Journal of Econometrics 15 (1981) 3--9. North-Holland Publishing Company

EDITOR’S INTRODUCTION TO PART II*

1. Objectives

This edition comprises the second in a two-part series containing some of the best econometric research that has originated within the Federal Reserve

System’ during the past two years. More’ detailed introductory information regarding the objectives and organization of these two editions is contained in the Editor’s Introduction to the previous edition.

I have found the research and policy content of the papers in both of these editions to be of unusual interest. I wish to thank Arnold Zellner and Dennis Aigner for the opportunity afforded by these editions to me and to the authors of these papers. I also wish to thank the following three groups of people: (1) David Pierce, Peter Tinsley, P.A.V.B. Swamy, and Alfred Norman for their advice at various stages of the organization of these editions, (2) the referees (listed at the end of this edition) for the assistance that made these two editions possible. and (3) the Federal Reserve Board members and the Federal Reserve System’s senior staff for their support of this research.

2. Topics in Part 11

As discussed in the introduction to the last edition, these two editions are divided into five sections, each containing research originating within the Federal Reserve System. The last edition contained the first two sections on (1) monetary aggregation and (2) time series. This edition contains the remaining three sections on (3) optimal control, (4) large structural models, and (5) financial structures modeling and institutional change.

The following brief discussions of the papers appearing in this edition are organized into three groupings and headed by the authors’ names.

3. Summaries of papers in Part II

3.1. Optimal control

Research effort within the system on large scale econometric models has been considerable during the past decade. As these models have improved,

*The views expressed in this introduction are those of the author and do not necessarily represent the views of the Federal Reserve System.

4 Editor’s Introduction to Part II

interest has grown in the possible use of optimal control methods for computing policy strategies conditionally upon such models. Currently the impact of the rational expectations hypothesis on that objective is as controversial as the state of development of large econometric models. Nevertheless, to the degree that development of such models continues and improves, the potential for productive use of numerical optimal control algorithms also increases.

For numerical policy analysis to achieve its potential, regardless of the limits of that potential, two existing problems must be overcome: (1) control strategies which are computationally attractive must be devised and efficiently implemented, and (2) objective functions must be developed which can serve as standards for comparing alternative strategies or models.

Two of the three papers in this section (by Norman and Palash) relate to the first problem. The other paper (by Tinsley and von zur Muehlen) relates to the second problem.

3.1 .I. Aljki Normrrn’

Currently the implementation of stochastic control strategies for implicitly defined models is greatly impeded by the computational cost. In his paper, Norman analyzes a strategy proposed by Gregory Chow in 1975’ and finds

that use of conventional matrix multiplication results in computational complexity of order b16, where n is the number of states. Norman then developes an equivalent alternative strategy which is only of order n4 in computational complexity.

Optimal control literature traditionally analyzes linear-quadratic-Gaussian formulations of macroeconomic policy design. In these formulations policy planners seek to minimize the distance between a direct target vector, y, and a vector of aspiration levels, y*, using a suitably dimensioned matrix, M, as a distance metric. Until recently, neither y* nor M were known and each was

arbitrarily selected. Since passage of the Humphrey-Hawkins Act, estimates of y* are available, but the metric, M, remains unknown. This paper suggests an approach to ex urzte policy evaluations using a Mahalanobis distance metric.

The proposed objective is to maximize the probability that the direct target vector, y, will lie in a region covering y*. By the Gaussian assumption,

‘Alfred Norman, on leave from the University of Texas at Austin, is a visiting professor in the Special Studies Section of the Federal Reserve Board’s Division of Research and Statistics.

‘G.C. Chow, Analysis and control ofdynumic s)stems (Wiley, New York, 1975). ‘P. Tinsley and P. van zur Muehlen are in the Special Studies Section of the Federal Reserve

Board’s Division of Research and Statistics.

this problem reduces to minimization of a quadratic form. in which the inverse of the covariance matrix of the selected policy design serves as the

effective distance metric. An important feature of this problem is the dependence of the covariance matrix on the selected policy design. Using stochastic properties of the MPS quarterly model, the authors compare the proposed direct target policy with a policy targeting monetary aggregates and conclude that direct targeting is about live times more efficient than intermediate targeting.

3.1.3. Carl Palush”

Currently there exist numerous codes for solving deterministic optimal control problems with implicitly defined nonlinear econometric models. In his paper, Palash examines the accuracy and computational cost reduction that can be achieved by using a low-order orthogonal polynomial

approximation to the optimal sequence of controls. The paper discusses problems of achieving computational accuracy when

polynomial constraints are incorporated into maximization algorithms and concludes that these problems are eliminated when ortho-normal polynomials are used. The ability of low-order polynomials to approximate optimal policy is analyzed on the basis both of historical policy and of a non-polynomial-constrained optimal solution. According to prescribed criteria, it is shown that low-order polynomials can well approximate historical policy over a time interval of sharp policy changes and can also approximate an optimal solution of a standard objective function constrained by the MPS (MIT-PENN-SSRC) model. Savings in computer time of 50 percent through the use of low-order polynomials in optimal control problems are demonstrated.

3.2. Large structural models

The Federal Reserve Board has allocated substantial resources to the development of two large-scale econometric models. One is the widely known MPS quarterly model of the United States economy. The other is a new large-scale multicountry model. The first paper (by Howe, Hernandez- Cata, Stevens, Berner, Clark and Kwack) reports the results of dynamic simulation experiments with the Board’s new multicountry model.

3.2.1. Hownrd Howe et al.”

This paper reports on some initial results with a large scale multicountry

‘Carl Palash 1s in the Research Processing Division of the Federal Reserve Bank of New York’s Research Support Department.

5When the research was undertaken, Howard Howe, Ernest0 Hernandez-Cata, Guy Stevens. Richard Berner, Peter Clark and Sung Y. Kwack were in the Quantitative Studies Section of the Federal Reserve Board’s Division of International Finance.

model. In recent years, development of this model has absorbed a significant fraction of the resources and talent existing within the Quantitative Studies Section of the Board’s International Finance Division. Through this paper we get a first look at the dynamic simulation properties of this important new model.

The multicountry model (MCM) is a system of linked national macroeconomic models, at the center of which is a medium-sized model of the U.S. economy. Linked to it, and to each other, are models for Canada, West Germany, Japan, the U.K.. and an abbreviated model representing the rest of the world. The country models are connected by trade and capital flows, exchange rates, interest rates. and prices.

The following two goals dictated the MCM model’s present form and size:

(1) endogenous determination of the most important (bilateral) exchange rates, and (2) elaboration of the key real and financial relationships among the U.S. and major foreign countries. In addition to serving these purposes. the individual country models and the MCM as a whole are shown in this paper to track satisfactorily in dynamic simulations inside and outside the sample period.

The simulations reveal the interdependencies within the MCM model among the world’s economies. Those interdependencies resulted in strong feedback effects upon the economy of the country initiating a monetary or fiscal policy change. The experiments also reveal that endogenizing exchange rates is important within the MCM model, since the impact of economic policies in the experiments often depended upon induced exchange rate effects.

While the apparent benefits of indexing are generally thought to be substantial, the concern has been expressed that the sensitivity of real economic activity to stochastic disturbances might be increased under indexation as a result of the attenuation of the Pigou effect and of automatic tax stabilizers. Flannery and Johnson modified the MPS quarterly econometric model to reflect the full indexing of all wage and financial contracts. Conditionally upon the MPS model, the paper then explores the macroeconomic consequences of indexing by comparing the simulated responses of the indexed and standard models to identical shocks. The authors also constructed separate models with wage indexation alone and with indexation of all sectors except wages.

The interpretation of the paper’s results depends upon one’s views

“LCWIS Johnson IS III the Speed Studies Sectmn of the Federal Reser~c Board‘s Dlbision of Research and Statistics. Mark Flannery is at the University of Pennsylvania’s Wharton School of Business.

Editor’s Introduction to Part II 7

regarding the merits of the MPS model and the plausibility of the results. In any case, the paper is highly revealing of the model’s properties and provides significant insight into the MPS model’s wage-price-expectations mechanisms.

Flannery and Johnson find that wealth effects play a key role in stabilizing the MPS model under fixed money growth rules. When these effects are substantially eliminated by indexing financial contracts, price level movements have a greater impact on inflationary expectations (the Fisher effect) than on nominal interest rates (the Keynes effect). As a result, real interest rates move perversely. At the same time, wage indexing amplifies price movements, and the system becomes explosive. On the other hand, indexing permits the direct control of real interest rates (e.g., open market policies could be conducted with indexed treasury bills). The indexed model under an interest rate policy behaves much like the standard model does under a money growth rule.

If the MPS structure is accepted, Flannery and Johnson reach the following conclusions. If the monetary authority alters its policy to focus on real interest rates, indexing poses no significant threat to macroeconomic stability. However, fixed money growth rules and indexing are incompatible; the combination is explosive. Such strong results either must provide fundamental insight into the effects of indexing or else must reveal fundamental deficiencies in the MPS model’s basic structure. In either case, there is much to be learned from Flannery and Johnson’s paper.

3.3. Financial structures modeling and institutional change

Through its regulatory functions, the Federal Reserve System has acquired substantial interest in modeling financial structures and institutional

processes and functions. In this area, data availability within the system has been a catalyst to quality research. The papers in this section explore three fundamentally different aspects of institutional and money market structure.

3.3.1. P.A. Tins& and Bonnie Garrett, with Monica Friur7

Since 1974 many traditional formulations of the transactions demand for money have persistently overpredicted the demand for checking deposits by as much as 20%. The authors suggest that the main difficulty with traditional formulations is not the functional specification of the demand for ‘money’ but the a priori definition of transactions balances to include only currency and demand deposits (i.e., the media of exchange). The closest substitute for demand deposits during the period examined, especially 1974--

‘P.A. Tinsley and Bonnie Garrett are and Monica Friar was in the Special Studies Sectlon of the Federal Reserve Board’s Division of Research and Statistics.

76, was immediately available funds (IF). Both unsecured (Federal funds) and secured (repurchase agreements) IF were used as transactions balances to circumvent the prohibition of explicit interest payments on demand deposits.

Because of the lack of accurate measures of participation in the IF market by non-bank sectors, three Federal Reserve Board data series are pooled to construct an estimate of net IF purchased by banks from non-bank sectors. This IF series is then disaggregated into two unobservable components. One component, IFY, is related to the demand for transactions balances stemming from variations in income (or GNP), and the other component, IFP, is related to transactions balances associated with variations in interest rates. Since the former component resembles an empirical definition of ‘money’, IFY is then incorporated into a traditional transactions demand formulation.

This respecification predicts a demand deposit series that eliminates about SOY0 of the errors generated by a traditional equation. In 1978 Tinsley et al.* found no alternative predictor that eliminates more than 25”/;, of the forecast overstatement.

3.3.2. Wil/iam Melton and Vunce Roley’

Following Brainard and Tobin, the importance of the balance sheet constraint in specifying and estimating a consistent set of asset supply and demand equations has been recognized for some time. However, little notice has been taken of the fact that the basic paradigm underlying the Brainard- Tobin analysis is a model of portfolio selection behavior in which the rates of return on assets are exogenous to both the demanders and suppliers of

assets. The exogenous-returns paradigm has been applied in the empirical

literature in two distinct ways. First, where asset markets are perfectly competitive, asset demanders and suppliers are price-takers, and the paradigm is clearly applicable. Second, in markets where some asset demands (supplies) are imperfectly elastic, the paradigm can still be applied, if the rate- setting decision of asset suppliers (demanders) is separated from the rest of their portfolio decision. Typically this is done through appeal to various considerations which allegedly prevent asset suppliers (demanders) from adjusting their prices to clear the market. Prices are assumed to be adjusted through some procedure which has no formal relationship to optimization of remaining components of the portfolio. Then the usual Brainard-Tobin consistency conditions can be applied to the rest of the portfolio decision.

Melton and Roley investigate the implications of the consistency

‘P.A. Tinsley, B. Garrett and M. Friar, The rneusurenlenl O! mane) duncuzd, Special Studies paper no. 133 (Federal Reserve Board, Washington, DC, 1978).

‘William Melton is in the Financial Markets Section of the Federal Reserve Bank of New York’s Domestic Research Department. V. Vance Roley (currently on leave at the Council of Economx Advisors) is on the Research Staff of the Federal Reserve Bank of Kansas City.

Editor’s Introductim to Purr II 9

conditions for the specification and estimation of portfolio balance models in

which some asset markets are imperfectly competitive and the asset supplier’s rate-setting (or quantity-setting) decisions are an integral part of his overall portfolio decision. This is done in the context of a simple stochastic model of portfolio choice, in which it is assumed that a financial firm confronts a set of imperfectly elastic asset demands. A procedure is suggested that results in a consistent set of asset demand and supply equations and allows the independent estimation of all price and quantity setting equations.

3.3.3. David Humphrey10

The Federal Reserve, in addition to its responsibility for monetary control,

plays an important role in the payments mechanism. Humphrey’s paper concentrates on Federal Reserve check processing operations and provides estimates of scale economies. This information can assist in determining whether or not check processing prices may appropriately be based upon average or marginal processing costs, when Federal Reserve pricing of this service is implemented. Scale economies were estimated using a translog cost function model with annual cross-section data on 36 Federal Reserve (Bank and branch) check processing offices.

Evidence of significant scale diseconomies was found at one-half of all Federal Reserve offices and covering almost 80 percent of all processed checks. This evidence satisfies a necessary condition for marginal cost pricing; but, depending upon pricing practices in the private sector, diseconomies to scale may or may not be sufficient to justify adopting such a pricing policy.

Various restrictions on the cost function model were imposed and tested. Prior stochastic information on a necessary second-order condition was incorporated into the cost function model. Use of the prior information yielded results which met all first and second-order theoretical duality conditions regarding model behavior. The scale economy results were found to be insensitive to whether or not the second, order conditions were satisfied.

William A. Barnett

Board qf Gowrnors of the

Federal Reserce System Washington, DC

April 1980

“David Humphrey is in the Financial Studies Section of the Federal Reserve Board’s Division of Research and Statistics.