Jordan Kyle







'V' graphs


‘V’ graphs plot coefficients and standard errors from separate regressions on different panels of data. They are ideal for cases when you expect the coefficient of an independent variable to either operate in opposite directions for separate panels or when you expect the coefficients to be insignificant for particular panels.

For example, in a current working paper on the determinants of bilateral aid fragmentation, my coauthors and I expected donor countries to allocate foreign aid differently based on recipient country characteristics. We therefore decided to run separate regressions for each donor country. We find negative and significant, positive and significant, and insignificant relationships between the recipient country’s bureaucratic quality and aid fragmentation depending on the donor country. In the pooled model, these countervailing effects resulted in an insignificant coefficient, even including donor country fixed effects. Running separate regressions for each donor and plotting the coefficients and standard errors for recipient bureaucratic quality for each different donor allows the reader to quickly see the more nuanced (and interesting) pattern. Some donor countries give significantly more fragmented aid to countries with high bureaucratic quality (South Korea, France, and New Zealand), while other donors give significantly less fragmented aid to recipient countries with high bureaucratic quality (USA, Switzerland, and Norway):


The dotted line represents the ratio between coefficient size and standard error required for 95% statistical significance (1/1.96). Therefore, all points beneath the dotted line are statistically significant, and all points above the dotted line (inside the 'V') are not significant at the 95% level. To the extent that points cluster in one region of the graph, we can have greater confidence that a pooled model is appropriate. For example, we find consistently positive and significant associations between donor fragmentation and aid fragmentation:

R code to run separate regressions over different panels and store the coefficients and standard errors from each regression, then to produce the 'V' graphs can be found here. The code has been generalized to so that it can easily be used for any dataset. STATA code to produce the 'V' graphs can be found here (STATA version does not include the code for the loop that stores coefficients and standard errors). Specific code to produce the graphs shown here can be provided upon request.

Thanks to Macartan Humphreys for providing the idea for these graphs and to Neelanjan Sircar for help with the R code.