Annex 4A Meta-regression analysis

A random-effects model assumes that there is a distribution of true effects rather than a common fixed effect across studies (DerSimonian and Laird 1986). In particular, a study-specific estimate of the informal-formal wage gap has a sampling distribution 2ˆ ( , )i iN θ θ σ ∼ , where σ 2 is the within study variance of the estimate due to a sampling error; and the true effect has the following distribution θi ~ N(μ, τ 2 ). Meta-analysis pools information across many studies to estimate μ and τ 2, where τ 2 measure the degree of across-study variations.25 The proportion of total variation in study estimates is equal to I 2 = τ 2 /(τ 2 + σ 2 ) and reflects the impact of across-study heterogeneity (Higgins and Thompson 2002). The meta-regression analysis (MRA) can be performed to associate this variation with any characteristics of the study or sample.

The MRA of estimated wage differentials between formal and informal jobs uses estimates of the wage gap drawn from each study as the dependent variable. The set of regressors, or moderator variables, includes study characteristics that are deemed consequential for the reported results, for example, identification and estimation methods, study design, and data sources. This, in particular, helps clarify the diversity of research outcomes on the size of the informal-formal wage gap and identify the sensitivity of reported wage gaps to study-specific methods and data. A random-effects MRA is performed by estimating the following regression:

k ˆ j j i i ii X θ = µ + α + ∈ +ϑ  ,

(4A.1)

ˆ

j iθ where is a study-specific estimate of the informal-formal wage gap, ϵ i is a sampling iϑ error with a standard deviation that may vary across studies, and is an error term reflecting across-study variation of true effects with a constant across-study variance τ 2 ; finally, the set of moderator variables, X, includes the following: • A dummy variable accounts for differences in methodology: FEi is 1 if fixed effects were used to correct for unobserved workers’ characteristics and 0 otherwise.

• Two dummy variables reflect the gender composition of the sample: FEMALEi is 1 if estimates were obtained for female workers only and 0 otherwise, –MALEi 1 if estimates were obtained for male workers only and 0 otherwise. The reference categories for this set of dummy variables are estimates obtained with samples containing both female and male workers. • Regional dummy variables are included to account for regional heterogeneity. • Self-employedi is a dummy variable indicating that a study measured the wage gap between self-employed and formal employees.

25 The random-effects meta-analysis estimate is a special case of a generalized method of moments estimator, where each estimate is weighted proportionally to its sampling error. Thus, it can only be applied to studies that reported standard errors of their inform-formal wage gap estimates.