# Household Permanent Income Components

## Changes to the FRB/US Model

YHGAP: Income, household, total, ratio to XGDP, cyclical component
Old model

    yhgap - yhgap_aerr = 100*(yhshr/zyhst - 1)

New model

    yhgap - yhgap_aerr = 100*log(yhshr/zyhst)

YHTGAP: Income, household, transfer, ratio to YH, cyclical component
Old model

    yhtgap - yhtgap_aerr = 100*(yhtshr/zyhtst - 1)

New model

    yhtgap - yhtgap_aerr = 100*log(yhtshr/zyhtst)

## Some Details of the Simplifications

- A slightly different convention has been adopted for the “permanent income” group of variables.

- We have replaced the percentage deviation convention by a log change approximation. This change facilitates the automation of the linearization of FRB/US.

- The equations of the trend shares were respecified accordingly.

ZYHST: Expected trend ratio of household income to GDP
ZYHPST: Expected trend share of property income in household income
ZYHTST: Expected trend share of transfer income in household income
Old model

    zyhst - zyhst_aerr = zyhst(-1) + y_zyhst(1)*(yhshr - zyhst(-1))

    zyhpst - zyhpst_aerr = zyhpst(-1) + y_zyhpst(1)*(yhpshr - zyhpst(-1))

    zyhtst - zyhtst_aerr = zyhtst(-1) + y_zyhtst(1)*(yhtshr - zyhtst(-1))

New model

    log(zyhst) - zyhst_aerr = log(zyhst(-1)) + y_zyhst(1)*yhgap(-1)/100

    log(zyhpst) - zyhpst_aerr = log(zyhpst(-1)) + y_zyhpst(1)*yhpgap(-1)/100

    log(zyhtst) - zyhtst_aerr = log(zyhtst(-1)) + y_zyhtst(1)*yhtgap(-1)/100