deviation of those returns.

5. Calculating Weighted Average Return

At any given time t, we calculate the weighted average return as follows:

R=\frac{\sum\limits_{n=1}^N \frac{q_t^n-q_{t_n}^n}{q^n_{t_n}}m^n}{\sum\limits_{n=1}^N |m^n|}.

Where:

  • q_t^n​ is the implied  probability of the event at time t (0 or 1 if resolved).
  • q_{t_n}^n​ is the implied probability at the time when the bet was made.
  • m^n is the position size (either positive for long bets or negative for short bets).
  • N is the total number of bets placed by the economist.

6. Calculating Weighted Standard Deviation

The weighted standard deviation at time t is given by:

\sigma=\sqrt{\frac{\sum\limits_{n=1}^N \big(\frac{q_t^n-q_{t_n}^n}{q^n}-R\big)^2 |m^n|}{\sum\limits_{n=1}^N |m^n|}}\sqrt{\frac{\sum\limits_{n=1}^N |m_n|}{ \sum\limits_{n=1}^N |m^n|-\frac{ \sum\limits_{n=1}^N |m^n|^2}{ \sum\limits_{n=1}^N |m^n|}}}

7. Final Ex-Post Sharpe Ratio

Finally, the ex-post Sharpe ratio for any economist at time t is:

\text{Sharpe ratio}= \frac{R}{\sigma}

A higher Sharpe ratio indicates that the economist has made more accurate predictions relative to their risk, while a lower ratio suggests that their predictions were less reliable.

8. Public Display of Results

Finally, to encourage accountability and transparency, we propose that economists publicly display their standings on their professional websites. This will provide a public mechanism for identifying the economists whose predictions have been the most accurate over time.