Parameter Estimation for Elliptical Time-Dependent Hysteresis

• Activity Number: 246
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Fan Yang*+ and Anne Parkhurst
• Companies: University of Nebraska-Lincoln and University of Nebraska-Lincoln
• Keywords: Constrained Least Squares ; Economic Downturn ; Economic Upturn ; Ellipse-specific Nonlinear Regression ; Generalized Eigen-system

Abstract

Hysteresis is defined as the relationship between the output and the input of a system which has memory. A system displays hysteresis if there is a lag between the output and the input. Consider the labor market. Hysteresis appears as the delay in unemployment rate (output) when the business cycle fluctuates from recession to boom (measured as the growth in GDP, input). That is, during an economic recession, an individual becomes unemployed. With diminishing skills and time spent out of the workforce, an individual's chance of being rehired immediately in an economic boom may be diminished. Hence, understanding hysteresis will be helpful to estimate the duration of unemployment and setup training programs as a policy strategy. When hysteresis occurs, the output-input trajectory forms a closed loop. If the input is sinusoidal, the loop shows an elliptical pattern. The loop parameters can describe the system. To estimate the parameters, three methods, linear, nonlinear, and two-step, are developed. Simulations using both the delta method and bootstrap are performed to evaluate the statistical efficiency. Overall, two-step method with bootstrap produces the most efficient estimates.