Real term structure forecasts of consumption growth

Essays on forecasting interest rates, economic activity and inflation, based on factor models of the yield curve

“…where vi is the eigen value of matrix R and tr(V ) stands for the trace of the matrix of the eigen values of R, denoted as V . 9 Note that these two factors explain a total variation in real interest rates Rt( ) which is analogous in magnitude to that of nominal interest rates captured by three factors (see, e.g., Litterman and Scheinkman [81], and, more recently, Argyropoulos and Tzavalis [7]).…”

“…Our PC analysis relies on a set of N = 60 real interest rates R t ( ), spanning a very wide maturity spectrum from one month to …ve years (sixty months). This is a large cross-section set of R t ( ) which guarantees that the retrieved by the PC analysis common factors pc it will 7 As shown in Bai and Ng [9], and Bai [8] consistent estimates of principal component factors can be obtained by PC analysis of interest rates Rt( ), if the following condition holds:…”

“…where SSR( ) = P b 2 t ( ) is the sum of squared residuals b t ( ) = d(R t ( )j ) d(D t j ) 0 b ( ) 7 See Elliott et al (1996).…”

“…Second, we conduct principal component (PC) analysis with the aim of determining the maximum number of common factors (state variables) K which explain the total variation of R t ( ) in our sample. Since principal component factors constitute well diversi…ed portfolios of interest rates which are net of measurement or pricing errors e¤ects in R t ( ), they can be employed as instruments in the estimation of the GDTSM to minimize the bias e¤ects of the above errors on the parameter estimates of the model (see, e.g., Argyropoulos and Tzavalis [7]). Third, we estimate and test the GDTSM, with and without consumption data.…”

“…where N > K, is a diagonal matrix of dimension (N N ). 7 The elements of are the eigen values of matrix R . is a (N N )-dimension orthogonal matrix whose columns are the eigen vectors corresponding to the eigen values of matrix R .…”