# Business Investment

## Changes to the FRB/US model

### Business investment

- We consolidated three different business investment variables (EPD, EPS, EPI) into a single business fixed investment variable (EBFI). This page only shows the changes relative to EPD for simplicity.

Old model

    dlog(epd) - epd_aerr =
    (y_epd(1)*(log(qepd(-2)/epd(-2)))
     + y_epd(2)* dlog(epd(-1))
     + y_epd(3)* dlog(epd(-2)) + zxbd(-1) + zvpd(-1))*(1
     - y_epd(4))
     + y_epd(4)*(dlog(xbo(-1)) + hgvpd(-1))

    epdn - epdn_aerr = 0.01*ppdr*pxp*epd

New model

    dlog(ebfi) - ebfi_aerr =
    (y_ebfi(1)*(log(qebfi(-1)/ebfi(-1)))
     + y_ebfi(2)*dlog(ebfi(-1))
     + y_ebfi(3)*dlog(ebfi(-2))
     + y_ebfi(4)*zebfi)*(1
     - y_ebfi(5))
     + y_ebfi(5)*(dlog(xb(-1)) - hgpbfir(-1)/400)

    ebfin - ebfin_aerr = 0.01*ebfi*pbfir*pxp

- We consolidated the relative price variables (e.g. PPDR), trend growth rate (e.g. HGVPD), and target level (e.g. QEPD).

Old model

    log(ppdr) - ppdr_aerr - log(ppdr(-1)) = y_ppdr(1) + pipxnc/400
     + dpadj - d(log(pxp))

    hgpdr - hgpdr_aerr = y_hgpdr(1)*hgpdr(-1)
     + y_hgpdr(2)*400*log(ppdr/ppdr(-1))

    hgvpd - hgvpd_aerr = y_hgvpd(1)*hgvpd(-1)
     + y_hgvpd(2)*log(vpd/vpd(-1))

    log(qepd) - qepd_aerr = y_qepd(1)
     + y_qepd(2)*log(xbo)
     + y_qepd(3)*log(vpd)
     + y_qepd(4)*log(hgx/100 + jrpd)

New model

    log(pbfir) - pbfir_aerr = log(pbfir(-1)) + pipxnc/400 + dpadj - d(log(pxp))

    hgpbfir - hgpbfir_aerr = .975*hgpbfir(-1)
     + .025*400*(log(pbfir*pxp/pxb/(pbfir(-1)*pxp(-1)/pxb(-1))))

    qebfi - qebfi_aerr = xb*vbfi*(hxbt/100 - .01*hgpbfir + jrbfi)

### Capital stock

- Variables relating to business capital were simplified to reflect the aggregate representation of business capital: capital stock equations (KPD), depreciation rates (JRPD), multiplicative factor (UPKPD), price ratio (PKPDR), and income from capital stocks (YKPDN)

Old model

    kpd - kpd_aerr = 0.25*epd + (1 - jrpd/4)*kpd(-1)

    pkpdr - pkpdr_aerr = upkpd*ppdr

    ykpdn - ykpdn_aerr = .01*rtpd*pxb*(kpd + kpd(-1))/2

New model

    kbfi - kbfi_aerr = (pbfir/pkbfir)*ebfi/4 + (1 - jrbfi/4)*kbfi(-1)

    pkbfir - pkbfir_aerr = upkbfir*pbfir

    ykbfin - ykbfin_aerr = .01*rtbfi*pxb*(kbfi + kbfi(-1))/2

- Exogenous factors were created for the fixed business investment series: the depreciation rate has become JRBFI and the multiplificative factor associated with the relative price of capital has become UPKBFIR.

### User costs and capital taxes

- The user costs and tax rates that previously applied to the three different types of capital now apply to the aggregate capital measure. These include the depreciation allowance (TAPDD), investment tax credit (TAPDT), after tax cost of capital (RPD), user cost of capital (RTPD), and the target capital to output ratio that depends on these tax rates (VPD).

Old model

    rpd - rpd_aerr = 0.5*(7.2 + (1 - trfcim)*(rg5e + rbbbe - rg10e) - zpib5)
     + 0.5*req

    rtpd - rtpd_aerr = (.01*rpd + jrpd - .01*hgpdr)
    *((1 - .01*tapdt - trfcim*(1 - tapddp*.01*tapdt)*tapdd)/(1 - trfcim))
    *((pxp*pkpdr + pxp(-1)*pkpdr(-1))/2)/pxb

    vpd - vpd_aerr = uvpd/rtpd

New model

    rbfi - rbfi_aerr = 0.5*(7.2 + (1 - trfcim)*(rg5 + rbbb - rg10) - zpib5)
     + 0.5*req

    rtbfi - rtbfi_aerr = (.01*rbfi + jrbfi - .01*hgpbfir)
    *((1 - .01*tritc - trfcim*(1 - tapddp*.01*tritc)*tdpv)/(1 - trfcim))
    *(pkbfir*pxp/pxb)

    vbfi - vbfi_aerr = uvbfi*(pkbfir/pbfir)/rtbfi

- The present value of depreciation allowances for BFI is represented by the exogenous factor (TDPV) and the investment tax credit for BFI by the exogenous factor (TRITC).