Combined monetary and fiscal policy: the Nash Equilibrium for the case of non-cooperative game

Abstract

The importance of the central bank and the government conducting their policies has increased recently, with more attention being given to the effectiveness of policy mix. The non-cooperative models of the monetary and fiscal game are frequently employed to study interactions between both authorities. The models assume that the authorities take into account each other's choices when making decisions. It is also important to remember when seeking equilibrium in the non-cooperative models that in the Nash Equilibrium (which is sought in this study) the parties try to come up with the best response to the opponent's decision. The aim of the paper is to present the Nash Equilibrium in a non-cooperative game between the government and the central bank using a non-cooperative model of a fiscal-monetary game (a policy-mix MODEL). This study demonstrates that in the Nash Equilibrium in the model, the budget deficit and interest rate of an EU member state depend on the exogenous data (external to the model), such as inflation target, base inflation and the Maastricht deficit limit. This study is enhanced by an analysis of the government and central bank's sensitivity to the deep parameters of economic variables.

The Nash equilibrium in the policy mix model for Czechia, Hungary, and Romania

“…It means that the central bank will respond to an increase in the budget deficit by raising interest rates, and is due to the fact that higher deficits are likely to increase inflationary pressure, which requires monetary policy tightening on the central bank's side. The result (the positive value of parameter b 3 ) is also in line with our non-cooperative theoretical game (Stawska et al, 2019) and many previous research studies (cf. Bennett & Loayza, 2000;Blinder, 1982;Dixit & Lambertini, 2001;Nordhaus, 1994, etc.…”

“…They constructed a model of strategic cooperation between both authorities using various loss functions, which differ in design from our proposal in this paper. The mathematical model (presented in the study by Stawska et al, 2019) shows that in the Nash equilibrium, the level of the budget deficit and the interest rate-as the policy tools of the government and the central bank, respectively-depend on exogenous factors such as the inflation target, base inflation, and the Maastricht deficit limit. Therefore, the inflation target rate and the Maastricht deficit limit, which are set institutionally, are important determinants of the fiscal-monetary balance in the EU countries.…”

“…The following model is presented and thoroughly analyzed in terms of the theoretical properties in the paper by Stawska et al (2019). It describes a simple economic game between the government (responsible for the fiscal policy in a given economy) and the central bank (which shapes the monetary policy).…”

“…6. Exact analytical formulas for the reaction functions of the model can be found in the paper Stawska et al (2019). 7.…”

“…7. Detailed analytical formulas for the Nash equilibrium of the model can be found in the paper Stawska et al (2019). However, the exact formulas indicating the relationship between parameters a � 1 ; a � 2 ; a � 3 ; b � 1 ; b � 2 ; b � 3 and ã 1 ;ã 2 ;ã 3 ;b 1 ;b 2 ;b 3 can be found in part 4.3. of this article in Equation (10).…”