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Food safety regulations are evolving to more performance-based regimes in ... ability of industry-level compliance and therefore the resultant level of food safety.

Selection of Food Safety Standards

Bo-Hyun Cho Centers for Disease Control and Prevention

Neal H. Hooker The Ohio State University

Selected Paper prepared for presentation at the American Agricultural Economics Association Annual Meeting, Long Beach, California, July 23–26, 2006

Copyright 2006 by Bo-Hyun Cho and Neal H. Hooker. All rights reserved. Readers may make verbatim copies of theis document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies. This paper is a part of Bo-Hyun Cho’s dissertation in his private capacity. No official support or endorsement by the Centers for Disease Control and Prevention, Department of Human and Health Services is intended nor should be inferred.

Abstract Food safety regulations are evolving to more performance-based regimes in which firms have greater flexibility and responsibility for adopting effective controls. Within this context, this paper compares performance and process standards modeling the variability of industry-level compliance and therefore the resultant level of food safety. Monte Carlo simulations are conducted manipulating five factors: the variances of input use of efficient and inefficient firms, the proportion of inefficient firms in the industry, the mean of the error term for inefficient firms, and the policymakers’ level of risk aversion. Results suggest that process standards may be preferred over performance standards when inefficient firms prevail in the industry, when input use is highly variable and when the regulator pays less attention to the variability of industry-level compliance and more to the level of the standard. Keywords: Performance Standards, Process Standards, Food Safety, Monte Carlo Simulation JEL Classification: Q180 Agricultural Policy & Food Policy

Introduction The design of socially optimal food safety standards has received increased attention in recent years. Food safety regulatory standards take three forms according to Antle (2000)1 ; process (design), performance and combined standards. Performance standards can be described as controls that regulate the upper limit (or maximum tolerance level) of risk in food. Process standards require the firm to use at least a minimal amount of a risk control input. In practice, most food safety regulations do not neatly fall into one single category. Rather, regulations combine elements of both process and performance standards as discussed in Unnevehr and Jensen (1996). In this paper, we focus on two aspects of regulatory standards - control through inputs or outputs. As one option a food safety regulation may apply a performance standard requiring all food (output) to at least meet the required criterion2 . Conversely, a process standard can be the basis of a regulation with a requirement that firms use, at least, a particular level of a certain risk control input such as a sterilizer, washing fluid, hot water or irradiation equipment. Comparing these standards, 1

Standards can also be defined based on the degree of intervention. For example, Henson and

Heasman (1998) distinguish target, performance and specification standards. Target standards impose liability for prespecified harmful consequences caused by products while no specific prescription of the product is made. Performance standards dictate the safety level for the product while allowing the firm to choose the method of production. Specification standards require either the product or its’ production process or both meet a predefined goal. 2

An extreme example is the use of zero-tolerance standards for pathogens such as Listeria mono-

cytogens (Institute of Medicine, National Research Council, 2003)

1

economists seem confident of the superiority of performance standards in terms of cost minimization (Antle, 1996), simply because performance standards allow for a flexible adjustment to the firm’s unique production environment leading to lower distortions in the economy 3 . From the perspective of social welfare optimization, the argument is valid if benefits under two alternative standards are the same. This paper examines if the two different standards provide the same level of benefit from the viewpoint of food safety risk reduction.

Motivation The model and motivation are an effort to characterize a regulator’s comparison of these standards. Most of the existing literature has focused on incentives for compliance by firms. Naturally, the standard with the lower compliance cost is preferred. However, the regulator here is assumed to be more interested in the public health impact of standards. That is, unable to observe the actual compliance behavior of firms (e.g., managerial intensity or effort), the regulator needs to select a standard which minimizes the probability of foodborne illness outbreaks and sporadic events. Thus, the regulator is assumed to act like an investor balancing a portfolio, choosing a standard less likely to result in deviation by firms in the relevant industry. The approach applied here to compare the effectiveness of standards is therefore borrowed from the field of financial economics: a safety-first rule. This is relevant as food 3

See Marino (1998).

2

safety policy has a goal of not only minimizing the level of risk (standard) but also the deviation around the standard given the stochastic nature of most food safety attributes4 . Among other risk measures used in the area of financial economics, the safetyfirst rule is simple and conservative, though old. As a key advantage, the measure is distribution-free, providing an upper-bound of the probability of violation of the standard. A process standard is assumed different from a performance standard in the sense that the former requires a minimum level of input use directly affecting the reduction of food risk. Contrast this to a performance standard which regulates output quality. Therefore, a “truncated” distribution of input use supports the process standard. It is obvious, therefore, that a process standard results in a lower (or no greater) level of food safety risk. However, to compare the degree of public health protection, higher moments of the resultant food safety distribution must be assessed, which quickly becomes intractable for even the most straightforward of standards. Hence, simulation results are provided here to illustrate potential factors which may influence the optional standard design.

Previous Research Besanko (1987) showed that in an oligopolistic market the economic impact of dif4

During food production, manufacturing, distribution and preparation, microbial pathogens may

be introduced, reduced or redistributed through cross-contamination while chemical and physical hazards may be introduced or eliminated in a different manner.

3

ferent standards depends on demand and cost functions. Marino (1998) presented evidence that process standards are preferred to performance standards if an asymmetric information environment exists between the firm and the regulator. Recently, Hueth and Melkonyan (2003) argued that process standards are different to design standards in the presence of mandatory monitoring and asymmetric information. Their approach compares expected social surplus under each standard to determine the most efficient form. The model presented here is different, providing a focus on possible stochastic deviations from the targeted level of food safety risk. When regulators evaluate or compare policies, the expected level of risk and variance of risk control should be carefully considered. This situation is analogous to choosing a portfolio of risky assets in financial economics. Various methods such as the safety-first rule, mean-variance, stochastic dominance and other expected utility models can be applied, as described below.

Models The Setting Assume that there are a finite number of firms producing food (N ). Accordingly, N types of firms (θ) are realized when drawn from a random variable Θ. The regulator cannot tell which firm is of which type, but is assumed to know the distribution of the random variable Θ. Assume that the targeted level of food safety risk s∗ is

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given exogenously based on a science-based food safety risk assessment. Following Lichtenberg and Zilberman (1988), the regulator is assumed to select a standard which minimizes social cost while limiting the probability of violation of the food safety target (s∗ ). Formally, mini SCi

(1)

subject to prob(si ≤ s∗ ) ≤ 1 − p where i ∈ {process, performance}, SCi refers to the resultant social cost under a regulatory standard i, and si refers to the observed level of food safety. The optimization problem in equation (1) suggests which food safety standard minimizes social cost given a certain level of food safety risk (or acceptable level of protection). A simple cost-effectiveness analysis applies such a selection rule when comparing alternatives. However, it is more common to see regulatory agencies being provided a budget to implement a range of control policies. This is like the dual of the optimization problem: which standard minimizes the probability of violation given a budget constraint? Furthermore, if the ex-post loss resulting from foodborne illness is included within a more complete cost-benefit framework, the regulator is encouraged to select the policy with the lowest possibility of safety deviations. Such an approach allows for deviations from the target, which may result in a food safety recall or life-threatening outcomes such as foodborne illness outbreaks. The standard selection problem becomes a broader comparison of risk, specifically, the probability of violation under each standard. 5

Assumptions Two types of players - the regulator and firms - are assumed throughout this paper. Firms have multioutput technologies producing food and food safety risk jointly. Cost minimization determines their optimal input level based on the targeted safety level (s∗ ) set by the regulator. Assumption A1 (Cost Minimization). The firm minimizes its cost constrained by a production technology g(z|θ). Formally, min wz + λ(s∗ − g(z| θ)) z

(2)

Input demand z ∗ is a function of input prices w, s∗ and the firm type θ, z ∗ = z(w, s∗ | θ). The optimal value function, a cost function, depends on input prices, the targeted safety level and the type of firm, C ∗ = w · z ∗ = C(w, s∗ | θ). Asymmetric information about the firm’s technology is also assumed: the regulator does not know which firm has the greater ability to apply a certain food safety technology but does know the technology adopted. The food safety technology is represented as a risk control function. Assumption A2 (Risk Control Function). Food safety technology can be represented as the following risk control function, gs . s = gs (z| θ)

(3)

where s is the resultant level of safety produced by the firm, z refers to risk control inputs and θ is an index of the type of firm, determining the efficiency of risk control 6

achieved by a particular technology. The risk control function gs is non-decreasing in input level z and type θ,

∂gs ∂z

> 0, and

∂gs ∂θ

> 0, respectively.

Firms are assumed to have different marginal products for their risk control inputs. This assumption allows heterogeneity in firms technology. Efficient firms are assumed to have higher marginal productivities of risk control input than inefficient firms 5 . Assumption A3 (Efficient Food Safety Technology). For θ0 > θ1 , ∂gs ¯¯ ∂gs ¯¯ ¯ ∗ > ¯ ∂z z=z , θ0 ∂z z=z∗ , θ1

(4)

.

Risk Measures As introduced above, this study compares the resultant levels and distributions of food safety risk for process and performance standards. The financial decision-making literature provides a large range of risk measures6 . In quantitative studies, due to limited knowledge of the true distribution, risk is often measured using moments such as mean, variance, or a combination of both 7 . Among other factors, it is 5

Such heterogeneity can arise through differences in managerial efficacy or optimization error.

6

It is important to distinguish two concepts of risk: food safety risk and risk as a quantitative

measure. Food safety risk arises from the presence of hazards in food. In this paper the probability of observing foodborne illness is modelled as a measure of risk. 7

For example, Domar and Musgrave (1944) formulate a quantitative measure of risk taking into

account all possible negative or relatively low probability outcomes. A dispersion parameter such as variance or standard deviation is used as a risk index. A semi-variance measure uses a similar

7

important to measure risk resulting from the two different standards in a conservative sense. Thus, Roy’s Safety First rule is used to provide one method to compare probability. Roy (1952) suggests such a “safety first” rule for regulators trying to avoid a “disaster.” His risk measure is represented in terms of the probability that the outcome will be lower than a constant s∗ , the acceptable level of risk determined by the policymaker. However, given limited knowledge of the distribution, in particular the mean (E(S)) and variance (σS2 ) of outcomes, it is useful to elaborate on this measure using Chebychev’s inequality to represent the probability of a “bad” event8 . An advantage of the safety first rule is that it provides an upper bound probability of violation of the targeted food safety level. Therefore, using the safety first rule the different distributions of food safety risk can be compared. More interestingly, the risk measure allows for the interpretation of consequences of differences between the two standards in terms of the probability of violation.

prob(S ≤ s∗ ) ≤ 2 σS (E(S)−s∗ )2

σS2 (E(S) − s∗ )2

(5)

is the upper bound of the probability of a disaster which can be used

to select the least risky standard. The greater the upper bound, the riskier the standard. Intuitively, assuming the same mean values of two different distributions, formula replacing the mean with a constant in order to consider only negative deviations from the constant (Levy, 1998). 8

This inequality is useful as it provides a universal bound for probability regardless of the distri-

bution of the random variable (Casella and Berger, 1990).

8

the distribution with the larger variance will be riskier. For distributions with the same variance, a larger mean value suggests a less likely disastrous outcome. Recall that the optimal risk control input demand z ∗ (θ) depends on the type of firm which is uncertain to the regulator. Suppose that the probability density function of z, fZ (z) is also unknown to the regulator. For simplicity, assume that the risk control function is a monotonic transformation of the random variable, Z. Then: Z

z∗



pr(z ≤ z ) =

fZ (x)dx Z

(6)

0 g −1 (s∗ )



pr(s ≤ s ) =

fZ (g −1 (y))

0

d −1 g (y)dy dy

(7)

Equations (6) and (7) show the probabilities that input use or the resultant safety level respectively are lower than the predetermined targeted levels in terms of the density function. Without knowing fZ (z) it is impossible to assess which standard is riskier. In order to compare the upper bound of each standard, the expected value and variance of the safety level under each regime must be calculated. Conceptually, these measures can be calculated as follows. First, under the performance standard, 2 the expected value (Epf (S)) and variance (σpf ) are derived as follows.

Z



Epf (S) = Z 2 σpf

0

=



g(x)fZ (x)dx

(8)

(g(x) − Eg(Z))2 fZ (x)dx

(9)

0

Since there is no restriction on input usage, the expected value and variance of the safety level are calculated on the domain of Z. However, under a process standard, because of the minimum input use require9

ment, the safety level is derived on [z ∗ , ∞]. Thus, the expected value (Epc (S)) and 2 variance (σpc ) are defined as follows.

Z



Epc (S) = 2 σpc =

∗ Zz ∞

g(x)fZ (x)dx

(10)

(g(x) − Eg(Z))2 fZ (x)dx

(11)

z∗

Note that since g(z) is assumed to be a non-stochastic, monotonic transformation the process standard is equivalent to the case of a combined standard. The comparison of expected values and variances depends upon the parameter (z ∗ ) and the distribution (fZ (z)). To highlight the role of these factors a Monte Carlo simulation is presented below.

Monte Carlo Simulations Procedures As assumed above firm type θk is exogenous, known to the firm but not perfectly known to the regulator. The regulator is assumed to observe, imperfectly, the level of risk-control input demands or final food safety level. For the purpose of the Monte Carlo simulation a linear error term is assumed for the input demand function : z ∗ (θk ) = z ∗ + θk for k = 1, 2, ... , N . Suppose that N firms are partitioned into two groups: n1 inefficient firms and (N − n1 ) efficient firms. Accordingly, the distribution of θi is assumed to differ for two different groups; θi for (N − n1 ) efficient firms and θ˜j for n1 inefficient firms. For simplicity, the risk control function is assumed to be 10

gs (z) = log10 (z). The expected value of θ˜j is assumed to be larger for inefficient firms9 . Finally, the resultant level and dispersion of food safety is calculated by inserting z, drawn from the simulated distribution, into gs (z). With these assumptions, sample means and variances of the safety level under a performance standard can be calculated using the following equations based on N randomly drawn input levels zθ∗k .

d Epf (S) = 2 σc pf =

N 1 X gs (zk ) N k=1

(12)

N

X 1 d (gs (zk ) − Epf (S))2 (N − 1) k=1

(13)

By the same token, the mean and variance of the safety level under a process standard can be calculated using N randomly drawn input levels z tr using a truncated distribution at the critical value, z ∗ . An acceptance-rejection method is applied 9

10

.

The marginal product of the risk control function is 1/z so, by assumption 3, z ∗ (θi ) = z ∗ + θi >

z ∗ + θ˜j = z ∗ (θ˜j ). Therefore, θi > θ˜j . To reflect this result, a larger mean for θi is assumed. 10

This method is used when the functional form of a distribution is difficult or time consuming

to generate random numbers. Assuming a “source” distribution considered close to the true distribution, draw a number from the source distribution then compare how close it is to the true distribution. If considered close enough, accept the draw. Otherwise, repeat the same procedure. For a detailed algorithm, refer to Martinez and Martinez (2001).

11

Ed pc (S) = 2 σc pc =

N 1 X gs (zktr ) N k=1

(14)

N

X 1 2 (gs (zktr ) − Ed pc (S)) (N − 1) k=1

(15)

The experiments were designed to vary five parameters: the mean value of the error term for inefficient firms, the variances of distributions of θi and θ˜j (for efficient and inefficient firms respectively), the proportion of inefficient firms in the industry (ratio =

n1 N

× 100) and a risk-aversion parameter for the policymaker (h). The first

four parameters are related to characteristics of the industry of which the regulator has a limited knowledge. The risk-aversion parameter represents the regulator’s attitude toward risk from foodborne illness. The distributions of θ and θ˜ represent stochastic variations of risk control input use by firms. The mean value of the error term for inefficient firms is set to be 110, 150 and 190 percent of the mean value of the distribution for efficient firms, 100. The variances of the distributions represent the dispersion of risk-control inputs used by the firms. The proportion of inefficient firms in the industry reflects how many firms are inefficient in controlling food safety risk, which can be determined through facility inspection or monitoring. The parameter h captures the level of risk-aversion of the regulator. Baumol’s risk measure (µ − h · σ) incorporates not only the mean value of the resultant safety level but also its variability (Baumol, 1963). For larger h, Baumol’s risk measure decreases, which penalizes deviations from the mean value. 12

When determining the targeted food safety level, a lower level of h suggests stricter food safety control. The variance of distributions of θ and θ˜ is varied between 10 and 100 in units of 10. The proportion of inefficient firms in the industry ranges over 10 %, 30 %, 50 %, 70 %, to 90 %. The targeted safety level is assumed to be determined by µpf − h · σpf where, for this experiment, three different values of h are evaluated: 1, 3, and 5

11

.

Based on these simulations, Roy’s risk measures are calculated for each standard. This experiment is repeated 10,000 times using the Statistics Toolbox 4.0 installed in MATLAB.

Results Not surprisingly, resultant levels and dispersions of food safety risk are influenced by all five parameters. Two presentations of the comparative risk measures under each of the standards are provided - three-dimensional figures and a table, with illustrative examples of parameter values. First, the surfaces of Roy’s risk measures with varying mean values of risk-control input use by inefficient firms are reported in Figures 1, 2, and 3. In each Figure, the X-axis presents the variance of distribution of θ˜ for inefficient firms while the variance of distribution of θ assigned to efficient firms are represented on the Y11

A value of h=0 implies that the regulator is risk neutral. In this experiment, the targeted level

is equal to the mean of resultant food safety level under a performance standard. Consequently, the denominator of Roy’s risk measure becomes zero.

13

axis. Both axes range from 10 to 100. The Z-axis plots the Roy’s risk measures for each standard. Thus, the surfaces represent differing risk measures corresponding to changing variances. For the purpose of illustration 10, 50 and 90 % proportions of inefficient firms in the industry are presented here. Note that under a performance standard Roy’s risk measure simply becomes

1 12 . h2

Therefore, the surface becomes a

flat plane under a performance standard providing an easy comparison for the factors which affect the relative risk measure under a process standard. A review of the various Figures reveals some notable patterns. First, as the mean of the distribution of risk-control input use by inefficient firms increases, Roy’s risk measure under a process standard decreases. That is, when inefficient firms prevail, a process standard may prove to be more effective by controlling the minimum use of risk-control inputs. Therefore, when the regulator believes that the industry has a considerable proportion of inefficient firms, optimal risk control occurs through a process standard. However, it is also notable that there are two cases when a performance standard is preferable to a process standard (Table 1). Second, as the proportion of inefficient firms in the industry increases, so Roy’s risk measure under a process standard also increases. Thus, compared to the results under a performance standard, an increased proportion of inefficient firms may be more likely to harm the safety reputation of the industry. Regarding the role of variances, when the propor12

Recall that Roy’s risk measure is

2 σS (E(S)−s∗ )2 .

standard.

14

Substituting s∗ yields

1 h2

under a performance

tion of inefficient firms is relatively low, as the variance of input use by inefficient firms increases, so the risk measure under a process standard increases for any given variance of input use by efficient firms. In contrast, the process standard risk measure decreases as the variance of input use by efficient firms increases for a given variance of input use by inefficient firms. However, as the proportion of inefficient firms and the variance of input use by inefficient firms increases, the process standard risk measure decreases. The result that a larger variance associated with inefficient firm’s input use influences the risk measure relatively less occurs because under a process standard input use is clearly regulated. Therefore, even with a higher variance the possibility of inefficient firms controlled by a process standard using a lower level of the risk control input is greatly restricted. Yet, even a relatively low variance and control through a process standard may be associated with higher overall risk for food products if the industry is dominated by inefficient firms. When a higher h is imposed, the risk measures under a process standard become closer to those under a performance standard. For example, when h=2, the risk measure under a process standard exceeds those under a performance standard in some cases such as those with a small proportion of inefficient firms when the variance of inefficient firm’s input use is large and the variance of efficient firm’s input use is small. The results suggest that a performance standard can provide a riskier situation compared to a process standard with the same targeted safety level (s∗ ) under specific conditions.

15

Summary and Discussion In comparing standards, performance standards are most often preferred due to their lower compliance costs. Yet such a comparison implicitly assumes that all standards result in the same level of compliance or benefit. However, this paper compares the effectiveness of risk reduction achieved by process and performance standards from the viewpoint of a regulator with a limited administrative budget. Consequently, unlike previous research such as Hueth and Melkonyan (2003), the approach presented here characterizes stochastic deviations from a targeted level of safety. In addition, this evaluation of standards focuses on the relationship between the regulator and an industry consisting of many different types of firms while most other papers model the compliance decision of an individual firm. By permitting such heterogeneity in food safety technology or its management, one firm’s efforts towards compliance may not mirror another firm’s experiences. From the viewpoint of a regulator concerned with industry-level compliance and performance, incorporating the probability of deviation from the standard is an important dimension of policy design and one which appears to have received little attention. This paper is designed to explore such circumstances. The results differ to the previously held belief that a performance standard is always superior to a process standard. As an additional tool to traditional economic benefitcost analyses for policy evaluation, such a statistical simulation can help to highlight the circumstances under which one standard may be preferred in terms of the average resultant industry-level safety. The simulation presented here is designed to vary in 16

five factors: the variances of input use, the proportion of inefficient firms in the industry, the mean of the error term for inefficient firms, and the degree of risk aversion of the regulators. The prescription of a socially optimal food safety standard based on this Monte Carlo experiment is that process standards may be preferred over performance standards when inefficient firms prevail in the industry, when input use is highly variable and when the regulator pays less attention to the variability of industry-level compliance and more to the level of the standard.

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Table 1: Summary of Preferred Standard based on Roy Risk Measure The mean of the Risk Control Input Use by Inefficient Firms = 110 Proportion of Inefficient Firms 10 %

50 %

90 %

h=1

Pc

Pc

Pc

h=2

Pc

Pc

Pc

h=3

Pc

Pc

Pc

The mean of the Risk Control Input Use by Inefficient Firms = 150 10 %

50 %

90 %

h=1

Pc

Pc

Pc

h=2

Pc

Pc

Pc

h=3

Pc

Pc

Pf

The mean of the Risk Control Input Use by Inefficient Firms = 190 10 %

50 %

90 %

h=1

Pc

Pc

Pc

h=2

Pc

Pc

Pc

h=3

Pc

Pc

Pf

Note: Pc suggests a process standard has a lower risk measure Pf a performance standard is optimal.

18

Figure 1: Roy’s Risk Measures under Performance and Process standard when the

mean value of risk-control input used by inefficient firms is 110% of the mean value 60

j

2

σz

40 20 0 0

20

i

2

σz

40

60

80

100

0.2

0.1

80 60

j

z

σ2

40 20 0 0

20

i

2

σz

40

60

80

0 100

0.01

0.02

0.03

0.04

0.05

80 60

z

j

σ2

40 20 0 0

20

100

j

0.1

40 20 0 0

20

i

2

σz

40

60

80

80 60

j

σ2z

40 20 0 0

20

i

σ2z

40

60

80

80 60

z

j

0 100

0.01

0.02

0.03

0.04

0.05

40 20 0

0

20

i

2

σz

40

60

80

100

100

Roy’s Risk Measures with 50% of inefficient firms (h=5)

0 100

0.05

σ2

100

z

σ2

i

80

60

σ2 z

40

60

Performance Standard Process Standard

Roy’s Risk Measures with 10% of inefficient firm (h=5)

0 100

0.05

0.15

0.2

0.3 0.25

0.15

80

100

Roy’s Risk Measures with 50% of inefficient firms (h=3)

0.3

Performance Standard Process Standard

Roy’s Risk Measures with 10% of inefficient firm (h=3)

80

0 100

0.2

0.4

0.6

0.8

1

1.2

Roy’s Risk Measures with 50% of inefficient firms (h=1)

0.25

0 100

0.2

0.4

0.6

0.8

1

1.2

Performance Standard Process Standard

Roy’s Risk Measures with 10% of inefficient firm (h=1)

Roy Risk Measures

Roy Risk Measures

Roy Risk Measures

Roy Risk Measures Roy Risk Measures

Roy Risk Measures

Roy Risk Measures Roy Risk Measures

19 Roy Risk Measures

of efficient firms 80 60

j

2

σz

40 20 0 0

20

i

σ2z

40

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100

80 60

j

2

σz

40 20 0

0

20

i

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σ2

40

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0.01

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80 60

j

2 z

σ

40 20 0

0

20

i

2

σz

40

60

80

100

Roy’s Risk Measures with 90% of inefficient firms (h=5)

0 100

0.05

0.1

0.15

0.2

0.25

0.3

100

Roy’s Risk Measures with 90% of inefficient firms (h=3)

0 100

0.2

0.4

0.6

0.8

1

1.2

Roy’s Risk Measures with 90% of inefficient firms (h=1)

Figure 2: Roy’s Risk Measures under Performance and Process standard when the

mean value of risk-control input used by inefficient firms is 150% of the mean value 60

2

σz

40 20 0 0

20

40

60

80

100

i

2

σz j

z

σ2

40 20 0 0

20

i

z

σ2

40

60

80

100

0.2

60

2

σz

40 20 0 0

20

40

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σz

0 100

0.02

0.04

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0.08

0.1

80 60

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σz

40 20 0 0

20

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2

σz

40

60

80

Performance Standard Process Standard

100

Roy’s Risk Measures with 10% of inefficient firm (h=5)

j

80 60

z

σ2

40 20 0 0

20

40

60

80

j

z

i

σ2

0 100

0.02

0.04

0.06

0.08

0.1

80 60

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2

σz

40 20 0

0

20

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σz

40

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100

Roy’s Risk Measures with 50% of inefficient firms (h=5)

0 100 80

0 100

0.1 0.05

0.05

0.1

0.15

0.2

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60

j

z

σ2

40 20 0 0

20 z

i

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40

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80 60

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σ2

40 20 0

0

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σz

40 20 0

0

20

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2 z

σ

40

60

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Roy’s Risk Measures with 90% of inefficient firms (h=5)

0 100

0.05

0.1

0.15

0.2

0.3 0.25

0.3 0.25

0.15

80

100

Roy’s Risk Measures with 90% of inefficient firms (h=3)

0.25

100

60

Roy’s Risk Measures with 50% of inefficient firms (h=3)

80

0 100

0.2

0.4

0.6

0.8

1

1.2

Roy’s Risk Measures with 90% of Inefficient Firms (h=1)

0.3

Performance Standard Process Standard

Roy’s Risk Measures with 10% of Inefficient Firm (h=3)

j

0 100

0 100 80

0.2

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0.6

0.8

1

1.2

Roy’s Risk Measures with 50% of Inefficient Firms (h=1)

0.2

0.4

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0.8

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Performance Standard Process Standard

Roy’s Risk Measures with 10% of Inefficient Firm (h=1)

Roy Risk Measures

Roy Risk Measures

Roy Risk Measures

Roy Risk Measures Roy Risk Measures

Roy Risk Measures

Roy Risk Measures Roy Risk Measures

20 Roy Risk Measures

of efficient firms

Figure 3: Roy’s Risk Measures under Performance and Process standard when the

mean value of risk-control input used by inefficient firms is 190% of the mean value 60

2

σz

40 20 0 0

20

40

60

80

100

z

i

σ2

0.2

60

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σ2

40 20 0 0

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z

σ2

z

σ2

20 0 0

20

40

60

z

i

σ2

60

80

100

60

j

2

σz

40 20 0 0

20

i

z

σ2

40

60

80

0.04

0.06

0.08

0.1

80 60

2

σz

40 20 0

0

20

40

60

80

100

Roy’s Risk Measures with 50% of inefficient firms (h=5)

80

100

j i

z

σ2

j

z

i

σ2

1

60

z

j

σ2

40 20 0

0

20 z

i

σ2

40

60

80

100

80 60

j

2

σz

40 20 0

0

20

i

z

σ2

40

60

80

100

Roy’s Risk Measures with 90% of inefficient firms (h=3)

80

Roy’s Risk Measures with 90% of inefficient firms (h=1)

0.04

0.06

0.08

0.1

80 60

j

2

σz

40 20 0

0

20 z

i

σ2

40

60

80

100

Roy’s Risk Measures with 90% of inefficient firms (h=5)

0 100

0.2

0.4

0.6

0.8

0 100

40

0

40

0.02

100

0

20

0 100

80

j

20

0 100

60

z

σ2

40

0.02

80

Performance Standard Process Standard

60

0 100

0.2

0.4

0.6

0.8

1

1.2

0.02

0.04

0.06

0.08

0.1

Roy’s Risk Measures with 10% of inefficient firm (h=5)

j

0 100 80

0.05

0 100

0.1

0.05

0.1

0.15

0.2

0.3 0.25

0.3

0.15

80

Roy’s Risk Measures with 50% of inefficient firms (h=3)

0.25

Performance Standard Process Standard

Roy’s Risk Measures with 10% of inefficient firm (h=3)

j

0 100

0 100 80

0.2

0.4

0.6

0.8

1

1.2

Roy’s Risk Measures with 50% of inefficient firms (h=1)

0.2

0.4

0.6

0.8

1

1.2

Performance Standard Process Standard

Roy’s Risk Measures with 10% of inefficient firm (h=1)

Roy Risk Measures

Roy Risk Measures

Roy Risk Measures

Roy Risk Measures Roy Risk Measures

Roy Risk Measures

Roy Risk Measures Roy Risk Measures

21 Roy Risk Measures

of efficient firms

References Antle, J. M. (1996): “Efficient Food Safety Regulation in the Food Manufacturing Sector,” American Journal of Agricultural Economics, 78(4), 1242–1247. (2000): “The Cost of Quality in the Meat Industry: Implications for HACCP Regulation,” in The Economics of HACCP-Costs and Benefits, ed. by L. J. Unnevehr, chap. 6, pp. 81–96. Eagan Press. Baumol, W. J. (1963): “An Expected Gain-Confidence Limit Criterion for Portfolio Selection,” Management Science, 10(1), 174–182. Besanko, D. (1987): “Performance versus Design Standards in the Regulation of Pollution,” Journal of Public Economics, 34(1), 19–44. Casella, G., and R. L. Berger (1990): Statistical Inference. Duxbury Press. Domar, E. D., and R. A. Musgrave (1944): “Proportional Income Taxation and Risk-Taking,” The Quarterly Journal of Economics, 58(3), 388–422. Henson, S., and M. Heasman (1998): “Food Safety Regulation and the Firm: Understanding the Compliance Process,” Food Policy, 23(1), 9–23. Hueth, B., and T. Melkonyan (2003): “Performance. Process, and Design Standards in Environmental Regulation,” presented in AAEA annual meeting. Institute of Medicine, National Research Council (2003): Scientific Criteria to Ensure Safe Food. National Academies Press, Washington, D.C. 22

Levy, H. (1998): Stochastic Dominance - Investment Decision Making Under Uncertainty. Kluwer Academic Publishers, Norwell, MA. Lichtenberg, E., and D. Zilberman (1988): “Efficient Regulation of Environmental Health Risks,” The Quarterly Journal of Economics, 103(1), 167–178. Marino, A. M. (1998): “Regulation of Performance Standards versus Equipment Specification with Asymmetric Information,” Journal of Regulatory Economics, 14, 5–18. Martinez, W. L., and A. R. Martinez (2001): Computational Statistics Handbook with MATLAB chap. 4, pp. 79–110. CRC Press, Chapter 4 Generating Random Variables. Roy, A. D. (1952): “Safety First and Holding of Assets,” Econometrica, 20(3), 431–449. Unnevehr, L. J., and H. H. Jensen (1996): “HACCP as a Regulatory Innovation to Improve Food Safety in the Meat Industry,” American Journal of Agricultural Economics, 78, 764–769.

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