The STIFS model consists of over 300 equations (excluding equations used to convert standard units into energy equivalents such as British thermal units (Btu's)), of which just over 100 are estimated. The estimated equations are regression equations that together form a system of interrelated forecasting equations. The selection of functional form and the estimation technique is generally done on an equation-by-equation basis. The general method of estimation is ordinary least squares. Some equations incorporate a correction for autocorrelation of the error term.
The historical energy data used to estimate the model come primarily from the IMDS electronic database. IMDS merges data regularly reported in several EIA publications: Quarterly Coal Report, Petroleum Supply Monthly, Petroleum Marketing Monthly, Electric Power Monthly, Natural Gas Monthly, and Monthly Energy Review. Because of data limitations there are inconsistencies in the level of disaggregation of each type of fuel. For example, electricity and natural gas demands are represented by market sector, but petroleum products are generally represented only as national totals or for a combination of sectors (distillate and residual fuel oil are exceptions). Market-level data are available for the regulated industries (electricity and natural gas) while product-level data are available for the petroleum product markets, particularly for data frequencies higher than annual.
These energy price and volume data are supplemented by data from outside sources; the most common are listed below.
Most of the data sources provide monthly data and are used directly. Quarterly data are interpolated into monthly series.
Over 600 variables are used in the STIFS model for estimation, simulation and report writing. Most of these variables follow the following naming convention:
| Characters | MG | TC | P | US | A |
| Positions | 1 and 2 | 3 and 4 | 5 | 6 and 7 | 8 |
| Identity | Type of energy | Energy activity or consumption end-use sector |
Type of data | Geographic area or special equation factor |
Data treatment |
In this example, MGTCPUSA is the identifying code for motor gasoline total consumption in physical units in the United States which is deseasonalized.
The physical units for data series in the STIFS model, represented by a "P" in the fifth character, include some of the following:
Conversion factors, represented by a "K" in the fifth character, are applied to the physical unit data to convert the data to Btu's, a common unit for all forms of energy.
This section summarizes the characteristics of the equations that appear in the STIFS model.
Most equations are estimated using either ordinary least-squares (OLS) or Maximum Likelihood (ML) for equations with auto-regressive error corrections. In all equations, the estimated coefficients appear before their associated right-hand-side variable. A standard naming convention for coefficients is used in most equations. The first three or four letters of the coefficients correspond to the first three or four letters of the dependent (endogenous) variable, followed by an underscore, then followed by two letters from the associated independent right-hand side variable. For example, for nonutility distillate fuel demand:
DSTCPUS(t) = DSTC_01 + DSTC_AC * DFACPUS
The coefficient DSTC_01 is the estimated equation intercept and DSTC_AC is the estimated coefficient associated with distillate demand in the transportation sector, DFACPUS.
When time series data are used in regression analysis, often the error term is not independent through time. If the error term is autocorrelated, the efficiency of ordinary least-squares parameter estimates is adversely affected and standard error estimates are biased. The Durbin-Watson statistic is used to test for the presence of first-order autocorrelation in OLS residuals and is reported in the regression results. For equations in which a lagged dependent variable is present, the Durbin h statistic is reported.
Autocorrelation correction involves estimating the parameters of a linear model whose error term is assumed to be an autoregressive process of a given order p, denoted AR(p). The model for an autoregressive process is of the form:
y(t) = b0 + b1 x(t) + u(t)
The autoregression coefficients, ai, are designated in the regression estimation results as the name of the endogenous variable followed by "_Lp", where p refers to the specified order (usually 1). For example, the nonutility distillate fuel demand is estimated with a first-order autoregressive error term:
DSTCPUS = DSTC_01 + DSTC_AC * DFACPUS + u(t)
Some equations explain the current values of endogenous variables as functions of past values of exogenous variables using a polynomial distributed lag structure. For a regression equation in which the effect of a right hand side variable, x(t), has a polynomial distributed lag structure of the form:
y(t) = b0 + b1 x(t) + b2 x(t-1) + b3 x(t-2) + ... bk+1 x(t-k)
The polynomial distributed lag is identified in the text as:
distlag( exogenous, degree=j, lags=i)
For example, air travel capacity (equation for RMZT) involves a distributed lag on aircraft utilization (RMZZ):
RMZT(t) = ...+ distlag( RMZZ, degree = 2, lags = 2) +...
The estimated coefficients. aj, are reported in the Appendix A estimation results as the name of the endogenous variable followed by "k_j", where k refers to the distributed lag term (usually equal to 1 unless an equation contains more than one distributed lag term) and j refers to the degree of the polynomial (j = 0 to n).
RMZT(t) = ...+ b0 RMZZ(t) + b1 RMZZ(t-1) + b2 RMZZ(t-2) + ...
Several regression equations are estimated using seasonally-adjusted data. If the variable ends in an "A", such as ETTCPUSA, then the data for ETTCPUS has been deseasonalized using seasonal factors (in this case, ETTCPUSS) from the U.S. Census X-11 multiplicative seasonal adjustment routine. To obtain non-seasonally adjusted projections, the forecasts developed from seasonally-adjusted equations are the reseasonalized using the Census X-11 seasonal adjustment factors.
File last modified: June 6, 1998
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