This paper examines the effects of heterogeneous biased expectations between the young and old on business cycles and explores its policy implications. Empirical findings reveal that individuals, particularly the young, can have more optimistic or pessimistic views about the future state of the economy compared to the data-generating measure. This study relates these results to the learning-from-experience literature, which suggests that individuals, particularly the young, place greater weight on recent observations when forming their expectations. Incorporating household weighting schemes into a life-cycle learning model, I show that household sensitivity to recent observations amplifies the effects of economic shocks. However, the amplification effects become less extensive as the population ages due to the lower sensitivity of the old. My simulation results indicate that a 10 percentage point increase in the old population ratio leads to a 16 percent decrease in output volatility. Regarding policy implications, this paper suggests that the government spending multiplier declines by approximately 10 percent when the old population ratio rises by 10 percentage points due to weak amplification effects. Moreover, the weakened output effects deteriorate the welfare of the population, particularly that of the young.

A single dataset is rarely sufficient to address a question of substantive interest. Instead, most applied data analysis combines data from multiple sources. Very rarely do two datasets contain the same identifiers with which to merge datasets; fields like name, address, and phone number may be entered incorrectly, missing, or in dissimilar formats. Combining multiple datasets absent a unique identifier that unambiguously connects entries is called the record linkage problem. While recent work has made great progress in the case where there are many possible fields on which to match, the much more uncertain case of only one identifying field remains unsolved: this fuzzy string matching problem, both its own problem and a component of standard record linkage problems, is our focus. We design and validate an algorithmic solution called Adaptive Fuzzy String Matching rooted in adaptive learning, and show that our tool identifies more matches, with higher precision, than existing solutions. Finally, we illustrate its validity and practical value through applications to matching organizations, places, and individuals.

A network modelling approach to educational mapping leads to a scalable computational model that supports adaptive learning, intelligent tutors, intelligent teaching assistants, and data-driven continuous improvement. Current educational mapping processes are generally applied at a level of resolution that is too coarse to support adaptive learning and learning analytics systems at scale. This paper proposes a network modelling approach to structure extremely fine-grained statements of learning ability called Micro-outcomes, and a method to design sensors for inferring a learner’s knowledge state. These sensors take the form of high-resolution assessments and trackers that collect digital analytics. The sensors are linked to Micro-outcomes as part of the network model, enabling inference and pathway analysis. One example demonstrates the modelling approach applied to two community college subjects in College Algebra and Introductory Accounting. Application examples showcase how this modelling approach provides the design foundation for an intelligent tutoring system and intelligent teaching assistant system deployed at Arapahoe Community College and Quinsigamond Community College. A second example demonstrates the modelling approach deployed in an undergraduate aerospace engineering subject at the Massachusetts Institute of Technology to support course planning and teaching improvement.

This paper uses Bayesian methods to estimate a small-scale New Keynesian model with heterogeneous expectations (HE). Agents form expectations via Euler equation adaptive learning (AL) and differ by the model they use to forecast. Type A agents use a correctly specified model, while type B and type C agents use misspecified models. Quarterly US data from the pre-Great Moderation and Great Moderation periods are used to jointly estimate the degree of agent heterogeneity, the AL parameters, and the deep model parameters. Results show that the data exhibit significant expectational heterogeneity, and that the HE model fits the data better than a model with homogeneous agent AL.

A simple asset pricing model with both endogenous stock market participation and subjective risk can explain the negative cross-country correlation between participation rates and the volatility of excess returns, along with the time-varying participation rates in the data. Belief-driven learning dynamics can explain the interplay between participation rates, subjective risk, and stock price volatility. When agents adaptively learn about the risk and return, my model generates 25% of the excess volatility observed in US stock prices, while also matching key moments. With learning about risk, excess volatility of stock prices is driven by fluctuations in the participation rate that arise because agents’ risk estimates vary with prices. I find that learning about risk is quantitatively more important than learning about returns.

The expectational stability (E-stability) property of rational expectations equilibria (REE) in linear macroeconomic dynamic stochastic general equilibrium (DSGE) models is known to be sensitive to the information available to decision makers as well as the structure of the economic environment considered. Models featuring news shocks as a source of macroeconomic fluctuations depart from traditional assumptions regarding both the structure of the economy and the information set of agents. This paper investigates whether E-stability of REE is affected by either the inclusion of news shocks by themselves or the complementary structural changes. The main results find that the E-stability property of REE is robust to the inclusion (or exclusion) of news shocks and that well-known news-shock DSGE models permit REE which are simultaneously E-stable and capable of producing qualitatively realistic expectationally driven business cycles.

Table 4 of this article was incorrectly published with subheadings in Table 4 missing. The publisher regrets this error and the correct version of Table 4 is presented here. Table 4.

Present-value multipliers for different specifications of fiscal policy in the new Keynesian model with rational expectations and with adaptive learning

	Rational expectations				Adaptive learning
	Impact	1 year	4 years	6 years	Impact	1 year	4 years	6 years
Strategy 1: Lump-sum financing (baseline model)
$\frac{{PV\left( {\Delta Y} \right)}}{{PV\left( {\Delta G} \right)}}\$	0.51	0.50	0.46	0.43	1.01	1.00	0.99	0.97
$\frac{{PV\left( {\Delta C} \right)}}{{PV\left( {\Delta G} \right)}}\$	−0.29	−0.30	−0.34	−0.37	0.09	0.09	0.07	0.06
$\frac{{PV\left( {\Delta I} \right)}}{{PV\left( {\Delta G} \right)}}\$	−0.20	−0.20	−0.20	−0.20	−0.08	−0.08	−0.09	−0.09
Strategy 2: Capital tax financing
$\frac{{PV\left( {\Delta Y} \right)}}{{PV\left( {\Delta G} \right)}}\$	0.32	0.29	0.12	0.02	0.43	0.38	0.20	0.08
$\frac{{PV\left( {\Delta C} \right)}}{{PV\left( {\Delta G} \right)}}\$	−0.23	−0.26	−0.40	−0.48	−0.08	−0.12	−0.27	−0.37
$\frac{{PV\left( {\Delta I} \right)}}{{PV\left( {\Delta G} \right)}}\$	−0.68	−0.69	−0.70	−0.71	−0.80	−0.80	−0.81	−0.82
Strategy 3: Labor tax financing
$\frac{{PV\left( {\Delta Y} \right)}}{{PV\left( {\Delta G} \right)}}\$	−0.64	−0.68	−0.85	−0.95	0.48	0.47	0.43	0.40
$\frac{{PV\left( {\Delta C} \right)}}{{PV\left( {\Delta G} \right)}}\$	−1.07	−1.10	−1.24	−1.33	−0.37	−0.38	−0.41	−0.43
$\frac{{PV\left( {\Delta I} \right)}}{{PV\left( {\Delta G} \right)}}\$	−0.71	−0.71	−0.73	−0.74	−0.17	−0.18	−0.18	−0.18

In a canonical monetary policy model in which the central bank learns about underlying fundamentals by estimating the parameters of a Phillips curve, we show that the bank’s loss function is asymmetric such that parameter overestimates may be more or less costly than underestimates, creating a precautionary motive in estimation. This motive suggests the use of a more efficient variance-adjusted least-squares estimator for learning about fundamentals. Informed by this “precautionary learning” the central bank sets low inflation targets, and the economy can settle near a Ramsey equilibrium.

This paper examines the government spending multiplier when economic agents combine adaptive learning and knowledge about future fiscal policy to form their expectations. The analysis shows that the effects of a government spending shock substantially change when the rational expectations hypothesis is replaced by this learning mechanism. In contrast to the dynamics under rational expectations, a government spending shock in a small-scale new Keynesian DSGE model with learning crowds in private consumption and is associated with a positive comovement between real wages and hours worked. In the baseline calibration, the output multiplier under learning is above one and about twice as large as under rational expectations.

This paper examines the stability of sunspot equilibria in one-sector RBC models under infinite horizon learning. We present general conditions under which the reduced-form model can possess E-stable sunspot equilibria and apply these conditions to three prominent one-sector RBC models. We find that the rational expectations sunspot equilibria are generally unstable under learning.

In this paper, we investigate real-time behavior of constant-gain stochastic gradient (SG) learning, using the Phelps model of monetary policy as a testing ground. We find that whereas the self-confirming equilibrium is stable under the mean dynamics in a very large region, real-time learning diverges for all but the very smallest gain values. We employ a stochastic Lyapunov function approach to demonstrate that the SG mean dynamics is easily destabilized by the noise associated with real-time learning, because its Jacobian contains stable but very small eigenvalues. We also express caution on usage of perpetual learning algorithms with such small eigenvalues, as the real-time dynamics might diverge from the equilibrium that is stable under the mean dynamics.

The aim of this study was to provide adaptive assistance to improve the listening comprehension of eleventh grade students. This study developed a video-based language learning system for handheld devices, using three levels of caption filtering adapted to student needs. Elementary level captioning excluded 220 English sight words (see Section 1 for definition), but provided captions and Chinese translations for the remaining words. Intermediate level excluded 1000 high frequency English words, but provided captions for the remaining words, and 2200 high frequency English words were excluded at the high intermediate caption filtering level. The result was that the viewers were provided with captions for words that were likely to be unfamiliar to them. Participants in the experimental group were assigned bilingual caption modes according to their pre-test results, while those in the control group were assigned standard caption modes. Our results indicate that students in the experimental group preferred adaptive captions, enjoyed the exercises more, and gained greater intrinsic motivation compared to those in the control group. The results confirm that different students require different quantities of information to balance listening comprehension and indicate that the proposed adaptive caption filtering approach may be an effective way to improve the skills required for listening proficiency.

If private sector agents update their beliefs with a learning algorithm other than recursive least squares, expectational stability or learnability of rational expectations equilibria (REE) is not guaranteed. Monetary policy under commitment, with a determinate and E-stable REE, may not imply robust learning stability of such equilibria if the RLS speed of convergence is slow. In this paper, we propose a refinement of E-stability conditions that allows us to select equilibria more robust to specification of the learning algorithm within the RLS/SG/GSG class. E-stable equilibria characterized by faster speed of convergence under RLS learning are learnable with SG or generalized SG algorithms as well.

We study adaptive learning in economic environments subject to recurring structural change. Stochastically evolving institutional and policymaking features can be described by regime-switching models with parameters that evolve according to finite state Markov processes. We demonstrate that in nonlinear models of this form, the presence of sunspot equilibria implies two natural schemes for learning the conditional means of endogenous variables: under mean value learning, agents condition on a sunspot variable that captures the self-fulfilling serial correlation in the equilibrium, whereas under vector autoregression learning (VAR learning), the self-fulfilling serial correlation must be learned. We show that an intuitive condition ensures convergence to a regime-switching rational expectations equilibrium. However, the stability of sunspot equilibria, when they exist, depends on whether agents adopt mean value or VAR learning: coordinating on sunspot equilibria via a VAR learning rule is not possible. To illustrate these phenomena, we develop results for an overlapping-generations model and a New Keynesian model.

This study examines the expectational stability of rational expectations equilibria (REE) under alternative Taylor rules when trend inflation is nonzero. We find that when trend inflation is high, the REE is likely to be expectationally unstable. This result holds true regardless of the nature of the data (such as contemporaneous, forecast, or lagged data) introduced in the Taylor rule. Our results suggest that high macroeconomic volatility during the period of high trend inflation can be explained well by introducing the concept of expectational stability.