# «Discussion Paper No. 97-01 E Businessmen's Expectations Are Neither Rational nor Adaptive Marc Nerlove Til Schuennann :, ~ ZEW Zentrum fOr ...»

Discussion'

Paper

Discussion Paper No. 97-01 E

Businessmen's Expectations Are Neither

Rational nor Adaptive

Marc Nerlove

Til Schuennann

:",

~

ZEW

Zentrum fOr Europaische

Wirtschaftsforschung GmbH

Industrial Economics and

International Management

Series

Businessmen's Expectations Are Neither

Rational nor Adaptive

by

Marc Nerlove*)

Til Schuermann**)

*)Department of Agricutural and Resource Economics,

University of Maryland

**)AT&T Bell Laboratories

January 1997

Abstract

A framework which allows for the joint testing of the adaptive and rational expectations hypotheses is presented. We assume joint normality of expectations, realizations and variables in the information set, allowing for parsimonious interpretation of the data; conditional first moments are linear in the conditioning variables, and we can easily recover regression coefficients from them and test simple hypotheses by imposing zero restrictions on these coefficients. The nature of the data, which are responses to business surveys and are all categorical, requires simulation techniques to obtain full information maxiI11-um likelihood estimates. We use a latent variable model which allows for the construction of a simple likelihood function. However, this likelihood contains multifour)dimensional integrals, requiring simulators to evaluate. Simulated maximum-likelihood estimation is carried out using the Geweke-HajivassilouKeane (GHK) method, which is consistent and has low variance. The latter is crucial when maximizing the log-likelihood directly. Identification of the parameters is achieved by placing restrictions on the response thresholds and/or the variances. We find that we can reject both hypotheses.

I. Introduction How expectations are formed is an issue of profound importance in economic theory, and m'odels of expectation formation have a long history. Testing theories of expectation formation, however, requires that we find data on this intangible object called an expectation,. Direct observations are rare. Usually, the effects of changing expectations can only be inferred indirectly through observations of the aggregated outcomes of individual decisions. Ideally we would like micro-level data on both expectations and realizations. The quarterly business surveys, such as the one conducted by the ~onfederation of British Industries of UK manufacturing firms or the Konjunkturforschungstelle of Switzerland, contain questions about both expectations and realizations of such variables as demand, prices, and production.

The importance of using surveys to test empirically models of expectation formation is succinctly expressed by Pesaran (1987, p. 207): "Only when direct oDservations on expectations are available is it possible to satisfactorily compare and contrast alternative models of expectations formation." But not all the difficulties associated with indirect testing disappear and several new ones emerge.

The principal new difficulty is the categorical nature of almost all tl;1e data available.

Our primary focus in this paper is on how to analyze qualitative data on expectation's.

In business surveys, firms are asked questions about observed changes in their demand, production and prices, their expectations of future changes in these variables, and other aspects of the firm's behavior. Their responses are primarily ordered and categorical; that is, they answer "increase", "remains the same", or "decrease" in comparison with the previous month or quarter. As a result, standard time series techniques applied directly to the categorical data are not appropriate for testing expectations hypotheses.

Traditionally, business survey data have been analyzed by means of conditional log-linear probability models (CLLP) (Nerlove, 1983). CLLP models permit reduction of the parameter space to manageable size, but they essentially treat the data as truly discrete and unordered and are perhaps best suited for data analysis. Nerlove (1988) proposed an alternative approach of treating the survey responses as being triggered by continuous latent structural variables as they cross certain thresholds.' The data are arranged in a JQ contingency table, where J is the number of categories (for the business survey model, J=3) and Q the number of variables under consideration. A standard tool in the econometrician's kit for Nerlove (1988) compares the latent variable regression to a regression of a continuous variable I y on two continuous variables XI and X2 and uses this to illustrate the use of correlations for determining the structural relationship among latent variables under the assumption of multivariate normality.

contingency table analysis is the method of minimum chi-square. 2 While this·· method may be appealing on grounds of familiarity, maximum likelihood is preferable in the present application. 3 The relationships among the latent variables can be summarized in a covariance matrix that can theoretically be estimated by maximum likelihood. However, standard ML procedures are not feasible even in small models due to problems involving the computation of multi-dimensional integrals. This is not to say that such models have not been estimated. However, conventional econometric techniques, either the pairwise calculation of polychoric correlations (Pearson and Pearson, 1922, and Olsson, 1979) by maximum likelihood (Poon and Lee, 1987) or the two-step method (Martinson and Hamdan, 1971) ignore the true multivariate nature of the data and thus bias the usual tests. The second method, although simpler, has the disadvantage of not necessarily producing a matrix of estimated correlations that is positive definite. 4 In this paper we formulate a method for testing jointly the rational and

**adaptive expectations hypotheses using business survey data from two countries:**

Switzerland and the United Kingdom. We use data on demand in the form of responses about incoming orders rather than data on prices. Since the majority of firms surveyed are in manufacturing, it is unlikely that they operate in anything near to a perfectly competitive market. Thus these firms are likely to be price setters rather than price takers. Demand is less under their direct control and therefore less endogenous to their own actions than are prices.

This paper extends Horvath, Nerlove and Willson (1992), who test (and reject) only rationality of British manufacturing firms' expectations for several periods using numerical (not simulation) full-information maximum-likelihood (FIML) methods; it builds on Nerlove and Schuermann's earlier paper (1995).

Horvath, Nerlove and Willson did not provide a specific alternative to rational expectations, as we do here. We also formulate a lower dimensional version of the rational expectations hypothesis test, which can in fact be computed numerically, and compare the results with the higher dimensional version which requires simulation-based estimation. The lower (3) dimensional version of the model eliminates the future value of expectations, and thus the effects of overlapping information sets discussed below. Since our finding that future expectations are correlated with current ones is one of the most significant of OUI: results, with far reaching implications for all work on testing models of expectation formation, we emphasize the results based on the 4-dimensional model, the estimation of which requires a more elaborate technique.

See Rao (1955).

For a discussion of first-order asymptotic equivalence of minimum chi-square and maximum likelihood, see Rao (1961, 1963). For a direct comparison of these two methods in a simulation context, see Schuermann (1993).

See Nerlove, Ross and Willson (1991).

Simulation techniques, developed by McFadden (1989), Pakes and Pollard (1989) and Hajivassiliou et al. (1990), lend themselves naturally to the estimation of latent-variable models. In these seminal papers, it is shown how various simulators, can be used to calculate multivariate integrals in the context of limited dependent variable (LDV) models. In this paper, we employ the smooth recursive conditioning simulator of Geweke, Hajivassiliou and Keane (GHK) to obtain simulated maximum likelihood (SML) as a way of testing the joint hypotheses. The GHK has low variance which is crucial when maximizing the likelihood function directly.s A recent related papeli by Pesaran and Samiei (1995) examines limited dependent variable rational expectations models using simulation-based estimators similar to those proposed here.

The latent variable framework as proposed originally by Nerlove (1988) is introduced in Section II. The rational and adaptive expectations hypotheses are

- formulated in this framework and are presented in Section III. We then present formulation for joint testing.

In Section IV, we discuss maximum likelihood estimation for contingency tables where we will demonstrate the inf~asibility of numerical FIML procedures and show how simulation methods may be used.

In Section V, we test the joint hypothesis formulation with Swiss monthly and UK quarterly surveys of manufacturing firms.

Section VI concludes with some remarks about the general implications of our results for studies of expectation formation.

II. A Latent Variable Framework When building models using data arranged in contingency tables, it is often useful to think of the categorical variables as being generated by underlying continuous latent variables. Specifically, the business survey model is part of a general class of latent variable models with an observation rule

** y = 't(y*)**

where y* is the unobserved latent random variable, and 't() is the many-to-one mapping from y* to the discrete observed variable y. In the case of business surveys we have 't:9\ ~ {I,2,3 }. In other words, 't() maps the entire real line into the integer set {1,2,3 }. Another better known example is the binary response model We do not describe the simulators themselves. See Hajivassiliou and Ruud (1994).

S (seen in probit and logit models) where 't( ) is just the indicator function. The model appropriate to business surveys differs from the standard LOY model in that both the left and right hand side observations are the result of the mapping 't( ).

Let z* = (y;.X;I.X;".... x~,) be a ((k+l)xl) vector of latent dependent and independent variables that satisfies the following linear relationship (1) where ~ is a (kx I) vector of coefficients, Et is a disturbance term and t is a time subscript. It is assumed that E(Et ) = 0 and that Et and x' are uncorrelated. For firm i we observe categorical indicators Zit = (Yit.Xil) of the unobservable latent variables z*t = (Y*t.x*t) such that

We assume further that y; and x; are jointly normally distributed with covariance matrix. It is in general not possible to identify all elements of e = (L ;

aijt. i = I, 2, j = I".., k, k+ 1) separately from a single cross-section of data. In particular, consider the contingency table obtained from the bivariate latent variable distribution h(y*,x*) with thresholds {ay\, a,z, ax\, axz}. This table will be identical to the one generated by the distribution hey leI,x*/czJ and thresholds { ayl/c\, ayz/c\, av,/c". a.,,/c~}, where Cl and C~ are arhitr~ry r(mst?T!t~ 9 Tht:'fefore, we may normalize each z* to have arbitrary location and variance. One common identifying restriction is to let z*i have unit variances; then L is simply a matrix of (k)(k+I)/2 correlations.

The conditions under which the categorical survey responses for expectations and realizations can be considered as independent draws from an aggregate distribution are developed in Theil (1952). In addition to cross,sectional independence, the major requirement is that individual firm's reporting thresholds are identical.

We do not consider the case of time-varying thresholds.

The same logic holds with respect to a non-zero mean of the latent variables. The contingency table obtained from h(y*,x*) and thresholds {a} will be identical to that obtained from h(y*y,x*-~x) and thresholds {a-~}. (See also Horvath, Nerlove and Willson (1992).) Specific assumptions of thresholds and variances will be treated in section II.C. In some instances, we can relax the unit variance assumption if we then restrict the thresholds to be equal.

Since the joint distribution of y and x, f(y,x), is normal, so is the conditional distribution of y given x, fey I x). The parameter vector in (l) can be inferred from L using (3)