5.2. Turnover and average performance
The above analysis implicitly assumes that the central government makes decisions on the turnover of provincial leaders solely on the basis of annual economic performance. While this assumption is easy to justify empirically, it overlooks the fact that provincial leaders are appointed officially for a 5-year term. While no detailed evidence is available on how the central government evaluates provincial leaders, casual observation suggests that evaluations may rely on the cumulative or multiple-year performance rather than simply on annual performance. The central government may prefer the average performance over a span of years because it is a less noisy measure than the simple annual performance, which puts too much weight on short-term shocks. Evaluations based on cumulative or average performance can average out short-term shocks.
Although the official term of a provincial leader is 5 years, in reality the term varies from 1 to 12 years (Table 1). In order to incorporate the effect of past performance so as to make it fit the personnel evaluation procedure discussed above, we create an average measure of the relative GDP growth rate over the tenure T, g˜T, which is defined as