The classical Oaxaca-Blinder decomposition assumes the linearity of the conditional mean, which may not hold (Barsky et al., 2002). However, Fortin et al. (2011) propose the application of reweighting technique to deal with the possibility of the linearity assumption breaking down. This according to Barsky et al. (2002) prevents the estimates of consistent endowment and return effects. However, Barsky et al (2002) argue that in the presence of non-linearity, as in the case of wealth-earnings relationship, Oaxaca-Blinder decomposition is likely to produce inconsistent estimates. The literature suggests two approaches to deal with this problem. The first is the use of a non-parametric approach to estimate the conditional expectation. Barsky et al (2002) however proposed the use of a non-parametric method by adopting the reweighting approach put forward by DiNardo et al (1996). Though their paper concentrated on estimation of counterfactual densities, the approach is applicable to any statistical distribution. We follow this approach of using the reweighting technique as in Fortin et al (2011). The technique uses a reweighting function to estimate counterfactual densities.
The underlying principle of the reweighting technique is to make the characteristics
of firms in group “A” similar to firms in group “B” and perform decomposition using
RIF regression technique. The reweighting technique allows us to superimpose the characteristics of firms in group “A” on firms in group “B”. To obtain the
counterfactual densities we reweight group “A” firms with weights (X), which depends on the values of the covariates. Baye’s rule is used to determine these
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(4.15)
where is the probability of a firm belonging to group “A”. and are the samples proportions for group “A” and “B” respectively. The reweighting factor given in equation 4.15 indicates that weights are calculated
from the probabilities of belonging to a particular group, say “A”, conditional on the
covariates (X). In this regard, the reweighting factor is obtained by estimating a
probability model of a firms belonging to group “A”. Empirically, we estimate either a probit or logit model for the probability of belonging to group “A” and “B” using
the pool data for the two groups. The estimated probabilities are then used to
compute the reweighting factor for each firm in group “B”. We proceed by calculating the counterfactual statistics of interest using observations from group “B”
reweighted using the computed reweighting factors. Next, we perform decomposition similar to the Oaxaca-Blinder approach using the reweighting factor, the RIF regression and also the counterfactual distribution of turnover for any unconditional
quantile ( ). The total turnover gap at the the quantile is then given as the difference
between actual averages and the reweighted counterfactual average of both endowment and returns components. It is written as:
(4.16)
Where, superscript C represents the reweighted sample estimates of the counterfactual distribution. The turnover gap can be decomposed further into a true endowments and returns effects and error terms which are given by:
(4.17)
(4.18)
The terms and represent respectively the pure endowment (pure composition) and pure return (pure structure) effects. The second term ( ) in equation 4.17 captures the specification (approximation) error, it captures errors in estimation resulting from the RIF being non-linear, thus measures error due to the fact that the RIF regression procedure is based on the local approximation of the unconditional distribution of interest (turnover). The smaller the specification the
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more robust the RIF estimation is and vice versa. In equation 4.18 the second term, , is the reweighting error capturing the fact that the endowment effect obtained from the reweighted RIF regression decomposition differs from that obtained from the standard Oaxaca-Blinder decomposition when the reweighted mean is different from the non-reweighted mean. The reweighting error turns to zero if the reweighting factor is consistently estimated especially when large samples are employed. The reweighting-RIF regression technique like the RIF regression provides results that are path independent. However the sum of the share of each covariate is not equal to the total contribution of covariates. This difference is an interaction effect between the different covariates which is difficult to interpret (Fortin et al, 2011).
The chapter examines the contribution of individual covariates to turnover differentials, as it enables an assessment of the contribution of ICT capital to turnover differentials in each country. This is a major contribution of this chapter to the empirical literature. Each decomposition analysis is conducted at the country level. Specifically, the chapter assesses differentials in turnover of firms with access technology type, j, relative to those with no access to technology40 j. The chapter also analyses the gaps in turnover of micro sized firms against small-medium sized firms. Decomposition by managerial control type is also estimated to assess the differential (gap) in turnover, and the contribution of endowment and returns to this gap, focusing on the contribution of ICT capital.
3 Empirical results
Having outlined the relevant methods in the previous section, we present the results of decomposition analyses evaluated at the mean and at different quantiles (mean and quantile decompositions). For the mean decomposition analysis, we present 4 decomposition41 results specified in the previous section. With respect to quantile decomposition, we present results of 2 decomposition analyses. For easy of
40 The study uses two technology types, which are internet and computer accessibility. Here
decomposition is undertaken by these two types of technology.
41The study also performed decomposition by SME’s age, industrial sector and by formality index of the SME. In all these decomposition analysis the study found no significant differences across the various groupings. In the case of quantile decomposition we drop firm size decomposition since we find no significant differences between small and micro firms.
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discussion, we grouped these 2 sets of decomposition results into one broad heading: decomposition by technology type. As discussed in the previous section detailed decomposition of turnover by these groupings allows us to assess the relative
contribution of firms’ endowment of ICT capital, and the return to these endowments
to turnover differentials.
The return effect captures the variation in the returns to the characteristics between groups of firms. The third component of the threefold decomposition is the interaction term which estimates the simultaneous effect of differences in endowments and returns. That is, it accounts for the fact that differences in endowments and returns exist simultaneously between two groups. In addition to the mean decomposition, we also decompose the individual effect of the explanatory variables along different quantiles rather than only at the mean of the distribution. Decomposing at the mean does not allow for assessment of differences in turnover among the various groupings at various quantiles of the distribution, as differences may differ along the distribution. We therefore apply an unconditional quantile decomposition to assess the contribution of both endowments and its returns to turnover gaps of firms along the distribution laying emphasis on contribution of ICT capital. We present two sets of quantile decomposition results: the RIF regressions results and the reweighting RIF results. We base the discussion of the quantile decomposition results on the latter.