Was it something I ate? Implementation of the FDA seafood HACCP program.

Let [y.sup.*.sub.2] be a latent continuous variable denoting propensity to be in compliance, which may be influenced by the expectation of an inspection at time t. Formally,

(14) [y.sup.*.sub.2it] = [z.sub.it[gamma]] + h([w.sub.it];[x.sub.it][beta], [theta]) x [delta] + [[eta].sub.it]

where z is a set of regressors (some of which may overlap with the independent variables in x), [gamma] is a set of regression coefficients, h(*) is the hazard function of w, [[eta].sub.it] is a normally distributed error term, and [gamma] and [delta] are unknown regression coefficients. The hazard function is the density function divided by the survival function of w:

(15) h(w) = f(w)/S(w) = [theta]/[sigma] [(w/[sigma]).sup.[theta]-1]

and is interpreted as the density of an inspector visit right now, conditional on the fact that there has been no visit since the last inspection. The hazard is in this context is the most natural replacement for the "probability" of an inspection at time t, which is often included in conventional probit or logit models of compliance (see Cohen 1999).

The latent propensity to be in compliance, [y.sup.*.sub.2], remains unobserved. What we do observe is whether the plant is in violation ([y.sub.2it] = 1), which occurs when [y.sup.*.sub.2it] [greater than or equal to] 0, or in compliance ([y.sub.2it] = 0), which implies that [y.sup.*.sub.2it] < 0. This results in a probit equation where the probability of a violation is

(16) Pr([y.sub.2it] = 1)

= [PHI]([Z.sub.it][gamma] + h([w.sub.it];[x.sub.it][beta], [theta]) x [delta])

and [PHI] denotes the standard normal distribution.

Since [beta] is unknown and hence h(x) in (14) is not observed, estimation is done in two steps. In the first step, we fit the duration model, obtain estimates of [beta] and [theta], and form predicted values for h(*). In the second step, we enter the latter in the right-hand side of (14) in lieu of the true h(*), and run probit regression (16). This two-step procedure introduces heteroskedasticity in the probit equation. To address this problem, note that (14) can be rewritten as follows:

(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The error term in brackets is heteroskedastic, and its variance is (1 + [[delta].sup.2]Var([[??].sub.it])). We calculate the variance of the hazard hit using the delta method:

(18) var([??]) = ([partial derivative]h/[partial derivative][GAMMA]')var([??])([partial derivative]h/[partial derivative][GAMMA])

where [GAMMA] = [[beta][??][theta]] is the vector of parameters from the duration model, and finally amend the likelihood function of the probit model to:

(19) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The parameters in this likelihood function are estimated by maximum likelihood. (4)

Model Specification

Specification of the Inspection Model

Our measure of inspection frequency (monitoring precision) is the time elapsed between inspections, measured in days. The theoretical framework in the section "A Model of HACCP Enforcement and Compliance" predicts that the FDA should inspect more frequently plants processing products that pose greater food safety risks (scombroid fish, smoked fish, and cooked ready-to-eat products; Proposition 4) and plants suspected of exerting less precautionary effort (Proposition 5). The principal measure of precautionary effort is a plant's past performance. We expect plants that were out of compliance with HACCP or sanitary regulations in the past to exert less precautionary effort in the future and to be the target of more frequent inspections.

To control for operational plant size, we use the annual sales of the plant. All else equal, public exposure to food safety hazards should be greater for larger-volume plants. At the same time, if there are economies of scale or scope in precautionary effort, larger plants would be expected to exert greater precautionary effort. Larger plants might be less costly to inspect as well. Since the coefficient on size of operation reflects the influence of a number of potentially offsetting effects, it is not possible to make a priori predictions about its sign.

We also include (1) dummies indicating the type of plant (e.g., manufacturing plant or repackager), (2) dummies indicating FDA regions, and (3) dummies for the quarter when the previous inspection took place. The latter two variables could be proxies for variations in monitoring costs, in resource constraints, or other factors. Since they proxy for a large number of underlying factors, we have no a priori predictions about the signs of their coefficients.

Many of these regressors are also entered among the determinants of the plant's violation status--z in equation (16)--except the quarter dummies. This exclusion restriction aids in the identification of the coefficients in equation (16), along with the fact that h(*) is nonlinear (Wooldridge 2002, p. 234).

Specification of the Compliance Model

Observed precautionary effort is measured in our data by a discrete indicator of compliance status that takes on a value of 1 if the plant is not in compliance and 0 otherwise. We estimate independent probit equations where the dependent variables are dummies for various aspects of compliance. (5) The theoretical framework in "A Model of HACCP Enforcement and Compliance" predicts that the firm should exert greater precautionary effort when inspections are expected to be more frequent (Proposition 2), when it poses a greater food safety risk and thus faces a stricter standard (Proposition 1), and when compliance is less costly (Proposition 3).

Anticipated inspection frequency is represented by the hazard rate predicted from the inspection model, which should have a negative coefficient if FDA inspections are a deterrent to noncompliance. Past noncompliance is likely an indicator of greater compliance costs, hence firms out of compliance in the previous inspection should be less likely to be in compliance in the current one. Current compliance status should also depend on dummies for the plant's sales, which are correlated with plant size and may thus capture any economies of scale in safety.

Are HACCP and Sanitation Standards Complements or Substitutes?

We study this issue by fitting probit models of compliance that control for both the outcome of the previous HACCP inspection and that of the previous sanitation inspection. If HACCP and sanitation standards are complements, plants in compliance with sanitation standards in previous inspections should be more likely to be in compliance with HACCP requirements in subsequent inspections and vice versa. Thus, the coefficients of lagged sanitation violations in the HACCP violation equation and the coefficients of lagged HACCP violation in the sanitation violation equations should all be positive.

By contrast, HACCP and the sanitation program would be viewed as substitutes if being in compliance with one reduces the likelihood of being in compliance with the other program, as could happen if firms reallocate resources from one to the other. The problem could be exacerbated by the firm's perception of HACCP as imposing a completely new set of standards and requirements.

Results

Inspection Strategy

The results from the duration model, reported in table 3, provide little evidence that FDA inspections target plants that, on the basis of past experience, would be expected to exert less precautionary effort and modest evidence that it targets inspections based on products viewed as higher risk. To begin with, the coefficient on the lagged HACCP violation dummy is negative and significant at the 10% level, implying that, all else the same, a plant previously found to be out of compliance with its HACCP plan is visited 3% sooner--about 23 days. However, it took FDA inspectors 7% longer to re-inspect plants that were required to develop a HACCP plan but had, thus far, failed to do SO.

Turning to the dummies for past sanitation violations, two are negatively and one is positively associated with time until the next in spector visit. The magnitude of the effect is small, and at any rate only two are individually significant at the conventional levels (when the records did not reflect actual conditions at the plant and when monitoring records are inadequate).

Evidence of targeting based on the riskiness of the fish product(s) processed at the plant is somewhat stronger: The strongest coefficient is that on the dummy for smoked fish, which is negative and significant, implying that the time between inspection is, all else the same, 16% shorter for such plants. This is about 118 days for a mid-sized or large manufacturing plant, and 115 days for the average plant of any type. (6) Plants that process breaded products, histamine-producing (scombroid) fish and cooked ready-to-eat products (all classified as high-risk) are visited 6.6%, 4%, and 7% sooner than "other" plants, corresponding to about 48, 31, and 51 days, respectively.

Targeting seems to have been based primarily on plant size, as measured by annual sales. For larger plants in our sample (annual sales of $1 million or more), the interval between inspector visits is about one-third shorter than for the smallest plants, while the interval between inspections for small and medium sized plants (sales of $25,000 to $1 million) is 20-25% shorter than for the smallest plants.