The initial factor loading matrix Aq is chosen as follows. Let Rj = var( E J=0Xij0Ft-j)/[var( £ 5=0XijOFt-j) + var(eit)l- XijO = MXijO- where XijO is

i.i.d. N(0,1) and independent of {e^, v-t, fyt, vj, and X* is chosen so that R- has a uniform distribution on [0.1,0.8].^ The initial values of the factor Fq are drawn from the stationary distribution of Ft. Finally the {X*t} are transformed to have sample mean zero and sample variance one (this transformation is used in the empirical work presented in the next section).

The scalar variable to be forecast obeys,

The factors were estimated as discussed in section 2 for the balanced panel using {Xjt}, i = 1,… ,N, t = 1,…,T. Estimates were based on the static framework, that is, an augmented X constructed by stacking X and its lags as discussed in section 2.5 was not used. The coefficients f3 in the forecasting regression were estimated by the OLS coefficients $ in the regression of yt_j_ j on £t, t=2,…,T; in particular no lags of were introduced into the forecasting equation. The out-of-sample forecast yj + i was constructed as ут + 1 = fi’Pj. For comparison purposes, the infeasible out-of-sample forecast Уу+1 was also computed, where fP are the OLS coefficients in the regression of yt+ j on F^, t=2,…,T.

The free parameters to be varied in the Monte Carlo experiment are N, T, a, a, b, and h. The results are summarized by two statistics. The first is a trace R of the multivariate regression of P on Fq:

where P denotes the expectation estimated by averaging the relevant statistic over the Monte Carlo repetitions. According to theorem 1, if к > (q+ l)r then p0 ^ 1. Values of this statistic considerably less than one indicates a case in which theorem 1 provides a poor approximation to the finite sample performance of P.