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Abstract
Objective The objective of this study is to better understand the inter-temporal variation in workers' compensation claim rates using time series analytical techniques not commonly used in the occupational health and safety literature. We focus specifically on the role of unemployment rates in explaining claim rate variations.
Methods The major components of workers' compensation claim rates are decomposed using data from a Canadian workers' compensation authority for the period 1991–2007. Several techniques are used to undertake the decomposition and assess key factors driving rates: (i) the multitaper spectral estimator, (ii) the harmonic F test, (iii) the Kalman smoother and (iv) ordinary least squares.
Results The largest component of the periodic behaviour in workers' compensation claim rates is seasonal variation. Business cycle fluctuations in workers' compensation claim rates move inversely to unemployment rates.
Conclusions The analysis suggests that workers' compensation claim rates between 1991 and 2008 were driven by (in order of magnitude) a strong negative long term growth trend, periodic seasonal trends and business cycle fluctuations proxied by the Ontario unemployment rate.
- Statistics
- injuries
- worker's compensation
- occupational health practice
- mathematical models
- time series study
Statistics from Altmetric.com
- Statistics
- injuries
- worker's compensation
- occupational health practice
- mathematical models
- time series study
What this paper adds
This study applies time series analytical techniques not commonly used in the occupational health and safety literature to better understand variation in monthly workers' compensation claim rates.
These rates were deconstructed into structural time series components with a level of fidelity that is unmatched in previous studies on this subject.
It was found that claim rates are driven (in order of magnitude) by a strong negative long term growth trend, periodic trends and business cycle fluctuations proxied by the Ontario unemployment rate.
Understanding these trends to the level presented in this work could help policy makers moderate these fluctuations with improved efficiency.
Introduction
Much of the literature that describes the pattern of workers' compensation claim rates over time has either discussed the impacts of long term growth trends, made comparisons with the economic activity of the business cycle (generally proxied with the unemployment rate), or both. Most studies find that the relationship between the business cycle and some facet of the workers' compensation claim rate is pro-cyclical (ie, during up cycles, when unemployment rates are low, the claim rate increases; and during down cycles, when unemployment rates are high, the claim rate decreases). While this is an important finding, there has been little investigation of the multiple temporal components (ie, growth trend, seasonal fluctuations and business cycle) that influence claim rates using sophisticated time series analytical techniques. In contrast, the physical sciences, climatology, seismology, engineering and economics have advanced the analyses of time series using techniques that offer substantially more insight into the various components of inter-temporal variation than those used in the social sciences. In this study we use these methods to investigate workers' compensation injury/illness claim rate trends over the period 1991–2007.
Regarding the impact of the business cycle on claim rates, Kossoris1 looked back to the great depression in the USA where he found that year-to-year changes in claim frequency during the beginning of the last great depression (1929–1931) closely paralleled the drop in employment. He found that claims for minor injuries (ie, with time off work lasting 1 week or less) generally decreased as the unemployment rate increased. In a study of claim rates in the USA from 1979 to 1993, Hartwig et al2 also found that the claim rate is significantly and negatively associated with the unemployment rate, and that the overall level of employment is positively associated with the occurrence of filed claims. Controlling for age and gender, Brooker et al3 investigated lost time claim rates for back pain and for acute injuries across several sectors over the years 1975–1993 in the Province of Ontario, Canada. The study found that lost time claim rates increased in boom times and fell in recessions. More recently, Davies et al4 investigated the impact of the business cycle on occupational injuries in the UK. They found that the rate of minor injuries is directly correlated with economic activity (ie, increased in upturns and decreased in downturns), whereas the rate of major injuries is not. In a regional study in the Canadian Province of Quebec between 1976 and 1986, Fortin et al5 also found that the unemployment rate has a negative association with claim rates.
Robinson6 summarised three hypothesis suggested by economists interested in exploring reasons for the association of claim rates with economic cyclical fluctuations. First, during upturns in business activity less experienced workers are hired and are more likely than more experienced workers to suffer an injury on the job. During downturns, the less experienced workers are the first to be laid off. Second, during business cycle upswings, the pace of production increases and worker safety deteriorates. Third, during periods of increased management power (usually during downturns in the economy), injury rates increase, while during periods of increased labour power (usually during upturns in the business cycle), injury rates decrease. This last hypothesis is in contrast to the first two and with the empirical evidence.
As described above, much of the previous research using time series data on workers' compensation claim rates is focused on better understanding the business cycle effects, that is, aperiodic behaviour of non-constant frequency which is typically, but not always, associated with business cycle dynamics. Periodic behaviour of a constant frequency, such as seasonal variation, has a recurring pattern that is predictable. Not all periodic behaviour in workers' compensation claim rate time series is seasonal, as many periodic cycles exist outside of the 12-month annual cycle. This is something we explore in the analyses undertaken in this study. Most of the studies mentioned use annual data, so seasonal variation was not an issue. However, a large share of the variance is attributed to seasonal periodic behaviour, as discussed in this work. Barsky and Miron7 treated seasonal fluctuations as worthy of study in their own right and found them to be an important source of variation in all macroeconomic activity. While these fluctuations are not widely discussed in the occupational health and safety literature, in the broader arena of accident analysis, Kuhn et al8 did investigate the phenomenon with child injury rates in the USA. They compared two statistical methods to quantify time trends in child injury rates using Poisson regression and time series analysis, and found a strong 12-month seasonal effect in the 5–16-year-old age category.
Some recent studies address the long term growth trend of workers' compensation claim rates. Ussif9 states that the long term decrease in lost time injuries over the period 1970–1999 may reflect a better educated workforce, improved safety measures, more advanced technology and legislative reforms. Shuford et al10 suggested that the falling claim rate could be a reporting phenomenon attributable to the influence of global competition. However, despite the overall downward trend, he found that there is a tendency for workers' compensation claim rates to move in the direction opposite to that of unemployment rates (ie, when unemployment rates increase, claim rates decrease). Although several researchers have suggested that the downward trend may be due to decreases in reporting of claims, few studies have empirically investigated the factors driving the trend. Mustard et al11 investigated the ‘reporting hypothesis’ using data from Ontario from two data sources, administrative claims data and self-reported work absences from a labour and health survey. The study found that the downward trend over the period 1993–1998 existed in both data sources, suggesting that the trend reflects real decreases in injuries rather than simply decreases in reporting. Conway et al12 discussed reasons why injury rates decreased from 1992 to 1996 in the USA. The study noted a shift in the economic industrial base from high to low hazard industries over this period. The authors suggested that automating high hazard jobs played a role in the decline since it resulted in most remaining jobs being inherently less dangerous. The authors also noted that various audits have revealed that the decline is not due to an increase in under-reporting.
In this study we introduce new tools, that is, tools not previously used in the occupational health and safety field, to study the inter-temporal variation in workers' compensation claim rates. Through the use of the multitaper spectral estimator, the harmonic F test and the Kalman smoother, we introduce new insights into the non-constant and constant periodic behaviour of these rates.
Materials and methods
Data and samples
The data for this study come from two sources, the administrative data files of the workers' compensation authority in Ontario, and a labour force survey that identifies the size of the labour force and level of unemployment. The Ontario workers' compensation authority is a non-profit monopolistic provincial fund that covers approximately 70% of the paid labour force. The administrative files contain detailed information on all workers' compensation claims.
To develop claim rates the administrative data was used to identify the number of claims in a particular month, that is lost time injuries (LTI), no lost time injuries (NLTI) and total injuries (TI). This value was the numerator for the rate. The denominator, which reflects the exposure or labour time input, was developed from Statistics Canada's Labour Force Survey. The unemployment rate was also estimated using the Labour Force Survey. The monthly survey contains information on the size of the labour force in each province, and the number of unemployed participants.
Time series methods
Below we discuss the various time series methods used in this study, specifically we describe their purpose and how they are used in time series analysis. There are four methods: (i) the multitaper spectral estimator, (ii) the harmonic F test, (iii) the Kalman smoother and (iv) linear least squares fit. Some of these methods are used in conjunction with each other in order to identify the components of the variation in the data sample. As regards the decomposition of economic time series into cyclic components, Harvey13 14 has carried out a substantial amount of work on the application of spectral methods, specifically the Kalman filter15 16 and state space smoothing, to time series phenomena.
Using the methods described below, we partition the workers' compensation claim rates trends into three main time series components: (i) seasonal and periodic fluctuations, (ii) business cycle fluctuations and (iii) negative growth trend.
Multitaper spectral estimator
While the concept of data in the time domain is generally understood, many people have difficulty visualising the formal mapping between the time and frequency domains. This mapping is called the Fourier transform, which entails a mathematical transformation of the data to make observations in the frequency domain. Analysis in the frequency domain provides insights into the periodic behaviour of the data under investigation. For example, weekly and seasonal periodicities may be known, but detection of other periodic components may require frequency domain analysis.
When it comes to the choice of spectral estimators to identify the periodic components in the frequency domain, the multitaper method has been shown to be the most effective overall due to its statistical robustness.17 For this study a multitaper is used to determine the seasonal nature of the data. For instance, if we see a distinct impulse at 2.0 cycles a year in a spectral estimate, we know that there is a 6-month cycle. If we see a distinct impulse at 0.5 cycles a year, then there is a 2-year cycle.
Harmonic F test
Like the well-known classic F test, this statistic is described as a ratio of two χ2 values. However, unlike the classic F test, this test is applied in the frequency domain. To enhance the insights of this test, we suggest that it is used in conjunction with Thomson's multitaper method to identify significant periodic behaviour.18 For instance, we may see a noticeable impulse at 1.0 cycles/year in the multitaper spectral estimate. Simultaneously, we may detect its significance with p<0.05 using the harmonic F test.
Sometimes there may be instances when the harmonic F test will detect periodic behaviour which is not noticeable in the spectral estimate. This phenomenon is common and may be due to other masked stochastic events occurring in the time series. Alternatively, there may be instances when there is a clearly noticeable spike at a particular frequency in a spectral estimate and the harmonic F test does not detect a significant frequency. This raises more concern, as it could be caused by aperiodicity, or by undersampling in the frequency at which the measurements were collected. This effect is known as aliasing.19
We used the harmonic F test to detect and reconstruct all significant (p<0.05) periodic components in monthly claim rates. Using the harmonic F test in the recursive procedure described by Moore et al,20 all significant periodic components were removed from the data in order to identify non-periodic cycles and trends. A large amount of literature deals with estimating these types of periodic trends in autocorrelated data, including chapter 8 of Granger et al.21 Unlike many of these methods, this technique tests all significant periodic activity in the frequency domain.
Kalman smoother
To study business cycle fluctuations in claim rates, we use an advanced smoothing operation known as the Kalman smoother. Developed by Kalman in the early 1960s, the original purpose of this smoother was to address trajectory estimation problems commonly found in aerospace engineering. Since then, Harvey has used the methods to analyse state space models in business and econometrics. To study business cycle dynamics, Stock and Watson used Harvey's approach in a well-known economic index model to mimic the business cycle behaviour of gross domestic product.22–25
The Kalman smoother builds on the Kalman filter. The Kalman filter is a recursive system of linear algebraic equations used to remove noise or error from repeated measurements taken over time. It is considered optimal in that its estimates minimise the mean squared error between the raw measurements and the underlying true values. The method assumes that the error (ie, the part to be removed) is Gaussian. The Kalman smoother is an extension of the Kalman filter in that it is conditional on a full set of input time series observations,14 whereas the Kalman filter is conditional on the set of input time series observations up to time t.
Linear least squares fit
As described above, we use ordinary least squares to estimate the underlying linear growth trend in our time series data of workers' compensation claims. Under certain initial assumptions, essentially those of the well-known Gauss-Markov theorem (see chapter 2.6 of Wonnacott et al26), this estimate is theoretically the minimum variance estimate. The significance of this estimated slope is validated using the t ratio test.
Using the methods described above, we partitioned the workers' compensation claim rates into three main time series components: (i) negative growth trend, (ii) seasonal and periodic fluctuations and (iii) business cycle fluctuations.
Results
Long term growth trend
We found that the long term negative growth trend of the TI claim rate is the largest contributor to the variance in the workers' compensation TI claim rate. The rate of decline is −0.023% per month over the study period (January 1991 to December 2007). The significance of this slope was tested and found to be statistically significant using a t ratio test.
Seasonal and periodic fluctuations
As noted, to study the periodic components we first used a least squares fit to remove the long term trend, followed by the application of the harmonic F test in conjunction with Thomson's multitaper method using the iterative procedure described by Moore et al.20 In figure 1, we see that the majority of periodic activity in the LTI claim rate, NLTI claim rate (also known as healthcare only) and TI claim rate is seasonal, indicated by 1 cycle per year. In table 1 we see its subsequent Fourier harmonics of 2, 3, 4 and 5 cycles per year. The highest frequency (6 cycles per year) in these plots is the Nyquist frequency,27 which is half the sampling frequency (12 samples per year) of the input data. Referring to table 1, cycles that occur at non-integer periods are not seasonal and contribute a small share of the total variance in the periodic behaviour. Interestingly, there is non-seasonal periodic behaviour that occurs every 2.75 and 4.71 years in the TI claim rate. The periodic behaviour occurring every 4.176 cycles per year for both the NLTI and LTI claim rates is a calendar effect discussed by Grether et al28 and Cleveland et al.29 This effect is due to the interaction of the various months, which are unequal in length, to the nearly periodic week.
Multitaper spectral estimates of unprocessed rates of no lost time injuries (NLTI), lost time injuries (LTI) and total injuries (TI) over 17 years starting in January 1989. The rectangular ‘bumps’ and the typical responses to periodic effects are 1.0, 2.0, 3.0, 4.0, 5.0 and 6.0 cycles/year and are explained by the periodicity from the seasonal cycle. However, other periodic behaviour (ie, 4.5 cycles/year) do not have such a simple explanation.
Highly significant non-trivial frequencies (cycles/year) with corresponding F test p values derived from Thomson's harmonic F test
Business cycle fluctuations
In figure 2 and table 2, we compare the estimated fluctuations of the business cycle for both the Ontario unemployment rate and the workers' compensation claims rate. We can see the inverse relationship between the work injury rate and the unemployment rate, particularly around the major dip in unemployment experienced in Ontario around 2001.
Total injury and Ontario unemployment rate trends: (top) raw trend; (centre) smoothed trend with measurement error (ie, periodic behaviour and minor idiosyncratic behaviour) removed; and (bottom) measurement error with linear growth trend removed which represents the business cycle fluctuations. Referring to the major dip in unemployment experienced around 2001, we validate the negatively correlated behaviour between the total injury and unemployment rates.
Confidence intervals of variance explained (in order of relevance) found in claim rates: growth trend, periodic cycle and business cycle
Discussion
Knowing the factors driving workers' compensation claim rates is useful for analysts and for policy makers as benchmarks for their models and decision making practices. To consolidate these observations with previous work, we conjecture that the factors investigated in this analysis (ie, seasonal and business cycles and growth trend) can be further subdivided. The negative growth trend is least understood and can possibly be explained by a number of factors: (i) farming out of risk to smaller businesses and foreign nations due to increases in global competition, (ii) better practices driven by technological advances and (iii) health and safety improvements as a result of legislative reform.9 10
Although there has been very little investigation of the seasonal component in the literature, we speculate that it may be explained by the influences of high risk seasonal work and reduced exposures to risks during holiday periods (ie, summer months, Christmas break, etc). The business cycle might be explained by changes in the proportion of inexperienced workers, in the pace of work and in the propensity to file a claim.1–5 Also noteworthy is the large dip in the unemployment rate and its corresponding inverse relationship with the worker injury rate seen around the year 2001 in figure 2. This could be attributable to the mild recession experienced in the USA, and to a lesser degree in Canada, at that time.
We classify factors associated with the variance in claim rates into three categories to provide analysts with a platform to model these rates in a multivariate framework. The contributions to variances in the claim rate associated with these subcategories are as follows (from highest to lowest): (i) negative growth trend, (ii) seasonal effects and (iii) the business cycle. Knowing this order of relevance can also help policy makers prioritise administrative resource allocation over the short and long term.
It should be noted that some limiting factors to the time series analytical techniques used in this study are not addressed, such as the idiosyncratic disturbances in claim rate that are often associated with the introduction of new legislative reforms and interventions. Investigating the impact of such phenomena requires different analytical techniques.
Conclusion
The focus of this paper was to describe the variance contribution of the major components that drive workers' compensation claim rates using time series analytical techniques not commonly used in the occupational health and safety literature. We established that the variances in monthly claim rate time series are due, in order of relevance, to (i) a negative growth trend, (ii) seasonal effects and (iii) the business cycle. We also validated the inverse relationship between workers' compensation claim rates and unemployment rates. As noted, most papers that discuss the effect of the business cycle on workers' compensation claim rates leave the discussion of seasonal factors virtually untouched. What are least understood are the factors that drove the negative growth trend that occurred over the study period (1991–2007). In general, our methods and analyses provide a good example of the potential for using advanced time series analytical techniques borrowed from other disciplines to better understand time series phenomena in the social sciences.
Acknowledgments
We would like thank Dr Peter Smith for aggregating the data sample that was used for this study.
References
Footnotes
Funding The WSIB Research Advisory Council provided funding for this study. Grant # 09025.
Competing interests None.
Provenance and peer review Not commissioned; externally peer reviewed.