Feedback policy rules for government spending: an algorithmic approach

Abstract

One of the most important objectives of economic policy is to ensure, via the appropriate manipulation of the available policy instruments (control variables), that the economic system tracks, as closely as possible, a desired path for the policy targets (outputs). One of the approaches that has been utilized for the design of economic policy is the feedback approach, stemming from the mathematical control theory literature. Various aspects of the feedback methodology have been utilized for the purposes of policy design for more than 50 years, starting with the use of PID controllers in the seminal paper by Phillips (1954). These aspects range from (stochastic) optimal feedback control (see, The importance of feedback rules for policy design is evident from the fact that for more than 20 years monetary policy decisions have been, to a large extent, based on the Taylor rule (see Taylor 1993); this is a linear feedback policy rule stipulating (in its simplest form) that the interest rate is set based on deviations of inflation and GDP from target levels of inflation and potential GDP, respectively. It is interesting to note here that Taylor presented a rule that had fixed settings for the parameters; in particular:among(1) r = p + 0.5y + 0.5(p − 2) + 2 AbstractWe present an algorithmic approach for the design of fiscal policy rules. In particular, using algorithmic feedback control techniques, we design linear feedback policy rules such that predetermined target levels for GDP and public debt are simultaneously, exactly tracked. We run a number of simulations in order to examine the effects of different policy response rates and the overall effectiveness of the proposed methodology.

Public debt dynamics: the interaction with national income and fiscal policy

“…The model we use is a form of the discrete time multiplier-accelerator model, that was firstly proposed by Samuelson (1939) and then was adopted by a great number of economists, such as Hicks (1950), Hommes (1993), Hommes (1995), Kotsios and Leventidis (2004), Puu et al (2005), Puu (2007), Sushko et al (2010), Westerhoff (2006a), Westerhoff (2006b), Westerhoff (2006c), Dassios et al (2014), Kostarakos and Kotsios (2017) and Kostarakos and Kotsios (2018). Specifically, it is a deterministic discrete time bilinear system of difference equations, which has two dynamic equations, for the national income and the sovereign debt.…”

Controlling national income and public debt via fiscal policy. A model matching algorithmic approach

“…In particular, it amounts to calculating appropriate linear, causal feedback laws such that the resulting closed-loop system is identical to a desired one that produces the requested output values. Although the linear model matching approach has been extensively studied and is well documented in the control literature (see, among others [1][2][3][4]), it has not, to the extent of our knowledge, been used in the economic policy literature (for some exceptions, see [5,6]) and for a nonlinear application, (see [7,8]) in spite of its advantages. The main advantage of this approach is that it relies only on the use of algebraic tools.…”

“…The λ i parameters indicate that the decision regarding government expenditures in period t affects the level of GDP in period t + i; that is, there is a delay in the realization of the effects of changes in government expenditures on GDP levels. Equations (1)-(5) constitute a variant of the standard multiplier-accelerator model introduced in [9] whereas equation (6) is the government budget constraint. Regarding the parameters of the system, s ∈ (0, 1) is the marginal propensity to save, τ ∈ (0, 1) is the (constant) tax rate, ν > 0 is the accelerator and r ∈ (0, 1) is the constant interest on previously issued public debt.…”