5. Firm performance and workers’ wages Evidence from Microenterprises in Uganda 85
5.4. Estimation Model
When analysing the relationship between firm profits and workers’ wages a methodological challenge arises from the multilevel structure of the data. Multilevel data structures exist when some units of analysis are considered as subsets of other units, while data for both units are available. In our data, there are two levels of analysis, the worker level (level 1) and the firm level (level 2), with workers being nested into firms. When estimating multilevel data, one has to account for variance in the dependent variable that is measured at the lowest level of analysis while considering information from the higher level of analysis as well. Ignoring the multilevel
2 Information on the workers’ tenure and the age of the employer is only available for 2012.
Firm performance and workers’ wages: Evidence from microenterprises in Uganda 99
data structure creates both conceptual and statistical problems. If the contextual levels, i.e.
firms, are dropped, the arenas for wage determination are ignored. Aggregating the data to the firm level and ignoring the individual level opens for the ecological fallacy3. Through “naive pooling” (Burton et al., 1998) and thereby ignoring the multilevel data structure, it appears as if all individuals are independent observations. However, in this context, error terms are likely to be correlated in a nested way. First, worker observations are not independently distributed among and within firms. Similar workers might be hired into the same firms and therefore build homogenous clusters. Second, workers could be commonly affected by unobserved firm effects. Third, it is very likely that a large share of workers is employed in the same firm for multiple waves, leading to correlated worker observations within firms over time. These problems may lead to incorrect standard errors, inflated Type 1 error rates and biased parameter estimates (Peugh, 2010).
Therefore, we estimate the multilevel model using the estimated dependent variable (EDV) approach (Hanushek, 1974; Lewis & Linzer, 2005). This is a two-stage approach: In the first step, a separate model for individuals nested within each level 2 unit is estimated. In the second step, the estimates obtained in the first step are used as the dependent variable to be explained by a set of aggregate predictors. That is, first, individual wages are regressed on workers’ human capital and a firm-fixed effect. The estimated firm-level fixed effect is an unambiguous measure of the firm-specific wage premium, which is then regressed on firm characteristics to explain differences in firm wage policies (Cardoso, 2000).
The first-stage model looks as follows:
𝑤𝑖𝑗𝑡= 𝛽1 𝐼𝑖𝑗𝑡+ 𝐹𝐸𝑗𝑡+ 𝜑𝑖𝑗𝑡+ 𝜀𝑖𝑗𝑡 (23) where the dependent variable 𝑤𝑖𝑗𝑡 is the individual wage of worker 𝑖 in firm 𝑗 at time 𝑡, 𝐼𝑖𝑗𝑡 is a vector of controls for worker productivity, 𝜑𝑖𝑗𝑡 is unobserved worker heterogeneity, 𝜀𝑖𝑗𝑡 is the error term, 𝐹𝐸𝑗𝑡 is a firm-fixed effect allowed to vary over time. By using firm- and time-fixed effects, we eliminate bias from unobservables that change over time but are constant over firms and unobservable factors that differ across firms but are constant over time. The estimated firm-time-fixed effect 𝐹𝐸𝑗𝑡 is used as dependent variable 𝑤̂𝑗𝑡 in the stage 2 model, given by
ŵjt=β0+ β1 Fjt + β2 πjt +yt + ejt (24) where 𝑤̂𝑗𝑡 is the estimated dependent variable representing the firm wage premium, 𝐹𝑗𝑡 is a vector of firm controls (capital intensity, firm age, firm size, the entrepreneurs’ education,
3Ecological fallacy is referring to the bias stemming from deducing inferences about individuals from the group they belong to (Steenbergen & Jones, 2002).
100 Firm performance and workers’ wages: Evidence from microenterprises in Uganda
industry), 𝜋𝑗𝑡 is the firms’ profit per working hour, 𝑦𝑡 are year dummies and 𝑒𝑗𝑡 represents the error term.
Since the dependent variable of the stage 2 regression is based on estimates, the regression residual can be thought of as having two components (Lewis & Linzer, 2005). The first component is the usual random shock that is part of every regression. The second component is the sampling error, which is the difference between the true and the estimated value of the dependent variable. If the sampling variance differs across observations, the second component will be heteroscedastic. The first component, the random shock, however, could well be homoscedastic. When running a simple Ordinary Least Squares (OLS) regression, heteroscedasticity of the second error component is ignored. A weighted least squares regression (WLS), on the other hand, assumes that the entire residual (the first and second component) is heteroscedastic. Both, OLS and WLS are inefficient and might produce inconsistent estimates of the error term. Lewis and Linzer (2005) argue to use a Feasible Generalized Least squares (FGLS) estimator which uses the variance-covariance matrix from the standard errors of the first stage to generate a weight, which can be used to adjust the second stage regression. The weights (adjusted for a panel dimension) are calculated as follows:
𝑤𝑒𝑖𝑔ℎ𝑡𝑗𝑡 = 1
√𝑆𝐸 𝑤̂𝑖𝑗𝑡2+ 𝜎̂𝑗𝑡2
(25)
where 𝑆𝐸 𝑤̂𝑖𝑗𝑡 are the standard errors of the dependent variable from the first stage and 𝜎̂ is 𝑗𝑡 an estimate of the variance of the error term in the second stage that is not due to the sampling error of the dependent variable (ibid.). To account for the special structure of the error term, we estimate the second stage model using OLS with robust standard errors and using FGLS.
The estimation may further be biased due to the possibility of worker sorting, meaning that more productive workers sort into higher paying firms. A correlation between profits and wages would hence rather be driven by productivity differences between workers than by different firm wage policies. As we have panel data for the firm but only repeated cross-sectional observations for their employees, it is not possible to control for unobserved heterogeneity in workers across firms. By regressing wages on workers’ human capital and a firm-level fixed effect, wages are purged from (some) observed differences between workers (and unobservable differences correlated with them) (Fafchamps & Söderbom, 2006). Brown and Medoff (2003), Criscuolo (2000), Arai (2003) and Söderbom et al. (2005) examine the relationship between firm size and wages for a variety of countries and conclude that omitting controls for worker heterogeneity yields a bias of relatively moderate magnitude.
Firm performance and workers’ wages: Evidence from microenterprises in Uganda 101