American trade policy towards Sub Saharan Africa –- a meta analysis of AGOA

Sterne, 2001). Borenstein, et al. (2009), Stanley (2005, 2008), Stanley, et al. (2008), Sterne (2001) have
emphasised the need to carry out formal testing of publication bias since the visual inspection of the graphs
can be subjective. The formal testing is discussed in the MRA models below.

Fixed effect vs. Random effects models

Two major approaches exist for summarising the study effects reported in each study to obtain a pooled
estimate. The random effect models (REM) and fixed effect models (FEM) are the main approaches. The
FEM assumes all studies have the same effect size (μ) and that any departure from the observed effect are
purely due to random errors (ei) (Borenstein, et al., 2009). On the contrary, the REM assumes that the
effect size varies across studies and are randomly distributed within each study (Borenstein, et al., 2009).
The pooled estimates provided by these models are simply the weighted means of the observed study effects
(in our case, the weighted means of the reported coefficients) (Borenstein, et al., 2009). In the FEM model,
the summary effect is given by a weighted average of the study effect sizes and the weights are the inverse
of the variance of the coefficients reported in each study (Equations (1) - (3)). The weights calculated in the
FEM model penalises smaller studies while giving more weight to larger studies (Borenstein, et al., 2009).
The REM on the other hand, does not penalise smaller studies and incorporates all studies without having
any particular study strongly influencing the summary estimate (Borenstein, et al., 2009). Equations (3) -
(7) represent the REM. The REM uses a moments based estimator in calculating the weights for θ^REM this
is known as the DerSimonian and Laird method (Borenstein, et al., 2009). The Q calculated in Equation
(6) can also be taken as a test for the presence of homogeneity between studies distributed as χ² with k - 1
degrees of freedom (Borenstein, et al., 2009, Feld and Heckemeyer, 2011) in addition to the I² discussed
below.

Where, Vb_i is the variance of bi , Wi are the weights assigned to each study, bi are the observed effect size
in the studies selected, and θ^FEM , θ^REM are the FEM and REM pooled estimates of the various effect
sizes respectively, df = k - and k is the number of studies. The variances of the pooled estimates are

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