Hysteresis

Hysteresis is the time-based dependence of a system's output on present and past inputs. The dependence arises because the history affects the value of an internal state. To predict its future outputs, either its internal state or its history must be known. If a given input alternately increases and decreases, a typical mark of hysteresis is that the output forms a loop as in the figure.

Such loops may occur purely because of a dynamic lag between input and output. This effect disappears as the input changes more slowly. This effect meets the description of hysteresis given above, but is often referred to as rate-dependent hysteresis to distinguish it from hysteresis with a more durable memory effect.

Hysteresis occurs in ferromagnetic materials and ferroelectric materials, as well as in the deformation of some materials (such as rubber bands and shape-memory alloys) in response to a varying force. In natural systems hysteresis is often associated with irreversible thermodynamic change. Many artificial systems are designed to have hysteresis: for example, in thermostats and Schmitt triggers, the principle of hysteresis is applied to avoid unwanted frequent switching. Hysteresis has been identified in many other fields, including economics and biology.

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Hysteresis (economics)

In economics, hysteresis refers to the possibility that periods of high unemployment tend to increase the rate-of-unemployment-below-which-inflation-begins-to-accelerate, commonly referred to as the natural rate of unemployment or non-accelerating inflation rate of unemployment (NAIRU). The term is based on the physical phenomenon of hysteresis in magnetic materials.

Implication for statistical characterization of unemployment

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

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.