An Application of the First-Order Linear Ordinary Differential Equation to Regression Modeling of Unemployment Rates

Abstract

The unemployment rate investigates the relationship between labor market outcomes and poverty, evaluates the effect of labor market policies and programs, and provides ways to improve their performance. This study analyzes data-driven regression modeling for the economy, specifically the first-order linear ordinary differential equation (ODE). Consider a collection of actual data for the Ilocos Region's unemployment rate and calculate the numerical derivative. Then, a general equation for the first-order linear ODE is presented, with two parameters that will be determined using regression modeling. Following that, a loss function is defined as the sum of squared errors to reduce the difference between estimated and real data in the presence of fluctuations. After this, a loss function is defined as the sum of squared errors to minimize the differences between estimated and actual data. A set of necessary conditions is derived, and the regression parameters are analytically determined. Based on these optimal parameter estimates, the solution of the first-order linear ODE, which matches the actual data trend, shall be obtained. The observations show that the relationship between the actual data and the adjusted predicted regression dynamics closely matches. Results also indicate that the new insight includes the analysis of fluctuations in the unemployment rate for regression modeling dynamics. This research helps Filipino economists provide insights and inform policy decisions aimed at the labor market, and they can focus their efforts on improving these indicators to stimulate job creation and reduce unemployment.