# Petroleum imports (EMP)

## Changes to the FRB/US model

Old model

    emp - emp_aerr = uemp*(ceng - xeng)

    dlog(ceng) - ceng_aerr =
    y_ceng(1)*(log(ceng(-1)) - log(xg(-1)*veoa(-1)))
     + y_ceng(2)*dlog(xg)
     + y_ceng(3)*dlog(xg(-1))
     + y_ceng(4)*dlog(ceng(-1))
     + y_ceng(5)*dlog(veoa(-1))
     + y_ceng(6)*hgx(-1)/400

    xeng - xeng_aerr = uxeng*xgpot

    d(log(pcengr)) - pcengr_aerr =
    y_pcengr(1)
     + y_pcengr(2)*d(log(pcengr(-1)))
     + y_pcengr(3)*log(pcengr(-1))
     + y_pcengr(4)*log(poilr(-1))
     + y_pcengr(5)*d(log(poilr))

New model

    log(emp/xgdp) - emp_aerr = log(emptrt)
     + y_emp(1)*d(log(pmp/pxb))
     + y_emp(2)*xgap2(-1)

## Some details about the changes

- Past experience has shown that there is no obvious benefit in specifying petroleum imports (EMP) as the difference between demand (CENG) and supply (XENG). In conjunction with the elimination of the adjusted concept of business output (XG) from the model, EMP is now modeled in a reduced-form fashion.

- In the new verion of the model, the deviation of the ratio of real petroleum imports over real GDP from its long-run counterpart is affected in the short-run by relative price of petroleum imports and economic activity represented by the output gap.

- The oil imports to GDP ratio, EMPTRT, is an exogenous process.

- The simplification of the energy sector has led to simplification to the PCER equation. PCE energy inflation is now directy influenced by petroleum import inflation (relative to PCE core inflation).

PCER: Price index for personal consumption expenditures on energy
Old model

    d(log(pcer)) - pcer_aerr =
    y_pcer(1)*log(
    (y_pcer(2)*pceng(-1) + (1
     - y_pcer(2))*pcxfe(-1))/(pcer(-1)*pcxfe(-1)))
     + y_pcer(3)*d(log(
    (y_pcer(2)*pceng + (1
     - y_pcer(2))*pcxfe) /pcxfe))
     + y_pcer(4)*d(log(
    (y_pcer(2)*pceng(-1) + (1
     - y_pcer(2))*pcxfe(-1))/pcxfe(-1)))

New model

    d(log(pcer)) - pcer_aerr =
    y_pcer(1)*d(log(pmp/pcxfe))

- The change implied the elimination of the following energy-related variables:
  - CENG: Consumption of crude energy (oil, coal, natural gas), $
  - XENG: Crude energy production, cw
  - UXENG: Multiplicative factor in XENG identity
  - UEMP: Multiplicative factor in EMP identity
  - EMPT: Petroleum imports trend, cw
  - PCENG: Price index for aggregate energy consumption
  - PCENGR: Price index for aggregate energy consumption (relative to PXB)