Factor Model Forecasts of Inflation in Croatia

Transcription

1 Factor Model Forecasts of Inflation in Croatia Davor Kunovac Croatian National Bank Econometric Modelling Department

2 Contents 1. Motivation & Objective 2. Forecasting model: de nition and estimation 3. Forecast evaluation 4. Principal component as a summary statistics

3 Motivation 1. Many evidences that there exist few unobservable variables - common factors, governing the whole economy. How to construct or identify these driving forces? (Stock and Watson, JBES, 2002) 2. Most empirical analysis of monetary policy wrongly pressume that central bankers decisions are grounded on only few key macro variables while in practice the thousands of variables are being monitored. How to formalise this? (Bernanke and Boivin, JME, 2003) 3. Transition economies are dealing with data having quite short time spans (less than 10 years of reliable in ation data for Croatia). So, any sort of data compression methods - welcomed!

4 Objective I This analysis tests whether information extracted from 144 economic variables can help in forecasting CPI in ation in Croatia

5 Forecasting Model Model (James Stock & Mark Watson, JBES, 2002) I Assume that for given observations of N = 144 variables X 1 ; : : : ; X N there exist r ( N; hopefully just 2 or 3) factors F 1 ; : : : ; F r such that: X it = i1 F 1t +: : :+ ir F rt +" it ; i = 1; : : : ; N; t = 1; : : : ; T I Forecasting model (h - steps - ahead forecast): X = F + " y t+h = h + 0 F t + : : : + p F t p + 0 y t + : : : + q y t q + t+h I (Too) many unknows: ; F and noise variances, so in order to estimate the system some restrictions need to be imposed!

6 Forecasting Model Estimation Assume = I r and minimise the sum of squares: V (F; ) = NX i=1 TX " 2 it = jjx ^F jj 2 F ; (1) t=1 Applying (multiple multivariate version) least squares we estimate factors: ^F = ( ) 1 X = ( = I r ) = X ; (2) By plugging (2) into (1) we have: V ( ^F ; ) = jjx ^F jj 2 F (3) = jjxjj 2 F tr( X X): (4)

7 Forecasting Model Estimation I Solve the problem: max tr( X X), = I r I Setting ^ equal to k eigenvectors of X X corresponding to k largest eigenvalues yields the principal components estimator ^F = X ^

8 Results I Factor model X = F + " y t+h = h + 0 F t + : : : + p F t p + 0 y t + : : : + q y t q + t+h challenged against non-trivial AR benchmark in in ation forecasting exercise I forecasts evaluated using MSE relative to benchmark (Relative MSE<1 ) factor model beats benchmark): Horizon Relative MSE

9 Results R 2 statistics between rst two factors and 144 variables of Croatian economy R 2 Prices, Ex. rates External Money Real Labour R Prices, Ex. rates External Money Real Labour

10 Results R 2 statistics between tenth and eleventh factor and 144 variables of Croatian economy R 2 Prices, Ex. rates External Money Real Labour R Prices, Ex. rates External Money Real Labour

11 Principal Component as a summary statistics I Recent analysis by CNB deals with the impact of USD/EUR rate on CEECs in ation rates I E ect seems to be quite strong, especially in countries xing their ER to EUR (Croatia, Bulgaria, Estonia) I Fixers in ation rates principal component highly correlated to USD/EUR ER I Common force driving CEECs in ation rates?

12 Principal Component as a summary statistics Fixers in ations principal component and EUR/USD exchange rate 3 2 Principal Component EUR/USD (YoY growth rates)

13 References Bai, J., and S. Ng (2002), Determining the number of factors in approximate factor models, Econometrica 70, pp Bernanke, B. and J. Boivin (2003), Monetary Policy in a Data-Rich Environment, Journal of Monetary Economics, 50, Stock, J. F. and M. W. Watson (2002), Macroeconomic Forecasting Using Di usion Indexes. Journal of Business and Economic Statistics 20: