1. 3D COORDINATE SYSTEMS May 27, 2011 - University of Kansas

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A Cost‐constrained Measure of Energy‐use Efficiency in U.S. Manufacturing:

An Inter‐state Comparison Using the Census of Manufacturing Data

Subhash C. Ray Department of Economics, U‐63

University of Connecticut 341 Mansfield Road Storrs, CT 06269

USA Email: [email protected]

Phone: (860) 486 3967

Kankana Mukherjee Department of Management

Worcester Polytechnic Institute 100 Institute Road

Worcester, MA 01609 USA

Email: [email protected] Phone: (508) 842 6440

Lei Chen

Department of Economics, U‐63 University of Connecticut

341 Mansfield Road Storrs, CT 06269

USA Email: [email protected] Phone: (860) 486 4633

May 31, 2009 Draft – Please do not cite or quote.

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A Cost‐constrained Measure of Energy‐use Efficiency in U.S. Manufacturing:

An Inter‐state Comparison Using the Census of Manufacturing Data

In recent years, large swings in energy prices as well as greater global competition have underlined the

need for industrial firms to attain energy efficiency in order to achieve sustainability as well as to keep

their costs low so as to be competitive in a global economy. The U.S. industrial sector accounts for about

one‐third of the total energy used in the economy – more than the residential, commercial, or

transportation sectors. Hence examining the energy efficiency of this sector deserves special attention.

The importance of achieving energy efficiency is recognized from several policy perspectives: (a) to

conserve energy derived from fossil fuels to prevent their depletion in the near future, (b) to enhance

the nation’s energy security. (c) to prevent further deterioration of environmental quality, resulting from

burning of fossil fuels, and (d) to achieve cost effectiveness during periods of high energy prices, by

suitably substituting other inputs for energy. Ever since the 1970s, a rich body of literature has emerged

that investigates the energy efficiency in the various end‐use sectors of the U.S. economy. The general

consensus from these studies is that energy intensity, (defined by the quantity of energy required per

unit of output), has been declining since 1992. The focus of this body of research has been to develop

improved methods to identify the important drivers of changes in aggregate energy consumption or

energy intensity. Ang and Zhang (2000) as well as Liu and Ang (2007) provide a comprehensive survey of

this literature. Deviating from this approach, Mukherjee (2008) adopts a production theoretic

framework and uses Data Envelopment Analysis (DEA) to measure energy efficiency for the overall US

manufacturing sector as well as for the six most energy intensive industries, over the period 1970‐2001.

Thus, in contrast to the earlier studies in the literature that measure energy efficiency by (the inverse of)

energy intensity, which is simply a descriptive measure, the energy efficiency measures suggested by

Mukherjee (2008) are normative measures. In that study, alternative measures of energy efficiency are

obtained using technical efficiency as well as cost efficiency models. In a recent paper, Mukherjee (2009)

utilizes DEA to measure energy efficiency using a directional distance function approach.

The present paper extends the literature on measurement of energy efficiency in several respects. First,

we provide an alternative measure of energy‐use efficiency for a firm, taking into consideration the cost

constraint faced by a firm. We use Data Envelopment Analysis to model the cost‐constrained energy‐use

minimization problem. Second, we take a regional approach and investigate the energy efficiency of the

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manufacturing sector across states in continental US. Thus our paper differs from previous studies that

measure the trend in energy efficiency at the overall US economy level over time.1 A regional analysis of

energy use reveals valuable insights for policy making that are often masked in a national level analysis,

since industry production processes, industrial structures, the age and composition of the capital stock,

as well as input price, quality, and availability differ markedly across regions and industries (Walton,

1981, Garofalo and Malhotra, 1984). Further, in order to capture the differences in industry‐mix across

states directly into our analysis, we conceptualize a multiple‐output, multiple‐input technology for the

state manufacturing sector and incorporate two outputs for each state – output produced in energy

intensive industries and output produced in non‐energy intensive industries. Thus, our paper departs

from existing studies using a production theoretic approach to analyze various aspects of state

manufacturing (e.g., Garofalo and Malhotra, 1984, Hulten and Schwab, 1984 and Moomaw and

Williams, 1991), which consider only one aggregate state manufacturing output, thereby ignoring the

interstate differences in the output‐mix.

Our results indicate that in 7 states (Arizona, Connecticut, New Jersey, New York, Rhode Island,

Vermont, and Wyoming), the ‘typical firm’ is energy efficient given their cost constraint. For all other

states, the actual energy use by the ‘typical firm’ is more than what would have been the optimal use,

given the cost constraint. 4 out of the 7 energy efficient states – Arizona, New Jersey, New York, and

Wyoming ‐ are also cost minimizing. The other 3 states that are energy efficient given the cost constraint

‐ Connecticut, Rhode Island, and Vermont – have a total cost that is higher than the minimum cost. For

each of these 3 states, the actual energy use (which is also the optimal energy use given the cost

constraint) is less than what the energy use would be if the ‘typical firm’ was cost minimizing. We find

that at the national level there would be considerable energy savings as well as increase in employment

if the manufacturing firms in all the states produced at the optimal point based on our model. Hence, in

the context of a policy direction that aims at energy conservation as well as increasing employment in

the US manufacturing sector without increasing cost (and therefore prices), our proposed measure of

cost constrained energy efficiency may provide valuable insights for policy makers.

The rest of the paper unfolds as follows. In Section 2 we present the existing measures of energy

efficiency as well as our proposed cost‐constrained measure. There we provide the DEA models for the

1 A notable exception is the study by Metcalf (2008) which decomposes the US state level energy intensity indexes into the pure intensity effect and activity effect and analyzes the determinants of these indexes.

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existing measures as well as formulate the model for our new measure. Section 3 discusses the data

construction as well as presents the main empirical findings. Section 4 concludes.

2. Methodology

Consider an industry producing a vector of m outputs from n inputs. An input‐output bundle (x, y) is

considered feasible when the output bundle y can be produced from the input bundle x. The technology

faced by the firms in the industry can be described by the production possibility set T = {(x, y): y can be

produced from x} based on a few regularity assumptions of feasibility of all observed input‐output

combinations, free disposability with respect to inputs and outputs, and convexity. If, in addition,

constant returns to scale is assumed, then it implies that all radial expansions as well as non‐negative

contractions of the feasible input‐output combination are also considered feasible.

Once the production technology is defined our goal is to measure energy efficiency of the observed

input‐output bundle. The optimal bundle which provides the norm against which the energy use of the

actual bundle is to be compared can be chosen based on several alternative objectives. For example, as

in Mukherjee (2008) the optimal bundle may be (i) one at which we reduce all inputs by the same

proportion as much as possible; or (ii) one at which we reduce the energy input only as much as possible

without increasing any other inputs; or (iii) one at which we produce output at the lowest cost (although

individual inputs may increase or decrease). The measured energy efficiency could differ based on which

of the above three objectives are adopted. This can be explained with the help of Figure 1 which depicts

an isoquant for output level y0. The area to the right, bounded by the isoquant is the input requirement

set L(y0). Suppose that A(E0, x0) is the actual bundle being evaluated. We find that B(E1,x1) is the radial

technically efficient bundle, C(E2,x2) is the energy‐oriented efficient bundle, and D(E3,x3) is the cost‐

minimizing bundle. Comparing A with B yields an energy efficiency measure of β = E0/E1. On the other

hand, comparing A with C provides an energy efficiency measure of θ =E0/E2. Again, comparing A with D

gives an energy efficiency measure of γ = E0/E3. Figures 2 and 3 provide some alternative cases. Figure 2

is similar to Figure 1 in all respects except that the cost‐minimizing bundle (D) shows an increase in the

quantity of the energy input compared to A. On the other hand, in Figure 3, the cost‐minimizing bundle

(D) shows a lower quantity of energy input compared to A, B, and C.

The relevant measure of energy efficiency to be used in a given situation depends on the objectives of

the firm (or in some cases that of the policy maker). For instance, if the objective is that of cost

minimization, γ is the most relevant measure of energy efficiency. Note however, that this objective may

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not necessarily lead to energy conservation. If the objective is that of energy conservation and there is a

priori reason to believe that inputs exhibit strong complementarities then β could be a useful measure.

On the other hand, if we do not have a priori reason to believe that inputs exhibit such strong

complementarities, we could use the measure θ. In this case we are interested in the optimal

(minimum) energy use that can still produce the same output or more without requiring any more of the

other inputs.

We now propose an alternative measure of energy efficiency. Examining Figure 1 we find that as we

move upward along the isoquant we could reduce the energy input without reducing the output.

However, the isocost line passing through the observed bundle A intersects the isoquant at the point F

(as well as at point G). This indicates that points on the isoquant to the southeast of point F (up until G)

are feasible given the current cost level of the firm while points beyond F would require the firm to incur

a higher cost. Hence at point F, the firm is using the lowest level of energy without requiring any

additional cost than its current actual cost. Thus, an alternative measure of energy efficiency is one

where we compare the observed bundle to an optimal bundle at which we reduce the energy input as

much as possible but allow other inputs to increase or decrease within the existing expenditure level.

Comparing A with F yields this energy efficiency measure of φ = E0/E4.

Comparing our new measure with the other three measures discussed above, we note several points.

First, unlike in the case of the cost minimization model, this new model is based on the objective of

energy conservation. Secondly, no increase in cost is called for in order to achieve this objective. Third,

unlike in the model for θ, we allow firms to increase or decrease the other inputs in order to achieve the

energy conservation (as long as no additional cost is incurred). Hence this model allows for a greater role

for substitution between inputs. From a policy standpoint, the substitution possibility between labor

and energy is of particular interest here.

The DEA Models

The conventional Charnes, Cooper, and Rhodes (CCR, 1978) DEA model for measuring radial input‐

oriented technical efficiency for a DMU with the input‐ output bundle (y10, y20, L10, L20, E0, M0, K0) is given

below:

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Min

Subject to

j

jj yy ;101 (output 1: energy‐intensive)

j

jj yy ;202 (output 2: non energy‐intensive)

j

jj LL ;101 (input 1: production labor) (1)

j

jj LL ;202 (input 2: non‐production labor)

j

jj EE ;0 (input 3: energy)

j

jj MM ;0 (input 4: materials)

j

jj KK ;0 (input 5: capital)

0j ; unrestricted.

In the above model all inputs are to be contracted by the same factor β.

Next, we present below the specifically energy‐oriented DEA model of technical efficiency (Mukherjee,

2008)

Min

Subject to

j


j


7

j

jj LL ;101 (input 1: production labor)

j

jj LL ;202 (input 2: non‐production labor) (2)

j

jj EE ;0 (input 3: energy)

j

jj MM ;0 (input 4: materials)

j

jj KK ;0 (input 5: capital)

0j ; unrestricted.

In model (2) only the energy input is contracted by the factor θ. Other inputs need not be reduced. But

they cannot be increased to save energy.

The conventional DEA model for cost minimization is provided next.

),;( 02

01

0 yywC Min KwMwEwLwLw KME000

2021

01

Subject to

j


j


j


j


j

jj EE ; (input 3: energy)

8

j

jj MM ; (input 4: materials)

j

jj KK ; (input 5: capital)

.0,,,,;0 21 KMELLj

In model (3) above, an input (including energy (E)) may be higher or lower than its observed quantity so

long as the optimal input bundle produces the target output bundle at the minimum cost.

The DEA model for our proposed cost‐constrained energy minimization problem is formulated below.

Min E

Subject to

j


j


j


j


j

jj EE ; (input 3: energy)

j

jj MM ; (input 4: materials)

j

jj KK ; (input 5: capital)

.00002

021

01 CKwMwEwLwLw KME (total cost constraint)

.0,,,,;0 21 KMELLj

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In model (4) the energy input is to be minimized allowing other inputs to increase or decrease so long as

the total cost (including energy cost) does not exceed the actual cost.

3. Empirical Application

Data Construction

In this paper we investigate the energy efficiency of the manufacturing sector across states in

continental US.2 We conceptualize a 2‐output, 5‐input production technology and use data constructed

from the US 2002 Economic Census ‐ Manufacturing. The average (i.e. per firm) input‐output bundle is

treated as a data point from each state. Further, the technology is assumed to exhibit constant returns

to scale. Output is measured by the gross value of production. The two outputs are: (1) Output

produced in energy intensive industries (textile, paper, petroleum and coal products, chemical, plastics

and rubber, nonmetallic mineral products, and primary metals), and (2) Output produced in non‐energy

intensive industries. Given the fact that the market for manufactured goods is nationally integrated, we

assume that the output price does not vary across states so that the value of output is a reasonable

measure of the quantity produced. The inputs included are: (1) production labor (L1), measured by the

number of hours worked, (2) non‐production labor (L2), measured by the number of non‐production

employees, (3) capital (K), measured by the average of beginning‐of‐the year and end‐of the year

(nominal) values of gross fixed assets, (4) energy (E), measured by the expenditure on purchased fuels

and electricity deflated by state specific energy price, and (5) materials (M), which is measured by the

total expenditure on materials parts and containers. Input prices for the first four inputs are,

respectively, wage paid per hour to production workers (w1), total emolument per employee (w2),

industrial sector total energy price (wE) (measured in nominal dollars per million Btu) and the user cost

of capital (wK), measured by the sum of depreciation, rent, and (imputed) interest expenses per dollar of

gross value of capital. The materials price (wM) was set equal to unity for every state.

Main Findings

Table 1 reveals that 20 of the 43 states in our sample were technically efficient. The technical efficiency

ranged from 0.863 and 0.865 for Mississippi and Alabama respectively, to 1 for the efficient states. The

average technical efficiency across states was 0.967, implying that on average the states could have

2 The states of Kansas, Montana, North Dakota, South Dakota, and West Virginia had to be excluded from our analysis as separate data for output of energy intensive vs. non‐energy intensive industries could not be obtained. This gave us a sample of 43 states.

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proportionately reduced all their inputs (including energy) by 3.3%. When we compare the total of the

optimal energy use across 43 states to the total of the actual energy used we find that the overall energy

efficiency across states is 0.8492.3 Of all states, Maine had the lowest energy efficiency.

Table 2 presents the results from model 2. The energy efficiency across the 43 states is 0.7316. We find

that the same 20 states were energy efficient by this measure. For these states no reduction in energy

input is possible since they lie on the frontier and apparently no slacks exist. The labor use by these

states is also optimal. Of the 23 states that are found to be energy inefficient, no further reduction in

labor is possible at the optimal bundle in case of 7 states (Colorado, Florida, Illinois, Maryland,

Minnesota, Nevada, and Utah). For the remaining 16 energy inefficient states both energy as well as

labor can be reduced at the optimal bundle from this model. The states of Alabama, Maine, Maryland,

Mississippi, and Texas were found to be the most energy inefficient states (with measured energy

efficiency of less than 0.5).

The results from the cost minimization model (model 3) are presented in Table 3. Comparing the total

energy used at the optimal bundle of all states with the total of the actual energy used by all states we

obtain an overall energy efficiency measure of 0.7156 for the 43 states. Only 4 states (Arizona, New

Jersey, New York, and Wyoming) were found to be cost minimizing. For these states, neither a reduction

in energy nor a reduction in labor was possible. Of the remaining 39 states, in case of 31 states energy

input should be reduced to arrive at the optimal bundle. Examining these 31 states we find that the

labor use is higher at the optimal bundle in case of 18 states. For these 18 states, therefore, the goal of

cost minimization is commensurate with the goals of energy conservation as well as increased

employment. For the remaining 8 cost inefficient states (California, Colorado, Connecticut,

Massachusetts, Missouri, New Hampshire, Rhode Island, and Vermont), energy should be increased at

the cost minimizing bundle. For these 8 states, labor is reduced at the cost minimizing bundle in each

case. Hence, for these 8 states, pursuing the goal of cost minimization would be at odds with the goals

of energy conservation as well as increase in employment.

Table 4 shows that 7 states are minimizing energy use for their current expenditure level. These states

are Arizona, Connecticut, New Jersey, New York, Rhode Island, Vermont, and Wyoming. A comparison

with Table 3 reveals that 4 of these 7 states (Arizona, New Jersey, New York and Wyoming) are also

producing at the minimum cost. For the remaining 3 states (Connecticut, Rhode Island, and Vermont)

3 This indicates that the energy constraint is not binding for many observations and so at the optimal point due to the presence of slacks it is possible to reduce energy use beyond the proportional reduction in all inputs.

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that have a higher expenditure than the optimal, the actual energy use (which is also the optimal energy

use based on model 4) is less than the energy use at the optimal based on model 3 (i.e., if the ‘typical

firm’ in these states were cost minimizing). For all 7 efficient states labor use is also optimal based on

model (4). Note that for Arizona, New Jersey, New York, and Wyoming, labor use is optimal by model (3)

as well. For Connecticut, Rhode Island, and Vermont, labor use is reduced at the optimal bundle of

model (3). Across the 43 states the overall energy efficiency from the cost constrained energy

minimization model (model 4) was 0.5448.

Table 5 provides an overview of the main results from the four models. We find that at the national level

energy savings is the highest at the optimal solution of model 4. Also, at the optimal solution of this

model employment would increase. The results of all other models show a decline in labor use at the

optimal solution. Hence in the context of a policy direction that aims at energy conservation as well as

increasing employment in the US manufacturing sector without increasing cost (and therefore prices),

our proposed measure of cost constrained energy efficiency may provide valuable insights for policy

makers.

One concern that arises from examining the results in Table 3 is that the structure of relative input

prices in several states is such that if manufacturing firms in these states pursue the goal of cost

minimization in order to be more competitive, this would result in higher use of energy as well as

reduction in employment. We, therefore, examined the effect of an energy tax on the energy and labor

inputs if the objective of firms is to minimize cost. Results from such simulation indicate that an effective

tax on energy use in US manufacturing would reduce the aggregate energy use in this sector, while at

the same time increasing the aggregate labor employment in this sector.

4. Conclusion

In this paper we provide an alternative measure of energy‐ efficiency of a firm taking into consideration

the cost constraint faced by a firm. We use DEA to model the cost‐constrained energy‐use minimization

problem. We apply this model to measure the energy efficiency of the manufacturing sector across

states in continental US. Results from this model are also compared to other measures of energy

efficiency suggested in previous studies.

Our results indicate that in 7 states (Arizona, Connecticut, New Jersey, New York, Rhode Island,

Vermont, and Wyoming), the ‘typical firm’ is energy efficient given their cost constraint. 4 out of the 7

energy efficient states – Arizona, New Jersey, New York, and Wyoming ‐ are also cost minimizing. For

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these 7 states, given the current technology, it is not possible to further reduce their energy use without

an increase in their cost. For all other states, the actual energy use by the ‘typical firm’ is more than

what should have been the optimal use, given the cost constraint. We find that at the national level

there would be considerable energy savings as well as increase in employment if the manufacturing

firms in the states produced at the optimal point based on our cost constrained energy efficiency model.

Our finding about possible substitutability between labor and energy is in agreement with previous

studies. In a regional study of input substitution in the US manufacturing sector, Garofalo and Malhotra

(1984) find that labor and energy exhibit considerable substitutability. Also, both Harper and Field

(1983) and Vlachou and Field (1987), examining the energy substitution at the regional level in the US

manufacturing sector find evidence of substitutability between labor and energy in most two‐digit

sectors. Hence, in terms of a policy direction that aims at energy conservation as well as increasing

employment in the US manufacturing sector without increasing cost (and therefore prices), our

proposed measure of cost constrained energy efficiency may provide valuable insights for policy makers.

One final caveat is worth noting. The results from the empirical study need to be used with caution since

it is based on data from a single year. At a minimum, this study suggests that such an analysis is feasible

and could lead to valuable insights.

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References

Ang, B. W., Zhang, F. Q. (2000) A Survey of Index‐Decomposition Analysis in Energy and Environmental

Studies. Energy 25, 1149‐1176.

Charnes, A., Cooper, W. W., Rhodes, E. (1978) Measuring the Efficiency of Decision Making Units,

European Journal of Operational Research, 3, 392‐444.

Garofalo, G. A., Malhotra, D. M. (1984) Input Substitution in the Manufacturing Sector During the

1970’s: A Regional Analysis. Journal of Regional Science 24, 51‐63.

Harper, C., Field, B. C. (1983) Energy Substitution in U.S. Manufacturing: A Regional Approach. Southern

Economic Journal 50, 385‐395.

Hulten, C., Schwab, R. (1984) Regional Productivity Growth in U.S. Manufacturing: 1951‐78. American

Economic Review, 74, 152‐61.

Liu, F. L., Ang, B. W. (2007) Factors Shaping Aggregate Energy Intensity Trend for Industry: Energy

Intensity versus Product Mix. Energy Economics 29, 609‐635.

Metcalf, G. E. (2008) An Empirical Analysis of Energy Intensity and its Determinants at the State Level.

The Energy Journal 29, 1‐26.

Moomaw, R., Williams, M. (1991) Total Factor Productivity Growth in Manufacturing: Further Evidence

from the States. Journal of Regional Science, 31, 17‐34.

Mukherjee, K. (2008) Energy Use Efficiency in US Manufacturing: A Nonparametric Analysis. Energy

Economics 30, 76‐96.

Mukherjee, K. (2009) Measuring Energy Intensity in the Context of an Emerging Economy: The Case of

Indian Manufacturing. European Journal of Operational Research (forthcoming).

Vlachou, A., Field, B. C. (1987) Regional Energy Substitution: Results from a Dynamic Input Demand

Model. Southern Economic Journal 53, 952‐966.

Walton, A. L. (1981) Variations in the Substitutability of Energy and Nonenergy Inputs: The Case of the

Middle Atlantic Region. Journal of Regional Science 21, 411‐420.

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Figure 1: Energy Saving under Various DEA Models (Case 1)

A (E0, x0) is the actual bundle.

B (E1, x1) is the radial technically efficient bundle.

C (E2, x2) is the energy‐oriented efficient bundle.

D (E3, x3) is the cost‐minimizing bundle.

F (E4, x4) is the cost‐constrained energy minimizing bundle.

Note that F lies on the expenditure line through A and costs the same amount of money as the

actual bundle.

G

15


A (E0, x0) is the actual bundle

B (E1, x1) is the radial technically efficient bundle





actual bundle.

G

16


A (E0, x0) is the actual bundle

B (E1, x1) is the radial technically efficient bundle





actual bundle.

G

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Table 1: Results from Model 1

Actual Model 1 Actual Model 1 DEA Actual Model 1 Actual Model 1 DEA

State Total L Total L E E* Efficiency State Total L Total L E E* Efficiency

AL 284127 210550 423338 230008 0.865 NE 103011 103011 56707 56707 1

AZ 168155 168155 55521 55521 1 NV 42503 35034 14360 13151 0.916

AR 210394 151294 176772 127664 0.953 NH 83545 67971 20404 19517 0.957

CA 1616289 1598808 642630 559680 0.989 NJ 368015 368015 171469 171469 1

CO 148831 133760 55869 50211 0.899 NM 33085 33085 21913 21913 1

CT 214721 214721 56133 56133 1 NY 641742 641742 287810 287810 1

DE 37287 37287 33485 33485 1 NC 623521 623521 342494 342494 1

FL 377092 337019 187359 123575 0.902 OH 868679 831379 532425 509563 0.957

GA 452834 426659 393756 326201 0.984 OK 149983 137956 103054 77659 0.945

ID 61538 61538 63121 63121 1 OR 184151 184151 126553 126553 1

IL 741754 682075 422728 388717 0.92 PA 715186 683677 472018 433272 0.958

IN 565559 530874 500302 448840 0.968 RI 62285 62285 13518 13518 1

IA 222968 222968 167927 167927 1 SC 289672 251167 274975 265496 0.966

KY 263202 263202 287806 287806 1 TN 411984 356365 308871 278654 0.911

LA 150360 150360 728030 728030 1 TX 855303 815771 1723413 1076201 0.954

ME 67738 52527 97642 26921 0.941 UT 110007 100159 51930 46228 0.91

MD 151307 141633 108952 64652 0.946 VT 43827 43827 11278 11278 1

MA 349148 349148 99806 99806 1 VA 311787 297947 239855 183317 0.996

MI 736165 736165 386587 386587 1 WA 265010 265010 263904 263904 1

MN 351188 323942 179804 137745 0.922 WI 503147 473955 284909 267396 0.942

MS 182822 126744 177745 116695 0.863 WY 9608 9608 32936 32936 1

MO 319761 319761 156041 156041 1 Total 14349291 13624825 10756150 9134403 ---

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Actual Model 2 Actual Model 2 Actual Model 2 Actual Model 2

State Total L Total L E θE* State Total L Total L E θE*

AL 284127 206962 423338 125254 NE 103011 103011 56707 56707

AZ 168155 168155 55521 55521 NV 42503 42503 14360 11802

AR 210394 146249 176772 90203 NH 83545 69384 20404 19251

CA 1616289 1606708 642630 523945 NJ 368015 368015 171469 171469

CO 148831 148831 55869 45973 NM 33085 33085 21913 21913

CT 214721 214721 56133 56133 NY 641742 641742 287810 287810

DE 37287 37287 33485 33485 NC 623521 623521 342494 342494

FL 377092 377092 187359 105879 OH 868679 827134 532425 422982

GA 452834 411112 393756 256843 OK 149983 139757 103054 69253

ID 61538 61538 63121 63121 OR 184151 184151 126553 126553

IL 741754 741754 422728 305233 PA 715186 638754 472018 351068

IN 565559 483991 500302 323593 RI 62285 62285 13518 13518

IA 222968 222968 167927 167927 SC 289672 272552 274975 217465

KY 263202 263202 287806 287806 TN 411984 369196 308871 191973

LA 150360 150360 728030 728030 TX 855303 849511 1723413 775058

ME 67738 52974 97642 23293 UT 110007 110007 51930 37216

MD 151307 151307 108952 53175 VT 43827 43827 11278 11278

MA 349148 349148 99806 99806 VA 311787 293407 239855 174185

MI 736165 736165 386587 386587 WA 265010 265010 263904 263904

MN 351188 351188 179804 111753 WI 503147 453274 284909 202483

MS 182822 129178 177745 67883 WY 9608 9608 32936 32936

MO 319761 319761 156041 156041 Total 14349291 13730385 10756150 7868802

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State Total L Total L E E* State Total L Total L E E*

AL 284127 277700 423338 127433 NE 103011 122251 56707 41636

AZ 168155 168155 55521 55521 NV 42503 39392 14360 13095

AR 210394 213803 176772 76656 NH 83545 57380 20404 24462

CA 1616289 1326521 642630 705957 NJ 368015 368015 171469 171469

CO 148831 126002 55869 57931 NM 33085 49448 21913 13776

CT 214721 144892 56133 91935 NY 641742 641742 287810 287810

DE 37287 59849 33485 30763 NC 623521 675714 342494 305133

FL 377092 309025 187359 137055 OH 868679 791001 532425 508893

GA 452834 469231 393756 256196 OK 149983 174440 103054 76543

ID 61538 63661 63121 20844 OR 184151 176844 126553 70827

IL 741754 764966 422728 372631 PA 715186 730942 472018 337191

IN 565559 535067 500302 329282 RI 62285 51353 13518 13630

IA 222968 305062 167927 82444 SC 289672 330572 274975 152706

KY 263202 315067 287806 183457 TN 411984 385651 308871 228070

LA 150360 214778 728030 670531 TX 855303 1162915 1723413 571670

ME 67738 48996 97642 27174 UT 110007 118399 51930 37834

MD 151307 120170 108952 75949 VT 43827 39456 11278 13176

MA 349148 261668 99806 150517 VA 311787 290725 239855 175052

MI 736165 833602 386587 350444 WA 265010 268230 263904 144862

MN 351188 287556 179804 142484 WI 503147 405264 284909 262220

MS 182822 167936 177745 74273 WY 9608 9608 32936 32936

MO 319761 305441 156041 194569 Total 14349291 14208491 10756150 7697038

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State Total L Total L E E* State Total L Total L E E*

AL 284127 284550 423338 104587 NE 103011 143912 56707 36787

AZ 168155 168155 55521 55521 NV 42503 39897 14360 11388

AR 210394 217529 176772 64064 NH 83545 81139 20404 18733

CA 1616289 2028170 642630 470591 NJ 368015 368015 171469 171469

CO 148831 182777 55869 42457 NM 33085 49634 21913 13136

CT 214721 214721 56133 56133 NY 641742 641742 287810 287810

DE 37287 67393 33485 26748 NC 623521 697438 342494 231528

FL 377092 378796 187359 99848 OH 868679 1129492 532425 327718

GA 452834 573972 393756 172627 OK 149983 179940 103054 57931

ID 61538 73219 63121 18165 OR 184151 211903 126553 57773

IL 741754 839222 422728 268303 PA 715186 742552 472018 298345

IN 565559 723434 500302 228165 RI 62285 62285 13518 13518

IA 222968 359853 167927 81021 SC 289672 337859 274975 128578

KY 263202 410418 287806 119145 TN 411984 512319 308871 146397

LA 150360 290522 728030 556502 TX 855303 1224138 1723413 538818

ME 67738 60385 97642 21129 UT 110007 119691 51930 33353

MD 151307 171431 108952 48774 VT 43827 43827 11278 11278

MA 349148 381724 99806 96697 VA 311787 389604 239855 111909

MI 736165 1167251 386587 271302 WA 265010 434351 263904 96632

MN 351188 443959 179804 99498 WI 503147 604272 284909 158401

MS 182822 173065 177745 56245 WY 9608 9608 32936 32936

MO 319761 453962 156041 117798 Total 14349291 17688129 10756150 5859758

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Table 5: Comparison of Results from Alternative Models

total L % change total E % change

actual 14349291 ‐‐‐ 10756150 ‐‐‐

model 1 13624825 ‐5.05% 9134403 ‐15.08%

model 2 13730385 ‐4.31% 7868802 ‐26.84%

model 3 14208491 ‐0.98% 7697038 ‐28.44%

model 4 17688129 23.27% 5859758 ‐45.52%

1. 3D COORDINATE SYSTEMS May 27, 2011 - University of Kansas

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