OSHA enforcement and workplace injuries: A ... - Springer Link

Journal of Risk and Uncertainty, 3:283-305 (1990) 0 1990 Kluwer Academic Publishers

OSHA Enforcement and Workplace Injuries: A Behavioral Approach to Risk Assessment JOHN T. SCHOLZ Department

of Political

Science, State University

of New York, Stony Brook,

NY 11794-4392

WAYNE B. GRAY* Department

of Economiq

Clark

University,

Worcester, MA 01570

Key words: regulation, enforcement, OSHA, deterrence, safety

Abstract We develop a model of risk assessmentthat incorporates assumptions from the behavioral theory of the firm into conventional expected utility models of compliance, and test the model using data on injuries and OSHA inspections for 6842 manufacturing plants between 1979 and 1985. Four hypotheses are supported-the specific deterrence effect of an inspection, the importance of lagged effectsof general deterrence, the asymmetrical effectsof probability and amount of penalty on injuries, and the tendency of injury rates to self-correct over a few years.The model estimates that a 10% increase in enforcement activities will reduce injuries by about 1% for large, frequently inspected firms. Prior analyses reporting lower impacts (Smith, 1979; Viscusi, 1986a) are replicated to distinguish between sampling and modeling differences. The results suggest that further compliance theory needs more detailed models of risk-assessment processes to be tested on samples of firms most affected by enforcement.

Risk assessment has played a central role in theories of enforcement and compliance at least for the last century, since Bentham focused attention on the deterrence effects of being caught and punished. With the development of the expected utility model by von Neumann and Morgenstern (1947) and its application to criminology (Becker, 1968; Erlich, 1973) enforcement research has taken great strides in modeling and verifying the role of risk assessment in compliance decisions, particularly in the domain of compliance with regulatory policies. Most empirical studies have investigated the deterrence hypothesis that greater enforcement activity (primarily arrests, inspections, citations, and penalties) increases the expected value of punishment for noncompliers, which in turn increases the motivation to comply. The results of these studies have not consistently demonstrated the expected *This project would not have been possible without the cooperation of the Bureau of Labor Statistics and the Occupational Safety and Health Administration. Special thanks are due to William Eisenberg at BLS and Frank Frodyma and Joe Dubois at OSHA. We are particularly indebted to John Ruser of BLS, who performed the data merging and solved numerous problems. The project was partially funded by NSF grant SES8420920. These individuals and institutions do not necessarily support the conclusions in this article.

284

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linkage (see Nagin et al., 1978, for an early review), although the insignificance of effects is sometimes interpreted as a sign of ineffective or inadequate enforcement rather than of a weak theory (Smith, 1976; Downing and Hanf, 1983). This article applies a model of risk assessment to compliance decisions in which the risk of being penalized by the Occupational Safety and Health Administration (OSHA) affects the firm’s decisions that are relevant to risk of injuries for workers in the firm. Our study combines elements of previous empirical research on OSHA enforcement that was based either on cross-sectional plant-level data (Smith, 1979; McCaffrey, 1983) or time series annual data aggregated by industry (Viscusi, 1979, 1986a; Bartel and Thomas, 1985) or injury category (Mendeloff, 1979), all of which are reviewed in Viscusi (1986b). As with other deterrence studies, these studies have found mixed evidence about the impact of enforcement actions on workplace injury rates, which compliance with OSHA standards is supposed to reduce. Our research emphasizes a process-oriented model of risk analysis based on the behavioral theory of the firm (Cyert and March, 1963), in which behavior is explained not only in terms of expected utility, the basis of prior OSHA research, but also in terms of managerial attention to risks. We find evidence supporting four hypotheses. 1. Firms monitor their injury experience, with unexpected changes in injury rates bringing corrective measures to reestablish prior levels of safety risk. 2. Firms monitor OSHA enforcement activity relevant to their particular circumstances, and respond in ways that decrease injury rates when perceived enforcement risk increases. A 10% increase in enforcement activity reduced injuries by about 1% in our sample, but this adjustment occurs over several years. 3. Firms respond in ways that reduce injury rates when OSHA assessespenalties against them. This specific detemence effect occurs even when controlling for the expected penalty associated with general deterrence, suggesting the importance of “surprise” in focusing managerial attention on enforcement risk. 4. Firms monitor the two dimensions of expected penalty (probability and amount) independently, and respond more to changes in probability than to changes in average amount of penalty. We find OSHA enforcement to be more effective in reducing injuries than has been found in previous studies, and we attribute this to two factors. First, our sample is composed of the kind of firms with which OSHA enforcement is most concerned: larger, frequently inspected firms with higher accident rates than average firms. By minimizing the number of firms for which OSHA is of little concern, we increase the analytic power to capture enforcement effects. Second, the plant-level data set for the 1979-1985 period provides richer information than has been available to other studies, thereby allowing us to include in our model more details of decision making under risk. The unique data set obtained by merging OSHA enforcement records and Bureau of Labor Statistics (BLS) injury data for 6842 manufacturing plants allowed us to account for individual plant injury experiences over the seven-year period and to test the four hypotheses listed above.

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285

Our discussion is organized into seven sections. The first develops hypotheses about plant decision making and risk based on the behavioral theory of the firm (Qert and March, 1963). The second section describes the data set, and the third and fourth discuss estimation methods. We present our results in section 5, compare these findings with our replication of other studies in section 6, and summarize the results in the conclusion.

1. Injuries, enforcement, and firm behavior

The level of risk of injuries at a plant depends on a variety of factors, including the technology in use at the plant (manufacturers of lumber and wood products averaged 11.1 lost workday incidents per 100 workers in 1979, compared with 5.6 for manufacturing as a whole), the size and quality of the plant’s work force (more workers, less experienced workers, and more tired workers are associated with more injuries), and the quality of supervision. Most of these factors are conceded to be beyond the direct influence of OSHA enforcement, at least in the short run. Consequently, most OSHA studies have focused on factors most likely to respond to changes in enforcement, primarily expenditures made by the plant to increase safety, both through physical capital (safer equipment) and human capital (better management of risk, more safety training for workers). The expected utility model that informs most empirical studies assumes that the level of risk in a plant reflects the optimal level of safety expenditures, which is determined by the marginal cost of the expenditure relative to the expected savings from accidents being prevented. OSHA inspections, citations, and penalties are assumed under specified conditions to increase incentives for safety expenditures that reduce the expected penalties for noncompliance. A detailed presentation of this theoretical model and an empirically testable derivation that provides the starting point of our analysis can be found in Viscusi (1979; see also Bartel and Thomas, 1985). Behavioral decision theory research has found considerable evidence that individual decision making under risk and uncertainty deviates consistently from behavior defined as optimal in expected value terms, and has investigated various heuristics or decision aids that account for systematic deviations (see Shoemaker, 1982, Kahneman, Slavic, and Tversky, 1982). The overall significance of such heuristics for the study of aggregate firm behavior, and thus for the existing studies of OSHA enforcement, is not yet clear. We suspect that models of the firm that analyze comparable heuristics in firm decision processes will lead to more powerful explanations of firm behavior in response to enforcement and worker injury risks. The behavioral theory of the firm (Cyert and March, 1963) provides a framework for considering decision processes within the firm. The theory includes four major concepts: quasi-resolution of conflict (addressing multiple goals sequentially rather than simultaneously); uncertainty avoidance (short-run reaction to feedback rather than long-run planning); problemistic search (solving particular problems, rather than general optimization); and organizational learning (adaptation of goals and attention rules as the environment changes).

286

JOHN

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B. GRAY

These concepts are based on observations of business decision making processes, in particmar observing that firms’ behavior deviates systematically from optimal performance (which would simultaneously maximize expected profit over all possible behaviors) because of limitations on the firm’s decision-making ability. Attention is focused in each period on that area in which the firm’s performance fell furthest below expectations. This sort of behavior, called “putting out fires,” has been examined in more mathematical detail by Radner (1975):!He showed that this is an effective strategy for survival (if there are any effective strategies), and that it tends to keep the firm’s performance on different areas close together. Our model of the decision process affecting accidents incorporates four hypotheses implicit in the behavioral model that extend the basic model described in Viscuisi (1979, 1986a). First, an unexpected increase in accidents will cause managers to pay more attention to safety. This should lead to a reduction in accidents in later years until the firm’s attention turns back to other areas. Similarly, a lower rate of accidents than usual should lead to less attention and the possibility of rising accidents in later years. Although managerial attention and safety expenditures are not measured directly in the data, the implication is that surprising changes in the number of accidents over time should be negatively correlated, which implies that the error term in the equation estimating current risk should be negatively correlated with past error terms. Second, several years could be required to observe the full effect on injuries of changes in OSHA enforcement. This is due to the time needed for organizational learning: the firm’s decision processes are only modified slowly, as the firm learns of the changes in its operating environment. The more peripheral the information to primary organizational processes, the longer the lag between environmental changes and responses by the firm. Previous models (Viscusi, 1979) have also tested for delayed effects of enforcement attributed to the lag between safety expenditures and their impact on injuries, which would predict permanent reductions in accidents. Alternatively, if firms responded to OSHA inspections with more transient changes in operations and administration, more immediate temporary reduction in risks could be followed by later increases, eventually returning the firm to the prior level of risk as management turns its attention elsewhere. Third, an actual penalty imposed on the firm can result in reduced injuries quite apart from the effect related to the firm’s subjective probability estimate about the likelihood of being penalized. Particularly for firms having problems in areas other than safety, behavioral theory suggests that a penalty might increase managerial attention to safety issues,just as a sudden increase in injury rates might do so. In the expected utility model, the actual penalty’s effect would suggest a Bayesian learning process in which the occurrence of an inspection with penalty produces a correction in prior estimates of the probability of being pena1ized.l Deterrence analyses of criminology and deviance behavior have long distinguished between general deterrence-the effect of an act of legal punishment on the subsequent behavior of the general populace-and specific deterrence-the effect of the punishment on the subsequent behavior of the individual being punished. These analyses suggest that specific deterrence could be considerably greater than the general deterrence associated with changes in the aggregate level of enforcement.

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Fourth, marginal changes in either the probability of a penalty or the average penalty amount may have quite different general deterrence effects on accident rates, depending on which of the two is most salient to the firm’s monitoring of the external environment. It may be that firms have good information on the number of similar firms that are penalized, but not on the amount of penalties (or conversely may pay more attention to a few extremely large penalties). Expected utility theory generally treats this issue in terms of risk preferences that affect how changes in probability will be weighted in comparison to changes in the value of outcomes. The issue is important in determining the optimal policy mix of wide-ranging coverage versus intensive inspections. Consequently, our model represents general deterrence by separate measures of the probability and average amount of penalties.

2. Data description

The data set assembled for this project combines information over time on both accident rates and OSHA enforcement, data that were not available at the plant level for previous studies. A data set produced by the BLS that contained plant-level accident records from 1979-1985 was merged with the OSHA’s Management Information System (MIS) file containing enforcement actions for all plants during the same period. The BLS file matched records from the BLS Annual Survey for all plants with data for each year from 1979 to 1985, based on a common identification number available in the annual files (Ruser and Smith, 1988). All plants in this file that were located in the 28 states with federal OSHA enforcement covered by OSHA’s MIS were then matched with the OSHA enforcement file. Since no common identification number was available in both OSHA and BLS data sets, we employed a sophisticated record-matching program based on the technique of Fellegi and Sunter (1969) as described in Gray (1987). Both data sets contain various characteristics of the plant, including firm name, address, zip code, city, state, employment, and industry. These characteristics were used to match plants in one data set to plants in the other, based on the probability of agreement on particular variables.2 To protect the confidentiality of firms in the BLS Annual Survey, all merging operations were done at BLS and identifiers of each plant were removed, thereby limiting our ability to add data not available in either data source. The final data set consists of 6842 plants with annual data from 1979 through 1985. For each year, we know employment and hours worked, as well as the number of lost workday injuries and the total number of lost workdays. Each OSHA inspection of the plant during the 1979-1985 period is recorded, including information about the kind of inspection and the citations and penalties assessedas a result of the inspection. The plants in the data set are not representative of the manufacturing sector, as can be seen by the comparisons in table 1. The BLS surveys are based on stratified random samples that oversample large plants, and so the plants included in seven consecutive surveys are considerably larger than the typical manufacturing plant. They averaged 523

288 Table 1.

JOHN T. SCHOLZ/WAYNE

B. GRAY

Comparison of sample with national manufacturing sector Sample (1979)

Number of plants Number of employees Average employees per plant Average lost workday injury rate Number of lost workday injuries Number of lost workdays Average injuries per plant Average lost workdays per plant Number of inspections Number of inspections w/ penalty Total penalties Average inspections per plant Average inspections w/ penalty per plant Average penalty per inspection Probability of inspectiond Probability of inspection w/ penaltyd

6,842 3575,394 523 6.97 171,333 2,484,704 25 363 3,458 1,145 $1,722,973 .51 .17 $498 .27 .13

Sample (1979-1985 average) 6,842 3,271,318 479 6.02 132,305 2,073,126 19 303 2,598 790 $691,657 .38 .12 $269 .26 .lO

National manufacturing sector (1979) 349,913a 18,510,49Sa 54 5.9b 1,243,000b 18,998,C00b 4 54 28,293c 9,453c $10,543,99OC .08 .03 $ 373

Sources: a. Census of Manufactures, 1977. b. Occupational Injuries and Illnesses in 1979: Summary (BLS: April, 1981). c. OSHA Management Information System. d. Differs from “average inspections” by eliminating multiple inspections of the plant within the year.

workers in 1979, compared with 54 workers for all manufacturing plants. The average lost workday incidence rate in 1979 was 6.97 for the sample, compared with 5.9 for manufacturing as a whole. The plants in the sample are relatively heavily inspected by OSHA, with 27% of them inspected in 1979, compared with 8% for all manufacturing plants. Furthermore, plants in the sample represent almost 20% of the employees in manufacturing in 1979, and account for an even greater percentage of accidents in the manufacturing sector. In short, the sample represents a considerable if not necessarily representative proportion of OSHA? enforcement effort in manufacturing. Since plants in our sample face greater enforcement pressure, we would expect them to pay more attention and be more responsive to OSHA enforcement than the typical manufacturing firm. Our sample therefore provides more analytic power than a representative sample for analyzing firm responses to enforcement.

3. Estimation

procedure

To estimate the response of firms to risks of enforcement and of injury, we use measures similar to those in previous studies of OSHA that were available in our plant-level

OSHA

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Table 2. Variables

AND

Injuries %CHG

289

INJURIES

used in analysis Sample mean

Variable 1. Injury

WORKPLACE

(Std. dev.)

Description

(40.4) (.80)

Number of lost workday injuries Percentage change in Injuries:

measures 19.3 - ,051

Injuries

Injuriesr (Injuriest Average

Injuries

Lost Workdays %CHG Lost Workdays

19.4

(37.8)

303 - ,036

(731) (1.0)

- InjurieS-

Lost Workdaysr of inspection with Penalty

.099

(.29)

Predicted

Probability

.106

(06)

- ,010

(.02)

.038

(.03)

.600 5.962

(1.8) (.31)

Predicted

Industry

Probability

3. Amount Penal@+ Predicted

- Lost Workdays, + Lost Workdays+

-r t)/2

with penalty

Inspection

%CHG

t)/2

Average injuries in past two years: (Injuriesrt + Injuries( -2)/2 Number of lost workdays Percentage change in Lost Workdays: (Lost Workdays,

2. Probability

t

+ Injuries,-

Probability of Penalty

Inspection with penalty during year (dummy variable for sample firms) Predicted probability of inspection with penalty (based on table 3 coefficients) Percent change in Predicted Probability [Predicted Probabilityt - Predicted Probability-i] Industry probability of inspection with penalty (inspections with penalty/establishments in industry, based on national totals from OSHA MIS, aggregated by two-digit SIC industry)

of penalty

Penaltya

%CHG

Predicted

Penalty

- ,086

(.17)

Industry

Average

Penaltya

4.833

(.69)

926 - ,019

(1912) (.25)

Log of total penalties assessed against firm during year Predicted log of penalties assessed when penalties were imposed (based on table 3 coefficients) Percentage change in Predicted Penalty as calculated by difference in logs of predicted penalty [Predicted Penal@ - Predicted Penalty-t] Industry average log (penalty) assessed if inspection with penalty occurred (two-digit SIC national totals from OSHA MIS)

4. Size of firm Hours of Work %CHG Hours

Hours worked during year (in thousands) Percentage change in Ln (Hours): Ln(HourQ (Ln(Hours,)

Employment %CHG Employment

479 - .019

(982) (.22)

- Ln(Hour+

1)

+ Ln(Hour+

i))/2

Average employment during year Percentage change in Ln(Employment,) (Ln(EmploymenQ

Total plant-year

observations

- Ln(Employmen& + Ln(Employment,-

1) t))/2

= 48,794

a. Note that Penalty is averaged over all plant-year observations in the data set, but Predicted Industry Average Penalty are based only on inspections with penalty.

Penalty

and

290

JOHN

T. SCHOLZiWAYNE

B. GRAY

data set. Summary statistics and descriptions of each variable are provided in table 2. As in most studies, two different measures of injury risk are used, one reflecting frequency (annual number of lost workday injuries) and one reflecting severity (annual number of lost workdays) of industrial accidents in a plant in the designated year. The frequency or severity of accidents in a given year (Ai,) is hypothesized to depend on the hazardousness of this particular plant (Ai), the number of hours worked at the plant (Hit), the experience level of the workers at the plant (Q& the expected enforcement faced by the plant (X,,*) and the “attention to safety” given by the plant management (&), as well as an unexpected residual component (&). Expressing this as a linear regression gives us

In order to remove the plant-specific hazardousness, we consider the first-differenced form of this equation (replacing Ail with aif, and so on, to reflect the movement to changes, rather than levels, of variables):

In fact, we use the proportional rather than the simple change in each variable, because the estimated coefficients obtained in the simple-change form of the regression are very sensitive to a few outliers (plants with very large changes in injuries). Switching to a proportional-change form reduced the influence of these outliers. The use of change rather than level as a dependent variable also minimizes the endogeneity problem caused by the relationship between inspections and injury rates: as noted in the next section, penalty inspections are strongly related to injury levels, but not to changes in level. This supports the plausible argument that inspectors tend to use penalties on more dangerous plants but take little account of recent changes injury rates? Of the variables in (2), we measure a and h directly, while the others are proxied by variables available in the data set. Changes in worker experience, q, is measured by changes in the number of workers at the plant (with a negative sign, since new workers have less experience). There are two components to expected enforcement, x*, corresponding to deterrence theory’s two components of expected penalty: the probability of (an inspection with) penalty and the expected level of penalty. Both are transformed to the change form, as discussed in the next section. We use two proxies for s, the changes in attention paid to safety by plant management. The specific-deterrence shock effect of having received a penalty from OSHA after a recent inspection of the plant is represented by the inspection history of the plant (Inspection with Penalty, a dummy variable equal to 1 in a year in which an inspection with penalty occurred).4 The feedback effect of having had an unexpectedly high number of injuries in the recent past is represented by an autoregressive structure for the error terms in (2). In other words, that component of change in the risk measure that could not be attributed to the measured variables (the estimation error) constitutes a surprise, and the effect of past surprises on current risk measures is reflected in the autoregressive errors.

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291

INJURIES

Since we expect the impact of enforcement and surprise to affect risk measures over several periods, these variables are included with multiple lags. The data rejected distributed lag models (that could represent Bayesian learning processes), so we entered lagged variables directly in the equation. Three period lags have been used in other studies (Viscusi, 1979), provide sufficient time to account for organizational delays, and do not exhaust the full seven years of the data set.5 The control variables representing hours worked and quality of the work force were not lagged, since they affect the risk measure directly. The final form of the equation to be estimated (with the firm subscript left out for presentational simplicity) is %CHG RISK, = PO + 2 Bri% CHG Predicted Probability-i i=O

+ Zpz%CHG

Predicted Penalty,-i

3

+ @s$nspection

with Penalty-i

+ Bh%CHG Hour+ + Bs%CHG Employment, +

f$(jj*YEARi i=83

+

f&i*SICi

+

Vt

i=21

3

withv, = et + Cai*vt-i. . I=1 Here et is assumed to be an independent, normally distributed series with a mean of zero. The general deterrence variables and firm characteristics are entered in percentage change form (designated by %CHG), and the dummy variables for Inspection with Penalty, Year, and SIC are not modified. As noted in the variable descriptions in table 2, the logged form is used for Penalty, Hours, and Employment. Separate estimations were made for each of the risk variables, %CHG Lost Workday Injuries and %CHG Lost Workdays. The autoregressive coefficients (ai) address our first hypothesis, which predicts that they will be negative and sum in magnitude to less than one (to make the feedback model stable). Enforcement is expected to affect accidents with a substantial lag (hypothesis 2) both general (pii and Bz) and specific deterrence (psi) measures are included (hypothesis 3) and the general deterrence effect is separated into predicted probability and predicted amount of penalty (hypothesis 4). Industry and year dummies are included to control for any systematic changes in injuries along those dimensions. We expect Bii, Bz, and psi to be negative, and control-variable coefficients B4 and Bs to be positive.

4. Estimating

predicted probability

and amount of penalty

Deterrence is dependent on the firm’s expectation that it will be penalized if it does not comply. Generally, empirical studies have relied on aggregate enforcement measures as

292

JOHN T. SCHOLi7WAYNE

B. GRAY

proxies for general deterrence, since changes in aggregate penalties are presumably linked to changes in a firm’s expectations about penalties. Our study is able to model this linkage explicitly, making use of the enforcement experience of firms as recorded in the data set to predict the expected probability and amount of penalty in terms of both industry-level enforcement measures and firm-level characteristics. For the experienced, routinely inspected firms that dominate our sample, the resultant predictions provide richer proxies for an individual firm’s expected probability and amounts of penalty than is provided by aggregate enforcement measures alone.(j The equation used to estimate the probability of penalty reflects the role of OSHAs current level of enforcement as well as the size of the firm and its injury experience in the recent past: Inspect w/ Penaltyi, = pa + BrIndustry Probabilityi, + BzIndustry Average Penal& + ps[Injuriesi,- r + Injuriesi,-$2 + &% CHG Injuries+ r 85 + BsHoursi, i- &$lTlplOpel& + 1 P-/jYearj -l- eip (4) j=80

The unit of analysis is the plant. The two industry-level measures of OSHA enforcement are based on national aggregates for the plant’s industry, with Industry Probability measuring the number of inspections with penalty per firm in the industry and (the log of) Industry Average Penalty measuring the average amount of penalty for inspections that imposed a penalty. The size of the firm is represented by Hours and Employment, both entered in log form. Since OSHA targeting and penalizing decisions may reflect the plant’s injury experience, we include measures of both the level and change of injuries in the recent past. The same equation is estimated for the total annual penalty (in log form), with OLS used to estimate coefficients for Penalty (for inspections that had penalties) and probit for the dichotomous Inspections with Penalty variable. These coefficients are then used to calculate the predicted penalty and predicted probability for each firm, which are used as independent variables in the final analysis. These results are presented in table 3. As mentioned earlier in explaining why change rather than level was used for the primary analysis, note that the Average Injuries variable is highly significant in predicting Inspections with Penalty, while the Change in Injuries is not.

5. Discussionof results

Table 4 reports the basic estimations of enforcement effects on lost workday incidents and lost workdays. As expected, the independent variables explain less of the variance in lost workdays (6%) than of the variance in lost workday incidents (12%). Both equations support the same conclusions about the importance of the behavioral theory of the firm and about the impact of enforcement actions on accidents, although the estimated effects are slightly different in the two equations.

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Table 3. Equation

AND

used to predict

WORKPLACE

probability

293

INJURIES

and amount

of penaltya

Predicted probability

Predicted penalty

Intercept Average Injuries Change in Injurieytl Industry Probability Industry Average Penalty Hours of Work Employment

,041 (6.2) .OOO50 (18.4) JO24 (1.3) ,793 (14.6) .0087 (2.7) - ,039 (- 16.6) ,044 (15.2)

3.803 (4.9) .000001 (.004) ,048 (1.7) 2.096 (3.0) ,058 (1.2) ,167 (1.7) -.0035 (-.03)

Year Dummies 1980 1981 1982 1983 1984 1985

- ,011 - ,010 -007 - ,016 - ,010 -.008

-.173 - .385 -.535 - .436 - ,509 - ,424

No. observations Mean (dependent F-test R2

47,894 .0989 172.1 -

variable)

a. Based on estimation in parentheses)

of Inspection

(-2.7) ( - 2.2) (-1.3) ( - 3.0) (- 1.9) (-1.8)

with Penalty

(probit)

(-3.6) ( - 6.2) (-6.9) ( - 6.0) ( - 7.2) ( - 7.0)

4,735 6.07 52.2 ,115 and Penalty

(OLS on nonzero

penalties)

(t-statistic

5.1. Self-cowecting mechanisms

One of the most striking and robust findings in this and all other estimations we ran is the strong tendency of surprises in the accident rate to be compensated for and to return to zero within three years. The autoregressive coefficients q, 012,and or3 are consistently negative and highly significant, and their sum approaches - 1. The estimated impact on accidents decreases for more distant shocks, consistent with the assumption that recent shocks are most important in driving firm behavior. In the estimation based on Percentage Change in Injuries, any change in a given year is compensated by a 49% change in the opposite direction in the following year, a 32% change in the second year, and a 13% change in the third year. The effect of the residual (unexplained) variation is almost fully (94%) compensated during the next three years. This process alone explains more vari-, ante than the other variables combined, raising the explained variance from 12% for all independent variables to 29% for the autoregressive estimate for injuries, and from 6%’ to 27% for lost workdays. It should be noted that this autoregressive process is not explained by a stochastic process in which an unusually high number of accidents in one year is followed by a regression to the mean in the next year, since such a process would not produce multiyear correlations among residuals. Furthermore, the autoregressive process associated with

294 Table

JOHN T. SCHOLZ/WAYNE

B. GRAY

4. Estimated impact of enforcement (Maximum Likelihood estimates, t-statistic in Darentheses) %CHG in Injuries

%CHG in Lost Workdays

Surprise (autoregressive errors) One-year lag (cul) Two-year lag (a~) Three-year lag (cq) General

- .548 (- 63.8) -.329 (-31.1) - .141 (- 11.4)

deterrence

%CHG in Predicted Probability Year t Yeart - 1 Yeart -2 %CHG in Predicted Penalty Year t Yeart - 1 Yeart - 2 Specific

- .489 ( - 49.8) - ,316 (- 29.5) - .127 (-9.8)

1.208 (4.6) - 1.357 ( - 5.6) -.591 (-2.3) - .897 ( - 7.8) - .294 (- 3.8) - .381 (-4.9)

1.023 (3.0) - ,840 (-2.6) -.401 (-1.2) -.446 (-3.6) -.140 (-1.5) - .280 (- 2.9)

deterrence

Inspection with Penalty Yeart

Yeart - 1 Yeart - 2 Yeart - 3 Firm

-

.036 ,049 ,043 .006

(- 2.4) (-3.1) ( - 2.8) ( - 0.4)

-.OOl - ,058 - ,043 - ,006

(-.05) ( - 2.7) (-2.1) (-0.3)

characteristics

%CHG in Hours %CHG in Employment

,672 (16.0) ,516 (13.1)

,546 (10.3) .467 (9.0)

,354 (9.3) .356 (9.7) .574 (11.2)

,160 (3.6) .198 (4.4) ,331 (5.4)

Year dummies

1983 1984 1985 Tbo-digit

SIC

Intercept

No. observations Mean (dependent variable) R2 (with autoregression) R2 (regression only)

(19 dummies) - 0.442 (- 11.3) 27,368 - ,046 ,289 ,123

(19 dummies) - .24.5 ( - 5.2) 27,368 - ,026 ,274 .063

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ENFORCEMENT

AND

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INJURIES

295

safety investments, a variable we could not control for directly, would generally lead to positive rather than negative coefficients as one year’s investments continue to reduce risk over several years. We believe the self-correcting process is consistent with the behavioral model suggestion that a year with a surprisingly high number of injuries induces increased attention to plant safety, which in turn reduces injuries in following years.

5.2. Lagged effects of general deterrence

The results in table 4 demonstrate that both the expected probability and the amount of penalties exert an overall permanent negative effect on accident rates.7 The total effect of a unit increase in predicted probability, obtained by adding the coefficients for the current and lagged values, equals - .75 for injuries and - .21 for lost workdays, with the comparable figures for predicted penalty being - 1.57 and - .87, respectively. The significant positive coefficient in both equations for the current value of predicted probability is unexpected, but may be due to the inclusion of both measures of general deterrence (when the equation is estimated without predicted penalty, the troublesome coefficient approaches zero). The insignificance of some lagged terms in the lost workday equation may also be explained by the multicollinearity between these general deterrence measures. The length of time required for changes in enforcement to produce their full effect is longer than had been found previously. While other enforcement studies have found one-year lags between enforcement and effect (Viscusi, 1986a; Scholz, 1987), our estimates suggest that the effect continues into later years. Studies using only a single period may not capture the full effect of enforcement changes.* This length of delay is consistent with the assumption that implementation of changes to affect accidents takes considerable time. The fact that the coefficients do not become positive in longer lags indicates that the initial effect does not decay over time, so the effects appear to be due to permanent safety investments rather than quick administrative fixes. Our attempts to force the lagged coefficients to follow some smooth decay pattern over time were rejected by the data in favor of the separate (and fluctuating) coefficients reported here.

5.3. Specific deterrence The results in table 4 confirm the behavioral hypothesis that the surprise involved in the actual imposition of a penalty has an effect on behavior over and above the general deterrence effect of expected probabilities and amounts of penalties. In both equations, the primary effect occurs in the first and second year after an inspection, confirming the long period of time over which enforcement effects must be measured. Although the effect remains negative in the third year after an inspection, the coefficient is not significant in either equation. The effect of the Inspection with Penalty variable in the current year is insignificant for lost workdays.

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As with general deterrence, this pattern is most consistent with permanent investments rather than transient administrative changes. It does not reflect a pattern of consistent decay associated with a Bayesian adjustment process. These results are quite robust to changes in the measures of general enforcement used, the lag lengths for the enforcement variables, or the inclusion of other controls. On the other hand, the magnitude of the specific deterrence effect is relatively small when compared to the general deterrence effect, as illustrated in table 5 and discussed in the next section.

5.4. Asymmetrical effectsof probability and amount of penalty

Expected utility theory generally assumes that the expected penalty for noncompliance (the predicted probability multiplied by the predicted penalty) captures all relevant information for decisions under uncertainty. However, when we added this expected penalty variable to the regression in table 4 (in results not shown here), the coefficients for predicted probability and predicted penalty remained much the same, and the expected penalty variable was only significant in one lagged term. The superior performance of the independent components (probability and penalty) over the product is consistent with the behavioral theory’s suggestion that the probability and the amount of penalty affect accident rates independently, as they would if monitored and fed into the decision process independently.9 As noted earlier, the impact of changes in probability and in amounts of penalty may not be symmetrical-that is, a 10% increase in either variable could have the same impact on expected value but different impacts on accident rates. Table 5 compares the impact on injuries of a 10% increase in inspections with a 10% increase in the average penalty (assuming that the additional inspections, on average, are as likely to impose penalties as current inspections). The calculation of impacts follows the two steps used in our estimation procedure. First, the impact on predicted probability and predicted penalty is calculated separately for an increase of 10% in the Industry Probability and Industry Average Penalty variables, based on the coefficients in table 3. Second, the Table 5. Impact of policy changes on injury measures (Effect of a 10% change in enforcement variables) General deterrence

Specific deterrence

Total effect

Predicted Probability

Predicted penalty

Inspection with penalty

I. Lost Workday Injuries Industry Probability of Inspection Industry Average Penalty

- .22% - .06%

- 1.26% - .87%

- .13%

- 1.61% - .93%

II. Lost Workdays Industry Probability of Inspection Industry Average Penalty

- .07% - .02%

- .70% - .48%

-.ll%

- .88% - SO%

Enforcement Measure

OSHA

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calculated changes in predicted probability and penalty are multiplied by the appropriate coefficients in table 4, giving the separate impacts of probability and penalty on the risk variable reported in table 5. These effects can be summed for the combined general deterrence effect. Table 5 also estimates the specific deterrence effect, assuming a 10% increase in actual inspections, and sums the separate effects to give the total effect on injuries. The results confirm that changes in probability and penalty are not symmetrical. The simulated increase in inspections reduced injuries and lost workdays more than a comparable increase in penalty. These results are consistent with the general conclusion from most empirical research on deterrence (Lempert, 1982; Nagin, 1978) as well as Viscusi’s (1986a) study of OSHA, which finds that the probability of being punished has a greater effect on compliance than does the amount of the punishment. The results are less consistent with standard assumptions that firms on average are risk-neutral or riskaverse, since only risk-seeking firms would be expected to respond more to probability changes than to penalty changes. Thus, different capabilities for monitoring information related to the probability and amount of penalty may provide a more reasonable explanation than differences in risk preference. On the other hand, specific deterrence has considerably less impact on injuries than general deterrence. The relatively minor role of the shock of being penalized suggests that the firms we studied do have relatively effective means of monitoring OSHA enforcement and drawing appropriate implications about the risks of penalty. Once these general effects are controlled for, the remaining surprise of being penalized accounts for only a small proportion of the effect on injuries.

6. The impact of OSHA enforcement on injuries

Estimates of OSHA enforcement’s impact on injuries in this and comparable studies provide a relatively consistent picture of small but significant effects, with the estimates from our model and our data higher than estimates reported in other studies. If we compare studies finding significant results in the percentage reduction in injury measure brought about by a 10% annual increase in enforcement, impacts range from no signihcant impact in McCaffrey (1983) and Bartel and Thomas (1985) to ranges of .15% to .36% in Viscusi (1986a), .20% in Smith (1979), .48% to .73% in Cook and Gautschi (1981) to our estimates in table 5 of .5% to 1.6%. Several explanations might account for our higher estimates: 1. 2. 3. 4.

The inclusion of both specific and general deterrence effects The inclusion of three-year lagged effects Our use of inspection with penalty rather than inspection Our sample, which overrepresents larger, more dangerous, and more heavily inspected plants 5. Our model specification, which differs from those used in earlier studies.

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We have explored these explanations empirically by using our data set to replicate two previous studies as closely as possible, one measuring specific deterrence and the other measuring general deterrence.

6.1. Specific deterrence

To estimate the impact of an inspection on subsequent injuries in the inspected plant, Smith (1979) used an ingenious research design in which plants that were inspected late in the year (November-December) were used as a comparison group for plants inspected earlier in the year (March-April). If inspections had an immediate impact on injuries due to the immediate abatement of violations, this impact would show up in the injury rates of the group inspected earlier, but not in those of the group inspected later in the year. The problem of endogeneity of inspections is minimized by comparing the two groups of inspected plants, eliminating plants inspected in the previous year, and including other factors influencing injury rates (prior injury rate, employment changes, and size and industry dummies). The data source was the annual BLS surveys used in our study, but from an earlier period. In table 6, Smith’s results are compared both with McCatiey’s (1983) and with our replications. Whereas Smith found significant effects from inspections in 1974, McCaffrey found no significant results for 1976. Our results, based on inspections during the Table 6. Comparison using Smith’s specific deterrence estimates: Impact of inspections on lost workday injury rates (t-statistics in parentheses)

Specific

McCatTreyb 1976

- .63 (-2.9) -

.25 (9)

Early inspection with penalty Rate _ 1

..51

(26.6) Employment&mploymen& R2

N

Our data 1982-1985

1982-1985

deterrence

Early inspection

Injury

Smitha 1974

-1

2.19 (3.7) .35 2362

-

.21 (7) -

.63 (32.9) 49

(2.0) .44 1990

ii5 (34.9) .72 (2.7) .55 1208

-.22 (-.4) .70 (20.7) - .14 (- 4 .58 415

Notes: All regressions include industry and size-class dummies. Regressions on our data also include year dummies to preserve comparability while making use of the multiple years in our data. a. Source: Smith (1979). b. Source: McCaffrey (1983).

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1982-1985 period of our previous analysis, are comparable to McCaffrey’s. As he suggested, the easily accomplished reductions in risk that OSHA inspections could impose may have already been implemented in 1976, leaving more complex issues of risk reduction less amenable to quick fixes. What is it that accounts for the difference between the significant specific deterrence effect we found with our model (table 4, column 2) and the insignificant effect in table 6, since both analyses are based on the same time period, data set, and measure of risk? The final column in table 6 indicates that limiting inspections to those in which a penalty was imposed (as we did in our model) at least produces the expected negative impact on injuries, although still not at significant levels. Given that the impact of an inspection is spread over a three-year period (table 4) the most plausible explanation is that the single-year design is too short to capture significant effects of OSHA. Cook and Gautschi (1981) also found significant specific deterrence effects in a study designed to analyze long-term impacts of enforcement actions. Our finding that specific deterrence contributes a relatively small amount to the overall impact of OSHA (table 5) also makes the lack of significant effects in short-term studies more likely.

6.2. General deterrence

Viscusi’s (1986a) study analyzes the general deterrence effect on an industry’s injury rate of the total annual inspections and penalties in the given industry, and uses the prior year’s injuries, several production measures, and year and SIC dummies to control for other impacts on injuries. To replicate Viscusi’s analysis with our data set, we aggregated measures of injuries, hours of work, and employment in the data set to the two-digit SIC level, added national aggregate measures of overtime, percentage of female workers, and percentage of production workers, and used Viscusi’s estimation procedure to measure the impact of national OSHA enforcement activities on aggregate lost workday injuries in our sample (using Viscusi’s log-odds form of the dependent variable). As in Viscusi’s study, independent regressions were estimated for inspections and penalties. We also estimated regressions using inspection with penalty and average penalty variables comparable to those in our model. Both current and lagged values of the enforcement variable were included in each regression. The resulting estimates for inspections were comparable to those reported in Viscusi (1986a, table 2) in terms of signs and significance of the control variables and the explained variance (r2 = .98), so in table 7 only the relevant enforcement coefficients were compared with Viscusi’s results (1986a, table 3). Table 7 provides two comparisons between Viscusi’s and our analysis. Taken together, they indicate that the different samples and different measures of enforcement contribute most to our higher estimation of general deterrence impacts, with the greater detail in our model contributing a relatively smaller amount. The first two columns provide a direct comparison of differences in coefficients for Viscusi’s model obtained from his national data and our sample data. Using Viscusi’s

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Table 7. Comparison using Viscusi’s general deterrence estimates: Impact of aggregate enforcement measures on log-odds of Lost Workday Injuries (r-statistics in parentheses)

Coefficients National datab (1973-1983) Inspections Year t Yeart - 1 Penalty (per worker) Year t Yeart - 1

9.61 (1.26) - 16.64* (- 2.00)

,016 (0.94) - ,026 ( - 1.52)

Probability (inspections with penalty) Year t NA Yeart- 1 NA Average penalty per inspection with penalty Year t NA Yeart- 1 NA

Sample data (1980-1985)

Impact of 10% increase in enforcementa

national

sample

Behavioral model (sample)

-.16%

- 1.27%

NA

- .04%

- .09%

NA

NA

-.81%

- 1.48%

NA

- .66%

- .93%

Viscusi model

-.898* (-3.38) ,028 (0.20)

- .00003 (- 0.01) - .031 ( - 0.77)

-3.27* (-2.55) 0.89 (0.93)

- .057* ( - 5.47) - ,009 (- 0.99)

Notes: The coefficients for each enforcement variable are estimated in separate regressions. Following Viscusi (1986a), each regression also includes year and industry dummies, as well as percent female, percent production workers, average hours per week, average overtime hours, and the change in employment. An asterisk indicates significance at the .05 level; NA indicates not available. a. Since the Viscusi model uses a semi-log form, the percentage impact of a 10% increase in enforcement on injuries is given by 100 x (Coefficientr + Coefficient,- 1) x (0.1 x mean of enforcement variable). Only the average penalty model is in log-log form, for comparability with the behavioral model. For average penalties, then, the impact of a 10% increase is simply 10 x (Coefficien& + Coefficientr- 1). Values for the behavioral model are taken from the general deterrence calculations in table 5, excluding the impact of specificdeterrence. b. Source: Viscusi (1986a), table 3.

inspection and penalty-per-worker measures, both data sets indicate that only inspections have a significant impact on injuries. However, the variables from our model corresponding to deterrence theory’s concepts of probability (inspections with penalty) and amount of penalty (average penalty) are both significant for the sample data. The significance of the current rather than the lagged value in the sample data indicates one possible difference in data sets, although the significance of multiple lags rather than current values in behavioral-model estimates on the sample data suggests that this difference might not occur if more lagged values were included. The difference between national and sample data becomes clear when the estimated magnitude of effects (columns 3 and 4) are compared. For the two variables used by Viscusi, the negative impact on injuries of a 10% increase in enforcement actions is eight times greater for inspections ( - .16% versus - 1.27%) and twice as great for penalty per

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worker (- .04% versus - .09%) in the sample as in the national data. Substituting the deterrence variables for Viscusi’s variables in the sample data set produces more balanced estimates of the impact of inspections with penalty (- .Sl%) and average penalty (- .66%). Finally, comparing the impact of these variables as estimated by the Viscusi and behavioral model on the sample data set, we see that the behavioral model estimates are somewhat greater (- .81% versus - 1.48% for inspections with penalty, - .66 versus - .93% for average penalty). However, the difference between these estimates is less than the difference between estimates on the two data sets using the Viscusi model, indicating that the more OSHA-relevant sample provides the primary difference in estimated impacts. The richer detail in our model, made possible by the plant-level information in our data set, accounts for a smaller portion of the difference in estimated impacts. Regardless of which model one uses on the sample data set, a 10% increase in either of the general deterrence variables is estimated to decrease lost workday injuries by .66% to 1.48%. In actual terms, a 1% reduction in injuries for our sample translates to 1.9 injuries per plant, one injury per 2500 workers, or 1300 injuries per year. A 10% increase in enforcement in 1979, the first year of our sample period, would amount to 2800 inspections, 950 inspections with penalty, or $1 million in penalties. These estimates are clearly not generalizable to the entire manufacturing sector, which would presumably be affected at a lesser rate. The sample is important in its own right, however, since it accounts for around 20% of the total work force in manufacturing and over 10% of all industrial accidents. Furthermore, the differences between plants in the sample and in the total manufacturing sector (table 1) suggest three factors that may account for the greater effectiveness of enforcement in the sample. Our sample plants are larger, somewhat more dangerous, and more heavily inspected than the average manufacturing plant. Larger firms may be more attentive to OSHA enforcement, since they are more visible. The concentration of workers makes an attractive target for inspections, particularly in larger firms with injury rates above the average of manufacturing. Furthermore, larger firms may have more adequate managerial and investment resources to control the risks that are brought to their attention during inspections. Cook and Gautschi (1981) found size to be related to enforcement effectiveness; significant effects of inspections were found only for firms with over 200 employees, with even greater effects for firms with over 300 employees. Finally, the relatively high inspection probability in our sample (over 25% annually, compared with less than 8% for all firms nationally) may be important to increase the sensitivity of a firm to enforcement activities, since more intense scrutiny of critical subgroups within the industry may enhance enforcement effectiveness (Scholz, 1984a). If frequency of inspection is important, plant size becomes doubly important, because larger plants allow OSHA to inspect each firm more frequently for a given ratio of enforcement resources per worker. The sample accounted for a 20% share of employment in manufacturing in 1979, but for only 12% of all inspections in manufacturing, despite the unusually high frequency of inspections. Multiple inspections of a plant

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during a given year appear to be a less effective concentration of resources-in exploratory anaIyses, we found muhiple inspections to have no additional impact on injury rates. However, some minimal frequency of inspection is likely to prove critical to effective enforcement.

7. Conclusions

We find evidence that OSHA enforcement has a significant impact on injuries in a substantial portion of the manufacturing sector. The number of lost workdays and the number of Iost workday injuries decrease significantly after increases in general enforcement and after specific contacts with enforcement agencies, even though (1) compliance is only indirectly related to accidents (Mendeloff, 1979), (2) expenditures on compliance may compete with more productive expenditures to improve safety (Bartel and Thomas, 198.Q (3) OSHA resources do not permit extensive monitoring of most workplaces (Smith, 1976), and (4) OSHA penalties are relatively small compared to compliance costs. Enforcement effects are relatively modest, as other studies have found; a 10% increase in enforcement would reduce injuries by around 1% for the large, frequently inspected firms represented in our sample. In explaining how firms deal with risks associated with industrial accidents and OSHA enforcement, several extensions to the expected utility model were used, based on the behavioral theory of the firm. These extensions, including the self-correcting feedback mechanisms that focus managerial attention on risks, the relatively long lags between enforcement changes and changes in injury risks, the difference in effects between the expected probability and the expected amount of a penalty, and the independent (specific deterrence) effect of inspections, all proved significant in our model. Although the behavioral hypotheses we have developed and tested fall considerably short of a welldeveloped theory of compliance, they suggest that further extensions to the basic expected utility model of deterrence can contribute to an understanding of how firms respond to accident and enforcement risks. A richer model of compliance may help improve the effectiveness and efficiency of enforcement strategies. Just as undue reliance on simple microeconomic models in other policy domains has led to myopic policy advice (Stern, 1985), reliance on unduly simple deterrence models limit the enforcement debate to a relatively narrow spectrum of the practical concerns facing enforcement officials. For example, given OSHA’s normal level of activities and the responses of our sample firms, our results suggest that increasing the number of penalties has about a 50% greater effect in reducing accidents than a comparable percentage increase in the average amount of penalty. This implies that OSHA might increase its impact by shifting its resources from the more intensive inspections that are required in order to impose high penalties to more frequent inspections that imposed some penalty. Further research may be able to clarify threshold levels for the frequency of inspections and the amount of penalty that could be used to increase the effective deployment of enforcement resources.

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The efficiency of safety standards in reducing accidents, while important, may be less important than the need to focus the firm’s attention on safety problems. We cannot say whether the decreases in accidents found in this study are efficient (from society’s point of view), but to the extent that the firm’s safety expenditures were suboptimal because of inattention, the decreases in accidents may be due more to focusing the firm’s efforts on an effective risk-reduction program than to safety improvements directly related to compliance with regulations. If the behavioral model proves to be as powerful as these preliminary results suggest, then the conventional wisdom on the role of regulation and enforcement in the economy will need to be reevaluated to include this attentioncorrection function (Scholz, 1984b).

Notes 1. Viscusi (1986b) argues that higher penalties for repeated violations may provide an alternative reason for firms to make investments in compliance (and safety) after an inspection that they would not have been willing to make before being inspected. 2. Those cases where it was not clear whether the records were properly matched were hand-checked. Hand-checking, used to examine the matches on two state samples, indicated that our error rates for false matches and missed matches were less than 1%. To ensure that no plant in the final set contained ambiguous matches, 198 plants were dropped from the original file. 3. For purposes of comparison, we note the distinctions that led us to use a different formulation than that of Viscusi (1979,1986a). First, our fixed effects refer to plant rather than industry-specific characteristics, so we use the first-differenced form to control plant-level effects in addition to the industry and year dummy variables used by Viscusi. Second, we use the measure of inspections with penalty, rather than just inspections, because it corresponds to the theoretical concern with the probabilityofbeing penalized (see note 4). Third, as noted in the text, endogeneity between inspectionswith penalty and injury rates would be a major problem if we did not use the change form for the dependent variable. The alternative of using instrumental variables to predict enforcement measures would not have allowed us to distinguish between general deterrence (the predicted enforcement) and specific deterrence (the actual event), and becomes more complex because of the laged variables. Finally, using the lagged dependent variable as an independent variable (rather than as part of the dependent variable) would cause problems in our plant-level data set, because we assume (and demonstrate) that the estimation error follows an autoregressive process. OLS would then overestimate the coefficient of the lagged dependent variable and underestimate the remaining coefficients of independent variables (Ostrom, 1978). In addition, the autoregressive process represents our theoretical interest in feedback on the change variable, so we use the change form and model the autoregressive process instead of using the lagged dependent variable. 4. For theoretical and empirical reasons,we focus on the occurrence of a penalty rather than on an inspection or on the amount of penalty. On theoretical grounds, inspections that do not result in penalties are not likely to focus additional managerial attention on accidents. In fact, they may lead to more complacency among management toward safety although good inspectors presumably also point out potential safety problems that management may have overlooked. From the viewpoint of behavioral decision theory, managerial attention will increase only if the amount of penalty is higher than some threshold amount. We tested the hypothesis that any penalty is sufficient to attract attention. See Klepper and Nagin (1989) for a similar conclusion about criminal penalties and tax evasion. Empirically, preliminary analyses found that inspections without penalty had less robust effectsthan inspections with penalties, and that the amount of penalty did not explain any more variance than the dummy variable representing inspections with penalties. The single indicator was selected to avoid multicollinearity problems, and also because of the straightforward

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interpretation of the coefficient for the dummy variable. It should be noted that inspections without penalty may have more significant effects on firms inspected less frequently than those in our sample. The results are not sensitive to varying the lag lengths from l-4 years on either the autoregressive process or the enforcement variables. Estimates of our general model were run using two-digit SIC industry aggregates in place of the predicted values. The results indicated a significant effect only for the current measure of the number of penalties. We believe that the more significant results obtained in table 4 for predicted values indicate the greater amount of information that is contained in the predicted values, which therefore represent a closer proxy to the firm’s expectations. The use of predicted or aggregate proxies for the test of general deterrence had almost no effect on the coefficients or significance of the specific deterrence measures. These predicted values are not instrumental variables in the usual sense, since we include the actual enforcement experience of the plant in our measures of specific deterrence. They are intended to measure the firm’s expectation of the OSHA enforcement that it will face (general deterrence). Consequently, we do not adjust the error of estimation. Viscusi (1979) tested for lags up to three-period, but found no effects.The differences between his findings and ours are probably due to the nature of our data set, which includes firms more likely to be impacted by OSHA enforcement and which utilizes firm-level data. For a discussion of the differences between additive and multiplicative theories of risky decisions as applied to the compliance domain, see Casey and Scholz (1989). Viscusi suggests that the disparity in effectsbetween amount of penalty and inspections (with or without penalty) may be due to costsother than penalties associated with inspections.

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