Yes, partisan bias in forecasting is consistent with rationality: a Bayesian approach

At a superficial glance, this paper challenges the notion of rationality inherent in standard economic models.

"Republican-affiliated forecasters project 0.3-0.4 percentage points higher growth when Republicans hold the presidency, relative to Democratic-affiliated forecasters. Forecast accuracy shows a similar partisan pattern: Republican-affiliated forecasters are less accurate under Republican presidents, indicating that partisan optimism impairs predictive performance. This bias appears uniquely in GDP forecasts and does not extend to inflation, unemployment, or interest rates."

Leaving aside the notion that this bias is strangely only observed in GDP forecasts, as opposed to forecasts for any other variables we care about, do we see the same pattern for Democratic-affiliated forecasters? Is there asymmetry in accuracy? If not, the average of the two should, on average, be correct, as LLN will eliminate any idiosyncratic forecasting errors. If so, then this is consistent with a Bayesian view of beliefs-formation, with ideology as the priors.

Rational expectations assumes that all agents have complete information regarding all variables and parameters in the model. A more realistic approach recognises that information is often noisy and uncertain, and that there exists search costs to information acquisition. A Bayesian framework modelling how agents form beliefs can resolve this, whilst maintaining the core assumption of rationality (that individuals act sincerely in accordance with optimising their interests given all available information).

Indeed, this is how I believe individuals form beliefs (a probability distribution over statements about the world). They start with a prior, then update based on the information they encounter. In this sense, two agents with heterogenous priors (in this case, partisanship and ideological beliefs) can rationally disagree, even if they hold the same information.

Let the expected value of a variable in period t+1 be a random variable X. Our agent yields prior [1]:

X ~ N(μ0, σ²x)

for μ0 = μ + ε0, where ε0 incorporates partisan bias. If μ for X is unknown (incorporating the inherent noise in our real-life understanding of the world), then E[X] = μ0, yet if μ is known then ε0 = 0 so standard rational expectations holds.

With no additional signal, expected loss is given by:

E[(μ0 - X)²] = Var(X) = σ²x

Now suppose the agent pays a fixed cost k to observe a signal s = θ + ε for ε ~ N(0, σ²ε). Our posterior variance is given by:

σ²1 = 1/(1/σ²x + 1/σ²ε)

Greater precision in our information reduces posterior variance, making our signal more valuable for any k~R. A higher k, holding signal precision constant, means our agent will consume less signals.

Moreover, we seek to minimise:

L = σ²x - σ²1

Therefore if our priors are more uncertain, we will acquire more information. Our agent will acquire information if the posterior variance exceeds the fixed cost.

However, what if our choice of precision is endogenous? Our agent now chooses τ = 1/σ²ε at cost C(τ) = kτ for k~R, then observes s with precision τ. The agent posterior is E[X|s], so the ex-ante expected loss is the posterior variance. To maximise expected utility, the agent chooses τ to minimise:

L = σ²1 + C(τ) = 1/(1/σ²x + τ) + kτ

Our FOC follows…

δL/δτ = -(1/σ²x + τ)^(-2) + k = 0,

so τ* = 1/√k - 1/σ²x

therefore σ²1(τ*) = √k.

The intuition remains the same as in the fixed cost example, with our FOC more precisely determining how much information our agent consumes.

I will now incorporate my model of Bayesian belief formation with search costs into an NK DSGE model. My reasoning for doing so is simple - to check whether this theory is internally consistent with our other theories. The core difference is that we replace rational expectations with the agent’s posterior mean under these Bayesian microfoundations.

Our IS curve is given by:

xt = Et[xt+1|Sx] - (it - Et[πt+1|Sπ] - r)/σ - νt

where Et[xt+1|Sx] and Et[πt+1|Sπ] are the agent’s posterior means for the future output gap and inflation respectively, given their information on output and inflation, Sx and Sπ respectively.

Our PC is given by:

πt = βEt[πt+1|Sπ] + kxt + ut

whilst monetary policy is determined by a Taylor rule. Our agent chooses to minimise posterior variance under our framework embedding endogenous choice of precision, as this maximises forecast accuracy given search costs, thereby maximising expected utility. Under fixed costs to information acquisition, our agent will purchase signals until the posterior variance equals the fixed cost.

By now, the issue with departing from rational expectations has become apparent. Our aggregate variables are dependent upon individual posterior means, formed via possibly biased priors and private information acquisition, aggregated across all agents. Therefore, under representative agent models, any systematic bias in the priors (in this case, partisan bias) will distort realised aggregate outcomes, which contradicts the notion that a biased individual behaves consistently with rationality. Moreover, this result would not hold empirically; business cycles can be driven by which party wins an election if the representative agent is biased, which contradicts the data.

This would not be an issue if we assume that there is no asymmetry in bias or in information acquisition, so when posterior means are aggregated, LLN will eliminate any idiosyncratic forecasting errors. Yet a) we simply return to standard rational expectations, albeit with microfoundations that allow individual bias and information frictions to be consistent with rationality, provided that the errors average out to zero. B) our microfoundations on information acquisition are set at the individual level, so the formation of posteriors depends upon private signals and search frictions.

Under representative agents, all agents acquire the same information (so biased priors must wash out), or again any heterogeneity must wash out. Therefore, bias in forecasting is consistent with rationality, only if all idiosyncratic errors average to zero. Luckily, this is consistent with this empirical data.

Comments are welcome.

1. Note that I am experiencing technical difficulties incorporating LaTeX, so the presentation looks a bit clunky. As soon as I can edit to resolve this, I will do so.