Micro-level tests for rational expectations in South Africa

Marais, D. J.; Smit, E. V.D.M.; Conradie, W. J. Article Micro-level tests for rational expectations in South Africa South African Journal of Business Management Provided in Cooperation with: University of Stellenbosch Business School (USB), Bellville, South Africa Suggested Citation: Marais, D. J.; Smit, E. V.D.M.; Conradie, W. J. (1997) : Micro-level tests for rational expectations in South Africa, South African Journal of Business Management, ISSN 2078-5976, African Online Scientific Information Systems (AOSIS), Cape Town, Vol. 28, Iss. 1, pp. 15-26, https://doi.org/10.4102/sajbm.v28i1.785 This Version is available at: https://hdl.handle.net/10419/218165 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Box 61 O, Bellville, 7535 Republic of South Africa W.J. Conradie Department of Statistics, University of Stellenbosch, Stellenbosch, 7300 Republic of South Africa Received January 1997 The article investigates entrepreneurial expectations formation along the lines of the rational expectations hypothesis. It utilizes micro-level business survey data from the Bureau for Economic Research and distinguishes between phases of the business cycle, consumer and capital goods industries and various degrees of sectoral economic concentration. Very little evidence of weak form rationality is present in the data which concurs with similar international evaluations. * Author to whom correspondence should be addressed. Introduction In the process of constructing microfoundations of macroeconomic theory it is required that entrepreneurial behaviour in a dynamic economic environment be investigated. Business survey data, such as that of the Bureau for Economic Research (BER) at Stellenbosch, offer an unique opportunity to accumulate empirical evidence on expectation formation and decision-making patterns at a micro-level. Such empirical evidence allows the verification of related microand macroeconomic theories in a manner distinctly different to that normally obtained from aggregated data analyses of economic behaviour. This study investigates entrepreneurial expectations formation along the lines of the rational expectations hypothesis. The next section provides a brief overview of the hypothesis while a third section deals with measures of forecasting performance within the framework of contingency table analysis. This is followed by a fourth section which deals with the data used and method followed, while the results are presented in a fifth section, followed by a conclusion. Rational expectations hypothesis According to Begg (I 982: xi): 'The Rational Expectations Hypothesis asserts that individuals do not make systematic mistakes in forecasting the future'. It is an economic view very similar to that of the classical economics. In essence it claims that (a) people make the best possible use of the information available to them, and that (b) prices and wages are sufficiently flexible so that the market always clears. The rational expectations hypothesis (REH) was introduced by Muth who summarized the underlying ideas in these often quoted phrases: ' ... expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory' and ' ... that expectations of firms (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the prediction of the theory (or the "objective" probability distribution of outcomes)' (1961: 316). The essentials of the REH, mentioned above, are probably stated too vaguely. Shaw draws the attention to the distinction between what is considered to be a 'stronger', and a 'weaker' level of interpretation of the theory: 'Whilst it is the strong Muthian version of the theory which has dominated academic discussion and generated the major implications and policy conclusions, other weaker statements of rational expectations formation have influenced popular debate. At one extreme, for example, the statement is taken to imply no more than that economic agents will form expectations optimally by taking all available information into consideration where availability is defined with respect to cost. Such a statement amounts to little more than the belief that agents are utility maximisers.' '... At a somewhat stronger level, ... rational expectations formation amounts to an assertion that economic agents will learn to eliminate systematic expectational error, and this version carries far greater implications for the conduct of macro-economic policy' ( I 984: 58). The REH has certainly proven to be controversial. The basic assumptions of unbiased forecasts (no systematic error), and flexible prices and wages (clearing markets) have come under intense scrutiny by the Neo-Keynesian movement, and outright rejection by some Post-Keynesian fundamentalists. Some proponents recognize the limitations of the REH (see Pesaran, 1987), while others like Lucas ( 1980), Begg ( 1982) and Sargent (1983) state that even Keynes recognized the importance of uncertainty and expectations in macroeconomics but lacked the technical tools to develop his insights. A new approach is to argue for 'exploration rather than confrontation' (Wren-Lewis, 1985) to encompass the REH in a more general Keynesian framework (see Gerrard, 1994). To test the REH a variety of properties of the theory have been transformed into testable format. It is possible to condense the variety of tests into basically four different tests. Sheffrin ( 1983) summarized these by stating that the theory requires tests for (i) unbiasedness, (ii) efficiency, (iii) forecast error unpredictability, and (iv) consistency. . Unbiasedness Let the variable V,_kl, indicate the reported expectation for variable V, in period t made in period (t-k). 16 It is common to hypothesize that an expectation of a particular variable is an unbiased predictor of the variable. A regression of form: v, = a + b v,.kll + e:, (1) according to such a hypothesis, should yield the coefficient estimates a= 0, b = I, and E(e:,)=0. The stochastic element, e:,, in the equation should be uncorrelated with the expected value V,.u· If that is the case, then e:, must be correlated with the actual realization, V,. Hence, the variance of V, is larger than the variance of V,.1<1,· If expectations are formed rationally, it means that: e:,=V,-V,.kJI (2) Thus, the error term is really the difference between the eventual realization and expectation of the variable. For expectations to be rational in the Muthian sense, it is a necessary, but not sufficient condition, that the property of unbiasedness is not rejected. Efficiency Efficiency implies that the past history of the variable is utilized when forming the expectation, in the same way as the variable would evolve through time. In the following two regressions: V, = a,V,.1 + a2 V,. 2 + ... +a,, V,. 0 + 0, v,.,k = b,v,_, + b2V,.2 + ... + b.v, .• + 11, (3) (4) the REH requires that lli = b; for all i. If the REH were to be a true representation of reality, one would expect 0, and 11, to be identically distributed. To eliminate the precondition that the error terms in these two equations are to be identically distributed, Mullineaux (1978) proposed that (4) be subtracted from (3) to yield: V,-V1-111 = (a1 - b1>Y1-1+(a2 - bi)Vt-2 + ... +(l3n-b 0 )V 1 .0 +(0 1 -TJ,) (5) Th~s relationship does not require homogeneity of variance, only mdependence. The one-period forecast error of a particular v~riable is now related to its recent history. The null hypothesis, Hi, : (lti - b;) = 0 is then tested for all i. Note that informatio~ require~ in equation (5) is limited to the history o~ the part1c~lar vanable only. Rejection of the null hypothesis does not imply that there does not exist an alternative set of information which could be used to reduce the forecast error. 'f!te efficien~y test is also referred to as the test for orthogonality. A _spe~1al case of the orthogonality property of the REH, which 1s related to the above Mullineaux proposal as expressed in equation (5), is that the expectation errors are serially uncorrelated with mean zero. Evans & Gulamani ( J 984) proposed a test for serial correlation which is based on the regre~sion of the forecast error c; (as specified in equation (2)) on its past values. This is estimated by: n £,+1 = Ld;&,_;+u, i =O for which the null hypothesis, Hi, : d, = O, is tested for all i. S.Afr.J.Bus.Manage.1997 28 (1) Forecast error unpredictability To earn the distinction of full rationality, the prediction error of the expectation must be uncorrelated with the entire set of information that is available to the respondent at the time the prediction is made. This will be a sufficient condition for the rationality concept. It will resemble the statistical concept of a 'sufficient estimator', which may be loosely defined as an estimator that utilizes all the available information in the sample. This requirement implies, amongst others, that the prediction error of a variable has to be uncorrelated with historical information on prior realizations of that particular variable (as required in equation [5]). This is generally referred to as the weak version of the REH. The strong version requires that all other variables that might be known to have an effect on the predicted variable, at the time of prediction, also have to be uncorrelated with the prediction error. This is normally not determinable when testing the REH against survey data, and investigators generally revert to testing the weak version. Consistency When forecasts are made for a particular variable at different points in time, then the forecasts should be consistent. In the following regressions: V,.,k = a1 V1•1 +a 2 V1_2+ ... + a,, V,_ 0+0, V,_2h = c1 V1• 211 •1 +c2V1•2+ ... + c0 V,_ 0+m1 (6) (7) the REH requires that C; = lli for all i. Assuming that this is the case, then subtracting (7) from (6) yields: V,.11t - V,.2h = a, (V,_, - V,. 21 ,. 1 ) + (0, - m,) (8) which is the well-known error-learning model. These tests might appear to differ, yet they are merely alternative tests of the properties of conditional expectations. For example, if a, :t: b,, but all other coefficients in equation (5) are zero, then: V, - V,. 111 = (a, - b,)V,_, (9) and according to equation (2) the difference between the expected and realized values forms the prediction error. Thus, if a, :t: b., then the prediction error is correlated with the previous realized value of the variable, and is therefore biased. In other words, the orthogonality property of conditional expectations is violated as long as V,_, is contained in the information set. It can therefore be concluded that the unbiasedness and orthogonality tests are actually equivalent. It would be desirable for expectation mechanisms to survive at least one of the above-mentioned four tests. However, conditional expectations, that is conditional on all information available at the time of the forecast, must satisfy all four properties. Measures of forecasting performance The four tests described above are appropriate when quantitative expectations data are available. However, the survey data of the BER, which will be utilized for testing the REH in expectations formation by the South African manufacturing industry, is qualitative in nature. The conventional tests for unbiasedness and orthogonality, described above, can S.Afr.J.Bus.Manage.1997 28( I) therefore not be used. Instead the analytical measures developed by Kawasaki & Zimmermann ( 1986) have been adopted. Whereas nearly all empirical studies of the REH have been done with time series and regression analysis on aggregated survey data, the Kawasaki-Zimmermann approach provides a method of studying expectational phenomena at a microlevel. Frequencies of individual firms' expectations and realizations of specific variables are noted in a contingency table cross-classified by prediction and realization. The terms 'prediction' and 'forecast' will be used interchangeably with expectations. Kawasaki & Zimmermann stressed the importance of testing expectational behaviour at the microlevel using the following simple example: 'Suppose that the whole industry consists of two homogenous groups, each of which contains the same number of producers. The first group predicts, say, I 0% increases in their selling prices, while the prices decrease by I 0%. The second group does exactly the opposite. Therefore, the prediction is totally wrong at the micro-level. However, the prediction after aggregation turns out perfectly correct. Although this is an unlikely case, such an aggregation problem certainly persists in reality to some extent' (I 986: 1336). Kawasaki & Zimmermann (1986) followed the Theil (1958; 1966) proposals for a system of measures for qualitative expectations which are based upon cross-classified tables of prediction and realization data. In these tables a reported increase (prediction or realization) is indicated by a '+', no change in the variable by a'=' and a decrease by '-'. The relative frequencies of prediction and realization for individual firms can be summarized as follows in the cells of the contingency table: + Prediction = Realization + = f{+,+) f{+,=) f(=,+) f{=,=) f{-,+) f(-,=) f(+,-) f{=,-) f{-,-)] The sum of the relative frequencies in the diagonal from f( +,+) through f( =,=) to f(-,-) indicates the proportion of predictions that turned out to be correct. The proportion of incorrect predictions (labelled EE) is therefore measured by: EE= I - [f(+,+) + f(=,=) + f(-,-)] (10) Theil also proposed a measure of overestimation of level (labelled OEL) which is the proportion of predictions with levels greater than the realized levels: OEL = f{+,=) + f(+,-) + f(=,-) (11) Similarly, a measure of underestimation of level (labelled UEL) is defined by: UEL = f(=,+) + f{-,+) + f(-,=) (12) The bias of prediction can also be measured by considering changes as opposed to level. A measure of overestimation of change (labelled OEC) indicate the proportion of predictions which are exaggerative, that is, changes were predicted but none oc1:urred: OEC = f(+,=) + f(-,=) (13) 17 The measure for underestimation of change (labelled UEC) is the sum of relative frequencies indicating conservative prediction, that is, no changes were predicted but some actually occurred: UEC = f(=,+) + f(=,-) (14) Kawasaki & Zimmermann ( 1986) formulated bias indices (labelled BL and BC) for the Theil measures of level and change as follows: BL = (OELUEL) (OEL+ UEL) and (OECUEC) BC= (OEC+ UEC) (15) (16) Note that Kawasaki & Zimmermann (1986) refer to these measures as Bl and B2 respectively. However, to enhance adaptability of the two measures, the references to level and change are preserved here. These parameters are reminiscent of the definition of the Goodman-Kruskal gamma coefficient for two-way contingency tables. The indices BL and BC provide simple measures of the direction of bias; they measure the degree of overestimation relative to underestimation out of the total bias. A value of '+I' indicates no underestimation and only overestimation, while a value of 'O' indicates balanced proportions of overestimation and underestimation, and a value of '-1' indicates total domination by underestimation. Since predictions and the associated eventual realization for individuals can vary, it is appropriate to consider statistical prop.!rties of the above measures. Assuming multinomial sampling for the trichotomous prediction and trichotomous realization, which fix the total number of observations, then the maximum likelihood estimators of the (relative) frequencies are exactly the observed sample (relative) frequencies. Since the forecasting measures are all well-conditioned functions of the relative frequencies, the calculated (sample) forecasting measures are just the maximum likelihood estimators of these measures. The estimators are therefore consistent and asymptotically normal. The asymptotic variance of a measure (M) is then determined by, either using the d-method (see Bishop et al., 1975; and Agresti, 1984) or by calculating it from: Var(M) = [a~f] ·~[a~f ]T (17) where f is the vector of relative frequencies which appear in the cross-classified table, and L is the 9 x 9 asymptotic covariance matrix of the estimators of the relative frequencies (Kawasaki & Zimmerman, 1986). The covariance matrix is determined by: (18) where -the indices i, i', j, and j' can each take values I, 2, or 3 for '+', '=', and '-' respectively: -indices i and i' are used for prediction, while j and j' are used for realization in the original cross-classified table of relative frequencies; 18 -indices i and j are also used to indicate the rows of L while i' and j' indicate the columns; - N is the total number of observations; - fi 1 is a relative frequency; and -the terms O;i take on values of I when i = j, and O when i :;t j. Besides Kawasaki & Zimmermann (1986) who used the BL and BC-measures on the German IFO survey data, it has also been applied with success by Buckle et al. ( 1990) and Buckle & Meads (1991) on the New Zealand survey data, which are very similar to that of the BER. Data and method Since it is so difficult to determine how much additional information is needed for individual firms to be able to form their expectations rationally, only the weak form tests of unbiasedness and orthogonality on previous realized values of the particular variable are considered here. The unbiasedness test can be applied on qualitative data without further ado. The cross-classified table of prediction and realization, described earlier, already represents the structure of forecast errors. If the forecasts are unbiased, the relative frequency patterns in the off-diagonal cells in the table should not be systematically biased over time. Consistent bias would violate the unbiasedness property of the hypothesis. The BL and BC-measures defined above can be used to measure systematic bias from the diagonal cells; the hypothesis can be rejected if either BL or BC is consistently biased over time. Kawasaki & Zimmermann (1986) made use of the proposals by Mullineaux ( 1978) to reformulate the orthogonality test (equation [5]). Mullineaux did not intend it to be used on qualitative survey data, but the reformulation provides an opportunity to apply it with a fair amount of ease. According to the orthogonality property of the hypothesis, the prediction error (Vt - V,.,1t) is not systematically related to the past history of the variable. To test this property, it is necessary to construct a new variable referred to as a 'surprise' (denoted here by S,). The above-mentioned prediction-realization table is utilized to determine the various elements of the one-period surprise, S,. A surprise is considered positive (indicated by a '+' in the table) when a particular variable realizes at a higher level than has been expected. The opposite would yield a negative surprise (indicated by a '-'). Expectations which are subsequently realized are equated on the diagonal. The surprise table is then constructed (with derived changes indicated in the cells of the table) as follows: Realization + = Prediction :1.____.__: I _: ~' :1 Thus, the new variable, S,, is also trichotomous like the rest of the survey data, and it can be constructed for any variable in the BER survey data for each individual response. Since the BL and BC-measures provide indications of systematic bias, Kawasaki & Zimmermann ( 1986) suggest that it be used to test the orthogonality property as well (similar to the way it is applied for the unbiasedness test). A contingency S.Afr.J.Bus.Manage.1997 28(1) table relating the surprise, S,, to the one-period lagged change in the variable, V,_ 1, is constructed and used for estimating the BL and BC-measures. However, there is a problem with this application of the BL and BC-measures. The null hypothesis for the unbiasedness test evaluates the error bias when a direct relationship between the expected value and subsequent realization of a variable is anticipated. In the Mullineaux version of the orthogonality test, the null hypothesis anticipates no correlation between the surprise and the one-period lagged change in the variable. The structure of the BL and BC-measures is such that it can only be used to determine the pattern of frequencies (or predictions) of cells which do not appear on the diagonal relating the positive predictions to positive realizations, and the negative predictions to negative realizations. The null hypothesis for the orthogonality test anticipates that the majority of the observed and calculated frequencies ( or probabilities) will appear in the diagonal cells. The BL and BCmeasures will therefore be of limited use in this case; it can really only be used to evaluate the error bias appearing in equation (5). A more reliable method of testing the orthogonality property would be to estimate the Goodman-Kruskal gamma coefficient for the contingency table relating the surprise, S,, to the one-period lagged change in the variable V,_ 1• The asymptotic standard deviation of gamma can also be estimated from the information in the table, and the associated probability estimated for testing significance. A significant non-zero gamma coefficient will provide the evidence to reject the null hypothesis for the orthogonality property. This approach was proposed by Buckle et al. ( 1990). Despite the fact that the BL and BC-measures are not used to evaluate orthogonality (the Goodman-Kruskal gamma coefficient will fulfil that purpose), they are also estimated and reported as an indication of error bias. Besides measuring systematic bias, the forecasting performance can also be evaluated by comparison with some naive forecasts. A simple method of generating naive predictions is to assume that the future value of a variable will be equal to the most recent realization, H0: V, -V,_ 1 = 0. This is referred to as static expectation formation, and needs to be distinguished from the REH for which the unbiasedness test null hypothesis is Hi,: V,-V,_ 111 = 0. The proportion of incorrect predictions (EE) of such static expectations can be calculated similarly to that of observed predictions and realizations. In this study the Static Expectations Hypothesis is included to provide a contrast background for the REH. The data for the various BER surveys are accumulated by means of business questionnaires. The surveys are based upon the 'Konjunktur Test' approach that has been developed by the IFO Institut ftir Wirtschaftforschung, Mtinchen, and which has been utilized to monitor the economy of the Federal Republic of Germany since November 1949. These surveys have a longitudinal character as they monitor individual responses over time and are constructed to be tendency surveys rather than opinion or market research surveys. The qualitative responses in the BER surveys reflect trends rather than measurable quantities. The respondents are asked to compare current business activities (including plans) with that of the corresponding period a year ago and they are S.Afr.J.Bus.Manage.1997 28( I) requested to reply either 'up', 'same' or 'down'. Normally the answers to the questions are quantified by balancing the 'ups' and 'downs' and reporting the differences in a percentage format. When collated over time, the surveys form a qualitative time series with a longitudinal character and statistically analytical information. The BER manufacturing survey data seem to be more comprehensive than most encountered in literature; it considers not only expectations and realizations of selling prices, costs of raw materials, labour costs, employment, output and stocks of finished goods, but also demand for products, stocks of raw materials, unfilled orders and hours worked. The data is collected with enough auxiliary information to enable division of the manufacturing industry into 21 main sectors. Two distinct phases in the economic cycle were identified; an expansion period from the second quarter of 1986 to the first quarter 1989, and a recession phase from the second quarter 1989 to the fourth quarter 1991. The phases could be subdivided to examine quarterly data, to test for consistent bias. However, the number of quarterly records available is often not sufficient to conduct tests which yield significant results in the various main sectors. Therefore, the data will be grouped into four subdivisions of the manufacturing industry for investigations of the expansion and recession phases, as well as for the full cycle. The sectorial subdivisions are as follows: -Consumer goods; -Capital goods; -High economic concentration (which is associated with markets exhibiting monopolistic competition); and -Low economic concentration (which is associated more with markets approaching perfect competition). The CRIO (concentration ratio for the ten largest firms) measure is utilized as an index for categorizing the threedigit industries (Du Plessis, 1978). One serious limitation in the current data set is the fact that expectations and realizations are recorded for individual establishments for one-period intervals only. If the history of parameters extending two and more periods in the past need to be examined in the orthogonality test, the number of consistent respondents diminishes markedly. Too many records are lost that way to warrant good test results from which proper conclusions can be made. The orthogonality test is therefore conducted such that the null hypothesis associated with equation (5) is reduced to H0: (a1 -b1) = 0. In the following sections the rationality of predictions on sales volume, production volume, orders received, unfilled orders, stocks of finished goods, general business conditions in their individual sectors, number of factory workers employed, average hours worked per factory worker, the rate of increase in average total cost and selling price per unit of production are tested for the above-mentioned sectorial subdivisions in the BER manufacturing industry survey. Results Total manufacturing industry All the respondents in the BER manufacturing industry survey were pooled and analysed over the expansion phase, recession phase, and the full economic cycle. The results are presented in Tables 1, 2 and 3. In the expansion phase the 19 estimated measures are all significant at a 10% level, that is, the null hypotheses Hi, : µ = 0 (µ representing any one of the measures reported in Table 1) are rejected at levels markedly lower than a 10% level of significance (associated probabilities p < 0.1 ). Except for six cases in the recession phase which have associated probabilities larger than 10% (e.g. H.,: BL= 0 in the unbiasedness test for stocks of finished goods is rejected at a 50.5% level of significance [p = 0.505)), the various measures are generally non-zero at a 10% level of significance. In the full economic cycle four instances of associated p > 0.1 occur, again indicating that the null hypotheses Hi, : µ = 0 are generally rejected at significance levels below 10%. Static expectations Contrary to what would be anticipated, the static expectations are (consistently) slightly more accurate than the corresponding expectations formed by the entrepreneurs (smaller prediction error). This is a surprising result and exactly the opposite to the results obtained by Kawasaki & Zimmermann (1986). It can probably be ascribed to the political instability which plagued the South African economy right through the particular expansion and recession phases considered here. This appears to confirm the notion that a stable political and economic environment is conducive to reliable and consistent expectation formation by entrepreneurs at the micro level. The South African evidence seems to indicate that exogenous variables can have a detrimental impact on expectation formation in endogenous variabl.es. Odd as it may seem, in times of economic instability, it is probably better to rather forecast according to the static method, which assumes that current changes are going to persist; the probability of encountering an error is lower than for the case where expectations are formed according to some complicated (rational) method. Unbiasedness test Considering the BL-measure for the unbiasedness test, it is concluded that entrepreneurs tend to underestimate levels of change in sales, production, orders received, unfilled orders and general business conditions during the expansion phase, and overestimate levels of change during the recession phase. The net effect over the full economic cycle indicates a significant underestimation of these endogenous variables. On the other hand, entrepreneurs seem to consistently expect factory workers to spend more hours on the job than they eventually do, although this conclusion is not so well supported in the recession phase. There also seems to be a general tendency to underestimate the rate of increase in average total cost of production, and to overestimate stock levels of finished goods, albeit not so pronounced in the recession phase. The BC-measures for the unbiasedness test indicate a tendency to form expectations conservatively for all variables except selling price inflation rate and average hours worked. The fact that entrepreneurs rather expect variables to remain unchanged (while changes eventually occur) may also be a contributing factor to the above-mentioned surprise of static expectations being more accurate than more complicated methods. Changes in the external environment were probably so disturbing, and happened at such a rapid pace, that 20 Table 1 Total industry tests: expansion phase: 2/86-1/89 Static Main sector Number EE EE Sales 6265 0.3657 0.3984 Probability 0.000 0.000 Production 6160 0.3769 0.4037 Probability 0.000 0.000 Orders received 6061 0.3829 0.4242 Probability 0.000 0.000 Unfilled orders 4811 0.3498 0.3901 Probability 0.000 0.000 Stocks of finished goods I 183 0.3466 0.3156 Probability 0.000 0.000 General business conditions 6 275 0.4376 0.4696 Probability 0.000 0.000 Factory workers employed 4677 0.3517 0.3761 Probability 0.000 0.000 Average hours worked 4 707 0.3612 0.3867 Probability 0.000 0.000 Production cost inflation rate 4044 0.2507 0.2713 Probability 0.000 0.000 Selling price inflation rate 4679 0.3411 0.3458 Probability 0.000 0.000 entrepreneurs found it difficult to respond to the questionnaire which requires that variables be • ... compared with the same quarter of a year ago .. .'. Although convenient for the statistician, the requirement that seasonality be eliminated from the entrepreneurs' answers is conjectured to cause difficulty in generating these answers in times of political and economic instability. In an unstable economic climate, entrepreneurs would, therefore, tend to rather respond with a conservative 'no change expected', even though changes have realized in the period in which the expectations are formed. If it can be assumed that the entrepreneurs did understand the questionnaire correctly and provided true opinions, a significant tendency to conservatively underestimate levels during the expansion phase would indicate that changes, which eventually occur, are normally upwards. Similarly, conservative overestimation of levels during the recession phase, would indicate that changes are generally downwards. Against this background, it is noteworthy that the entrepreneurs were generally optimistic about the production cost inflation rate with a consistent, conservative underestimation of levels; although the production cost inflation, compared to that of a year ago, was expected to remain unchanged, it always increased, regardless of the economic phase. This result does not appear to be consistent with the evolution of production price inflation which, according to the figures supplied by the South African Reserve Bank, showed a general downward tendency during the full economic cycle of 1986 to 1991. However, it could be argued that entrepreneurs did not really consider the change in cost inflation rate, but rather responded with their estimates of cost inflation rate levels which always tended to be lower than the levels finally experienced in the last quarter of 1991. This argument would reS.Afr.J.Bus.Manage.1997 28(1) Unbiasedness Onhogonality BL BC EE GAMMA BL BC -0.1571 -0.2350 0.7464 -0.1505 0.4795 0.5728 0.000 0.000 0.000 0.000 0.000 0.000 -0.1411 --0.1964 0.7334 -0.1968 0.4524 0.4988 0.000 0.000 0.000 0.000 0.000 0.000 -0.1637 -0.2256 0.7497 -0.1920 0.4212 0.5256 0.000 0.000 0.000 0.000 0.000 0.000 --0.1486 -0.2813 0.7842 -0.1795 0.4365 0.6588 0.000 0.000 0.000 0.000 0.000 0.000 0.1377 -0.2281 0.4718 -0.3319 -0.1866 0.0927 0.006 0.000 0.000 0.000 0.000 0.059 --0.2128 -0.1903 0.7232 -0.3038 0.2331 0.2920 0.000 0.000 0.000 0.000 0.000 0.000 -0.1620 -0.1185 0.5279 -0.2900 0.1657 0.0755 0.000 0.000 0.000 0.000 0.000 0.001 0.0780 0.1114 0.5022 -0.2556 0.2733 --0.0742 0.001 0.000 0.000 0.000 0.000 0.002 -0.1139 -0.1462 0.8677 -0.6161 0.7526 0.7687 0.000 0.000 0.000 0.000 0.000 0.000 -0.3115 -0.087771 0.8288 -0.6626 0.5395 0.6541 0.000 0.002 0.000 0.000 0.000 0.000 ject the assumption that they interpreted the questionnaire correctly. Orthogonality test The gamma coefficients, as well as the BL and BC-measures, for the orthogonality tests, indicate that there were consistent biases in the relations of all the variables with their respective one-period lagged changes. From these results it can safely be concluded that surprises were systematically related to the information incorporated in the (recent) history of the respective variables. Although this conclusion is obvious from the gamma coefficients, which generally indicate a significant inverse relationship between surprise and preceding realization for each of the variables, the conclusion might not be so obvious when considering the BL-measures only. The BL-measures for the full economic cycle analysis indicate significant bias in orders received, unfilled orders, general business conditions, number of factory workers employed, and hours worked per factory worker. However, the bias appears to change direction from being all significantly positive in the expansion phase, to significantly negative in the recession phase. Note that the exact opposite is observed for stocks of finished goods. Even though the biases do not seem consistent right through the full economic cycle, it is significant in both the expansion and recession phases. Therefore, it is concluded that for these variables too, there appears to be a systematil: relationship between the surprises and the information contained in the past history. The gamma coefficients indicate that recent upward movements in the variables are predominantly associated with negative future surprises, that is, when upward movement is S.Afr.J.Bus.Manage.1997 28(1) 21 Table 2 Total industry tests: recession phase: 2/89-4/91 Static Unbiasedness Orthogonality Main sector Number EE EE BL BC EE GAMMA BL BC Sales 5 167 0.4438 0.4720 0.0381 --0.1186 0.7434 -0.1483 0.0200 0.3891 Probability 0.000 0.000 0.059 0.000 0.000 0.000 0.214 0.000 Production 5 108 0.4383 0.4571 0.0433 --0.0921 0.7222 --0.1920 0.0323 0.3391 Probability 0.000 0.000 0.036 0.000 0.000 0.000 0.050 0.000 Orders received 5 027 0.44IO 0.4663 0.0802 --0.1187 0.7571 -0.2152 -0.0515 0.4161 Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 Unfilled orders 3 970 0.4033 0.4307 0.0573 --0.1990 0.7922 --0.2075 -0.1320 0.5829 Probability 0.000 0.000 O.ol8 0.000 0.000 0.000 0.000 0.000 Stocks of finished goods I 124 0.3254 0.3390 0.0341 --0.2000 0.4607 -0.2047 0.0697 0.0289 Probability 0.000 0.000 o.sos 0.000 0.000 0.000 0.094 0.573 General business conditions 5 130 0.4158 0.4355 0.0734 --0.0835 0.7409 -0.3147 --0.3160 0.3694 Probability 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 Factory workers employed 5 103 0.3296 0.3471 0.0198 --0.0658 0.5414 --0.3354 --0.21 IO 0.1694 Probability 0.000 0.000 0.405 0.008 0.000 0.000 0.000 0.000 Average hours worked 5066 0.3360 0.3421 0.0179 --0.1090 0.4955 -0.3573 --0.2032 0.0607 Probability 0.000 0.000 0.456 0.000 0.000 0.000 0.000 0.008 Production cost inflation rate 5 108 0.2678 0.2872 --0.0484 --0.0588 0.8375 --0.5199 0.7265 0.7002 Probability 0.000 0.000 0.063 0.034 0.000 0.000 0.000 0.000 Selling price inflation rate 5 095 0.3209 0.3386 0.0713 0.0409 0.7973 -0.4072 0.6790 0.6029 Probability 0.000 0.000 0.003 0.108 0.000 0.000 0.000 0.000 * Figures printed in bold indicate rejection of null hypothesis at significance level higher than I 0% observed in the most recent period, the variables are generally predicted to be higher than the actual subsequent realization. The inverse is observed when the variables have adjusted downward in recent history, that is, downward movements of variables are normally associated with positive subsequent surprises. Accuracy of forecasts The estimated prediction errors (EE in the unbiasedness test) for cost, stocks of finished goods and price inflation are consistently smaller than that of any other variable. This phenomenon was also observed by Buckle et al. (1990) and can probably be explained by the notion that during periods of inflation (and inflation rate changes) it would be easier to predict the direction of movement in prices and costs. This view is supported by a conclusion in Nerlove & Press (1986), as well as Konig et al. (1981 ), that French entrepreneurs tend to correctly estimate price changes, or at least have more consistency in the bias between expected and realized prices, during periods of high inflation rates. For the other variables, such as sales, production volume, and factory workers employed, there may be comparatively little change from one period (quarter) to the next, making it more difficult to predict the direction of change. This confirms the suggestion of Buckle et al. that ' ... the proportion of correct expectations would be related to the distribution of reported realizations across the three categories (up, same, down)' (1990). The relationship should be of an inverse nature, in other words, the higher the distribution, the smaller the proportion of correct expectations, or the higher the estimated error, EE. The forecast errors estimated for the South African manufacturing industry are consistent with those found by Theil (1966), Kawasaki & Zimmermann (1986), Stalhammar (1988), and Buckle et al. (1990). However, the New Zealand observations and results reported by Buckle et al. ( 1990) appear to bear the closest resemblance to that found in analysis of the BER manufacturing survey data. Price and cost expectations One additional interpretation of the entrepreneurial behaviour on price expectations needs to be mentioned. The EEmeasures in the unbiasedness test indicate a relatively strong association between price expectations and realizations. As pointed out by Nerlove & Press (1986), and Buckle et al. (1990), such an association may occur either because price expectations are very good estimates (confirming the REH). or because the entrepreneurs are setting prices rather than accepting (taking) prices set by exogenous supply-demand forces. However, the consistent bias observed in the unbiasedness and orthogonality tests, indicates that the weak form REH can be rejected at the I 0% level of significance. Therefore, assuming the above-mentioned impact of inflation can be ignored, it seems reasonable to assume that the manufacturing industry entrepreneurs are generally price setters, and not price takers. Whether the relatively small estimate error is a stronger function of the inflation rate, or of the characteristics of entrepreneurial behaviour, will be 22 S.Afr.J.Bus.Manage.1997 28(1) Table 3 Total industry tests: full economic cycle: 2/86-4/91 Static Unbiasedness Onhogonality Main sector Number EE EE BL BC EE GAMMA BL BC Sales 11432 0.4010 0.4317 ~.0606 ~.1785 0.7450 ~.1102 0.2723 0.4931 Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Production 11268 0.4048 0.4279 ~.0518 --0.1466 0.7283 ~.1564 0.2636 0.4294 Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Orders received 11 088 0.4093 0.4433 --0.0474 --0.1755 0.7531 ~.1467 0.2057 0.4774 Probability 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 Unfilled orders 8 781 0.3740 0.4085 ~.0505 ~.2432 0.7878 ~.1440 0.1781 0.6253 Probability 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 Stocks of finished goods 2 344 0.3360 0.3268 0.0863 ~.2142 0.4664 ~.2702 ~.0641 0.0619 Probability 0.000 0.000 0.017 0.000 0.000 0.000 0.026 0.081 General business conditions 11405 0.4278 0.4543 ~.0894 --0.1450 0.7312 ~.2129 -0.0171 0.3274 Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.117 0.000 Factory workers employed 9 780 0.3402 0.3609 ~.o708 ~.0919 0.5350 ~.2767 ~.0333 0.1252 Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.016 0.000 Average hours worked 9 773 0.3481 0.3636 0.0487 0.0031 0.4987 ~.2993 0.0279 -0.0046 Probability 0.000 0.000 0.004 0.860 0.000 0.000 0.051 0.780 Production cost inflation rate 9 152 0.2603 0.2802 ~.0764 ~.0957 0.8509 ~.5569 0.7383 0.7312 Probability 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Selling price inflation rate 9774 0.3306 0.3420 ~.1140 -0.0173 0.8124 ~.5363 0.6108 0.6278 Probability 0.000 0.000 0.000 0.357 0.000 0.000 0.000 0.000 • Figures printed in bold indicate rejection of null hypothesis at significance level higher than I 0% elucidated in the following discussions of the various groupings of the economic sectors in the manufacturing industry. A similar argument can be constructed for cost expectations. Rational expectations hypothesis The significant biases detected for the individual variables subjected to the unbiasedness and orthogonality tests, indicate that the weak form of the REH is not supported by the BER survey data when all the respondents are pooled together in the manufacturing industry. Consumer goods industries The data for the expansion and recession phases, as well as for the full economic cycle were analysed in the same manner as for the total manufacturing industry. To conserve space, tables are not presented here, but are available in Marais (1995). Very similar results are obtained (and characteristic behaviour concluded) for the consumer goods industries, although a greater number of null hypotheses were rejected at significance levels higher than I 0% for the BL and BC-measures in the recession and total cycle cases. It can be concluded that the weak form of the REH is not supported by the BER survey data when considering the consumer goods manufacturers. For the consumer goods industries, the unbiasedness test estimation errors (EE) for cost and price inflation expectations are consistently smaller than those of the other variables. Whereas price inflation expectations were generally Jess accurate than that of stocks of finished goods for the total manufacturing industry, the opposite appears to be true for the consumer goods industry. The conclusions derived for the total manufacturing industry, with regard to price and cost expectations, can also be derived for the consumer goods industries, that is, price expectations appear to behave more like plans than forecasts. The entrepreneurs in the consumer goods industries, therefore, seem to be price setters rather than price takers. Costs appear to have a similar plan-like character. No further light is thrown on the question (mentioned in the discussion of the total manufacturing results) about the strength of the relation between price/cost expectations and the general CPI and PPI inflation rates, on the one hand, price/cost expectations and entrepreneurial behaviour with regard to price/cost setting, on the other hand. Capital goods industries The results follow a similar pattern (although with a greater number of rejections of the null hypotheses at significance levels higher than I 0%) to those of the total manufacturing industry and consumer goods manufacturers. For the capital goods manufacturers, it can also be concluded that the weak form of the REH is not supported by the BER survey data on a variety of business activities. The above conclusions regarding cost expectations can also be derived for the capital goods industries -cost expectations appear to behave more like plans than forecasts. Although the REH is rejected when considering all the various measures estimated for cost inflation expectations, it is noteworthy that