Forward-looking Model Research Articles

Robust Monetary Policy with Misspecified Models: Does Model Uncertainty Always Call for Attenuated Policy?

This paper explores Knightian model uncertainty as a possible explanation of the considerable difference between estimated interest rate rules and optimal feedback descriptions of monetary policy. We focus on two types of uncertainty: (i) unstructured model uncertainty reflected in additive shock error processes that result from omitted-variable misspecifications, and (ii) structured model uncertainty, where one or more parameters are identified as the source of misspecification. For an estimated forward-looking model of the U.S. economy, we find that rules that are robust against uncertainty, the nature of which is unspecifiable, or against one-time parametric shifts, are more aggressive than the optimal linear quadratic rule. However, policies designed to protect the economy against the worst-case consequences of misspecified dynamics are less aggressive and turn out to be good approximations of the estimated rule. A possible drawback of such policies is that the losses incurred from protecting against worst-case scenarios are concentrated among the same business cycle frequencies that normally occupy the attention of policymakers.

Robust Monetary Policy With Misspecified Models: Does Model Uncertainty Always Call For Attenuated Policy?

This paper explores Knightian model uncertainty as a possible explanation of the considerable difference between estimated interest rate rules and optimal feedback descriptions of monetary policy. We focus on two types of uncertainty: (i) unstructured model uncertainty reflected in additive shock error processes that result from omitted-variable misspecifications, and (ii) structured model uncertainty, where one or more parameters are identified as the source of misspecification. For an estimated forward-looking model of the U.S. economy, we find that rules that are robust against uncertainty, the nature of which is unspecifiable, or against one-time parametric shifts, are more aggressive than the optimal linear quadratic rule. However, policies designed to protect the economy against the worst-case consequences of misspecified dynamics are less aggressive and turn out to be good approximations of the estimated rule. A possible drawback of such policies is that the losses incurred from protecting against worst-case scenarios are concentrated among the same business cycle frequencies that normally occupy the attention of policymakers.

Quality, user cost, forward-looking behavior, and the demand for cars in the UK

This paper applies an extended version of the superior goods model to the UK car market. The model involves the estimation of separate equations for the demand for new cars and the rental price of used cars. We have allowed for the direct influence of quality on car demand by using a measure derived from hedonic price equations. We have employed three measures of the user cost, reflecting different assumptions about price expectations and the depreciation rate. The empirical results reject the forward-looking model in favor of the error correction formulation. Income, wealth and price elasticities for new and used cars support the superior goods hypothesis.

Where Forward-Looking and Backward-Looking Models Meet

The present paper begins by deriving an instantaneous formulation for the backward-looking (reinforcement based learning) satisfaction balance model of Gray and Tallman (1984). This model is then used to generate interactional data from four simulated agents in a network interaction experiment. Because this initial model does not generate stable interaction structures in the network experiment, it is altered step by step in the direction of a forward-looking (agent with goals) model that has been shown to generate such stable interaction structures. The purpose of the modifications are to learn what aspects of the forward-looking model are needed to evolve a stable interaction structure, and to learn how these aspects may be incorporated into a model that remains essentially reinforcement based.

Simplicity Versus Optimality: The Choice of Monetary Policy Rules when Agents Must Learn

The monetary policy rules that are widely discussed--notably the Taylor rule--are remarkable for their simplicity. One reason for the apparent preference for simple ad hoc rules over optimal rules might be the assumption of full information maintained in the computation of an optimal rule. Arguably this makes optimal control rules less robust to model specification errors. In this paper, we drop the full-information assumption and investigate the choice of policy rules when agents must learn the rule that is in use. To do this, we conduct stochastic simulations on a small, estimated forward-looking model, with agents following a strategy of least- squares learning or discounted least-squares learning. We find that the costs of learning a new rule can, under some circumstances, be substantial. These circumstances vary with the preferences of the monetary authority and with the rule initially in place. Policymakers with strong preferences for inflation control must incur substantial costs when they change the rule; but they are nearly always willing to bear those costs. Policymakers with weak preferences for inflation control, on the other hand, may actually benefit from agents' prior belief that a strong rule is in place.

Simplicity versus Optimality: The Choice of Monetary Policy Rules When Agents Must Learn

The monetary policy rules that are widely discussed--notably the Taylor rule--are remarkable for their simplicity. One reason for the apparant preference for simple ad hoc rules over optimal rules might be the assumption of full information maintained in the computation of an optimal rule. Arguably this makes optimal control rules less robust to model specification errors. In this paper, we drop the full-information assumption and investigate the choice of policy rules when agents must learn the rule that is in use. To do this, we conduct stochastic simulations on a small, estimated forward-looking model, with agents following a strategy of least- squares learning or discounted least-squares learning. We find that the costs of learning a new rule can, under some circumstances, be substantial. These circumstances vary with the preferences of the monetary authority and with the rule initially in place. Policymakers with strong preferences for inflation control must incur substantial costs when they change the rule; but they are nearly always willing to bear those costs. Policymakers with weak preferences for inflation control, on the other hand, may actually benefit from agents' prior belief that a strong rule is in place.

An algorithm competition: First-order iterations versus Newton-based techniques

Abstract The development and use of forward-looking macromodels in policy making institutions has proceeded at a much slower pace than what was predicted in the early 1980s. An important reason for this is that researchers have not had access to robust and efficient solution techniques for solving nonlinear forward-looking models. This paper discusses the properties of alternative algorithms for solving MULTIMOD, the IMF's multicountry model of the world economy. Relative to traditional first-order algorithms in use today, we find that Newton-based techniques are considerably faster and much less prone to simulation failure.

A robust method for simulating forward-looking models

Methods of computing the type II iterations involved in extended path algorithms for the solution of economic models with forward-looking expectations are described. Particular attention is directed at a method involving the application of a Newton algorithm to a ‘stacked’ equation system that includes a separate equation for each endogeneous variable at each time point. Analytical results that establish convergence properties for linear models are presented. Both the analytical results and empirical comparisons of the stacked Newton method and the popular Fair-Taylor approach indicate that the stacked Newton method is a viable alternative for medium-sized economic models.

The (Un)Importance of Forward-Looking Behavior in Price Specifications

The seminal work of Edmund S. Phelps (1978), John B. Taylor (1980), and Guillermo A. Calvo (1983) developed forward-looking models of price determination that imparted inertia to the price level. These models incorporate expectations of future prices and excess demand by imposing constraints (typically lag-lead symmetry constraints) that force future variables to enter the specification. In this paper, the author tests the empirical significance of future prices in specifications like those of Taylor. He finds that expectations of future prices are empirically unimportant in explaining price and inflation behavior. However, the dynamics of a model that includes a purely backward-looking inflation specification differ substantially--and not altogether pleasingly--from those with a forward-looking specification. Copyright 1997 by Ohio State University Press.

Precision Performances of Terminal Conditions for Short Time HorizonsForward-Looking Systems

In this paper we investigate theoretically the numerical bias due to the truncation of structurally infinite time forward-looking models, by the means of various terminal conditions. On a general multivariate optimal growth model, we first analytically confirm some well-known heuristic properties for certain extreme spectral cases. However, we show that the heuristic findings stated in the literature, relying on intermediate spectral configurations, lack theoretical basis as that they omit, among other relevant features, the crucial role of initial conditions: in this case, comparison criteria exclusively based on spectral considerations lack theoretical sense. Numerical evidence is proposed to illustrate this point and other related empirical findings are presented.

Decision-Making Under Uncertainty: Capturing Dynamic Brand Choice Processes in Turbulent Consumer Goods Markets

We construct two models of the behavior of consumers in an environment where there is uncertainty about brand attributes. In our models, both usage experience and advertising exposure give consumers noisy signals about brand attributes. Consumers use these signals to update their expectations of brand attributes in a Bayesian manner. The two models are (1) a dynamic model with immediate utility maximization, and (2) a dynamic “forward-looking” model in which consumers maximize the expected present value of utility over a planning horizon. Given this theoretical framework, we derive from the Bayesian learning framework how brand choice probabilities depend on past usage experience and advertising exposures. We then form likelihood functions for the models and estimate them on Nielsen scanner data for detergent. We find that the functional forms for experience and advertising effects that we derive from the Bayesian learning framework fit the data very well relative to flexible ad hoc functional forms such as exponential smoothing, and also perform better at out-of-sample prediction. Another finding is that in the context of consumer learning of product attributes, although the forward-looking model fits the data statistically better at conventional significance levels, both models produce similar parameter estimates and policy implications. Our estimates indicate that consumers are risk-averse with respect to variation in brand attributes, which discourages them from buying unfamiliar brands. Using the estimated behavioral models, we perform various scenario evaluations to find how changes in marketing strategy affect brand choice both in the short and long run. A key finding obtained from the policy experiments is that advertising intensity has only weak short run effects, but a strong cumulative effect in the long run. The substantive content of the paper is potentially of interest to academics in marketing, economics and decision sciences, as well as product managers, marketing research managers and analysts interested in studying the effectiveness of marketing mix strategies. Our paper will be of particular interest to those interested in the long run effects of advertising. Note that our estimation strategy requires us to specify explicit behavioral models of consumer choice behavior, derive the implied relationships among choice probabilities, past purchases and marketing mix variables, and then estimate the behavioral parameters of each model. Such an estimation strategy is referred to as “structural” estimation, and econometric models that are based explicitly on the consumer's maximization problem and whose parameters are parameters of the consumers' utility functions or of their constraints are referred to as “structural” models. A key benefit of the structural approach is its potential usefulness for policy evaluation. The parameters of structural models are invariant to policy, that is, they do not change due to a change in the policy. In contrast, the parameters of reduced form brand choice models are, in general, functions of marketing strategy variables (e.g., consumer response to price may depend on pricing policy). As a result, the predictions of reduced form models for the outcomes of policy experiments may be unreliable, because in making the prediction one must assume that the model parameters are unaffected by the policy change. Since the agents in our models choose among many alternative brands, their choice probabilities take the form of higher-order integrals. We employ Monte-Carlo methods to approximate these integrals and estimate our models using simulated maximum likelihood. Estimation of the dynamic forward-looking model also requires that a dynamic programming problem be solved in order to form the likelihood function. For this we use a new approximation method based on simulation and interpolation techniques. These estimation techniques may be of interest to researchers and policy makers in many fields where dynamic choice among discrete alternatives is important, such as marketing, decision sciences, labor and health economics, and industrial organization.

A Robust and Efficient Method for Solving Nonlinear Rational Expectations Models

The development and use of forward-looking macro models in policymaking institutions has proceeded at a pace much slower than predicted in the early 1980s. An important reason is that researchers have not had access to robust and efficient solution techniques for solving nonlinear forward-looking models. This paper discusses the properties of a new algorithm that is used for solving MULTIMOD, the IMF’s multicountry model of the world economy. This algorithm is considerably faster and much less prone to simulation failures than to traditional algorithms and can also be used to solve individual country models of the same size.

A Robust and Efficient Method for Solving Nonlinear Rational Expectations Models

The development and use of forward-looking macro models in policymaking institutions has proceeded at a pace much slower than predicted in the early 1980s. An important reason is that researchers have not had access to robust and efficient solution techniques for solving nonlinear forward-looking models. This paper discusses the properties of a new algorithm that is used for solving MULTIMOD, the IMF`s multicountry model of the world economy. This algorithm is considerably faster and much less prone to simulation failures than to traditional algorithms and can also be used to solve individual country models of the same size.

Underemployment of production factors in a forward-looking model

This paper proposes a dynamic efficient bargaining model with a putty-clay technology and aggregation over heterogeneous micro markets. We analyse the agents' optimal response to unexpected real changes in their economic environment. The model gives a useful description of the linkages between unemployment and the rate of utilisation of productive equipment.

An alternative methodology for solving nonlinear forward-looking models

This paper presents a new methodology for solving nonlinear deterministic forward-looking models. Based on a relaxation algorithm described by Laffargue (1990), the methodology is theoretically founded on a general multivariate linear model. Then, a complete experimental scheme is provided in the nonlinear case, including solution time horizon selection and saddlepoint path testing strategies. The proposed experiment is mathematically robust and it does not require any expert knowledge in numerical analysis. It is especially adapted to the simulation exercises conducted on medium scale economic models.

AN ANALYSIS OF THE IMPACT OF FINITE HORIZONS ON MACROECONOMIC CONTROL

THIS PAPER is concerned with the practical application of optimal control techniques to the macroeconomic policy design problem using empirically based econometric models which embody forward-looking behaviour. In the context of UK models, such work can be divided into two broad approaches. One involves the application of well known non-linear optimal control algorithms directly to non-linear rational expectations models, as in Holly and Zarrop (1983) and Westaway and Wren-Lewis (1993).1 In the other, linearised versions of non-linear models are derived, allowing the more tractable properties of linear rational expectations models to be exploited, as in Christodoulakis et al. (1991) and Weale et al. (1989). Surprisingly, relatively little work has been done to reconcile these two approaches, in particular to compare the policy implications which might emerge from applying the different techniques to the same problem. In this paper we explain why these differences are important by emphasising the role of the finite horizon. We show that this can seriously distort the optimal control outcome. Typically, macroeconomic models are large and non-linear; for example the National Institute model of the UK economy on which the empirical analysis in this paper is based contains just over 350 variables with the behavioural content embodied in around half of these (see NIESR 1991). Inevitably, this forward-looking model can only be solved using numerical techniques, such as the extended Gauss-Seidel method discussed by Fisher and Hughes Hallet (1988). These solution techniques can be computationally expensive especially when the dominant unstable root of the model associated with this forwardlooking behaviour is close to the unit circle. By contrast, linear models, or linearised versions of non-linear models, can be solved at much less computational expense, even for rational expectations models (using, for example, the method suggested by Blanchard and Kahn 1980). When considering the policy design problem, an important implication of having to solve models by numerical methods is the need to replace analytic infinite horizon solutions by finite horizon approximation. The significance arises in two ways. First, in the presence of forward-looking expectations, any finite horizon model solution requires the imposition of a terminal condition

The monetary exchange rate model in the long run: An empirical investigation

The Monetary Exchange Rate Model in the Long Run: An Empirical Investigation. — This paper uses the Johansen multivariate cointegration method to examine three variants of the monetary approach to the long-run exchange rate model: flexible price, forward-looking and sticky price monetary models. Evidence is provided for four bilateral sterling exchange rates. The sensitivity of the results to the measurement of monetary aggregates is also examined. The cointegration results provide dismal evidence for the flexible price and forward-looking models irrespective of the measurement of money. The findings are more mixed for the sticky price model, particularly when broad money is used.

A BUFFER STOCK MODEL OF THE DEMAND FOR MONEY BY THE PERSONAL SECTOR

This paper examines the forward-looking rational expectations buffer stock model of Cuthbertson and Taylor (1987) in the context of the personal sector of the UK. The buffer stock model is evaluated for both narrow and broad money definitions in the UK using the encompassing the VAR methodology of Mizon (1984). This suggests that the buffer stock model is a congruent model, and that the broad definition is the most appropriate aggregate with which to model buffering behaviour — in line with previous studies, Mizen (1992). Further analysis of the models, in the light of Hendry (1988), confirms this view.

The demand for Indonesian narrow money: long-run equilibrium, error correction and forward-looking behaviour

Since the 1960s, the banking and financial sector has been at the forefront of the Indonesian development strategy. Thus in order to gain an understanding of the problems and opportunities facing Indonesia, it is essential to understand the workings of the monetary sector of the economy. The aim of this paper is to analyse the narrow component of money demand, using modern econometric techniques. But the major innovation of the paper (in the context of a developing country) is the use of an explicit forward-looking model. This approach, the consequence of financially sophisticated behaviour on the part of Indonesian agents, has significant policy implications. One of these is that announced changes in policy, if credible, will lead to a more rapid response from the private sector than if agents were purely backward looking. This may make the operation of monetary (and other) policy more effective than would otherwise be the case.

Financing the Transition of Previously Centrally Planned Economies: Macroeconomic Effects on Western Europe

Under alternative assumptions on the likely developments in external financing of PCPE transition, and based on a multi-country, forward-looking model that includes a simplified PCPE block, we simulate the response of PCPEs to a transfer of capital from the industrial countries, and assess the potential implications for Western Europe over the next ten years. Real interest rates in Western Europe are likely to experience only mild upward pressure, and most macroeconomic aggregates are likely to change by substantially smaller magnitudes than typical over the business cycle.