The efficiency of the Taylor rule : A stochastic analysis using the Macsim model

The MacSim package is designed for teaching macroeconomics, focusing on international trade. It uses a set of simplified models, describing the economy of countries belonging to the European Union. It brings together single-country mechanisms, including some financial elements, and international trade, through bilateral flows. Behaviors are estimated for each country, using the same standard formulation. Alternatives are allowed for interest and exchange rates rules, and participation to the EMU. Although the primary goal of the model is teaching, its behavioral equations and the subsequent realism of its properties allow it to be used also for more research-oriented purposes. Recent papers, such as (Augier P, Brillet JL, Cette G, Gambini R, The MacSim project, General Presentation, 1999) present the global architecture of the system, and its response to demand and supply shocks, according to the choice of the above rules. One of the main conclusions is that the Taylor rule smoothes the response to demand shocks, by making the main cycles converge faster. The stochastic properties In this paper, after summarizing the above, we concentrate on the consequences of the same choices for the variability of forecasts. In particular, we observe if the introduction of the Taylor rule reduces the uncertainty of both real elements (GDP) and prices, and what are the consequences of EMU participation, both on the uncertainty itself and the efficiency of the Taylor rule. For this we conduct a series of Monte Carlo simulations, drawing residuals for demand and supply oriented behavioral equations. We consider 8 cases, combining: - No EMU, the present state - Residuals on demand or supply - Two exchange rate rules: nominal fixed, purchasing power parity (PPP) For each case we interpret the real exogenous interest rate, then the consequences of using the Taylor rule, through graphs: - Standard errors on French GDP then inflation according to the interest rule - The standard error ratio (Taylor / real exogenous cases) for French GDP and inflation - The standard error ratio on GDP then inflation for all countries. We shall draw random normal samples using estimated standard errors of the French sub-model, for consumption (demand case) and the GDP deflator (supply case). They will be used to simulate the system over a fifty-year period, with at least 500 replications. 1 No EMU 1.1 Residual on consumption 1.1.1 Fixed exchange rate Standard errors of GDP and inflation grow with time, converging after ten to twenty periods to double the short-term value. The Taylor rule reduces the error for all countries, at first (the variability of GDP is lower) but essentially in the long run (and more for GDP than inflation). This is due to the faster convergence of cycles (proven on a very small model). The process feeds itself: reducing the cycles smoothes the interest rate variation, and variability of real elements in turn. 1.1.2 PPP Unchanged competitiveness and loose prices give GDP and inflation a higher variability. The standard error grows, but converges faster, as the dynamic effects (error correcting) are reduced. The efficiency of the Taylor rule stays. 1.2 Residual on the GDP deflator 1.2.1 Fixed exchange rate Slow corrections and adverse effects reduce inflation dynamics, stabilizing its standard error. But the output gap lasts, and the GDP standard error grows fast. The Taylor rule is quite inefficient for France, as its two determinants have opposite effects. For other countries, standard errors are small (they lose competitiveness but export more to France). More demand oriented, the shock favors the Taylor rule. 1.2.2 PPP The main effect is the adverse role of the Taylor rule for France. The real interest rate decreases with disinflation, increasing GDP variability. 2 EMU 2.1 Residual on consumption 2.1.1 Fixed exchange rate With a common interest rate, increased demand brings the French real rate down, with higher standard errors on both criteria. But real rate increases in other EMU countries limits the loss through trade elements. 2.1.2 PPP The differences from 2.1.1 are small but logical. Some (limited) conclusions The Taylor rule is quite efficient in reducing variability of both GDP and inflation, if uncertainty comes from the real side. The efficiency grows with the horizon, converging in the long run. But it is very inefficient if it comes from the price side, as this affects the rule directly. It can even have a negative efficiency, in the PPP case. The role of the exchange rate rule is important. EMU participation limits the effect of PPP. It also makes the Taylor rule more inert, and reduces its role. But the global effects brings back some of its efficiency through trade.