Interest rate movements and inflation risk in the Philippines Alma dela Cruz David Dickinson Euro-Philippines Network on Banking and Finance ASIA-LINK research workshop 27 August 2007

Outline of presentation Introduction Related Literature Framework Methodology Preliminary Estimates

Introduction The research done so far is part of a longer study whose objective is to model interest rate movements in the Philippines. The framework chosen was the CCAPM which requires us to estimate the inflation risk premium. This presentation is limited to the estimates of inflation risk in the Philippines obtained from a BEKK model to be used in future empirical work on CCAPM based interest rate modeling The literature on inflation risk is related to the nominal and real interest rate relationship which is reviewed next.

Related Literature 1 Barnea, A., Dotan, A, and J, Lakonishok (1979) “The Effect of Price Level Uncertainty on the Determination of Nominal Interest Rates: Some Empirical Evidence,” Southern Economic Journal, Vol. 46, No. 2, pp Benninga, S., and A. Protopapadakis, (1983), Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure, Journal of Political Economy, Vol. 91, No. 5 pp Chan, L., (1994), “Consumption, inflation risk, and real interest rates: An empirical analysis,” Journal of Business, Vol. 67 No. 1, Shome, D., Smith, S., and J. Pinkerton, (1988) “The Purchasing Power of Money and Nominal Interest Rates: A Re-Examination,” Journal of Finance, Vol. 43, No. 5, pp

Related Literature 2 The Fisher hypothesis under certainty: i = r + , where  is the inflation rate. When uncertainty is present, the nominal rate is the sum of the real rate and expected inflation. Incorporating uncertainty to the analysis inevitably leads to a nonlinear relationship. Benninga and Protopapadakis (1983) show that in addition to expected inflation, a covariance term (between the real value of an asset and inflation) that shows purchasing power riskiness and a term due to Jensen’s inequality showing inflation variability is needed to explain the relation more fully. Subsequent articles make use of the CCAPM as the framework in analysing the relation. This framework is discussed next.

Framework - 1 The representative agent in the CCAPM solves a consumption/portfolio allocation problem by maximizing an intertemporal expected utility function :

Framework - 2 The standard solution to the problem is a set of Euler equations:

Framework - 3 Assume CRRA utility function. Apply this to the above solution for a one period bond to get its nominal price:

Framework - 4 Linearize the nominal asset price in the previous slide to get: We are interested in estimating the covariance term above. Chan(1994) takes the product of residuals of univariate time series regressions on purchasing power growth and consumption growth to obtain estimates of covariance risk. Here, we make use of multivariate GARCH to produce estimates of covariance risk.

Methodology - BEKK

Quarterly Data Data sources: Sample: quarterly, 1986 – 2005 Real consumption – National Statistical Coordinating Board CPI – National Economic Development Authority Quarterly Macroeconometric Model Interest rates to be used in the interest rate model 91 day Treasury bills rate – Bangko Sentral ng Pilipinas Money market rate ­– IFS CDROM, March 2006 Discount rate – IFS CDROM, March 2006 _________________ Notes:Consumption was deseasonalized using the X12 method MATLAB was used in the estimation

DATA – graphical representation

BEKK estimates

Volatility estimates

Estimate of inflation risk

Unit Root tests

GMM estimates