3 Stylised facts about data
Figures (1) - (5) show various features of the underlying data for the meta analysis. Figure (1) and (2)
show various funnel plots to provide a visual aid in identifying any publication bias present in the meta
analysis. The Sub-figure (a) plots the precision of the estimated agoa effect against a partial correlation
of the agoa coefficient. Here all estimates are included. However, the remaining 3 sub-figures exclude 6
large estimated coefficients reported in one of the studies. These coefficients are larger than 300 while the
remaining coefficients used in the plots are less than 4, hence their exclusion in this case. Panel (b) shows
a funnel plot with the missing estimates to the left of the mean included. Figure (1) and (2) indicate that
publication bias is plausible. There are more positive effects than negative effects as shown by the vertical
line at the mean of zero. Borenstein, et al. (2009) note that the interpretation of the funnel plot can be sub-
jective and there is the need for other tests to be carried out (also, Stanley, 2005, 2008, Stanley, et al., 2008).
Following Stanley (2005, 2008) and Stanley, et al. (2008) we carry out formal tests of publication bias in
addition to the funnel plots shown in this section. Figure (5) also depict funnel plots. The difference here
is that, the number of years of data available after the passage of agoa is varied. The figure indicates that
among the studies chosen, publication bias tends to increase as more data becomes available. This might not
be indicative of publication bias but an indication of the fact that with the passage of time more and more
countries adopt agoa and increase their exports to the US under the program. If that is the case, then more
positive coefficients would be expected as displayed in the various sub-figures of Figure (5). Sub-figure (g)
shows that studies with 8 years of post-agoa data only reported positive coefficients without any negative
coefficients in their analysis.
We include two Galbraith plots in Figure (3). A considerable number of coefficients obtain t-statistics
greater than 2 in absolute value. Two lines of fit are also included in the diagram. The green line indicates
the fit for unpublished studies while the thick red line indicates the fitted values for the published studies.
The large reported estimates were present in one unpublished study hence, the line of fit becomes very steep
in the second panel. Panel (a) excludes the six large estimates whiles Panel (b) includes them. Both figures
are consistent with the funnel plots shown earlier. Finally, Figure (4) plots the coefficients (and T-stats)
reported against the number of post-agoa years of data available as well as the number of years after agoa,
the paper was written. A quadratic fit is added in each sub-figure. The figures indicate a slight U-shaped
relationship. In the initial years after agoa, large coefficients and highly significant results were reported.
However, this tended to reduce till 6 years after agoa when larger and more significant coefficients were
reported again. Thus with the passage of time smaller coefficients are reported while larger t-statistics are
reported. This is similar to the findings of Stanley, et al. (2008) for the relationship between t-statistics
and unemployment. Although, they show an inverted-U shaped quadratic fit1 they also find larger absolute
t-statistics reported with the passage of time.
1 Their t-statistics are all negative compared to ours that are mostly positive. Thus considering absolute values we both display a
similar trend. To establish this result further, we would require more annual data on published studies post-agoa