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Milan Ščasný

    Jan Urban


    The aim of the paper is to test hedonic wage model on survey data collected in 2007 in the Czech Repulic (N=1040) and to derive VSL. In order to test the relationship between the work-related risk and wage risk premium, we run several model with Box-Cox transformation of wage and different types of indicators for subjectively perceived and objective work-related risk. We found that the indicator of objective work-related risk is statistically significantly associated with risk-premium as expected. We also found that subjectively perceived work-related risk is statistically significantly associated with risk premium to.

1. Introduction

    The idea that higher risk of occupational mortality may result in higher wage payment to the worker is 1quite plausible. The economists have therefore been focusing their effort to reveal a trade-off between money and fatality risk in order to derive a compensating wage differential. Such a wage differential is then used to derive the so-called value of statistical life.

    Viscusi and Aldy (2003) documented more than 50 labour market studies that provide a value of statistical life (VSL) derived from the wage compensating differential. According to their comprehensive literature survey, most of these studies are dominated geographically by the US labour market. Only six of them were conducted in developing Asian countries (Hong Kong, India, Taiwan), and another six in Europe; however, five of those were conducted in the UK (with the one in Austria). There is, however, an amount of studies that do not confirm any statistical relationship between the workplace risk and the wage level even when their authors treated properly risk endogeneity and 2corrected unobserved heterogeneity.

    The VSL estimated form of the hedonic wage differentials range between $0.5 to $21 million (2000 dollars) in the US, $4 to $74 million in the UK, or $0.2 to $4.1 million in Asia (excluding Japan). The central estimate of the VSL value provided by a meta-analysis by Mrozeck-Taylor (2002) yields $1.6 to $2.7 million; by CSERGE (1999) it is as high as ?6.5 million and Viscusi-Aldy (2003) provide a

    mean VSL of ?5 million.

    Most hedonic wage studies estimate the wage differential econometrically on individual worker data. There is also a group of empirical studies that examine the relationship between the statistical rate of occupational injuries and the wage for industries. For instance, Jennings and Kinderman (2003), using industry-specific data, examine the statistical relationship between changes in occupational mortality rate and in hourly wages in the USA.

     1 Adam Smith in his well-known book „The Wealth of Nations‟ (1776; Chapter X, part I) has already noted that “The wages

    of labour vary with the ease or hardship, the cleanliness or dirtiness, the honourable or dishonourableness of the employment… A journeyman blacksmith, though an artificer, seldom earns so much in twelve hours as a [labourer] does in

    eight. His work is not quite so dirty, is less dangerous…”. 2 For instance, Hintermann et al. (2007) do not confirm statistical relationship between workplace risk and wage level in a panel dataset of UK workers.

    Considering the econometric problems related to risk endogeneity and unobserved heterogeneity, an estimation of a wage compensating premium might indeed be a challenge, particularly when work-related injuries decline over time. In fact, working conditions have been significantly improving in the Czech Republic since 1990. While the official statistics of the State Labour Inspection Office (SUIP) recorded almost 300 cases of fatal injuries and about 100,000 cases of non-fatal injuries annually in the mid nineties, there are only 137 fatal injuries and less than 80,000 cases of non-fatal injuries 3recorded just recently.

    The aim of our paper is threefold. Firstly, we aim to examine the statistical relationship between changes in occupational mortality rate and average wages while controlling an effect of labour productivity. We follow here a similar logic as Jennings and Kinderman (2003) who examined the relationship between the changes in occupational mortality rates and in hourly wages in order to examine the reliability of using the WTP/WTA concept for valuing life. We assume that statistically significant evidence for the relationship between risks and wages being found in an individual employee‟s behaviour could be, on average, also found for the economic industries. Secondly, we estimate the hedonic wage differential from hedonic wage models in order to be able to derive a value of statistical life. We intend to estimate a wage compensating differential from three datasets in total. Finally, we would like to compare our VSL estimates with those obtained using other methods in the Czech Republic and/or abroad.

    The structure of the paper is as follows: first, we describe the econometric model. Then we describe the data collection. Finally we provide results of our model estimates.

2. Method

    Econometric estimation of a wage compensating differential from a hedonic wage function is a well-documented exercise. The wage-risk relationship in labour markets is mostly estimated from the following equation (Viscusi-Aldy, 2003; or Haab-McConnell, 2002):

     (1) w;WORKER;JOB;RISK;RISK(COMP;X;i01i2i3i4i5ii

    where WORKER is a vector of personal characteristic variables including human capital measures such as education, experience and skills for worker i, JOB is a vector of job characteristic variables for

    the concerned worker, RISK might be a vector of variables describing risks of fatal and non-fatal injuries and occupational illnesses, COMP describes compensations (pecuniary or in-kind) provided

    to this worker, and X might include other variables including interactions of the fatality risk and personal characteristics (gender, age, trade union status) to capture the heterogeneity in the risk perception and aversion; ε is the random error capturing unmeasured factors affecting the worker‟s i

    wage rate.

    Most hedonic wage studies have estimated the wage equation using linear and semi-logarithmic specifications. Although, as argued by Rosen (1974), choosing a preferred functional form from these specifications cannot be determined on theoretic grounds, one can employ a flexible functional form given by the Box-Cox transformation to identify the specification with the greatest explanatory power (Moore and Viscusi, 1988).

    Transformation of the dependent variable in our hedonic wage models is the typical form for Box-Cox models and its form is as follows:

     3 In relative terms, while SUIP statistics recorded 0.6 cases of fatal and almost 230 non-fatal injuries per 10,000 employees per year in 90‟s, job-related risks declined at 0.3, respectively 180 injuries per 10,000 in 2005.

    w1 = for λ ? 0

    w(λ) (2)

     = ln(w) for λ = 0.

    Then, the marginal effect of fatal risks obtained from the hedonic wage function (1) is given as (see e.g. Haab-McConnell, 2002):

    w1i for a linear form of fatal risk, or w(3iRISKi

    1w((;2) for a quadratic form of fatal risk (3) i33q

where β is a coefficient for the square of fatal risk being estimated in the hedonic model. 3q

The value of statistical life can then be derived as:

    1w((;2)33qVSL (4)


where the β‟s are the coefficients estimated for the fatal risk variable(s), w is the annual average wage,

    λ is the best parameter for the Box-Cox transformation of the dependent variable, and R describes a denominator of fatal risk, i.e. 1 in 10,000 per year.

3. The survey

    Individual data from a survey on the “Value of health” is used in our hedonic wage model testing. The survey was conducted jointly by the Sociological Institute of the Academy of Sciences Public

    Opinion Research Centre, Occupational Safety Research Institute, and Charles University Environment Center in May 2007 with a quota sampling strategy applied to the economically active population of the Czech Republic. The dataset consists of 1,040 observations.

The survey collected information about respondents‟ incomes and incomes of their households as well

    as detailed information about characteristics of the workplace, job, and other socioeconomic characteristics of respondents. Further, number of question has focused also on subjective perception of work-related risks and risks of fatal injuries in particular (for description of variable used in this study see the appendix 1).

    The objective work-related mortality risk has been determined using the characteristics of the respondent (age, gender, occupation or KZAM, and the branch he/she was working in or OKEČ). Using the records of all work-related fatal injuries in the Czech Republic in the last 5 years and the abovementioned characteristics of respondents, we have assigned objective risk of fatal injury to each individual worker.

4. Results

    In the table 1 bellow we present estimates of hedonic wage models for transformed wage using best lambda.

    Model 1 is a standard hedonic wage model where wage is explained statistically significantly, ceteris paribus, by the statistical risk of fatal injury, plus other characteristics of the worker and the workplace.

    Model 2 uses perceived risk (expressed by respondent as cardinal variable in OE question). Interestingly, we see that the subjectively perceived risk of fatal injury is worse predictor of wage in terms of statistical significance that the statistical risk of fatal injury (in model 1).

    Model 3 uses statistical risk as well as perceived hazardousness of the job (HIGHER.RISK) compare to mean risk in the population. It is interesting to see that objective statistical risk explains only part of the wage risk premium. Apparently, certain fraction of the risk premium can be attributed to whether the worker perceives his or her job as riskier than what is average fatal work-related risk in the economically active population.

    In all the 3 models are the socioeconomic variables associated with transformed wage as expected: males have higher wages, people with college or high-school education, people with longer work experience and workers who have subordinates (SMALLBOSS, BIGBOSS) receive higher wages. Interestingly, also people who have more children in the household have higher wages. Our hypothesis is that these people may be willing to take more demanding jobs in order to get higher wages. However, the quality of the jobs was not captured in our model.

    Now we can estimate VSL using the information about risk premium and lambda used for the transformation of wage in our model. The resulting VSL are displayed in the bottom rows of the table. As we can see, the VSL estimated using risk premium derived with statistical risk indicator is similar in model 1 and 3 and amounts to 8.7 mil.?. However, if we use indicator

    of subjectively perceived risk, we derive lower VSL amounting only to 1.96 mil. ?. This is a very interesting phenomenon indeed. One hypothesis explaining this may be that people underestimate risks that they are exposed. The other possible explanation is that the labor market in the Czech Republic regulates the work-related risks well beyond of what people may subjectively perceived as risk.

    Table 1: Estimated nedonic wage models

     Model 1 Model 2 Model 3

     Coeff. P-value Coeff. P-value Coeff. P-value (Intercept) 2.160 0.0000 2.248 0.0000 2.149 0.0000 FATRISK 0.009 0.0214 0.009 0.0505 SUBJ.RISK 0.002 0.0568 HIGHER.RISK 0.211 0.0014 HIGHER.RISK*FATRISK -0.003 0.6448 MALE 0.302 0.0000 0.315 0.0000 0.292 0.0000 COLLEGE 0.389 0.0000 0.351 0.0000 0.397 0.0000 HIGHCHOOL 0.112 0.0053 0.109 0.0513 0.112 0.0049 KIDS 0.037 0.0365 0.066 0.0064 0.041 0.0217 EXPERIENCE 0.004 0.0018 0.004 0.0279 0.004 0.0012 BREADWINNER 0.045 0.1991 -0.010 0.8566 0.051 0.1437 SMALLBOSS 0.188 0.0000 0.146 0.0128 0.189 0.0000 BIGBOSS 0.309 0.0000 0.198 0.0266 0.299 0.0000 KZAM1 0.527 0.0000 0.498 0.0000 0.542 0.0000 KZAM2 0.501 0.0000 0.489 0.0004 0.515 0.0000 KZAM3 0.366 0.0000 0.243 0.0159 0.377 0.0000 KZAM4 0.307 0.0000 0.182 0.0583 0.328 0.0000 KZAM5 0.230 0.0003 0.054 0.5285 0.233 0.0002 KZAM6 0.408 0.0000 0.503 0.0001 0.381 0.0000 KZAM7 0.287 0.0000 0.188 0.0475 0.281 0.0001 KZAM8 0.297 0.0001 0.100 0.3276 0.296 0.0000 OKEC1 0.061 0.7058 0.093 0.6238 0.054 0.7389 OKEC2 0.544 0.2154 0.554 0.2037 OKEC3 0.500 0.0124 0.692 0.0040 0.432 0.0300 OKEC4 0.134 0.3829 0.201 0.2527 0.125 0.4128 OKEC5 0.164 0.3593 0.260 0.2212 0.157 0.3759 OKEC6 0.120 0.4485 0.121 0.5063 0.084 0.5946 OKEC7 0.118 0.4381 0.124 0.4747 0.120 0.4277 OKEC8 0.096 0.5412 0.294 0.1152 0.087 0.5756 OKEC9 0.331 0.0385 0.502 0.0071 0.277 0.0829 OKEC10 0.297 0.0781 0.372 0.0598 0.284 0.0898 OKEC11 0.406 0.0227 0.451 0.0375 0.402 0.0230 OKEC12 0.238 0.1321 0.283 0.1235 0.217 0.1674 OKEC13 0.066 0.6730 0.144 0.4222 0.061 0.6960 OKEC14 0.077 0.6255 0.245 0.1834 0.071 0.6501 OKEC15 0.161 0.3061 0.211 0.2369 0.159 0.3069 Log likelihood -4124.663 -1952.163 -4117.433 Adj. R-square 0.410 0.470 0.435 Lambda 0.101 0.101 0.101

    247.336 VSL (mil. CZK) 55.714 247.094

    8.709 VSL (mil. ?) with PPP=14 1.962 8.700

5. Concluding Remarks

We confirm a statistically significant effect of objective fatal risk rate on the employee‟s wages in the

    Czech labour market. We have also confirmed that subjectively perceived work-related risk is

    associated with wage premium. Even more, this compensation seems to be somehow independent on

    the objective statistical risk.

    Based on an estimation of the hedonic wage function, we derive the wage differential from which the VSL on the Czech labour market was obtained.

    The VSL obtained from the wage differentials estimated from the survey data is about 8.7 million 2007. The VSL estimates from the subjectively perceived risk is lower and amount only to 1.96 mil. ?. ?

    Due to heterogeneity in employees and relevant labour markets, the VSL estimates provided by empirical literature used to lay in wide interval. A review by Viscusi (1992) supports a range of VSL between $0.8 to 17.7 million; more recent estimates of VSL lie between $0.2 million (Loomis and du Vair, 1993) to $87.6 million (Arabsheibani and Marin, 2000). The latest comprehensive review of hedonic wage studies by Viscusi and Aldy (2003) displays a VSL range between $0.5 to 21 million in the US, $4 to 74 million in the UK, or 0.2 to 4.1 million $2000 in Asia. Based on 197 VSL estimates, Kochi et al. (2006) display a mean composite distribution of empirical Bayes-adjusted VSL as high as $5.4 million with a standard deviation of $5.4 million. Our results, that range between ?3 to ?10 million, lay in this wide interval. Moreover, Giergiczny (2006) who is the only researcher to have

    conducted a hedonic wage study in the CEE region displays a sample mean of VSL of 2.26 million

    ?2005 obtained from a wage differential estimated for Polish blue-collar workers.

    Our VSL estimates obtained from hedonic wage models are also practically comparable with the VSL just obtained from our contingent valuation study on the willingness to accept compensations paid through higher wages for risk rates increased by 50%. Urban and Ščasný (2007a) found a mean VSL as high as ?10.7 million (with a median of ?8.4 million)4. Moreover, the VSL derived from the WTP

    for a mortality risk reduction from cardiovascular and respiratory diseases by the contingent valuation method is about ?1.3 million (mean), or ?0.58 million (median) in the Czech Republic (Alberini et al., 2006).


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Appendix 1: Description of variables

    Variable Type Description FATRISK cardinal Statistical risk of fatal injury SUBJ.RISK cardinal Subjectively perceived risk of fatal injury

    S/he thinks that his/her risk of fatal injury is higher than the population

    HIGHER.RISK dummy average

    MALE dummy Male

    COLLEGE dummy College degree

    HIGHCHOOL dummy Highschool eduaction

    KIDS cardinal Number of kids in the household EXPERIENCE dummy Number of years working in the profession BREADWINNER dummy His/her income makes up more than 50% of household income

    SMALLBOSS dummy Has 1 to 5 subordinates

    BIGBOSS dummy Has more than 5 subordinates Classification of occupation

    KZAM1 dummy Legislators, senior officials and managers KZAM2 dummy Professionals

    KZAM3 dummy Technicians and associate professionals KZAM4 dummy Clerks

    KZAM5 dummy Service workers and shop and market sales workers KZAM6 dummy Skilled agricultural and forestry workers KZAM7 dummy Craft and related trades workers KZAM8 dummy Plant and machine operators and assemblers Branches

    OKEC1 dummy Agriculture, forestry

    OKEC2 dummy Fishing

    OKEC3 dummy Mining

    OKEC4 dummy Manufacturing

    OKEC5 dummy Energy supply

    OKEC6 dummy Construction

    OKEC7 dummy Wholesale and retail trade

    OKEC8 dummy Hotels and restaurants

    OKEC9 dummy Transport

    OKEC10 dummy Finance intermediation

    OKEC11 dummy Real estate

    OKEC12 dummy Public administration and defence OKEC13 dummy Education

    OKEC14 dummy Health and social work

    OKEC15 dummy Other service activities

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