# Fixed weight aggregation

## Changes to the FRB/US Model

- The old version of FRB/US used the Divisia index for most of its aggregation. It introduced undesirable non-linear dynamics in the stochastic simulations and dependence on the initial conditions with respect to projecting the model forward. The costs of these features motivated us to rely instead on a fixed-weigthed aggregation scheme.

- The new version of the model uses fixed, constant shares over time for aggregation. For example, for adjusted final sales (XP), the changes entail the new equations:

XP: Final sales plus imports less government labor
Old model

    log(xp) - xp_aerr = log(xp(-1))
     + .5*(ecnian/xpn + ecnian(-1)/xpn(-1))*d(log(ecnia))
     + .5*(ehn/xpn + ehn(-1)/xpn(-1)) *d(log(eh))
     + .5*(epdn/xpn + epdn(-1)/xpn(-1)) *d(log(epd))
     + .5*(epin/xpn + epin(-1)/xpn(-1)) *d(log(epi))
     + .5*(epsn/xpn + epsn(-1)/xpn(-1)) *d(log(eps))
     + .5*(egfon/xpn + egfon(-1)/xpn(-1)) *d(log(egfo))
     + .5*(egfin/xpn + egfin(-1)/xpn(-1)) *d(log(egfi))
     + .5*(egson/xpn + egson(-1)/xpn(-1)) *d(log(egso))
     + .5*(egsin/xpn + egsin(-1)/xpn(-1)) *d(log(egsi))
     + .5*(exn/xpn + exn(-1)/xpn(-1)) *d(log(ex))

New model

    log(xp) - xp_aerr = log(xp(-1)) + y_xp(1)*log(ecnia/ecnia(-1)) + y_xp(2)*log(eh/eh(-1))
     + (y_xp(3))*log(ebfi/ebfi(-1))
     + (y_xp(4))*log(egfe/egfe(-1))
     + (y_xp(5))*log(egse/egse(-1)) + y_xp(6)*log(ex/ex(-1))

PXP: Price index for final sales plus imports less gov. labor
Old model

    d(log(pxp)) - pxp_aerr =
    .5*(ecnian/xpn + ecnian(-1)/xpn(-1))*d(log(pcnia))
     + .5*((xpn - ecnian)/xpn + (xpn(-1) - ecnian(-1))/xpn(-1))*d(log(pxnc))

New model

    log(pxp) - pxp_aerr = log(pxp(-1))
     + y_pxp(1)*log(pcnia/pcnia(-1))
     + y_pxp(2)*log(pxnc/pxnc(-1))

- The other variables that have been affected by that change are: PXP, ECNIA, PCOR, PICNIA, WPON, XFS and XGDP.