–Weisiger (2014) “A good understanding of when resistance is likely after conquest should inﬂuence leaders’ decisions about whether to ﬁght in the ﬁrst place, whether to accept compromise settlements prior to a ﬁnal military victory, and when it may be worthwhile to encourage resistance among friendly conquered populations”

0 50 100 150 50 100 150 200 Sample Size Relative Contribution of Variance Compared to Bias Number of Variables 3 6 9 Intercept −1 −0.5 0 The Relative Contribution of the Variance Compared to the Bias as the Sample Size Varies

PML in Short • Always better in theory. • Easy to implement. • Makes a big difference in small samples. • Makes a small, but noticeable, difference in much larger samples.

1. Choose the number of covariates k randomly from a uniform distribution from 3 to 12. 2. Choose the sample size n randomly from a uniform distribution from 200 to 3,000. 3. Choose the intercept cons randomly from a uniform distribution from -4 to 4. 4. Choose the slope coefﬁcients 1, ..., k randomly from a normal distribu- tion with mean 0 and standard deviation 0.5. 5. Choose a covariance matrix ⌃ for the explanatory variables randomly using the method developed by Joe (2006) such that the variances along the diagonal range from from 0.25 to 2. 6. Choose the explanatory variables x1, x2, ..., xk randomly from a multivari- ate normal distribution with mean 0 and covariance matrix ⌃ . Generating a Random DGP