Approximation of Large, Computer-Based Economic Models

Approximation of Large, Computer-Based Economic Models

Andrew Buck

George Lady

This paper demonstrates methods of processing the solution files to a large, computer-based forecasting system (the Energy Information Administration’s National Energy Modeling System) in order to reveal features of the model’s underlying structure and provide a diagnostic tool in support of model development. A small set of variables from the model’s solution, describing energy production, imports, consumption, associated prices, and macroeconomic activity, are approximated using three methods: ordinary least squares and quantile regression, and kernel regression. Many of the approximations achieved are accurate and reveal stable underlying relationships within the model. Some relationships reflected changes in modeling assumptions. The effort is a pilot study designed to demonstrate the feasibility of working with the solution sets of large models in support of interpreting model results and as a diagnostic for model development.

September 2005

Department of Economics

Fox School of Business and Management’

Temple University

Approximation of Large, Computer-Based Economic Models

Andrew Buck

George Lady

Introduction. Tools for economic analysis and forecasting often take the form of computer-based mathematical systems. Advances in computer and analysis technology have allowed ever larger data sets to be submitted to increasingly sophisticated analysis and processing routines. Such systems are commonly used in government and elsewhere in support of forecasting, contingency analysis, and other analytic purposes. We are familiar with the National Energy Modeling System (NEMS) maintained and used by the U.S. Department of Energy’s (DOE) Energy Information Administration (EIA). This system and its predecessors have been in place to support the publication of annual projections of U.S. energy production, distribution, and consumption, as well as specialized policy analysis studies since the mid 1970’s. The modeling system was initially developed at that time to support the policy analytic response to the 1973 Arab oil embargo. We believe that NEMS is a generic example of many systems that involve large data sets, sophisticated processing and forecasting goals, large professional staffs to enable their development, maintenance and use, and a substantial period of evolution and development. [1]

The distinct nature of NEMS is associated with its purpose as a tool for energy policy analysis. Although projections are provided for twenty and more years ahead, the methodologies employed are not typically those used for time series or trend analysis. Instead, the analytic approach might be termed “bottom up.” The consumption of energy is related to the inventories and technical nature of the associated energy consuming devices. These in turn correspond to the various purposes at issue such as heating and cooling, illumination, transportation, and industrial activity. The quantity supplied of alternative forms of energy is determined based upon estimates of fossil fuel geology, the technologies of electric power generation and refining, the availability and market penetration of alternative, new forms of renewable and other energy sources, all embodied in the national system of energy transmission and distribution. It is this rich and substantial detail that enables policy analysis, since it is precisely with respect to these detailed factors that energy policies, and associated environmental policies, will be formulated. Accordingly, NEMS must be configured to enable its projections to provide a differential analysis of policies, or contingencies, with respect to this wide range of factors underlying the operation of the U.S. energy system.

Nevertheless, NEMS is a model of a portion of a market economy.[2] As such, the solution concept of the model is that of intertemporal, multi-market equilibria. The details of how this is done are briefly discussed in the next section. The point here is that, as such, the model’s results can be interpreted and understood in terms of the economist’s paradigm of market equilibrium and the associated comparative statics as measured by the price and other elasticities of market supply and demand. Further, we argue that processing model solutions in a fashion that reveals model functionality in these terms is a resource for understanding the basis for model results, characterizing the nature of model changes as the model evolves, and (even) auditing model performance to assist in the quality control of using or changing the model. In most respects the features of this “top down” description are implicit to the model’s operation. Although the isolation of the various sensitivities at issue as explicated in terms of market supply and demand can be extracted from the comparison of solutions configured with an appropriate experimental design of assumptions, such a process is expensive and time consuming and is not generally attempted, given the NEMS workload and available resources. We argue that in large measure the desired, “top down,” description can be extracted from the way the model is already used. The point of the results presented here is to demonstrate the degree to which this can be done and solicit comments and suggestions on the appropriate approaches to take.[3]

II. Approximating NEMS: An Overview. A summary of NEMS is provided in DOE/EIA(2003), including citations of individual NEMS component documentation. In brief, NEMS is comprised of twelve distinct modules that represent energy supply (oil and gas, natural gas transmission and distribution, coal supply, and renewable fuels), conversion (electric power and refining), sectoral end-use energy demand (residential, commercial, industrial, and transportation), energy-economy interactions, and international energy markets. Each of these modules embodies a substantial, associated detail as noted above. In solving the model an initial price vector, and the value of other assumptions, are specified. These values are passed to the demand modules which generate the associated demands for energy products. [4] The demands are then passed to the supply and distribution modules which generate the associated “supply prices” and related magnitudes corresponding to the given demands. These values are compared to the initial values assumed. If sufficiently close (currently in the range of 4%), the model is considered solved. If not, the initial assumptions are amended appropriately and the process is repeated.

It is beyond our scope to attempt to reproduce in any form the large, detailed results of NEMS solutions. Instead, we have selected a small number of solution series sufficiently comprehensive to provide (at the national level) a fuel specific expression by forecast year of balanced energy production, imports, exports, and consumption. In addition, approximations are made of energy consumption itemized by consuming sector, fuel specific and sectoral prices, and a small number of macroeconomic variables. Altogether, thirty-one variables (excluding derivative totals and the balance table discrepancy) were projected as endogenous variables based upon eight NEMS solution variables treated as exogenous variables. From the standpoint of the balance of energy production and consumption, there were an additional five series that were not modeled (i.e., the supply of nuclear power, “other” energy imports, and energy exports), but were included in the balance table. These series either showed little variation across the NEMS solutions used as data for the estimation and/or were in any case modeled outside of the standard comparative statics that our method is intended to reveal. The variables used are given in Table 1 below. Exogenous variables are indicated by an “*.” The first eight are the exogenous variables with respect to the regression analyses described in the next section. The remaining variables marked “*”, as explained above, are included, but not modeled. Totals are derived as the sums of the appropriate variables. Energy quantities are in quadrillion Btu’s (quads).

Table 1. Variable Listing

1) *World Oil Price ($ per bbl)

2) *Households (millions)

3) *Population (millions)

4) *Elec. Price Tax Comp. (Mills per Kwh)

5) *Elec. Price T&D Comp. (Mills per Kwh)

6) *Avg. Price. Delivered. Petroleum ($ per million Btu)

7) *Gas Price Markup ($/Mcf)

8) *Coal Price Markup ($/Ton)

9) Production: Crude Oil & Lease Condensate

10) Production: Natural Gas Plant Liquids

11) Production: Dry Natural Gas

12) Production: Coal

13) Production: *Nuclear Power

14) Production: Renewable Energy

15) Production: Other

16) Production: Total

17) Consumption: Petroleum Products

18) Consumption: Natural Gas

19) Consumption: Coal

20) Consumption: Renewable Energy

21) Consumption: Other

22) Consumption: Total

23) Imports: Crude Oil

24) Imports: Petroleum Products

Table 1. Variable Listing (Continued)

25) Imports: Natural Gas

26) Imports: *Other Imports

27) Imports: Total

28) Exports: *Petroleum

29) Exports: *Natural Gas

30) Exports: *Coal

31) Exports: *Total

32) Price: Gas Wellhead Price ($/Mcf)

33) Price: Coal Minemouth Price ($/Ton)

34) Price: Electricity (cents/Kwh)

35) Price: Residential ($ per Million Btu)

36) Price: Commercial ($ per Million Btu)

37) Price: Industrial ($ per Million Btu)

38) Price: Transportation ($ per Million Btu)

39) Residential: Delivered Energy

40) Commercial: Delivered Energy

41) Industrial: Delivered Energy

42) Transportation: Delivered Energy

43) Total Delivered Energy

44) Electricity Related Losses

45) Total Consumption

46) Electric Power Consumed

47) Real Gross Domestic Product

48) Real Disposable Personal Income

49) Industrial Shipments (billion $1996)

50) Avg. Delivered.Price Gas ($/Mcf)

51) Avg. Delivered Price Coal ($/Ton)

52) Discrepancy

The data used to derive the regression results were taken from the five principal solutions (scenarios) prepared for EIA’s annual publication of energy system projections, the Annual Energy Outlook (AEO). We used the solution values for the 2005 AEO (DOE/EIA (2005)). These five solutions have been codified over the last several decades as cases that are presented each year. An important feature of projections prepared for twenty or more years ahead is the range of potential values associated with the uncertainty surrounding the assumptions and methods of the analysis. The uncertainties at stake include fossil fuel geology, the level of economic activity and economic growth, and the development of new technologies. In the initial versions of the predecessor reports to the AEO (FEA (1974, 1976)) these uncertainties were investigated, but the cases specified to do so were not configured in design to correspond to the standard comparative statics of market supply and demand. This was changed for the forecasts released in 1978 (FEA (1978), pp. xvi-xix). Now five basic scenarios (in addition to other specialized cases) are formulated: a base case, high and low world oil price (WOP) cases (corresponding to shifts in energy supply) and high and low economic activity cases (corresponding to shifts in energy demand).[5] Since that time, these cases have provided the core of alternative assumptions against which the annual projections are formulated.

We used these cases as the data set for the regression analyses. For prices and the macroeconomic variables we used all of the scenarios. To accommodate problems of identification, to estimate demand relationships we used the base case and the two WOP scenarios. Given the way the NEMS solution algorithm works, i.e., demand estimates are passed to the supply modules which are then used to find “supply prices,” we used estimated demand as the explanatory variable for estimated supply. Of course this is an expedient. Accordingly, it is the market demand relationships for which our efforts reveal the underlying comparative statics. An exception is oil supply and petroleum demand. Given imports and the assumption that the WOP is exogenous, it is expected that all of the cases can be used to detect the comparative statics of each of these relationships. In general, the included variables in the regressions presented here are not intended to be definitive; rather, the point is to show the potential for extracting the features of market supply and demand from model solutions.

The NEMS approximation, based upon the regression results, is a “triangular” system. Specifically, the equations are applied in a sequence such that endogenous variables used as explanatory variables in a given equation are first estimated before so used. For example, GDP is an explanatory variable in the equation for the demand for petroleum products. But, GDP is itself estimated as a function of the WOP and population (both exogenous). Accordingly, when the simulation is run, GDP is estimated first. Then, this estimated value is used to derive the estimate of the demand for petroleum products. An exception is the kernel regression approach, as discussed in the next section. For this, the kernel functions used as weights are derived from the eight exogenous variables above and then applied uniformly in estimating the values of all of the remaining variables.

Given the use of the five principal scenarios as the source of the regression results, there is the issue of what additional cases to use as an out-of-sample test of the degree of fit of the approximation. In addition to the five principal scenarios, other cases are run to investigate uncertainty for each AEO. We chose sixteen of these to use to test the accuracy of the approximation. Inspection revealed that these cases did not always provide significant variations in all of the (eight) exogenous variables used for the simulation. We report results for these cases, but wanted better examples to use to test the simulation.[6] For these we selected the five principal scenarios prepared the year before for the 2004 AEO. Not only do these provide an interesting test of the method, but the same regression specifications were run for these solutions as well. As a result, changes in the model between the two years could be detected due to changes in the underlying comparative statics of market supply and demand.

The regression specifications are given in Appendix A. The scenario definitions and detailed results are given in Appendix B. The OLS regression results are given in Appendix C.

III. Approximating NEMS: Methodology. NEMS approximations were constructed based upon three methodological approaches. The estimation of a (triangular) system of thirty-one equations (plus derivative totals and the discrepancy) based on ordinary least squares and quantile regression. A third approximation was constructed using kernel regression. These approaches are described in more detail below.

III. 1 Ordinary Least Squares and Quantile Regression. Some of the statistical properties of ordinary least squares (OLS) have been known for more than 200 years; since the earliest statement of the Gauss-Markov Theorem. Under the assumption of independent errors uncorrelated with the regressors, the OLS estimator is minimum variance in the class of linear unbiased estimators. In a theorem attributed to Rao, the OLS estimator is known to be minimum variance among linear and nonlinear estimators when the errors follow a normal distribution and are uncorrelated with the regressors.

When the errors in the garden variety regression model are normal then constructing test statistics is a simple matter and the power of the tests is well known. If the distribution of the errors is unknown, but the sample is large, researchers often invoke the law of large numbers and proceed by constructing their test statistics as though the error had a normal distribution.

In spite of the import of these theorems there are some features of modeling that OLS does not illuminate particularly well. To begin with, the statistical properties of OLS depend on either the linearity of the process being modeled or the assumption of normal errors. Secondly, as a conditional mean, the OLS estimator does not capture any of the possible richness of an asymmetric conditional distribution of the dependent variable. A third related problem that OLS has is its sensitivity to outliers in the data.

An alternative estimation strategy that overcomes the linearity question is kernel regression, discussed in the next section. The second and third issues are overcome by quantile regression discussed below.

We say that a student scores at the q^th percentile of an exam if she performs as well as the proportion q and worse than the proportion (1-q). Hence half the students perform better than the median student. Similarly, the quartiles divide the population into four segments with equal proportions. Quantiles refer to the general case. When there is a set of regressors that purport to explain the dependent variable then we may speak of conditional quantile functions, as introduced by Koenker and Bassett (1978). For example, if one were to plot Engel’s (1857) data on household food expenditure against household income the scatter would look like a cone rising from the origin. Expenditure is more disperse among high income households. Fitting a single conditional mean function, even one corrected for heteroscedasticity, would mask some of the richness of the data. By fitting a set of quantile functions to the data one reveals the increasing dispersion of the data conditional on household income.

The OLS estimator minimizes the weighted sum of squared errors,

The associated loss function is a smooth, symmetric parabola. Quantile regression minimizes the sum of weighted absolute errors,

where,

The loss function is now a v-shape tilted from the vertical by the choice of p. Minimizing a sum of absolute errors permits the characterization of quantile regression as the solution to a linear programming problem. The difference in the optimization scheme accounts for the robustness of quantile regression to outliers in the data. When using OLS an outlier produces a large error that is then squared, giving it even more weight in the loss function. An outlier in a quantile regression may produce a large error, but the magnitude of the error doesn’t matter; only its position relative to the quantile function matters. The upshot is that an outlier can substantially change both the intercept and the slope of an OLS line, but it will change the intercept and have little impact on the slope of a quantile function.

To reiterate, quantile regression is robust to outliers in the data and also allows the researcher to make some inference about the asymmetry in the conditional distribution of the dependent variable. In the present exercise we estimate the median regression for the 31 equations in the system. Thus we produce estimates that are robust to outliers, but do not explore any asymmetry in the conditional distributions of the dependent variables.

In thinking about outliers one might imagine an observation that lies quite apart from an otherwise well ordered scatter of data points. The data used in the present analysis are actually multiple scenario forecasts from a large and complex model. Any given scenario will likely produce very smooth data series, but a collection of them may be quite different from one another, producing what may appear to be outliers relative to a base case. It is this consideration that prompted our use of quantile regression as a technique against which to juxtapose OLS.

III.2 Kernel Regression. Returning to OLS: With just two numbers, the mean and the variance, one can characterize the conditional density for a variable to be explained if one can assume normality. But suppose that the imposition of a parametric assumption like normality obscures part of the story to be seen in the data. For example, consider wage inequality. In 1979 the minimum wage was binding on a high proportion of working women, resulting in a large spike in the empirical density of wages at the legal minimum. By 1989 real wages had risen substantially relative to the legal minimum, so that the minimum wage was no longer binding, resulting in a much more symmetric distribution. Using a parametric model of the wage distribution in both years would be very misleading. A smoothed empirical density would be much more revealing. The nonparametric empirical density can be generalized to a conditional density via kernel regression.

The method of kernel regression estimates the values of the endogenous variables as a weighted average of the corresponding values from the supporting data set. The weights used, called kernel functions, are based upon the “proximity” of the out-of-sample exogenous variables. The advantage of this method is that the “estimation” does not require that a particular functional form be fit to the underlying data. Accordingly, very nonlinear or very irregular “shapes” of the manifold describing the endogenous variable and the corresponding explanatory variables can be accommodated.[7] This problem is replaced by the need to select the form of the kernel function and the values in the data base to use. The database used was the five principal scenarios for the 2005 AEO. Assume that the kernel regression estimation involves just one exogenous variable. The method, as spelled out below, was applied to every year for which a solution was approximated.

Let z be an out-of-sample exogenous variable, x_i the corresponding variable in the ith solution in the database, m(z) the approximation of the endogenous variable, and y_i the corresponding value of the endogenous variable in the i^th solution in the database. The general idea is to find solutions in the database that are “close” to the out-of-sample solution in terms of the value of the exogenous variable.

Smoothing Parameter (u_i). The proximity of the i^th solution's exogenous variable (i.e., the degree to which it is "close") to the out-of-sample value for that variable is measured by the smoothing parameter u_i,

u_i = (z – x_i)/BW,

where BW = bandwidth is as defined below. The sense of the measure is that the i^th solution is "close" as |u_i| is small.

Bandwidth (BW). In the measure above, "sufficiently close" is specified by the criterion that |u_i| < 1. This outcome is influenced by the value assigned the bandwidth, BW, e.g., a variable is more likely to be "sufficiently close" as BW is large. A standard formula for the initial size of BW (for a given exogenous variable) is,

BW = 1.06sQ^(-1/5),

where s is the standard deviation of the exogenous variable at issue and Q is the number of solutions in the database.[8] Given this, the particular out-of-sample values at issue may not be such that any, or enough, solutions are "sufficiently close," as specified by the criterion |u_i| < 1. Given this, the user specifies a minimum number of solutions that must be sufficiently close. We chose the requirement that four (of the five) solutions must be “sufficiently close.” In our method, the initial bandwidth value given above is incremented by 1% until, for each year, at least the specified minimum number of solutions satisfy the criterion for all of the exogenous variables.

Kernel Function (K(u_i)): The approximation of the value of each of the out-of-sample endogenous variables is made as a weighted average of the corresponding values in the sufficiently close solutions in the pseudo database. Five kernel functions, K(u_i), are identified below that can be used for constructing the weights. For all of these K(u_i) = 0 for |u_i| > 1 or the value given below for |u_i| < 1. We used the triangle kernel function for the results presented here. An immediate increase in the scope of the effort calls for a comparison of the accuracy of this with the other kernel functions.

(1) Uniform: K(u_i) = 1.

(2) Triangle: K(u_i) = 1 - |u_i|.

(3) Epanechnikov: K(u_i) = (1 - |u_i|²).

(4) Quartic: K(u_i) = (1 - |u_i|²)².

(5) Triweight: K(u_i) = (1 - |u_i|²)³.

For more than one exogenous variable, the case here, the kernel-function value corresponding to a solution is the product of the values for the individual exogenous variables. Inspection of the different functional forms reveals the sense of the weighting scheme. For the uniform kernel all sufficiently close solutions are treated the same and the approximated value (as shown below) is the simple average of all of the database values from the sufficiently close solutions. The four other forms provide alternative ways to give higher weights to closer solutions.

Approximation Formula. Given the values of the kernel functions (for the sufficiently close solutions with indices SC), the estimate of an out-of-sample endogenous variable is constructed as,

This particular form is sometimes termed the Nadaraya-Watson estimator.

As another expedient, the kernel regression algorithm was applied to all variables in the data set. Specifically, the weights were fashioned with respect to all eight exogenous variables and then applied uniformly to the estimates of all of the remaining variables. An alternative, and presumably a better fitting alternative, would be to apply the kernel approach equation by equation, using the same specification as used for the OLS and quantile regressions. The computational routines required for this approach could not be completed in time for this effort. Even so, the kernel regression approach as it was applied proved generally to be the most accurate method. A disadvantage of the kernel regression approach is that it does not explicitly reveal the comparative statics of market supply and demand, the core purpose of the other regression approaches. Given that there are a number of diagnostic purposes at stake in constructing the approximations, this suggests that using more than one method is appropriate.

IV. Approximation Results. Results of the simulation were tabulated for each of the five in-sample AEO2005 cases, the sixtenn AEO2005 out-of-sample cases, and the five principal scenarios for the AEO2004. The forecast years chosen for data were 2004-2025 inclusive. As discussed above, the simulation implemented the regression equations in sequence such that all endogenous variables used as explanatory variables were first estimated, ultimately in terms (as appropriate) of the eight exogenous variables. The degree of fit of the approximation was measured, for each endogenous variable by the absolute percent difference of the estimated from the actual variable value, error = 100abs(estimate – actual)/actual. A summary of results, averaged over the thirty-one endogenous variables for the projection period 2005-2025, is given below for each case and method considered. Detailed results are in Appendix B.

Table 2. Summary Results for AEO2005 In-Sample Scenarios (Abs % Error)

Scenario:

Method:

Base

Case

High Macro

Scenario

Low Macro

Scenario

High WOP

Scenario

Low

WOP

Scenario

Grand

Average

OLS

Regression

4.76

5.58

5.96

5.99

4.96

5.45

Quantile

Regression

6.69

6.74

9.09

6.99

6.93

6.79

Kernel

Regression

n/a*

n/a

*The kernel regression could not be run for the approximating database itself.

Table 3. Summary Results for Selected AEO2005 Scenarios (Abs % Error)

Scenario:

Method:

High Fossil Technology

Low Fossil Technology

Warmer Weather

Colder Weather

Grand

Average

OLS

Regression

4.95

4.87

4.78

4.82

4.86

Quantile

Regression

7.21

6.70

6.83

6.68

6.85

Kernel

Regression

.91

.54

1.49

1.10

1.01

Table 4. Summary Results For Selected AEO2005 Scenarios (Abs % Error)

Scenario:

Method:

High Oil & Gas Technology

Low Oil & Gas Technology

Integrated

2005

Technology

Integrated High Technology

Grand

Average

OLS Regression

5.07

5.44

5.94

5.68

5.53

Quantile

Regression

6.63

7.87

7.32

7.96

7.44

Kernel Regression

2.41

2.22

3.22

3.62

2.87

Table 5. Summary Results For Selected AEO2005 Scenarios (Abs % Error)

Scenario:

Method:

Somewhat

Higher

WOP

Very

High

WOP

Very Low

Cost

Nuclear

Low

Cost

Nuclear

Grand

Average

OLS Regression

6.03

9.39

4.77

4.82

6.26

Quantile

Regression

7 .22

9.32

6.87

6.97

7.60

Kernel Regression

1.61

4.30

.23

.39

1.61

Table 6. Summary Results for Selected AEO2005 Scenarios (Abs % Error)

Scenario:

Method:

SEER

Efficiency

Standard

Restricted

Gas

Supply

Low

Renewables

High Renewables

Grand

Average

OLS Regression

4.80

6.76

4.79

4.92

5.32

Quantile

Regression

6.85

6.14

6.82

7.09

6.73

Kernel Regression

.30

5.50

.15

.70

1.66

Table 7. Summary Results for AEO2004 Principal Scenarios (Abs % Error)

Scenario:

Method:

Base

Case

High Macro

Scenario

Low Macro

Scenario

High WOP

Scenario

Low

WOP

Scenario

Grand

Average

OLS

Regression

11.64

13.15

10.86

12.84

12.46

12.19

Quantile

Regression

12.23

13.29

12.06

13.54

12.45

12.23

Kernel

Regression

n/a*

n/a

*The kernel regression could not be run for these data.

For the sixteen out-of-sample AEO2005 scenarios all of the methods fit reasonably well, with the kernel regression generally best, OLS next, and the quantile regression marginally less accurate than OLS. For cases for which the fit is less satisfactory, the “larger” errors are associated with series involving less energy, e.g., “other” energy demand. This is highlighted by (say) the balance table for the year 2015 for the Very High Oil Price scenario reported on in Table 5 above. These results are given in Table 8 below.

For this approximation, the estimated prices are generally too high and, therefore, the corresponding estimates of consumption are too low. Alternatively, the estimated oil supply response was too low. The degree to which the regression results well approximate the NEMS structure can also be studied in terms of the changes in the regression results across the AEO2005 and AEO2004 data sets.[9] These changes can be studied in terms of the changes in the revealed elasticity values across the two model versions.

The functional approach to both the demand relationships and GDP was to use a price variable and an activity “driver” as explanatory variables. E.g., for GDP the price variable was the WOP and the driver was population; and, for the demand for petroleum products, the price variable was the WOP and the driver was GDP. The elasticities derived from the regression results based upon this functional approach are summarized below.[10]

Table 9.1 Elasticities: Projected GDP

Source	Price: WOP	Driver: Population
AEO2005:OLS	-.021	3.46
AEO2005: Quantile	-.002	2.15
AEO2004:OLS	-.012	3.50
AEO2004:Quantile	-.003	2.16

Table 9.2 Elasticities: Crude Oil Supply

Source	Price: WOP	Driver: Lag
AEO2005:OLS	.027	1.05
AEO2005: Quantile	.017	1.01
AEO2004:OLS	-.006	1.08
AEO2004:Quantile	-.009	1.07

Table 9.3 Elasticities: Demand for Petroleum Products

Source	Price:WOP	Driver: GDP
AEO2005:OLS	-.109	.495
AEO2005: Quantile	-.014	.484
AEO2004:OLS	-.204	.603
AEO2004:Quantile	-.227	.622

Table 9.4 Elasticities: Demand for Natural Gas

Source	Price: Average Delivered	Driver: GDP
AEO2005:OLS	-.258	.526
AEO2005: Quantile	-.216	.521
AEO2004:OLS	.300	.426
AEO2004:Quantile	.613	.350

Table 9.5 Elasticities: Residential Sector Demand for Energy

Source	Price: Average to Sector	Driver: # Households
AEO2005:OLS	-.256	.948
AEO2005: Quantile	-.282	.973
AEO2004:OLS	-.256	.966
AEO2004:Quantile	-.275	.985

Table 9.6 Elasticities: Commercial Sector Demand for Energy

Source	Price: Average to Sector	Driver: GDP
AEO2005:OLS	-.190	.672
AEO2005: Quantile	-.202	.674
AEO2004:OLS	-.284	.617
AEO2004:Quantile	-.309	.627

Table 9.7 Elasticities: Industrial Sector Demand for Energy

Source	Price: Average to Sector	Driver: Industrial Shipments
AEO2005:OLS	-.042	.395
AEO2005: Quantile	-.042	.389
AEO2004:OLS	-.064	.522
AEO2004:Quantile	-.058	.521

Table 9.8 Elasticities: Transportation Sector Demand for Energy

Source	Price: Average to Sector	Driver: Disposable Income
AEO2005:OLS	-.194	.551
AEO2005: Quantile	-.199	.556
AEO2004:OLS	-.344	.577
AEO2004:Quantile	-.297	.581

For these results, the price and driver elasticities of the four sectoral demand relationships are stable and quite similar for the OLS versus quantile regression approaches. The approximation of GDP was stable across the two methods; however, the quantile regression results were somewhat more inelastic compared to OLS for this variable. The other results are less stable, with sign changes for the price elasticities for crude oil supply and natural gas demand. Such an outcome is indicative of model changes and non-market influences embodied in NEMS with respect to the variable.[11] Indeed, such an outcome can provide a useful diagnostic as model versions are developed, i.e., the sign change in the elasticity should be investigated and the associated change in model characteristics determined. Additional simulation results are provided below in Appendix B. The associated data files are available at,

http://optima-com.com/buck_lady/AES_Files.htm

V. Conclusions. The basic NEMS modeling methodology may be termed a “bottom up” approach to estimating energy supply and demand. NEMS projections of the supply of energy products is expressed (as appropriate) in terms of the geographical presence of fossil fuel resources by category of extractability, the technologies of finding, recovering, and producing the associated energy products, technologies for creating other energy sources, the technologies for refining and electricity generation, and the inter-regional distribution of the resulting energy products. All of this is modeled in terms of the economics of energy extraction, production, and distribution, with the associated sensitivity of supply to market prices and costs.

For energy demand, inventories and vintages of energy consuming devices are projected within each of a variety of service demand areas, such as heating and lighting. These service demands are then related to (such as) the number of residential households, the square-footage of commercial floor space, and inventories of existing and projected energy consuming devices that satisfy the service. As with supply, energy demand is modeled in economic terms, including life-cycle costs and other factors that underlie the sensitivity of demand to the prices of energy products and other costs of energy consumption. In solution, the NEMS algorithm finds market prices such that energy supply and demand are in balance. NEMS forecasts are intended to portray the implications of prospective energy policies as they relate to the efficiency and environmental impacts of alternative configurations of energy production and consumption. The detail of the model is intended to capture the detail and content of energy policy initiatives.

The methods used here might be termed “top down.” The interrelationships, and associated sensitivities, among important energy system variables are estimated based upon alternative NEMS solutions. These relationships are implicit to NEMS, but in general cannot be revealed without implementing NEMS, or at least the components of NEMS at issue, with respect to a highly structured experimental design.

Our purpose was to use the simplest techniques to evaluate the internal consistency and plausibility of the NEMS solutions. Regression analyses were performed of important relationships among NEMS solution variables. The variable/parameter sensitivities were measured as elasticities and compared across the NEMS AEO versions to reveal changes in model structure and interrelationships.

The results here in many ways raise as many issues as are resolved. We believe that the results sustain the idea that reasonably straight-forward estimation techniques can be applied to the solution files of large models to reveal their underlying structure and provide a diagnostic tool for assessing model changes and stability. Many issues, such as the choice of estimation method or kernel function, the specification of the included variables in the regression equations, the experimental design (if any) of the solution sets used as data, remain open and provide an interesting agenda for further efforts in developing approximation approaches. The point of this effort is to show that the solutions of large models with a substantial time-frame of development and use can themselves support the construction of model approximations, i.e., a meta-model, that can be a resource in both interpreting and understanding the larger model and provide a diagnostic tool in support of model development.

References

DOE/Energy Information Administration, The National Energy Modeling Systsm: An Overview 2003, DOE/EIA-0581(2003), March 2003.

_________________________________, Annual Energy Outlook 2004, DOE/EIA-0383(2004), January 2004.

_________________________________, Annual Energy Outlook 2005, DOE/EIA-0383(2005), February 2005.

Engel, Ernst, 1857. “Die Produktions- und Konsumptionvrhaltnisse des Koenigsreichs Sachsen.” Reprinted “Die Lebenkosten Belgischer Arbeiter-Familien Fruher und Jetzt.“ International Statistical Institute Bulletin, 9, pp.1-125.

Eubank, R. (1988): Spline Smoothing And Nonparametric Rregression, Decker, New York.

Federal Energy Administration (FEA), Project Independence Report, Stock# 4118-00029, Government Printing Office, November 1974.

__________________________, National Energy Outlook, FEA-N-75-713, 041-018-00097-6, Government Printing Office, February 1976.

_______________________________, Annual Report to Congress, Vol . II, DOE/EIA-0036/2, CRN-780- 328-00127, SP-AN74/A(77), April 1978.

Gasser, T. and H. Müller (1984): "Estimating regression functions and their derivatives by the kernel method," Scandinavian Journal of Statistics, 11, pp. 171-185.

Hardle, W. (1990): Applied Nonparametric Regression, Cambridge University Press, New York.

_________(1991): Smoothing Techniques With Implementation In S, Springer-Verlag, New York.

Koenker, Roger and Gilbert Bassett. 1978. “Regression Quantiles”, Econometrica, January 46:1, pp. 43-50.

Nadaraya, E.A. (1964): "On estimating regression," Theory of Probablility and Its Applications, 10, pp. 186-90.

Watson, G.S. (1964): "Smooth regression analysis," Sankhya, Series A, 26, pp. 359-372.

Appendix A: Regression Specification

Thirty-one regression equations were formulated and estimated using both OLS and quantile regression approaches. The equations were specified such that, for the linear system formed by the equations as a group, any estimated variable subsequently used as an explanatory variable in an equation would be first estimated itself, with the first one(s) of these simulated using variables treated as exogenous to the simulation. The regression specifications which follow are generated by the simulation software (termed NEMSSIM5). The “file stem” referred to is the generic label to several files created by the regression routines that contain, respectively, the regression results, the coefficients, the coefficients reexpressed as elasticities, and the data used. The first character of the stem designates if the file reports on OLS (“L”) or quantile regression (“Q”). The specification given below was generated for the OLS version of the simulation. The filenames *.psd are those used for the regressions, which were run for the years 2004-2025. These files are available separately at the website provided in support of the paper:

http://optima-com.com/buck_lady/AES_Files.htm,

and the data used may be inspected using the program getdata.exe available from the website. The file faesa_*.psd contains solution data for all five of the principal AEO scenarios while the file faesd-*.psd. These data were used for most of the OLS and quantile regressions and was the supporting data base for all of the kernel regression-based approximations. the file faesd_*.psd contains the base case and high/low WOP scenarios. These data were used for estimating the demand relationships. The numbers associated with variables identify their placement in the data base.

Regression Specifications

Regression #1 with File Stem = LGDP with data from Faesa_sim05.psd

Endogenous Variable: 47) Real Gross Domestic Product

log = Yes and lag = No

Exogenous Variable(s):

1) *World Oil Price ($ per bbl)

3) *Population (millions)

Regression #2 with File Stem = LYD with data from Faesa_sim05.psd

Endogenous Variable: 48) Real Disposable Personal Income

log = No and lag = No

Exogenous Variable(s):

47) Real Gross Domestic Product

Regression #3 with File Stem = LVS with data from Faesa_sim05.psd

Endogenous Variable: 49) Industrial Shipments (billion $1996)

log = No and lag = No

Exogenous Variable(s):

47) Real Gross Domestic Product

Regression #4 with File Stem = LOilSupply with data from Faesa_sim05.psd

Endogenous Variable: 9) Production: Crude Oil & Lease Condensate

log = No and lag = Yes

Exogenous Variable(s):

1) *World Oil Price ($ per bbl)

Regression #5 with File Stem = LPetDemand with data from Faesa_sim05.psd

Endogenous Variable: 17) Consumption: Petroleum Products

log = No and lag = No

Exogenous Variable(s):

1) *World Oil Price ($ per bbl)

47) Real Gross Domestic Product

Regression #6 with File Stem = LGasPrice with data from Faesa_sim05.psd

Endogenous Variable: 32) Price: Gas Wellhead Price ($/Mcf)

log = No and lag = Yes

Exogenous Variable(s):

1) *World Oil Price ($ per bbl)

Regression #7 with File Stem = LGasDPrice with data from Faesa_sim05.psd

Endogenous Variable: 50) Avg. Price Del. Gas ($/Mcf)

log = No and lag = No

Exogenous Variable(s):

7) *Gas Price Markup ($/Mcf)

32) Price: Gas Wellhead Price ($/Mcf)

Regression #8 with File Stem = LCoalPrice with data from Faesa_sim05.psd

Endogenous Variable: 33) Price: Coal Minemouth Price ($/Ton)

log = No and lag = Yes

Exogenous Variable(s):

1) *World Oil Price ($ per bbl)

Regression #9 with File Stem = LCoalDPrice with data from Faesa_sim05.psd

Endogenous Variable: 51) Avg. Price Del. Coal ($/Ton)

log = No and lag = No

Exogenous Variable(s):

8) *Coal Price Markup ($/Ton)

33) Price: Coal Minemouth Price ($/Ton)

Regression #10 with File Stem = LGasDemand with data from Faesd_sim05.psd

Endogenous Variable: 18) Consumption: Natural Gas

log = No and lag = No

Exogenous Variable(s):

47) Real Gross Domestic Product

50) Avg. Price Del. Gas ($/Mcf)

Regression #11 with File Stem = LGasSupply with data from Faesa_sim05.psd

Endogenous Variable: 11) Production: Dry Natural Gas

log = No and lag = Yes

Exogenous Variable(s):

18) Consumption: Natural Gas

Regression #12 with File Stem = LCoalDemand with data from Faesd_sim05.psd

Endogenous Variable: 19) Consumption: Coal

log = No and lag = No

Exogenous Variable(s):

49) Industrial Shipments (billion $1996)

Regression #13 with File Stem = LCoalSupply with data from Faesa_sim05.psd

Endogenous Variable: 12) Production: Coal

log = No and lag = No

Exogenous Variable(s):

19) Consumption: Coal

Regression #14 with File Stem = LElecPrice with data from Faesa_sim05.psd

Endogenous Variable: 34) Price: Electricity (cents/Kwh)

log = No and lag = No

Exogenous Variable(s):

4) *Elec. Price Tax Comp. (Mills per Kwh)

5) *Elec. Price T&D Comp. (Mills per Kwh)

50) Avg. Price Del. Gas ($/Mcf)

51) Avg. Price Del. Coal ($/Ton)

Regression #15 with File Stem = LElecDemand with data from Faesd_sim05.psd

Endogenous Variable: 46) Electric Power Consumed

log = No and lag = No

Exogenous Variable(s):

34) Price: Electricity (cents/Kwh)

47) Real Gross Domestic Product

Regression #16 with File Stem = LElecLosses with data from Faesa_sim05.psd

Endogenous Variable: 44) Electricity Related Losses

log = No and lag = No

Exogenous Variable(s):

46) Electric Power Consumed

Regression #17 with File Stem = LNGLSupply with data from Faesa_sim05.psd

Endogenous Variable: 10) Production: Natural Gas Plant Liquids

log = No and lag = No

Exogenous Variable(s):

11) Production: Dry Natural Gas

Regression #18 with File Stem = LRenew with data from Faesa_sim05.psd

Endogenous Variable: 14) Production: Renewable Energy

log = No and lag = Yes

Exogenous Variable(s):

47) Real Gross Domestic Product

Regression #19 with File Stem = LOtherDemand with data from Faesd_sim05.psd

Endogenous Variable: 21) Consumption: Other

log = No and lag = No

Exogenous Variable(s):

6) *Avg. Price. Del. Petroleum ($ per million Btu)

47) Real Gross Domestic Product

50) Avg. Price Del. Gas ($/Mcf)

51) Avg. Price Del. Coal ($/Ton)

Regression #20 with File Stem = LOtherSupply with data from Faesa_sim05.psd

Endogenous Variable: 15) Production: Other

log = No and lag = Yes

Exogenous Variable(s):

21) Consumption: Other

Regression #21 with File Stem = LResPrice with data from Faesa_sim05.psd

Endogenous Variable: 35) Price: Residential ($ per Million Btu)

log = No and lag = No

Exogenous Variable(s):

6) *Avg. Price. Del. Petroleum ($ per million Btu)

34) Price: Electricity (cents/Kwh)

50) Avg. Price Del. Gas ($/Mcf)

Regression #22 with File Stem = LResDemand with data from Faesd_sim05.psd

Endogenous Variable: 39) Residential: Delivered Energy

log = No and lag = No

Exogenous Variable(s):

2) *Households (millions)

35) Price: Residential ($ per Million Btu)

Regression #23 with File Stem = LComPrice with data from Faesa_sim05.psd

Endogenous Variable: 36) Price: Commercial ($ per Million Btu)

log = No and lag = No

Exogenous Variable(s):

34) Price: Electricity (cents/Kwh)

Regression #24 with File Stem = LComDemand with data from Faesd_sim05.psd

Endogenous Variable: 40) Commercial: Delivered Energy

log = No and lag = No

Exogenous Variable(s):

36) Price: Commercial ($ per Million Btu)

47) Real Gross Domestic Product

Regression #25 with File Stem = LIndPrice with data from Faesa_sim05.psd

Endogenous Variable: 37) Price: Industrial ($ per Million Btu)

log = No and lag = No

Exogenous Variable(s):

6) *Avg. Price. Del. Petroleum ($ per million Btu)

34) Price: Electricity (cents/Kwh)

50) Avg. Price Del. Gas ($/Mcf)

Regression #26 with File Stem = LIndDemand with data from Faesd_sim05.psd

Endogenous Variable: 41) Industrial: Delivered Energy

log = No and lag = No

Exogenous Variable(s):

37) Price: Industrial ($ per Million Btu)

49) Industrial Shipments (billion $1996)

Regression #27 with File Stem = LTrnPrice with data from Faesa_sim05.psd

Endogenous Variable: 38) Price: Transportation ($ per Million Btu)

log = No and lag = No

Exogenous Variable(s):

6) *Avg. Price. Del. Petroleum ($ per million Btu)

Regression #28 with File Stem = LTrnDemand with data from Faesd_sim05.psd

Endogenous Variable: 42) Transportation: Delivered Energy

log = No and lag = No

Exogenous Variable(s):

38) Price: Transportation ($ per Million Btu)

48) Real Disposable Personal Income

Regression #29 with File Stem = LOilM with data from Faesa_sim05.psd

Endogenous Variable: 23) Imports: Crude Oil

log = No and lag = No

Exogenous Variable(s):

9) Production: Crude Oil & Lease Condensate

17) Consumption: Petroleum Products

28) Exports: *Petroleum

Regression #30 with File Stem = LPetM with data from Faesa_sim05.psd

Endogenous Variable: 24) Imports: Petroleum Products

log = No and lag = No

Exogenous Variable(s):

9) Production: Crude Oil & Lease Condensate

17) Consumption: Petroleum Products

23) Imports: Crude Oil

28) Exports: *Petroleum

Regression #31 with File Stem = LGasM with data from Faesa_sim05.psd

Endogenous Variable: 25) Imports: Natural Gas

log = No and lag = No

Exogenous Variable(s):

11) Production: Dry Natural Gas

18) Consumption: Natural Gas

29) Exports: *Natural Gas

Variable Listing

1) *World Oil Price ($ per bbl)

2) *Households (millions)

3) *Population (millions)

4) *Elec. Price Tax Comp. (Mills per Kwh)

5) *Elec. Price T&D Comp. (Mills per Kwh)

6) *Avg. Price. Del. Petroleum ($ per million Btu)

7) *Gas Price Markup ($/Mcf)

8) *Coal Price Markup ($/Ton)

9) Production: Crude Oil & Lease Condensate

10) Production: Natural Gas Plant Liquids

11) Production: Dry Natural Gas

12) Production: Coal

13) Production: *Nuclear Power

14) Production: Renewable Energy

15) Production: Other

16) Production: Total

17) Consumption: Petroleum Products

18) Consumption: Natural Gas

19) Consumption: Coal

20) Consumption: Renewable Energy

21) Consumption: Other

22) Consumption: Total

23) Imports: Crude Oil

24) Imports: Petroleum Products

25) Imports: Natural Gas

26) Imports: *Other Imports

27) Imports: Total

28) Exports: *Petroleum

29) Exports: *Natural Gas

30) Exports: *Coal

31) Exports: *Total

32) Price: Gas Wellhead Price ($/Mcf)

33) Price: Coal Minemouth Price ($/Ton)

34) Price: Electricity (cents/Kwh)

35) Price: Residential ($ per Million Btu)

36) Price: Commercial ($ per Million Btu)

37) Price: Industrial ($ per Million Btu)

38) Price: Transportation ($ per Million Btu)

39) Residential: Delivered Energy

40) Commercial: Delivered Energy

41) Industrial: Delivered Energy

42) Transportation: Delivered Energy

43) Total Delivered Energy

44) Electricity Related Losses

45) Total Consumption

46) Electric Power Consumed

47) Real Gross Domestic Product

48) Real Disposable Personal Income

49) Industrial Shipments (billion $1996)

50) Avg. Price Del. Gas ($/Mcf)

51) Avg. Price Del. Coal ($/Ton)

52) Discrepancy

Appendix B: Regression Results

The regression results are provided below for each of the thirty-one endogenous variables for each of the OLS, quantile, and kernel regression methodologies. The tabular presentations are reported by the simulation and have been simply inserted here to facilitate the assembly of results. The regressions are identified using the filestem ID’s given in Appendix A. The NEMS solutions used are identified by the filenames given these within the NEMS system itself. The glossary of these solution ID’s and their more intuitive designation given in the paper above is provided below. More detailed descriptions of the different scenarios are provided within the AEO. This may be accessed from the EIA website at: http://www.eia.doe.gov/. Once at the site access “Projections to 2025” linked under “Featured Publications.” Pdf and other formatted versions of the current and past AEO’s are available. The scenario descriptions are summarized in DOE/EIA(2005) on pp. 216-217 and elsewhere in the text as cited in the summary.

NEMS Solution Roster. AEO2005 cases

aeo2005.1020a.ran = base case

hm2005.1020a.ran = high macro

lm2005.1020a.ran = low macro

hw2005.1020a.ran = high WOP

lw2005.1020a.ran = low WOP

hfoss05.1021a.ran = high fossil technolgy

lfoss05.1021a.ran = low fossil technolgy

warmer.1026b.ran = warmer weather

colder.1026a.ran = colder weather

ogltec05.1027a.ran = oil & gas low technology

oghtec05.1027a.ran = oil & gas high technology

ltrkiten.1115a.ran = integrated 2005 technology

htrkiten.1116a.ran = integrated high technolgy

cf2005.1111a.ran = somewhat higher WOP

vhw2005.1203a.ran = very high WOP

advnuc20.1021a.ran = very low cost nuclear

advnuc5a.1108a.ran = low cost nuclear

seer12.1102a.ran = SEER efficiency standard

ressup.1027a.ran = restricted gas supply

loren05.1115a.ran = low renewables

hiren05.1116a.ran = high renewables

NEMS Solution Roster. AEO2004 cases

aeo2004.1017e.ran = base case

hm2004.1017a.ran = high macro

lm2004.1017a.ran = low macro

hw2004.1017b.ran = high WOP

lw2004.1017b.ran = low WOP

Note: The kernel regression results use the filestem ID’s with “K” as the first character

Summary of Average Absolute Percent Differences OLS Estimated Versus Actual

Series aeo2005.1020a.ran hm2005.1020a.ran lm2005.1020a.ran hw2005.1020a.ran lw2005.1020a.ran

1) LGDP .5998862 2.202668 2.470675 .6995581 .5643647

2) LYD .7065605 3.472149 3.465525 .6720447 .7085267

3) LVS .6187971 3.680192 4.422369 .4862138 .7977042

4) LOilSupply 9.716942 9.093307 10.23691 5.585875 13.67784

5) LPetDemand .399461 .7271433 .8599448 .6345757 .9764815

6) LGasPrice 11.18035 10.64171 11.64167 14.66256 12.4462

7) LGasDPrice 7.425991 7.325754 7.50969 9.698568 8.3103

8) LCoalPrice 4.063516 3.558633 5.591816 7.865088 3.516044

9) LCoalDPrice 2.736695 2.426964 3.769914 5.342011 2.382194

10) LGasDemand 2.082338 3.250385 1.853649 3.576514 2.195577

11) LGasSupply 1.711875 3.378774 1.918123 3.679173 1.986395

12) LCoalDemand 1.482682 2.183524 .9693661 1.483048 1.781572

13) LCoalSupply 1.688387 2.302947 1.029275 1.754934 2.035599

14) LElecPrice 1.989296 1.997065 2.522762 3.205044 2.274746

15) LElecDemand .4545453 1.416902 1.639602 1.128351 .3912342

16) LElecLosses .4212567 1.400429 1.491395 1.013558 .40211

17) LNGLSupply 1.556801 2.812364 1.695881 3.308612 1.872269

18) LRenew 1.340091 1.399954 1.615429 1.207529 1.56213

19) LOtherDemand 37.57455 48.48412 44.68779 63.65661 44.02177

20) LOtherSupply 25.51379 10.00731 27.72445 11.57753 15.23598

21) LResPrice 2.856818 2.95323 3.088042 3.66406 3.176798

22) LResDemand .8054771 .8652943 .7204781 .8620229 .7788018

23) LComPrice 3.421044 3.671695 3.194175 3.856827 3.887784

24) LComDemand .4938224 3.547609 3.909626 .8343942 .4075919

25) LIndPrice 3.616785 3.722832 3.44686 3.967775 4.021328

26) LIndDemand .4418205 4.230725 4.536951 .5501647 .6966943

27) LTrnPrice .7947609 .7990886 .7929158 .8041691 .5570571

28) LTrnDemand .857949 1.012754 1.669976 .6856034 .8760394

29) LOilM 7.431223 8.733582 8.319019 3.995608 8.195763

30) LPetM 10.52958 15.36248 10.69848 18.98066 8.738036

31) LGasM 3.038526 6.185875 7.171493 6.124212 5.394081

Avg 4.759729 5.575724 5.956911 5.9859 4.963517

Grand Average = 5.448357

Summary of Average Absolute Percent Differences Quantile Estimated Versus Actual

Series aeo2005.1020a.ran hm2005.1020a.ran lm2005.1020a.ran hw2005.1020a.ran lw2005.1020a.ran

1) QGDP .1448752 2.541449 2.622215 .2070524 .1385857

2) QYD .3662276 3.698995 3.72068 .5118558 .4834686

3) QVS .4115334 3.851246 4.569578 .3895671 .4958028

4) QOilSupply 14.37189 14.20027 14.45224 12.98024 15.28286

5) QPetDemand .472852 .7618558 .9336911 .6018405 .960119

6) QGasPrice 30.06709 22.91049 36.25401 30.05437 31.45309

7) QGasDPrice 20.13186 15.5754 23.93991 20.14811 20.95936

8) QCoalPrice 2.876264 3.14114 3.574256 5.548769 3.185227

9) QCoalDPrice 1.942387 2.160402 2.407086 3.760774 2.170342

10) QGasDemand 4.156388 4.346902 5.071711 4.8767 3.206878

11) QGasSupply 1.688873 3.334957 1.583692 3.799628 1.591179

12) QCoalDemand 1.371916 1.933127 1.234875 1.464992 1.364373

13) QCoalSupply 1.529714 2.068447 .9054594 1.811188 1.62093

14) QElecPrice 4.11121 2.835212 5.394137 4.720474 3.889199

15) QElecDemand 1.157881 1.697401 2.451451 1.386697 1.013665

16) QElecLosses 1.022401 1.569044 2.157653 1.204815 .9037367

17) QNGLSupply 1.402222 2.620852 1.466194 3.191583 1.376518

18) QRenew 1.793672 2.614753 1.766482 1.81593 1.823881

19) QOtherDemand 31.66237 39.1631 54.07744 47.64389 49.61553

20) QOtherSupply 30.38575 13.48543 32.67662 12.96622 20.06081

21) QResPrice 6.010362 4.450675 7.509195 6.167246 5.917233

22) QResDemand 1.77664 1.575292 1.830671 1.485119 1.71175

23) QComPrice 5.881284 5.210612 6.677905 5.907724 5.810217

24) QComDemand 1.118988 3.071701 4.854845 1.039448 1.145976

25) QIndPrice 6.694417 5.297837 8.307137 6.757074 6.717174

26) QIndDemand .3965529 4.47401 4.486738 .5961486 .4779871

27) QTrnPrice .8015343 .8051023 .7813538 .8126843 .5498552

28) QTrnDemand .6589487 1.269141 1.483494 .5826923 .6341662

29) QOilM 11.1801 12.89386 11.75459 9.427978 9.631456

30) QPetM 13.4182 18.12829 13.48057 13.42165 10.30317

31) QGasM 11.55523 7.157537 19.22426 11.41169 10.32375

Avg 6.792246 6.73692 9.085488 6.990135 6.929622

Grand Average = 7.306882

Summary of Average Absolute Percent Differences OLS Estimated Versus Actual

Series hfoss05.1021a.ran lfoss05.1021a.ran warmer.1026b.ran colder.1026a.ran

1) LGDP .6071386 .5850728 .6016914 .5910658

2) LYD .7227523 .6934496 .7002661 .70645

3) LVS .5971709 .6671143 .6190853 .6449105

4) LOilSupply 9.706338 9.71736 9.7193 9.716836

5) LPetDemand .3601129 .4016328 .4148414 .3887767

6) LGasPrice 11.64435 11.40228 11.28419 11.013

7) LGasDPrice 7.753867 7.599186 7.500937 7.327853

8) LCoalPrice 5.166329 4.056194 4.240225 4.02558

9) LCoalDPrice 3.476076 2.733314 2.857785 2.708614

10) LGasDemand 1.903949 2.071095 1.886651 2.247907

11) LGasSupply 1.514787 1.740474 1.68667 1.787938

12) LCoalDemand 2.502491 1.449805 1.444186 1.489675

13) LCoalSupply 2.789088 1.682582 1.646181 1.687334

14) LElecPrice 2.080531 2.21345 2.058042 2.108833

15) LElecDemand 1.05978 .8773972 .7971727 .3625957

16) LElecLosses 1.644375 1.060598 .7038557 .3504362

17) LNGLSupply 1.391489 1.61349 1.54135 1.649251

18) LRenew 2.10574 1.812319 1.566174 1.277463

19) LOtherDemand 36.89231 38.26107 36.29734 38.8476

20) LOtherSupply 25.39457 25.75538 25.32648 25.6237

21) LResPrice 2.986611 2.944653 2.90685 2.901681

22) LResDemand .8290009 .826781 .9440367 1.564788

23) LComPrice 3.543862 3.562311 3.420574 3.614196

24) LComDemand .4976886 .5174186 .4465171 .8793324

25) LIndPrice 3.778083 3.666496 3.746008 3.671193

26) LIndDemand .4649381 .4602462 .451499 .4622557

27) LTrnPrice .7912414 .7659396 .8015153 .7747205

28) LTrnDemand .8626719 .8358276 .851019 .8533909

29) LOilM 7.397748 7.374532 7.671693 7.133451

30) LPetM 10.58166 10.48628 11.15983 9.675446

31) LGasM 2.990958 2.985537 2.947424 3.332158

Avg 4.968959 4.865139 4.781916 4.81995

Grand Average = 4.858991

Summary of Average Absolute Percent Differences Quantile Estimated Versus Actual

Series hfoss05.1021a.ran lfoss05.1021a.ran warmer.1026b.ran colder.1026a.ran

1) QGDP .1510429 .1375909 .149561 .139491

2) QYD .3681486 .3575591 .3612509 .3634748

3) QVS .4269058 .4413509 .4184724 .4302629

4) QOilSupply 14.36206 14.37229 14.37407 14.37181

5) QPetDemand .4482872 .4466971 .5751152 .4176809

6) QGasPrice 29.93045 29.27101 30.76805 29.07569

7) QGasDPrice 20.01545 19.61702 20.61851 19.47093

8) QCoalPrice 3.149249 2.664018 3.01479 2.639513

9) QCoalDPrice 2.117071 1.79828 2.038603 1.777201

10) QGasDemand 4.160892 4.396166 3.858002 4.477489

11) QGasSupply 1.58447 1.824436 1.636572 1.886697

12) QCoalDemand 1.945989 1.248338 1.279277 1.363747

13) QCoalSupply 2.219499 1.442205 1.442979 1.511347

14) QElecPrice 4.544654 3.792949 4.209386 3.947969

15) QElecDemand 1.291623 1.599319 1.535145 .8953928

16) QElecLosses 1.688508 1.677038 1.326186 .7619414

17) QNGLSupply 1.293984 1.466805 1.340024 1.541937

18) QRenew 2.415291 2.52704 1.875605 1.785885

19) QOtherDemand 41.47397 28.19185 31.98145 29.66284

20) QOtherSupply 30.32803 30.55534 30.27864 30.41085

21) QResPrice 6.052052 5.882202 5.375479 6.567282

22) QResDemand 1.725509 1.782244 1.095541 2.77685

23) QComPrice 5.895307 5.793702 5.639225 5.999194

24) QComDemand 1.096125 1.143246 .9256015 1.531197

25) QIndPrice 6.508067 6.659017 7.610446 5.861544

26) QIndDemand .4307629 .4100862 .417221 .4086657

27) QTrnPrice .7977233 .7726335 .8082124 .7814776

28) QTrnDemand .6780586 .6628329 .6630476 .6678576

29) QOilM 11.14484 11.12164 11.42654 10.87399

30) QPetM 13.45836 13.38796 13.94411 12.61701

31) QGasM 11.71439 12.18661 10.81526 12.05612

Avg 7.206993 6.697725 6.832334 6.679785

Grand Average = 6.854209

Summary of Average Absolute Percent Differences Kernel Estimated Versus Actual

Kernel Function = Triangle: k(u) = 1 - abs(u)

Series hfoss05.1021a.ran lfoss05.1021a.ran warmer.1026b.ran colder.1026a.ran

1) KGDP .14293 .02622 1.33381 .32723

2) KYD .13501 .02087 1.02856 .24814

3) KVS .21133 .0757 2.2145 .55178

4) KOilSupply .18658 .15668 .31309 .84379

5) KPetDemand .26821 .10768 .9443 .57832

6) KGasPrice .85425 .70328 1.90197 1.63408

7) KGasDPrice .59538 .44685 1.51831 1.18783

8) KCoalPrice 1.45835 .37669 1.01932 .63477

9) KCoalDPrice 1.06292 .25063 .77972 .38259

10) KGasDemand .22599 .34627 .91459 1.08099

11) KGasSupply .28806 .23602 .70558 .89093

12) KCoalDemand 1.57804 .2229 .92368 .46398

13) KCoalSupply 1.60257 .23446 .92028 .42302

14) KElecPrice .88966 .81766 .72274 .40802

15) KElecDemand .95843 .32268 .46002 .23423

16) KElecLosses 1.57494 .5531 .41407 .20172

17) KNGLSupply .23382 .20755 .55502 .75804

18) KRenew .74829 1.10908 1.03815 .33307

19) KOtherDemand 8.96692 5.04356 7.06734 5.36952

20) KOtherSupply .87986 1.30667 5.16406 3.24472

21) KResPrice .40581 .47817 .93688 .53495

22) KResDemand .11562 .06975 1.40714 1.11947

23) KComPrice .6782 .74871 1.04052 .56855

24) KComDemand .13884 .1109 .97301 .52785

25) KIndPrice .55992 .5384 1.44027 2.18873

26) KIndDemand .14192 .07354 1.44804 .42677

27) KTrnPrice .52586 .43666 1.08183 2.4242

28) KTrnDemand .1649 .0613 .67684 .23155

29) KOilM .35934 .2044 .44074 .62622

30) KPetM 1.25152 .70285 5.08863 4.05329

31) KGasM .96923 .89144 1.82131 1.46197

Avg .9087977 .5445379 1.493365 1.095494

Grand Average = 1.010549

Summary of Average Absolute Percent Differences OLS Estimated Versus Actual

Series ogltec05.1027a.ran oghtec05.1027a.ran ltrkiten.1115a.ran htrkiten.1116a.ran

1) LGDP .6019671 .5868409 .6221067 .5625542

2) LYD .7001057 .7499338 .6575133 .8059419

3) LVS .6806338 .5875162 .4978047 .8088747

4) LOilSupply 6.726144 12.28944 9.546678 9.612748

5) LPetDemand .4839119 .4114133 2.914999 3.100151

6) LGasPrice 10.70744 14.76728 11.68224 11.95301

7) LGasDPrice 7.345252 9.493358 8.020853 7.743562

8) LCoalPrice 3.972288 5.3094 3.767776 7.01

9) LCoalDPrice 2.6938 3.572013 2.573981 4.702275

10) LGasDemand 2.834244 4.118892 3.926641 2.359488

11) LGasSupply 4.201825 6.173363 3.107902 2.154433

12) LCoalDemand 1.856101 2.901785 2.188797 4.671797

13) LCoalSupply 2.017007 3.211231 2.169884 4.982244

14) LElecPrice 1.93903 2.179957 2.44335 3.093314

15) LElecDemand .5711467 .4322081 2.605985 2.723986

16) LElecLosses .6108514 .5020391 2.578932 2.950481

17) LNGLSupply 2.885702 4.813926 2.629142 1.90242

18) LRenew 1.222129 1.617546 1.196577 3.07083

19) LOtherDemand 42.16037 35.73203 49.4784 33.06944

20) LOtherSupply 28.76863 21.16032 26.31903 21.45222

21) LResPrice 2.784547 3.194528 3.079664 3.209267

22) LResDemand .7465205 .9480781 2.37291 1.998093

23) LComPrice 3.470233 3.617908 3.918209 4.200972

24) LComDemand .4291314 .7675671 1.40191 .9121695

25) LIndPrice 3.524599 3.92073 3.856481 3.850208

26) LIndDemand .6675066 .6840895 4.322324 3.943879

27) LTrnPrice .7360528 .8171396 .7850053 .7964343

28) LTrnDemand .7665291 .9669666 2.825631 2.314935

29) LOilM 5.603345 8.865632 4.111739 11.03617

30) LPetM 10.57292 9.475336 12.57844 9.338085

31) LGasM 4.994542 4.902574 5.849208 5.595015

Avg 5.073371 5.444228 5.936455 5.675001

Grand Average = 5.532264

Summary of Average Absolute Percent Differences Quantile Estimated Versus Actual

Series ogltec05.1027a.ran oghtec05.1027a.ran ltrkiten.1115a.ran htrkiten.1116a.ran

1) QGDP .1523576 .1432448 .1582448 .1409229

2) QYD .3596376 .3828248 .3505081 .4155752

3) QVS .466001 .51737 .3529919 .5705086

4) QOilSupply 11.57153 16.78272 14.21272 14.27529

5) QPetDemand .4969804 .4940743 2.716504 3.330782

6) QGasPrice 22.79775 40.43307 24.23108 35.58157

7) QGasDPrice 15.46319 26.49267 16.42389 23.46045

8) QCoalPrice 3.521089 3.288049 3.543532 4.949883

9) QCoalDPrice 2.403675 2.209645 2.440339 3.320159

10) QGasDemand 3.22507 6.940676 6.771474 1.769303

11) QGasSupply 3.739421 6.544626 3.500072 1.744313

12) QCoalDemand 2.178676 2.333392 2.651731 4.045423

13) QCoalSupply 2.242949 2.63779 2.617082 4.352417

14) QElecPrice 3.745651 4.640911 2.904363 5.875334

15) QElecDemand 1.320491 .9700119 3.343934 2.123832

16) QElecLosses 1.239802 .8254235 3.205765 2.405807

17) QNGLSupply 2.536058 4.971771 2.802493 1.502339

18) QRenew 1.887221 2.004182 2.134007 4.439759

19) QOtherDemand 35.23276 34.35204 33.66735 39.37824

20) QOtherSupply 33.67453 25.99568 31.31758 26.32626

21) QResPrice 5.012547 7.247765 4.950722 7.083917

22) QResDemand 1.495526 2.106129 3.593571 1.67048

23) QComPrice 5.207199 6.735127 4.697683 7.979696

24) QComDemand .9796204 1.390655 2.097559 1.00176

25) QIndPrice 5.61429 7.952627 5.544485 7.767235

26) QIndDemand .446319 .8697132 4.467116 3.760404

27) QTrnPrice .7430252 .8265567 .7907519 .8078748

28) QTrnDemand .6826496 .6653643 2.513188 2.51593

29) QOilM 9.285992 12.6664 7.564332 14.9006

30) QPetM 13.44385 12.32873 16.03952 11.5178

31) QGasM 14.2166 8.168844 15.42124 7.663923

Avg 6.62524 7.868326 7.323414 7.957348

Grand Average = 7.443582

Summary of Average Absolute Percent Differences Kernel Estimated Versus Actual

Kernel Function = Triangle: k(u) = 1 - abs(u)

Series ogltec05.1027a.ran oghtec05.1027a.ran ltrkiten.1115a.ran htrkiten.1116a.ran

1) KGDP .91988 .47247 .33723 .97108

2) KYD .69925 .42053 .288 .80828

3) KVS 1.66946 .9404 .63067 1.4646

4) KOilSupply 3.77148 3.02645 .4791 .48794

5) KPetDemand .63709 .44419 2.89757 2.80793

6) KGasPrice 5.88126 8.06729 4.92365 3.47592

7) KGasDPrice 4.24977 5.54809 3.20147 2.07273

8) KCoalPrice 1.4209 1.41175 2.593 3.10128

9) KCoalDPrice 1.07007 1.06756 1.86795 2.34648

10) KGasDemand 3.41509 3.29292 3.21147 2.84885

11) KGasSupply 5.90643 5.39 2.24819 2.30403

12) KCoalDemand 1.24927 1.81465 2.19381 3.94349

13) KCoalSupply 1.20635 1.85711 2.11238 3.91457

14) KElecPrice 1.16328 1.43245 2.57491 2.3285

15) KElecDemand .39872 .15799 2.01347 2.65291

16) KElecLosses .30669 .20481 2.02793 2.94348

17) KNGLSupply 4.13261 3.9398 1.69944 1.83324

18) KRenew .51633 .3964 .81086 3.0616

19) KOtherDemand 8.45515 8.93272 21.93247 29.92618

20) KOtherSupply 8.64536 2.26247 4.86385 3.39972

21) KResPrice 1.43476 1.86683 1.83849 1.29913

22) KResDemand .53619 .68743 1.73719 1.85084

23) KComPrice 1.65892 2.12522 3.28038 2.89522

24) KComDemand .67669 .69733 .78266 .86687

25) KIndPrice 1.8347 1.9956 2.48399 1.56628

26) KIndDemand 1.5478 1.03132 4.43068 3.43953

27) KTrnPrice 1.77984 .95757 1.22636 1.7165

28) KTrnDemand .55168 .40395 2.14545 2.00153

29) KOilM 1.30447 1.07798 1.54245 1.84358

30) KPetM 4.02902 3.18675 12.897 13.95013

31) KGasM 3.54824 3.56812 4.662 4.20169

Avg 2.406992 2.215424 3.22368 3.623358

Grand Average = 2.867363

Summary of Average Absolute Percent Differences OLS Estimated Versus Actual

Series cf2005.1111a.ran vhw2005.1203a.ran advnuc20.1021a.ran advnuc5a.1108a.ran

1) LGDP .6339837 .8373128 .5968124 .6046153

2) LYD .7171572 .65166 .7048238 .7099628

3) LVS .5931853 .7538124 .629251 .6069201

4) LOilSupply 4.948163 7.584007 9.717772 9.717983

5) LPetDemand .6975747 1.415856 .3955629 .3929205

6) LGasPrice 15.14665 17.13944 11.08022 10.79407

7) LGasDPrice 9.996798 11.50142 7.352773 7.145912

8) LCoalPrice 7.655152 8.532174 3.982318 4.192743

9) LCoalDPrice 5.183825 5.844971 2.682421 2.822462

10) LGasDemand 3.641176 4.148622 2.106328 2.161698

11) LGasSupply 2.604183 6.975243 1.675936 1.687936

12) LCoalDemand 1.453189 3.688169 1.334912 1.421174

13) LCoalSupply 1.659273 5.625619 1.524531 1.666955

14) LElecPrice 3.168746 4.669886 2.047231 2.033455

15) LElecDemand 1.120586 1.475158 .4582442 .5771133

16) LElecLosses .992817 1.106589 .440221 .6262414

17) LNGLSupply 2.374168 6.069205 1.533928 1.53618

18) LRenew 1.389082 1.665979 1.37491 1.46278

19) LOtherDemand 69.94705 95.15082 38.51152 39.52503

20) LOtherSupply 14.00875 12.28727 25.41076 25.25748

21) LResPrice 3.448372 4.478721 2.904403 2.877231

22) LResDemand .5937734 .5786681 .8184928 .8125143

23) LComPrice 3.908662 4.488848 3.494279 3.521671

24) LComDemand .7840518 1.062264 .5110748 .5013995

25) LIndPrice 4.222825 7.105075 3.65803 3.640793

26) LIndDemand .6612353 2.753324 .4491686 .4334776

27) LTrnPrice .86776 .8505918 .7985261 .804872

28) LTrnDemand .7785586 1.243734 .8534467 .8597448

29) LOilM 3.910287 6.533766 7.405609 7.415677

30) LPetM 13.91028 54.68384 10.34611 10.34219

31) LGasM 6.006447 10.2566 3.169548 3.419322

Avg 6.033025 9.392216 4.773198 4.82492

Grand Average = 6.2558

Summary of Average Absolute Percent Differences Quantile Estimated Versus Actual

Series cf2005.1111a.ran vhw2005.1203a.ran advnuc20.1021a.ran advnuc5a.1108a.ran

1) QGDP .1651543 .2335924 .1434943 .1501172

2) QYD .4557528 .6677561 .3631743 .3669095

3) QVS .5452667 .6057323 .4245391 .4061886

4) QOilSupply 12.29412 11.54293 14.37266 14.37286

5) QPetDemand .6065096 .91518 .4804924 .4888257

6) QGasPrice 33.24308 27.89376 30.23683 30.67991

7) QGasDPrice 22.30078 18.87625 20.24073 20.5297

8) QCoalPrice 5.302188 6.090951 2.95515 2.957905

9) QCoalDPrice 3.583946 4.15591 1.999101 1.998086

10) QGasDemand 5.336409 4.608291 4.143026 4.085392

11) QGasSupply 2.808971 6.928646 1.710258 1.723049

12) QCoalDemand 1.356466 3.917081 1.216558 1.125465

13) QCoalSupply 1.500242 5.909451 1.373992 1.32244

14) QElecPrice 5.136448 5.56404 4.030912 4.092385

15) QElecDemand 1.530765 1.4712 1.165971 1.284329

16) QElecLosses 1.329622 1.140741 1.04648 1.230071

17) QNGLSupply 2.36551 5.816055 1.36439 1.365706

18) QRenew 1.913672 2.701307 1.814343 1.923833

19) QOtherDemand 53.20413 82.60532 34.42508 36.86869

20) QOtherSupply 15.5124 11.97076 30.36002 30.26315

21) QResPrice 6.365863 6.106887 5.973407 6.026496

22) QResDemand 1.161142 .8813581 1.770142 1.769793

23) QComPrice 6.363359 6.097524 5.792221 5.812689

24) QComDemand 1.087064 .9864724 1.125206 1.117688

25) QIndPrice 7.343787 9.018555 6.668945 6.706347

26) QIndDemand .6787115 2.674703 .4037438 .3990905

27) QTrnPrice .8611405 .857621 .8053181 .8117847

28) QTrnDemand .6016428 .9824519 .6655638 .6631342

29) QOilM 7.813241 7.522701 11.15337 11.16375

30) QPetM 8.630603 37.72126 13.2377 13.23211

31) QGasM 12.36225 12.56683 11.49777 11.24453

Avg 7.218072 9.32359 6.869696 6.973628

Grand Average = 7.596246

Summary of Average Absolute Percent Differences Kernel Estimated Versus Actual

Kernel Function = Triangle: k(u) = 1 - abs(u)

Series cf2005.1111a.ran vhw2005.1203a.ran advnuc20.1021a.ran advnuc5a.1108a.ran

1) KGDP .13383 .21143 .01534 .02145

2) KYD .23446 .45782 .02466 .03236

3) KVS .30559 .38828 .03477 .03552

4) KOilSupply 1.21736 2.86332 .11953 .16007

5) KPetDemand .96566 1.86187 .11008 .15783

6) KGasPrice 1.32098 4.46149 .32369 .53592

7) KGasDPrice .87637 3.16547 .22072 .38242

8) KCoalPrice .48587 3.14745 .19062 .40302

9) KCoalDPrice .311 2.12061 .16468 .41612

10) KGasDemand .45815 1.97257 .07457 .11673

11) KGasSupply 1.17475 3.35628 .26658 .30359

12) KCoalDemand .26603 2.91308 .21797 .54713

13) KCoalSupply .38627 4.77403 .222 .57322

14) KElecPrice .30829 .90953 .13873 .22327

15) KElecDemand .10522 .51727 .04082 .18181

16) KElecLosses .12256 .67432 .05549 .25878

17) KNGLSupply .93396 2.77016 .22361 .28446

18) KRenew .3692 .98192 .07717 .18295

19) KOtherDemand 7.89802 9.92498 1.08448 2.19898

20) KOtherSupply 6.74783 5.25569 .76751 1.43159

21) KResPrice .95971 2.40016 .13926 .22386

22) KResDemand .90661 1.71505 .04189 .07637

23) KComPrice .65877 2.10289 .16516 .25865

24) KComDemand .27097 .71404 .03693 .05169

25) KIndPrice 2.47839 4.56421 .31231 .39425

26) KIndDemand .23288 1.94029 .03652 .03802

27) KTrnPrice 4.30563 9.11912 .41761 .43261

28) KTrnDemand .71409 1.50786 .06697 .08417

29) KOilM 1.09623 3.17072 .1733 .21345

30) KPetM 11.8552 36.61357 .69055 1.06253

31) KGasM 1.77719 16.65223 .64741 .8184

Avg 1.608937 4.297668 .2290619 .3903615

Grand Average = 1.631507

Summary of Average Absolute Percent Differences OLS Estimated Versus Actual

Series seer12.1102a.ran ressup.1027a.ran loren05.1115a.ran hiren05.1116a.ran

1) LGDP .6004914 .5901148 .5986947 .6046491

2) LYD .7053776 .6580457 .7040596 .7091181

3) LVS .6192967 .9498948 .6241663 .6029643

4) LOilSupply 9.718577 7.249979 9.71865 9.717062

5) LPetDemand .3992657 1.385738 .3956024 .3932915

6) LGasPrice 11.25225 17.19471 11.1865 10.97257

7) LGasDPrice 7.49466 12.46081 7.43493 7.272633

8) LCoalPrice 4.195689 3.632075 3.946723 4.142689

9) LCoalDPrice 2.82918 2.469041 2.656881 2.787431

10) LGasDemand 2.103566 8.636392 2.078429 2.054285

11) LGasSupply 1.700196 5.380018 1.694046 1.822064

12) LCoalDemand 1.442978 2.461934 1.484956 1.471113

13) LCoalSupply 1.654407 2.578415 1.694356 1.688467

14) LElecPrice 2.028006 1.900919 1.98536 1.964548

15) LElecDemand .5893582 1.083709 .4644566 .8487442

16) LElecLosses .5091943 1.310793 .4362858 1.031759

17) LNGLSupply 1.560727 4.565184 1.543315 1.654498

18) LRenew 1.463505 3.023701 2.066972 6.363632

19) LOtherDemand 38.00974 55.67597 38.02403 36.46544

20) LOtherSupply 25.5497 22.10715 25.5326 25.46777

21) LResPrice 2.895091 3.494766 2.860391 2.834397

22) LResDemand .880622 1.396922 .8061181 .8021739

23) LComPrice 3.500172 3.824407 3.447047 3.39304

24) LComDemand .5251014 .642601 .4868191 .4915162

25) LIndPrice 3.709242 4.071102 3.628101 3.602107

26) LIndDemand .4471038 1.731572 .4554343 .514999

27) LTrnPrice .7794661 .605768 .7908524 .802069

28) LTrnDemand .8562062 .6835111 .8554562 .8588823

29) LOilM 7.371586 4.940956 7.421244 7.440193

30) LPetM 10.3289 10.29998 10.44694 10.4838

31) LGasM 3.109076 22.57907 3.031552 3.288421

Avg 4.800927 6.760814 4.790354 4.920849

Grand Average = 5.318236

Summary of Average Absolute Percent Differences Quantile Estimated Versus Actual

Series seer12.1102a.ran ressup.1027a.ran loren05.1115a.ran hiren05.1116a.ran

1) QGDP .1458224 .2172172 .1447119 .1491252

2) QYD .3649814 .3619543 .3643081 .3672014

3) QVS .4101605 .7133982 .4153538 .4031443

4) QOilSupply 14.37342 12.05892 14.37349 14.37199

5) QPetDemand .4563595 1.20357 .4707548 .4839109

6) QGasPrice 29.54647 12.43199 29.88676 30.68159

7) QGasDPrice 19.80328 8.631629 20.01832 20.52535

8) QCoalPrice 2.983175 3.340894 2.716717 2.717338

9) QCoalDPrice 2.01865 2.283986 1.832111 1.829368

10) QGasDemand 4.29848 6.718895 4.19941 3.902637

11) QGasSupply 1.721317 4.904708 1.699065 1.783351

12) QCoalDemand 1.307961 2.906815 1.374064 1.341002

13) QCoalSupply 1.46126 2.926763 1.534053 1.493675

14) QElecPrice 4.098511 2.97673 4.045389 4.215944

15) QElecDemand 1.314772 1.871565 1.130921 1.55205

16) QElecLosses 1.124491 1.970741 .9781762 1.633666

17) QNGLSupply 1.46312 4.097453 1.427884 1.44767

18) QRenew 1.808628 4.446649 2.453272 7.783275

19) QOtherDemand 33.62461 42.48618 32.73964 33.50713

20) QOtherSupply 30.45967 26.26729 30.42165 30.38446

21) QResPrice 5.658917 3.640014 5.961428 6.137107

22) QResDemand 1.936486 1.587657 1.769819 1.796674

23) QComPrice 6.008 4.445676 5.804662 5.960616

24) QComDemand 1.159102 .9574291 1.116151 1.121103

25) QIndPrice 6.783895 4.344707 6.664187 6.707742

26) QIndDemand .3967034 1.483223 .3911552 .7031386

27) QTrnPrice .7861515 .5863548 .7976096 .8088457

28) QTrnDemand .6603656 .8349143 .6598387 .6567224

29) QOilM 11.11844 6.12811 11.16991 11.18892

30) QPetM 13.23257 10.14044 13.34222 13.3627

31) QGasM 11.78716 13.40973 11.61773 10.77015

Avg 6.848804 6.141149 6.82325 7.089921

Grand Average = 6.725781

Summary of Average Absolute Percent Differences Kernel Estimated Versus Actual

Kernel Function = Triangle: k(u) = 1 - abs(u)

Series seer12.1102a.ran ressup.1027a.ran loren05.1115a.ran hiren05.1116a.ran

1) KGDP .15063 1.89648 .00781 .01863

2) KYD .11496 1.47049 .01229 .04158

3) KVS .22355 3.27723 .01624 .03464

4) KOilSupply .12069 2.7528 .04271 .25913

5) KPetDemand .13293 .98147 .05931 .21695

6) KGasPrice .35691 17.57619 .17995 .72531

7) KGasDPrice .20725 13.51333 .10934 .46489

8) KCoalPrice .23236 1.74171 .25012 .52803

9) KCoalDPrice .1433 1.45067 .155 .35747

10) KGasDemand .2014 10.60347 .09435 .31868

11) KGasSupply .16269 6.09674 .07244 .34827

12) KCoalDemand .20646 1.85218 .03413 .21944

13) KCoalSupply .20656 1.84592 .03666 .24417

14) KElecPrice .1888 3.42693 .10806 .31149

15) KElecDemand .12247 .84182 .04271 .45735

16) KElecLosses .08424 .64454 .06256 .67763

17) KNGLSupply .14161 4.75763 .06477 .29537

18) KRenew .18923 2.23588 .76231 6.34952

19) KOtherDemand 2.22005 25.31086 .97005 3.27485

20) KOtherSupply .9893 6.5199 .29446 1.24608

21) KResPrice .41302 4.89454 .09111 .34646

22) KResDemand .15189 2.18121 .01769 .11324

23) KComPrice .18535 5.33454 .13783 .39865

24) KComDemand .04545 1.94621 .01949 .08845

25) KIndPrice .32542 5.2994 .17912 .59077

26) KIndDemand .15481 3.27476 .06275 .41722

27) KTrnPrice .35408 2.585 .21737 .7807

28) KTrnDemand .07938 1.30075 .03037 .13535

29) KOilM .17027 1.34791 .08437 .26239

30) KPetM .70303 5.81933 .35389 1.5137

31) KGasM .32859 27.82724 .14128 .7741

Avg .3002154 5.503456 .1519535 .7035652

Grand Average = 1.664798

Summary of Average Absolute Percent Differences OLS Estimated Versus Actual (Using AEO2005 Coefficients)

Series aeo2004.1017e.ran hm2004.1017a.ran lm2004.1017a.ran hw2004.1017b.ran lw2004.1017b.ran

1) LGDP .7016914 2.490288 2.822904 .8037167 .6945699

2) LYD 1.229326 3.655835 4.132198 1.452454 1.015622

3) LVS 7.873103 10.74073 4.668758 8.063489 7.625661

4) LOilSupply 7.257217 7.168223 7.281933 5.725765 14.89241

5) LPetDemand 1.475926 1.445611 1.842502 4.177486 4.033893

6) LGasPrice 7.662213 10.17408 6.229326 9.102113 9.699544

7) LGasDPrice 5.108164 7.090541 3.947319 5.989889 6.431235

8) LCoalPrice 3.112175 2.006802 5.597505 8.347366 2.786926

9) LCoalDPrice 2.039657 1.30734 3.704769 5.514043 1.851906

10) LGasDemand 1.922122 2.825282 1.220173 4.9109 4.829215

11) LGasSupply 3.783877 6.409425 2.178046 7.936382 2.18471

12) LCoalDemand 3.017722 1.713131 3.988405 4.484418 1.949885

13) LCoalSupply 2.582634 1.733624 3.045884 4.439671 1.574303

14) LElecPrice 31.10622 31.15716 30.88101 28.74623 33.02756

15) LElecDemand 7.399656 8.638289 6.700303 6.752901 7.669079

16) LElecLosses 6.438355 7.728929 5.74752