Behavioral New Keynesian Models: Learning versus Cognitive Discounting

It solves the forward guidance puzzle by discounting the distant future more heavily, and it costs the model its response to ordinary monetary policy. Under rational expectations the New Keynesian model “implies only minimal discounting of the future by households and firms”, so expected shifts in interest rates have “unrealistically large effects on current output, and effects that become even larger the further into the future they are set to take place” — the puzzle documented by Del Negro, Giannoni, and Patterson (2015). Cognitive discounting captures the idea that “agents cannot fully understand events that will take place in the distant future”, which the authors gloss as agents mentally simulating future paths of the economy and progressively shrinking the more distant simulations toward steady-state values. The cost appears in this paper’s estimates: “the addition of severely myopic agents comes at a cost: the implied responses to conventional, unanticipated, monetary policy shocks are also attenuated.”

They limit different things, and in opposite directions over time. Under cognitive discounting, expectations remain rational but are shrunk toward steady state more quickly at longer horizons. Under adaptive learning, expectations come from agents’ own perceived models: agents often have correctly specified models in the sense of including every relevant variable, but “they cannot know the values of some aggregate parameters, such as the degree of price stickiness in the economy, or the monetary policy reaction coefficients”, and so form and update beliefs about the reduced-form relationships from observed data. The authors draw the contrast carefully in both directions. Agents’ understanding is in one sense more limited under learning — they lack knowledge of the magnitudes of dynamic interactions and can even misinfer steady states, since they learn about intercepts. But in another sense cognitive discounting is the deeper departure: there “agents have a biased model of the economy … and the bias is permanent: they are prevented from learning the truth even in the long run”, whereas under learning agents “have imperfect beliefs during transition phases, but they may converge to the rational expectations equilibrium (or to a distribution around it) in the long run.” The authors note the two can in principle coexist, or myopia may become redundant once expectations are boundedly rational.

How far ahead agents must forecast, which turns out to determine how much myopia the data demand. Under infinite-horizon learning “current macroeconomic variables are influenced by expectations far into the future” — the model equations become, in the authors’ words, “extremely forward-looking, with long-horizon forecasts about future output gaps, inflation, and interest rates, until the indefinite future mattering for current realizations.” Under Euler-equation learning “the New Keynesian model resembles the one under rational expectations, with output and inflation expressed as a function of one-period-ahead expectations.” This is the mechanical reason for the paper’s central result: the more farsighted the specification, the more myopia is needed as a counterbalance.

US quarterly data on three observables, 1960:Q1 to 2007:Q2, estimated jointly by full-information Bayesian methods. The output gap is the log difference between Real GDP and the Congressional Budget Office’s Real Potential GDP, inflation is the log first difference of the implicit GDP price deflator, and the short rate is the federal funds rate converted to a quarterly rate, all from FRED. Data from 1954:Q3 are used but only to initialize the learning process; the likelihood starts in 1960:Q1. The sample ends before the 2007–09 recession specifically “to avoid having to deal with the binding effective lower bound constraint in policy rates”. Structural and behavioral parameters are estimated jointly by Metropolis-Hastings with 1,500,000 draws per specification, discarding the first 40% as burn-in and thinning by saving one draw in a hundred. Three parameters are fixed rather than estimated: the discount factor at 0.99, the inverse Frisch elasticity at 2, and the elasticity of substitution across differentiated goods at 11, implying a 10% steady-state markup.

0.416 under rational expectations, about 0.2 under infinite-horizon learning, and 0.9366 under Euler-equation learning. Under rational expectations the authors report that “substantial levels of inattention are needed to fit the data”, with the entire 95% posterior density interval for the cognitive discounting parameter falling well below one — in contrast with the benchmark New Keynesian model, which implies a discount factor of one for output and of beta for inflation. Infinite-horizon learning pushes the requirement further, to a posterior mean around 0.2, “which indicates even stronger discounting than under rational expectations”. Euler-equation learning brings it back “much closer to 1”. The authors’ conclusion from this is stated as a conditional, not a dismissal: “the addition of another behavioral feature, such as deviations from rational expectations and learning by the agents, can substantially reduce the empirical need for cognitive discounting.”

Euler-equation learning, decisively — while rational expectations and infinite-horizon learning achieve similar, lower fit. Comparing log marginal likelihoods, the authors report that rational expectations and infinite-horizon learning are close, with rational expectations slightly ahead, and that Euler-equation learning “leads to sizable improvements in model fit: the resulting Bayes factor would suggest ‘decisive’ evidence in favor of Euler-equation learning versus the alternatives, based on Jeffreys’ (1961) widely-used interpretative scale.” The ordering is stable across the split samples as well.

No — and the authors test this directly rather than inferring it. Re-estimating the Euler-equation learning model with the discounting parameter fixed at one lowers the log marginal likelihood to −270.4209, so “the specification with both Euler-equation learning and (moderate) myopia is, therefore, preferred by the data.” The result also survives dropping the informative prior: with a Uniform[0,1] prior the posterior mean is 0.9382 and the log marginal likelihood −268.7747, and with a Gamma(0.3, 0.3) prior placed on one minus the parameter — which puts most weight on no myopia at all — the estimate is 0.9437 and the log marginal likelihood −267.9884. Both still beat the fixed-at-one case. The authors’ summary is that “independently of the prior, the data always indicate modest degrees of discounting, and favor a specification where learning and modest cognitive discounting coexist.”

It reverses the horizon profile: with empirically estimated myopia, near-term announcements matter most and anticipations beyond about two years are largely ineffective. Plotting the response of inflation to an anticipated policy shock at horizons from 0 to 80 quarters, the benchmark case with no discounting reproduces the pattern in McKay, Nakamura, and Steinsson (2016) and Gabaix (2020), where “the impact of forward guidance is magnified for longer anticipation horizons, making the model potentially unstable.” Fixing the parameter at its estimated posterior mean of 0.416 makes the response “drastically different, with shocks at the lowest horizons now having the largest effects”, and “anticipations with horizons above two years are largely ineffective, given that agents strongly discount them.”

A comparison against a VAR: only Euler-equation learning matches the estimated response of the output gap to an unanticipated policy shock. The authors estimate a VAR on the same three endogenous variables and compare its impulse response with the three structural specifications. The Euler-equation learning model “generates output responses that track very closely the responses from the VAR”, while rational expectations and infinite-horizon learning, “in consequence of the sizable degree of myopia that they require to dampen the effects of anticipations, end up severely underestimating the effects of monetary policy.” This is the paper’s sharpest argument that the myopia estimated under rational expectations is doing double duty rather than measuring a behavioral primitive.

The ordering holds; the level of estimated myopia moves, and one posterior is bimodal. Splitting at Volcker into 1954:Q3–1979:Q2 and 1982:Q1–2007:Q2, the rational-expectations estimate shifts from 0.63 to 0.409; infinite-horizon learning requires the largest discounting in both; and Euler-equation learning gives values almost identical to the full sample before 1979 but a lower posterior mean of 0.79 after 1982. The authors read this as inattention being “more prevalent in periods characterized by overall macroeconomic stability”, but immediately qualify it: “for post-1982 data, the posterior distribution for [the parameter] displays a clear bimodality: the posterior mode is obtained at a value of 0.9112, suggesting more limited inattention not far off its full-sample estimate, but there is also a lower-probability mode that concentrates around lower values.” In each sample the data are “clearly best explained by the model with Euler-equation learning and only limited degrees of cognitive discounting.”

The estimates put the inflation response below one before Volcker, with bounded rationality supplying determinacy instead. The authors flag indeterminacy as an issue for pre-Volcker samples and point to Ilabaca, Meggiorini, and Milani (2020), who estimate a cognitive-discounting model allowing for both determinacy and indeterminacy and find indeterminacy rejected in each sample, with the data preferring “a specification where monetary policy in the 1960-70s is indeed passive, but where bounded rationality is pervasive enough to induce determinacy.” Their own estimates here are similar: policy coefficients below one toward inflation before Volcker, “but agents’ inattention is strong enough to restore determinacy.” They note that under learning the estimation “doesn’t pose particular problems and can be performed whether the equilibrium is E-stable or E-unstable”.

Yes — adding anticipated policy shocks to the Taylor rule leaves both the myopia estimates and the model ranking essentially unchanged. The authors re-estimate with monetary shocks anticipated four and eight quarters in advance entering the policy rule alongside the unanticipated shock, using Gamma(0.3, 0.3) priors for the news-shock standard deviations following Schmitt-Grohé and Uribe (2012) and Milani and Rajbhandari (2020). The posterior means for the discounting parameter “remain similar to those estimated in the model with only unanticipated monetary policy shocks, and the Euler-equation learning specification still outperforms the alternatives.”

Mainly the persistence the model has to load onto the shocks — a familiar consequence of learning. Monetary policy estimates are similar across specifications and price stickiness stays around 0.8, while the elasticity of intertemporal substitution is lower under rational expectations. The substantive difference is in the disturbances: rational expectations and infinite-horizon learning “require large autocorrelation coefficients in the natural rate and cost-push disturbance processes”, with those coefficients around 0.9, whereas under Euler-equation learning they fall to 0.2278 and 0.0654. The authors connect this to Milani (2007, 2017): “learning helps the models match the observed persistence in macroeconomic data.” The constant-gain estimates also differ sharply between the learning models, 0.0454 under infinite-horizon and 0.0049 under Euler-equation learning, meaning much heavier discounting of older observations in the former. Allowing separate gains per variable, the posteriors imply agents perceive more instability in inflation (0.0370) than in the interest rate (0.0198) or the output gap (0.0059), with the discounting parameter at 0.88 and an improved marginal likelihood of −266.2732.

Because the two behavioral features point in opposite directions on price-level targeting. The authors state the implication without adjudicating it: “If learning matters, then price-level targeting may become optimal, as illustrated by Eusepi and Preston (2018). If cognitive discounting is an important feature of the data, instead, the analysis in Gabaix (2020) shows that price-level targeting may lead to lower-welfare outcomes.” Since the paper’s own estimates favor a specification with substantial learning and only modest cognitive discounting, the weight of its evidence leans toward the first branch — though the authors do not draw that conclusion themselves, framing the point as a reason why identifying the right behavioral features matters for policy choice.

One model class, one country, a pre-2007 sample, and a myopia parameter that is deliberately not allowed to vary. The estimation covers the United States through 2007:Q2, excluding the lower-bound period entirely, so nothing here speaks to behavior in the episode that motivated much of the forward guidance literature. The result is a comparison among three expectation assumptions within a single small New Keynesian model, so “sensitive to the modeling of expectations” is established for this model rather than in general. The authors also record an identification limit they chose not to work around: while agents might plausibly be myopic to different degrees about different variables, “the corresponding parameters will not be separately identifiable in our framework”, so the paper estimates one general degree of myopia rather than a variable- or agent-specific one. And the headline contrast rests on marginal-likelihood comparisons, which are sensitive to prior choice — which is why the authors run the uninformative-prior robustness check, and why that check matters to the argument.