Appendix I. Coefficient of AR(1) Process of Inflation in an Example in Fuhrer (2009)
A simple example to illustrate the effects of structural parameters to inflation persistency presented in Fuhrer (2009) consists of the following three equations.
Solving the above system yields
Suppose that inflation is estimated in AR(1) uni-variate process: πt = α + φπt –1 + et. Probability limit of coefficient of a lag of inflation is given by the following formula.
The right hand side of the above equation suggests that inflation inertia, measured by the coefficient in the uni-variate autoregressive process, has positive correlation to (γ,ρ) and negative correlation to the ratio of the variance of the shock to inflation to that output gap (i.e.,
Appendix II: Why is Inflation Inertia Overestimated when the Inflation Target Has Been Reduced during the Sample Period?
Suppose the behavior of inflation with the true model, counting a change in the targeted inflation rate, is described as follows.
If only one specification of the model is applied to the above data generating process, πt –π* = β(πt – 1 – π*) + εt for all t,
the estimated inertia of the inflation, defined by
Therefore, inflation inertia tends to be overestimated when the inflation target has been reduced during the sample period.
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The author is grateful for helpful comments from Alan MacArthur, Hassan Al-Atrash, Ralph Chami, and participants in the seminar held at the Central Bank of Egypt in January 2011.
Egypt’s per capita GDP (PPP base) reached US$ 6,000 in FY 2008/09 (July/June) and is projected to be around US$ 9,000 in FY 2014/15 under the current macroeconomic framework. Moreover, along this the trend, per capita GDP will surpass US$ 12,000 by 2020. Comparing Egypt with countries with per capita GDP from US$ 6,000 to US$ 15,000 (for example, Russia: US$ 14,900 and Argentina: US$ 14,600) should, therefore, give insights on the location of inflation in Egypt and the inflation which Egypt should seek in the medium/long-term in the context of international comparison.
Argentina, Brazil, Bulgaria, Chile, China (Mainland), Colombia, Dominican Republic, Ecuador, Egypt, El Salvador, Hungary, Indonesia, Kazakhstan, Lebanon, Malaysia, Mexico, Pakistan, Panama, Peru, Philippines, Poland, Russia, Serbia, South Africa, Sri Lanka, Tunisia, Turkey, Ukraine, Uruguay, Venezuela, and Vietnam.
The sum of conditional probabilities in each row is 100 percent, by its construction.
Companion paper of this paper, “Adding Egypt to the Global Projection Model: Spillovers, Inflation Dynamics, and Implications to Monetary Policy” by Arbatli and Moriyama (2011) follows the structural model approach to investigate inflation inertia in Egypt by estimating the hybrid Phillips curve.
Interestingly, the two features are also generally considered as preconditions for the adoption of full-fledged inflation targeting monetary policy framework.