To develop a time series methodology using regression with ARIMA errors, that explores the relationship between economic activity and rates of workplace injury.
A number of analyses have been produced that explore the effect; the most recent published analysis for Great Britain covers a period from 1986 to 2005. Currently there is no time series analysis that covers the 2008 recession. This analysis extends the currently available data up to 2012 and uses a time-series regression technique to examine the relationship between economic activity and workplace injury.
In order to produce RIDDOR injury data that covers the period of interest (1986/87 - 2012/13) a number of data sources have been combined to form a single injury series. As the period covers a number of different industry classifications (SIC80, 92 & 07) a probabilistic method for translating the older codes into the latest classification has been developed. The analysis is restricted to employees, mainly due to the high levels of under-reporting by self-employed workers in the RIDDOR data. To produce quarterly employee injury rates, quarterly employee jobs data from the Workforce Jobs dataset was used from Nomis1 official labour market statistics.
For Gross Domestic Product (GDP) data, the time series published with the second estimate for Q1 20132 was used. For the all industry figures the log of overall quarterly GDP data was used. To produce historical sector Gross Value Added (GVA) figures, the GVA by sector figures were combined with earlier data from Economic Trends Annual Supplement 20063. The Economic Trends data was adjusted so that the two series match when they first overlap in 1997.
The time series method used for the analysis was a regression model with ARIMA errors, where a regression model is fitted to the data and an ARIMA model removes any remaining auto-correlation within the residuals. The GDP term was tested with up to a year lag and the model with the best GDP fit was chosen. All the series used in the analysis are differenced in order to make the data stationary and therefore the ARIMA methods used are applicable.
Major injuries (the largest component being slips & trips) are more likely to occur when it is colder i.e. in the winter. To allow for this effect, a quarterly temperature series was constructed, that used the minimum quarterly temperature from the Met Office's historical weather data (Durham weather station4). This series was used as a proxy for temperature and seasonal effects.
Three step functions have been defined:
All these step functions were tested with each injury series, but only functions with significant coefficients where left in the final models.
Table 1 shows the results of the analysis. Because the whole economy models use a different independent economic variable in the regression than the industry breakdown models (i.e. log (GDP) rather than Indexed GVA) the value of the coefficients are much larger for these models.
|All industry†: Major injurya||9.772(4.667)**||-0.167(0.033)**|
|All industry†: Over-3-day injurya||110.885(33.536)**||---|
|Manufacturing: Major injury||0.19(0.08)**||---|
|Manufacturing: Over-3-day injury||1.278(0.482)**||---|
|Construction: Major injury||0.482(0.085)**||---|
|Construction: Over-3-day injury||0.87(0.298)**||---|
|Services: Major injury||-0.1(0.046)**||-0.168(0.028)**|
|Services: Over-3-day injury||0.193(0.333)||---|
a GDP variable for all industry: log(GDP)
** Significant at 95% level
--- No significant temperature term
† All industry refers to the entire economy
The methodology developed within this analysis seems to produce results that are consistent with previous analyses. Davies, R & Jones, P (2006). Trends and context to rates of workplace injury detected a pro-cyclical relationship between major injury rates and GDP while in Davies, Rhys et al (2009) The impact of the business cycle on occupational injuries in the UK. Social science & medicine. 69 (2), pp. 178-182 a pro-cyclical relationship was detected between over-3-day injury rates and GDP. This analysis detects both of these effects. As well as the overall effect, the analysis also detects stronger effects within the construction and manufacturing sectors than in services (which actually produces a small significant negative coefficient for major injuries), which again is consistent with previous analysis. [It is worth noting that major injuries are not necessarily more serious than over-3-day injuries. The major injury definition covering the majority of the analysis period is given in Annex A].
Further analysis was performed on individual service industries, although the results are not clear, producing a mixture of positive and negative GDP coefficients that are not easy to interpret.
The analysis for agricultural employees indicated a negative correlation between injury and GDP. However, the recession may have had an effect on the employee/self-employed breakdown in agriculture and could have affected these results.
An attempt to analyse the two recessions separately using two dummy variables failed to produce any significant GDP terms. Performing analysis with dummy GDP variables that split the analysis period into two equal halves, gave similar results to those quoted in Table 1 with a single GDP term.
Table 2 calculates an estimate of the effect on the reported injury rates due to changes in GDP between 2007/08 and 2009/10. This is calculated for:
The percentage is calculated by multiplying the change in the GDP variable between Q1 2008 and Q1 2010 by the relevant coefficient from Table 1; this is then divided by the change in injury rates between 2007/08 and 2009/10 for the injury series being modelled. This calculation can be applied to any industry/severity combination that contains a significant GDP term.
|Fall in injury rate (2007/08 - 2009/10)||% of fall due to change in GDP|
|Actual||Predicted by GDP|
|All Industry||4.4||0.55 ± 0.51||12% ± 11.6%|
|Construction||54.3||9.1 ± 3.1||17% ± 6%|
|Manufacturing||23.0||2.5 ± 2.1||11% ± 9%|
|All Industry||40.2||6.2 ± 1.9||15% ± 5%|
|Construction||88.9||16.4 ± 5.6||18% ± 6%|
|Manufacturing||136.1||16.7 ± 6.3||12% ± 5%|
This analysis has assumed a consistent reporting level across the period and no adjustment has been made for under-reporting. Now the methodology has been developed, the next step would be to introduce an adjustment for under-reporting to see what effect, if any, this has on the results. It may then be possible to construct models for workers (i.e. employees + self-employed) which may help with the analysis in agriculture.
Reportable major injury definition: