3.1 Data

The data used in this study come from multiples official sources. First, information on the total working population at industry level was obtained from the Statistical Yearboos of Peru’s Ministry of Labor and Employment Promotion (MTPE). Second, data on macroeconomic figures-i.e., Gross Domestic product (GDP) and workers’ wage-was obtained from the National Institute of Statistics and Information Technology (INEI, Peru). For analytical purposes, GDP figures are deflected by inflation and economic values are expressed in million of Peruvian soles at 2021 constant prices (URL: https://www.gob.pe/institucion/inei/informes-publicaciones/3655985-compendio-estadístico-peru-2022).

Third, the information on the number of occupational accidents for the period 2016-2021 was obtained from the records made available by the Ministry of Labor and Employment Promotion (MTPE), through the Computer System for Work Accidents, Incidents and Occupational Diseases (SAT) (URL: https://www2.trabajo.gob.pe/estadisticas/estadistica-de-accidentes-por-actividad-economica ).

The key variables used in this study to evaluate the relationship between economic cycle and work accidents in 15 Peruvian industries over the period 2016-2021 follow: economic activity measured as the level of GDP per worker, and the rate of work accidents defined as the number of accidents by 100,000 workers. Finally, the mean wage per worker is defined as the average monthly economic compensation of workers. ¹

Table 1 summarizes the analyzed data, whereas Figure 1 presents the evolution of both GDP per worker and work accident rates during the studied period.

Figure 1: Evolution of work accident rates (accidents per 100,000 workers) and GDP per worker (at constant 2021 prices) in Peru between 2016 and 2021.

3.2 Method

To evaluate the relationship between the rate of work accidents and economic activity in Peru between 2016 and 2021 I employ a two-step methodology based on panel-data models (Wooldridge, 2002) and panel-data VAR model (Holtz-Eakin et al., 1988).

The analysis is conducted at industry level (i= 1,…, N=15), and in the first stage the model used to test the empirical connection between work accident rates and GDP per worker is based on a standard Cobb-Douglas production function:

(1)

In equation (1), Y is the rate of work accidents for each industry (i) during the study period (t), A is the constant term, T is the set of variables capturing time-related effects (λ), and ε is the error term. For the variables GDP per worker (G) and mean wage per worker (W) the terms β and δ are, respectively, the model coefficients to be estimated. The variables GDP per worker and mean wage per worker are deflated with respect to inflation and are expressed at constant 2021 prices.

The resulting log-linearized Cobb-Douglas function used in this study follows:

(2)

In equation (2) T is a set of (T-1) dummy variables that account for potential time effects linked to unobserved changes in environmental conditions that are common to all industries (i), while the error term has two components: a time-invariant effect controlling for industries’ unobserved heterogeneity (η), and a normally distributed error (ε) that varies cross-industries and cross-time (t).

Equation (2) is estimated via fixed-effects models with robust standard errors to correct for autocorrelation of errors due to constant industry-specific effects (Wooldridge, 2002).

In the second stage, I complement the analysis by applying the following panel VAR model (Holtz-Eakin et al., 1988):

(3)

In equation (3) Y is the rate of work accidents, GDP/w is the GDP per worker, the terms β and δ are the model parameters, η _i is the industry-specific fixed effects term, and ε _it is the error term. Following Holtz-Eakin et al. (1988) , the panel-data VAR model assumes that, for the analyzed industries, coefficients (β and δ) are estimated by a homogeneous data generation process. Equation (3) is computed using the GMM estimator (Arellano & Bond, 1991).

With model estimations in hand (equation (3)), the Granger causality Wald test which evaluates whether one times series is valid to forecast another (null hypothesis: all parameters on the lag of the study variables are jointly zero in each equation), is used to corroborate the causal relationship between economic activity and work accident rates.

4.1 Baseline results

This section presents the results of the fixed-effects model analyzing the relationship between the rate of work accidents, economic activity (GDP per worker) and workers’ mean wage (equation (2)). In Table 2, model 1 includes GDP per worker while model 2 incorporates workers’ compensation into the analysis.

Concerning the key variable analyzed in this study, the results for the coefficient linked to the (ln) GDP per worker indicate that economic activity is positively correlated with the rate of work accidents. The coefficients for the GDP per worker are stable and statistically significant, and they range between 1.1319 (model 1) and 1.5094 (model 2). From the result of the full model (specification 2) it can be seen that a 1% variation in the GDP per worker is associated with a change in the work accident rate of 1.51% (∆Y = ∆Y ^β ∴ ∆Y= 1.01^1.5094 = 1.51%).

This finding highlighting the pro-cyclical relationship between economic activity and the rate of work accidents has been widely documented in previous research (Boone & Van Ours, 2006; Asfaw et al., 2011; Boone et al., 2011; Cioni & Savioli, 2016; Fernández-Muñíz et al., 2018; Lafuente & Daza, 2020; Lafuente & Abad, 2021; Murrell-Blanco, 2023). Based on the notion that work accidents occur within work environments, this finding corroborates that work accidents are a negative, unintended consequence of economic activity.

The coefficient for the variable linked to workers’ economic compensation is negative and significant. Among Peru’s industries and during the 2016-2021 period, the result suggests that a 10% increase in workers’ average wage is associated with a fall of 19.32% in the rate of work accidents. This finding indicates that industries reporting higher wages, which can be linked to higher levels of human capital among workers, will likely show lower work accident rates.

4.2 Complementary analysis: panel VAR results

This section presents the complementary analysis based on the panel VAR model. Table 3 shows the findings of the VAR model (equation (3)), whereas the results of the Granger causality test evaluating the connection between economic activity (GDP per worker) and work accident rates are shown in Table 4.

In constructing vector autoregression models, the lag length and the evaluation of the stability of parameters are relevant aspects that should be considered. Concerning the lag length notice that, given the exploratory nature of this study and the limited time-span of the available data series, all models were estimated using 1 lag of the key variables. To ensure the goodness of fit of the proposed approach the stability test was conducted. Here, the diagnostic statistics for the eigenvalue stability condition show that all eigenvalues are below unity, thus corroborating the validity and stability of the panel-data VAR model (range: 0.0402-0.5908).

Additionally, in order to evaluate the stationarity in the time series unit root tests were performed on the data. The results for panel unit root tests (Im-Pesaran-Shin test) (Im et al., 2003), presented in Table 3, indicate that the two analyzed data sets are stationary, which validates the use of the Granger causality test to study the potential causal relationships between the rate of work accidents and GDP per worker.

From the results in Table 4 it can be observed that, despite the magnitude and significance of coefficients is weaker compared to the fixed-effects model (Table 2), the results of the panel VAR model in Table 4 are qualitatively similar to those computed via the fixed-effects regression: at the industry level, economic activity (GDP per worker) is a significant predictor of the rate of work accidents in Peru between 2016 and 2021.

In the case of the equation modeling the work accident rate, the coefficient for the variable GDP per worker indicates that a 1% growth in GDP per worker would increase the work accident rate by 1.422%. That is, changes in industries’ economic activity are positively correlated with work accident rates in the short-run.

When the dependent variable is the GDP per worker, the results in Table 3 indicate that variations in the work accident rate do not affect GDP per worker in a significant way.

The results in Table 5 for the Granger causality Wald test after the panel VAR model support the findings presented in Tables 2 and 4 for Peruvian industries: there is causal relationship in the short-run from economic activity to the rate of work accidents.

Finally, Table A1 in the Appendix presents, for the 15 industries analyzed in this study, the results of the Granger causality Wald test evaluating the connection between economic activity and the rate of work accidents. The findings indicate that the general panel VAR model (Tables 4 and 5), which suggests a unidirectional causal relationship in the short-run between economic activity and work accident rates, is especially evident in six industries often considered accident-prone sectors because they are labor intensive or involve high-risk industrial processes: Agriculture, livestock, hunting, and forestry, fishing, utilities, construction, manufacturing, transport and warehousing.

On contrary, the analysis detected partial evidence that the rate of work accidents affects GDP per worker in the short-run in industries related to trade (wholesale and retail), business- and consumer-oriented services (i.e., real estate, financial intermediation, accommodation and food services, and other services), and public administration and defense.