Figure 1.12, in contrast, plots the naïve relationship between average picker productivity and piece rate wages, temperature, and two other observable characteristics: time of observation and worker tenure by season. First, note that productivity and piece rate are negatively correlated, since farmers lower the piece rate when fruit is plentiful in the fields. Second, note that there are no sharp decreases to average productivity at particularly high temperatures, as one may hypothesize. Finally, note that there is a clear increasing and concave relationship between worker tenure within a season and productivity. In other words, there is learning-by-doing in berry picking, and this learning has decreasing marginal returns over time. While most employees out-earn the hourly minimum wage under the piece rate system, some fall below this threshold and are paid according to the minimum wage for the day. As Graff Zivin and Neidell note, if there is not a credible threat that these workers could be fired for their low output, they may shirk and provide less effort than they otherwise would. Figure 1.13 plots the distribution of normalized daily productivity that identifies those picker days where shirking could be a problem. Observations to the left of one are picker-days where the picker’s effective hourly wage is below the minimum wage, raspberry cultivation pot and observations to the right of one are picker-days where the picker out-earns minimum wage under the piece rate scheme.
A picker with a normalized productivity measure of two is earning twice the minimum wage. Productivity in this figure is normalized because both piece rate wages and the hourly minimum wage vary over the sample period. Shirking, if it occurs, could bias my results. In particular, if high temperatures or low wages lead to more pickers earning the minimum wage, and these pickers subsequently shirk, my econometric estimates will be biased upward. I address this concern in section 1.6 by re-estimating my primary results using only those picker-days where employees out-earn the minimum wage. My findings do not change when I eliminate these observations, suggesting that the threat to a picker of being fired if they consistently slack off is a sufficient incentive to keep them from shirking.The model presented in section 1.2.1 motivates my empirical strategy. In particular, my goal is to estimate the relationship between piece rate wages and labor productivity . The primary challenges to this undertaking are twofold. First, many observable and unobservable factors contribute to worker productivity which – if unaccounted for – could lead to omitted variable bias in my estimates of temperature and wage effects. Second, piece rate wages are endogenous to labor productivity. To address factors other than the piece rate wage that could drive labor productivity, I exploit the richness of my data and include flexible controls for temperature, and a host of fixed effects.
Most importantly, I include time fixed effects to capture seasonality , work patterns , and season-specific shocks . I also include field-level fixed effects to capture variation in the productivity of different varieties and plantings of blueberry bushes. The combination of time- and field-level fixed effects gives me a credible control for the average density of blueberries available for harvest at a given time in a given field. In other words, these fixed effects allow me to control for resource abundance . Further, I include worker-specific fixed effects to capture heterogeneity in picker ability. Lastly, I include a quadratic of worker tenure to allow for learning-by-doing. When estimating the effect of temperature on productivity, my identifying assumption is that individual realizations of temperature are as good as random after including the controls described here and the piece rate wage. To address the endogeneity of piece rate wages to labor productivity, I instrument for these wages using California market prices for blueberries. In order for these prices to be a valid instrument for wages, they must be correlated with farms’ piece rates, but not affect labor productivity through any other channel. Figure 1.10 plots piece rate wages and market prices over time and suggests a strong correlation between the two variables. I provide formal evidence of this relationship in table 1.4, which I describe in detail in the following section. As evidence that the exclusion restriction holds – that market prices do not affect labor productivity except through wages – I rely on the size and heterogeneity of the California blueberry industry.
Statewide market prices capture supply shocks from growing regions around the globe, each with different weather, growing conditions, and labor markets. To the extent that environmental conditions agronomically drive blueberry production, they do so differentially across different growing regions of California. Therefore, any one farm’s temperature shocks in a given growing season do not determine aggregate blueberry supply. Additionally, both of the farms I study are quite small in comparison to the statewide market: they are price-takers and cannot independently affect average prices. As a result, market prices capture exogenous variation in aggregate supply shocks and serve as an effective instrument for piece rate wages.While the richness of my data allows me to exploit intra-day variation in temperature, I can also collapse my data to the day-level and investigate how daily temperature affects daily worker productivity. Figure 1.15 reports the results of three different day-level temperature specifications. The first uses time-weighted average daily temperature experienced by each picker, the second uses daily maximum temperature, and the third uses daily minimum temperature. Overall, the results from these specifications support the qualitative results of my primary specification: extreme temperatures lower picker productivity, and cool temperatures are more damaging than very hot temperatures. One threat to the credibility of my findings in tables 1.2 and 1.3 is that temperature and wages may affect workers’ labor supply, both on the intensive and extensive margins. That is, workers may decide to work fewer hours on a particularly hot day, or choose not to come to work at all if the piece rate wage is particularly low. Such behavior would bias my estimates of how temperature and wages affect productivity by introducing unobserved systematic selection into or out of my sample. I investigate this possibility in table 1.5 by regressing temperature, wages, and controls on both hours worked and the probability of working. In column , the dependent variable is the number of hours worked by a picker in a single day, and temperature is measured as a time-weighted average experienced by the picker during that day. Here, I control for a picker’s start-time rather than their picking “midpoint.” In column , the dependent variable is an indicator for whether a picker worked at all in a given day, and temperature is measured as a daily midpoint temperature: /2. I use daily midpoint temperature in column in order to provide a consistent comparison between employees who show up to work and employees who do not, since I do not know when or for how long these absent employees would have worked had they come to work. Figure 1.16 displays the relevant temperature results from columns and of table 1.5. Overall, table 1.5 reports that neither wages nor temperatures affect labor supply in a statistically significant way. Similar to Graff Zivin and Neidell , I find the labor supply of agricultural workers to be highly inelastic in the short run.
This also matches the findings of Sudarshan et al. for weaving workers in India. This evidence gives me confidence in the validity of my baseline results. I now turn to how temperature affects berry pickers’ wage responsiveness. Table 1.6 reports the results of estimating a variant of equation separately across eight temperature bins. I find that wages have no meaningful effect on productivity at most temperatures, low round pots but have a statistically significant and positive effect on productivity at cool temperatures: those between 50 and 60 degrees. In particular, my estimate suggests an increase in the piece rate wage of one cent per pound at temperatures below 60 degrees increases average productivity by 0.28 pounds per hour. This reflects an elasticity of productivity with respect to the wage of roughly 1.6 at cool temperatures, and an elasticity statistically indistinguishable from zero at other temperatures. This “productivity elasticity” is considerably smaller than the 2.14 number estimated by Paarsch and Shearer . Table 1.7, which repeats the analysis from table 1.6 using ordinary least squares , highlights the importance of instrumenting for piece rate wages. This table highlights two important things. First, the effects of wages on productivity at low temperatures do not show up in a statistically significant way without correctly instrumenting for wages with market prices. Second, I am able to rule out any dramatically large effect of wages on productivity at most temperatures. Another threat to my findings is that workers who do not out-earn the hourly minimum wage in a given day may shirk when they know that additional productivity will not increase their take-home pay. Figure 1.13 reports the frequency with which workers fall below this minimum wage threshold. I face an econometric problem if the effects of temperature reduce workers’ productivity, increase the probability that workers earn the minimum wage, and hence encourage shirking. To ensure my findings are not meaningfully altered by this phenomenon, I re-estimate my main results using only picker observations where the picker out-earns the minimum wage for the day. This procedure drops my number of picking period observations from 305,980 to 257,689: a decrease of 15.8%. Figure 1.17 and table 1.8 present the results of my main temperature and piece rate wage specifications using this subsample. Finally, even if temperature and wages do not affect labor supply directly in a statistically significant manner, and even though worker-specific fixed effects capture individual workers’ average productivity levels, I still face a potential adverse selection problem. Specifically, if variation in temperature and wages affects which sorts of workers choose to show up for work, my results may capture workforce compositional effects rather than individual productivity effects. To address this concern, I re-estimate my results only using observations from those workers who work more than thirty days in the relevant season. The intention here is to focus on workers who are likely to have the least elastic extensive labor supply. The results of this robustness exercise are presented in figure 1.18 and table 1.9. Taken together with the other available evidence, these results largely support my baseline findings.My primary finding is that labor productivity, on average, is very inelastic with respect to piece rate wages: I can reject with 95% confidence even modest positive elasticities of up to 0.7. This upper bound is considerably lower than the estimates derived by Paarsch and Shearer and Haley . I show that, without controlling for seasonality, a regression of productivity on piece rate wages results in a negative and significant point estimate . However, even once I control for seasonality, a naïve OLS regression of productivity on piece rate wage may be biased toward zero of table 1.4. By instrumenting for piece rate wages with the market price for blueberries, I can identify a precisely-estimated inelastic effect of table 1.2. However, my primary specification makes the restrictive assumption that wages affect productivity linearly and in the same manner at all temperatures. Table 1.6 confirms that piece rates’ effect on productivity is very much non-linear across different temperatures. Specifically, wages seem to spur productivity at cool temperatures . At other temperatures, wages do not affect productivity in a statistically significant way. This empirical finding directly challenges one of the core assumptions of the model presented in section 1.2.1: that productivity always rises with the wage . What is going on? One possible explanation for my findings is that, at moderate to hot temperatures, workers’ face some binding physiological constraint on effort that prevents them from responding to changes in their wage. Put bluntly, blueberry pickers in general may already be “giving all they’ve got” at the temperatures and wages I observe. Figure 1.19 summarizes this possibility using the theoretical framework developed in section 1.2.1. While the model in section 1.2.1 is straightforward and tractable, it is not the only way to conceptualize worker effort and productivity. In particular, rather than modeling effort as an unrestricted choice variable, one could assume each worker has a finite daily budget of effort that must be allocated across different activities throughout a day and Becker . Such a model would allow Xr to be zero or even negative under certain conditions, implying a backwards-bending effort supply curve, somewhat analogous to the canonical backward-bending labor supply curve .