Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

Abstract

This paper aims to connect the bridge between analytical results and the use of the computer for numerical simulations in economics. We address the analytical properties of a simple dynamic aggregate demand and aggregate supply (AD-AS) model and solve it numerically. The model undergoes a bifurcation as its steady state smoothly interchanges stability depending on the relationship between the impact of real interest rate on demand for liquidity and how fast agents revise their expectations on inflation. Using code embedded into a unique function in Matlab, we plot the numerical solutions of the model and simulate different dynamic adjustments using different parameter values. The same function also accommodates the analysis of the impacts of fiscal and monetary policy and supply side shocks on the steady state and the transition dynamics of the model.

Structural Stability Analysis in a Dynamic IS-LM-AS Macroeconomic Model with Inflation Expectations

“…Finally, equal to the results reported by Gaspar [2], when the adaptive expectations parameter (the speed with which economic agents adjust their expectations about future inflation) is equal to the inverse of the semi-elasticity of real money demand with respect to the nominal interest rate, the model presents a degenerate Hopf bifurcation in which periodic solutions are obtained and in which the passage from a stable to an unstable spiral occurs, as the real part of the complex-conjugate eigenvalues changes signs (from negative to positive). However, the linearity of the system of ordinary differential equations (ODEs) governing the dynamics of our model prevents the occurrence of limit cycles ( ere are dynamic models in the business cycle literature, which use the Poincaré-Bendixson theorem as an analytical tool to verify the existence of limit cycles (Chang and Smyth [16]; Dana & Malgrange [17]; Schinasi [18]; Semmler [19]).…”

“…In the literature, there are several versions of models based on IS curve, LM curve, and Phillips curve (PC) structures augmented by inflationary expectations or an aggregate supply (AS) function (i.e., IS-LM-PC [AS]) in which the dynamics of said models is incorporated through different assumptions on the adjustment mechanism of expectations, money supply, prices, and potential GDP, among others, and that allow the analysis of the fluctuations of the main macroeconomic variables by means of the quantitative and qualitative tools of ordinary differential equation (ODE) systems or through systems of difference equations. Some of these versions are presented in textbooks [1,3,4,[6][7][8][9] and others in working papers or scientific articles [2,5,10,11]. (Nozaki (see [11]) performed both theoretical and computational analyses of policy implications of the Kaldor-Phillips business cycle using a nonlinear dynamic IS-LM-PC model along with the Hopf bifurcation theorem in R 3 .…”

“…Likewise, using generic functional forms and modifying their base assumptions, they are able to analyze different economic schools, although they do not carry out a numerical analysis. Gaspar (see [2]), based on the work of Shone [see [4], analyzed economic fluctuations in real GDP and expected inflation with a continuous version of a dynamic linear AS-AD (some discrete and stochastic versions of a dynamic AS-AD model are found in the work of Alpanda et al [12], Buttet and Roy [13], Lizarazu [14], and Mankiw [15]) model in R 2 , where the AD is obtained from an IS-LM model and the AS (a Lucas-type function) is obtained from a Phillips curve augmented by inflation expectations (PC), finding a "degenerate" Hopf bifurcation when the value of the real money demand sensitivity to changes in the nominal interest rate parameter equals the inverse of the value of the expectations parameter.…”

“…In this document, adopting assumptions very similar to those assumed by de La Fuente [1], Gaspar [2], and Shone [3,4], we extend the qualitative analysis developed by these authors in R 2 to the three-dimensional phase space. In addition, based on the theoretical model developed by Szomolányi et al [5], the present paper aims to theoretically and numerically analyze a specific case of the IS-LM-AS macroeconomic model with expectations regarding future inflation.…”

“…e purpose of this study is carried out the structural analysis of an IS-LM-AS macroeconomic model with adaptive in ation expectations, exploring the presence of a possible local bifurcation. e rst contribution of this research lies in the extension of the qualitative analysis of the IS-LM-AS model developed by de La Fuente [1], Gaspar [2], and Shone [3,4] from the two-dimensional phase space to three-dimensional phase space. e second contribution of this paper consists in analytically and numerically solving the theoretical model developed by Szomolányi et al [5] for a speci c case of the IS-LM-AS macroeconomic model with future in ation expectations.…”