Fatigue, Rest, Productivity, and Work Schedule: An empirical analysis using personnel records 

Fatigue, Rest, Productivity, and Work Schedule: An empirical analysis using personnel records 

Fatigue, Rest, Productivity, and Work Schedule: An empirical analysis using personnel records:

Many firms and organizations offer jobs with fixed working schedules. Perhaps the most common schedule in western countries requires working five consecutive days before taking two days of rest. The five consecutive day schedule is believed to have been introduced in 1908 by a New England spinning mill in order to allow its Jewish workers to observe the Sabbath (see Rybczy´nski, 1991). Over time, other firms and nations have adopted similar work schedules primarily as a way to harmonize work practices, and not necessarily because it maximizes worker productivity. Worker productivity may decrease because of accumulated fatigue and insufficient rest. When strong enough, the negative effects of fatigue and the positive effects of resting may require that firms adjust their work schedules in order to increase productivity (see Saez, 2011, for a recent theoretical analysis). This can be especially important for physically demanding jobs. Empirical evidence on the relationship between worker productivity, fatigue, and rest is rather limited in economics. Hamermesh (1990) estimates the marginal effect of on-the-job rest on wages using panel data on self-reported time allocation. He concludes that the first few minutes of rest increase subsequent productivity (wages). However, this increase is just enough to compensate for the non-working period, and longer break times are predicted to reduce productivity. Biddle and Hamermesh (1990) model sleep as a choice variable jointly determined with wages and leisure. Their results suggest that the relationship between sleep and wages has an inverted-U shape.

Tree-planting:

Our data come from a mid-sized tree-planting firm operating in British Columbia, Canada. This province is the largest producer of timber in North America; therefore, extensive reforestation is central to a steady supply of the market. Typically, tree-planting firms are chosen to plant seedlings on harvested tracts through a process of competitive bidding. Depending on the land tenure arrangement, either a timber-harvesting firm or the Ministry of Forests and Range call for sealed bids concerning the cost per tree planted in a number of areas. Forestry firms estimate the cost at which they can complete each contract and submit offers. The lowest bidders are selected to perform the work. Bidding for contracts takes place in the late autumn. After this process, the selected firms commit to reforest their corresponding areas dispersed across the province. The following year, from early spring to late summer, the firms fulfill their planting contracts.

Estimation Results:

Different approaches can be used to estimate the effect of fatigue and rest on productivity. A na¨ıve method is to estimate equation (1.1) using panel data estimators such as fixed effects (FE) or random effects (RE). As we know, these estimators produce biased and inconsistent results due to the endogeneity of fatigue and rest. We compute FE and RE to measure the magnitude of association between regressors and productivity, but not causality. To measure causal effects we estimate the system of equations (1.3). We combine Instrumental Variables (IV) and RE to obtain unbiased estimates. The variables holiday and contract serve as instruments to identify the causal effects of fatigue and rest. The RE account for individualspecific factors that may affect observations over several periods. This two-steps approach has at least two limitations. First, it does not take into account the discrete nature of fatigue and rest. Second, it requires the model equations to be correlated only through the endogenous variables. The error variances εit are assumed to uncorrelated between equations, while the individual effects ηi are simply ignored in the fatigue equation and the rest equation.

Model Predictions:

We have provided estimates of the response of worker productivity to exogenous changes in fatigue and rest. Yet, it may be of interest to use these estimates to predict the potential gain in productivity for alternative work schedules.

The Role of Productivity Shocks in the Effort Choice of Agents: Using experimental data to test for additivity in the production function :

The principal-agent problem often refers to a situation in which a worker (the agent) chooses an effort level that optimally balances remuneration against an increasing cost of effort. In this context the employer (the principal) can be confronted with a problem of moral hazard because observed outcomes do not necessarily reflect effort on the part of the agent. This happens for example when performance depends on random productivity shocks unobserved by the firm. These shocks consist of unexpected unpredictable factors independent of the will of the agents that affect their outcome.

Tree-planting:

The province of British Columbia is the largest timber producer in North America. Our data comes from a medium-sized tree-planting firm actively participating in this competitive market. For each contract, the firm divides the planting areas into blocks to separate different types of terrain. On each block, a price per tree planted is assigned depending on the soil conditions. The piece rate paid to tree planters is endogenous because it depends on the block’s characteristics and the expected number of trees that a regular worker can plant. For instance, since steep and rocky terrain slows workers and make planting more difficult, the firm sets a higher piece rate in these conditions to induce planters to put more effort into their jobs. The firm subdivides blocks into plots and allocates each planter for a day of work. Planters are naturally exposed to random productivity shocks within a given block. Even though all workers receive the same price per tree planted within a block there are random variations of planting conditions that are beyond the firms’ control because it is not possible to completely know the undersoil conditions. A block may appear uniform on the surface, but some portions can have a rocky soil underneath which slows planting. As a result some planters end up working in more difficult conditions under the same piece rate. In this sense planters can be said to be exposed to random productivity shock.

Experimental Design and Data:

We combine payroll data from our tree-planting firm with experimental outcomes from a field experiment, which exogenously incentivize planters to work hard by changing their piece rate. Our data set spans the period between April 28th to May 22nd, 2013. In our analysis we use an unbalanced panel of 270 observations from 21 tree planters in their natural work environment. We observe daily individual outcomes and the piece rate paid by the firm in each planting block. The field experiment consists of two exogenous changes in planters’ piece rate while holding all other conditions constant. These two changes incentivize workers’ effort and consequently their productivity. For this experiment, a large planting block with homogenous soil conditions was fictitiously divided into three blocks with different piece rates, which correspond to different experimental treatments. The first block corresponds to a baseline treatment in which workers received their regular compensation of $0.14 CAD per tree planted. In the second block there was a small increase of 3¢ in the piece rate paid to planters ($0.17). Finally, in the third block there was a relatively large increase of 5¢ per three planted ($0.19). In order to avoid potential Hawthorne effects, the different piece rates were presented to planters in a context of normal daily operations, as if they were associated to different soil conditions. We have chosen to restrict our sample to the observations a few days before the treatments and exclude obs

ervations far away in time. Using a short counterfactual avoids strong seasonal weather variations that may affect workers productivity. We use only pre treatment data to exclude potential biases created by persistent effects of the treatments.

Estimation Results:

In this section we estimate workers’ productivity. We test the validity of an additive production function by computing parametric and semi-parametric tests for homoskedasticity. As discussed in Subsection 2.4.2, homoskedasticity is consistent with an additive production function, while heteroskedasticity and other distributional effects are consistent with a multiplicative form. The empirical evidence rejects the additive structure, which suggests an interaction between the observed productivity shocks and workers’ choice of effort. Table 2.2 shows the estimates of an additive production function using mean regression and quantile regression analysis. Column (a) shows mean productivity of tree planters conditional on the experimental treatments and weather conditions. These are the estimates of equation (2.4) using Correlated Random Effects (CRE), which control for unobserved individual characteristics in a way that approaches fixed effects models (FE). In addition to the standard linear regressors the CRE include individual time averages to capture worker-specific effects that may create serial correlation within indiviuals. These estimates result from the minimization of a simple squared error loss function and have at least two clear advantages. First, unlike FE, CRE allow to estimate time invariant factors. Second, they are less demanding than random effects models (RE), because they do not require unobserved individual factors to be independent of regressors. We also found that CRE estimates are similar to other point regression estimates. Appendix 2.6 compares CRE to other mean regression models such as OLS, FE, RE, and to the least absolute regression model.

Mean Regression Test
We are not directly interested in heteroskedasticity, but on the structural form of the production function. Separability of the productivity shock, and additivity in particular, are consistent with homoskedasticity with respect to the piece rate in the linear regression model. We concentrate our study on the potential heteroskedasticity associated to the experimental changes in the workers’ incentives and how these changes interact with the productivity shocks in the production function. Unlike weather conditions or other exogenous factors, wages and piece rates are incentives that can be easily modified by a firm and constitute a powerful tool for inducing workers productivity in a principal-agent context.

Conclusions:

Structural assumptions about the production function have important consequences on the analysis of agents’ optimal behaviour and ultimately on the choice of adequate incentives to enhance their productivity. Using statistical tools to test between models with additive and multiplicative shocks is a relevant question for agency models. On the one hand, a separable production function rules out uncertainty considerations. In this case the optimal effort choice is independent of productivity shocks, which are the only source of randomness. For example under an additive structure, both the principal and the agent would gain from contracts that induce effort by only rewarding performance. On the other hand, a multiplicative production function would lead to an effort choice that is sensitive to productivity shocks. This form may imply potential gains in designing state dependent incentives that change with the realization of the productivity shock, offering workers a wider range of piece rate depending on the working conditions, insuring their risk, sorting them across working environment, or even designing contracts according to their specific risk preferences. Moreover, a multiplicative structure would allow for convenient transformations of the production function such as the logarithmic transformation, which facilitate the empirical estimation of workers productivity.

Table des matières

Introduction 1
1 Fatigue, Rest, Productivity, and Work Schedule: An empirical analysis
using personnel records 
1.1 Introduction
1.2 Tree-planting
1.3 Data
1.4 Model
1.5 Estimation Results
1.6 Model Predictions
1.7 Conclusions
1.8 Bibliography
Appendix
2 The Role of Productivity Shocks in the Effort Choice of Agents: Using
experimental data to test for additivity in the production function 
2.1 Introduction
2.2 Tree-planting
2.3 Experimental Design and Data
2.4 Model
2.5 Estimation Results
2.6 Conclusions
2.7 Bibliography
Appendix
3 Conditional and Unconditional Cooperation in a Public Goods Game:
Experimental evidence from Mali 
3.1 Introduction
3.2 Background
3.3 Experimental Design
3.4 Model
3.5 Data and Descriptive Analysis
3.6 Estimation Results
3.7 Model Predictions
3.8 Conclusions

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