JEL Code: Q12 -Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets < Q1 -Agriculture

Keywords:

Technology involving genetic modification of crops has the potential to make a contribution to rural poverty reduction in many developing countries. Thus far, pesticide-producing 'Bt' varieties of cotton have been the main GM crops under cultivation in developing nations. Several studies have evaluated the farm-level performance of Bt varieties in comparison to conventional ones by estimating production technology, and have mostly found Bt technology to be very successful in raising output and/or reducing pesticide input. However, the production risk properties of this technology have not been studied, although they are likely to be important to risk-averse smallholders. This study investigates the output risk aspects of Bt technology by estimating two 'flexible risk' production function models allowing technology to independently affect the mean and higher moments of output. The first is the popular Just-Pope model and the second is a more general 'damage control' flexible risk model. The models are applied to cross-sectional data on South African smallholders, some of whom used Bt varieties. The results show no evidence that a 'risk-reduction' claim can be made for Bt technology. Indeed, there is some evidence to support the notion that the technology increases output risk, implying that simple (expected) profit computations used in past evaluations may overstate true benefits.

2 substantial reduction in pesticide (over)use, with only a marginal effect on yields. These results have been reported and analyzed in [START_REF] Pray | Impact of Bt Cotton in China[END_REF] and Huang, et. al. (2003). On the other hand, in South Africa and India, pesticide inputs are more likely to be underused (applied below the economic optimum) due to credit and labour availability constraints and market failure problems associated with the availability of timely supplies. Here, the contribution of the Bt variety has been to increase yields substantially, with modest changes in pesticide use. These results are reported and discussed in, among others, [START_REF] Qaim | Yield Effects of Genetically Modified Crops in Developing Countries Science[END_REF]; Thirtle, et. al. (2002); [START_REF] Shankar | Pesticide Productivity and Transgenic Cotton Technology: The South African Smallholder Case[END_REF]; Qaim (2003); [START_REF] Qaim | Bt Cotton and Pesticide Use in Argentina: Economic and Environmental Effects[END_REF].

All the studies mentioned above have undertaken their farm-level performance evaluation via the estimation of production technology, with a dummy variable representation for the use of Bt technology. Standard production functions have been estimated, in Qaim (2003), [START_REF] Qaim | Yield Effects of Genetically Modified Crops in Developing Countries Science[END_REF] and [START_REF] Qaim | Bt Cotton and Pesticide Use in Argentina: Economic and Environmental Effects[END_REF]. 'Damage Control' production functions, which account for the special, damage abating nature of pesticide inputs and Bt technology, have been used in all the previous studies with the exception of Thirtle et. al. (2002). Thirtle Valuable as the information contained in these studies is, it is important to note that the representations of production technology used in the above studies do not consider the production risk element. Agricultural production is inherently risky, and smallholders in developing countries are likely very risk-averse. More complete production impact evaluation of inputs and technologies will therefore need consideration of their interactions with the riskiness of output. Thus it has been long recognized in the agricultural economics literature that it is important to allow inputs, particularly pesticides (and therefore technologies that embody pesticides, such as Bt), to freely affect variance and higher moments of output. 3 However, typically employed production functions, such as the Quadratic and the Cobb-Douglas, do not allow production inputs and technologies to flexibly affect variance and higher moments of output [START_REF] Just | Production Function Estimation and Related Risk Considerations[END_REF]. This is also true of the standard damage control production functions [START_REF] Saha | The Economics and Econometrics of Damage Control[END_REF] and stochastic frontier functions [START_REF] Battese | A Stochastic Frontier Production Function with Flexible Risk Properties[END_REF]. Thus these studies only consider the effect of technology on the expected value of output.

The objective of this paper is to help reduce this gap in knowledge about the production risk impact of Bt technology 1 . It accomplishes this by applying two 'flexible risk' production function models to the South African cotton smallholder data previously reported in Thirtle et. al. (2002) and [START_REF] Shankar | Pesticide Productivity and Transgenic Cotton Technology: The South African Smallholder Case[END_REF]. The first model, which applies a Just-Pope production function [START_REF] Just | Production Function Estimation and Related Risk Considerations[END_REF] to the data, is seen as a preliminary step prior to the application of a second, more complex model. This second model is an adaptation of Saha et. al.'s (1997) model which incorporates flexible risk properties while retaining the 'damage control' representation of pesticides and Bt technology. From both models, we simply wish to test the hypothesis that Bt technology reduces yield (output) risk. To our knowledge, no previous studies have empirically measured the production risk properties of Bt technology in a developing country setting.

If the risk-reduction hypothesis is confirmed, GM technology can be said to possess an additional 'insurance' function beyond the pesticide reduction/yield increase attributes analyzed before. The benefits from the technology would then include a positive risk premium obtained in addition to benefits (expected value of profits) obtained from mean output increases. On the other hand, a risk-increasing result would imply that computed profits overstate the true benefits from the technology. Thus the study of the risk properties is important for more complete impact evaluation of Bt technology.

II. Analytical Background

The simple bioeconomics of pesticides and risk Bt technology embodies a pesticide, and hence notions relating to the risk effects of Bt technology are parallel to those concerning conventional pesticides. While there is intuitive appeal on the surface to suggest that pesticides should decrease risk, [START_REF] Pannell | Pests and pesticides, risk and. risk aversion[END_REF] suggests that this is misleading, and several empirical studies instead find a risk-increasing effect (eg. [START_REF] Antle | Pesticide Policy, Production Risk, and Producer Welfare[END_REF]; [START_REF] Horowitz | Insurance, Moral Hazard, and Chemical Use in Agriculture[END_REF]). [START_REF] Horowitz | Risk-increasing and Risk-reducing Effects of Pesticides[END_REF] provide an elegant exposition explaining why a risk-increasing effect is at least as plausible as a riskdecreasing effect. We lean heavily on their exposition in heuristically outlining the arguments below.

Consider a production function, f(z, x, e), where z is pesticide input, x is a vector of all other inputs, and e is random production error. Without loss of generality, suppose e is ordered from bad states of nature to good states of nature, implying f e (z, x, e) > 0 where the subscript denotes the partial derivative. We would expect pesticide to not decrease output in any state of nature, i.e., f z (z, x, e) > 0. Risk averse producers may be characterized as choosing (z, x) to solve Max ∫U(pf(z, x, e) -w z z -w x x)de , where U(.) is the utility function, p is output price, w z is pesticide price and w x is the vector of other input prices. Then input z can be said to be risk-decreasing (increasing) if f ze (z, x, e) < 0, i.e., z increases output more in bad (good) states of nature than in good (bad). [START_REF] Quiggin | A Stronger Characterization of Increasing Risk[END_REF] demonstrates that this definition is equivalent to alternative definitions of risk-decreasing (increasing) inputs used in the literature, such as that we have the conventional wisdom that pesticide and Bt technology should be risk-decreasing, since they raise output more in bad states of nature, i.e., when pest density is high.

Intuitive as this logic seems, [START_REF] Horowitz | Risk-increasing and Risk-reducing Effects of Pesticides[END_REF] show that it is untenable when alternative or multiple sources of uncertainty are considered. In developing country agricultural situations such as the rainfed cotton cultivation case we consider, rainfall, or crop growth conditions more generally, are at least as important as sources of randomness as pest density. In a situation where pest density is relatively stable, but there is considerable uncertainty over rainfall, rainfall becomes the main source of randomness in e. In such a case, during the good states of nature (high rainfall) there is more crop to save given the pest density, and pesticides raise output more in this good state of nature, making pesticide a riskincreasing input. In many agricultural situations, both sources of randomness, pest density and rainfall, are important. More so, they are likely to be negatively correlated, i.e. pest density is high (bad state of nature with regard to pest density) when rainfall is high (good state of nature with regard to rainfall). In cases of strong negative correlation between these two, Horowitz and Lichtenberg's analysis suggests again that pesticides are likely to be riskincreasing.

Thus, we are able to take away two major lessons from this previous literature:

(i) The risk effect of pesticides and Bt-technology can differ from situation to situation, and is a matter for empirical determination in any given situation, and (ii) It may be important to explicitly account for multiple sources of randomness in empirical analysis.

Note, however, that even though the above bioeconomic framework goes significantly beyond the standard production framework in its consideration of risk, ground realities can be more F o r P e e r R e v i e w 6 complex still. High rainfall may not always represent a good state of nature even in the absence of pest considerations. The effect would depend on the amount of rainfall at various stages of plant growth. Rainfall and pest control interactions may also be affected by considerations such as pesticide wash-off caused by high rainfall. In Makhathini, there is anecdotal evidence that the latter effect might have occurred in the season for which our analysis has been conducted. However, consideration of such effects requires much more detailed data than are available to us, and is thus beyond the scope of this paper. Work by [START_REF] Antle | Sequential Decision Making in Production Models[END_REF][START_REF] Antle | Pesticide Policy, Production Risk, and Producer Welfare[END_REF] provides an example of how pest control input determination can be viewed as a sequential problem, and how data from multiple stages during the season can be used to enhance empirical production models.

Risk and damage abatement properties of production functions

Conventional production functions are incapable of displaying flexible risk properties.

Production functions additive in the error term, such as the Quadratic, do not allow inputs to either decrease or increase risk. In other words, where f(z, x, e) = g(z, x) + e, f ze = 0. Those with mutiplicative exponential error terms, such as the Cobb-Douglas and the Translog only allow risk-increasing effects, i.e., where f(z, x, e) = g(z, x)exp e , f ze > 0. Apart from their inflexibility in allowing the data to determine risk properties, these production functions also lump all sources of randomness into a single error term. Another critical shortcoming for agricultural applications is that they treat all inputs symmetrically, not accounting for the special nature of inputs like pesticides. The last point is also true of 'stochastic production functions' such as the Just-Pope production functions, y = q(z, x) + h(z, x)e, which are able to allow flexible risk properties, but do not account for the special, damage abating nature of pesticide inputs. 7 [START_REF] Lichtenberg | The Econometrics of Damage Control: Why Specification Matters[END_REF] presented a critique of traditional production functions, and offered an alternative, more intuitive way to model the role of pesticide in the agricultural production process. Drawing inspiration from the bioeconomic literature, they posited that pesticides belong to a class of 'damage control' inputs. Damage control inputs are different from conventional inputs in that they affect output only indirectly, by reducing the extent of damage in the event that damage occurs. In contrast, conventional inputs such as fertilizer and labour increase output directly.

If y denotes output, x is a vector of 'conventional' inputs, and z is the damage control (pesticide), then y = f( x, g(z) ), with f(.) concave in x and g(z). g(z), the 'abatement function', is defined on the [0, 1] interval and is increasing in z. as z increases, 1 ) z ( g  and )

x ( f y  , i.e., a greater part of maximum potential output is realized. As z decreases, 0 ) z ( g  , and ) 0 , x ( f y  , i.e., output falls towards the level consistent with maximum destructive capacity. For reasons of econometric identification, the practice in empirical work is to simplify the damage control function to a proportional one, i.e., y = f(x)g(z).

In the context of pest management, the above specification implies that as pesticide input z increases, abatement 1 ) z ( g  , and at the limit y = f(x), i.e., there is no destruction due to pest damage and maximum potential output is realized. As pesticide application declines towards 0, 0 ) z ( g  , and 0 y  . Since y is now proportional to g(z) and g(z) is between 0 and 1, g(z) represents the percentage of maximum potential output realized for a given level of pesticide use, z. Since g(z) lies in the [0,1] interval, a choice of several cumulative distribution functions is available to model g(z), with the Weibull, Exponential and Logistic widely used in applications. Where the damage control representation is appropriate, Lichtenberg & Zilberman demonstrate that using conventional specifications can lead to serious bias and erroneous conclusions about the productivity and use efficiencies of pesticides as well as the other conventional inputs included in the analysis. As discussed before, most of the Bt cotton evaluation papers have accordingly used damage control specifications in their analysis. However, even though this corrects the potential bias caused by the special nature of pesticide inputs, it does not provide flexibility with regard to risk effects. It is easy to show that the usual damage control functions cannot allow mean and variance effects of inputs (or technologies) to be qualitatively independent of each other.

Damage control specification with flexible risk properties

The above discussion points to the need for a specification that allows a damage control characterization for pesticide and Bt technology, flexible risk properties for the input and the technology, and explicit accounting for multiple sources of uncertainty. [START_REF] Saha | The Economics and Econometrics of Damage Control[END_REF] present such a model (henceforth referred to as the SSH model), which we use as the main basis for our empirical work. Their model is described briefly below.

The SSH production function is described by:

y = f(x, β) g(z, α, e) exp(ε) (1)
Here, β is a vector of parameters attached to the 'conventional' inputs in x, while α is the parameter vector attached to the 'damage control' inputs in z. A key difference relative to the ordinary damage control function specification is that (1) contains two error terms: e, attached to the damage control function g(.), that represents pest and pesticide application related implication of the SSH model is that output is distributed lognormally. Although there may be other parametric distributions that describe farm output better, the lognormal does have a history of farm output applications (e.g. [START_REF] Sherrick | Crop Insurance Valuation under Alternative Yield Distributions[END_REF][START_REF] Saha | The Economics and Econometrics of Damage Control[END_REF]; [START_REF] Tirupattur | Crop Yield and Price Distributional Effects on Revenue Hedging[END_REF]). Most importantly, Saha, et. al. demonstrate that marginal effects of inputs and technologies contained in g(.) on the variance of output can be either positive or negative, and independent of the marginal effects on the expected value of output. In other words, flexibility with respect to risk is achieved while retaining the damage control specification.

Two comments are worth making at this stage:

(i) With the two error terms as specified in (1), the SSH model has a resemblance to stochastic frontier models. Indeed, all damage control production functions are similar in spirit to stochastic frontier models, since both types of models posit a maximum possible output f(x), with firms achieving some proportion of that output. The SSH model is closer to stochastic frontier specifications, given that it incorporates two, instead of one, error terms.

However, standard stochastic control specifications do not allow correlation between the two error terms.

(ii) We have started referring to marginal effects of inputs and technologies on variance, rather than on risk. As is well known, these are not generally equivalent. It is fully acknowledged here that theoretical assumptions are necessary to obtain equivalence. The first model we use, the Just-Pope production function, assumes normality of output. With this model, variance and risk effects are equivalent since the normal follows the location-scale condition of Meyer (Meyer (1989); [START_REF] Leathers | Interactions between Agricultural and Resource Policy: The Importance of Attitudes Toward Risk[END_REF] and Stiglitz (1981) show that the necessary equivalence is obtained. Thus we invoke the CRRA assumption. While the assumption is open to debate (see Wik, et. al. (2004) and [START_REF] Miyata | Household's Risk Attitudes in Indonesian Villages[END_REF] for a discussion of and evidence against this assumption in agricultural settings) we note that CRRA is often employed in analysis in agricultural economics (e.g. [START_REF] Myers | Econometric testing for risk averse behavior in agriculture[END_REF]; [START_REF] Pope | On Testing the Structure of Risk. Preferences in Agricultural Supply Analysis[END_REF]).

III. Empirical Matters

Empirical setting

The empirical focus is on cotton growing smallholders in Makhathini flats, Kwa-Zulu Natal, South Africa (described extensively in [START_REF] Ismael | Benefits from Bt Cotton Use by Smallholder Farmers in South Africa[END_REF]; [START_REF] Gouse | BT Cotton In South Africa: Adoption And The Impact On Farm Incomes Amongst Small-Scale And Large Scale Farmers[END_REF]). About 3,000 Zulu smallholders growing rainfed cotton in Makhathini Flats, and another 500 in Tonga, in Mpumalanga together account for about 98% of smallholder cotton grown in South Africa [START_REF] Hofs | Genetically Modified Cotton in South Africa: The Solution for Rural Development[END_REF]. In 1998/99, with strong support provided by a private input Agriculture is the main livelihood source in Makhathini. Smallholder farms grow between 1 and 3 hectares of rainfed cotton. Some maize and beans are grown, predominantly for subsistence, but cotton occupies the most acreage and is the main source of cash income.

Smallholder cotton cultivation in the area is marked by relatively low yields. Irrigated cotton yields in China, for example, are on average in excess of 3000 kg/ha, while smallholder dry land cotton yields in Makhathini seldom exceeded 600 kg/ha prior to the introduction of Bt technology. Lack of irrigation is a major constraining factor.

Data

The dataset for the 1999-00 cotton season that we use has been discussed in detail by Thirtle et. al. (2003) and [START_REF] Shankar | Pesticide Productivity and Transgenic Cotton Technology: The South African Smallholder Case[END_REF], and so we restrict ourselves to a brief sketch.

Survey data were originally obtained on 100 Makhatini cotton smallholders. After deletion of observations with missing values, and removal of outliers, 86 observations were used in analysis here, with 58 Bt adopters and 33 non-Bt farmers. The data included quantities of inputs and outputs, cost and revenue information for the cotton crop, as well as information on a set of socio-economic variables. Sample means for the key variables are presented in Table 1. adopters on average had a significantly larger farm size. This reflects a policy adopted by VUNISA of targeting larger farmers in the early years [START_REF] Shankar | Pesticide Productivity and Transgenic Cotton Technology: The South African Smallholder Case[END_REF] and is further discussed below in the context of selectivity issues in estimation.

Estimation details:

All the production functions estimated in this article assume constant returns to scale and use a per-hectare specification for output and variable inputs. This is in line with most of the previous literature on Bt cotton impact assessment cited before, and also helps attenuate multicollinearity problems resulting from strong correlation between land and variable inputs such as pesticide and seed. Also, logic dictates that farm level applications of damage control models should specify at least pesticide input on a standardized (per-hectare), rather than on a whole farm basis. Since the abatement function g(z) is a proportion, expressing z on a whole farm basis would give misleading results. Henceforth, when we refer to the output y or the input sets (x, z), the implication is that all of these are expressed on a per-hectare basis.

The first model applied to the data is the Just-Pope production function, given by y = q(z, Bt, x, α) + h(z, Bt, x, β)e, e ~ N(0, 1)

Here, Bt represents a dummy variable, 1=Bt adopter, 0=non-adopter, and the rest of the notation is as before. Under this Just-Pope setup, expected value of output, E(y) = q(z, Bt, x), while variance of output V(y) = h 2 (z, Bt, x), allowing all inputs as well as Bt technology to affect output variance independently of effects on the mean of output.

Cobb-Douglas forms are used in q(.) and h(.), i.e.

( In (4), x seed , x fert , x lab and z pest represent seed, fertilizer, labour and pesticide inputs, respectively, Bt is the Bt dummy variable, and (A, B, α, β) is the parameter set to be estimated. Although the Cobb-Douglas form is restrictive, it proved to be the most practical choice for estimation here due to the relatively small sample size. Besides the problem with conserving degrees of freedom, alternative forms such as the quadratic and the translog were found to worsen extant collinearity problems.

) Bt pest lab fert seed Bt pest lab fert seed exp ) z ( ) x ( ) x ( ) x ( A (.) q       Bt pest lab fert seed Bt pest lab fert seed z x x x B h      exp ) ( ) ( ) ( ) ( 4
The estimation of (3) was accomplished using the three-step process originally described by [START_REF] Just | Production Function Estimation and Related Risk Considerations[END_REF]. Suppose i indexes the farmers. First, a nonlinear least squares (NLS) regression y i = q(z i , Bt i , x i , α) + e i * was estimated, resulting in first round estimates of α.

Given (3), this is a heteroskedastic regression. The second step involved an OLS regression of ln|e i *| (using e i * estimated from the first step) on ln [h(z i , Bt i , x i , β)], to provide estimates of β. Finally, a NLS regression of produced revised estimates of α . [START_REF] Just | Stochastic Specification of Production Functions and Economic Implications[END_REF] show that the resultant estimates are consistent and asymptotically efficient.

The SSH model features have already been described in section II. To recap, we estimated

y i = f(x i , β) exp[-A(z i , Bt i , α)e i ]exp(ε i ), ε i ~ N(0, 1), e i ~ N(μ, 1), cov(ε i , e i ) = ρ
(5) [START_REF] Saha | The Economics and Econometrics of Damage Control[END_REF] derive the loglikelihood function (LLF) for this model, given by:

LLF(α, β, μ, ρ) =              i i 2 i i i i (.) B ] (.) A (.) f ln y [ln (.) B ln 2 1 2 ln 2 n (6)
where B i (.) ≡ [1 + A i (.) 2 -2A i (.)ρ]. We estimated the parameter vector (α, β, μ, ρ) by

maximizing (6) directly. ) , Bt , z ( h ) , Bt , z ( q on ) , Bt , z ( h y i i 1 i i i i 1 i β , x α , x β , x i i i   F o r P e e r R e v i e w
14 Alternative functional forms were experimented with for f(.) and A(.) 2 , and a decision was made to use Cobb-Douglas forms for both functions. Ease of convergence in nonlinear estimation was a key factor in making this decision. Saha et. al. in their original application used a Cobb-Douglas form for f(.) and a linear form for A(.). Note, however, that a linear form sits uneasily with the abatement function interpretation of exp[-A(.)]. To take a simple example, if A(z, α) = α 0 + α 1 z, to keep abatement within the [0,1] interval and to have a positive marginal product for z, it would be necessary to have α 0 > 0 and α 1 < 0. However, the implication then is that beyond a certain value for z, A(.) would become negative, and abatement exp[-A(.)] > 1. The Cobb-Douglas form improves on the linear specification in this regard 3 , and also has the virtue of parsimony.

Selectivity

Selectivity can be a serious issue in production function estimation of farm-level impacts of a technology using cross-sectional data. While survey datasets such as the one used in this research may contain information on both adopter and non-adopters, there is usually no random assignation of individuals into such groups. There is then the very real possibility that adoption patterns of individuals are related to their productivity patterns. Often, 'better' or more efficient farmers, who are able to get more output out of a given technology and a given set of inputs, are also the ones to adopt technologies that improve productivity. Thus production function estimation using cross-sectional data is likely to exaggerate the impacts of technology adoption, confounding the inherent efficiency of adopting farmers with the actual performance of the technology itself.

Selectivity is an issue to be considered seriously in farm-level GM crop impact estimation as well. However, there has been surprisingly little explicit attention devoted to this issue in the literature. Where panel data are available, it is possible to control for farmer-specific effects, thereby isolating the technology effects accurately. In a cross-sectional context, one solution is to use Heckman's correction, where inverse Mills ratios derived from first step adoption 15 probit models can be used to correct selectivity bias in second step production function estimation. A common problem with this strategy, however, is that instruments derived from adoption probits are often poor. However, as Barnow, Cain and Goldberger (1980) point out, assuming the effects that cause the sample selection problem are observable, including those variables in the outcome regression would correct for the sample selection problem. This standard regression based method has been called 'ignorability of treatment' [START_REF] Rosenbaum | The central role of the propensity score in observational studies for causal effects[END_REF], and 'selection on observables' [START_REF] Heckman | Alternative methods for evaluating the impact of Interventions[END_REF] in the literature. Loosely, treatment is random/ignorable conditional on those variables that affect both selection and outcomes. In Makhathini, [START_REF] Shankar | Pesticide Productivity and Transgenic Cotton Technology: The South African Smallholder Case[END_REF] have argued that farm size was the main variable determining adoption. VUNISA launched the technology by promoting it to larger farmers in the initial years, with the expectation that smaller farmers would be picked up via copy adoption in later years. Indeed, farm size was the only strongly significant variable in adoption models reported by Thirtle et. al. (2003) and [START_REF] Shankar | Pesticide Productivity and Transgenic Cotton Technology: The South African Smallholder Case[END_REF]. Thus, inclusion of a farm size variable in our production function regressions may be an effective control for any existing selectivity. Other socio-economic variables such as farmer education and age have also been used in production functions estimated in the Bt cotton literature (eg. Qaim 2003;[START_REF] Qaim | Bt Cotton and Pesticide Use in Argentina: Economic and Environmental Effects[END_REF]. A similar set was used in initial runs in this research.

However, these other variables were largely insignificant in all regressions. The farm size variable alone was retained in the final set of estimates, because of farm size being a potential determinant of yields and also because of its role in selectivity control. As noted before, the first step (mean) regression in the three-step procedure is implicitly a heteroskedastic regression. We therefore tested for heteroskedasticity in the first step. Two tests were carried out, White's (1980) test and [START_REF] Breusch | A simple test of heteroskedasticity. and random coefficient variation[END_REF] The variance effects of the inputs, seen in the bottom half of the table, are however far weaker as estimated by the Just-Pope model. A positive (negative) coefficient sign indicates a risk increasing (decreasing) effect for the input it is attached to. Seed is seen to be the only variable input with a statistically significant effect on output variance, and that only at the 10% level. The positive sign of the pesticide coefficient indicates a risk increasing effect for the input. However, it is insignificantly different from zero. The Bt dummy on the other hand, bears a negative sign indicating a risk-decreasing effect, but is even more strongly insignificant. Opposing signs for the pesticide and Bt dummy are not in line with expectations 4 , and along with the very low t-ratios suggest that the Just-Pope model cannot confirm any strong evidence for the hypothesis that Bt technology reduces risk.

IV. Results

Just-Pope production function results

However, noting again that the Just-Pope function is estimated only as a preliminary step in the investigation of risk properties, and that it does not have a damage control specification appropriate for the pesticide and Bt variables, we now turn to results obtained from the SSH model.

SSH model results

Table 3 presents results from the SSH model. For comparison, we also present results from a damage control model obtained by imposing restrictions on the SSH model in (5), i.e.,

y i = f(x i , β) exp[-A(z i , Bt i , α)]exp(ε i ), ε i ~ N(0, σ 2 ) (7)

Table 3 about here

The labour and seed production elasticities from the two models, seen in the top half of Table 3, are not substantially dissimilar to the mean function estimates produced previously by the Just-Pope model. However, the SSH model produces a somewhat lower and statistically insignificant estimate for the seed coefficient, 0.16, compared to the significant 0.22 under the damage control model. The farm size effect is seen to be indistinguishable from zero under both models. An obvious a-priori expectation is that pesticide input and Bt technology should not reduce abatement. Equivalently, ∂y/∂z pesticide ≥ 0 and (y| Bt -y| NonBt ) ≥ 0, all else held equal.

For these to hold, it can be verified that the coefficients attached to pesticide input and the Bt technology dummy in the two models need to be non-positive. As can be seen from the table ,   this is indeed so. In both models, the negative valued coefficients α pesticide and α Bt are also significant at conventional significance levels, although these coefficients seem more

precisely measured with the damage control model.

As Saha, et. al. note, a necessary condition for rejecting the SSH model in favour of the damage control one is the restriction ρ=0 where ρ is the covariance between the two random variables e and ε, since one of the random variables is missing in the damage control model.

Table 3 shows that the estimated value of ρ is highly significant, with a t value of 25.89. Thus random variable e and rainfall random variable ε would appear to contradict the earlier notion that e and ε should be negatively correlated. However, this is misleading. It can be calculated from (5) that ∂y/∂ε >0, i.e., the rainfall random variable is ordered from bad states of nature (poor rainfall) to good states (good rainfall). However, ∂y/∂e<0, i.e., the pest density random variable is ordered from good states of natures (low pest density) to bad (high pest density) in the SSH model (5). Therefore, ρ should indeed be positive. Our finding of a positive, strongly significant value for ρ is thus consistent with the earlier interpretation of the two random variables in the model, and lends support for the SSH model in comparison to a simpler damage control alternative.

The mean and variance effects of pesticide input and Bt technology were calculated at the sample mean values of the variables. At the baseline, it was assumed that non-Bt technology was being used, and all other independent variables were being held fixed at overall sample mean values. Given this baseline, the pesticide effects were calculated as ∂E(y)/∂z pesticide and ∂V(y)/∂z pesticide , i.e., the marginal effects on expected yields and yield variance 5 of a one unit increase in pesticide. The Bt technology effect is a discrete one, where the technology provides the equivalent of an unknown number of units of pesticide upon adoption. Thus the Bt effects were calculated as E(y)| Bt -E(y)| Non-Bt and V(y)| Bt -V(y)| Non-Bt , with all other variables held fixed. These effects were calculated for both the damage control model and the SSH model. Approximate standard errors were also calculated using the Delta method. The results are reported in Tables 4 and5. Both models in Table 4 are seen to predict a positive and statistically significant effect of pesticide on expected yields. Indeed, these effects are almost identical across the models. since the damage control model forces the variance effect to be in the same direction as the marginal product. However, the SSH model, which provides flexible risk effects, predicts the same qualitative risk effect, i.e. that pesticide increases risk. In fact, the increase in yield variance is significantly higher in the SSH model than in the damage control model, in response to the same marginal unit increase in pesticide.

Since Bt technology embodies a certain type of pesticide, the expectation is that the mean and variance effects of Bt technology adoption would be along the same lines as those for pesticide. This is verified in increasing effect is likely. This strong correlation has been confirmed for our case, and is consistent with the risk increasing effect we find.

V. Conclusion

This research has investigated an important, but previously unexplored, aspect of GM technology -it's production risk aspects. Specifically, we have been interested in testing the hypothesis that Bt cotton technology reduces risk in South Africa, in addition to the (expected) yield-boosting effect measured and analyzed by previous studies. The risk notion is of importance in a developing country smallholder setting since small farmers have relatively few avenues available to shift risk. The risk aspect is also intimately tied up with notions of vulnerability that are given much prominence in the poverty literature.

Our review of the bioeconomics of pesticide and risk revealed that the risk effects of this technology can be hard to predict and are probably situation-dependent. Where multiple sources of uncertainty abound, such as rainfall and pest-density, depending on the relative importance of each random variable and the correlation between them, either risk-increasing or risk-decreasing effects can plausibly be found. [START_REF] Saha | The Economics and Econometrics of Damage Control[END_REF] also argued that a case can be made for including 'conventional' inputs such as labour in the A(.) function since they may also have a damage abating role. We tried including other variable inputs in A(.) but they were strongly insignificant and were therefore dropped.

3 Stochastic frontiers are more effective in ensuring that the proportion of potential output achieved stays within [0.1], by having a truncated distribution specification for the achieved proportion. They would be good candidates for modelling the problem specified here. However, the introduction of the correlation between the error terms complicates stochastic frontier estimation very considerably, as can be verified. 4 It is possible that occasional events like rainfall wash-off of pesticide can cause the technology and conventional pesticide application to have different qualitative risk effects. This is likely to be an exception rather than a rule, however. et. al. (2003). However, this first year of data was collected more than one year in retrospect, ie, after the 1999-2000 season, jointly with data collection for 1999-2000. In our judgement, these data from long recall were almost surely too inaccurate to be worthy of inclusion in the analysis here.

  et. al. instead used a stochastic frontier representation of technology. Almost without exception, these studies indicate superior performance of Bt varieties relative to local counterparts.

  by considering the analytic insights available from previous literature on how pesticides, and thus Bt technology, may affect risk. Section III sets out the empirical framework, and section IV presents and discusses the results. Section V concludes and offers suggestions for future work.

  averse producers use more (less) of risk-decreasing (increasing) inputs than less risk averse producers, all else equal. If e mainly represented randomness of pest density, then

  randomness, and ε, related to randomness in crop growth conditions such as rainfall variability. e and ε are allowed to be correlated. The SSH model makes two key assumptions that facilitates the identification and estimation of the model: (i) The damage control function is specified as g(z, α, e) = exp[-A(z, α)e], where A(.) is a continuous and differentiable function, and (ii) ε ~ N(0, 1), e ~ N(μ, 1) and cov(ε, e) = ρ. This specification gives: .) ≡ [1 + A(.) 2 -2A(.)ρ]. A log-likelihood function can be easily derived under this specification, and estimation can use standard nonlinear optimization methods. One

  supply company called VUNISA, a few smallholders in Makhathini Flats started planting a Bt cottonseed variety, NuCOTN 37-B. This insecticide produced by this variety provides resistance to bollworm, which is the most troublesome class of pests in the area, followed by cotton aphids and jassids. The Bt gene, used by Delta Pineland in developing NuCOTN 37-B, belongs to Monsanto. In addition to a premium payable per bag of Bt seed over conventional seed, Bt users also pay a technology fee. At the time of the data collection for this research, VUNISA Cotton was the sole supplier of seed, chemicals and support services for the farmers through their extension officers, including credit for land preparation, chemicals and seed, based on their credit history. VUNISA bought cotton from the farmers at prices fixed by Cotton South Africa, but has faced competition from a new gin since 2002. Diffusion of the technology was very rapid in the initial years, with some estimates putting the adoption rate at /03. Reports suggest that significant disadoption has occurred since then due to the removal of institutional support (credit and buy-back guarantees initially offered by VUNISA).

  error term specification, potential output function f(.) and abatement function exp[-A(.)], (7) is a traditional damage control function. It can allow only risk-increasing inputs and technologies, in contrast to the SSH model, (5), which allows the data to determine the risk effects of inputs and technologies. This damage control model was estimated using nonlinear least squares.

  we cannot find evidence to support discarding the SSH model in favor of the simpler damage control model. ρ has a positive value of 0.86. This positive correlation between pest density

  increase in the variance (risk). As discussed earlier, this is as expected,

  The lognormal does not follow the location-scale condition in spite of its two-parameter nature. However, if the utility function is characterized by constant relative risk aversion (CRRA) and the random variable is lognormally distributed, Newberry

	is lognormally distributed.
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). In the SSH model, output

Table 1 about here.

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Information in Table

1

reveals that Bt provided a substantial yield advantage in the year 1999-2000. It also enabled pesticide application to be lowered considerably. Note that adoption in Makhathini flats was characterized by complete adoption or non-adoption

(Thirtle, et. al., 2003)

, i.e. the data do not contain partial adopters. One additional aspect of interest is that the

  test. In both tests, the test statistic is distributed as chi-squared under the null hypothesis of no heteroskedasticity. The White test makes no assumptions about the form of the heteroskedasticity and simply tests H 0 : σ 2 i = σ 2 for all i against H 1 : Not H 0 . The Breusch-Pagan test on the other hand is a Lagrange multiplier test that assumes that if any heteroskedasticity exists, the error variance varies with a set of regressors. In our case, the natural set of regressors to use is the set of regressors used in the variance regression step of the Just-Pope function, i.e., a constant, the three variable inputs, farm size, and the Bt adoption dummy. The White test value was 56.82, which is considerably in excess of the 95%Table 2 presents the estimates of the mean and variance portions of the Just-Pope production function, following implementation of the three-step procedure outlined earlier. Even though the mean portion is estimated as a Cobb-Douglas function with an additive, instead of the usual exponential error term, it retains an elasticity interpretation. Thus the elasticities of expected value of yield with respect to the variable inputs are all positive and have plausible values, although the seed elasticity is insignificant. Increasing farm size is seen to have a depressing effect on the expected value of yields, although the parameter is significant only at

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level chi-square critical value of 38.80. Thus the White test strongly rejects the null hypothesis of homoskedasticity. The Breusch-Pagan test value was 25.83, which is also substantially higher than the 95% level chi-square critical value of 11.07 with 5 degrees of freedom. The Breusch-Pagan test thus bolsters the evidence provided by the White test that the null hypothesis of homoskedasticity can be rejected, and provides further rationale for the investigation of how output variance or risk is affected by inputs and technology. the 10% level. The Bt dummy variable parameter is the most strongly significant of all, and the positive value confirms previous findings that Bt varieties provide a strong boost to (expected value of) yields.

Table 2 about here.

 2

Table 4 about here.

 4

Table 5 about here.

 5

Table 5 .

 5 Once again, the mean effects of Bt technology adoption are positive, strongly significant, and almost identical across the two models. Since Bt technology is likely to provide the equivalent of several litres of bollworm pesticide during the season, the technology effect is much stronger than that of a marginal unit of pesticide seen in Table4. Under the damage control model, the variance effect of Bt technology is positive, i.e. risk-increasing, as expected. However, again the SSH model reaffirms this qualitative finding in a flexible risk setting. Under the SSH model, Bt technology adoption is found to increase risk. What is more, the increase predicted by this flexible risk model is more than ten times the quantitative increase found under the damage control model. Although there is some imprecision in the estimation of this effect under the SSH model, the effect is nevertheless significant at the 10% level.Thus neither the Just-Pope model nor the SSH model is able to confirm a strong and statistically significant risk-decreasing effect for Bt technology. Therefore, the available evidence does not allow claim of this potentially valuable additional benefit for the technology in Makhathini. On the contrary, the SSH model predicts a strong risk-increasing effect. This is intuitively plausible given the bioeconomic theory of pesticide and risk discussed previously. We have noted before that cotton cultivation in Makhathini is rainfed, and that lack of irrigation is a major constraining factor. Under these circumstances, rainfall is as important a source of randomness as pest density. Where rainfall is relatively low, there is less crop to protect, and Bt technology is relatively less effective. Where rainfall is relatively high, there is more crop to protect, and the technology is more effective in raising marginal cotton product. In other words, the technology in these circumstances is a 'fair weather friend'. Even where the rainfall and pest density random variables are strongly negatively correlated in the Horowitz and Lichtenberg sense (strongly positively correlated from the SSH model perspective), Horowitz and Lichtenberg have shown that a risk

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Table 1 . Summary Statistics by Adoption Category, 1999/2000

 1 The first model applied was a Just-Pope model that is the workhorse of production risk investigation. In accordance with the notion of multiple sources of randomness, we also chose to apply the SSH production function model that can display flexible risk effects in addition to accommodating two distinct sources of randomness and a damage control representation.Our results showed that neither model can provide any support for the risk-reduction hypothesis. The Just-Pope model shows the risk effect of Bt technology to be insignificant, while the SSH model shows a strong, statistically significant risk-increasing effect. This is consistent with the notion of rainfall being a key source of randomness in irrigated smallholder cotton production. Thus a plausible interpretation of the results is that Bt technology best produces its effects in Makhathini when the going is good, i.e., when the crop-growth conditions (rainfall) are good.It must be emphasized that this research is just one preliminary piece in a potentially larger puzzle concerning GM technology and production risk. There are a number of limitations to this study, and there is much scope for future investigation. Firstly, risk effects are almost certainly situation dependent, and so similar applications to other parts of the world are warranted. Secondly, we have only used cross-sectional data 6 , and further analysis with panel data models can provide richer specifications controlling for heterogeneity and selectivity, if present. To provide an example of how panel specifications might be important, note that one potential cause of correlation between the random variables e and ε is individual heterogeneity. Lacking panel data, we have been unable to control for such heterogeneity and have simply interpreted the correlation in terms of natural production randomness. The Bt cotton evaluation literature has thus far avoided proper panel-data analysis, even where such data were available, possibly because of the difficulty of including heterogeneity effects within nonlinear models such as the damage control ones commonly applied. However, multiplicative panel data models(Wooldridge, 1997) have potential in this regard, andCarpentier and Weaver (1999) have shown how these can be adapted to damage control models. Thirdly, we have only calculated the risk effects of the technology, but have not been able to further explore implications for the smallholders. This is due to a lack of data for this study, but where household wealth data are available, it is possible to compute welfare equivalents of the increased risk for individuals in the data set or for representative agents.Ismael, Y., Piesse, J. and Beyer L. (2003) Can GM-technologies help the poor?The impact Bt cotton in the Makhathini Flats of 31

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Wooldridge, JM (1997)

, "Multiplicative Panel Data Models without the Strict Exogeneity Assumption," Econometric Theory 13, 667-678.

Page 28 of 33 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
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Table 2 . Just-Pope Production Function Estimates ±

 2 * implies significance at 10% level, ** at 5% level, *** at 1% level.

	Page 29 of 33		Submitted Manuscript
	Parameter	Estimate	t Value
		Mean Regression
	α farmsize	-0.11	-1.67*
	α labour	0.25	2.44**
	α seed	0.20	0.87
	α pesticide	0.20	2.00**
	α Bt	0.12	4.77***
	Variance Regression
	β farmsize	-0.01	-0.06
	β labour	-0.04	-0.15
	β seed	0.44	1.74*
	β pesticide	0.15	0.75
	β Bt	-0.06	-0.24

±

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3 . SSH model estimates

 3

			±
		Damage Control	SSH Model
			Model
	Parameter Estimate t Value	Estimate t Value
	β labour	0.25	2.28**	0.24	1.78*
	β seed	0.22	1.91*	0.16	1.28
	β farmsize	-0.03	-0.35	-0.03	-0.29
	α pesticide	-0.25	-2.86*** -0.29	-1.83*
	α Bt	-0.87	-3.57*** -0.58	-2.43**
	σ	0.49	12.57***
	ρ			0.86	25.89***
	μ ± * implies significance at 10% level, ** at 5% level, *** at 1% level 0.24	1.82*

Page 30 of 33 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
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Table 4 . Mean and Variance Effects of Pesticide ± Mean Effect: ∂E(y)/∂z pesticide Variance Effect: ∂V(y)/∂z pesticide

 4

		Submitted Manuscript
	Damage control model 0.036 (0.0001)	0.006 (0.00001)
	SSH model	0.040 (0.002)	0.040 (0.009)
	± Approximate standard errors in parantheses.

Page 31 of 33 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 5 . Mean and Variance Effects of Bt Technology ±

 5 Other dimensions of risk, such as price and marketing risk associated with Bt technology are recognised as important, but are beyond the scope of this paper. 2

		Submitted Manuscript
		Mean Effect:	Variance Effect:
		E(y)| Bt -E(y)| Non-Bt	V(y)| Bt -V(y)| Non-Bt
	Damage control model 0.215 (0.004)	0.049 (0.0007)
	SSH model	0.213 (0.019)	0.610 (0.336)
	± Approximate standard errors in parantheses.

Page 32 of 33 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  5 Although the summary statistics table expresses output and yields in kilograms, the original dataset expressed these in bales of 200 kgs each. The latter unit, i.e, bales were used during econometric estimation. Those interested in the quantitative values of these estimates should multiply by 200 to get values in kilograms.6 Another year of data (1998-99 season) for these Makhathini smallholders are available, as detailed in Thirtle

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Lukas Menkhoff
email: menkhoff@gif.uni-hannover.de

Rafael Rebitzky

Michael Schröder

Do Dollar

Keywords: exchange rate expectations, forecasting, fundamental analysis, technical analysis, purchasing power parity JEL-Classification: F31 (foreign exchange), G14 (information) Exchange rate expectations, forecasting, fundamental analysis, technical analysis, purchasing power parity JEL-Classification: F31 (foreign exchange), G14 (information) Exchange rate expectations, forecasting, fundamental analysis, technical analysis, purchasing power parity

published or not. The documents may come

Introduction

Since about 20 years we know that exchange rate forecasts of professionals show some degree of "irrationality" (Dominguez, 1986, p.281). It has become a stylized fact that these forecasts do not hold predictive power and that forecasters do not even use the entire information available (surveys by Takagi, 1991, Sarno and[START_REF] Sarno | The Economics of Exchange Rates[END_REF]. Too little is known about possible sources of this pattern. Our research contributes towards a better understanding of this seemingly "irrational" behavior by using a new database. This enables us to analyze monthly US-Dollar/Euro and US-Dollar/Deutsche Mark forecasts for more than 12 years, i.e. significantly longer than earlier studies. Additionally and for the first time on this literature, the forecasts of professionals are examined in groups defined by their relative reliance on fundamental analysis. We determine that forecasters in general rely too much on mean reversion on exchange rates, mean represented by purchasing power parity (PPP). The revealing fact is that fundamentalists show even more biased forecasts -this is consistent to the opinion that Dollar forecasters believe too much in PPP.

Right from its beginning the thorough analysis of exchange rate expectations have been motivated under the issue of market efficiency. The Frankel and Froot (1987a) "finding of systematic expectational errors" (p.150) set the ball to roll and was confirmed by numerous authors and various samples (see [START_REF] Macdonald | Expectations Formation and Risk in Three Financial Markets: Surveying what the Surveys Say[END_REF].

The many repetitions of the early results might have been responsible for the fact that a caveat has been readily neglected so far: Frankel and Froot (1987a) reveal systematic errors but they also report that the sign of the error may depend on the sample period. This puts into question, whether deeper forces at work appear that may play a responsible part upon the changing sign. An analysis of this issue requires longer time series exceeding the often used two to four years.

Another important issue already addressed by [START_REF] Frankel | Chartists, Fundamentalists, and Trading in the Foreign Exchange Market[END_REF] is the forecast heterogeneity. Earlier studies, such as [START_REF] Dominguez | Are Foreign Exchange Forecasts Rational? New Evidence from Survey Data[END_REF] or Frankel andFroot (1987a, 1987b), are based on consensus forecasts. More recent studies though analyze individual expectation data to reveal indeed different pattern in forecasts (e.g. [START_REF] Bénassy-Quéré | Models of Exchange Rate Expectations: How Much Heterogeneity?[END_REF]. This line of work describes and examines heterogeneity but does not allow inferences on possible sources of heterogeneity. For the latter purpose one would need additional, exogenous information (see, [START_REF] Moosa | Expectation Formation Mechanisms, Profitability of Foreign Exchange Trading and Exchange Rate Volatility[END_REF]Shamsuddin, 2004, p. 1606). A rare example is shown in the analysis of the exchange rate forecasts of commercial services [START_REF] Goodman | Foreign Exchange Rate Forecasting Techniques: Implications for Business and Policy[END_REF], where technically-oriented services perform better than economics-oriented services. However, the data spans less than three years and considers only 13 forecasting services. Another example is the examination of a relatively short Japanese sample which allows classification of six groups, such as exporters etc. This data indicates that expectations can be affected by private information (Wakita, 1989) but is also influenced by wishful thinking [START_REF] Ito | Foreign Exchange Rate Expectations: Micro Survey Data[END_REF]. It is again [START_REF] Frankel | Chartists, Fundamentalists, and Trading in the Foreign Exchange Market[END_REF] who suggest another cut in the data that might be warranted: they speculate that there may be forecasters "who think long-term" and consequently form regressive expectations then again others "who think short-term" form rather static expectations. We know that professionals picture expectations differently, though we need a rationale for this behaviorsuch as the one suggested by Frankel and Froot -provided that we want to reach beyond description and build an economic understanding instead.

We read the suggestion of long-term motivated regressive exchange rate expectations as a hint towards the possible importance of PPP. PPP is a core part in many exchange rate models, it is an intuitively plausible benchmark for thinking about exchange rates and -most important -it has received credit as an empirically valid concept as surveyed by [START_REF] Rogoff | The Purchasing Parity Puzzle[END_REF] or [START_REF] Taylor | The Purchasing Power Parity Debate[END_REF]. To pinpoint it further: as there is no single exchange rate theory that holds empirically (Frankel andRose, 1995, Sarno and[START_REF] Sarno | The Economics of Exchange Rates[END_REF], which economic concept forecasters ought to be used if not PPP? An examination of this issue would therefore profit from data that fulfils two conditions: the time series should be long and there should be information indicating that the economic concept of PPP drives expectations. The long period is needed in order to cover exchange rate movements to and from PPP. Additional information towards motivation of forecasters is useful to derive directly the importance of PPP. To the best of our knowledge, there is no data set in the literature that would fulfil these two conditions except for the data used here.

We show that professionals from Germany, covering more than the past 12 years, behave very conventionally: our first result shows that according to standard surveys their expectations are not purely rational and they seem to apply different kinds of expectation formation. As this is in unison to the literature, we declare it as Third, according to their reliance on fundamental analysis and as soon as the sample is divided into three groups, the forecasters who rely most strongly on fundamentals analysis -"fundamentalists" -reveal an even stronger bias. The group who relies the least on fundamentals -prefer technical analysis instead: "technicians" -shows a much smaller bias. So, stronger belief in fundamentals and thus PPP is revealed as a source of bad forecasting performance. Fourth, though, the technicians' "advantage" in this respect is compensated by another bias not unexpected for technicians, showing too much expectation of trend extrapolation. Fifth, we illustrate, that forecasting biases of fundamentalists and technicians will get stronger when the exchange rate is further away from PPP. Finally, 'point forecasts' performance of both groups is of similar poor quality. Interestingly, all groups distinguished show some directional forecasting ability.

The remainder is structured as follows. Section 2 describes data, whereas results are presented in Section 3. Section 4 concludes.

Data

Our expectation data is based upon the ZEW Financial Market Survey. The Centre for European Economic Research (ZEW) of Mannheim (Germany) collects every month numerous economic and financial forecasts with a horizon of six months.

The ZEW survey is a qualitative questionnaire, which has been driven since December 1991 and soon grew up to a stable panel with more than 300 participants in Germany. Around 75 per cent of the participants work in the banking sector (as analysts, fund managers etc.) and 25 per cent work either in the insurance or in the industrial sector. 1 In comparison to other surveys the amount of participants is relative large and its composition according to their profession is similar to others (Consensus forecasts, London, contain 75 per cent participants from financial institutions).

The forecasts collected are standardized by fax and are usually processed on the last Friday of each month. 1 The ZEW publishes out of the ZEW Financial Market Survey regularly amongst others the ZEW Indicator of Economic Sentiment, which is a leading indicator for the German economy and of similar prominence like the ifo Index. We are aware about criticism regarding the use of survey data for modelling expectations in general and for financial forecasts in particular. Nevertheless, incentives for participants not to reveal their true beliefs are very limited as the ZEW publishes the aggregated forecasts (consensus forecasts) only. Moreover manipulating the data with extreme forecasts is practically impossible, due to around 300 participants and the qualitative responses given. Additionally the incentive to participate at the survey in order to get an extensive summary of the consensus data with additional background information from the ZEW directly seems to be quite strong as this data is well covered by the financial media.

To get a first impression of the exchange rate forecasts, some descriptive statistics are presented in Table 1. For comparison we include the corresponding six month forward rates and the realized exchange rates at the same time. With respect to the level statistics one recognizes that consensus forecasts as well as forward rates behave similar to realized exchange rates though forward rates resemble exchange rates even better. If one looks at the change statistics, consensus forecasts still behave similar to realized exchange rates, in contrary to forward rates which differ especially on their variability measures. Finally the consensus expects a slightly stronger US-Dollar on average towards the Euro whereas the US-Dollar actually weakens on average.

Additionally in a specific survey ZEW participants were asked on which information they actually base their exchange rate forecasts (see ZEW Financial Market Report, 2004). 3 This enables us to categorize the participants according to their use of 2 Recently [START_REF] Stadtmann | Biases in FX-Forecasts: Evidence from Panel Data[END_REF] uses the Wall Street Journal survey which covers a longer time period (1989 -2003), but at the cost of semi yearly data only, which generates just 30 data points. 3 Participants were asked to distribute 100 points amongst the categories fundamental, technical and flow analysis according to the way how they do their exchange rate analysis. analytical instruments. We base our classification on the use of fundamental analysis and organize the survey participants in fundamentalists, technicians and intermediates. We could not find any significant difference between people who use primarily technical analysis or flow analysis due to the fact, that flow analysis is used to a much smaller degree than other instruments of analysis (the average share of flow analysis in the forecasting process sums up to 10 per cent, whereas technical analysis adds up to 30 per cent and fundamental analysis to 60 per cent). 4 The respective outcome of this questionnaire is summarized in Table 2. One can see that the group of fundamentalists is about as big as the group of technicians, due to the threshold values being chosen. The average numbers of these two groups representing more than 35 seem big enough for our analysis.5

Results

In the following regression analysis we use OLS estimators corrected for Newey-West standard-errors (see, [START_REF] Newey | A Simple Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix[END_REF]. We choose five lags as a result of the overlapping problem attributed to monthly forecasts with a six month forecast horizon, which imparts a fifth order moving average error process (see, for example [START_REF] Hansen | Foreign Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis[END_REF]. In addition and owing to the qualitative nature of the expectation data we use the quantification technique from [START_REF] Carlson | Inflation Expectations[END_REF] to generate point forecasts. 6 Due to non-stationarity characteristics of the time series, we use change forecasts rather than point forecasts. Detailed descriptions of the calculations and analyzed variables are given in each of the attached tables.

Rationality of expectations

In order to check characteristics of our survey participants with well established results in the literature, we perform conventional tests of forecast rationality. Since (1986) and for this purpose primarily it is common to check the degree of unbiasedness as well as efficiency.

Test of unbiasedness: e t t s s

6 6 + + + = (1)
Test of efficiency:

6 6 6 + + + + = t t e t FD s s (2)
The unbiasedness test is modelled in equation ( 1), where the change of the exchange rate ( s t+6 ) is regressed on the corresponding expectation change ( s e t+6 ). To satisfy the postulate of rationality, the estimated value of has to be one, whereas needs to be zero. Additionally in equation ( 2) the difference of the expected exchange rate change and the actual change is regressed on the six months forward rate premium (FD t+6 ). To confirm efficiency and rationality of the expectations, it is required that as well as are both zero.

Table 3 presents results on the test of unbiasedness which reject the hypothesis of rational expectations, because is significantly below unity. Furthermore the test of orthogonality shows evidence of irrationality too, since is significantly above null which implies that even data easily available such as the forward premium is not completely processed in exchange rate forecasts. 7 All in all, the unbiased expectations hypothesis (and therefore the assumption of rationality) on consensus forecasts has to be rejected, being well in-line with the literature (e.g. [START_REF] Kim | Testing the Rationality of Exchange Rate and Interest Rate Expectations: An Empirical Study of Australian Survey-Based Expectations[END_REF][START_REF] Macdonald | Expectations Formation and Risk in Three Financial Markets: Surveying what the Surveys Say[END_REF].

Bias of expectations

However, our primary interest lies on the sources for the irrationality of FXforecasts. To reveal the kind of forecast pattern we estimate a hybrid model. Since the work by Frankel and Froot (1987a) a lot of analyses have been carried out to estimate the expectation formation for exchange rates, i.e. extrapolative, adaptive, regressive expectations and some sort of mixed models on former (see e.g. [START_REF] Cavaglia | Further Evidence on Exchange Rate Expectations[END_REF], Ito, 1994[START_REF] Bénassy-Quéré | Models of Exchange Rate Expectations: How Much Heterogeneity?[END_REF]. Summarizing it figures out that depending on the forecast horizon, short-term forecasts exhibit evidence of destabilizing behavior whereas long-term forecasts show stabilizing evidence. Here we use a mixed model to regress the exchange rate forecasts on an extrapolative and a regressive term, since the former term covers well technical orientated forecaster behavior, whereas a regressive term should display the way how fundamentalists form their expectations. Furthermore, this procedure fits well into the relevant literature for comparative purposes (e.g. [START_REF] Moosa | Expectation Formation Mechanisms, Profitability of Foreign Exchange Trading and Exchange Rate Volatility[END_REF] (4) Equation ( 3) shows the expectation mechanism. The expected change of the exchange rate is regressed on an extrapolative term (s t -s t-1 ), which contains the previous one month change of the exchange rate. The second term on the right side of the equation displays the regressive formation ( s t -s t ). The latter one is based upon the difference between a fundamental equilibrium and the current exchange rate. To generate the fundamental variable we have chosen the well known relative PPP model and calculated corresponding rates upon PPI differences. In addition to that we would like to find out, whether the consensus relies too much on these expectations concepts on average. Doing so, we use again the expectation errors (see notes to equation 2) and follow the approach of Frankel and Froot (1987a, pp. 147-150) in equation ( 4), regressing them on the expectations mechanisms.

The results in Table 4 show that the consensus is based upon a mixture of extrapolative and regressive expectation, so both mechanisms seem to matter. More interestingly the results for equation (4) show that forecasters rely too much on regressive expectations on average, whereas the same doesn't hold in respect to the extrapolation of current trends. We can summarize that the participants of the ZEW panel rely too heavily on the concept of PPP when forming US-Dollar/Euro forecasts in some way.

Expectations of fundamentalists and technicians

In this section we run the same regressions for the separated groups as in section 3.2. We would like to know, whether there are any differences in the way that groups form exchange rate expectations (indicator i separates the different groups). 5 shows that the i coefficient of equation ( 5) differs between the different groups. Technicians seem to rely most heavily on the extrapolative term and fundamentalists least, whereas intermediates take a position in between. On the other hand forming regressive expectations seems to be most important for fundamentalists, followed by intermediates and least important for technicians. Not surprisingly when we compare the biased coefficients in equation ( 6) fundamentalists rely significantly too much on the regressive term but not on the extrapolative term. Contrary, technicians orientate on a smaller degree too much on the regressive term, but additionally, they seem to follow too much on trend extrapolation (here the statistical significance is less obvious). Again intermediates find themselves between the other two groups with biased forecasts towards the regressive term.8

F

A threshold analysis of expectations

Following our last results we use a switching regression model with different regimes in order to get deeper insights into the structures of US-Dollar/Euro forecast biases. We determine the absolute value of the regressive term as the transition variable (c t = | s ts t |), set the number of regimes to two (r = 2) and choose the threshold level ( i ) via a grid search method (see e.g. Franses and Dijk, 2000, p. 84).

Function (I i [c t ]) indicates the valid regime in time t. The expectations model (f r,i [•])

shows different parameters, depending on the regime and the group. We follow this approach to see, whether the group specific forecast biases differ between periods, where the US-Dollar/Euro shows large deviations from PPP and periods, where exchange rates are in line with the fundamental concept. Earlier research by [START_REF] Taylor | Non-Linear Mean Reversion in Real Exchange Rates: Toward a Solution of the Purchasing Power Parity Puzzles[END_REF] has in fact indicated that adjustment speed in real exchange rates towards PPP may change faster in periods of large deviations from PPP.

]) [ 1 ( ] [ ] [ ] [ , 2 , 1 , 6 t i i t i i i e t c I f c I f s • + • = + (7) Systematic bias: ]) [ 1 ( ] [ ] [ ] [ , 2 , 1 6 , 6 t i i t i i t i e t c I f c I f s s • + • = + + (8) with ) ( ) ( ] [ 1 , t t i r t t i r i r i r s s s s f + + = • and 2 , 1 = r with | | t t t s s c = and ) ( t i c I 0 1 = = i t t i t t s s if s s if < | | , | | ,
Table 6 represents the corresponding results and explains our procedure in detail. Summarizing and focusing on the estimation results of equation ( 7), the group of fundamentalists forms regressive expectations in both regimes, whereas the extent in regime 1 is greater (periods of major exchange rate deviations from PPP). This could contribute to stabilization in exchange rates and the utility of PPP. Additionally fundamentalists rely on trend extrapolation, but only in regime 2 (periods of minor exchange rate deviations from PPP). Contrary, technicians show a mix of regressive and extrapolative formation in both regimes. Further and looking at the parameter estimations of equation ( 8), all groups show a regressive bias in regime 1 but not in regime 2.9 Finally we reveal also an extrapolative bias in the expectation formation of technicians but only for regime 1, while fundamentalists still do not show any adherence on an extrapolative bias. These results on forecasting bias may cause some worries: they indicate that expectations about mean reversion in exchange rates towards PPP might appear too optimistic; moreover, some professionals -the technicians -seem to form even extrapolative expectations to an unjustified degree and might consequently destabilize the market.

Performance of expectations

Our last analyses examine the forecast ability of the separated groups. Additionally we deal with related forward rates and random walk forecasts. The results are shown in Table 7 and include four accuracy tests applied to corresponding point forecasts and a hit rate (share of right direction forecasts) applied to underlying trend forecasts.

To cut a story short, one can not detect significant differences in the performance between fundamentalists, intermediates and technicians. However, if we con- 12 centrate on the analysis for point forecasts such as MAE (mean absolute error) and RMSE (root mean square error), the random walk beats all groups of forecaster as well as the forward rate, even though the latter one performs also better than the forecaster groups. On the other hand if we consider the hit rate, which is calculated upon underlying trend forecasts, that all groups perform significantly better than the random walk, whereas forecasts based on the forward rate are significantly worse than the random walk. 10 In addition to that, corresponding differences between the forecaster groups and the forward rate are highly significant. 11Taken together, both groups, fundamentalists and technicians, perform upon point forecast measures significantly worse than the random walk, as well as the forward rate. On the other hand, if we consider just the implicit trend forecasts, than these forecaster groups outperform the other forecast series. It definitely shows that participants of the ZEW survey have forecasting abilities despite all kinds of biases revealed (see also Wakita, 1989). If they would be able to avoid systematic distortions there would be an even better chance to forecast. This result stands in line with Elliott and Ito (1999, p. 455), "that more is going on in the models of the respondents than static expectations with random noise".

Conclusions

Our study on exchange rate expectations intends to bring fresh evidence into an established field. Thus, we first reproduce the stylized fact of non-rational expectation formation and conclude that our participants do not differ in this respect from those of earlier survey studies. We also notice -largely in line with the literature -that forecasts are biased, in particular that the sign of the bias does change over time. Our objective is, however, not just to perform the conventional tests for another survey at another time. We rather aim for adding a completely different and most interesting kind of information to the field in order to understand biased forecasts better: our survey is the first to combine a large data set of forecasts with information on the forecasters' preferred analytical instrument, e.g. their reliance on fundamental analysis. We reveal that the preference of fundamental analysis is useful information to understand the way how exchange rate expectations are formed. Moreover, we detect that the preference of fundamental analysis helps to understand specific biases: fundamentalists believe too much in mean reversion of the US-Dollar/Euro, more than other participants. So, this misguided belief is consistent with poor forecasting performance. However, any claim of superior performance due to reliance on technical analysis is premature. Although the technicians' expectations are less distorted by too much reliance on PPP, they also show a misguided belief: they extrapolate shortterm trends as one would assume, yet, they extrapolate too much. Consequently, this additional expectation distortion hinders them to form appropriate forecasts.

Overall, we argue that our data provide new evidence on possible sources of systematic forecasting biases. In addition to [START_REF] Ito | Foreign Exchange Rate Expectations: Micro Survey Data[END_REF] discovery of wishful thinking we reveal too much belief in mean reversion which can be interpreted usefully as too much belief in PPP. One ought to speculate whether Ito's and our detections may be connected to behavioural distortion in decision making: in this sense, our participants possibly overestimate the precision of their knowledge of exchange rate changes relying too much on their interpretation of PPP. However, there is also a competing explanation for fully rational forecasters, who show proper understanding of fundamentals: as we are covering professionals with somewhat long-term orientation, markets might act inconsistent to them. Then, foreign exchange markets are possibly dominated by short-term considerations which are less consistent with the directions that fundamentals advise. Note:

F

This figure shows actual realizations of the US-Dollar/Euro and US-Dollar/Deutsche Mark exchange rates, where the latter are transformed on the official exchange rate between the Deutsche Mark/Euro of 1.95583 (left scaled). In addition to that it shows PPP exchange rates, which are calculated upon the PPP concept (left scaled) and consensus change predictions (right scaled). The consensus data were generated with the quantification method introduced by Carlson and Parkin, 1975 (for further details see note in Table 1). To calculate the fundamental exchange rates we used the PPP concept (further explanations are given in chapter regressive expectations). Whereas the US-Dollar/Euro as well as the PPP exchange rates are presented in their levels (corresponding left axis), the consensus data are shown in their changes (corresponding right axis). It can be seen, that the swap of the consensus forecasts from an appreciation of the US-Dollar/Euro to a depreciation occurred around the same time, when the US-Dollar/Euro crossed the line of the PPP exchange rates. Furthermore the amplitudes show a similar pattern, at least in their peaks. Using the method of [START_REF] Carlson | Inflation Expectations[END_REF] to derive aggregate point expectations requires two assumptions. First, each individual forecast is based upon a subjective probability distribution concerning the outcome of this forecast. However, applying the logistic distribution did not yield the results in any qualitatively different way. Second, the corresponding means of the individual probability distributions follow-up a normal distribution, which can be justified with the Central Limit Theorem. Furthermore we have to set a scaling factor, which displays the threshold, of which the forecasters perceive noticeable changes in the exchange rate. We choose a symmetric scaling factor of three percent. In a special survey the participants of the ZEW Financial Market Survey were asked to reveal their individual thresholds in correspondence to their different forecasts. The average median for the US-Dollar/Deutsche Mark was a symmetric threshold of roughly three percent. Nevertheless, choosing other thresholds around three percent, didn't show any qualitatively different results. [START_REF] Taylor | Expectations, Risk and Uncertainty in the Foreign Exchange Market: Some Results Based on Survey Data[END_REF] also uses the normal distribution and sets his scaling factor on 2.5 per cent. Other methods like choosing the threshold that the mean expected change is equal to the mean actual change or that squared prediction errors are minimized seem inappropriate because of overwhelming evidence towards irrational and inaccurate exchange rate expectations. Finally, in order to rescue some data points, in cases where the probability of a category is zero, we used neighboring estimated volatilities to compute the forecast (Carlson and Parkin, 1975, p. 130-131). veys from 12.1991 to 04.2004. Accordingly the number 35 that corresponds to the combination "Mean" and "Fundamentalists" represents the average number of people amongst all surveys, who use fundamental analysis to a degree of 80 or more per cent. Furthermore the combination "Max." and "Technicians" shows 58 and implies the maximum number of technicians in one survey. Concerning the participants in the survey, whom we categorized as technicians, their mean of technical analysis adds up to 52 per cent (considering the mean of the whole survey is 30 per cent) whereas they use 17 per cent on flow analysis on average (the corresponding overall mean is 10 per cent). In fact we are dealing with 237 individuals as not all participants of the ZEW survey responded to our questionnaire. Here, as in the following tables of this paper (except for Table 7), all variables are calculated in natural logarithmic form so that their differences represent corresponding changes: s t+6 is defined as the difference between the current Euro/US-Dollar rate (Deutsche Mark/ US-Dollar-) and their prior six month rate. s e is defined as the difference between the expected Euro/US-Dollar consensus rate (Deutsche Mark/US-Dollar-) and their subsequent actual realization. FD is defined as the forward discount of the Euro/US-Dollar (Deutsche Mark/US-Dollar), calculated upon the difference of 6 month Libor rates. All regressions are estimated with Newey-West standard-errors (see, [START_REF] Newey | A Simple Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix[END_REF]. Asterisks refer to the level of significance: *: ten per cent, **: five per cent, ***: one per cent. Regime one represents the periods, when the Euro/US-Dollar deviates ten percent or more from his fundamentally fair value based upon the relative PPP theory. Regime two therefore represents the periods, when the realized exchange rates deviate less than ten percent from PPP exchange rates.

F

]) [ 1 ( ) ( ] [ ) ( , 2 , 1 , 6 i t i i t i i e t c I f c I f s • + • = + (7) Systematic bias: ]) [ 1 ( ) ( ] [ ) ( , 2 , 1 6 , 6 i t i i t i t i e t c I f c I f s s • + • = + + (8) with ) ( ) ( ) ( 1 t t i r t t i r i r r s s s s f + + = • and 2 , 1 = r with | | t t i t s s c = and ) ( i t c I 0 1 = = i t t i t t s s if s s if < | | , | | , r i r t: 0 = i r i r t: 0 = i r i r t: 0 = i r adj.
The indicator function I(c t ) shows in which regime exchange rates are currently located. Concerning the grid search method, we restrict the search for the threshold in a range of 2.5 -25.0 per cent (with intervals of 2.5 per cent in between). Additionally we require that the number of observations in each of the regimes contains 30 per cent at minimum. Finally, the threshold is selected, if the overall residual sum of squares is minimized. Alternatively, setting wider threshold ranges results in slightly different thresholds between the separated groups; however, the outcomes do not show any qualitative changes.

Page represents the share of right direction forecasts. In brackets you find the p-values of the chi-square test statistic in correspondence to the hypothesis of no directional forecast ability (Diebold and Lopez, 1996, pp. 256-258). Differences between the forecast series were tested upon contingency tables in connection with

  results derived from our data can be generalized too. Second, biases in expectations are identified in the consensus forecasts, as professionals significantly belief too much in mean reversion, mean being represented by PPP.

6

  Our dataset contains the individual six months exchange rate forecasts of the US-Dollar/Euro (respectively the US-Dollar/Deutsche Mark) from December 1991 to April 2004 and sums up to a total of 149 surveys. To our knowledge no other study uses a panel of monthly exchange rate expectations with a dataset as long as ours. 2 Additionally we use daily US-Dollar/Euro and US-Dollar/Deutsche Mark rates from the Deutsche Bundesbank, six month Libor rates from EcoWin and price index data from the International Financial Statistics (IFS) of the International Monetary Fund (IMF).

F

  .

	Expectations formation:	e t s +	6	=	+	(	t s	t s	1	)	+	(	s	t	t s	)	(3)
	Systematic bias:	e t s +	6		t s	+	6	=	+		(	t s	t s	1	)	+		(	s	t	t s	)

  Wakita, Shigeru (1989), Are Survey Forecasts Trusted? American Trade Account Deficit and Yen/Dollar Rate, Economics Letters, 29:4, 339-344. ZEW Centre for European Economic Research (2004), Financial Market Report, 13:2. US-Dollar/Euro realizations, PPP exchange rates and consensus forecasts

		Submitted Manuscript		Page 16 of 22
			16
	0.40 0.60 0.80 1.00 1.20 1.40 FIGURE 1 0.20 1.60	o F o F o o F	Time per iod		-0.25 -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85
		r r r r US-Dollar/Euro	PPP exchange rates	Consensus forecasts	Reihe4
		P e P e P e P e
			e e e e
			r r r r
			R e R e R e R e
			v i v i v i v i
			e w e w e w e w
	Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

TABLE 1 .

 1 Statistics of consensus forecasts, forward rates and exchange rates

	o
	r
	P e
	e
	r
	R e
	v i
	e w

Note:

TABLE 2 .

 2 Descriptive statistics of the numbers of participants divided by groups

	S	e	is defined as the (consensus) forecast of the US-Dollar/ Euro, whereas s	e represents the
			percentage change forecast of the US-Dollar/ Euro.
	S	f	is defined as the implicit forecast of the US-Dollar/ Euro based upon the 6 month LIBOR rate
	S		difference and s is defined as the US-Dollar/ Euro and s f represents the corresponding change forecast in percentage. t t+6 represents the percentage change of the US-
			Dollar/ Euro from t to t+6.

TABLE 3 .

 3 Testing

								rational expectations: Unbiasedness and efficiency tests
	Test of unbiasedness:			s	t	+	6	=	+	s	e t +	6	(1)
	Test of efficiency:			+ e t s	6	t s	+	6	=	+	t FD	+	6	(2)
								t:	=	0	t:		=	0	DF	adj. R 2	F-test
													=	, 0 =	1
	s	t	+	6				0.00	0.02	0.00	-0.07	147	-0.01	19.86 ***
	+ e t s	6	t s	+	6	1.79 ***	3.73	0.02	1.35	147	0.23	-

Note:

  The extrapolative term represents the previous one month change of the Euro/US-Dollar rate. Longer periods e.g. 3 months or 6 months changes show less significant results therefore we use the one month changes. The equilibrium rate of the foreign exchange rate is based upon the relative PPP concept. Corresponding rates are calculated upon PPI differences between the Euro area and the USA. The use of CPI data could not reveal qualitatively different results. In addition to that robustness checkups show that the parameters indeed vary over time. Specifically we separated by equal time periods, up and down periods of the exchange rate as well as over-and undervaluation periods upon the PPP concept. However, in the majority of cases their signs remain equal.

												20
	TABLE 4.			Hybrid model for consensus expectations
	Expectations formation:		e t s +	6	=	+	(	t s	t s	1	)	+	(	s	t	t s	)	(3)
	Systematic bias:			e t s +	6		t s	+	6	=	+		(	t s	t s	1	)	+	(	s	t	t s	)	(4)
						t:	=	0							t:		=	0	t:	=	0	adj. R 2
	e t s 6 +				0.38 ***	3.81		0.35 ***	10.25	0.00	0.72	0.68
	+ e t s	6	t s	+	6	0.34	1.26		0.26 ***		2.96		0.01	0.56	0.16
	Note:
					o
						r
						P e
						e
							r
								R e
											v i
													e w

TABLE 5 .

 5 Hybrid model for group expectations

	Expectations formation:

21 of 22 Editorial

  Random walk forecasts are calculated on current exchange rates, respectively no change forecast. ME represents the mean error based on Euro/US-Dollar forecasts and realized exchange rates. MAE represents corresponding absolute mean error. RMSE represents corresponding root mean square error. Differences between groups and other forecast series were examined upon Theil's U represents the relation between the group specific RMSE and the RMSE of the random walk. Prob. shows the p-value for statistical significance. Hit rate

			Submitted Manuscript
				22
	TABLE 7.	Tests of accuracy and quality of performance
			ME	MAE	RMSE	Theil's U	Hit rate
	Fundamentalists	-0.0157	0.0964	0.1226	1.5367	0.6154 ***
	Intermediates	-0.0319	0.0974	0.1246	1.5613	0.5946 **
	Technicians		-0.0392 *	0.0956	0.1247	1.5681	0.5959 **
	Forward rate	-0.0006	0.0746	0.0912	1.1455	0.3289 ***
	Random Walk	-0.0010	0.0656	0.0796	-	-
	Note:
	F o
		r
			P e
			e
			r
			R e
				v i
				e w

Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

This could be connected to the panel composition, i.e. analysts being more represented than traders. We know that traders rely significantly more than others on flow analysis (see[START_REF] Gehrig | Extended Evidence on the Use of Technical Analysis in Foreign Exchange[END_REF]. The high representation of technical analysis seems very plausible, however, as it is known that fund managers -which are represented here too -heavily rely on technical investment strategies, such as momentum trading[START_REF] Menkhoff | The Use of Trading Strategies by Fund Managers: Some First Survey Evidence[END_REF].

 5 This average number of responses reflects the fact that we include only those observations in the sample where the person responding to the "use of information-question" does not change during time. Therefore, it seems almost unavoidable that the sample becomes smaller the more we go back into

history.6 Taylor (1989), among others, also uses this method to quantify categorical responses.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UKSubmitted Manuscript

Not surprisingly, running the unbiasedness test for the forward rate reveals strongly biased results as well.

To test whether expectation coefficients are statistically different between groups, t-tests are performed. Between fundamentalists and other groups all coefficients are significantly different, whereas this applies between technicians and intermediates only for the regressive term in equation (5).

The different behavior of the bias depending on the currently valid regime approves, that in conventional regressions the bias varies over time (see,Frankel and Froot, 1987a, p. 150).

Note that the origin of the individual forecasts is of qualitative nature. Derived point forecasts are only used for comparative purposes.

 11 Performance statistics separated by PPP regimes show, that the groups perform better in regime 2. Moreover, if we pull up the hit rate, their out performance to the forward rate will get even bigger.

Acknowledgement

For helpful comments we would like to thank Michael Frömmel.

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