If the unemployment rate exhibits hysteresis, then it follows a statistically
non-stationary process, because the
expected value of the unemployment rate now and in the future permanently shifts when the rate itself changes. The process with hysteresis is a
unit root process, which in its simplest form can be characterized as U_t = U_{t-1} + e_t, where U_t is the unemployment rate at time
t and e_t is a stationary error term representing outside shocks to the rate. According to this characterization, E_{t-1}(U_{t+\tau}) = U_{t-1} for all \tau = 0, 1, \ldots, where E_{t-1} refers to an expectation conditional on values observed no later than time
t–1; any temporary shock to unemployment, represented by a single non-zero value of e_t, results in a permanent change to expected unemployment (even for \tau indefinitely large so the expectation is for indefinitely far into the future). A more elaborate model would allow E_{t-1}(U_{t+\tau}) to go up positively but less than one-for-one with e_t. In contrast, a non-hysteresis model of unemployment would have U_t following a stationary process, so that E_{t-1}(U_{t+\tau}) for arbitrarily large \tau would always equal a permanently fixed natural rate of unemployment. ==Causes==