Is Workers' Compensation a Substitute for Unemployment Insurance?

Journal of Risk and Uncertainty, 18:2; 165᎐188 Ž1999. 䊚 1999 Kluwer Academic Publishers. Manufactured in The Netherlands.

Is Workers’ Compensation a Substitute for Unemployment Insurance?* BERNARD FORTIN

[email protected]

´ Professor, Department of Economics and CREFA, Uni¨ ersite´ La¨ al, Quebec, Canada, G1K 7P4 PAUL LANOIE

´ ´ Professor, Ecole des Hautes Etudes Commerciales and CIRANO, Montreal, Canada, H3T 2A7 CHRISTINE LAPORTE Human Resources De¨ elopment Canada

Abstract This paper examines how the Workers’ Compensation ŽWC. and Unemployment Insurance ŽUI. programs interact to influence the duration of claims due to workplace accidents. We use longitudinal WC administrative micro-data on more than 30,000 workers in the Canadian construction industry for the period 1976᎐1986. For the estimations, we use the Meyer Ž1990. semi-parametric proportional hazard model. Our results show, in particular, that a reduction in the UI replacement ratio is associated with an increase in the duration of claims due to severe accidents that are difficult to diagnose. Moreover, the duration of spells on WC is much higher when an accident occurs in December, a month which corresponds to the beginning of the lay-off season in the construction sector. This result is consistent with the fact that WC benefits are more generous than UI benefits in Canada. Key words: moral hazard, unemployment insurance, workers’ compensation, risk, uncertainty JEL Classification: J3, H8, D81, J28, J65

Introduction The social cost of workplace accidents is large. In a typical year in the United States, from one-third to one-half as many working days are lost to work injuries as are lost to unemployment Žsee Krueger, 1988.. Recently, economists have paid more attention to the economic issues involved in occupational safety and health Žsee Lanoie Ž1994. for a survey.. In particular, they have investigated the different effects of government intervention in this area. For example, it has been found that, in general, safety regulations and their enforcement have little impact on the incidence of workplace accidents. There also seems to be a consensus on the fact that an increase in the generosity of workers’ compensation ŽWC. benefits is associated with an increase in both the frequency and the duration of claims due to workplace accidents ŽFortin and Lanoie, 1998..

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FORTIN, LANOIE AND LAPORTE

In this connection, some researchers have raised a potentially important issue: the possible substitution between WC and unemployment insurance ŽUI.. In most countries, WC is more generous than UI in terms of wage replacement,1 and there may therefore be an incentive for workers about to be laid off to try to benefit from WC instead of UI. Workers suffering from a workplace accident may also be tempted to take action in order to obtain a longer period of recovery compensated by WC. These ex ante and ex post moral hazard problems are likely to be particularly important when injuries are hard-to-diagnose Že.g., low-back injuries. and in industries where the level of unemployment is such that many workers may expect to be unemployed and to receive UI benefits after their recovery Že.g., in seasonal industries such as the Canadian construction sector, which is less active during winter because of climate constraints .. Fortin and Lanoie Ž1992. were the first authors to investigate some of these issues. In particular, from Quebec aggregate data at the industry level, they found that a reduction in the generosity of UI was associated with an increase in the average duration of work absences compensated by WC following a workplace accident. More investigation is required to provide further support for this initial result. In particular, as in Dionne and St-Michel Ž1991. and Butler et al. Ž1996., our data on the nature of the diagnosis lead us to explicitly test for the existence of moral hazard behavior. Indeed, hard-to-diagnose injuries introduce an informational asymmetry that can be used for personal gain. The theoretical model, based on an extension of a discrete choice model to continuous time, considers the hazard of returning to the labor market after an absence due to a workplace accident.2 Previous authors who have examined this hazard have used, in general, a standard job search theoretical approach where a worker goes back to work if he receives a wage offer greater than his reservation wage Že.g., Johnson and Ondrich, 1990.. This framework may not be appropriate for two reasons. First, it does not explicitly take into account the physician’s behavior in the process and the possibility of the worker being controlled by the Workers’ Compensation Board-WCB Žsee Dionne and St-Michel, 1991.. Second, most accident victims Ž75% in our sample. eventually go back to their previous job with no job search Žsee Butler and Worrall, 1985.. Our approach takes these issues into account in modeling the worker’s decision to leave WC. Moreover, we explicitly model the fact that workers’ health condition must improve before they are able to go back to the labor market Ži.e., before they can accept a wage offer.. For this purpose, we suppose that the recovery process is stochastic. To our knowledge, only Butler et al. Ž1995. have considered this issue, but their analysis is based on permanent disability cases for which total recovery is not possible. In a sense, our analysis generalizes their approach to temporary total disabilities. Finally, we introduce the possible interaction between WC and UI, i.e., when a worker goes back to the labor market, he does not necessarily return to his previous job immediately, he may also be unemployed and entitled to UI payments for a certain period. Amongst the theoretical predictions of the model, we find that the WC replacement ratio should have a negative impact on the hazard of

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returning to the labor market, while the UI replacement ratio should have a positive impact. The econometric section presents reduced-form estimates of the theoretical model and provides tests of its main predictions. For these estimates, we use the now familiar mixed proportional hazard model, devised by Meyer Ž1990., which does not impose a parametric form on the baseline hazard and takes unobserved heterogeneity into account using a gamma distribution. The database is composed of longitudinal WC administrative micro-data on more than 30,000 workers for 1976᎐86. The rest of the paper is organized as follows. Section 1 presents a brief description of the Quebec WC and UI systems. Section 2 discusses the theoretical model and its implications. Section 3 presents the estimate strategy and the data. Section 4 analyzes the results. In brief, these results support the hypothesis that a reduction in the UI replacement ratio and an increase in that of the WC program are both associated with an increase in the duration of accidents, especially in the case of workers with injuries that are difficult to diagnose. Furthermore, there seems to be an important seasonal effect in the duration of accidents; i.e., those occurring in December Žat the end of the construction season for a majority of workers. are likely to last longer, ceteris paribus. This result is also consistent with the presence of a significant interaction between WC and UI in determining individuals’ risk of accident. Section 5 presents concluding remarks.

1. Description of the workers’ compensation and unemployment insurance systems Estimating the model for the province of Quebec is of interest given the nature of its WC and UI systems. Before discussing the model, it is useful to provide a short description of both programs. The Quebec WC plan is mainly a public plan administered by a public corporation, the Commission de la Sante ´ et de la Securite ´ ´ Ž . du Travail du Quebec CSST . Firms are considered liable for workplace accidents ´ and pay insurance premiums to the CSST, which then compensates accident victims. The plan is partially experience rated. If the premium paid by a firm is greater than a threshold level, it is adjusted to reflect the firm’s own claim experience. More than 95% of the workforce is covered by WC insurance. Since 1979, the CSST has paid the accident victim 90% of net income Žnon-taxable . up to a maximum Ž$961 per week in 1998., in case of a temporary total disability Žthe most common case.. Before 1979, an accident victim received 75% of his gross wage Žnon-taxable .. The year 1979 was in fact characterized by many institutional changes in Quebec WC. All the inspection activities that were under the jurisdiction of four different government departments were concentrated in the same organization ŽCSST.. Furthermore, the board opened new regional offices to handle local compensation claims, an operation which, until that date, was performed centrally in Montreal and Quebec City.

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When an accident occurs, the worker provides a medical certificate from his own physician Žattesting the validity of the claim. to the WC Board, and is immediately entitled to compensation. This contrasts with many other jurisdictions where the physician is designated by the WC Board. The compensation lasts as long as his physician attests that the worker is not rehabilitated. When the worker comes back to work, his employer is forced to rehire him Žhowever, this feature of the law was not in force at the time our data was collected.. The UI plan is also a public plan, administered by the federal government of Canada and covering around 90% of the workforce. Employers and employees contribute to the UI system, but there is no experience rating mechanism. In order to qualify for UI payments, an employee must have worked a minimum number of hours, with this threshold level varying regionally across the country depending on local economic conditions. A worker who quits his job voluntarily is not entitled to UI payment Žthis feature of the law was not in force for the period covered by our data.. Once eligible, a worker is entitled to UI payments for a maximum number of weeks, which also varies by region. He receives 55% of his gross wage Žsubject to taxation. up to a maximum. This percentage was as high as 60% between 1970 and 1979, and 60% between 1979 and 1994. In 1998, the maximum gross weekly insurable income was $750. The waiting period is two weeks.

2. Theoretical model As in many other papers Že.g., Dionne and St-Michel, 1991., for tractability, we concentrate on workers’ behavior.3 The model is assumed to be a standard discrete choice model in continuous time Že.g., Olsen et al., 1986. that is consistent with a hazard framework. Let us consider a representative construction worker who faces an illness or injury that prevents him from doing his job. During his absence from the labor market, he receives compensation from WC. Conditional upon receiving new information at time t, his choice whether or not to continue his recovery period depends on a comparison between his indirect utility at t when he receives WC payments ŽUt w c . and his indirect expected utility if he goes back to the labor market ŽUt l .. Under the assumption that his preferences and constraints are both temporally separable, his choice is consistent with maximizing his discounted expected utility over the rest of his lifetime. The formulation of the hazard associated with this model first requires the derivation of the indirect utility attached to each alternative. There are two possible states of nature associated with the alternative of re-entering the labor market. First, with a probability Pt , the worker can return to his previous job in the construction industry, which yields an ex-post utility Ut j. Second, with a probability Ž1 y Pt ., seasonal or economic conditions are such that the worker cannot find a job in the construction industry and he receives unemployment payments Žassuming he is eligible..4 His ex-post utility is then Ut u. It is assumed that the individual’s ex-post utility is greater when he is working in the


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construction sector than when he is unemployed. More precisely, we assume that, in the range of the values of the variables that influence U j and U u, one has Ut j ) Ut u. The expected utility of the worker when he is on the labor market is thus: Ut l s Pt Ut j q Ž 1 y Pt . Ut u ,

Ž 2.1.

where Pt s P Ž m t , u t , ␹ t , st . .

Ž 2.2.

The variable m t refers to the month of the year corresponding to time t. It is expected that during the pre-winter months Žsay, November and December., the probability of finding a job Žor going back to an earlier job. is lower. u t is a variable capturing the cyclical evolution of economic activity in the construction industry Že.g., regional unemployment rate.. It is expected that Pu - 0. The variable ␹ t is a t vector of individual characteristics that may influence the probability of finding a job Žage, qualification, etc... Finally, st is a measure of the severity of residual disability at t, with Ps t assumed to be negative. The variable st is the realization of a random process since the recovery process is itself random. It is assumed that the residual disability declines over the recuperation period but also depends on the initial severity of the injury Žor illness ., s, on individual characteristics, ␹ t ,5 and on a random term, ⑀ t , reflecting the randomness at time t in the recovery process. ⑀ t is unknown to the econometrician but is assumed to be observed by the worker before he makes his decision at t. We thus have: st s S Ž t , s, ␹ t , ⑀ t . .

Ž 2.3.

It is assumed that St F 0, S s G 0 and S⑀ t ) 0 where, for convenience, we make no notational distinction between the random term and its realization. Moreover, for simplification, we suppose that ⑀ t is a white noise with a distribution function F Ž ⑀ t .. Therefore, the ⑀ ’s are assumed to be temporally independent.6 The individual’s ex-post level of utility in each state of nature is influenced positively by his net income, the level of leisure Žwhich, for simplicity, only takes two values: 0 when the individual works, 1 when he does not., his residual disability and a vector of personal characteristics. When the individual returns to his job, his utility is given by: Ut j s U j Ž wt , 0, st , ␹ t . , with Uwj t ) 0; Us t - 0,

Ž 2.4.

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where wt denotes his net wage rate at t. When the individual receives UI payments, his utility level is: Ut u s U u Ž ui t , 1, st , ␹ t . ,

Ž 2.5.

with Uuiu t ) 0; Usut - 0, where ui t is the net UI compensation. Substituting Ž2.2., Ž2.3., Ž2.4. and Ž2.5. into Ž2.1. yields the individual’s indirect expected utility, conditional upon his returning to the labor market: Ut l s V l Ž z tl , t , ⑀ t . ,

Ž 2.6.

where z tl s Ž m t , u t , ␹ t , wt , ui t , s . , with Vult - 0; Vwl t , Vuil t ) 0; Vsl ,V⑀ lt F 0, Vt l G 0. The alternative choice for the worker is to receive WC compensation. In deriving the worker’s utility in this situation, one must take into account the cost he incurs to obtain an additional period of compensation. Its level partly depends on the behavior of both the physician and the WCB. In our framework, it is assumed that the physician is a neutral agent of the worker, who is the principal. This is justified by the fact that, in Quebec, the role of the worker’s own physician is crucial in determining the validity of a workplace accident Žsee Lanoie, 1994.. The physician decides the number of days of absence covered by the WCB, with possible revisions of his decision Žinvolving new medical reports to the WCB., as new information on the recovery process is received. His choice is assumed to maximize the worker’s expected utility of each period subject to the latter’s constraints and to any cost the worker faces in this decision. This cost reflects Žin certainty equivalence. the probability of rejection of the physician’s reports by the WCB. This may involve a costly and stressful process of examinations by other physicians, testifying at arbitration hearings, and possible delays in WC benefit payments. One expects the cost of obtaining an extra day on WC to be decreasing with the initial severity of the accident but increasing with the number of extra days desired. Moreover, this cost is likely to be lower in the case of an injury that is hard to diagnose Že.g., low-back injury.. In line with this discussion, the individual’s utility when receiving WC is given by: Ut w c s U w c Ž wc t y c Ž t , s, ␹ t , d . , 1, st , ␹ t . ,

Ž 2.7.

with UwwcctycŽ⭈. ) 0; Uswt c - 0, where wc t is the WC compensation net of taxes Žit is assumed that wc t ) ui t ., d is a measure of the difficulty of the diagnosis and cŽ⭈. is the cost of obtaining an extra


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period of compensation under WC, with c t Ž ⭈ . G 0; c s Ž ⭈ . F 0; c d Ž ⭈ . F 0. Substituting Ž2.3. into Ž2.7. yields the indirect utility of the worker on WC: Ut w c s V w c Ž z tw c , t , ⑀ t . ,

Ž 2.8.

where z tw c s Ž ␹ t , s, wc t , d . , with Vs w c F 0; Vwwcct , Vdw c ) 0; Vt w c s ?; V⑀ wt c - 0. The decision process is assumed to take the following form. New values of the error term Ž ⑀ ., reflecting the randomness of the recovery process, arrive at random intervals. When this new information arrives, the preferred alternative is chosen.7 Following Olsen et al. Ž1986., we assume that the arrival of new information follows a Poisson process with constant rate ␯ . Since the error terms are temporally independent, the instantaneous rate of exit from WC at t, given that the duration has lasted until t, is given by:

␭Ž z t , t . s ␯ Prob Ž V l Ž z tl , t , ⑀ t . G V w c Ž z tw c , t , ⑀ t . . ,

Ž 2.9.

where z t s z tl D z tw c. Equation Ž2.9. yields the hazard function of the model. Let us define ⑀ tc as the critical level of ⑀ for which V l Ž⭈. s V w c Ž⭈.. Isolating ⑀ tc in this equation yields ⑀ tc s ⑀ c Ž z t , t .. Moreover, assuming that a more severe residual disability reduces the worker’s utility level more when he is on the labor market than when he is on WC, one obtains: V⑀ wt c G V⑀ lt. Therefore, Ž2.9. becomes

␭Ž z t , t . s ␯ Prob Ž ⑀ t F ⑀ c Ž z t , t . . s ␯ F Ž ⑀ c Ž z t , t . . .

Ž 2.10.

It is easy to show that:

␭ u t , ␭ w c t - 0; ␭ d , ␭ s F 0; ␭ w t , ␭ ui t , ␭ t ) 0. Hence, the level of unemployment in the construction industry Ž u t ., the level of wc t , the degree of difficulty in diagnosing the nature of the injury or illness Ž d . and its initial severity Ž s . all have a negative influence on the rate of exit from WC. The wage Ž wt . has a positive influence on this hazard since it can be thought of as a component of the worker’s opportunity cost of time during his recovery period. Similarly, an increase in the level of ui t will have a positive effect on the hazard of leaving WC. The effect of the spell duration Ž t . on the rate of exit from WC is expected to be positive for two reasons: first, as time goes by, the worker is likely to have recovered from his injury, which increases his utility at work relative to his utility on WC. Second, the cost of obtaining extra days on WC is likely to be increasing, since a worker is less likely to find an accommodating doctor as this number increases.

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Moreover, Dionne and St-Michel Ž1991. have convincingly argued that, by stimulating moral hazard, a more difficult diagnosis is likely to amplify the effect of variables such as the wage rate and the generosity of WC Žand of UI. on the rate of exit from WC. In terms of our model, these hypotheses imply the following inequalities:

␭ w t , d , ␭ ui t , d G 0; ␭ w c t , d F 0. One other implication of our model is that the rate of exit from WC is likely to be lower, ceteris paribus, in the pre-winter months, the lay-off season in the construction sector. The reason is that a worker facing a workplace accident in December, for example, has a higher probability of becoming unemployed upon his return to the labor market after his recovery, than if the same accident occurs, say, in July. This is the case since the duration of claims is usually not very long Ž31 days on average, in our sample.. Therefore, he has a greater incentive to attempt to prolong his period on WC, given that the WC replacement ratio is greater than the UI ratio.

3. Empirical methods and data To estimate the reduced-form model given by Equation Ž2.10., we adopt the following mixed proportional hazard specification with unrestricted baseline hazard ŽMeyer, 1990.:

␭Ž z, t . s ␭0 Ž t . exp Ž z⬘␤ q ⑀ . ,

Ž 3.1.

where ␭0 Ž t . is the baseline hazard Ži.e., the part common to all individuals., z is a vector of covariates, ␤ is a vector of parameters to be estimated and ⑀ is a random variable reflecting unobserved heterogeneity. Note that, since the duration of spells on WC is of 31 days on average, we do not allow for time varying covariates. This approach has the advantage of providing non-parametric estimates of the baseline hazard while accounting for unobserved heterogeneity. As is well known, ignoring unobserved heterogeneity may lead to a dynamic selection bias in the parameter estimates and in the estimate of the baseline hazard ŽLancaster, 1990.. For example, as time goes by, it is possible that workers who do not return to the labor market are those with an intrinsic bad health condition. If one does not account for this unobserved heterogeneity, one may end up with the mistaken impression that the hazard declines through time Žnegative bias on the estimate of the baseline hazard.. A convenient and commonly used distribution for exp Ž ⑀ . is the gamma distribution with mean normalized to one and variance ␴ 2 . Under this assumption and given observations of failure times over the discrete periods t s t 0 , t 1 , t 2 , . . . , t Ty1

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for individuals i s 1, . . . , N, the resulting log-likelihood is given by ŽMeyer, 1990.: N

LŽ␥ , ␤ , ␴

2

.s Ý is1

log

½

y␴ y2

k iy1

1q␴ ⭈ 2

Ý

exp ␥ t j q

zXi

␤4

js0 y␴ y2

ki

y␦ i 1 q ␴ 2 ⭈

Ý js0

exp ␥ t j q

zXi

␤4

5

Ž 3.2.

where ␥ t j s lnŽ Ht tj jq 1␭ 0 Ž␷ . d␷ ., ␥ s w ␥ t 0 , ␥ t 1, . . . , ␥ t Ty 1 x, z i is a vector of covariates for individual i, ␦ i s 1 if the duration for individual i is not Žright. censored, s 0 otherwise, t k i is the observed Žcensored or not. duration of individual i’s spell on WC, and expŽ␥ t j .rŽ t jq1 y t j . represents the average baseline hazard over the interval w t j , t jq1 x. Data and ¨ ariables The analysis uses longitudinal administrative micro-data. The original data source for this study follows the evolution of 30,341 workers in the construction industry who worked at least one hour at the James Bay hydro-electric project Ža major dam construction undertaking in Northern Quebec. during the period 1976᎐86. These data from the Quebec board responsible for the construction industry ŽCommission de la construction du Quebec or CCQ. were matched with data from the Quebec ´ Ž . WCB CSST , so that we were able to follow the work pattern Žnumber of hours worked, occurrence of an accident, etc.. of the workers throughout this period as long as they were working in the construction industry.8 During the period, we count in the sample 8,523 workplace accidents with time lost involving 6,067 workers.9 Descriptive statistics for the sample are given in Table 1. From this table, one can see that the average duration of accidents is 31.2 days with a relatively large standard deviation of 66.1. We now turn to the explanatory variables Žthe vector z . used in the estimates. As in other studies using micro-data Že.g., Moore and Viscusi, 1990., the WC replacement ratio Žbenefits divided by the pre-WC net marginal wage. has been calculated individually using information on the WC parameters and on the provincial and federal income tax systems in place in each year Žsee Appendix.. The mean WC replacement ratio in our sample Žsee Table 1. is 114%. One reason why it is greater than 100% is that, under the Quebec WC regulations, benefits calculation is based on the earnings of the 12 months preceding the accident. In this calculation, the worker is imputed the same average weekly income for his period off construction as he earns during the construction season, which tends to increase the numerator of the ratio. Second, since WC benefits are not taxable and are based either on gross wages Žbefore 1979. or on net average wages Žafter 1979.,

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Table 1. Descriptive statistics.a, b

Variable Duration Žin days. on WC WC replacement ratio UI replacement ratio Real marginal weekly wage rate Real weekly WC benefits Real weekly UI benefits Žbefore tax. Regional unemployment rate Mineasy Majeasy Minhard Majhard Age Dependents Years of qualification Quebec Abitibi James Bay January February March April May June July August September October November December Censored Žs 1 if right-censored. a b

Mean

Standard deviation

Minimum

Maximum

31.22 1.14 0.57 288.99 329.25 272.48 12.55 0.40 0.12 0.18 0.29 37.17 0.52 1.41 0.15 0.06 0.22 0.05 0.05 0.06 0.06 0.08 0.09 0.08 0.12 0.12 0.13 0.11 0.07 0.01

66.12 0.11 0.07 114.77 135.29 122.72 2.81 0.49 0.33 0.39 0.45 9.75 0.17 1.50 0.35 0.24 0.42 0.22 0.23 0.23 0.23 0.26 0.28 0.26 0.32 0.32 0.33 0.31 0.25 0.11

2.00 0.47 0.20 5.33 3.81 4.08 6.90 0.00 0.00 0.00 0.00 18.00 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1869.00 1.43 0.67 1158.28 910.98 680.65 21.60 1.00 1.00 1.00 1.00 66.00 0.65 4.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

N s 8523. Benefits and wage are in 1981 Canadian dollars.

the Žmarginal. replacement ratio may be higher than 100% for workers with a marginal tax rate higher than a critical level. Because of the institutional changes introduced in 1979 in the Quebec WC system Žas described in Section 2., in most specifications, we introduce two variables to capture the generosity of WC: log WCRB79 Žlog WCR times a dummy equal to one for each observation before 1979. and log WCRA79 Žlog WCR times a dummy equal to one for each observation in the years 1979᎐1986 inclusively.. The UI replacement ratio is also calculated individually and is 0.57, at the mean of our sample. The variable UNEMP is defined as the monthly regional unemployment rate as determined by Statistic Canada Žavailable for 12 regions.. We take the


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unemployment rate prevailing at the moment the accident occurs. The WAGE is measured by the worker’s hourly wage rate Žin 1981 dollars.. There is substantial literature showing that the wage and occupational safety levels are the result of a simultaneous decision process Že.g., Garen, 1988., making the wage rate Žand replacement ratios. an endogenous variable.10 Moreover, individual unobservable characteristics that affect the wage rate Že.g., motivation to work. may also influence the rapidity of return to work after an accident. For these reasons, in most specifications, the wage variable and the two replacement ratios Žall in log. have been replaced by generated regressors in the likelihood function, following a two-step approach suggested by Pagan Ž1984. and used, for instance, by Dolton and Van Der Klauw Ž1995. to estimate a mixed proportional hazard model.11 The initial severity of the injury and the nature of the diagnosis are also part of the analysis. Of course, more severe injuries should be followed by longer recovery periods. Moreover, it may be easier for workers to extend their recovery period when they have a hard-to-diagnose injury Že.g., low-back injury., and one should also account for the fact that hard-to-diagnose injuries may be intrinsically more or less severe than others. For these reasons, and following Dionne and St-Michel Ž1991., we consider four categories of accident: Ž1. minor injuries with easy diagnosis, MINEASY; Ž2. minor injuries that are hard to diagnose, MINHARD; Ž3. major injuries with easy diagnosis, MAJEASY; and Ž4. major injuries that are hard to diagnose, MAJHARD. These are entered as dummy variables ŽMINEASY is default.. As discussed in Dionne and St-Michel, this categorization was established in consultation with a physician specializing in work-related health problems.12 As shown in the theoretical section, the difficulty of establishing the diagnosis may also interact with some other explanatory variables in influencing the individual’s decision over the possible extension of his recovery period. For instance, it may be more tempting for a worker whose injury is hard to diagnose to seek such an extension when UI becomes less generous and when he knows that he will be laid off if he goes back to work. Interaction terms between the dummies MINHARD and MAJHARD Žwhich, in particular, refer to various categories of back disorders. and other covariates such as the wage rate and replacement ratios have therefore been introduced in some specifications. Initial investigation showed that four interaction terms persistently had a significant coefficient: Žlog UIR.) MAJHARD, Žlog WCRB79.)MINHARD, Žlog WCRA79.)MINHARD and Žlog WAGE.)MINHARD. In keeping with our theoretical discussion, we also consider monthly dummy variables to capture the fact that workers may have more incentive to extend their period of recovery if their accident happened just before the usual lay-off season in the construction industry. Therefore, we expect the coefficients of dummy variables for months like NOVEMBER and DECEMBER to be positive and significant ŽJULY is default.. Furthermore, three personal characteristics Ž ␹ t . are taken into account. First, the AGE of the accident victim is introduced, since it is generally accepted Že.g., Butler and Worrall, 1991. that, ceteris paribus, the capacity to recover physically

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from the effects of injuries declines with age. Second, a variable capturing the level of QUALIFICATION of the worker is included. It is defined as the number of working years required to qualify as a registered member of a given occupation within the construction industry Že.g., carpenter.. This variable is intended to capture the worker’s skill level. As in Johnson and Ondrich Ž1990., it is expected that more skilled workers are better able to avoid severe accidents, or that they have more flexibility to re-enter the labor force rapidly than less skilled workers. Another interpretation may be that longer qualification time signals less physically difficult Žand less dangerous. jobs. Third, a proxy for the number of dependent children ŽDEPENDENTS. is included. Our data set does not provide direct information on the latter variable. However, given the age of each worker and general demographic information on workers in the Quebec construction industry Žfrom the 1981 Canadian Census., we were able to calculate a variable approximating the number of dependent children. The expected sign of the coefficient on this variable is positive. Indeed, if the worker provides income support to a large family, he may be induced to leave WC rapidly. In addition, we consider 12 REGIONAL dummies to capture the fact that the nature of the construction projects may vary from one region to another Žespecially at James Bay., leading to different types of accidents. After some experimentation, dummies for the regions of Quebec, James Bay and Abitibi were used in estimates Žother regions are default.. Finally, we introduce year dummies to capture omitted fixed influences that vary across time, but not across individuals. These dummies may be useful to account for institutional changes in unemployment insurance and occupational safety policies Žlike changes in safety-enhancing measures. during the period that may not be captured with our WC and UI variables.

4. Empirical results Our estimate results are presented in Table 2. The preceding discussion leads to a general specification using the two-step estimating method involving generated regressors for the wage and replacement ratios. In order to identify the model, we adopted the standard approach used in the estimation of labor supply models Že.g., Mroz, 1987.; that is, in the first step, we introduce a polynomial in some exogenous variables that appear in the hazard function. After some experimentation, the variables we used in the first-step regressions are all the exogenous covariates used in the second step and age 2 , age 3 , qualification 2 , qualification 3 , plus interaction terms between age and qualification Žup to the second degree.. These additional variables Žwhich are all statistically significant . impose over-identifying restrictions to the model. This specification is presented in column Ž1.. In order to assess the validity of the general specification and to test certain specific restrictions, six other specifications are presented. In particular, we examine how our main results are affected when we do not consider the institutional changes occurring in 1979

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Table 2. Hazard model estimates Žstandard errors in parentheses .. Specification Variable Log UIR ŽLog UIR.*MAJHARD Log WCR ŽLog WCR.*MINHARD Log WCRB79 Log WCRA79 ŽLog WCRB79.* MINHARD ŽLog WCRA79.* MINHARD Log WAGE ŽLog WAGE.* MINHARD Log UNEMP MAJHARD MAJEASY MINHARD DEPENDENTS QUALIFICATION Log AGE QUEBEC ABITIBI JAMES BAY JANUARY FEBRUARY MARCH

Ž1.

Ž2.

Ž3.

Ž4.

Ž5.

Ž6.

Ž7.

y0.377 Ž0.844. 2.844 Ž1.415. ⭈ ⭈ ⭈ ⭈ y0.913 Ž1.857. 0.839 Ž1.883. y5.936 Ž1.828. y9.082 Ž2.528. y2.276 Ž0.569. 0.397 Ž0.148. 0.461 Ž0.146. 0.407 Ž0.716. y2.176 Ž0.101. 1.919 Ž1.441. y0.445 Ž0.696. 0.115 Ž0.027. y0.896 Ž0.110. 0.158 Ž0.070. y0.574 Ž0.099. y1.709 Ž0.097. 0.082 Ž0.126. 0.093 Ž0.124. 0.063 Ž0.123.

y0.148 Ž0.782. 2.378 Ž1.385. y0.946 Ž1.323. y3.029 Ž1.522. ⭈ ⭈ ⭈ ⭈ ⭈ ⭈ ⭈ ⭈ y2.279 Ž0.564. y0.549 Ž0.693. 0.466 Ž0.145. y0.175 Ž0.702. y2.170 Ž0.101. 1.100 Ž1.412. 0.422 Ž0.142. 0.116 Ž0.027. y0.873 Ž0.101. 0.160 Ž0.070. y0.577 Ž0.098. y1.706 Ž0.096. 0.083 Ž0.126. 0.093 Ž0.123. 0.061 Ž0.122.

y0.342 Ž0.209. 0.601 Ž0.318. ⭈ ⭈ ⭈ ⭈ 1.432 Ž0.385. 3.520 Ž0.284. 2.312 Ž0.661. 0.522 Ž0.538. y0.089 Ž0.079. 0.119 Ž0.125. 0.430 Ž0.130. y0.635 Ž0.184. y1.886 Ž0.089. 1.978 Ž1.009. y0.373 Ž0.142. y0.003 Ž0.014. y0.998 Ž0.085. 0.175 Ž0.063. y0.479 Ž0.089. y1.348 Ž0.081. y0.036 Ž0.114. y0.036 Ž0.112. y0.060 Ž0.111.

y0.314 Ž0.541. 0.814 Ž0.797. ⭈ ⭈ ⭈ ⭈ 0.020 Ž1.018. 1.268 Ž0.950. y2.741 Ž0.882. y3.569 Ž1.122. y0.851 Ž0.270. 0.105 Ž0.076. 0.223 Ž0.067. y0.146 Ž0.405. y0.850 Ž0.045. 0.476 Ž0.664. y0.075 Ž0.325. 0.045 Ž0.013. y0.512 Ž0.054. 0.119 Ž0.031. y0.274 Ž0.051. y0.714 Ž0.044. y0.049 Ž0.059. y0.030 Ž0.062. y0.029 Ž0.060.

y0.020 Ž0.946. 5.256 Ž1.746. ⭈ ⭈ ⭈ ⭈ y1.814 Ž2.314. 1.531 Ž2.342. y6.839 Ž2.305. y11.184 Ž3.240. y2.877 Ž0.717. y0.660 Ž0.879. 0.631 Ž0.190. 1.434 Ž0.884. y3.317 Ž0.111. 2.615 Ž1.819. 0.502 Ž0.183. 0.138 Ž0.034. y1.095 Ž0.135. 0.195 Ž0.092. y0.629 Ž0.125. y2.337 Ž0.112. 0.146 Ž0.158. 0.225 Ž0.156. 0.135 Ž0.153.

y0.715 Ž0.484. 1.032 Ž0.706. ⭈ ⭈ ⭈ ⭈ 0.321 Ž0.915. 1.511 Ž0.812. y3.665 Ž0.758. y4.929 Ž0.932. y1.252 Ž0.223. 0.754 Ž0.267. 0.250 Ž0.058. y0.094 Ž0.359. y0.868 Ž0.030. y1.000 Ž0.544. 0.104 Ž0.063. 0.046 Ž0.011. y0.570 Ž0.044. 0.164 Ž0.027. y0.251 Ž0.042. y0.754 Ž0.035. y0.011 Ž0.050. 0.020 Ž0.054. y0.028 Ž0.047.

⭈ ⭈ 2.735 Ž1.283. ⭈ ⭈ ⭈ ⭈ ⭈ ⭈ ⭈ ⭈ y5.838 Ž1.719. y8.911 Ž2.368. y2.312 Ž0.555. 0.427 Ž0.139. 0.465 Ž0.146. 0.351 Ž0.649. y2.175 Ž0.101. 1.882 Ž1.443. y0.442 Ž0.696. 0.117 Ž0.026. y0.869 Ž0.096. 0.159 Ž0.070. y0.574 Ž0.099. y1.713 Ž0.094. 0.081 Ž0.126. 0.094 Ž0.124. 0.063 Ž0.123.

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Table 2. ŽContinued.. Specification Variable APRIL

Ž1.

Ž2.

0.181 Ž0.123. 0.184 Ž0.116. y0.055 Ž0.111. 0.099 Ž0.105. 0.026 Ž0.104. 0.010 Ž0.103. y0.111 Ž0.105. y0.284 Ž0.116. ⭈ ⭈ ⭈ ⭈ 1.508 Ž0.100. 8523

0.180 Ž0.123. 0.180 Ž0.116. y0.059 Ž0.110. 0.098 Ž0.105. 0.022 Ž0.104. 0.009 Ž0.103. y0.112 Ž0.104. y0.293 Ž0.116. ⭈ ⭈ ⭈ ⭈ 1.496 Ž0.100. 8523

Ž3.

Ž4.

Ž5.

Ž6.

Ž7.

0.069 0.005 0.276 0.057 0.181 Ž0.112. Ž0.059. Ž0.155. Ž0.051. Ž0.123. MAY 0.091 0.073 0.209 0.090 0.183 Ž0.105. Ž0.056. Ž0.145. Ž0.044. Ž0.116. JUNE y0.103 y0.032 y0.041 y0.041 y0.057 Ž0.101. Ž0.056. Ž0.137. Ž0.040. Ž0.111. AUGUST 0.089 0.051 0.150 0.027 0.098 Ž0.095. Ž0.052. Ž0.130. Ž0.039. Ž0.105. SEPTEMBER 0.005 y0.080 0.078 y0.149 0.026 Ž0.095. Ž0.050. Ž0.130. Ž0.037. Ž0.104. OCTOBER y0.004 y0.040 0.046 y0.094 0.011 Ž0.093. Ž0.051. Ž0.128. Ž0.039. Ž0.103. NOVEMBER y0.154 y0.166 y0.044 y0.208 y0.110 Ž0.095. Ž0.051. Ž0.132. Ž0.040. Ž0.105. DECEMBER y0.311 y0.209 y0.231 y0.340 y0.284 Ž0.105. Ž0.060. Ž0.145. Ž0.040. Ž0.116. ␩ ⭈ ⭈ 0.003 0.074 ⭈ Ž0.001. Ž0.002. ⭈ ⭈ ⭈ ␣ ⭈ ⭈ 2.746 0.808 ⭈ Ž0.073. Ž0.006. ⭈ ⭈ ⭈ Heterogeneity 1.137 ⭈ 2.814 ⭈ 1.508 Ž0.079. Ž0.113. Ž0.100. variance ⭈ ⭈ Sample size 8523 8523 8523 8523 8523 40 Log-likelihood y27942.00 y27946.69 y27860.78 y28209.73 y28764.02 y30639.83 y27942.25 value a Fixed effects for years have also been introduced.

Žspecification Ž2.., when the two-step estimating method is not used Žspecification Ž3.., when we do not account for unobserved heterogeneity Žspecification Ž4.., and when a standard parametric form ŽWeibull. is assumed for the baseline hazard Žspecifications Ž5. and Ž6.: with and without gamma-distributed heterogeneity effects .. Specification Ž7. presents a slightly modified version of specification Ž1. where the coefficients of UI and WC replacement ratios Žnon-significant in specification Ž1.. are constrained to zero.13 In general, the sign, the magnitude and the precision of the covariate coefficients are robust across specifications using the two-step estimation method, although slight differences appear in the Weibull specifications. In discussing the results, we will first focus on specification Ž1. that is representative of the set of results. The UI replacement ratio Žwhen combined with MAJHARD. has a positive and significant coefficient, indicating that a reduction in this variable induces workers with a major hard-to-diagnose injury to stay longer on WC. Using specification Ž1.,


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our results imply that a reduction of 1% in the UI replacement ratio is associated with a decrease of 2.7% in the conditional hazard of leaving WC for these workers. Over all workers and at the sample mean of the covariates, the resulting elasticity of the expected duration of claims with respect to UI 14 is estimated at y0.54. The magnitude of this result is close to the elasticity of y0.5 reported in Fortin and Lanoie Ž1992.. Second, both the WC wage replacement ratios Žbefore and after 1979., when combined with MINHARD, have negative and significant coefficients, which means that WC induces workers suffering from a minor hard-to-diagnose injury to go back onto the labor market later. Based on results from specification Ž1., an increase of 1% in the generosity of WC is estimated to induce a 0.71% increase in the expected spell duration before 1979, and 1.09% after 1979, at the sample mean of the covariates. One possible explanation for the stronger impact after 1979 is that, as mentioned earlier, in 1979, the Quebec WCB opened new regional offices to handle local compensation claims, an operation which, until that date, was performed centrally in Montreal and Quebec City. According to WCB officials Žsee CSST, 1984., this has made accident reporting easier, thus enhancing any potential moral hazard effect that our WC variables are capturing. Note that in specification Ž2., where the WC replacement ratio is not divided into two components Žbefore and after 1979., its effect on the hazard rate Žwhen combined with MINHARD. is still negative, as in the rest of the literature, but less significant. Moreover, a likelihood ratio test Žwith an ␹ 2 statistic of 9.38. rejects the equality of the WCR coefficients before and after 1979. This suggests that it is warranted to account for the significant policy changes occurring in 1979᎐1980. The estimated impact of the WC ratio on duration for each sub-period is relatively strong compared with the rest of the literature. Typical WC duration elasticities vary between 0.2 and 0.6 Že.g., Meyer et al., 1995., although one study ŽKrueger, 1990. finds duration elasticities over 1.5. A number of reasons could be advanced to explain such a result. First, the construction industry presents certain characteristics Žregular lay-offs. that make substitution between the two insurance regimes much more likely than in other sectors of economic activity. Moreover, it is likely that intertemporal labor supply elasticity is higher in the case of individuals who choose to work in a seasonal industry. Second, as mentioned earlier, in Quebec, in contrast with other jurisdictions, the role of the worker’s doctor is crucial in determining the duration on WC. Therefore, moral hazard is likely to be more important than elsewhere. Third, the American studies do not account for the possible interaction between the two insurance regimes, which may bias their results.15 Fourth, there is no waiting period in Quebec before benefit payments can be received, unlike in most states of the U.S. Fifth, there is, in general, more experience rating in the U.S. than in Quebec, in particular for the period of our study during which there was no self-insurance in Quebec. Furthermore, it is interesting to discuss why the two insurance regimes have a significant effect when combined with different types of hard-to-diagnose injuries ŽWC is significant when combined with MINHARD, while UI is significant when

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combined with MAJHARD.. At least two reasons come to mind to explain this phenomenon. First, since major injuries that are hard to diagnose are intrinsically more severe and associated with longer durations than minor injuries of the same type, they are statistically more likely to end up during the industry’s dead season in which unemployment is higher, giving a stronger incentive to workers with MAJHARD injuries to stay on WC and avoid UI. Second, victims of major injuries that are hard-to-diagnose are more likely to be less employable and to face a period of unemployment at the end of their recovery period, giving them again a stronger incentive to stay on WC and avoid UI. In addition, as anticipated, the fact that an accident occurs in DECEMBER Žrather than July. induces a reduction in the conditional hazard of leaving WC of 28%, which corresponds to a 21.1% increase in the expected duration, at the mean of the other covariates. Such a finding, as well as those described in the preceding paragraphs, indicates that financial incentives play a role in the determination of durations, and is consistent with the existence of moral hazard leading to a substitution between the two insurance regimes.16 It is also noteworthy that the coefficient of the regional unemployment rate ŽUNEMP. is always significant, but never has the expected negative sign. One explanation for this phenomenon may be that, when unemployment increases, workers who quit the labor force are those with less seniority and experience, leaving in those who are less likely to have accidents involving a long recovery. This explanation is confirmed to some extent by the fact that, in all specifications, our variable QUALIFICATION has a positive and significant coefficient Žexcept in specification Ž2... Conversations with officials of the Association des entrepreneurs ŽAECQ. have provided us with further insight on this en construction du Quebec ´ issue. They added that, during cyclical downswings, employers in the construction industry do not lay off their ‘‘best’’ workers Žlike the foremen., with whom they have built a stronger relationship, and who are more likely to go back to work quickly after an accident. In line with these arguments, one can add that, when unemployment is high, workers’ status is more likely to be precarious, inducing them to re-enter the labor force more rapidly after an accident. Concerning the other variables, the coefficient of log WAGE is negative and significant Žexcept in specification Ž3... While a negative sign may partly be explained by the implied increase in the level of WC benefits Žsince the WC ratio is assumed constant., this result is surprising given what was found in the rest of the literature Že.g., Butler and Worrall, 1991.. Note however that the coefficient of the interaction term Žlog WAGE.)MINHARD is always positive Žexcept in specifications Ž2. and Ž5.. and is significant in specifications Ž1., Ž6. and Ž7., indicating that the negative wage effect is less significant for workers experiencing minor hard-todiagnose injuries. Moreover, the coefficient of the variable AGE is negative and significant, confirming that the capacity to recover from the effects of injuries declines with age. Furthermore, the behavior of the variable DEPENDENTS is somewhat erratic, its coefficient being positive in certain specifications and negative in others,


181

but rarely significant. This may suggest that the variable is not measured with enough precision Žremember that the number of dependents is deduced from general demographic data.. Finally, as regards REGIONAL dummies, it is noteworthy that workers who experienced an accident at JAMES BAY are predicted to go back later to the labor market. Again, officials of the AECQ provided us with a convincing explanation for this phenomenon. Because the project was located in a remote area in Northern Quebec far from the main urban centers of the province, the construction firms working on the project had adopted an informal policy of reporting only the more severe accidents to the WC board. In doing so, the employers avoided returning the workers with minor injuries to their families in Southern Quebec, such trips involving major expenses. Let us turn to the alternative specifications ŽŽ2. to Ž6.. and the different tests that can be made to assess the validity of our general specification. First, when the two-step estimating method is not used Žspecification Ž3.., one notices that the coefficients of the variables associated with the wage and replacement ratios are relatively different. In particular, the coefficients of WC replacement ratios become positive and significant, in contrast with all the other specifications and with the rest of the literature, the coefficient of the interaction term between the WC replacement ratio before 1979 and MINHARD becomes positive and significant, again in contrast with all the other specifications and with the rest of the literature, while the coefficient of the variable Žlog UI.)MAJHARD is still positive, but much lower in magnitude.17 These results suggest that the potential bias related to the endogeneity of the wage can be important and that the use of the two-step estimating method is warranted. Second, regarding the heterogeneity issue, in all the specifications estimated with the mixed proportional hazard model based on Meyer Žspecifications Ž1., Ž2., Ž3., and Ž7.., the estimate of the heterogeneity variance is everywhere strongly significant. Specifications Ž1. and Ž4. allow a direct comparison of estimates with and without unobserved heterogeneity. All the coefficients in the heterogeneity specification tend to be larger in absolute values, which is consistent with the theoretical prediction of Lancaster Ž1990.. Furthermore, from Table 3, it is clear that, in specification Ž1., which accounts for unobserved heterogeneity, the average conditional hazard per day Žat the sample mean of the covariates. is almost everywhere increasing with the duration on WC. However, it is noteworthy that the hazard rate is much lower Žexcept in the first intervals. and tends in fact to decrease with duration, when one does not account for unobserved heterogeneity Žsee specification Ž4... This provides a particularly strong piece of evidence of the negative heterogeneity bias on the effect of duration on the hazard. Third, along these lines, it is interesting to examine how the results are affected when one assumes a specific form for the baseline hazard often encountered in the literature ŽWeibull with and without gamma-distributed random effects..18 Specifications Ž5. and Ž6. impose a Weibull baseline, while specifications Ž1. and Ž4. estimate the baseline non-parametrically, yielding a comparison of the techniques

182


Table 3. Average Žper day. baseline hazard estimates Žstandard errors in parentheses .. Specification Intervals Žin days. 2᎐3 3᎐4 4᎐5 5᎐6 6᎐7 7᎐8 8᎐9 9᎐10 10᎐11 11᎐12 12᎐13 13᎐14 14᎐15 15᎐16 16᎐17 17᎐18 18᎐19 19᎐20 20᎐22 22᎐24 24᎐26 26᎐28 28᎐30 30᎐32 32᎐34 34᎐36 36᎐38 38᎐40 40᎐45 45᎐50 50᎐60 60᎐70 70᎐80 80᎐100 100᎐150 150᎐200

Ž1. 0.058 0.068 0.093 0.125 0.103 0.108 0.091 0.106 0.124 0.133 0.142 0.150 0.234 0.183 0.159 0.161 0.142 0.170 0.196 0.205 0.210 0.214 0.236 0.247 0.276 0.309 0.257 0.341 0.366 0.386 0.450 0.618 0.773 0.960 1.770 3.025

Ž3. Ž0.007. Ž0.008. Ž0.011. Ž0.015. Ž0.013. Ž0.014. Ž0.012. Ž0.015. Ž0.018. Ž0.020. Ž0.021. Ž0.023. Ž0.036. Ž0.030. Ž0.027. Ž0.028. Ž0.026. Ž0.031. Ž0.033. Ž0.036. Ž0.038. Ž0.041. Ž0.045. Ž0.049. Ž0.056. Ž0.064. Ž0.056. Ž0.074. Ž0.077. Ž0.086. Ž0.115. Ž0.154. Ž0.207. Ž0.279. Ž0.607. Ž1.222.

0.098 0.109 0.144 0.185 0.148 0.150 0.123 0.141 0.162 0.171 0.179 0.186 0.284 0.218 0.187 0.188 0.163 0.193 0.220 0.225 0.225 0.226 0.245 0.252 0.277 0.305 0.249 0.326 0.339 0.345 0.422 0.487 0.572 0.649 0.993 1.392

Ž4. Ž0.015. Ž0.016. Ž0.021. Ž0.028. Ž0.023. Ž0.024. Ž0.021. Ž0.024. Ž0.028. Ž0.029. Ž0.031. Ž0.033. Ž0.050. Ž0.040. Ž0.035. Ž0.036. Ž0.033. Ž0.038. Ž0.041. Ž0.043. Ž0.044. Ž0.046. Ž0.050. Ž0.052. Ž0.058. Ž0.066. Ž0.056. Ž0.073. Ž0.072. Ž0.077. Ž0.094. Ž0.116. Ž0.144. Ž0.173. Ž0.300. Ž0.486.

0.080 0.076 0.086 0.094 0.066 0.060 0.046 0.049 0.052 0.051 0.050 0.048 0.068 0.048 0.039 0.038 0.031 0.036 0.038 0.036 0.033 0.031 0.031 0.030 0.031 0.032 0.025 0.031 0.029 0.026 0.026 0.024 0.023 0.019 0.017 0.012

Ž0.005. Ž0.005. Ž0.006. Ž0.006. Ž0.005. Ž0.005. Ž0.004. Ž0.004. Ž0.004. Ž0.004. Ž0.004. Ž0.004. Ž0.006. Ž0.005. Ž0.004. Ž0.004. Ž0.004. Ž0.004. Ž0.003. Ž0.003. Ž0.003. Ž0.003. Ž0.003. Ž0.003. Ž0.003. Ž0.003. Ž0.003. Ž0.003. Ž0.002. Ž0.002. Ž0.002. Ž0.002. Ž0.002. Ž0.002. Ž0.001. Ž0.001.

with and without allowance for unobserved heterogeneity. In both cases, the likelihood ratio test strongly rejects the null hypothesis of a Weibull baseline, indicating that the Weibull model is misspecified. The chi-square statistics with 34 degrees of freedom are 1644.04 and 4860.2 for specifications Ž5. and Ž6. respectively. Also, it is noteworthy that ␣ is estimated at 2.746 in the Weibull specification Ž5. in which we allow for unobserved heterogeneity. This means that the hazard is monotonically increasing since ␣ is greater than 1. However, it is


183

estimated at 0.808 when we do not allow for heterogeneity, which implies that the hazard is monotonically decreasing. This provides further evidence of the presence of a strong downward bias in the effect of duration on the baseline hazard when we do not account for unobserved heterogeneity.

5. Conclusion In this paper, we have estimated the effect of Workers’ Compensation ŽWC. and Unemployment Insurance ŽUI. benefits on the expected duration of claims due to workplace accidents using longitudinal WC administrative micro-data on more than 30,000 workers in the Quebec construction industry for the period 1976᎐1986. For the estimates, we used a mixed proportional hazards model that does not impose a parametric form on the baseline hazard and that accounts for problems associated with unobserved heterogeneity. We extended this approach by using a two-step estimating method with generated regressors for potentially endogenous variables. Our results show that increases in the generosity of WC in Quebec led to an increase in the average duration of claims due to minor accidents that are difficult to diagnose. We also provided evidence that a reduction in the generosity of UI was associated with an increase in the duration of claims due to severe accidents that are hard to diagnose. Furthermore, there seemed to be a seasonal effect in the duration of claims: those occurring in December Žat the end of the construction season for most workers. are likely to last longer. This is another important piece of evidence that moral hazard is present through the substitution between WC and UI in the construction industry. Our research raises an interesting theoretical issue, i.e., that analyses of the optimal WC wage replacement rate Že.g., Viscusi and Evans, 1990. should account for the potential substitution between insurance programs. It also raises an important issue for policy-makers: the necessity of considering the possible interaction between social insurance programs when studying the impact of new key parameters in a given program. The present study further suggests that the interaction between programs may vary from one industry to another, enhancing the complexity of the problem. A useful extension to our research would be to investigate whether UI parameters influence the frequency of accidents in the construction industry.

Acknowledgments We thank Christian Belzil, Denis Bolduc, Georges Dionne, Jean-Yves Duclos, Christian Gaurieroux, Guy Lacroix, Gauthier Lanot, David Prescott and Marc Van ´ Audenrode for very helpful discussions and comments. We also benefited from the excellent research assistance of Claude Bilodeau, France Labrecque and Mark Thomas. Finally, we are grateful to the members of the Groupe interdisciplinaire

184


de recherche sur l’organisation, la sante ´ et la securite ´ ´ du travail ŽGIROSST. of Universite ´ Laval for providing us with the data and for their helpful advice. This research was undertaken while Christine Laporte was a research associate at Univeriste ´ Laval. The views expressed in this paper are those of the authors and do not necessarily reflect the opinion of Human Resources Development Canada or of the Government of Canada. Any remaining error is our own.

Notes 1. See Lanoie Ž1994. for a comparative analysis of the WC and UI system in Europe and North America. 2. Fortin and Lanoie Ž1992. provide evidence that UI affects the duration but not the probability of accidents. The present paper therefore focuses only on duration analysis. 3. However, our reduced form estimates take into account both workers’ and firms’ behavior. 4. In the theoretical section, it is assumed that the individual has accumulated rights to claim UI benefits. However, in our empirical work, we tried variables reflecting the regional minimum work requirement for eligibility to UI and the regional maximum duration of UI benefits as additional measures of UI generosity, but they were not statistically significant in any specification and have thus been excluded from the model. Note also that we assume that the individual is better off with UI payments than with a job in another industry. 5. For notational convenience, we assume that these are the same individual characteristics as those described earlier. 6. A more realistic process would involve autocorrelation of errors, but this would make the estimate much more complex, involving the calculation of a large number of high dimension integrals for the evaluation of the likelihood of the model. Using an autoregressive process would also lead to complex numerical problems in estimating the model. 7. For simplicity, we ignore the possibility that changes over time of the exogenous variables Ž z tw c ’s and z tl ’s. between the arrivals of the ⑀ would result in the choice of returning to the labor market so that the worker would leave WC at points in time when ⑀ did not change Žsee Heckman and Singer, 1984.. 8. If we lose track of them, we assume that they are unemployed and, if they have worked enough time to qualify for UI, we assume that they do indeed receive UI payments. This assumption seems reasonable. For instance, in 1985, the average worker in the Quebec construction industry was unemployed for eight weeks and received $1,565 in UI payments ŽFluet and Lefebvre, 1989.. 9. An accident with time lost is an accident involving more than one day off work. Permanent disability cases are excluded from the sample because their duration is calculated in an arbitrary fashion. 10. For instance, according to the theory of compensating wage differentials, more dangerous jobs Žwith longer duration of claims. lead to higher wages Žsee Thaler and Rosen, 1976.. 11. Note, however, that the standard errors of the corresponding estimated coefficients are generally inconsistent. While bootstrapping methods could theoretically be used to generate consistent standard errors estimates, such an approach would be highly time-consuming. One way to circumvent this problem is to interpret our analysis as conditional upon the value of the generated regressors. 12. The main types of occupational injuries that belong to each group are the following: Ž1. MINEASY: contusion, poisoning, amputation without permanent partial disability and friction burn; Ž2. MINHARD: minor low-back injuries, bursitis; Ž3. MAJEASY: fracture; and Ž4. MAJHARD: spinal disorders, major low-back injuries. 13. Since there are more than 315 different durations in our sample, we were unable to estimate a ␥ element for each of these durations. After some investigation, 36 elements of ␥ , corresponding to different time intervals, were used in all specifications considered. The 36 elements of ␥ correspond

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14. 15.

16.

17. 18.

to the following durations Žin days.: ␥ i , i s 0, . . . , 17:i q 2 days; ␥ 18 : 20᎐21; ␥ 19 : 22᎐23; ␥ 20 : 24᎐25; ␥ 21 26᎐27; ␥ 22 : 28᎐29; ␥ 23 : 30᎐31; ␥ 24 : 32᎐33; ␥ 25 : 34᎐35; ␥ 26 : 36᎐37; ␥ 27 : 38᎐39; ␥ 28 : 40᎐44; ␥ 29 : 45᎐49; ␥ 30 : 50᎐59; ␥ 31: 60᎐69; ␥ 32 : 70᎐79; ␥ 33 : 80᎐99; ␥ 34 : 100᎐149; ␥ 35 : 150᎐199; ␥ 36 : 200᎐2,716. This last interval is censored. Over 10 intervals, the ␤ coefficients appear to be highly robust to the number of elements of ␥ considered. The expected spell duration for a given level of the covariates is obtained by evaluating the integral of the corresponding survival function, over all time intervals Žsee Katz and Meyer, 1990.. Fortin and Lanoie Ž1992. actually show that the magnitude of the WC impact is reduced when one does not account for the UI variables. This result is not surprising since, as long as the UI and WC net wage replacement ratios are positively correlated, omitting the UI ratio will produce a downward bias in the estimates of the effect of the WC ratio. None of the other monthly dummies is significant. NOVEMBER is negative and significant in specification Ž4. without unobserved heterogeneity, while SEPTEMBER, OCTOBER and NOVEMBER are negative and significant in the Weibull specification Ž6. without unobserved heterogeneity. Furthermore, the coefficient of QUALIFICATION is negative only in specification Ž3.. Note that the conventional estimate of the Weibull was modified to allow for a comparison with the Meyer’s model, based on the same information set. More precisely, in contrast with usual calculations, in setting the likelihood function, we take into account only the information on the time intervals within which the actual durations in this sample are located. This allows the Weibull to be nested in the semi-parametric model. Thus, in the likelihood function Ž3.2., our Weibull ␣ formulation imposes the ␥ t j’s to be equal to lnŽ Ht tj jq 1 Ž␩␣ .␷ ␣y1 d␷ . s ln␩ q lnŽ t jq1 y t j␣ ., where ␩ and ␣ are the Weibull parameters to be estimated.

Appendix 1 Calculation of WC and UI wage remplacement ratios The following equations were used to generate the ratios, at the individual level: WCBt s min ŽWCBtp , WCBt., where WCBtp s

½

0.75yt

before 1979

0.9 Ž yt y T Ž 52yt , x . .

after 1979

5

52

with yt s

Ý wtyirn t . is1

WCt s WCBtrmyt , where 52

myt s yt 1 y t m

ž ž

Ý wtyi q UIBt Ž Ž 52 y n t . , x . is1

with UIBt s min Ž UIBtp , UIBt . , where UIBtp s UIt s UIBtr yt.

½

0.66yt

before 1979

0.6yt

after 1979

5

.

//

186


The definitions of the variables are the following: WCBt : WCBtp : WCBt: yt: x: nt : T Ž⭈.:

wtyi : myt : WCt : t m Ž⭈.:

amount of weekly WC benefits; potential amount of weekly WC benefits, i.e., with no WC maximum insurable income; amount of weekly WC benefits corresponding to the WC maximum insurable income; averagable weekly gross wage income in the weeks worked in the construction sector during the year preceding the accident; set of individual characteristics; number of weeks worked in the construction industry during the year preceding the accident; provincial q federal income taxes q UI and social security contributions, as a function of imputed total labor income Žas defined by WC regulations. and of a set of individual characteristics; weekly wage income in the construction sector at time t y i; weekly marginal labor income in the construction sector; WC wage replacement ratio; marginal tax rate, as a function of the sum of total wage income in the

construction sector during the year preceding the accident and of UI benefits received Žassuming that the individual received UI benefits during weeks not worked in the construction sector. and as a function of a set of individual characteristics; UIBt : amount of weekly UI benefits; UIBtp : potential amount of weekly UI benefits, i.e., with no UI maximum insurable income; UIBt: amount of weekly UI benefits corresponding to the UI maximum insurable income; UIt : UI replacement ratio.

N.B.: 1. Before, the 1979 reform, the level of WC benefits was set at 75% of the worker’s gross wage Žup to a maximum., while it has been set at 90% of the worker’s net wage Žup to a maximum. since then. 2. The tax variables are calculated for each individual using the individual’s age and general demographic information for workers in the Quebec construction industry Žproportion of workers who are married, have children, etc.. obtained from the 1981 and 1986 Canadian Censuses. 3. The gross UI replacement ratio is equal to the corresponding net ratio since the UI benefits are taxable.


187

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