Economic dynamics under heterogeneous adaptive learning: aggregate economy sufficient conditions for stability

We provide sufficient conditions for stability of a linear structurally heterogeneous economy under heterogeneous learning of agents, extending the results of Honkapohja and Mitra (2006), Kolyuzhnov (2011), and Bogomolova and Kolyuzhnov (2019). Sufficient conditions for stability under heterogeneous mixed RLS/SG learning for four classes of models: models without lags and with lags of the endogenous variable and with t or t-1- dating of expectations, are provided for the cases of the diagonal structure of the shock process behaviour or the heterogeneous RLS learning and are presented in terms of structural heterogeneity and are independent of heterogeneity in learning. The results are based on the negative diagonal dominance approach and are provided, first, in terms of the existence of the weights for aggregation of endogenous variables and of expectations across agents, interrelated in a special way, and then in terms of the E-stability of a suitably defined aggregate economy. The fundamental nature of the approach adopted in the paper allows one to apply its results to a vast majority of the existing and prospective linear and linearized economic models (including estimated DSGE models) with adaptive learning of agents.

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Economic Dynamics under Heterogeneous Adaptive Learning: General Criteria and Sufficient Conditions for Stability

WORLD OF ECONOMICS AND MANAGEMENT ◽

10.25205/2542-0429-2019-19-4-87-103 ◽

2019 ◽

Vol 19 (4) ◽

pp. 87-103

Author(s):

A. S. Bogomolova ◽

D. V. Kolyuzhnov

Keyword(s):

Adaptive Learning ◽

Necessary Conditions ◽

Learning Algorithm ◽

Sufficient Conditions ◽

Dsge Models ◽

Shock Process ◽

Sufficient And Necessary Conditions ◽

Process Behavior ◽

The Stability ◽

Sign Conditions

The article extends the results of Honkapohja and Mitra (2006) and Kolyuzhnov (2011) and provides criteria and sufficient conditions for stability in a structurally heterogeneous economy under heterogeneous adaptive learning of agents. The criteria for stability under heterogeneous mixed RLS/SG learning for four classes of models – without lags and with lags of the endogenous variable and with t or t – 1 – dating of expectations – and sufficient conditions for stability for the cases of the diagonal structure of the shock process behavior or the heterogeneous RLS learning are presented in terms of the corresponding Jacobian matrices. In addition, the study presents a very useful criterion for the stability for all types of models under mixed RLS/SG learning with equal degrees of inertia for each type of learning algorithm in terms of stability of a suitably defined average economy with two agents. The derived criteria and sufficient conditions for stability are based on the results of the theory of stochastic approximation and are presented in terms of mixture of structural and learning heterogeneity, which are essential to get sufficient and necessary conditions for stability irrespective of heterogeneity in learning presented in terms of E-stability of suitably defined aggregate economies, the “same sign” conditions and the E-stability of a suitably defined average economy and its subeconomies. The fundamental nature of the approach adopted in the paper makes it possible to apply the results to a vast majority of the existing and prospective linear and linearized economic models (including estimated DSGE models) with adaptive learning of agents.

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Optimum replacement of a system subject to shocks

Journal of Applied Probability ◽

10.2307/3214120 ◽

1986 ◽

Vol 23 (1) ◽

pp. 107-114 ◽

Cited By ~ 41

Author(s):

Mohamed Abdel-Hameed

Keyword(s):

Poisson Process ◽

Sufficient Conditions ◽

Sample Path ◽

Cost Structure ◽

Homogeneous Poisson Process ◽

Jump Size ◽

Shock Process ◽

Finite Period ◽

Periodic Replacement ◽

Non Homogeneous Poisson Process

A system is subject to shocks. Each shock weakens the system and makes it more expensive to run. It is desirable to determine a replacement time for the system. Boland and Proschan [4] consider periodic replacement of the system and give sufficient conditions for the existence of an optimal finite period, assuming that the shock process is a non-homogeneous Poisson process and the cost structure does not depend on time. Block et al. [3] establish similar results assuming that cost structure is time dependent, still requiring that the shock process is a non-homogeneous Poisson process. We show via a sample path argument that the results of [3] and [4] hold for any counting process whose jump size is of one unit magnitude.

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COORDINATION ON SADDLE-PATH SOLUTIONS: THE EDUCTIVE VIEWPOINT—LINEAR UNIVARIATE MODELS

Macroeconomic Dynamics ◽

10.1017/s1365100501010331 ◽

2003 ◽

Vol 7 (1) ◽

pp. 42-62 ◽

Cited By ~ 13

Author(s):

George W. Evans ◽

Roger Guesnerie

Keyword(s):

Information Structure ◽

Common Knowledge ◽

Sufficient Conditions ◽

Structural Heterogeneity ◽

Perfect Foresight ◽

One Step ◽

Univariate Model ◽

With Memory ◽

Forward Looking

We investigate local strong rationality (LSR) in a one-step-forward-looking univariate model with memory one. Eductive arguments are used to determine when common knowledge (CK) that the solution is near some perfect-foresight path is sufficient to trigger complete coordination on that path (i.e., the path is LSR). Coordination of expectations is shown to depend on three factors: the nature of the CK initial beliefs, the degree of structural heterogeneity, and the information structure. Our sufficient conditions for LSR precisely reflect these features and provide basic consistent justifications for the choice of the saddle-path solution.

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CONVERGENCE IN MONETARY INFLATION MODELS WITH HETEROGENEOUS LEARNING RULES

Macroeconomic Dynamics ◽

10.1017/s1365100501018016 ◽

2001 ◽

Vol 5 (1) ◽

pp. 1-31 ◽

Cited By ~ 46

Author(s):

George W. Evans ◽

Seppo Honkapohja ◽

Ramon Marimon

Keyword(s):

Steady State ◽

Adaptive Learning ◽

Steady States ◽

Fiscal Constraint ◽

Learning Rules ◽

Heterogeneous Learning ◽

High Inflation ◽

Parameter Values ◽

Globally Stable ◽

Theoretical Results

Inflation and the monetary financing of deficits are analyzed in a model in which the deficit is constrained to be less than a given fraction of a measure of aggregate market activity. Depending on parameter values, the model can have multiple steady states. Under adaptive learning with heterogeneous learning rules, there is convergence to a subset of these steady states. In some cases, a high-inflation constrained steady state will emerge. However, with a sufficiently tight fiscal constraint, the low-inflation steady state is globally stable. We provide experimental evidence in support of our theoretical results.

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Adaptive Learning in Macroeconomics

Oxford Research Encyclopedia of Economics and Finance ◽

10.1093/acrefore/9780190625979.013.508 ◽

2020 ◽

Author(s):

George W. Evans ◽

Bruce McGough

Keyword(s):

Adaptive Learning ◽

Rational Expectations ◽

Selection Criterion ◽

Economic Modeling ◽

Equilibrium Analysis ◽

Reduced Form ◽

Dsge Models ◽

Global Dynamics ◽

Stability Principle ◽

Dynamic Stochastic

While rational expectations (RE) remains the benchmark paradigm in macro-economic modeling, bounded rationality, especially in the form of adaptive learning, has become a mainstream alternative. Under the adaptive learning (AL) approach, economic agents in dynamic, stochastic environments are modeled as adaptive learners forming expectations and making decisions based on forecasting rules that are updated in real time as new data become available. Their decisions are then coordinated each period via the economy’s markets and other relevant institutional architecture, resulting in a time-path of economic aggregates. In this way, the AL approach introduces additional dynamics into the model—dynamics that can be used to address myriad macroeconomic issues and concerns, including, for example, empirical fit and the plausibility of specific rational expectations equilibria. AL can be implemented as reduced-form learning, that is, the implementation of learning at the aggregate level, or alternatively, as discussed in a companion contribution to this Encyclopedia, Evans and McGough, as agent-level learning, which includes pre-aggregation analysis of boundedly rational decision making. Typically learning agents are assumed to use estimated linear forecast models, and a central formulation of AL is least-squares learning in which agents recursively update their estimated model as new data become available. Key questions include whether AL will converge over time to a specified RE equilibrium (REE), in which cases we say the REE is stable under AL; in this case, it is also of interest to examine what type of learning dynamics are observed en route. When multiple REE exist, stability under AL can act as a selection criterion, and global dynamics can involve switching between local basins of attraction. In models with indeterminacy, AL can be used to assess whether agents can learn to coordinate their expectations on sunspots. The key analytical concepts and tools are the E-stability principle together with the E-stability differential equations, and the theory of stochastic recursive algorithms (SRA). While, in general, analysis of SRAs is quite technical, application of the E-stability principle is often straightforward. In addition to equilibrium analysis in macroeconomic models, AL has many applications. In particular, AL has strong implications for the conduct of monetary and fiscal policy, has been used to explain asset price dynamics, has been shown to improve the fit of estimated dynamic stochastic general equilibrium (DSGE) models, and has been proven useful in explaining experimental outcomes.

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ON THE EXISTENCE OF EQUIVALENT TARIFF VECTORS — WHEN THE STATUS QUO MATTERS

The Singapore Economic Review ◽

10.1142/s0217590805002074 ◽

2005 ◽

Vol 50 (spec01) ◽

pp. 345-359 ◽

Cited By ~ 3

Author(s):

MURRAY KEMP ◽

HENRY WAN

Keyword(s):

Sufficient Conditions ◽

Status Quo ◽

Exogenous Variables ◽

Endogenous Variables ◽

The Status ◽

The Given

It has long been recognized that, in a restricted world of just two countries and two commodities, any feasible non-distorting international transfer can be replaced by a pair of individually distorting but collectively non-distorting equivalent import duties. In recent years it has sometimes been suggested that equivalence persists in broader contexts and there have been two attempts to provide interesting sufficient conditions for equivalence. Our purpose is three-fold. We first note that the sufficient conditions so far provided relate to the equilibrium values of endogenous variables (like prices) rather than to the given values of exogenous variables (like endowments, technologies and preferences) and that conditions of the former kind may be difficult to empirically justify. It is then shown, by means of a robust example with conditions imposed on exogenous variables only, that equivalence cannot be relied upon when there are more than two countries, even when the countries have no extraordinary features. Finally, we emphasize some of the difficulties in implementing equivalent tariffs even when they do exist.

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Practical Criteria for H-Matrices

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1049-1050.1316 ◽

2014 ◽

Vol 1049-1050 ◽

pp. 1316-1319

Author(s):

Ming Da Zhang

Keyword(s):

Matrix Theory ◽

Sufficient Conditions ◽

Diagonal Dominance ◽

Diagonally Dominant Matrices ◽

Diagonally Dominant Matrix ◽

Diagonally Dominant ◽

Strictly Diagonally Dominant Matrix ◽

Dominant Matrix

Generalized strictly diagonally dominant matrix is very important in computing mathematics and matrix theory, many articles are searching simple and practical identification of generalized strictly diagonally dominant matrix. In this paper, using the concept of diagonal dominance, some sufficient conditions for generalized strictly diagonally dominant matrices are given.

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