Memorandum for the Record

 

Subject: Revised Price elasticities

 

From: George Lady

 

Date: 3/12/07

 

In my memo of 2/25/07 I reported on the outcome of eighty-two regression simulations of relationships within NEMS for the AEO1998-AEO2007 model versions for the residential and commercial sector demand for electricity, distillate natural gas, and delivered energy. All regressions had the same specification:

 

Qt = a + b(Pricet) + c(Drivert) + dQt-1.

 

The driver for the residential sector is the total number of households and for the commercial sector total commercial floorspace. The outcome of the estimation may be termed “consistent” if: b < 0, c > 0, and 0 < d < 1. For the regressions run, eighteen were not consistent in this way (in the 2/25/07 memo I miscounted and indicated that only sixteen regressions had consistency problems). Since it is not feasible to change the data sets at this point, the feasible re-specification that might resolve the consistency problem is to drop the lagged endogenous variable. This was done for the eighteen regressions at issue. Of these, the consistency problem was resolved for four of them: the AEO1998 residential demand for delivered energy and the commercial sector demand for distillate for the AEO2000, AEO2001 and AEO2007 versions of NEMS. Although consistent, the AEO2000 and AEO2001 price elasticities appear large. Below find the summary tables from my 2/25/07 memo with the revised results. The new elasticities are indicated with an “*.” Inconsistent regression results are indicated in bold.

 

The four, revised regression results are given in the Appendix.

 

 

 

 

 

 

 

Table 1: Consistency of Regression Results

Fuel:

Sector:

Electricity

Distillate Fuel

Natural Gas

Delivered Energy

 

Residential

 

 

Consistent = 11

 

Consistent = 3

Issues = 8

 

Consistent = 11

 

Consistent = 9

N/A = 2

 

Commercial

 

 

Consistent = 11

 

Consistent = 6

Issues = 2

 

Consistent = 7

Issues = 4

 

Consistent = 9

N/A = 2

 

 

In the elasticity tables below, the following explanatory notes are indicated for each value, as appropriate.:

 

A: Driver elasticity has the wrong sign.

B: Long run elasticity does not converge.

C: Negative lag term.

D: Price elasticity has the wrong sign.

E: Results not reported (for the AEO2006 elasticities the two-year results are provided in the data, but not reported).

F: Average sector price not reported for the AEO2007.

G: Lagged endogenous variable not included in the regression specification.

*: Revised

 

 

 

 

 

 

 

 

 

 

Table 2: Residential Sector

Fuel

Electricity

Distillate

Natural Gas

Delivered Energy

Horizon

 

1

year

2

year

Long Run

1

year

2

year

Long Run

1

year

2

year

Long Run

1

year

2

year

Long Run

Sim98

-.036

-.041

-.042

-.277A

-.305

-.308

-.133

-.178

-.201

-.288*

G

G

Sim99

-.187

-.313

-.573

-.221A

-.338

-.467

-.075

-.132

-.324

-.306

-.378

-.4

AEO99

-.23

E

-.31

-.28

E

-.53

-.26

E

-.43

E

E

E

Sim00

-.118

-.134

-.136

-.108A

-.192

-.49

-.032

-.046

-.056

-.241

-.32

-.358

Sim01

-.081

-.144

-.351

-.045

-.087

-.633

-.022

-.036

-.06

-.235

-.337

-.414

Sim02

-.02

-.039

-.308

-.061

-.116

-.601

-.061

-.104

-.202

-.066

-.122

-.439

Sim03

-.066

-.129

-1.449

-.135A

-.226

-.422

-.132

-.249

-1.163

-.087

-.161

-.587

AEO03

-.20

-.29

-.49

-.15

-.27

-.60

-.236

-.426

-1.22

E

E

E

Sim04

-.024

-.158

-.218

-.084A

-.15

-.384

-.119

-.166

-.197

-.209

-.281

-.318

Sim05

-.221

-.246

-.249

-.046A

-.089

-1.041

-.113

-.166

-.211

-.203

-.31

-.431

Sim06

-.03

-.048

-.08

-.056A

-.102

-.33

-.071

-.108

-.149

-.101

-.147

-.183

Sim06:pooled

-.044

-.076

-.16

-.061

-.11

-.35

-.072

-.12

-.211

E

E

E

AEO06

-.07

E

-.15

-.11

E

-.43

-.09

E

-.25

-.08

E

-.17

RSTEM06

E

E

E

E

E

E

E

-.042

E

E

E

E

Sim07

-.07

-.097

-.114

-.092A

-.159

-.336

-.083

-.127

-.176

F

F

F

 

 

 

 

 

 

 

 

 

 

 

 

Table 3: Commercial Sector

Fuel

Electricity

Distillate

Natural Gas

Delivered Energy

Horizon

 

1

year

2

year

Long Run

1

year

2

year

Long Run

1

year

2

year

Long Run

1

year

2

year

Long Run

Sim98

-.038

-.063

-.109

.002D

A & B

A&B

-.069

A& B

A&B

-.08

-.098

-.103

Sim99

-.144

-.24

-.431

-.007

B

B

-.0278

A&B

A&B

-.211

-.307

-.389

AEO99

-.23

E

-.24

-.47

E

-.87

-.28

E

-.34

E

E

E

Sim00

-.094

-.153

-.245

-.667*

G

G

-.001

-.002

-.004

-.129

-.203

-.299

Sim01

-.038

-.07

-.224

-.908*

G

G

-.007

A&B

A&B

-.057

-.106

-.377

Sim02

-.055

-.089

-.144

-.048

-.093

-1.025

-.017

-.031

-.122

-.067

-.118

-.275

Sim03

-.042

-.081

-.775

-.05

-.099

-2.329

-.065

-.128

-2.71

-.086

-.147

-.293

AEO03

-.1

-.17

-.45

-.13

-.23

-.39

-.14

-.24

-.4

E

E

E

Sim04

-.047

-.073

-.106

-.039

-.078

-3.532

-.0314

A&B

A&B

-.128

-.184

-.226

Sim05

-.086

-.123

-.149

-.036

-.073

-4.219

-.103

B

B

-.112

-.17

-.236

Sim06

-.034

-.063

-.209

-.015

-.029

-.924

-.12

-.189

-.283

-.085

-.145

-.281

Sim06:pooled

-.046

-.083

-.34

-.055

-.1

-.33

-.09

-.154

-.32

E

E

E

AEO06

-.09

E

-.24

-.12

E

-.17

-.13

E

-.28

-.11

E

-.24

RSTEM06

E

E

E

E

E

E

E

-.055

E

E

E

E

Sim07

-.042

-.074

-.174

-.327*

G

G

-.127

-.193

-.264

F

F

F

 

 

 

 

 

 

 

 

 

Regression Results

 

Endogenous Variable:

Table #2 Energy Consumption by Sector and Source (Quadrillion Btu per Year, Unless Otherwise Noted)

   Sector and Source:  Residential:      Delivered Energy...........

 

Exogenous Variables:

# 1) Table #3 Energy Prices by Sector and Source (1996 Dollars per Million Btu)

     Sector and Source:  Residential....................:

 

# 2) Table #4 Residential Sector Key Indicators and Consumption (Quadrillion Btu per year, Unless otherwise noted)

     Key Indicators and Consumption:  Households (millions):      Total......................

 

Exogenous

Variable              Mean                  Coefficient           Elasticity            t-statistic          

Variable# 1            12.08812             -.299046              -.288154              -17.753599           

Variable# 2            120.0041              .079289               .758467               99.879578           

Constant                                     6.644941            

 

Endogenous            Mean                  SER                   R-sq                  LR-Multiplier        

Variable               12.54504              .023936               .997694              n/a                  

 

Data pooled for the years  2005 to  2020 for the solutions given below:

 

aeo98b.ran

hwop98.ran

lwop98.ran

 

 

 

 

 

 

 

 

Endogenous Variable:

Table #2 Energy Consumption by Sector and Source (Quadrillion Btu per Year, Unless Otherwise Noted)

   Sector and Source:  Commercial:    Distillate Fuel..............

 

Exogenous Variables:

# 1) Table #3 Energy Prices by Sector and Source (1998 Dollars per Million Btu)

     Sector and Source:  Commercial.....................:        Distillate Fuel..........

 

# 2) Table #5 Commercial Sector Key Indicators and Consumption (Quadrillion Btu per year, Unless otherwise noted)

     Key Indicators and Consumption:  Total Floorspace(bill. sq. ft.):      Total......................

 

Exogenous

Variable              Mean                  Coefficient           Elasticity            t-statistic          

Variable# 1            5.525886             -.045996              -.666781              -29.238538           

Variable# 2            71.5889               .001933               .363027               3.186917            

Constant                                     .496975             

 

Endogenous            Mean                  SER                   R-sq                  LR-Multiplier        

Variable               .3811878              .009257               .950059              n/a                  

 

Data pooled for the years  2005 to  2020 for the solutions given below:

 

aeo2k.ran

hwop2k.ran

lwop2k.ran

 

 

 

 

 

 

 

 

 

 

 

 

Endogenous Variable:

Table #2 Energy Consumption by Sector and Source (Quadrillion Btu per Year, Unless Otherwise Noted)

   Sector and Source:  Commercial:    Distillate Fuel..............

 

Exogenous Variables:

# 1) Table #3 Energy Prices by Sector and Source (1999 Dollars per Million Btu, Unless Otherwise Noted)

     Sector and Source:  Commercial.....................:        Distillate Fuel..........

 

# 2) Table #5 Commercial Sector Key Indicators and Consumption (Quadrillion Btu per year, Unless otherwise noted)

     Key Indicators and Consumption:  Total Floorspace(bill. sq. ft.):      Total......................

 

Exogenous

Variable              Mean                  Coefficient           Elasticity            t-statistic          

Variable# 1            5.325486             -.074413              -.907896              -20.778467            

Variable# 2            77.29922              .006153               1.089658              6.381829            

Constant                                     .357151             

 

Endogenous            Mean                  SER                   R-sq                  LR-Multiplier        

Variable               .4364876              .022891               .906633              n/a                  

 

Data pooled for the years  2005 to  2020 for the solutions given below:

 

aeo2001.ran

hw2001.ran

lw2001.ran

 

 

 

 

 

 

 

 

 

 

 

 

Endogenous Variable:

Table #2 Energy Consumption by Sector and Source (quadrillion Btu, unless otherwise noted)

  Sector and Source:  Commercial:    Distillate Fuel Oil         

 

Exogenous Variables:

# 1) Table #3 Energy Prices by Sector and Source (2005 dollars per million Btu, unless otherwise noted)

    Sector and Source:    Distillate Fuel Oil:

 

# 2) Table #5 Commercial Sector Key Indicators and Consumption (quadrillion Btu, unless otherwise noted)

    Key Indicators and Consumption:  Total Floorspace (billion squar:      Total                     

 

Exogenous

Variable              Mean                  Coefficient           Elasticity            t-statistic          

Variable# 1            11.90756             -.013608              -.327468              -18.986104           

Variable# 2            93.38322              .003045               .574656               9.664773            

Constant                                     .372507             

 

Endogenous            Mean                  SER                   R-sq                  LR-Multiplier        

Variable               .494821               .020745               .878192              n/a                  

 

Data pooled for the years  2010 to  2030 for the solutions given below:

 

aeo2007.1121a.ran

hp2007.1121a.ran

lp2007.1121a.ran