Investigating the compatibility of econometric forecasts and subjective expectations: A suggested framework

Journal of Economic Psychology 9 (1988) 233-249 North-Holland

233

INVESTIGATING THE COMPATIBILITY OF ECONOMETRIC FORECASTS AND SUBJECTIVE EXPECTATIONS: A SUGGESTED FRAMEWORK *

Harinder SINGH

San Diego State University, USA

Received February 16, 1987; accepted September 3, 1987

The precise nature of expectations formation plays a pivotal role in economics. However, economists have generally relied on econometric forecasts as proxies for the underlying expectations process without adequate verification. This study suggests that Bnmswik’s Lens Model can be meaningfully utilized to analyze the correspondence between econometric forecasts and subjective expectations. The normative and descriptive aspects of expectations formation can be distinguished. More importantly, the similarity between ex ante subjective expectations and ex post realizations can be analytically broken down into specific components representing knowledge, response consistency and task uncertainty. The proposed model is estimated with Living- ston’s price survey data. The results indicate that lower achievement is attributable not to lower knowledge or response consistency but rather to relatively greater unpredictability in the statistical environment.

This article provides an integrated framework for jointly evaluating econometric forecasts and subjective expectations, based on the same information structure. ’ The statistical model implied by the framework

* The author is grateful to Prof. Raford Boddy and Roger Frantz for helpful suggestions and to Wesley Porter for research assistance. The usual caveat about errors applies.

Author’s address: H. Singh, Department of Economics, College of Arts and Letters, San Diego State University, San Diego, CA 92182, USA. ’ The uniform terminology employed in this paper is as follows: ‘Econometric forecasts’ imply statistical projections generated by empirical models (such as Ordinary Least Squares regressions or Time-Series models) based on realized objective data. On the other hand, ‘subjective expectations’ are cognitive estimates about the future values of the variable made by individuals on the basis of past information. These estimates can be obtained by surveys or verbal queries.

0167-4870/88/$3.50 0 1988, Elsevier Science Publishers B.V. (North-Holland)

234 H. Singh / Econometric forecasts and subjective expectatiom

is estimated to show how it can provide valuable insight into the process of expectations formation.

The motivation for providing such a framework is based on two major considerations. First, there is a general need for analyzing expectations at the empirical level. The precise nature of expectations formation plays a pivotal role in economics. For instance, in macroeco- nomic labor markets, the trade-off between inflation and unemploy- ment (the Phillips curve) is contingent upon how rapidly wage expectations adjust to price changes. Apparently, issues such as the speed of adjustment cannot be resolved at the theoretical level. Also, when an expectations model is employed to test a specific primary hypothesis, the final result is an inextricable joint hypothesis: whether expectations have been modeled correctly and whether the primary hypothesis is true. Consequently, greater independent testing of different expectations hypotheses should be undertaken.

Second, there is a specific need of analyzing the compatibility of econometric forecasts and subjective expectations. The general tendency among economists has been to employ econometric forecasts as proxies for expectations, without adequately verifying the validity of such substitutions. Although actual cognitive expectations are not directly observable, subjective estimates obtained by surveys and verbal queries can provide valuable information. There do not appear to be strong a priori reasons for favoring econometric forecasts over subjective expectations. Econometric forecasts tend to emphasize the final desired result rather than the process of expectations formation (-Simon 1978). Persistent violations of normative assumptions imply that these models may only have limited descriptive and predictive validity. Consequently, subjective expectations and econometric forecasts need to be regarded as two separate sets of clues for discerning the true underlying expectations process of economic agents. Rather than ini- tially preferring one to the other, the compatibility and complementary nature of these clues should be analyzed under specific circumstances.

The framework developed in this study provides a beginning in this respect. The proposed model allows the analytical decomposition of achievement (the correspondence between ex ante subjective expectations and actual realizations) into specific components representing knowledge, response consistency and task uncertainty, etc. Conse- quently, the precise reasons for the shortfall in achievement can be traced. It will be shown that when subjective expectations and econo-

H. Singh / Econometric forecasts and subjectioe expectations 235

metric forecasts are placed on an equal footing (based on the same information structure), the former are not necessarily suboptimal.

The article proceeds on the following lines. Section 1 analyzes two related issues: The importance of incorporating behavioral realism and the need for caution in interpreting subjective expectations data as suboptimal. Section 2 presents the Lens Model and analyzes specific components of the framework. Section 3 estimates the model based on price survey data. The article concludes with suggestions for future research.

1. The need for incorporating behavioral realism

In this section it is contended that although statistical forecasts are generally favored as proxies for the expectations process, they are not without major methodological limitations. On the other hand, subjective expectations should not be regarded as suboptimal without adequate verification. Econometric forecasts are usually constructed and evaluated on the basis of a normative optimality criterion. The optimal or rational forecasts is regarded as one that minimizes the variance of the forecasting errors. However, this evaluation principle is overtly narrow since learning costs of alternative information acquiring methods are not evaluated. Muth’s Concept of Rational Expectations carries this optimality criterion to its logical extreme (Muth 1960). According to Muth, expectations are not ‘rational’ if systematic prediction errors are made or if the prediction errors are correlated with any past information. In order to make this concept operational, unrealistic normative assumptions are implicitly made. First, it is assumed that convergence towards the true realized values takes place. It can be shown that Rational Expectations by themselves need not imply convergence (De Canio 1979). Second, extreme information availability assumptions are needed. In particular, economic agents are required to know the true structure of the model and the underlying stochastic processes (Friedman 1979). Third, the criterion concentrates on the final desired result, the explicit process by which information is gathered and processed is not given adequate attention (Simon 1978). Conse- quently, employing optimal economic forecasts as proxies for the expectations process has its own limitations.

236 H. Singh / Econometric forecasts and subjective expectations

Moreover, empirical evidence about the strong and systematic viola- tion of normative statistical assumptions has been rapidly accumulating (Wallsten 1980; Kahneman et al. 1982). The implication emerging from these investigations is that an experimenter needs to be cautious in imposing a realistic normative criterion. To a normative experimenter, an economic agent’s expectations may appear suboptimal because they are processed by a personalized schema (which is employed to cogni- tively simplify complex information). Since this personalized schema may not conform to a normative optimal schema (imposed by the experimenter), the subjective expectations of agents are generally regarded as suboptimal and not very relevant for economic analysis. However, a better understanding and prediction of actual economic behavior will be possible only if we analyze these subjective expectations. 2 An economic agent is going to behave on the basis of his subjective expectations, regardless of whether these expectations conform to a normative criterion. Consequently, a more accurate descriptive account of the expectations mechanism is desirable for two reasons. First, in order to make our analysis more relevant to the actual behavior of economic agents and the economy, we need to ascertain whether econometric forecasts are valid descriptive proxies for subjective expectations. Second, a more realistic capturing of subjective expectations will also improve our predictive ability of future economic events. 3

The overt reliance on normative statistical models, at the cost of descriptive validity can be demonstrated by evaluating previous empirical work on price expectations. Most of these studies have employed the data set of semi-annual survey on price expectations conducted since 1947 by Joseph Livingston, a financial columnist from Philadelphia (Carlson 1977).

Earlier studies applying Muth’s concept of rationality to the survey data found that these subjective estimates were not optimal predictors

* George Katona (1975) has consistently emphasized the crucial significance of actual consumer perceptions formed under the psychological limitations of specific environmental uncertainty. He

has conducted a periodic survey of ‘consumer sentiments’ which attempts to capture subjective expectations of consumers within these environmental limitations.

3 Recent clinical investigations reveal that subjective decision making is subject to specific

heuristics and biases which are not only widely prevalent but also robust to different specifications

(Kahneman et al. 1982). Incorporation of these robust subjective decision strategies into our models (after appropriate empirical verification) will not only improve their descriptive validity

but also their predictive performance.

H. Singh / Econometric forecasts and subjective expectations 237

of actual price realizations. 4 Consequently, these expectations were regarded as ‘irrational’. However, subsequent studies reveal another story. Carlson (1977) points out that when the six-months ahead predictions are made by the panelists in November and May for June and December of the following year, the latest actual price data available to them is for October and April respectively. Consequently, the series should be correctly employed to construct eight months instead of six months ahead forecasts. Moreover, Livingston sometimes adjusted the surveys to reflect new available information. When the unadjusted eight month ahead expectations are converted into appropriate inflation rates and compared with ex ante forecasts made by Data Resources Inc. (DRI) from 1973 to 1982, the similarity between the Livingston and DRI forecasts is remarkable (Caskey 1985). These comparative observations also apply to other major commercial forecasting establishments since they have basically similar performance records (McNees 1981). Rodney and Jones (1980) have developed a multilevel adaptive expectations model that takes observed prices as information available to participants. The agents revise their expectations not only on the basis of the previous price level but also on the basis of the underlying inflation rate and the trend in the inflation rate. When fitted to the Livingston survey data, such a model appears to provide an adequate explanation of price expectations from 1947 to 1975. Caskey (1985) finds that a credible set of 1958 prior beliefs about the inflation process, combined with Bayesian updating procedures (to reflect the forecaster’s subjective learning mechanism) accounts remarkably well for the Livingston forecasts.

These recent empirical investigations point towards the following implication: When a reasonable learning mechanism is incorporated into ex ante statistical forecasts, the results are remarkably similar to subjective expectations. Generally, subjective expectations should not be regarded as suboptimal if they do not correspond closely with ex post realized values. Rather, the specific reason for this lack of correspondence should be investigated. The derivation of a framework which allows such an investigation is taken up next.

4 Examples of studies on Livingston price data which conclude that the subjective estimates are

inconsistent with Muth’s concept of rationality include Tumovsky (1970), Pesando (1975) and Pearce (1979).


2. The Lens Model framework

The Lens Model, based on Brunswik’s pioneering work, has been widely employed by clinical psychologists to study such diverse topics as depth perception, clinical inference, conflict resolution, decision behavior (Brunswik 1956; Beach 1967). It is suggested here that this framework can also provide insight into the precise nature of expectations formation. There are two basic reasons for this contention. First, the Lens Model provides an ideal setup for comparing the normative and descriptive aspects of expectations formation. In Section I, we have noted that economists tend to favor normative statistical models, without adequately verifying their descriptive validity. Since recent behavioral studies generally tend to show that most normative decision making models are incompatible with the actual cognitive processes, the relevance and predictive ability of these models need investigation (Schoemaker 1982). The Lens Model provides an appropriate framework for this analysis because it compares the objective (environmental) aspects with the subjective (psychological) components. Second, the framework can distinguish between availability and application of knowledge. If subjective expectations are not closely corresponding with actual realizations, the pertinent question becomes: Is the low achievement due to lack of knowledge or is it due to suboptimal application of available knowledge? The Lens Model can provide a meaningful answer to this question. The ‘black box’ of subjective expectations formation can be analytically broken down, to identify the precise reasons why expectations are not conforming to realizations.

The Lens Model is depicted in fig. 1. The right-hand side shows the subjective (psychological) aspects whereas the left-hand side depicts the objective (environmental) elements. Both sides are connected by pertinent cues basic to the task. Ex ante subjective expectations and actual realizations of the variable in question are assumed to be a linear function of pertinent environmental cues (deterministic component) and residuals (random component) 5 as follows:

0)

where Y, is a vector of the ex post realized values of the variable about which expectations are formed. Y, is a vector of the corresponding ex


Independent Variables (Cues)

Fig. 1. Investigating expectations with a Lens Model.

ante subjective expectations of the variable obtained by surveys or verbal queries. & and & are the multiple regression weights for predicting the variables Y, and Y, respectively. Z, and Z, are the random errors of the linear predictions from their realized values. x1, x,... X, are the environmental cues pertinent for forming subjective expectations and econometric forecasts.

The variable Y,, Y, and the environmental cues (XI, X2 . . . X,,) are standardized values. The predictive (deterministic) part of the model is

t = &IX, + &,2X2 + P*,.X,. (2)

Note that ?a and rS are the predicted components of the variables Y, and Y, based on the same information availability.

5 We need not assume linearity of the cues, nonlinear independent variables can generally be linearized by appropriate transformations. Consequently, the assumption of linearity is with regards to the coefficients. This assumption can be adequately tested by correlating the residuals of the two regressions as discussed subsequently.

240 H. Singh / Econometric forecasis and subjective expectations

By substituting eq. (2) into eq. (1) and rearranging the variances and covariances of these equations we can arrive at the following identity: 6

(3)

Eqn. 3 is the basic Lens Model equation that needs explicit elabora- tion. R,, the correlation between the actual realized values (Y,) and the ex ante subjective expectations (Y,) is generally termed as the achieue- ment index. It measures ex post performance by determining how closely hypothesized expectations conform with subsequent realized values. The achievement index is determined by a number of important components. First: R,, the correlation between the actual realized values (Y,) and the predicted realized values ( fe) measures the degree of task uncertainty. It shows how closely ex ante, optimal statistical forecasts can approximate the actual realized values, given the statistical uncertainty of a specific environment. Second: R,, the correlation between the actual subjective values (Y,) and the predicted subjective values ( gs) indicates the degree of response consistency. It measures the extent to which subjects are consistent in the execution of their knowledge by capturing the deterministic component of subjective expectations from the related cues. ‘. Third: G, the correlation between the predicted realized values (?J and the predicted subjective values (t) measures the amount of knowledge. It indicates the extent to which respondents have correctly detected the properties of the expectations variable from its statistical environment. ’ Finally: C, the correlation

6 A brief derivation of the basic Lens Model Identity can be found in Tucker (1964). A more

detailed and somewhat cumbersome derivation is available in Hursch et al. (1964).

’ The Lens Model framework has relatively easier application to individual-specific data. In the

individual context, R,, can be viewed as the degree of cognitive control exercised by a participant.

However, in this study we are concerned with a macro issue: whether aggregate (market level)

expectations are optimal. Consequently, consensus (average) estimates of price variation have

been employed. In this aggregate context, R, is more appropriately an index of the ‘response consistency’ of the whole group rather than a measure of cognitive control.

* To put it differently, G measures the degree to which regression weights in eq. 1 (j3, and 8,) are proportional to each other. However, since the environmental cues (X,) are likely to be correlated,

the beta coefficients may be unstable. Consequently, direct comparisons of these weights can

result in misleading conclusions. For a more detailed discussion of these issues, please see Schmitt et al. (1977). Also, note that the actual cognitive process of expectations formation need not

strictly conform with the statistical scratchwork. As Hoffman (1960) points out, the relationship is

essentially paramorphic. The statistical model provides a useful approximation of the actual

cognitive task.


between the residuals (Z,, 2,) indicates the variation in Y, and Y, which is not captured by the linear predictive models. We can test the validity of the linearity assumption by observing C. In general, a significant, positive value of C will indicate correct, non-linear utilization of environmental cues, resulting in higher achievement. It can also indicate that subjects may be utilizing cues which are unknown to the experimenter. 9 If C is not significantly different from zero, it implies that one or both of the residual variances are random and that the linear models are probably an adequate approximation.

It may be noted that the Lens Model framework analyzes the covariation between Y, and Y, and does not take into account the possibility that the mean levels of Y, and Y, may be dissimilar. To put it differently, the Lens Model analyzes the ‘efficiency’ property of the distribution of Y, and Y, and not the ‘bias’ property. However, the latter issue can be resolved by well known statistical tests involving inferences about the difference between the means of two populations. In section 3, the results of some of these tests are reported for the Livingston Data.

It has been indicated that in Livingston’s price survey, the subjective expectations (Y,) have generally been regarded as ‘suboptimal’ because they did not conform with the actual realized values (Y,). However, it is clear from the Lens Model configuration that achievement (correspondence between y and Ye) is a function of response consistency (R,), knowledge (G) and task uncertainty (R,). We have noted that even professional forecasting establishments such as Data Resources, Inc. (DRI) have not succeeded in making accurate, ex ante, statistical forecasts. This implies that task uncertainty may be the source of the problem. Consequently, it is not appropriate to make a judgment on subjective expectations by merely observing the achievement index.

9 Clinical studies indicate that nonlinearity in parameters is generally rare, implying that we do not generally have to resort to more sophisticated nonlinear models. However, since expectations are normally formed in a naturalistic environment, the possibility of missing cues can be a more formidable problem. Two strategies are suggested to overcome this difficulty. First, adequate a priori testing of potential environmental cues should be undertaken to select the most pertinent ones from the point of view of the respondents. Second, greater reliance should be placed on laboratory studies. In a contrived environment, the accessibility of different cues can be more adequately controlled. This issue provides another reason for not employing econometric forecasts as proxies for subjective expectations without empirical verification: even the subset of cues may not be the same for both cases. Note, however, that the Lens Model, comparisons can still be made as long as the same information is aoaifable for both the subjective and objective side.


Two respondents could conceivably have identical low achievement indices for wholely different reasons: one person because of a lack of knowledge or response consistency (low G and/or low R,) and another because he faces a more unpredictable environment (low R,). It is important to identify the precise component causing lower achievement. In order to correctly analyze subjective expectations, we need to ask the following pertinent question: Is achievement low because of relatively lower response consistency and knowledge or because of greater task uncertainty? Subjective expectations may be inferred as suboptimal, only if response consistency and knowledge of subjects deteriorates significantly relative to the degree of uncertainty implicit in the task. In the next section, these important issues are analyzed by estimating the Lens Model.

3. Estimation of the Lens Model

The Lens Model is estimated by utilizing Livingston’s price survey data. The subjective price expectations (Y,) about the Consumer Price Index (CPI) are obtained from Carlson (1977). These are biannual consensus (average) estimates for the period December 1950 to June 1976. The corresponding actual price realizations (Y,) are obtained from the Survey of Current Business (1950-1976, U.S. Department of Commerce Publications). Instead of employing currently available, revised CPI values, the unrevised numbers which were actually available to economic agents, at earlier points of time are utilized. Similarly, the subjective estimates obtained from Carlson (1977) are also the corresponding, unadjusted values. Since the movement of prices is generally conceptualized in relative terms, the unit of observation utilized in this study is percentage price changes.

Before estimating the basic kens Mcdel equation, appropriate forecasting models for generating Y, and Y, are required. As discussed in section 2, the ‘six months’ ahead subjective expectations are, in reality, eight months ahead estimates. This is due to the fact that the latest realization available to the respondents (when they form expectations in November and May each year) are for the months of October and April, respectively. Similarly, the ‘ twelve months’ ahead projections should be rightly viewed as fourteen months ahead estimates. The corresponding forecasting models employed to generate fc and ys,


should be based on the same information constraints. Consequently, the most recently available cue (independent variable) for the shorter projections is the eighth lag and for the longer projections is the fourteenth lag. A specification search of these lag structures revealed that autoregressive models utilizing past price changes have relatively good predictive power. lo The final predictive models arrived at are as follows:

c = 1.308 Pt_8 - 0.303 P,_ll, (12.54) (-2.93)

(4

Adjusted R2 = 0.996,

fe = 0.889 P,_, + 0.497 Pt_11, (2.12) (2.21)

(5)

Adjusted R2 = 0.979.

The t-values are shown in parentheses. These results need some clarification. Note that only the eighth and eleventh lags are significant. For a person forming expectations in November (for June next year), the CPI for October (eighth lag) is apparently important because it is the most recently available information about past price changes. The eleventh lag in this case is the actual price realization for the month of July. This is the most recent information input, after the latest expectations error (the difference between expectations for June, made eight months earlier, and the corresponding actual realized value). Viewed in this context, it is not surprising that the eleventh lag is significant in the formation of price expectations. A person is likely to pay relatively more attention to an observation which is available, immediately after he has appraised his error.

lo Once past price changes arc employed as cues (independent variables), it is found that other

potentially relevant data (such as money supply, interest rates, government expenditure) does not

provide any significant additional predictive power. In other words, these variables do not

‘Granger-cause’ prices (Granger 1969). The finding that additional data (other than prices) is not

significant as cues for future price expectations and forecasts, is not surprising. Past price changes,

being endogenous to the system, indirectly incorporate the influence of other variables. Also,

specific investigations by Carlson (1977) indicate that past price changes were uppermost in the minds of most respondents. Although an extended specification search process for locating

significant cues has been carried out, we cannot rule out the possibility of missing cues.


The predictions for Y, and x are-generated on the basis of this lag structure. I1 Since the Lens Model does not take into account the differences between the mean levels of q and Y,, a t-test for making an inference about a significant difference in the mean levels is employed. The resultant test statistic is only 0.13, A second, more precise test involving the differences between ~a~~~~~ observations of Y, and 2: also leads to a similar conclusion (test statistic = 0.80). Since both these test statistics have a t distribution, the results imply that the Null Hypothesis of no significant difference in the mean levels of 5 and Y, is strongly supported. I2 Subsequently, the relevant correlations are estimated for obtaining the values for eq. 3. The results are shown in table 1. The results for the eight months projections indicate that the achievement index ( R,) is highly significant at the one percent level. (The threshold significance level is 0.363). The high achievement level stems from highly significant levels of response consistency (R,) and knowledge (G). However, task uncertainty (R,) is marginally lower. The correlation of the residuals of the subjective and objective equations {C> is positive but not significant at the one percent level. As discussed in section 2, this result implies that nonlinear cue usage is minimal and respondents are correctly utilizing the cue structure. In general, given the difficulty of the task f R,), a relatively high amount of response consistency and knowledge contributes to a significantly high achievement index.

Next, the Lens Model equation is estimated for the fourteen months projections (second row of table 1). In this case, achievement index shows a marginal decline. But this decline is attributable relatively to an increase in task uncertainty (indicated by a marginally lower value of R,). Although the statistical environment is relatively less predictable for the longer projections, the respondents still reveal a relatively high degree of knowledge and response consistency. Note that this implication will not be evident if we merely correlate Y, and Y,, without investigating the precise reasons for the deterioration in the achievement index. However, since the increase in task uncertainty is

l1 The results of equations 12 and 13 are after correction for first order serial correlation. This is necessary in order to corr~tly interpret t-vsllues for selecting important cues. The subsequent generation of $< and fS on the basis of the selected cues is without such a correction, because the residuals of the two equations need to be correlated without extracting the deterministic compo-

nent. ” For specific details about these two tests refer to Ben-Rorim and Levy (2984: 453-461).

Tab

le

1

Est

imat

es

of

spec

ific

co

mpo

nent

s of

th

e ac

hiev

emen

t in

dex.

*

Typ

e of

mod

el

Obs

er-

Ach

ieve

men

t K

now

ledg

e C

ogni

tive

Tas

k N

onlin

ear

com

pone

nt

vatio

ns

inde

x G

= C

orr

(2c)

co

ntro

l un

cert

aint

y

R,

= C

ot-r

@‘&

) R

,=C

orr(

Y,t)

R

,=C

orr(

Y,?

J c=

C

orr(

Z,Z

,)

C&

-iQ

1_

Mod

el

for

eigh

t m

onth

s

expe

ctat

ions

Mod

el

for

four

teen

mon

th

expe

c-

tatio

ns

Mod

el

for

eigh

t

mon

th

pro-

ject

ions

Mod

el

for

four

teen

mon

th

pre

ject

ions

1-52

0.

9864

*

0.99

91

* 0.

9972

*

0.98

81

* 0.

1800

0.

0200

1-52

0.

9687

*

0.99

74 l

0.99

13

* 0.

9795

*

0.08

02

0.00

02

1-16

0.

9926

*

0.99

84

* 0.

9985

*

0.99

42

* 0.

2367

0.

0014

17-5

2 0.

9719

*

0.99

93

* 0.

9963

*

0.97

30

* 0.

1656

0.

0033

1-16

0.

9746

*

0.99

18

* 0.

9919

*

0.98

64

* 0.

1996

0.

0042

17-5

2 0.

9538

*

0.99

98

* 0.

9922

*

0.96

08

* 0.

0432

0.

0007

a T

he

abov

e es

timat

es

are

for

the

basi

c L

ens

Mod

el

iden

tity,

R

, =

R,R

,G

+ C

/x/_

. T

he

corr

elat

ions

m

arke

d w

ith

an

aste

risk

ar

e

sign

ific

ant

at

one

perc

ent

leve

l.


only marginal, further investigation needs to be undertaken to confirm the robustness of the result. This is accomplished by dividing the sample into two components and re-estimating the model for both components separately. This procedure will also indicate the existence of an implicit learning curve. l3 The results are depicted in the last four rows of table 1.

In the earlier sample (observations 1 to 16) for the eight month projections, the achievement index is relatively high because all components (including task certainty) are relatively high. But in the subsequent sample period (observations 17 to 52), the achievement index declines marginally because of greater task uncertainty (lower value of R,). This result is to be expected, since the subsequent sample period consists of data from the 1960’s and early 1970’s when prices were relatively more erratic and unpredictable. Again, achievement is low not due to lack of knowledge or response consistency, but because of relatively greater task uncertainty. This finding is more clearly discemi- ble when the corresponding sub-samples of the fourteen month projections are estimated (last two rows of table 1). In this case, there is an additional marginal decline in the achievement index of the second sample (observations 17 to 52) because of greater task uncertainty brought about by a longer projection period as well as greater variation in price realizations. But note that in spite of a greater degree of task uncertainty, knowledge and response consistency are still able to hold their own (indicated by relatively high values of G and R,). The deterioration in the achievement index from 0.9864 (first row) to 0.9538 (last row) and the relative increase in task uncertainty (fall in R, from 0.9881 to 0.9608) are statistically significant, t-values of 2.80 and 2.77 respectively. l4

The important implication which emerges from this analysis is that the compatibility of actual price realizations and ex ante subjective expectations (the achievement index) is marginally lowered not due to a

I3 When a scatter plot of the price series data is analyzed, it is observed that the first sixteen observations appear to be relatively more stable as compared to subsequent observations. Consequently, the sample is divided at this point, to ascertain whether response consistency and knowledge deteriorates in the subsequent, relatively more unstable period. I4 Since the population correlation coefficients (p) are likely to be positive, the distribution of the sample estimates (r) is skewed and Fisher’s r to Z transformation has to be applied to obtain a standard normal variate. The reported t-values are based on this conversion. One consequence of this transformation is that the same differential in the r values is statistically more significant at

higher than at lower levels. For more details, refer to Hays (1983).


lack of response consistency or knowledge but rather because the statistical environment is relatively less predictable. In fact, the results indicate an implicit learning curve: A continued high level of response consistency and knowledge in spite of an increasingly complex environment implies that respondents are actually improving their relative performance given the difficulty of the task. This finding indicates that premature judgments about subjective expectations should not be made, without investigating the precise reasons for lower achievement. The results, while providing an explanation for the precise nature of the incompatibility between ex post realizations and ex ante subjective expectations, are consistent with recent empirical investigations discussed in section 2. It also validates our general inference that ex ante econometric projections made by forecasting establishments do not appear to perform significantly better than subjective expectations, once they are evaluated within the same environmental uncertainty.

Conclusion

This study has contended that the descriptive and normative aspects of expectations formation can be meaningfully investigated in a Lens Model framework. It can be verified how closely subjective expectations match up with optimal statistical forecasts, given the same information availability. More importantly, the specific reason for the lack of conformity between these two separate sources of information about the true underlying expectations process can be identified. Since the precise nature of expectations formation plays a pivotal role in economics and the general tendency has been to rely on econometric forecasts as proxies for the true expectations process without adequate verification, this line of inquiry should be pursued more extensively. The compatibility of subjective expectations and econometric forecasts needs to be investigated in controlled settings. In a contrived environment, the accessibility of different cues and the relative complexity of the tasks can be more effectively controlled. Such behavioral workshops can provide important insight into the reliability and complimentary nature of econometric forecasts and subjective expectations.

248 H. Singh / Econometric forecasts and subjective expeciaiions

References

Beach, L.R., 1967. Multiple regression as a model for human information utilization. Orgamza- tional Behavior and Human Performance 2, 276-289.

Ben-Horim, M. and L. Levy, 1984. Statistics, decisions and applications in business and econom-

ics. New York: Random House, pp. 451-461.

Brunswik, E., 1956. Perception and the representative design of experiments. Berkeley, CA:

University of California Press.

Carlson, J.A., 1977. A study of price forecasts. Annals of Economic and Social Measurement 6, 27-56.

Caskey, J., 1985. Modeling the formation of price expectations: A Bayesian approach. American

Economic Review 75, 768-776.

De Canio, S., 1979. Rational expectations and learning from experience. Quarterly Journal of Economics, 118-157.

Figlewski, S., and P. Wachtel, 1981. The formation of inflationary expectations. The Review of

Economics and Statistics 63, l-10.

Friedman, B., 1979. Optimal expectations and the extreme information assumptions of ‘rational

expectations’ macro-models. Journal of Monetary Economics 5, 23-41.

Friedman, M., 1967. The role of monetary policy. American Economic Review 58, l-17.

Granger, C.J., 1969. Investigating causal relationships by econometric methods and cross spectral

methods. Econometrica 37.

Hays, W., 1983. Statistics for the social sciences. 2nd ed. New York: Holt, Rinehart and Winston,

pp. 661-664.

Hoffman, P.J., 1960. The paramorphic representation of clinical judgement. Psychological Bulletin 57, 116-131.

Hogarth, R.H., and H.J. Einhom, 1972. An examination of the mathematical formulation of the

lens model in judgement research. Unpublished report. Graduate School of Business, Univer-

sity of Chicago, Chicago, IL.

Hursch, C.J., K.R. Hammond and J.L. Hursch, 1964. Some methodological considerations in

multiple cue probability studies. Psychological Review 71, 42-60.

Kahneman, D., P. Slavic and T. Tversky, eds., 1982. Judgement under uncertainty: Heuristics and

biases. Cambridge: Cambridge University Press.

Katona, G., 1975. Psychological economics. New York: Elsevier.

Lockheed, G., 1982. ‘Know, then decide.’ In: T. Wallsten (ed.), Cognitive processes in choice and

decision behavior. Hillsdale, NJ: Erlbaum pp. 143-154.

McNees, S.K., 1981. The present record of thirteen forecasters. New England Economic Review,

5-21.

Muth, J.F., 1960. Optimal properties of exponentially weighted forecasts. Journal of American

Statistical Society 55, 299-306.

Pearce., K.D., 1979. Comparing survey and rational measures of expected inflation. Journal of

Money, Credit and Banking 11,447-456. Pesando, J.E., 1975. A note on the rationality of the Livingston price expectations. Journal of

Political Economy 83, 849-858.

Rodney, J., and R. Jones, 1980. Price expectations in United States, 1947-75. American Economic

Review 70, 269-277. Schmitt, N. and R.L. Levine, 1977. Statistical and subjective weights: Some problems and

proposals. Organizational Behavior and Human Performance 20, 15-30.

Schoemaker, P., 1982. The expected utility model: Its variants, purposes, evidence and limitations. Journal and Economic Literature 2, 529-564.


Simon, H., 1978. Rationality as a process and as a product of thought. American Economic Review, 1-16.

Slavic, P. and S. Lichtenstein, 1968. Relative importance of probabilities and payoffs in risk taking. Journal of Experimental Psychology, l-18.

Tucker, L.R., 1964. A suggested alternative formulation in the developments by Hursch, Ham- mond and Hursch and by Hammond, Hursch and Todd. Psychological Review 71, 528-530.

Tumovsky, S.J., 1970. Empirical evidence on the formation of price expectations. Journal of the American Statistical Association 65, 1441-1454.

Wallsten, T., ed., 1980. Cognitive processes in choice and decision behavior. Hillsdale, NJ: Erlbaum.

Documents

Investigating the compatibility of econometric forecasts and subjective expectations: A suggested framework