 presentation is also about aid and growth and it's in a way related to the previous presentations in the sense that I'm also going to talk about the impact of aid on growth, but unlike the two presentations, my focus will be like in analyzing the accumulated evidence of aid on growth in the past three or four decades using data analysis. So before I move on to the main discussion regarding aid and growth, let me just try to give you a brief highlight of what meta-analysis is about. Meta-analysis is a method which is commonly applied in medical science research, but nowadays it's becoming very common to apply meta-analysis in the field of social science like economics as well. The main idea here is to quantitatively combine empirical results from range of independent studies that have been accumulated over the years and to get or calculate a single estimate of the effect of interest. For instance, in our case, the effect of interest is the impact of aid on growth and this single effect estimate is calculated as a weighted average from the existing empirical evidence. So in doing so, one can either allow for or ignore the heterogeneity or difference between the studies under consideration depending on the assumption that the meta-analysis makes regarding the true impact of aid on growth, for instance, in this case. If the meta-analysis decides to ignore the heterogeneity between the studies, then the underlying assumption is that there's only one single true effect, in our case, effect of aid on growth, that all papers are targeting to estimate. And in this case, any variation in the reported effect estimates is only due to chance or only due to sampling error. The idea here is that, let's say, if all studies have got infinitely large sample size, then this assumption implies that all of the studies will converge to a single true effect. In the language of meta-analysis, this is what's termed as fixed effect model. By way of contrast, if the meta-analysis decides to allow for heterogeneity, then this means that, or the underlying assumption is that each paper targets to estimate a different true effect. In this case, the variation is due to chance or sampling error, just like above. But in addition, there's also a true variation between the studies. So in the language of meta-analysis again, this is what's termed as random effects model. Having said this, let me try to give you some idea or information about our motivation and objective of the paper. Over the last decades, the empirical evidence on aid and gross has been accumulated. But the results are very mixed. Some say that aid works, and others claim that aid doesn't work. While others argue that aid works, but its effectiveness depends on various factors. For instance, the level of aid or institutional quality or policy. And there are also other scholars who take a middle ground and argue that aid works, but the effect is modest. In recent years, we've positive yet modest and significant impacts are emerging. Despite this, the debate is still on. And at times, we also hear very pessimistic views about the ability of aid in buying gross. So against this background, it's interesting to ask what the accumulated empirical evidence on average has to say about the impact of aid on gross. And this is the question that we have addressed in our meta-analysis paper. In particular, we try to address two specific questions that are standard to every meta-analysis. The first question is whether the overall empirical effects of aid on gross, in this case, is different from zero when one combines all the existing empirical evidence. Then if the answer to this question turns out to be to the positive, then the next interesting question is whether this observed effect is genuine or is it an artifact of publication selection, which is also known as a file drawer problem. Let me try to define what publication bias is. This is basically a phenomenon which arises when researchers, reviewers, or editors tend to favor statistically significant results, causing other studies with small effect or insignificant effect to remain in the file drawer or to remain unpublished. Whether this is really a case in the aid gross literature is something that we're going to see in a while. In order to answer the above two questions, we rely on a database of six state aid gross empirical studies that are identified by the Suliagos end pile down 2008. Henceforth, I'll refer some DP08. And since each paper reports one or more regressions, at the end, we got 541 observations for our meta-analysis. These authors, using a meta-analysis of the above six state studies, reach out a pessimistic conclusion. In particular, they point out that the impact of aid on gross is nonexistent when one calculates the accumulated evidence from the existing literature. And they also add that any positive impact that one sees in the literature is a result of publication selection or publication bias. So we decide to make a careful assessment of their analysis and we fully replicate their results. In due course of our work, we identify three major concerns in the DP08 analysis. The first relates to problems with econometric model choice. This is basically a decision between the choice between random effect and fixed effects model that I mentioned in my introduction. DP08 rely on fixed effects model. That means they assume that all studies estimate a single true effect of aid on gross. So we believe that this is an unrealistic assumption. And as we clearly show in our paper that this assumption is rejected based on theoretical and empirical grounds. The second concern that we came across is the inappropriate statistical choice that DP08 made. One problem here is a miscalculation of the partial effect of aid on gross for papers that include terms like aid square, aid policy interaction terms, and aid institution interaction terms. And these papers include these terms with the aim of capturing the nonlinear relationship between aid and gross. So we took this into account when we calculate the weighted average effect of gross in the empirical literature. And the second problem is the reliance of DP08 analysts on sample size as a measure of study precision. Whereas the preferred estimate of the precision is the precision estimate is the inverse of standard error. And certainly we also came across errors in data entry and coding and we try to rectify these errors in the data. In general, we have to keep in mind that the conclusions of any meta-analysts are only as valid as the methods used to code and analyze the data. So cognizant of this fact, we try to follow more appropriate methods that reflect the econometric statistical and data challenge at hand and also which are in line with the best practice and guidelines and meta-analysis. So what did we find? Our assumption of heterogeneity in the true effect of aid on gross across the six state studies gets clearly confirmed both with statistical tests and graphical tools. So while we calculate the weighted average effect from the existing empirical literature, we control for the heterogeneity across the studies and our weighted average effect result clearly shows a positive impact of aid on gross from the existing aid gross literature. At this point, it's worth noting that our results are quite in contrast to DP08. As I just mentioned, the authors assume a homogeneous or a single true effect of aid on gross, but as we show in our paper, this is clearly unfounded in the data. And their claim of the nonexistent impact of aid on gross from the existing aid gross literature is also not supported by the evidence as I just mentioned. Having said this, the next important question is, is the effect which I just mentioned, is it genuine or an artifact of publication selection? In meta-analysts, one can assess the presence or absence of publication selection using a visual inspection of a simple graph called a funnel plot, which is very common in meta-analysts. And this simply plots a measure of study precision and the effect size. The main idea is that if there's no publication bias, then we should be able to see an inverted funnel shape. So do we have that in the aid gross literature? This is the graph we got while we do the funnel plot of the aid gross literature. As you can see, it's pretty much similar to an inverted funnel shape. And the intuition here is that the vertical line in the middle of the graph is the estimate of the true effects from the literature. So as you can see, the estimates are distributed on both sides of the true effect. The idea is the effect estimate of less precise studies will be widely distributed across the true effect. And then as precision of the estimates increases, then they start to converge to the true effect. So this will give us an inverted funnel shape. And that's what we got from the aid gross literature, suggesting that there is no publication or directional bias. But we don't make a firm conclusion out of this graph because this is based on visual inspection. So in order to make a firm conclusion regarding absence of publication bias, we also run regression-based tests which are available in metanalysts. In particular, we run a multivariate regression for publication bias by including all the important study characteristics, like the methods that are used in the papers, the data, and the sample and things like that. And the evidence from all multivariate regression clearly shows the absence of publication bias in the aid gross literature. Moreover, our multivariate regression analysis also confirm or corroborate the authenticity of the positive impact of aid on gross in the literature. Again, our conclusions are in stark contrast with DP08, but this shouldn't come as a surprise because as we clearly indicate in our paper, their analysis is exclusively based on a bivariate regression which fails to control important study characteristics. So in conclusion, if one considers economic gross as an outcome indicator, then the existing aid gross literature on average shows a positive and statistically significant impact of aid on gross. And above all, the meta-analysis clearly shows that this effect is genuine and it's not an artifact of publication selection. But we don't believe that this is the whole story about ed effectiveness. As some rightly mentioned, aid has multifaceted objectives and it's given for various reasons. And economic gross is only one of the objectives. In fact, perverted reduction and improvement in quality of life is among the main targets of foreign aid programs, particularly following the adoption of the Millennium Development Goals. So we need to keep those important outcomes in mind while we make assessment of ed effectiveness. And last but not least, even if we see a positive and significant impact of aid on gross from the literature, there is still a need to further improve the design and the implementation of foreign aid programs in order to further maximize the benefits out of them. So thank you for your attention.