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Probability Distributions for Economic Surplus Changes: TheCase of Technical Change in the Australian Wool Industry

Xueyan Zhao, William E. Griffiths, Garry R. Griffith and John D. Mullen

Using a specific set of market parameters in an equilibrium displacement model, Mullen,Alston and Wohlgenant (1989) (MAW) found that while Australian woolgrowers benefitedfrom new technology in the processing sector, their share of benefits was (a) not as large asfrom production technology, and (b) sensitive to the substitution elasticity between farm andprocessing inputs. These conclusions are revisited by examining the probability distributionsof changes in the welfare measures, given uncertainty about the parameters. Subjectiveprobability distributions are specified for the parameters and correlations among some of theparameters are imposed. Hierarchical distributions are also used to model diverse viewsabout the specification of the subjective distributions. Sensitivity of the estimated researchbenefits to individual parameters is examined through estimation of response surfaces andsensitivity elasticities. MAW's conclusions are found to be robust under the stochasticapproach to sensitivity analysis demonstrated in this paper.

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1. IntroductionThe returns from new technologies are typically measured by changes in economic surplusareas. The estimated price and quantity changes required for the surplus calculations are takenfrom structural econometric models if possible, but often such models are not available. Inthese circumstances, synthetic models, also called equilibrium displacement models (EDM),can be used instead (for example, Muth 1964; Freebairn, Davis and Edwards 1982; and Alston1991). The estimation of research benefits using this approach relies in part on thespecification of a set of market parameters that describe demand and supply responsiveness inthe industry. In most EDM applications, the choice of these market parameters is based onpublished econometric estimates, economic theory and the modeller’s subjective judgement,and a point estimate of the welfare change is calculated.

While there are many risk issues relating to a research project when eliciting the research-related parameters for the model (Alston, Norton and Pardey 1995, p366), the focus of thispaper is on the robustness of the estimated research benefits with respect to uncertainty aboutthe values of the market parameters. Australian farmers pay levies which can be used tofinance research into new production or processing technologies. Freebairn, Davis andEdwards (1982) demonstrated that when farm and processing inputs are used in fixedproportions, the share of benefits to producers from production and processing research wasthe same. Alston and Scobie (1983) showed that this conclusion did not hold when inputswere not used in fixed proportions and pointed out that depending on the relationship betweenthe elasticity of substitution between farm and processing inputs and the elasticity of demandfor the final product, producers may actually lose from processing research. Mullen, Alstonand Wohlgenant (1989) (MAW), taking the particular case of the world wool top market,found that, while Australian woolgrowers received benefits from processing research, theirshare of the benefits from traditional production research was much larger. While MAW didsome rudimentary sensitivity analysis, the extent to which their findings were dependent on theparticular set of market parameters they chose was not clear. Our objective of this paper is todevelop a more formal probability-based approach to sensitivity analysis and to demonstrateits usefulness by revisiting the MAW findings. Uncertainty about the parameters is quantifiedvia subjective probability distributions for the parameters. The implied probability distributionsfor the research benefits are simulated. From the distributions, levels of confidence about thepolicy-related conclusions can be calculated as various probabilities. In particular, we estimatethe likelihood that Australian woolgrowers might lose from wool processing research as wellas the probabilities for differences in benefit shares to Australian woolgrowers fromproduction and processing research. We also examine the sensitivity of benefit to individualparameter variation.

In Section 2, we outline the stochastic approach to sensitivity analysis that we promote in thispaper. In Section 3, we assign a base probability specification of subjective truncated normaldistributions, that centers at the MAW parameter values and has correlation among somemarket parameters, and report the simulated distributions for the research benefits. Becausethe base distributions represents a particular opinion on the parameter values, other individualswith other opinions may not relate to the simulated research-benefit distributions. To accountfor this, in Section 4 we specify hierarchical distributions to allow for the uncertainty inspecification of the subjective distributions on the parameters. The hierarchical specificationattempts to cover a variety of views on the most likely value for each parameter, and/or thevariation around it, by embedding a uniform distribution for the mode, and/or standard

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deviation, within the parent distribution of the parameter itself. In Section 5, we estimatequadratic response surfaces that describe the relationships between the welfare measures andthe parameters. Using these response surfaces, the sensitivity of the EDM results to variationin individual parameter values is studied by defining and calculating a sensitivity elasticity foreach welfare measure with respect to each parameter. These sensitivity elasticities indicatewhere research effort should be expended in attempting to be more certain about individualparameters. Conclusions are given in the last section.

2. A Simulation Approach to Sensitivity AnalysisA common approach to uncertainty about parameter values has been to undertake traditionalsensitivity analysis (Piggott 1992; Alston, Norton and Pardey 1995, p369). A review of thetheoretical and methodological issues in sensitivity analysis in agricultural economicsmodelling can be found in Pannell (1997). However, when a model involves more than a fewuncertain parameters, an extensive nonstochastic sensitivity analysis can becomeunmanageable. Also, a nonstochastic sensitivity analysis does not quantify the likelihood ofdeviations from what are considered to be most likely parameter values. An alternative butmore feasible and rigorous method for expressing uncertainty in the parameters is through asubjective probability distribution as is typically used in Bayesian inference. Modern Bayesianinference in econometrics is reviewed by Geweke (1997). Such a subjective distribution for theparameters can be formed from prior information (which is the approach adopted here) such aspublished econometric estimates, expert surveys or the modeller’s subjective judgement. Anyrestrictions or theoretically required correlations among parameters can also be imposedthrough the prior. Alternatively, a subjective distribution could be posterior and formed afterrevising the prior with current sample data using an econometric model.

The advantage of using a subjective probability distribution for the uncertain parameters is thatthe implied probability distribution for the welfare changes can easily be found via simulation.From that distribution, various probabilities can be calculated that represent the levels ofconfidence about the estimated research benefits and the resulting policy recommendations. Inparticular, the probability of a policy variable exceeding a break-even point, which wouldresult in a different policy recommendation, can be calculated. For example, the probabilitythat farmers share more of the total benefits from a research investment than their share ofresearch levy can be calculated. The approach can be viewed as a generalisation of that wherea single value of welfare change is calculated from a single set of parameters. When aresearcher calculates a welfare change from a single set of parameters, he or she is implicitly orexplicitly using the most likely values or expected values or medians from a subjectiveprobability distribution with zero standard deviation. Specification of the complete subjectiveprobability distribution and calculation of the corresponding probability distribution of theresulting research benefits is therefore a more general and complete approach. Tulpule, et. al.(1992) and Scobie and Jacobsen (1992) used a similar though less sophisticated approach(with triangular distributions) than that attempted here.

After completing an earlier version of this paper (Zhao et. al. 1998), we became aware of apaper by Davis and Espinoza (1998). They advocate the same general approach as we do,however, there are a number of important differences. Our application is different. Weexamine probability distributions for welfare changes among various wool industry sectors;while they look at the sensitivity of changes in farm-retail price ratios. Our results on therelative sensitivity of research benefits to individual industry sectors, with respect to

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uncertainty in individual parameter values, are of empirical significance in the applications ofEDM in research evaluations. In terms of the methodology we promote, we accommodate abroad range of prior views on parameters by using hierarchical distributions and we introducea mean sensitivity elasticity as a general measure of the importance of having more preciseinformation about a parameter.

3. A Base Specification of Parameter Distributions3.1 The MAW ModelThe MAW model of the world wool top industry was developed to examine the returns fromvarious types of research. The industry was modelled as using Australian raw wool (X1), rawwool from other competing countries (X2) and top processing inputs (X3) to produce wool top(Y). Constant returns to scale was assumed for the underlying production function. Therelationships among input and output variables were described with a set of demand andsupply conditions under equilibrium (MAW Equations (1)-(8)). Impacts of different types ofresearch were modelled as parallel demand or supply shifts using exogenous shifters: N is ademand shifter resulting from downstream textile research, and T1, T2 and T3 are supplyshifters representing the effects of cost reduction resulting from Australian farm research,other wool growing countries’ farm research and wool top processing research, respectively.When the adoption of a new technology causes a small shift in a supply or demand functionfrom the initial equilibrium, the price and quantity changes for all the input and outputvariables can be solved through the following equations (MAW equations (9)-(16)):

(1) EP = (1/η)EY + EN

(2) EP = κ1EW1 + κ2EW1 + κ3EW1

(3) EX1 = -(κ2σ12 + κ3σ13)EW1 + κ2σ12EW2 + κ3σ13EW3 + EY

(4) EX2 = κ1σ12EW1 - (κ1σ12 + κ3σ23)EW2 + κ3σ23EW3 + EY

(5) EX3 = κ1σ13EW1 + κ2σ23EW2 - (κ1σ13 + κ2σ23)EW3 + EY

(6) EW1 = (1/ε1)EX1 + ET1

(7) EW2 = (1/ε2)EX2 + ET2

(8) EW3 = (1/ε3)EX3 + ET3

where E(.)=∆(.)/(.) represents relative change of variable (.); P is the price for Y; Wi is theprice for Xi (i = 1, 2, 3); η is the own price demand elasticity for wool top; κi is the cost sharefor input Xi (i = 1, 2, 3); σij is the elasticity of input substitution between inputs i and j (i<j, i, j= 1,2,3); and εi is the own price supply elasticity for input Xi (i = 1, 2, 3). Using these priceand quantity changes, the returns from different types of research are estimated as changes ineconomic surplus using the following formulae:

(9) ∆CS = PY (EN -EP)(1+0.5EY)

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(10) ∆PS1 = W1X1 (EW1 - ET1)(1+0.5EX1)

(11) ∆PS2 = W2X2 (EW2 - ET2)(1+0.5EX2)

(12) ∆PS3 = W3X3 (EW3 - ET3)(1+0.5EX3) and

(13) ∆TS = ∆CS + ∆PS1+ ∆PS2 + ∆PS3

where ∆CS is the surplus change to consumers of wool top, ∆PS1, ∆PS2 and ∆PS3 areproducer surplus changes to the Australian wool industry, other countries’ wool industry andwool top processors, respectively, and ∆TS is the total economic surplus change.

Four research scenarios were considered in MAW’s base run: (1) a 0.5% upward shift of wooltop demand (EN = 0.005) resulting from textile research; (2) a 1% downward shift inAustralian wool supply (ET1 = -0.01) resulting from Australian farm research; (3) a 1%downward shift in supply of other inputs (ET3 = -0.01) as a result of top processing research;and (4) 1% and 0.5% downward shifts in the Australian and other countries’ wool supply (ET1

= -0.01, ET2 = -0.005), respectively, to model the situation when a new technology developedin Australia is partly adopted by its competitors. The estimated returns and the percentageshares of the total benefits to different industry groups for these scenarios, using MAW’sparameter values, are summarised in the “MAW” rows in Table 1.

3.2 Base Probability Distributions for the ParametersThere are ten market-related parameters in Equations (1)-(8). The three input shares κi (i = 1,2, 3) were calculated exactly after setting the initial price and quantity levels for the timeperiod modelled. The other seven parameters are price elasticities which MAW selected “onthe basis of the theory of derived demand and after reviewing past studies of supply anddemand conditions in the world wool industry” (p35). The values were chosen for a mediumrun situation (MAW p43). The difficulty in having to choose one value for each parametergiven the limited information available about each is obvious. A natural question is how robustthe estimated research benefits are to errors in the parameter values. MAW considered twoscenarios of limited input substitution and a shorter displacement period by varying some ofthe parameter values. This variation gave a limited picture of the sensitivity of estimatedresearch returns, but not a complete representation of the effects of parameter uncertainty.

In the following, probability distributions are assigned to the seven elasticity parameters whichspecify the possible values of each parameter and the corresponding probabilities. Assigning atype of probability distribution is subjective and hence must be arbitrary to some extent. Wechoose to use the truncated normal distribution in the base simulation. It represents asubjective view that a parameter has a higher probability of taking values around a most likelyvalue, ie. the mode, and lower possibility of taking values far away from the mode. Comparedto alternatives such as the triangular distribution or uniform distribution, the normaldistribution can cover a wide range of values without tails that are too thick.

A truncated normal distribution is a normal distribution with values of the random variablerestricted within a certain range. It is often used to impose sign or other theoretical restrictionson parameters (Griffiths 1988). For example, we may believe that the most likely value for aninput substitution elasticity, σij, is 0.1, but it could be as large as 0.5 although with a smaller

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chance. If we use a symmetric normal distribution, say N(0.1, 0.22), it allows the parameter tobe greater than 0.5 with 2.5% probability. However, it also allows the parameter to benegative with a probability of about 30%. In this case, we truncate the distribution at its lefttail by restricting the parameter to be positive. The asymmetric truncated version, N(0.1,0.22|σ ij >0), serves the purpose.

Typically, a normal distribution is specified by a mean/mode, µ, and a standard deviation (SD),σ. When we truncate it, the mean is no longer equal to µ and the SD is no longer equal to σ.However, the truncations we employ here are usually well into the tails and change thesevalues little. Consequently, for convenience we still refer to µ and σ as the mean/mode and theSD respectively.

For comparison with MAW’s results, the base distributions are set with MAW’s base runparameter values as the means. The SDs are chosen after another review of the publishedestimates combined with our judgement on the possible ranges of the parameter values. Forconvenience, in each case we choose to specify σ as a certain percentage of the mean µ. It isthen more convenient to refer to the coefficient of variation, CV, which is the ratio of the SDto the mean (ie. CV = σ/µ ). Sign restrictions and correlations among parameters are imposedwith truncated distributions and conditional distributions.

The demand elasticity for wool top was set as -1.0 by MAW. As they noted, the publishedestimates for wool demand elasticity were mostly for raw wool and at the retail level, andmany were for individual countries. However they can be used as reference points whenchoosing the range of elasticity values for wool top demand. For example, the published rawwool demand elasticities with annual data summarised in MAW (Table 1) are mostly between-0.3 and -1.6. Hill, Piggott and Griffith (1995) also reviewed some of the more recentestimates of elasticities for raw and retail wool demand for various countries. They were allinelastic. Watson (1994) discussed some different views about the wool demand elasticity andpointed out some problems with empirical estimates of this parameter. In light of thisinformation, a CV of 20% is chosen for the normal distribution. This is equivalent to assuminga 68% probability that η lies between -0.8 and -1.2, and a 95% probability for values between-0.6 and -1.4. The base probability distribution for η thus becomes:

(14) η ~ N(-1, 0.22 η <0 ).

The published estimates for the substitution elasticity for wool from different countries arebetween 0.6 and 1.68 (MAW p36), although it could be argued that wool of the same typefrom different countries should be very good substitutes. Another point to consider is that thewool inputs from the two sources in the MAW model are similar types of raw wool that aresuitable for top making. So the substitution elasticity between the two cannot be very low.Given the very limited empirical studies and very different views on this parameter, a 40% CVis assigned to MAW’s base value of 5. This gives the following distribution for the substitutionelasticity between Australian wool and wool from competing countries:

(15) σ12 ∼ N(5, 22 | σ12 > 0).

The elasticity of substitution between wool and other processing inputs was assumed to be 0.1in MAW. No empirical estimates are available for this parameter. A 50% coefficient of

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variation is assumed in the base specification which we hope will cover most of the possiblevalues of this parameter. Technical substitutability between Australian wool and processinginputs, σ13, and between wool from other countries and processing inputs, σ23, should besimilar. Even if different individuals may have very different views on the substitutabilitybetween wool input and processing inputs, the same individual would choose similar values forboth σ13 and σ23. This fact is accommodated by making the distribution for σ23 conditional onσ13:

(16) σ13 ∼ N(0.1, 0.052 | σ12 > 0) and

(17) σ23 ∼ N(σ13, 0.012 σ23 > 0).

A raw wool supply elasticity of 1.0 was used in MAW’s base run for both Australian wool andcompetitors’ wool. It was argued that it was difficult to assign different supply elasticities towool from different countries on either a priori or empirical grounds (p38-39). A CV of 0.2 isselected for the distribution of the Australian wool supply elasticity. The supply elasticity forwool from other countries is centred at the Australian elasticity and is allowed to deviate onlya small amount from it. The distributions for wool supply elasticities are:

(18) ε1 ∼ N(1, 0.22 | ε1> 0) and

(19) ε2 ∼ N(ε1, 0.052ε2 > 0).

Finally, the supply elasticity for other processing inputs was assumed to have a value of 20 inMAW given the common belief that it is almost perfectly elastic. A CV of 20% is set for thenormal distribution, which gives the following distribution for ε3:

(20) ε3 ∼ N(20, 42 | ε3> 0).

3.3 Results For the Base DistributionsWhen all the seven parameters are allowed to change according to the probability distributionsspecified above, the distributions of the resulting surplus changes can be obtained throughMonte Carlo simulation. In the simulation, 5,000 sets of parameter values are randomly andindependently sampled from the base distributions in Equations (14)-(20). For the conditionaldistribution for σ23 in Equation (17), σ23 is drawn from the Normal distribution using σ13,drawn from Equation (16), as the mean. ε2 is drawn similarly. For any one research scenario,the EDM is then run repeatedly 5,000 times with each run using a different set of parametervalues. This gives 5,000 observations for the price and quantity changes, so 5,000 estimatesfor each of the surplus changes can then be calculated using Equations (9)-(13). For each ofthe five surplus measures, probability distribution functions can be obtained. Figure 1 showsthe graphs of the probability density functions of the total surplus change and its fourcomponents resulting from Australian farm research (ET1=-0.01). Presenting the results in thisway gives an immediate visual impact of possible surplus changes and how likely they are tooccur. We observe that the welfare changes going to Australian woolgrowers will almostcertainly lie between $8m and $16m; that going to other woolgrowers will lie between -$5mand $1m; that going to top processors will lie between $0.05m and $0.25m; that going to topconsumers will lie between $7m and $16m; and the total change in welfare will lie between$21.28m and $21.33. Thus, while there is considerable uncertainty about the benefits that will

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accrue to the various industry groups, there is almost no uncertainty about the change in totalbenefits. The jagged nature of some of the distributions is typical of unsmoothed densityestimates obtained by joining the midpoints of histogram classes. This is particularly so for thetotal benefit because a large number of classes were defined over a relatively narrow interval.The procedure is repeated for each of the four research scenarios considered by MAW, but toconserve space, the figures for the other three research scenarios are not presented.

We can also calculate some summary statistics and probability intervals from the simulationdata and these are summarised in Table 1. The columns represent the four research scenariosconsidered by MAW in their Table 3, Part A (p40). The rows represent the total benefit and itsfour components for each research scenario. Within each row are reported the MAW pointestimates, and the means, SDs, CVs and 95% probability intervals (PIs) from the simulationdata. A 95% PI represents the range of values for a research benefit for which we have 95%confidence, given our beliefs on the possible parameter values specified in the priordistributions. Because it is derived from subjective prior distributions, it is different from aconventional sampling theory confidence interval. The bold figures in parentheses are thepercentage shares of the total industry benefits accruing to the different groups (calculated assummary statistics using the sets of 5,000 observations of benefit shares) .

For example, the cell for the ∆PS1 row and the ET1 = -0.01 column gives summary statisticsfor the distribution in the first segment of Figure 1. The mean of ∆PS1 from this researchscenario is $12.20m and the average share of the total benefits is 57.3%. These values are veryclose to the MAW point estimates of $12.38m and 58.1% respectively. The SD from thesimulation data is $1.39m which implies a CV for the actual benefit of 0.11. The SD alsoimplies a variation of 6.5 percentage points around the Australian woolgrowers’ share ofbenefits of 57.3%. Finally, the 95% PI is from $9.24m to $15.82m, or alternatively, we have95% confidence that Australian woolgrowers’ share of the benefits from this research scenariowill lie between 43.4% and 69.5%.

Several things can be observed from Table 1. First, the differences between the means of thedistributions of surplus changes and the corresponding MAW point estimates of surpluschanges are very small. This result is not necessarily expected because of the implicit nonlinearrelationship between the surplus measures and the parameters1.

Second, in line with Figure 1, the very small standard deviations for ∆TS show that thesimulated total surplus changes (∆TS) vary very little. This implies that, given the cost sharesfor inputs, uncertainty about the elasticities creates uncertainty about the distribution ofresearch benefits, but relatively little uncertainty about total benefits. Presumably, total benefitsare more responsive to the input cost shares, the amounts of research-induced supply/demandshifts and where the research occurs.

Third, the CVs for the surplus changes are generally less than the CVs of 20-50% in the baseparameter distributions for all four research scenarios. They are less than 20% for both

1 S(E(Θ)) ≠ E(S(Θ)) when S(Θ) is nonlinear, where S(Θ) represents the surplus measure as a function of theparameter values, E(.) is the mean of random variable (.), E(S(Θ)) is the mean of the distribution for surplusmeasure and S(E(Θ))=MAW is the surplus for the mean of the parameter Θ which equals the MAW pointestimates.

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Australian woolgrowers gains (∆PS1) and top consumers gains (∆CS) and mostly less than35% for top processors gains (∆PS3) and other woolgrowers gains (∆PS2).

Fourth, one of the major conclusions in the MAW study is that ‘on-farm’ research (ET1) givesa greater share of the total benefit to Australian woolgrowers (∆PS1/∆TS) than ‘off-farm’research (EN or ET3). Looking at the first row of Table 1, especially the probability intervalsfor benefit shares, we see that there is no overlap between the PI for ∆PS1/∆TS for the ET1

scenario with those for the EN and ET3 scenarios. So it seems that there is little chance foroff-farm research to be more beneficial than farm research for Australian woolgrowers.Probabilities such as these can be quantified by counting the proportion of times the differencein benefit shares lies within a specified interval. In this case, we find that

(21) P ( 0.25 < (∆PS1/∆TS | ET1)-(∆PS1/∆TS | EN) < 0.82 ) = 100% and

(22) P (0.03 < (∆PS1/∆TS | ET1)-(∆PS1/∆TS | ET3) < 0.47 ) = 100%

That is, Australian woolgrowers will always share more of the total benefit from Australianfarm research than they do from the two types of processing research (25% to 82% more, and3% to 47% more, respectively). In other words, given the large variation of the parametersspecified in the base distributions, MAW’s conclusion, that farm research is more beneficial forAustralian woolgrowers, is remarkably robust.

4. Hierarchical Distributions for the Parameters4.1 Hierarchical Probability SpecificationThe distributions for the estimated research benefits derived in Section 2 are based on a baseprobability specification for the parameters, which represents MAW’s view on the most likelyvalues for the parameters and our view, after considering the published empirical estimates, ontheir possible variation around the MAW values. However, other researchers may not agreewith the particular distributions we have given in the base specification. There are two ways ofresponding to this criticism. On the one hand we can argue that at least our base-distributionspecification is more general than that of MAW, who bet on one particular value for aparameter with 100% certainty. Our approach demonstrates a method of deriving a probabilitydistribution for the research benefits as long as we can quantify our uncertainty about theparameter values with subjective distributions. The procedure can be repeated using any otherindividual’s parameter specifications.

On the other hand, hierarchical distributions for the parameters can be specified to account forthe uncertainty about the specification of the subjective distributions. A hierarchicaldistribution allows for different views on both the most likely value for a parameter(mode/mean) and the possible variation around it (SD). The mode/mean and SD for adistribution are allowed to vary by being assigned their own probability distributions within theparent distribution for the parameter. The effect of more diverse views about the parameterson the uncertainty about the research benefits can thus be analysed. Ideally, a survey of expertopinions can be conducted to obtain information on the range of possible views about aparticular parameter.

In the following, a uniform distribution is assigned to the mode of the truncated normaldistribution to account for different opinions on the most likely value for a parameter. The

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range of the uniform distribution is chosen, after considering the past empirical estimates, tobe wide enough to cover most of the possible values for a parameter. Given the wide variationpermitted in the mode and also to simplify the procedure, a fixed CV of 0.1 is consideredreasonable for the truncated normal distributions. This gives the following specifications forthe seven hierarchical distributions:

(24) (a) η_

∼ U (-2.0, -0.3), (b) η∼ N(η_

, (0.1η_

)2η<0);

(25) (a) σ 12 ~ U(2, 5), (b) σ12 ∼ N(σ 12, (0.1σ 12)2σ12 > 0);

(26) (a) σ 13 ∼ U(0, 1), (b) σ13 ∼ N(σ 13, (0.1σ 13)2σ13> 0);

(27) (a) σ 23 = σ13, (b) σ23 ∼ N(σ 23, 0.012 σ23 > 0);

(28) (a) ε 1 ∼ U(0.2, 2.0), (b) ε1 ∼ N(ε 1, (0.1 ε 1)2ε1 > 0);

(29) (a) ε 2 = ε1, (b) ε2 ∼ N(ε 2, 0.052ε2 > 0);

(30) (a) ε 3 ∼ U(2, 30), (b) ε3 ∼ N(ε 3, (0.1 ε 3)2ε3 > 0).

Of particular interest is the input substitution elasticity between wool and processing inputsthat we have allowed to be between zero and one. This is a significant increase from the MAWvalue of 0.1. A more recent empirical study by Wohlgenant (1989) for various US farmproducts revealed values as big as 0.96 (Table 3, p250), which suggested that this elasticitycould be larger than previously thought. By allowing the range of zero to one, we take intoaccount the two extreme views on the value of this parameter and study the effect of theseviews on the results.

4.2 Results for the Hierarchical DistributionsGiven the wide range allowed for the parameter values and the hierarchical nature of thedistributions, a sample size of 10,000 is used for the hierarchical simulation. To obtain eachdraw of the 10,000 observations, the modes are firstly drawn from the uniform distributions inthe (a)’s of Equations (24)-(30). The SDs are calculated as 10% of the modes whereapplicable, and the parameter values are then drawn from the truncated normal distributions inthe associated (b)’s. The EDM is then solved using the chosen set of parameters and the fivesurplus measures are calculated. Repeating this process 10,000 times gives 10,000observations on each of the five surplus measures. Again, this is done for the four researchscenarios.

Graphs of the probability density functions for the five surplus measures resulting fromAustralian farm research (ET1=-0.01) based on the hierarchical parameter distributions areshown in Figure 2. The corresponding curves from Figure 1 are superimposed on Figure 2 forcomparison, and the scales on the horizontal axes are changed slightly. The impact of theadditional uncertainty specified through the hierarchical distributions is readily observed.Naturally, because we allow for a wider range of parameter values in the hierarchicalspecification, the variation of the research benefits is larger than that in the base distribution.Uncertainty about the benefits to top processors (∆PS3), Australian woolgrowers (∆PS1) and

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top consumers (∆CS) is significantly increased; for other woolgrowers' benefits (∆PS2), therange has changed very little, but the centre of the distribution has shifted noticeably to theright. Also, there is now a non zero probability that the benefits to top processors (∆PS3) willbe negative.

A summary of the simulation results (similar to that in Table 1) is given in Table 2. Thedifferences between the MAW estimates and the mean values of the welfare distributions aregreater in Table 2 than that in Table 1. This is because the hierarchical distributions are notcentred at the MAW parameter values. There continues to be relatively little uncertainty abouttotal benefits despite considerable uncertainty about how this total is distributed among itscomponents.

Let us examine again the Australian woolgrowers’ benefit share (∆PS1/∆TS) from Australianfarm research (ET1) versus processing research (EN and ET3). Looking at the first row inTable 2 and the corresponding density functions in Figure 3, there appears to be a chance forprocessing research to generate a greater share of benefits to Australian woolgrowers thanthat from farm research. Both the 95% probability intervals and the distribution densitiesoverlap. However, examining only the marginal distributions of the surplus changes, ratherthan the joint distribution, ignores correlation between the surplus changes. When we look atthe simulation data to calculate the probability, it turns out that the parameter values that givelarger values of ∆PS1(EN and ET3) also produce larger values of ∆PS1(ET1). As a result, it iscalculated that

(31) P ( 0.16 < (∆PS1/∆TS | ET1) - (∆PS1/∆TS | EN) < 0.54 ) = 100% and

(32) P ( 0.16 < (∆PS1/∆TS | ET1) - (∆PS1/∆TS | ET3) < 1.25 ) = 100%

That is, Australian woolgrowers will always receive at least 16% more of the total benefitfrom Australian farm research than they do from the two types of processing research. This isan interesting result because it may imply that even when we increase the range of the possiblevalues for the parameters, which may result in an even larger overlap of the distributions of∆PS1/∆TS(ET1) and ∆PS1/∆TS(EN or ET3) than that observed here, ∆PS1/∆TS(ET1) maynever be smaller than ∆PS1/∆TS(EN or ET3) because of common dependency on theparameter values. Further experimentation is necessary to test this suspicion.

Much of the attention in the EDM literature regarding sensitivity to parameter values has beenon the input substitution elasticity (for example, Alston & Scobie 1983; Holloway 1989;Mullen, Wohlgenant & Farris 1988). When the input substitution elasticity (σij) is allowed tobe greater than zero, the shares of the total research benefits to producers and processors willbe dependent on where the research occurs. Also, when σij is allowed to be greater than theoutput demand elasticity (η), the provider of input Xi will lose from research in the productionof Xj. Since we do allow for the possibility that the input substitution elasticity may be biggerthan the output demand elasticity in the hierarchical distribution, there is a chance that farminput suppliers (∆PS1) can lose from top processing research (ET3), and, symmetrically, thattop processors (∆PS3) can lose from farm research (ET1). Given the parameter uncertaintyspecified in the hierarchical distributions, the probability of these situations occurring can becalculated as:

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(33) P ( ∆PS1(ET3) < 0 ) = P ( ∆PS3(ET1) < 0 ) = P( |η| < σ13 ) = 15%

In other words, there is a 15% chance that Australian woolgrowers can lose from researchdollars invested in the top processing sector.

5. Response Surface and Sensitivity to Individual Parameters5.1 Response SurfaceThe simulation study defines a relationship between a particular welfare measure S and a set ofparameters Θ = (θ1, θ2, ..., θn), which can be written in general as:

(34) S = S(Θ) = f(θ1, θ2, ..., θj, ..., θn)

It is this relationship that was used to numerically estimate the probability density function forS from the joint probability density function for Θ (as shown in Figures 1 and 2). In thissection, we define a measure of the sensitivity of S to changes in a particular parameter θj.This measure depends not only on the responsiveness of S to θj but also on the likelihood ofvariations in θj (j=1, ..., n).

In general, functions like Equation (34) are often complicated and analytically unavailable. Forthe case of the MAW model, the welfare changes described in Equations (9)-(13) arequadratic functions of price and quantity changes, where the price and quantity changes arecalculated by multiplying the inverse of an 8 by 8 parameter matrix by an 8 by 4 parametermatrix, by an exogenous shifter matrix. Obviously the resulting relationship between each ofthe welfare changes and the seven market-related parameters is laborious to deriveanalytically.

Given the complicated nature of the relationship and the large number of simulatedobservations that reflect the relationship, it is reasonable to try to estimate it with its secondorder approximation, ie., a quadratic function. Such an estimated function is frequently calleda response surface in the simulation literature. The response surfaces to be estimated are

(35) Sk = α0 + i=∑

1

7

αiθi + i=∑

1

7

βiθi2 +

i ji j, =<

∑1

7

γijθiθj + ek (k = 1, ..., 5),

where Sk (k = 1, ..., 5) represent the five welfare changes, θi (i = 1, ..., 7) represent the sevenmarket-related parameters, α0, αi, βi and γij (i,j = 1, ..., 7) are coefficients to be estimated, andek (k = 1, ..., 5) are error terms. .

For each of the four research scenarios, the Equations in (35) are estimated using the 10,000observations drawn from the hierarchical distributions. Details of the estimated coefficients arenot presented but the R2’s for the regressions are listed in Table 3. They are all very highexcept for the total benefit (∆TS), which, as we have already seen, is little affected by changesin the parameter values.

5.2 Sensitivity Elasticities For Individual ParametersOne of the objectives of this study is to examine the sensitivity of the estimated researchbenefits to individual parameters. From an empirical point of view, identification of theparameters to which the results are most sensitive provides information on where effort should

13

be focused in the estimation of the parameters. In empirical applications, it is often importantto know the parameters for which careful choice of values is crucial.

Given the response functions we estimate, one way to present the responsiveness of thewelfare measures to individual parameters is to plot the welfare measure Sk in Equations (35)against changes in one individual parameter with the other six parameters fixed, say, at theMAW values. For example, Figure 4 presents the graphs of Australian woolgrowers benefit(∆PS1) from farm research (ET1) against changes in each of the individual parameters. It canbe seen that, for Australian farm research, Australian woolgrowers benefit is negatively relatedto Australian wool supply elasticity (ε1) and positively related to the other six marketparameters.

Alternatively, some kind of sensitivity index can be calculated that summarises the sensitivityof a welfare measure to individual parameters. A straightforward sensitivity index is the ratioof the percentage change of the welfare measure to the percentage change of a parameter, or,in other words, the sensitivity ‘elasticity’. We could calculate this elasticity by changing anindividual parameter by 1%, from its MAW base value, while holding the other parametersfixed at the MAW values, and calculating the percentage change of the research benefits fromthe MAW point estimate. An example of this approach is the sensitivity analysis for theABARE textile model TEXABARE (Tulpule et. al. 1992). However, there are at least threedisadvantages with this measure. First, it only measures sensitivity with respect to a singlepoint. The sensitivity could be very different for other values of Θ away from the MAWvalues. Second, it only considers a 1% change from the MAW value, while in practice, even ifthe MAW value were the true value, the possible deviation from the true value in empiricalapplications can be much larger. Third, this definition does not take into account theprobability of a particular parameter value being true. It is simply a non-stochastic one pointsensitivity analysis.

In the following, we define a sensitivity elasticity using the estimated response function andthe probability density functions of the parameters, p(Θ). This sensitivity elasticity representsthe ‘average’ sensitivity of a research benefit across all possible values of all parameters. Thevariation of the parameters is specified by the hierarchical distributions in Equations (24)-(30).The possibility of a parameter value being true is also taken into account by using theprobability distribution p(Θ) as a ‘weight’ in the average.

The sensitivity elasticity of Sk (k = 1, ..., 5) to parameter θi (i = 1, ..., 7) at any parameter pointΘ is given through partial differentiation of the quadratic response functions in Equations (35):

(36) Eki = (∂Sk/∂θi)(θi/ Sk)

= (αi + 2βiθi + jj i=≠

∑1

7

γijθj )(θi/ Sk) = gki(Θ) (k = 1, ..., 5; i = 1, ..., 7)

The sensitivity elasticity Eki is a function of all parameters Θ and is therefore different atdifferent points of Θ. When possible values of Θ and the probability of each value occurringp(Θ) are specified by the hierarchical distribution, the possible values of the sensitivity

14

elasticity Eki and the probability distribution for Eki, are defined. This distribution can beobtained from the simulation. In particular, the mean and SD for Eki are:

(37) Mean(Eki) = Θ∫ gki(Θ) p(Θ) dΘ

(38) SD(Eki) = (Θ∫ [gki(Θ) - Mean(gki(Θ))]2p(Θ) dΘ )1/2

Numerically, these quantities can be estimated using the simulation data as follows. The10,000 observations of Θ from the hierarchical distribution are used to calculate, fromEquation (36), the 10,000 observations of Eki. The sample mean and SD of Eki are theestimates for the population mean and SD in Equations (37) and (38). Results for the meansensitivity elasticities for all four research scenarios are given in Table 4. These values can beused as a guide for the sensitivity of a welfare measure to a particular parameter and thus forcomparison of the relative importance of different parameters. The signs of the meansensitivity elasticities in Table 4 provide information on the direction of the relationshipbetween each welfare measure and each parameter. Conversely, any signs that are counterintuitive may suggest possible flaws in the model.

From Table 4, a 1% increase in an individual parameter only changes the total surplus by atmost 0.002%. Thus the total benefit is insensitive to all elasticity parameters. The variation ofparameter values only affects the distribution of the total benefit among the four industrygroups. For all research scenarios, all four components of the total benefit are relativelysensitive to wool top demand (η) and Australian raw wool supply (ε1) elasticities, as predictedby theory. Increasing η will increase ∆PS1 but decrease ∆CS, while the directions of thebenefit changes for other woolgrowers (∆PS2) and top processors (∆PS3) depend on theresearch scenarios considered. An increase in ε1 will result in the benefit moving fromAustralian woolgrowers to other industry groups in all research scenarios. Only the benefit toother woolgrowers (∆PS2) is sensitive to other countries’ wool supply elasticity (ε2) for allfour research scenarios. Input substitution between wool from the two sources (σ12) onlyaffects the two raw wool providers for the case of farm research. Input substitution elasticitiesbetween farm and processing inputs (σ13 and σ23) seem to be important for other inputsuppliers. ∆PS3 shows large percentage changes for some parameters although the change inthe actual term may not be large because of the small magnitude of the benefit. In the case ofprocessing research, σ13 and σ23 also influence benefits to other groups.

Concentrating on Australian woolgrowers’ benefit (∆PS1) from various types of research, thewool top demand elasticity (η) and Australian raw wool supply elasticity (ε1) are shown to bethe most influential parameters. A 1% increase in η will result in a 0.21% to 0.54%, onaverage, increase in ∆PS1; and a 1% increase in ε1 will result in a 0.35% to 0.41% decrease in∆PS1. ∆PS1 is also shown to be sensitive to the input substitution elasticity between raw wooland processing inputs (σ13 and σ23) and the supply elasticity for processing inputs (ε3) for thescenario of top processing research (ET3).

15

6. ConclusionsUncertainty about parameter values, and hence uncertainty about model results, is a commonissue in any economic modelling exercise. This is especially so when using synthetic modelslike EDM to estimate research benefits in terms of economic surplus changes. The robustnessof estimated benefits to errors in model parameter values, and thus policy recommendationsfor research fund allocations and priorities, has often been questioned. Traditional discretesensitivity analysis becomes unmanageable when there are more than a few parametersinvolved in the model and, more importantly, says nothing about the likelihood of alternativescenarios occurring. The stochastic procedure demonstrated in this paper represents theuncertainty about model results with a probability distribution that is derived from thesubjective probability distribution that quantifies the modeller’s uncertainty about theunderlying parameter values. Various probabilities can also be calculated that represent thelevels of confidence about the model estimates and resulting policy conclusions. Although theprocedure can be repeated with different subjective distributions representing differentindividuals’ views on the possible values of the parameters, a hierarchical distribution is alsoillustrated in order to incorporate these different views on both the most likely value and thevariation around it for particular parameters. Response surfaces that describe the relationshipsof the welfare measures to the parameters are estimated. A sensitivity elasticity is defined andcalculated from the response surfaces to summarise the sensitivity of the results to individualparameters. These sensitivity elasticities provide information on which parameters should bemore precisely estimated for empirical applications of a model.

An EDM application by Mullen, Alston and Wohlgenant (1989) that evaluated the returnsfrom various research scenarios for the Australian wool industry is chosen to illustrate themore formal probability-based approach to sensitivity analysis. The robustness of their majorconclusions to a range of parameter values are tested. A base specification, that uses MAW’sparameter values as the modes and our choice of the variation around the modes, and ahierarchical specification, designed to cover most of the different views on the most likelyvalues and the spread of the parameters, are specified, and the corresponding probabilitydistributions of the total research benefit and its four components, are derived. Meansensitivity elasticities of welfare changes with respect to individual parameters, were calculatedfrom response surfaces.

A number of important results were derived. The total research benefit was shown to beextremely robust to changes in parameter values, as is consistent from intuition, but itsdistribution among different industry groups was not.

Important conclusions in MAW’s paper were that Australian woolgrowers gain a bigger shareof benefits from farm research than from processing research and that they do not lose fromprocessing research (as is possible if substitution possibilities are large relative to the responseof demand for the final product to price changes). Given the wide range of the parametervalues specified in the hierarchical distribution, we found that these results were robust. Underno set of parameter values did woolgrowers share more from processing research than fromproduction research. Further there was only a 15% probability, given the hierarchicaldistributions used here, for Australian woolgrowers to lose from top processing research.

Another result of MAW was that the distribution of research benefits is very sensitive to theinput substitution elasticity between farm inputs and processing inputs. In this study, the

16

estimated mean sensitivity elasticities for these two parameters were found to be relativelylarge for the processing research scenario, but mostly small for the farm and textile researchscenarios. Thus estimated research benefits from top processing research can involve largeerrors if the choice of input substitution parameters is not precise.

To summarise, the approach demonstrated in this paper provides a feasible procedure fordealing with uncertainty in parameters in economic models. Ideally, a more formalisedBayesian approach can be used to combine prior distributions, possibly elicited from surveysof expert opinions, and current sample information using econometric models to deriveposterior distributions for the parameters and model outputs. However, given that data forestimation of some parameters are unavailable, or costly to obtain, the procedure we havedescribed provides a rigorous framework for evaluating research benefits in the presence ofparameter uncertainty.

17

ReferencesAlston, J. M. (1991), ”Research Benefits in a Multimarket Setting: A Review”, Review ofMarketing and Agricultural Economics 59(1), 23-52.

Alston, J. M., G. W. Norton and P. G. Pardey (1995), Science Under Scarcity: Principles andPractice for Agricultural Research Evaluation and Priority Setting, Cornell University Press,Ithaca and London.

Alston, J. M. and G. M. Scobie (1983), ”Distribution of Research Gains in MultistageProduction Systems: Comment”, American Journal of Agricultural Economics 65(2), 353-56.

Davis, G. C. and M. C. Espinoza (1998), “A Unified Approach to Sensitivity Analysis inEquilibrium Displacement Models”, American Journal of Agricultural Economics,forthcoming.

Freebairn, J. W., J. S. Davis and G. W. Edwards (1982), “Distribution of Research Gains inAmerican Journal of Agricultural Economics 64(1), 39-46.

Gardner, B. L. (1975), “The Farm-Retail Price Spread in a Competitive Food Industry”American Journal of Agricultural Economics 57(3), 399-409.

Geweke, J. (1997), “Using Simulation Methods for Bayesian Econometric Models: Inference,Development and Communication”, paper presented to the Australasian Meeting of theEconometric Society, Melbourne, July 2-4.

Griffiths, W. E. (1988), “Bayesian Econometrics and How to Get Rid of Those Wrong Signs”,Review of Marketing and Agricultural Economics 56(1), 36-56.

Hill, D., R. R. Piggott and G. R. Griffith (1995), “Assessing the Impacts of Incremental WoolPromotion Expenditure: An Equilibrium Displacement Modelling Approach”, technical reportto the International Wool Secretariat, Department of Agricultural and Resource Economics,University of New England.

Holloway, G. J. (1989), “Distribution of Research Gains in Multistage Production Systems:American Journal of Agricultural Economics 71(2), 338-343.

Mullen, J. D., J. M. Alston and M. K. Wohlgenant (1989), “The Impact of Farm andProcessing Research on the Australian Wool Industry”, Australian Journal of AgriculturalEconomics 33(1), 32-47.

Muth, R.F. (1964), ”The Derived demand for a Productive Factor and the Industry SupplyOxford Economic Papers 16, 221-34.

Pannell, D. J. (1997), ”Sensitivity Analysis of Normative Economic Models: TheoreticalFramework and Practical Strategies”, Agricultural Economics 16(2), 139-52.

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Piggott, R. R. (1992), ”Some Old Truths Revisited”, Australian Journal of AgriculturalEconomics 36(2), 117-40.

Scobie, G. M. and V. Jacobsen (1992), “Allocation of R&D Funds in the Australian WoolIndustry”, Department of Economics, the University of Waikato, Hamilton, New Zealand.

Tulpule, V., B. Johnston and M. Foster (1992), TEXTABARE: A Model for Assessing theBenefits of Wool Textile Research, ABARE Research Report 92.6, AGPS, Canberra.

Watson, A.S. (1994), ”Economics and the Wool Industry”, paper presented to a conferenceorganised on the occasion of the retirement of Ross Parish, Sydney, February 18-19.

Wohlgenant, M. K. (1989), “Demand for Farm Output in a Complete System of DemandAmerican Journal of Agricultural Economics 71(2), 241-52.

Zhao, X., W.E. Griffiths, G.R. Griffith and J.D. Mullen (1998), "Probability Distributions forEconomic Surplus Changes", paper presented to the 42nd AARES Annual Conference,University of New England, Australia, 19-21 January.

19

Table 1. Summary Statistics for Research Benefits and Shares of Total Benefits Usingthe Base Distributions for Parameters (N=5,000) ($m)

EN = 0.005Textile Research

ET1 = -0.01Aust. Farm Research

ET3 = -0.01Processing Research

ET1= -.01; ET2= -.005Farm Research Adoption

∆∆PS1:Aust. Woolgrowers

MAW mean SD CV** 95% PI***

5.82 (27.3%)*5.82 (27.4%)0.94 (4.4%)0.16(3.99, 8.45)((18.7%,36.2%))

12.38 (58.1%)12.20 (57.3%)1.39 (6.5%)0.11(9.24, 15.82)((43.4%,69.5%))

2.08 (24.4%)2.076 (24.4%)0.39 (4.6%)0.19(1.30, 3.17)((15.3%,33.5%))

10.97 (39.6%)10.89 (39.3%)1.38 (5.0%) 0.13 (8.24, 14.82)((29.8%, 49.4%))

∆∆PS2:Other Woolgrowers

MAW mean SD CV 95% PI

3.49 (16.4%)3.493 (16.4%)0.57 (2.7%)0.16(2.40, 5.07)((11.3%,21.8%))

-2.80 (-13.1%)-2.62 (-12.3%)0.90 (4.2%)-0.35(-3.95, 1.73)((-18.6%,-1.9%))

1.25 (14.7%)1.246 (14.6%)0.24 (2.8%)0.19(0.78, 1.91)((9.2%, 20.1%))

1.46 (5.3%)1.56 (5.6%)0.77 (2.8%)0.49(0.13, 4.06)((0.5%,11.3%))

∆∆PS3:Top Processors

MAW mean SD CV 95% PI

0.13 (0.6%)0.130 (0.6%)0.037 (0.2%)0.28(0.08, 0.26)((0.4%,1.0%))

0.10 (0.5%)0.106 (0.5%)0.03 (0.15%)0.30(0.058, 0.22)((0.3%, 0.8%))

0.09 (1.1%)0.091 (1.1%)0.03 (0.4%)0.34(0.045, 0.20)((0.5%, 1.9%))

0.14 (0.5%)0.138 (0.5%)0.04 (0.15%)0.30(0.076, 0.29)((0.28%,0.85%))

∆∆CS:Top Consumers

MAW mean SD CV 95% PI

11.85 (55.7%)11.84 (55.6%)1.51 (7.1%)0.13(8.82, 15.89)((41.4%,69.5%))

11.63 (54.5%)11.616 (54.5%)1.51 (7.1%)0.13(8.59, 15.62)((40.3%, 74.5%))

5.09 (59.8%)5.094 (59.9%)0.63 (7.4%)0.12(3.85, 6.81)((45.2%,80.0%))

15.13 (54.6%)15.10 (54.6%)1.96 (7.1%)0.13(11.12, 20.41)((40.2%,68.4%))

∆∆TS:Total Benefit

MAW mean SD CV 95% PI

21.2821.2840.0090.0004(21.275, 21.295)

21.3121.3070.0210.001(21.289, 21.328)

8.518.5060.0190.002(8.505, 8.508)

27.6927.6840.0380.001(27.669, 27.706)

* Figures in brackets are the percentage shares of total benefits going to the various industry groups.** CV represents the coefficient of variation which is the ratio of standard deviation to mean.*** The 95% probability intervals are ranges of benefits and percentage shares (in brackets) with 95%probability.

20

Table 2. Summary Statistics for Research Benefits and Shares of the Total BenefitsUsing Hierarchical Distributions for Parameters (N=10,000) ($m)

EN = 0.005Textile Research

ET1 = -0.01Aust. Farm Research

ET3 = -0.01Processing Research

ET1= -.01; ET2= -.005Farm Research Adoption

∆∆PS1:Aust. Woolgrowers

MAW mean SD CV** 95% PI***

5.82 (27.3%)*5.81 (27.3%)2.16 (10.1%)0.37(2.02, 10.11)((9.5%, 47.5%))

12.38 (58.1%)11.36 (58.0%)2.93 (13.8%)0.24(7.43, 18.17)((34.9%, 85.4%))

2.08 (24.4%)1.17 (13.8%)1.15 (13.6%)0.98(-1.13, 3.41)((-13.3%, 40.1%))

10.97 (39.6%)11.41 (41.2%)3.23 (11.7%)0.28(5.86, 17.84))((21.2%, 64.5%))

∆∆PS2:Other Woolgrowers

MAW mean SD CV 95% PI

3.49 (16.4%)3.48 (16.4%)1.30 (6.1%)0.37(1.21, 6.06)((5.7%, 28.5%))

-2.80 (-13.1%)-1.90 (-8.9%)0.95 (4.5%)-0.50(-3.85, -0.33)((-18.1%, -1.5%))

1.25 (14.7%)0.70 (8.3%)0.69 (8.1%)0.98(-0.68, 2.04)((-8.0%, 24.0%))

1.46 (5.3%)2.18 (7.9%)1.46 (5.3%)0.67(-0.52, 4.96)((-1.9%, 17.9%))

∆∆PS3:Top Processors

MAW mean SD CV 95% PI

0.13 (0.6%)0.30 (1.4%)0.26 (1.2%)0.88(0.006, 1.07)((0.3%, 5.1%))

0.10 (0.5%)0.11 (0.5%)0.16 (0.8%)1.51(-0.009, 0.55)((-0.4%, 2.6%))

0.09 (1.1%)0.43 (5.0%)0.40 (4.7%)0.94(0.006, 1.63)((0.6%, 19.2%))

0.14 (0.5%)0.14 (0.5%)0.21 (0.8%)1.51(-0.12, 0.72)((-0.4%, 2.6%))

∆∆CS:Top Consumers

MAW mean SD CV 95% PI

11.85 (55.7%)11.69 (54.9%)3.49 (16.4%)0.30(4.84, 17.87)((22.7%,84.0%))

11.63 (54.5%)10.73 (50.4%)3.59 (16.8%)0.33(3.66, 17.04)((17.2%, 80.0%))

5.09 (59.8%)6.20 (72.9%)1.80 (21.1%)0.29(2.86, 9.90)((33.6%,116.3%))

15.13 (54.6%)13.96 (50.4%)4.66 (16.8%)0.33(4.79, 22.17)((17.3%, 80.1%))

∆∆TS:Total Benefit

MAW mean SD CV 95% PI

21.2821.2840.0140.0006(21.27, 21.31)

21.3121.300.0220.001(21.27, 21.34)

8.518.5080.0130.002(8.504, 8.510)

27.6927.6860.0260.001(27.65, 27.73)

* Figures in brackets are the percentage shares of total benefits going to the various industry groups.** CV represents the coefficient of variation which is the ratio of standard deviation to mean.*** The 95% probability intervals are ranges of benefits and percentage shares (in brackets) with 95%probability.

21

Table 3. R2 For Response Surfaces∆∆PS1:Aust. woolgrowers

∆∆PS2:Other woolgrowers

∆∆PS3:Top Processors

∆∆CS:Top Consumers

∆∆TS:Total benefit

EN=1%:Textile Research 0.99 0.99 0.88 0.99 0.71ET1=-1%:Aus.FarmResearch 0.99 0.99 0.84 0.99 0.56ET3=-1%:ProcessingResearch 0.98 0.98 0.89 0.98 0.045ET1=-1%;ET2=-0.5%:Farm ResearchAdoption

0.99 0.99 0.85 0.99 0.67

Table 4. Mean Sensitivity Elasticities of Various Research Benefits To IndividualParameters Resulting From Various Research Scenarios. (N=10,000)

ηη σσ12 σσ13 σσ23 εε1 εε2 εε3EN=1%:Textile Res. ∆∆PS1

∆∆PS2

∆∆PS3

∆∆CS ∆∆TS

0.530.530.66-0.440.7E-3

-0.004-0.0040.0280.0010.8E-5

-0.04-0.014-0.560.019-0.1E-3

-0.006-0.0320.910.0210.2E-3

-0.41-0.150.240.230.3E-3

-0.066-0.33-0.0950.130.2E-3

0.0020.002-0.270.0110.2E-4

ET1=-1%:Aus.Farm Res. ∆∆PS1

∆∆PS2

∆∆PS3

∆∆CS ∆∆TS

0.21-1.141.66-0.440.7E-3

0.121.060.130.0020.5E-3

0.037-0.052-3.13-0.043-0.1E-3

-0.001-0.0411.26-0.0060.2E-3

-0.410.481.330.560.8E-3

0.047-0.36-0.45-0.100.2E-3

0.002-0.0150.360.003-0.2E-4

ET3=-1%:Proces. Res. ∆∆PS1

∆∆PS2

∆∆PS3

∆∆CS ∆∆TS

0.541.910.95-0.430.2E-3

0.009-0.0160.21-0.0010.2E-4

0.19-0.97-0.220.140.2E-2

-0.097-0.861.950.097-0.2E-2

-0.35-0.15-1.260.110.7E-4

0.015-0.471.650.0480.6E-4

0.130.034-0.420.027-0.6E-4

ET1=-1% andET2=-0.5%:Farm Res.Adoption ∆∆PS1

∆∆PS2

∆∆PS3

∆∆CS ∆∆TS

0.303.30-2.03-0.440.9E-3

0.068-1.420.0030.0020.7E-4

0.0480.23-0.10-0.0390.4E-3

0.00050.0900.23-0.010-0.4E-3

-0.41-1.541.310.390.8E-3

-0.003-0.41-0.110.0650.5E-4

0.002-0.0641.660.003-0.1E-5

22

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