Reply to Golan and Rosenblatt: Revisiting the statistical analysis of the Israeli–Palestinian conflict confirms that both sides retaliate

We thank Golan and Rosenblatt (1) for their comments on our analysis (2), which we address in turn. First, Golan and Rosenblatt suggest that the time series may be nonstationary (that is, the distribution of the variables in the data may change over time). Our original paper addressed this concern in two ways. First, we tested for stationarity using the standard Dickey Fuller test. The results (table S2 in ref. 2) supported the stationarity hypothesis. Second, we included year dummy variables to control for structural breaks. We chose years rather than political events for these dummy variables to avoid the arbitrariness inherent in the latter approach. Thus, nonstationarity is not a concern for our conclusions. Nevertheless, Golan and Rosenblatt answer an interesting additional question by showing that the patterns of retaliation vary across subperiods. Golan and Rosenblatt also suggest a modified model in which (i) the same lag is used for all time series, (ii) a square rootstabilizing transformation is applied to the data before analysis, and (iii) all three variables (Qassam firings and Israeli and Palestinian fatalities) are included in the equation. We find that this alternative model does not fit the data better than ours. The mean-squared prediction error of our model was 7.894 ± 1.564 (mean ± 1 SE), and the mean-squared prediction error of the model by Golan and Rosenblatt (1) is 7.717 ± 1.466; the difference in fit is insignificant (t = −0.95, P = 0.34). However, we are pleased that this model confirms our main result, which is that both sides retaliate. Table 1, which replicates our original analysis with the modifications suggested by Golan and Rosenblatt, confirms this claim. Note that the F-tests that we use are consistent by standard results from large-sample theory (3), despite the claims of Golan and Rosenblatt to the contrary. An interesting difference between our original model and the model of Golan and Rosenblatt is that, in their analysis, Qassam attacks lead to Israeli retaliation, whereas in our model, they did not. Golan and Rosenblatt correctly say that it is more customary to fit vector autoregressions (VARs) using all predictor variables with the same number of lags, and although this does not lead to an improvement in model fit in this case, it lends weight to the view that Israel does indeed retaliate for Qassam firings. Golan and Rosenblatt further argue that figures 2 and 3 in ref. 2 do not take the autocorrelation of the data into account. We fully agree that plots of the VAR impulse response functions are more informative. We merely showed the response functions used by Jaeger and Paserman (4) to allow comparison of our results with their results. Of course, all statistical results and conclusions of our paper were based purely on the VAR results, which control for autcorrelation. Finally, Golan and Rosenblatt point out that, by computing the proportion of events that can be attributed to retaliation based on the first day rather than several days after an attack, our analysis provided a lower bound on the proportion of events that can be attributed to retaliation. This is correct; we chose this approach to be as conservative as possible and to avoid overstating our results. However, we are encouraged that lessconservative approaches confirm our findings.