Certainty equivalence and model uncertainty

Simon’s and Theil’s certainty equivalence property justifies a convenient algorithm for solving dynamic programming problems with quadratic objectives and linear transition laws: first, optimize under perfect foresight, then substitute optimal forecasts for unknown future values. A similar decomposition into separate optimization and forecasting steps prevails when a decision maker wants a decision rule that is robust to model misspecification. Concerns about model misspecification leave the first step of the algorithm intact and affect only the second step of forecasting the future. The decision maker attains robustness by making forecasts with a distorted model that twists probabilities relative to his approximating model. The appropriate twisting emerges from a two-player zero-sum dynamic game.

Acknowledgement Misspecification in Macroeconomic Theory

We explore methods for confronting model misspecification in macroeconomics. We construct dynamic equilibria in which private agents and policy makers recognize that models are approximations. We explore two generalizations of rational expectations equilibria. In one of these equilibria, decision makers use dynamic evolution equations that are imperfect statistical approximations, and in the other misspecification is impossible to detect even from infinite samples of time-series data. In the first of these equilibria, decision rules are tailored to be robust to the allowable statistical discrepancies. Using frequency domain methods, we show that robust decision makers treat model misspecification like time-series econometricians.

Efficient Estimation of Linear Asset Pricing Models with Moving-Average Errors

This paper explores in depth the nature of the conditional moment restrictions implied by log-linear intertemporal capital asset pricing models (ICAPMs) and shows that the generalized instrumental variables (GMM) estimators of these models (as typically implemented in practice) are inefficient. The moment conditions in the presence of temporally aggregated consumption are derived for two log-linear ICAPMs. The first is a continuous time model in which agents maximize expected utility. In the context of this model, we show that there are important asymmetries between the implied moment conditions for infinitely and finitely-lived securities. The second model assumes that agents maximize non-expected utility, and leads to a very similar econometric relation for the return on the wealth portfolio. Then we describe the efficiency bound (greatest lower bound for the asymptotic variances) of the CNN estimators of the preference parameters in these models. In addition, we calculate the efficient CNN estimators that attain this bound. Finally, we assess the gains in precision from using this optimal CNN estimator relative to the commonly used inefficient CMN estimators.

Robustness

The standard theory of decision making under uncertainty advises the decision maker to form a statistical model linking outcomes to decisions and then to choose the optimal distribution of outcomes. This assumes that the decision maker trusts the model completely. But what should a decision maker do if the model cannot be trusted? Lars Hansen and Thomas Sargent, two leading macroeconomists, push the field forward as they set about answering this question. They adapt robust control techniques and apply them to economics. By using this theory to let decision makers acknowledge misspecification in economic modeling, the authors develop applications to a variety of problems in dynamic macroeconomics. Technical, rigorous, and self-contained, this book will be useful for macroeconomists who seek to improve the robustness of decision-making processes.decision-making, uncertainty, statistical models, control techniques, economic modeling, dynamic microeconomics, misspecification

A Time Series Analysis of Representative Agent Models of Consumption andLeisure Choice Under Uncertainty

This paper investigates empirically a model of aggregate consumption and leisure decisions in which goods and leisure provide services over time. The implied time non-separability of preferences introduces an endogenous source of dynamics which affects both the co-movements in aggregate compensation and hours worked and the cross-relations between prices and quantities. These cross-relations are examined empirically using post-war monthly U.S. data on quantities, real wages and the real return on the one-month Treasury bill. We find substantial evidence against the overidentifying restrictions. The test results suggest that the orthogonality conditions associated with the representative consumer's intratemporal Euler equation underlie the failure of the model. Additionally, the estimated values of key parameters differ significantly from the values assumed in several studies of real business models. Several possible reasons for these discrepancies are discussed.

Managing expectations and fiscal policy

This paper studies an optimal fiscal policy problem of Lucas and Stokey (1983) but in a situation in which the representative agent's distrust of the probability model for government expenditures puts model uncertainty premia into history-contingent prices. This situation gives rise to a motive for expectation management that is absent within rational expectations and a novel incentive for the planner to smooth the shadow value of the agent's subjective beliefs to manipulate the equilibrium price of government debt. Unlike the Lucas and Stokey (1983) model, the optimal allocation, tax rate, and debt become history dependent despite complete markets and Markov government expenditures.

[Robust Control and Model Uncertainty], Belirsizlik Modeli ve Sağlamlılık Kontrolü

Belirsizlik Modelive Sağlamlılık Kontrol

A note on Wiener-Kolmogorov prediction formulas for rational expectations models

A prediction formula for geometrically declining sums of future forcing variables is derived for models in which the forcing variables are generated by a vector autoregressive-moving average process. This formula is useful in deducing and characterizing cross-equation restrictions implied by linear rational expectations models.

Assessing the feasibility of archetypal transition pathways towards carbon neutrality – A comparative analysis of European industries

Analyses of the future for manufacturing and heavy industries in a climate constrained world many times focus on technological innovations in the early stages of the value chain, assuming few significant changes are plausible, wanted, or necessary throughout the rest of the value chain. Complex questions about competing interests, different ways of organising resource management, production, consumption, and integrating value chains are thus closed down to ones about efficiencies, pay-back times, and primary processing technologies. In this analysis, we move beyond this to identify archetypal pathways that span across value chains in four emissions intensive industries: plastics, steel, pulp and paper, and meat and dairy. The pathways as presented in the present paper were inductively identified in a multi-stage process throughout a four-year European research project. The identified archetypal pathways are i) production and end-use optimisation, ii) electrification with CCU, iii) CCS, iv) circular material flows, and v) diversification of bio-feedstock use. The pathways are at different stages of maturity and furthermore their maturity vary across sectors. The pathways show that decarbonisation is likely to force value chains to cross over traditional boundaries. This implies that an integrated industrial and climate policy must handle both sectoral specificities and commonalities for decarbonised industrial development.publishedVersio