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MANTHY Date M011 (2‘ lché MS U i: an Affirmative Action/Equal Opportunity Institution 0- 12771 MSU RETURNING MATERIALS: Place in book drop to ”saunas remove this checkout from .—g—-. your record. FINES will be charged if book is returned after the date stamped below. i" as l 5 373 pm“! 61112800 FACTORS INFLUENCING COUNTY LEVEL HOUSEHOLD FUELWOOD USE by Kenneth Edward Skog A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Forestry 1986 ABSTRACT FACTORS INFLUENCING COUNTY LEVEL HOUSEHOLD FUELWOOD USE By Kenneth E. Skog This study explains household fuelwood consumption behavior at the county level by linking it to economic and demographic conditions in counties. Using this link, counties are identified where potential fuelwood use problems and benefits are greatest. A probit equation estimates household probability of wood use (percent woodburners in 21 county) based on county heating degree days, household income, nonwood fuel price, fuelwood price, percent forest land, population density, and fraction of households using various types of heating equipment. A linear-in-parameters equation estimates average wood consumed by a woodburner based on county heating degree days, household income, percent forest land, and price of nonwood. fuel divided by fuelwood price. Parameters are estimated using fuelwood use data for individual households from a 1980-81 nationwide survey. The probit equation predicts percentage of woodburners well over' a ‘wide range of county conditions. The wood consumption equation. overpredicts for counties with. high income and high population density (over 6000 persons per Kenneth Edward Skog square mile). The model shows average woodburning per household over all households decreases with increasing population density, and the influence of county economic characteristics varies with density. Elasticity with respect to relative nonwood fuel price (divided by wood price) is positive, but decreases as relative price increases. Relative nonwood fuel price elasticity is lowest where woodburning is greatest -- in counties with low density and high relative prices. Elasticity with respect to income is negative for higher density and lower income counties. This is caused by rapidly falling average wood use per woodburner as income increases (more households use fireplaces rather than stoves) even though participation increases. Elasticity is positive for low density/higher income counties. In these counties participation also rises with income, but amounts burned per woodburner decrease relatively little; overall, average amount burned increases with income. Certain states have a high proportion of their fuelwood consumption in counties where the fuelwood use per unit forest is high. The following have 70% or more of their consumption in counties where consumption is .15 cords/acre of forest or more: Connecticut, Indiana, Iowa, Maryland, Kenneth Edward Skog Massachusetts, Nebraska, New' Jersey, Ohio, Rhode Island, and Washington. ACKNOWLEDGEMENTS My first thanks go to Drs. Robert S. Manthy and Robert N. Stone. I thank Dr. Manthy for introducing me to the study of wood energy use and for encouraging and facilitating the completion of this dissertation. I thank Dr. Stone, my project leader at the 0.8. Forest Products Laboratory, for my assignment to study residential fuelwood use and for his helpful encouragement to finish this work. I thank my wife, Judy, for her enduring patience and support and my daughters Erica and Kate for their delightful diversions. Finally, but certainly not last in importance, I thank Mary Joan Kaminski for her patient and skilled typing of the drafts and final copy of this dissertation. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . I. II. III. IV. VI. VII. VIII. INTRODUCTION . . . . . . . . . . The problem . . . . . . . . . Fuelwood use problems . . Fuelwood use opportunities Objective of the study . . . . How data limitations influence 5 tudy (bee... h fleece. METHODS T0 PREDICT LOCAL FUELNOOD CONSUMPTION Household consumption modeling . . . . . . Models of aggregate household consumption . . . . . . . . . . . . Models of individual household consumption . . . . . . . . . . . . . A model of county level fuelwood consumption . . . . . . . . . . . . . . An equation to predict percent woodburners . . . . . . . . . . An equation to predict amount burned by woodburners . . . . . . . . . . . . . . MODEL SPECIFICATION AND PARAMETER ESTIMATION . A probit equation to estimate percent of woodburners . . . . . . . . . . . . . . A linear-in-parameters equation to estimate amount burned by woodburners . . . . . VALIDATION OF THE MODEL . . . . . Validation by correspondence . Validation by coherence . . . . Validation by pragmatic uses . IDENTIFYING COUNTIES WITH HIGH INTENSITY FUELWOOD USE O O O O O C O O O O O C O O O 0 CONCLUSIONS . . . . . . . . . . . . . . . . . APPENDIX - DATA SOURCES e e o e e o e o o e 0 LITERATURE CITED . . . . . . . . . . . . . . . iii 11/ 0‘0 \lflU‘lNl-‘H 86 110 121 125 10. LIST OF TABLES Fuel share elasticity with respect to price for selected residential fuels . . . . . . . . Variables and parameter estimates for probit equation 1 which excludes squared terms . . . Variables and parameter estimates for probit equation 2 which includes squared terms . . . Terms and parameter estimates for equations (18), (19) and (20) which predict amount of fuelwood used by a household . . . . . . . . . Values of selected county characteristics which divide households into four roughly equal Size groups, 1980-81 0 o o e e o e o e 0 Survey and probit equation estimates of average percent woodburners for subgroups of counties, 1980-81 . . . . . . . . . . . . . . Survey and equation estimates of average amount burned per woodburning household for subgroups of counties, 1980-81 . . . . . . . . Survey and combined equation estimates of average amount burned per household for subgroups of counties, 1980-81 . . . . . . . . Survey and equation estimates of percent burners, average fuelwood use by woodburners, and average fuelwood use, by population density of counties, 1980-81 . . . . . . . . . Total residential fuelwood consumption by state as estimated by the National Residential fuelwood use survey of 1980-81, by Model 111 and by other surveys . . . . . . . . . . . . . iv Page 12 30 32 42 50 51 55 59 66 68 Table 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. A comparison of signs of elasticities of fuelwood use from previous studies and from probit equation 2, amount equation (20) and Model III . . . . . . . . . . . . . . . . . . Elasticities of average amount burned by woodburners with respect to selected variables, for counties with various population densities . . . . . . . . . . . . . Elasticities of average amount burned over all households with respect to selected variables, for counties with various population densities . . . . . . . . . . . . . Ten counties in each region with the highest estimated percentage of woodburners, 1981 . . Ten counties in each region with the highest estimated average fuelwood use per woodburning household, 1981 . . . . . . . . . . . . . . . Ten counties in each region with the highest estimated average fuelwood use over all households, 1981 . . . . . . . . . . . . . . . Ten counties in each region with the highest estimated amount burned per square mile of countY’ 1981 O O O O O O O O O O O O O O I 0 Major cities in counties with the highest fuelwood use per square mile, 1981 . . . . . Selected counties in each region with high fuelwood use per square mile of forest, 1981 O O O O O O O O O O O O O O O O O O O 0 State level estimates of residential fuelwood consumption by intensity of forest use in individual counties, 1981 . . . . . . . . . . Page 74 77 80 88 91 95 98 101 104 105 I. INTRODUCTION In 1981, an estimated 42 million cords of fuelwood were burned for home heating-~an amount equal to one-fourth the amount going into all other wood products.1 This large use presents potential forest management and marketing problems and opportunities for certain local areas. It is the purpose of this study to determine local areas of heavy fuelwood use by linking local economic characteristics of households and areas to'fuelwood consumption. Using this link we can estimate local fuelwood use from local characteristics. We can also use the link to suggest how local consumption may change as economic conditions change. "Local areas" refers to individual counties in a state. The Problem Fuelwood use poses potential problems and opportunities for certain local areas. Fuelwood for home heating consumes roughly one-half as much roundwood as pulpwood lKenneth E. Skog and Irene A. Watterson. 1984. Residential fuelwood use in the United States. Journal of Forestry 82(12):742-747 (December). 2 (roundwood and chips).2- In certain areas high fuelwood consumption poses problems or opportunities, including: -Avoidable competition between pulpwood and fuelwood users —Air pollution health hazard from woodburning stoves -Damage to ecosystems from improper harvesting -An opportunity to increase the rate and quality of tree growth by thinning -An opportunity to increase local employment and income -An opportunity to decrease local export of dollars outside an area to buy nonwood heating fuels. These problems and opportunities can be better dealt with by business and government if, for local areas, they know current fuelwood consumption and the likely change in consumption as economic conditions change. Local use could be determined by surveys in each county of the U.S. But this study uses an alternative method to estimate local consumption by linking economic characteristics of households to much less detailed survey data on consumption. Fuelwood Use Problems. Without knowing amounts or locations of fuelwood use, many authors have speculated on the impact of heavy fuelwood use. The exception is direct evidence of air pollution impacts. In Oregon, wood stove .2_Ibid. p. 746. 3 particulate emissions increased from 1,000 tons/year in 1970 to 7,000 tons/year in 1983. Other Oregon industry is held to 4,000 tons/year by the Federal Clean Air Act of 1970.2 As a result, a new state law will require stoves sold after 1986 to meet clean burning standards. Pollution has also prompted restrictions on burning in Missoula, Montana, and in Aspen and Vail, Colorado. Recent surveys also show heavy woodburning in rural areas outside the already identified problem areas in the Northwest and New England.ié Unlike direct evidence of air pollution, evidence of competition between pulpwood and fuelwood cutters is sketchy. Some foresters have warned that high prices for fuelwood would encourage harvest of trees without regard to their‘ possible higher value as pulpwood or sawlogs.§’1- Some see expanded possibilities for fuelwood to be removed along with pulpwood, sawlogs and veneer logs in coordinated 2E. Carlson. 1983. Smoke from wood becomes big polluter in Northern U.S. Wall Street Journal. October 4. SSkog and Watterson. 1984. Residential fuelwood use in the United States. p. 743. EUSDOE Energy Information Administration. 1983. Residential energy consumption survey: consumption and expenditures, April 1981 through 1982, part 2: regional data. DOE/EIA-0321/2 (81), p. 207-211. EMichael Harris. 1980. The Boom in wood use: promise or peril. American Forests 86(9):57-60, (September). 1W. K. Murphey et al. 1981. Some implications of using wood as fuel. SEuthern Journal of Applied Forestry S(1):16-l9 (February). 4 operations.§- Others focus ("1 expanded opportunities for economical timber stand improvement by removing poor quality trees for fuelagtlg Local relationships 'between traditional timber markets and fuelwood markets will depend on key local conditions and public or private programs for constructive use of fuelwood harvests. Researchers speculate that ecological consequences of fuelwood harvesting will range from beneficial to tragic. Heavy cutting and gathering may cause nutrient loss, soil disturbance, regeneration of different plant species, fire hazard, erosion/leaching, and/or improved or damaged wildlife habitat.-1-l Heaviest cutting, using whole tree harvesting, is most likely with integrated operations where some roundwood is chipped to fuel industrial boilers or split into pieces and sold as residential fuelwood. Usually household cutting is not as severe, but to the extent that a household cuts all dead trees or all live trees or all logging waste from a §Robert Seidl. 1980. Energy From Wood: A new dimension in utilization. TAPPI 63(1):26-29 (January). 2D.B. Field. 1982. Economic benefits from harvesting in forest management. pp. 67-81. In Proceedings of fuelwood management and utilization seminar, Nov. 9-11, 1982 (East Lansing, MI: Michigan State University Dept. of Forestry) p. 67. lQArlyn W. Perkey. 1981. The New England fuelwood project. American Forests 87(8):13-15 (August). 11R. I. Van Hook gt_gl. 1982. Environmental effects of harvesting forests for energy. Forest Ecology and Management 4:79-94. 5 site, certain animals will suffer from a habitat change.l2’lé Over many‘ years fuelwood cutting and collecting will cause slow changes as millions of acres are harvested. Fuelwood Use Opportunities. Heavy fuelwood use provides an opportunity to thin stands and thereby increase timber quality and growth. In New England, federal funds have been used to pay foresters to supervise fuelwood removal in certain privately owned standsuli The program requires a stand to yield 5 cords of fuelwood per acre. At this removal level, the 42 million cords used nationwide in 1980-81 could have treated 8.4 million acres of the 187 million acres of jprivate nonindustrial forest land. In Georgia and North Carolina, the Tennessee Valley Authority, in partnership with farm cooperatives, buys scrub timber from farmers, converts it to fuelwood and distributes it in 3S-pound bundles to Atlanta retail stores.l§ liLouise M. Tritton and Thomas C. Siccarra. 1977. The fallacy of playing pick-up-sticks fuelwood. Connecticut Woodlands 42(4):17 (Winter). léJohn D. Gill. 1982. Wildlife and other multiple use considerations. pp. 106-109. In proceedings of fuelwood management and utilization seminar, Nov. 9-11, 1982 (East Lansin , MI: Michigan State University, Dept. of Forestryg. liPerkey. 1981. The New England fuelwood project. p. 13-15. liLeslie Henderson. 1981. Greenbacks from green junk. American Forests 87(4):12-15 (April). 6 Foresters currently influence practices for only a small fraction of fuelwood harvests. Only 12% of households that cut from land they own select trees to cut based on advice from a forester.l§- Households cutting from their own land removed 7.9 million cords in 1981. Households cut a total of 30 million cords and vendors cut about 12 million cords.ll Fuelwood harvesting and burning contributes immediately to a local economy by providing jobs, dollar income and expenditure, and by decreasing dollars sent out of the area to pay for nonwood fuel. In the long run, cutting fuelwood for timber stand improvement can produce more high valued forest products. These contributions are offset somewhat by loss of local employment and income for those selling nonwood fuels. To the extent that fuelwood demand drives up timber prices, there is a risk that increased fuelwood use could reduce production of high-value-added products-dumber and paper--which contribute more dollars per cubic foot of roundwood to an economy than fuelwood.l§. Economic léKenneth E. Skog and Irene A. Watterson. 1983. Residential fuelwood use in the United States: 1980-81. USDA Forest Service, Forest Products Laborabory, National Technical Information Service, ADA 131724. (Springfield, VA) p. 42. .1_7_Ibid. p. 38. l§Field. 1982. Economic benefits from harvesting in forest management. p. 73. 7 advantages of fuelwood use are also reduced by the increased health and financial costs of chain saw accidents, 'wood stove related house fires and air pollution.12 Objective of the Study The objective of this study is to predict near term household fuelwood consumption behavior at the county level by linking it to economic and demographic conditions in a county. These predictions are made in order to aid identification of counties having higher intensity fuelwood use and are therefore more likely' to Ihave fuelwood use related problems and benefits. How Data Limitations Influence the Study County fuelwood problems and opportunities could be pinpointed using surveys of several hundred households in each U.S. county but this method is costly. Instead, this study relies on the National Residential Fuelwood Use Survey of 5,569 households.£2- This survey was insufficient to estimate fuelwood use directly for individual counties. To use this limited data for county estimates additional knowledge must be used about the lBCurtis C. Travis, Elizabeth L. Etnier and H. Robert Meyer. 1985. Health risks of residential wood heat. Environmental Management. 9(3):209-Zl6. ZQSkog and Watterson. 1983. Residential fuelwood use in the United States. p. C-3. 8 economic behavior of households. County estimates may be made by combining the limited data and a hypothesis about how household behavior is uniformly affected by economic factors. The following section discusses means to link household behavior to economic factors. II. METHODS T0 PREDICT LOCAL FUELWOOD CONSUMPTION Literature helpful in linking household and area economic conditions to fuelwood use includes (1) theory and methods in household consumption economics, including methods used in residential energy demand models and (2) empirical findings from fuelwood use surveys. Household Consumption Modeling The theoretical basis for empirical models of aggregate household consumption has a weakness. Neoclassical economic theory explains that individual household consumption is the result of a household's choosing products so as to maximize utility subject to an income constraint. But this theory is not sufficient when economists want to justify a model of consumption for a group (aggregate) of Ihouseholds. Historically, empirical models of aggregate household consumption have been theoretically justified by stating that they model the "average household" by linking average consumption to 21 average household income and prices.—— Unfortunately, it has been shown that even if every consumer in a group 11A. Brown and Angus S. Deaton. 1972. Surveys in applied economics: models of consumer behavior. Economic Journal 328(82):ll4S-1235 (December), p. 1168. 9 10 behaves according to theory, the relation of average consumption to average income and prices may, itself, not conform to theory of "average" utility maximization subject to an "average" income constraint.££ Despite this theoretical weakness, data limitations have "forced" construction of many models of aggregate household consumption on the premise that they can still yield useful insights into household behavior. Some of these models for residential energy consumption are, discussed next to learn what economic factors they find influence energy' use. Following that, two theoretically justifiable models are discussed. These models require data on individual households. The second of these models will be used to predict county fuelwood consumption for this study. Models of Aggregate Household Consumption. Hartman reviews 19 residential energy demand models that explain three consumer decisions spanning the economic long rum-2-é -Should a home heating device be purchased? -What characteristics and fuel should the device have? ~How much fuel should be used in the device? illbid. ZéRaymond S. Hartman. 1978. A Critical review of single and interfuel substitution residential energy demand models. Massachusetts Institute of Technology Energy Research Lab Tech. Report MIT-EL-78-003. (Cambridge, MA) 121 p. 11 In the short run equipment is fixed and the consumer only decides how much fuel to use. Hartman's models explain, to varying degrees, demand for energy-using appliances, and demand for fuels. Certain models cover only use of single fuels such as electricity or gas. Most use pooled time-series, cross-sectional data aggregated by state. The dependent variable is state per capita or per household fuel use. In some cases demand for appliances is modeled separately. Explanatory variables include own fuel price, substitute fuel prices, income, climate, housing characteristics (e.g., rooms per house), degree of urbanization, and other demographic characteristics of households. Certain models explain the level of appliance stock separately using variables such as own fuel price, substitute fuel prices, income, and cost to buy and maintain equipment. Long run and short run behavior are most clearly separated where appliance stock and demand per appliance are modeled separately. In these cases, short run and long run price and income elasticities can be computed separately. Many models assume year to year demand for appliances is always in market equilibrium, others assume that demand lags ‘behind theoretical equilibrium (dynamic partial adjustment). Hartman judges superior those models which (1) have separate equations for stock level and stock utilization 12 and (2) allow partial adjustment of stock demand toward theoretical market equilibrium each period. Hartman also examines five models which predict use of several fuels at once. These models show how cross price elasticities vary. Like the single fuel models they vary in degree of data aggregation, treatment of long run versus short run and sophistication in behavioral assumptions. One detailed and flexible model by Lin, Hirst and Cohn found elasticities for fuel market shares that suggest rising natural gas or fuel oil price will shift consumption to other fuels while rising electricity price will only decrease electricity use without notably increasing use of other fuels (Table l).£i Table l.--Fuel share elasticity with respect to price for selected residential fuels Fuel Cross fuel Electricity Natural gas Fuel oil Electricity -2.6 .4 1.4 Natural gas .4 -l.6 .03 Fuel oil _ .03 3.5 -l.l This model suggests that similar price changes in various fuels have different effects on consumption of alternative fuels. 2Amid. p. 32. 13 The models Hartman reviews are usually linear-in-parameters with parameters often multiplying nonlinear transformations of one or more variables (e.g., log-linear or log-log forms). The residential energy models Hartman reviews do not include fuelwood. One simple aggregate demand model for fuelwood, proposed. by ILipfert, estimates the density of wood smoke pollution by relating average wood burning per household in New England counties to county climate (heating degree days) and population density.£§» His model is w - 3.09 - .32 In D (1) where W . standard cords of wood used per household per 10,000 heating degree days in a county, D a persons per square mile in a county. This model predicts that wood use density peaks at a suburban population density of about 5,000 per square mile (about 3 households per acre). He notes population density could be a good predictor because it is a good proxy for other factors influencing wood use including percent urbanization, percent land in forests, retail price of wood, and perhaps family income. ZEFredrich W. Lipfert and Jennifer L. Dungan. 1983. Residential fuelwood use in the United States. Science. 219 (25 March 83):l425-1426. 14 Models of Individual Household Consumption. The major theoretical weakness of aggregate models, linking average demand to average economic factors, can be removed by modeling behavior of individual households. But doing so makes predicting consumption for small areas problematic. We would need to know individual characteristics for many households in an area in order to make estimates or projections. As with aggregate models, models of individual household energy demand should account for decisions about (1) which kind of fuel to use and (2) how much fuel to use. Hardie and Scodari develop a theoretical model of individual household. fuelwood use and Hardie and Hassan develop a related empirical model. The model used in this study is a theoretical and empirical variation of these models.£§9£l Hardie and Scodari explain the fuelwood use of a single household in county i, Qi’ using the equation Q1 " Di . qi (2) where D1 is l with probability pi, the probability of their burning any fuelwood, zero otherwise, and Qi is the éélan W. Hardie and Paul F. Scodari. 1982. A model of residential demand for fuelwood. Univ. of Maryland Dept. of Agriculture and Resource Economics Scientific Paper A-3310. (College Park, MD) 61 p. lllan W. Hardie and A212 A. Hassan. 1984. An analysis of residential demand for fuelwood in the United States. Unpublished report to USDA Forest Service Northeast Forest Experiment Station, Broomall, PA. 59 p. 15 amount of wood used if the household burns wood. The total wood used by a group of m households would be (3) i=1 181 To explain the probability of a household burning wood, p, we first assume (1) utility gained from home heating is "weakly separable" from utility gained by using other products and (2) a representative utility function plus a random error can explain any household's utility gain from home heating. If a household's utility, U, is weakly separable into components for home heating, U1(q1) and other items, U2(q2), then total utility, U, may be expressed as: U . U(U1(q1), U2(q2)) and we may assert that demand for home heating is not influenced by quantities and prices of nonheating products used.£§- If we assume utility from home heating for a household has a fixed "representative household" component and a random component, then we may explain the probability of fuelwood use, p, as follows. Let U1n ' 51 + eln (5) 2§Angus Deaton and John Muellbauer. 1980. Economicgof Consumer Behavior. (Cambridge Univ. Press) p. 127-8. 16 be the utility consumer n obtains from burning wood plus, possibly, another fuel. Let UZn ‘ 5: * e2n (6) be the the utility consumer n obtains from burning a nonwood fuel only. Terms U1 and 0-2 are representative consumer utilities where Uin - Ui(yn’pn’an), i a l or 2 (7) and y - consumer income p - heating fuel prices (vector) a - other household characteristics (vector) Terms e1n and e2n are random differences between the representative consumer and consumer n. A household chooses to burn wood if Uln * eln > "2n * eZn (8) 0r _ _ _. > _ U1n U2n e1n + 62n (9) Let U12n ' U1n ‘ U2n and e12n ‘ “e1n * e2n Since e12n is a random variable, woodburning is chosen with probability 12“ < 012“] (10) An empirical model can be formed using theoretical equation pn - Prob [e (10) and data on individual households, provided 17 values of U12“ can be computed, and an assumption is made about the distribution of e12“. If e12n has a normal distribution and U12“ is a linear-in-paramaters function of prices, household income, and other household characteristics, then a probit function is formed. If e12n has a 29, 0 . . —. — formed.-—--—' Hardie and Scodari suggest U1n and U2n Weibell distribution, a logit function is and thus U12“ and pn should be determined by factors which influence nonwood heating costs: -type and price of nonwood heating fuel(s) used -type of heating appliances in the house -maintained indoor temperature -climate -amount of insulation -house size -type and location of house, by factors which influence wood fuel heating costs: -cost to own and maintain a wood heater -purpose of woodburning: heating or enjoyment -access to a wood supply .ngohn A. Hauseman and D.A. Wise. 1978. A Conditional probit model for qualitative choice: Discrete decisions recognizing interdependence and heterogeneous preferences. Econometrica 46(2):403-406. éQRaymond S. Hartman. 1979. A generalized logit formulation of individual choice. Massachusetts Institute of Technology Energy Research Lab Working Paper MIT-EL-79-010WP. (Cambridge, MA) 28 p. 18 -occupations of household members (influences time cost for wood cutting) and by factors determining a household's tastes and preferences: -household income -age of head of household -education -family size -number of employed household members. Hardie and Hassan prepare a probit model based on this theory which is discussed later.21 Hardie and Scodari develop a theory of (1) how much wood a household would burn (qi in equation (2)), (2) how much they would purchase or cut themselves and (3) how much nonwood fuel they would use.£ Fuelwood consumption may be modeled without reference to prices for nonhome-heating products consumed because we assume weak separability of home heating utility. Their theoretical fuelwood use equation is: Q ' q (PfaPestipcsPhscik) w w (11) where Pf a price of nonwood fuel used (natural gas, fuel oil, propane) élHardie and Hassan. 1984. An analysis of residential demand for fuelwood. éfiHardie and Scodari. 1982. A model of residential demand for fuelwood. 19 P8 . price of electricity Pw - price of wood purchased Pc - price of coal Ph - value of household labor per hour while harvesting wood C a last season's heating bill k - nonwood heating fuel used. Hardie and Hassan prepare several regional probit models for equation (10), the probability of burning, and a specially adjusted ordinary least squares (OLS) regression model for equation (11), amount burned.§-é Probit models for each of 5 census regions predict probability of burning wood based on -house area heated (sq. ft.) -heating degree days (under 50° f) -family size -firewood price ($/cord) -nonwdod fuel price ($/MMBtu) -household income (1000 $) -type of heating equipment used; wall or floor furnace, radiators, central warm air, electric wall units, gas or oil heaters, portable heaters An OLS regression predicts amount burned using a sample ééHardie and Hassan. 1984. An analysis of residential demand for fuelwood. 20 .14.. 5 bias correction. procedure developed. by IHeckma -—- and variables for -the ratio of firewood price to nonwood fuel price -house area heated -heating degree days -family size -household income -kind. of .nonwood fuel used (i.e., electricity, oil, gas, LP gas) -whether or not firewood was purchased. A regression to predict wood use for any household may be biased, if a correction is not made, because the regression is fit only on data for woodburning households. Binary variables were also included in the OLS regression for each of 5 census regions (regional shift variables). Hardie's model predicts probability of woodburning and average use given the characteristics of a single household. If we have characteristics of a large random sample of households in an area we can predict total use using equation (3) for each household. But in making éiJames J. Heckman. 1976. The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimation for such models. Annals of Economic and Social Measurement 5(4):153-6l. ééJames J. Heckman. 1979. Sample selection bias as a specification error. Econometrica 47(1):153-6l. 21 regional estimates Hardie and Hassan instead use average characteristics of households by region to predict probability of woodburning, and average characteristics over the whole U.S. to predict average wood use. In order to use Hardie's model correctly to predict county level fuelwood use we would need characteristics of a representative group of households in each county. These data are not readily available. Hardie's model could use average household characteristics from each county but the average may not reflect well the distribution of individual household characteristics in the county. A Model of County Level Fuelwood Consumption As an alternative to Hardie's empirical model, consider the following two equation model that explicitly links average household characteristics in a county to (1) the probability of woodburning, pi, and (2) the average amount burned per woodburning household, qi. Using these two equations we may compute wood burned per county as follows: ' <2,-1>,°c1,°Ni (12) where Q1 8 the quantity of wood burned in county i, pi - the percentage of households burning wood in county 1, q. - the quantity burned by an average woodburning household in county 1 22 Ni - the number of households in county i. To form the equation for pi, we assume (1) a household with average characteristics in a county has an average likelihood for burning wood among all households in the county, (2) these average households have utility for home heating which is weakly separable from utility for other products consumed and (3) the utility from heating for these average households may be modeled by an equation with two components--one component giving the value of utility of a representative average household and a component giving the difference in utility between the representative average household and the average household :n: a particular county. The representative average household's utility is expressed as a function of county characteristics and county level averages of household characteristics. To form the equation for qi--the amount burned per woodburning household--we assume (1) the average amount burned by woodburning households in a county can be expressed as a function of average woodburner characteristics in the county, and (2) the average characteristics of woodburners in a county are highly correlated with the average characteristics for all households in the county. An Equation to Predict Percent Woodburners. The assumptions above for predicting percent of woodburners, 23 pi, allows use of the household utility theory expressed in equations (4) through (10). The differences in formulation here are ‘ that (1) utility is for a representative average household in a county not a representative individual household and (2) utility of the representative average» household. is dependent on. average county characteristics not individual household characteristics. In order to explain the equation to estimate percent of woodburning households in a county the household utility’ hypothesis is restated for an average household in a county: Let U1i - fii(x1i) + eli and (13) where Uli = the utility of burning wood for the average household in county i, U2i - the utility of not burning wood for the average household in county i, 1(xli) - the utility for a representative average household for burning wood in a county based on average characteristics, X11, of households in county 1. 24 U2(XZi) - the utility for a representative average household for net burning wood in a county based on average characteristics, X21, of households in county 1. e11, eZi - differences between a representative average household and an average household in a particular county, 1. Assume U1 and U2 are linear-in-parameters functions of X11 and X21, and assume 611 and e21 have random normal distributions. Our hypothesis is that the probability that the average household will burn wood is the probability that UIi exceeds U21. That is; Prob (burning) - Prob (U1i U21) - Prob (U1i(Xli)+e1i U2i(x2i)+e21) - Prob (Uli(Xli)-U21(X2i) 311-321) (15) If eli and e2i are normally distributed so is e11'921- A. necessary condition. for e11 and e21 to be normally distributed random variables is that Uli(xli) and "21(x21) must account for all variables that influence utility and that the manner of the influence be properly specified by the form of the equations. 25 Equation (15) may be converted into an explicit probit model by first specifying the form of 611(xli) "21(x211' Let f1 ' ”11(x11) ’ ”21(x21) n = Z . Z.. 16 aJ J1 ( ) 1'1 where Zji a a vector of n variables X11 and X21. The probit model, expressing the probability that fi will exceed e1i - e2i for an average household in a particular county i is given by the cumulative normal distribution function: f1 . 1 2 pl 8 f ______. exp (-x /2) dx (17) Y2“ .00 where fi is given by equation (16). The parameters aj in equation (16) are estimated by a maximum likelihood procedure 'which uses data on individual households, and their county characteristics; from the National zji’ Residential Fuelwood Use Survey.3—6 The survey gave data on 6569 households, indicating whether or not they burned wood “and, if so, the amount burned during the 1980-81 heating season. Data on the households respective counties was obtained primarily from the 1980 Census of Population §§Skog and Watterson. 1983. Residential fuelwood use in the United States. 26 and Housing. County fuelwood price estimates came from the National Residential Fuelwood Use Survey and nonwood fuel prices came from the Los Alamos National Laboratory.fl See the Appendix for an explanation of data characteristics and sources. An Equation to Predict Amount Burned by Woodburners. To estimate average amount burned by woodburners in a particular county it would be best if we knew the average characteristics of woodburners to use as predictors. Unfortunately we only have average characteristics over all households in each county. There are two ways average county characteristics could ‘work well as predictors of wood use by woodburners. First, a variable may work well if it indicates the economic environment equally well for burners and nonburners, and if, second, the average value of the variable for burners is highly correlated with the average value for nonburners. These guides are used to form the equation to predict amount burned. .EZLos Alamos National Laboratory. 1980 Residential fuel price database for solar heating market analysis. Unpublished data for 280 U.S. regions obtained from Fred Roach. Los Alamos, NM (1982). III. MODEL SPECIFICATION AND PARAMETER ESTIMATION Model specification is the procedure by which (1) the independent variables are identified and (2) the mathematical linkage between independent and dependent variables is specified. The procedure of parameter estimation identifies the values of numerical constants in the equations of the model. A Probit Equation to Estimate Percent of Woodburners To specify a probit equation for pi (equation (17)) we seek county level variables, Zj, which determine the utility of burning wood, and not for equation (16) burning wood. Following the theoretical model of Hardie and Scodari we seek factors which influence - nonwood heating costs, - fuelwood heating costs, and - household tastes and preferences. Consider for inclusion factors identified as important by previous empirical work. Hardie and Hassan included, as determinants of heating costs; square foot area heated, heating degree days, number of household members, price of wood fuel and type of nonwood heating equipment used.§.3_ §§Hardie and Hassan. 1984. An analysis of residential demand for fuelwood. 27 28 To account for variation in tastes and preferences they constructed separate probit equations for each of 5 census regions. A second empirical model by Lipfert predicted average household fuelwood use in a county based on heating degree days, which has a major influence on heating costs, and logarithim of population density, which is related to the cost of heating with wooifl Population density is linked to cost of wood burning in so far as households in high density areas have greater difficulty in finding,. cutting and hauling wood, or have greater costs in buying wood; and greater inconvenience in tending a fire. Thus, households in high density areas are less likely to burn wood. The survey by Skog and Watterson confirms urban households are less likely to burn wood than rural households; 23% versus 45% respectivelyuI-Q Another factor which influences cost of woodburning, in addition to population density, is access to forest land for households or vendors to cut wood. The model presented here uses percent forest land in a county as one measure of costliness of obtaining wood. Using the guidance of these previous studies, 19 variables denoting county characteristics were selected for a probit equation to predict percentage of woodburners égLipfert. 1983. Residential fuelwood use in the United States. p. 1425. AQSkog and Watterson. 1984. Residential fuelwood use in the United States. p. 743. 29 in a county (Table 2). These include eight dummy (0, 1) variables to denote when a county is in one of 9 regions. Dummy variables account for regional differences in costs and tastes not accounted for by the other 11 variables. Certain variables are taken from the Hardie and Hassan model and used in the form of county averages: heating degree days, average nonwood fuel price, fuelwood price, and fraction of households using each of 6 types of nonwood heating equipment (5 variables). Median household income was included. as a chief determinant of tastes. Median number of household members was initially included but discarded since its coefficient was not significantly different from zero. A second probit equation was formed to allow for the possibility that the influence of 4 variables--heating degree days, household income, nonwood fuel price and wood price--is not strictly proportional to the value of the variable. These four variables were squared and included in the second probit equation (Table 3). Parameters were estimated using a maximum likelihood technique for probit models.-t-l-l Parameter estimates, statistics to test if parameters are significantly different from zero, and elasticities of woodburning probability with respect to model variables are shown in Tables 2 and 3. illnstitute for Research on Poverty. 1984. Probit - version 6. An unpublished computer program. 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Homecou Epsom cnm.n ofiecm. «mam :uuoz «om.~ Naoma. uflueeau< vwz ewm.~: NwmmH.u moumum “amazon o. moumam oxmg nu Newumwumum fldowumw>ov . anew mo mozfim> ouw=Um uumvemum acowuwmmoou save «a (“no on .uoou AHNV oaamwum> zucsou zuwufiummfim mo ewumm A.v.u:ouvttn manna 34 A Linear-in-Parameters Equation to Estimate Amount Burned by‘Woodburners To specify an equation for amount burned by woodburners in a county, qi in equation (12), we seek county level variables, Xj (j .. 1 . . . m) which influence amount burned. By using county level variables to predict individual household fuelwood use we lose the greater predictive power of individual household characteristics such as kind of nonwood fuel used. But we gain a direct. link between county level characteristics and county fuelwood use. County variables used should describe the economic environment of burners accurately. Previous studies suggest certain variables account for variation in fuel use. Lin, Hirst and Cohn, in their state level aggregate model use prices of all three fossil fuels to predict demand for residential heating fuels.fl Lipfert, in a county level aggregate model, uses county population density as a proxy for the influence of fuel prices, access to forests, and family incomeuié The only other variable in Lipfert's model is heating degree days. Hardie and Scodari suggest a theoretical model of individual household fuelwood use which uses prices of wood and of each nonwood fuel, the value of household fiéHartman. 1978. A review of residential energy demand models. p. 82. figLipfert. 1983. Residential fishwood use in the United States. p. 1425. 35 labor to harvest and haul fuelwood, last season's heating bill and type of nonwood fuel used.-4i Hardie and Hassan, in their empirical model of individual household fuelwood use, use relative price of nonwood fuel to wood fuel, area of the house that is heated, heating degree days, family size, income, kind of nonwood fuel and whether or not fuelwood was purchased.£§ Based on these previous studies five county variables were selected for use in the equation for fuelwood consumed by woodburners: -median household income, -heating degree days, -percent forest land -price of nonwood fuel divided by price of wood fuel, -population density The price of nonwood fuel, contained in the price ratio, is the average price per MMBtu heat output for electricity, fuel oil and natural gas in the county weighted by the percentage of households using each fuel in the county according to the 1980 Census of Housing. (See Appendix for an explanation of equipment efficiency adjustments). Individual prices for nonwood fuels were not used in order to simplify the model. It is assumed that consumers iiHardie and Scodari. 1982. A model for residential damand for fuelwood. p. 36. E ardie and Hassan. 1984. An analysis of residential demand for fuelwood in the United States. p. 32. 36 will exhibit rational economic behavior in that nonwood fuels of different types with the same price per unit of heat output will give a household the same incentive to burn wood. Since Lipfert's model found a strong association between population density and woodburning it is included here. Certain influences associated 'with population density are included separately - income, percent forest and fuel prices. Including these variables will help to determine the influence of density alone. Household income, while not included in Hardies' models, is included here as a proxy for area of house heated and family size. Since 72% of fuelwood is harvested by households rather than purchased from vendors, ease of access to forest land was included as an influence in the model by using percent forest land in the county. No distinction is made between public and private forest, a potentially important influence on access. One concern in using county wide variables covering all households' is that they may not represent the average woodburner well. Of the five county variables chosen for the model percent forest land and heating degree days are likely to be nearly the same for woodburners and nonwoodburners. Median household income for a county tends to be lower than for woodburners alone. Higher income 37 households more often burn wood. Population density for a county tends to be higher than the population density nearest the average woodburner. This is because woodburners tend to live in more rural areas than nonwoodburners. The county average price of nonwood fuel divided by the price of fuelwood is likely to be higher for woodburners than for nonwoodburners. The fact that certain county averages are not the averages for woodburners will not cause difficulties in our equation if the variation in county averages from one county to another is the same as variation in woodburner averages from one county to another. That is, we assume countywide averages are highly correlated to county averages for woodburners. Three equations were formed using the selected variables: X1 - 1n INC 8 ln(median household income) X2 -'ln HDD - ln(heating degree days) X3 - 1n FOR - ln(percent forest land) X4 - 1n REL = ln(price of nonwood fuel divided by price of wood fuel) X5 = 1n PD 3 ln(population density) Qw - ln(amount burned by household) e 3 error term 38 4 Qw a Z aj Xj + e 1'1 4 4 Qw - z ( ajkka1X + e 381 k=1 4 4 k k 2 Qw = ( Z alkxS )X1+( 2 akaS )(Xl) + k=1 k=1 4 4 k 3 k ( Z 33kX5 )(Xl) + ( 2 a4kXS )X2 + k=1 k=1 4 4 k 2 k ( Z a5kX 5 )(X2 ) ( Z a6kX 5 )X3 + k=1 k=1 4 4 k 2 k c 2 a7kx5 )(x3) + c z aakx5 )x4 + ksl k=1 (18) (19) 39 4 ( 2 agkxsk)(x4)Z + e (20) k-l Equations (18)-(20) are formed using natural logarithms of variables because error term estimates were more nearly normally distributed than linear equations tested, and because coefficients represent the elasticity of wood use with respect to independent variables. Equation (18) uses only four variables leaving out ln(population density). Equations (19) and (20) allow elasticities of wood use with respect to Xl-X4 to vary with ln(population density). Equation (20), in addition to allowing variation in elasticity depending on ln(population density), allows variation in elasticity depending on the value of each predictor variable. Although equations (19) and (20) are quite flexible, they make the simplifying assumption that the influence of each predictor variable is independent of the influence of other predictor variables, except for the influence of ln(population density). Parameters in equations (18), (19) and (20) were determined using ordinary least squares regression and data from the National Residential Fuelwood Use Survey. Dependent variables, Qw’ are amounts burned by individual households throughout the U.S. Independent variables are 40 county characteristics for those individual households. A test is needed for equations (18)-(20) to see if their parameter estimates are biased as a result of their being fit on. data for woodburners only. Equation (12) estimates total woodburning in a county by multiplying probit equation estimates of percent burners times amount burned from equations (18), (19) or (20). The probit models are fit on data from both woodburning and nonwoodburning households. Equations (l8)-(20) are fit on. data from woodburners only. Counties with a high proportion of woodburners are over represented in the determination of parameters for equations (l8)-(20). The effect of the over representation, or sample selection bias, on parameters in equations (18)-(20) can be tested by including an instrumental variable LAMBDA in equations (l8)-(20) and determining if it has a coefficient significantly different from zero. LAMBDA for a household in county j is given by LAMBDAj . :: : :i:.% (21) i 13 where f is the standard normal distribution function and F is the cumulative standard normal distribution function.52 and a. are variables and parameters 2ij 1 respectively from the probit model to predict probability .iflflardie and Hassan. 1984. An Analysis of residential demand for fuelwood. 41 of woodburning by households in county j (equation (16)). The coefficient for LAMBDA, when it is included in equation (20), is not significantly different from zero at the 82% confidence level. As a result LAMBDA was not used to estimate parameters for equation (20). The coefficients for LAMBDA in equations (18) and (19) are significantly different from zero above the 83% confidence level. LAMBDA is excluded from equations (18) and (19) so differences between their predictions and those of equation (20) are not due to use of LAMBDA. Parameter estimates for equations (18)-(20) are shown in table 4. Parameters in equations (18)-(20) were estimated in order of greatest contribution in accounting for variance in Qw' Parameters were estimated for successive terms until the inclusion of an additional term would not explain at least .01% of the variance not yet accounted for. Parameters for equation (19) were estimated before those of equation (20). Estimation for equation (20) began by retaining terms included in equation (19) (but not their coefficients). This procedure was used in order to conduct an F-test of the significance of additional terms contained in equations (19) and (20). The F-tests of the increased variance accounted for between equations (18) and (19), and between equations (19) and (20) are significant at the 99.99% confidence level. 42 Table 4.--Terms and parameter estimates for equations (18), (19) and (20) which predict amount of fuelwood used by a household. Equation parameters (aij) Term in equation (18) (19) (20) (In INC) -l.0895 -8.ll98E-l -l.826l (In PD) (1n INC) (In PD); Eln INC) 5.57125-3 -3.77sos-3 In PD ln INC (1n PD)4 (ln INC) -1.7073£-4 2.92455-4 (In INC)2 (In PD) (ln INC)2 (In PD)2 (In INC)2 (In PD)3 (1n INC)2 (1n PD)4 (1n INC)2 (In 1NC)3 7.0609E-2 (1n PD) (In INC)3 (In PD)2 (In INC)3 (In PD)3 (1n INC)3 (1n PD)4 (1n INC)3 -2.0205E-5 (1n HDD) 4.507E-l 3.4132E-l 5.8973E-l Eln PD;2 Eln HDD; -6.7259E-3 -l.2630E-2 1n PD ln HDD (In PD)3 (1n HDD) 2.6907E-4 4.92105-4 (ln PD)4 (1n HDD) 1.1787E-5 -6.8437E-5 (1n HDD)2 (1n PD) (1n HDD)2 (In PD)Z (In HDD)2 (In PD)3 (ln HDD)2 (In PD)4 (1n HDD)2 (In FOR) 1.969E-l 2.7496E-1 1.94325-1 (1n PD) (1n FOR) -8.0520E-2 -2.6608E-3 Eln PD); Eln FOR; 1.01705-2 -9.7183E-3 ln PD 1n FOR (1n PD)4 (1n FOR) -4.6857E-S 1.0058E-4 Table 4 (cont'd). 43 Equation parameters (aij) Term in equation (18) (19) (20) (In FOR)2 -8.5907E-3 (In PD) (1n FOR)2 (1n PD)2 (1n POR)2 2.0060E-3 (In PD)3 (In FDR)2 (In PD)4 (1n POR)2 -2.0894E-5 (In REL) 3.6316E-1 1.3950E-l 7.9l3lE-l (In PD) (ln REL) 7.0600E-3 (In PD)2 (1n REL) -2.7318E-3 (In PD)3 (In REL) (In PD)4 (1n REL) -2.8198E-5 1.0003E-4 (In REL)2 1.3998E-l (1n PD) 1n REL)2 (In PD)2 1n REL)2 (1n PD)3 1n REL)2 (In PD)4 1n REL)2 R2 .381 .413 .442 Standard error .703 .685 .676 44 The adjusted coefficient of determination (R2), indicating the fraction of variance in natural logarithm of fuelwood use accounted for by an equation is relatively high--.44 for equation (20). This is high for a model using cross-section data. The models by Hardie and Hassan using individual household characteristics as predictors obtained R2 values of .20 to .24.51 Equations (18)-(20) estimate Qwi which is In (amount burned) for an average woodburner in county i. Call this estimate Ogi. Qwi ' 6141 I e Amount burned by the average woodburner in a county, qi, is estimated by qi - exp (Gwi) exp (SEZ/Z) where SE is the standard error in estimating 6&1. Values for SE for equations (18)-(20) are given in Table 4. Since SE is only an estimate, an adjustment was made to the initial estimates of qi and Qi' Recall that Qi - piqiNi (see equation (12)) An adjustment factor k was computed for Models I-III such that total U.S. woodburning estimated by the model equals the survey estimate for 1980-81 -- 40.5 million cords. III R 2 piqiNi = 40.5 181 4_71bid. p. 32-43. 45 where m is the number of counties in the U.S. For Model III, k - .98508. q; - kqi Q1 ' in where qi and Q; are adjusted estimates for amount burned by the average woodburner and total amount burned in county 1 respectively. IV. VALIDATION OF THE MODEL Forester and Senge describe validation as the process of establishing confidence in the soundness and usefulness of a model.5§- Its objective is to convince potential users that the model is a useful basis for decision making. The fact that there may be several audiences may complicate validation because each audience has its own objectives and criteria for evaluating the model. For scientists, a model is useful if it (1) gives insight into the workings of a real system, (2) makes correct predictions or (3) stimulates questions for future research. For public leaders, and their analysts, a model is useful if it (1) explains the causes of problems and (2) provides basis for designing policies to alleviate lo '1» problems. The validation steps taken here are an effort to satisfy the validation interests primarily of scientists. Forrester and Senge suggest specific validation tests for ifiJay W. Forrester and Peter M. Senge. 1978. Tests for building confidence in system dynamics models. Massachusetts Instutute of Technology Alfred P. Sloan School of Management System Dynamics Group paper D-2926-4. (Cambridge, MA) p. 5. 11211314. 46 47 models constructed from a system dynamics perspective. Rather than adapt their tests of model structure, behavior and policy consequences to the two equation model in this study, certain general validation tests suggested by Kaplan are used here.-5--Q Kaplan suggests that theories are validated by evaluating how they meet norms of (1) correspondence (to the real world), (2) coherence (in a larger body of knowledge) and (3) pragmatism (performing useful functions for the scientific enterprise). Correspondence between a model and the real world is demonstrated, in part, when the model makes predictions which are fulfilled. The correspondence is more convincing if the model operates well under a heterogeneous range of conditions. Kaplan concludes his explanation of correspondence by noting that "what counts in the validation of a theory [by correspondence], . . ., is the convergence of data brought to bear upon it, the concatenation of evidence . . ."él The notion of concatenation of evidence suggests the coherence criterianthe model should fit into established theory. Coherence also favors a theory or model which is simple to explain and which has a mechanism for determining behavior which is simple. When developing EQAbraham Kaplan. 1964. The Conduct of In uir . (Scranton, PA: ChandlerTPubl. Co.) pp. gl2-322. illbid. p. 314. 48 models Kaplan asserts "We are to introduce a complicating factor only if we have reason to expect error from its omission . . .".§5 The pragmatic norm for validation suggests theories and models should do useful work. Useful work. may include success in "practical" applications, such as using a fuelwood use model to efficiently target resources to improve forest management in counties using the most fuelwood. But this kind of useful work is neither necessary nor sufficient to validate a model or theory. The pragmatic norm is most related to the work the model does for science itself. How does it guide or stimulate ongoing inquiry? What new questions does it raise? Does it serve to explain prior observations better? Does it systematize or unify knowledge?§§» Validation by Correspondence One way to examine the validity of our two equation model is to compare its predictions to results of surveys. We first compare percent burners and amount burned, as predicted by equations developed here, to results from the National Residential Fuelwood Use Survey. Comparisons are made between estimates for households in different income groups, different heating degree day groups and other 3211314. p. 318. éllbid. p. 319-322. 49 groups. The objective is to use a wide range of subgroups to discern the equations ability to predict over a wide range of county conditions. Table 5 shows how households are subdivided into approximately equal size groups (number of households) based on county characteristics. Table 6 compares predictions of probit equations 1 and 2 to survey results. Table 17 compares equation estimates of amount burned by woodburners to survey results. Table 8 compares predicted average amounts burned over all households, as. computed by combining probit equation 2 and each amount equation, to survey results. Probit equation 2 was Chosen to pair with each amount equation because results in table 6 suggest it predicts better than probit equation 1. Percent woodburners is predicted best by probit equation 2 which includes squared terms (table 3). For probit equation 2 predictions for various subgroups differ from survey results by 7% or less except for one fuelwood price category, one relative nonwood fuel price category, one "percent forest land" category and one "percent homeowners" category. The probit equation underpredicts the most for counties with low percent forest land (-10.9%). It overpredicts the most for counties with low median income (5.8%). Predictions of amounts burned by equations (18)-(20) show greater percent differences from survey estimates than predictions made by the probit models (Tables 6 and 7). 50 Table 5.--Values of selected county characteristics which divide households into four roughly equal size groups, 1980-81 County Units Quartile upper limit Characteristic l 2 3 Median income ($1000 dollaIS) 14.70 17.08 18.94 Heating degree days 2673 5064 6328 Nonwood fuel (3/MMBtu) Price 7.12 8.95 10.80 Price of fuelwood ($/cord) 55 68 94 Nonwood fuel price (cords/ .099 .120 .146 divided by MMBtu) price of wood Percents forest Land 3 15 45 Population density (persons/ sq. mile) 97 417 1508 Percent rural population 2.5 13.4 44.4 Percent homeowners 59.4 66.5 73.3 51 H.m N.m n.om H.Nm v.aN e H.N1 e.m H.mN m.NN o.mN m N.H¢ m.nx o.vn «.mm o.vn N H.o¢ m. m.HN H.nN a.NN H mNmu meadow mcHueoz m.N m.H: m.mN ”.mN N.om v N.H n.m n.eN «.mN v.v~ m e. m.m n.5N u.wN N.5N N w.m N.nt c.5N N.NN m.mN H oaoucH :choz w.H- e. n.5N m.u~ m.a~ pmnno>< N H N H xo>usw :oHummmo anopm mvHonomso: mo oHHuumsc new uHumHuouueumnu xuezou moueaHumo :oHumzdo wee xo>u=m eoozuon mucouommHu ommaeouuom vacancHeusn mcHozomso: mo Heouuom meome .moHuezou mo mqaouwnsm new muocuspvoos acounoa omwuo>a mo moueEHumo :oHumzco anoun wee >o>p=wux.o oHnmh 52 H.N n. m.en N.en H.vn v e.H1 o.H «.mN H.mN w.mN n n.51 o.m o.HN o.NN m.nN N N.H1 H.e n.eN e.mN o.vN H coo: mo ouHun Na wwNH>Mw oanQ Hosm nooseoz m.N1 m. 1 m.oN o.HN H.HN e m. 1 a.m v.nm o.mm n.mn n N.u1 >.H w.HN H.HN m.nN N e.n a. m.nn n.Nn v.Nn H coozHosu mo ouHum u.H1 v.H H.mN o.mN o.wN e a.v1 w.e1 o.om n.cn m.Nn n H.H N.N o.hN n.5N 5.0N N a. 1 m.n m.NN a.eN H.mN H ouHHm Hozm poo: :62 N H N H xo>usm moumEHumo :oHumavo can >o>usm :oosuon mucououmHu owmueouuom :oHummUo anoum mvHonomzo; mo oHHuuasc can uHumHuouumuagu xuesou c0031wechzn meonomso: mo acouuom A.v.u=ouv o oHnmh 53 n.H1 o.H1 a.nn c.mm v.wn v u. 1 a.n v.on m.Hn o.cn n o.H1 v. 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H0N. 00H. H whoc3ooaon HGOUHUA 11111111111111111Hm0ueeHW11111111111 HHH HH H HHH HH H 005000 HH00e2 m0Henem=ez we 50>N=m 0:0 H000: :003000 00:0H0wwH0 0000:0000: 0HHuu0ac 0:0 uHumHueue0u0zu 00:300 fififlhfib HCSOE< A.U.H=OUV m OHQMH 63 Discussion is focused on equation (20) since it provides the best fit of the amount data (multipLe R2 - .44). For equation (20), 23 categories (of 54) have differences from the survey of more than 7%. Five categories have differences of 17% or more: -Highest income counties are predicted 18% to high, ~Highest fuelwood price counties are predicted 27% to high, -Highest population density counties are predicted 30-36% to high, -Next to lowest percent rural households group is predicted 37% to high, -next to lowest percent homeowners group is predicted 17% to high, -the two Rocky Mountain regions are predicted 44% and 26% to high respectively. Certain patterns appear in comparing amount burned predictions to survey estimates. Equation (20) underestimates for low income groups and overestimates for high income groups. Also, predictions across income groups become worse as we move from equation (18) to equation (20). The greater flexibility of equations (19) and (20) does not improve predictions across income groups. Equation (20) also underpredicts for low percent forest counties and overpredicts for high percent forest counties (Table 7). Predictions for households in counties with low 64 population density are good, but are high for high density counties. Even though the influence of factors in equation (20) can change with population density, the change is not enough. to prevent overestimates at high. population density. It is possible that equation (20) is not flexible enough at high population density, or it is possible the combined influence of two or more factors, at high densities, decreases woodburning. For example, at high densities, high income and high fuelwood price may combine to cause very low fuelwood consumption. In equation (20), a move to a higher fuelwood price drives down fuelwood use by the same percentage regardless of income. Based on comparisons in Table 7 it appears equation (20) predicts amounts best for those counties with "near median" characteristics. Overestimates are most common and are greatest for high density counties and high income counties. The errors in predicting amount per woodburner are offset somewhat when a probit equation is combined with an amount equation to predict average amount used per household over all households in a county. Three models were formed by pairing probit equation 2 (Table 3) with amount equations (18) through (20) respectively (Table 4). The combined equations in Model III provide moderately better predictions at high population densities, on average, than does equation (20), and slightly better 65 predictions across income groups (Table 8). Predictions tend to be good for counties with "near median" characteristics. Model III predictions for 16 categories (of 54) differ from survey results by more than 7%. Six categories differ by 17% or more. Because of the importance of population density in determining fuelwood use a more detailed comparison of survey and Model III results was made for higher density counties (Table 9). For Model III, overpredictions of average amount burned becomes larger as density increases beyond 6000 persons per square mile. For counties with 1508-6000 persons per square mile predictions average 7.8% too high. For counties with 6000-13087 persons per square mile predictions average 44% too high, and for counties over 13087 persons per square mile predictions average 160% too high. Six and one half percent of households live in counties with 6000 persons per square mile or more. Model III overpredicts their fuelwood use by an average of 68 percent. Model III predicts well, on average, for counties under 6000 persons per square mile. It overpredicts by only 1.4% on average. The forgoing correspondence tests cannot indicate how well the equations will predict for individual counties. Essentially these comparisons are a qualitative test of the hypothesis that the equations predict well across a wide range of county conditions. The hypothesis is false for 66 00o. coo. 0m. 00. m m 0.0 n. 00o: no 00000 mNo. N00. 00. 50. 0.0 0.0 N.0 0000010000N 0N0. 000. 00. N0. 0.0 0.0 0.0 00m0N100om0 one. 00°. 00.0 Nu. 0.0 0.0 0.N 5000010000 050. 000. 00.0 00. 0.00 0.00 000010000 men. 000. Nm.0 N0.0 c.0N n.0N 0.00 00001000 000. N00. N0.N 00.N 0.00 0.00 0.00 000100 000. 000. 00.N 00.N 0.00 0.00 0.00 0010 11111111111111110000ouv111111111111 00:o0000sv 0000: 000000 00: 0:o000mv N 000 x0>0=m AoNV >0>0=m :o000zcm x0>0=m 000°: :0000acm 00noum 0000:0030: 000:0:00oo3 000:0:0 0000:00000 0000::ou 000 00>o 00:03; 00 00:0:0 :0 0000:00 0::os< 00000>< 0:=os0 00000>< 0000:0030: :o0000aqoa mo 000532 00::ou .0010000 .0000:=ou mo 0000:00 :o0000znon 00 .00: 0oo300=m 00on0maoz 00000>0 0:0 .000:0=00oo3 00 00: 0oo300sm 00000>0 .000:0=a 0:00000 00 000050000 :0000000 0:0 >0>0=mcu.0 0000b 67 prediction of amounts burned in counties with high income, or high density and for the two Rocky Mountain regions. Predictions for these counties are too high on average. To obtain an idea about the likely accuracy of individual county estimates it would be best if we could compare independent county estimates with model estimates. Such estimates are not available for 1980-81. As a substitute several state level estimates are compared to our model estimates. Unfortunately state level survey_ estimates vary widely in accuracy. So, the confidence we can place in comparisons is limited. Comparing model estimates of amount burned Ix) 9 state survey estimates for 1980-81 shows our model "understimates" by 20% or more in 4 states and "over- estimates" by 20% or more in 1 state (Table 10). Comparison of model estimates to state survey estimates for other years shows our model usually "underestimates" total consumption. If we place confidence in the individual state surveys we would expect the individual county estimates would be underestimates in many cases. Many state estimates are probably too high based on the fact that the resurvey conducted for the National Residential Fuelwood Use Survey found households overestimated by an average of 18% on the initial survey.§i The state §£Skog and Watterson. 1983. Residential fuelwood use in the United States. p. c-lO. 68 N0. 0:0000000 00. 000:0:00 0N. 000:00 00. 03o0 00. 00. 0:000:0 00.0 00.0 00.0 00o:0000 0m. 00. an. o:000 05.H 50. 05. 0000000 00. No. 0000o0m 0o. .o.a 00. 0003000: 00. 00. 00. 00. 0000000::ou 00. an. o00uo0ou 00.0 00.0 00:0om000u mm. 00. 000:000< 0N. 0:ou00< 00.0 00. 000000< 111111 11111111111111110000ou :00000501111111111111111111111111111 0010000 N001o0m0 001N000 N0100m0 0010000 0010000 000 000oz 00>000 m0020 00:0: 000E000m 0000:000000 000>0=0 00:0o 00 0:0 000 000oz 00 .0010000 00 00>0=m 00: 0oo300am 0000:000000 00:o000z 0:0 00 000020000 00 00000 00 :O00gszm:ou 0oo300=m 0000:000000 000o011.o0 00000 69 00.0 00.0 00.N 000000000000 00.0 00.0 00.0 000000 00. 00. 00000000 00.0 00.0 00.0 0000 00. 00. 000000 00002 00.0 00.0 00000000 00002 00.0 00.0 00.0 0000 :02 00. 00. 00000: :02 00.0 00. 00. 000000 :02 00. 00. 00. 00. 00000000: :02 00. 000002 00. 00000002 00. 00. 00. 000000: 00.0 00. 00.0 00000002 00. 0000000000: 00.0 00. 00. 00000000: 00.0 00.0 00.0 0000000: 0N.H no.0 mauvmsnummmmz 00. 00. 00. 0000000: 00. 00. 0000: 111111 1111111111111111000000 :00000501111111111111111111111111111 0010000 00010000 00-0000 00-0000 0010000 0010000 000 00002 000000 00<00 00 00: 000300=m 0003000 >0>0a0 00:00 0002000m 00000000000 0.0.00000 00 00000 70 He. no. mw=Mm~fi> “we: H~.H aa.~ so.H coumcwnmaz ea.Hl on. «Mcfiuuw> om. hm. mm. He. uncauo> on. as“: aa. ~n.~ waxes Net" hQ.H oommoguoh «H. NN. «Hogan susom mm. em. #0. «cwfiopau guaom HN. ON. usagmH econ: .. ..... - ..... u ...... --Amuuou :0wfifiwav- ...... -c---------- ........ . ~m-cwm~ _me-cmaH mm-~mmfi Nm-HmoH Hm-cwaH cm-anm~ HHH Howe: xo>uam meu=m Macao cumawumm amwucovwmom A.v.u:ouv ca canwh 71 .Auonouuov Hana .uw .uuoqou wonmfiansncs .omumuafi .vcmaov woozaoam Hmwucovfimou auomoccw: .amma .xuumouom . mouuaomom Hauzumz mo .unon «Homoacw: .m .n— .o~mc:opuau ..>w:= mwocwHHH unusuaom .xuumouom mo .uao: .mm-~ma~ .mwocfiaan :w xwuoco how coo: mo munwfifinmwz .vwma .ovusm .: snow vow xvuzuuz .m unwfizn .om-ona~ you a: .oH .<: .ao “on mouQEMHmm .om .uo>=ou=a> .o um=m=< .ow umo3How am voucomoum .umoznuuoz uflmwuom one a“ mcwumo: comma fimwucocwmou you woo: mo om: ugh .omofi .muuonom .4 oaks: was uHo>mm .u oucouuoh .- .a .uuoaou conmwapsqca .xo>u=m whom: xwuoco coo: Hawucovfimoa .vmoH .nowmw>wa xmuocm . unoaowmcmz was »Uwaom mo ouflmmo .uaufluuoccou mo ououm "mouusom nonuo .a~ .a .finwvfiemo- ”Hm—amumv HO HOHHQ Uhmflflmum O>MHMHOfi a”. «H. mafiaoxz mm.~ no.H mH.H m~.H camcoumw: ...................... Amvuou cowaawavuu--uuu-u------u-------u-c-- Hmuomma flmwuowaa nmu~mmH quawmy fiwuowmfi omumnmfi HHH “coo: xo>usm mauzm noguo ouaEwumm amwucovwmom A.v.u:ouv oH mange 72 surveys generally did not conduct resurveys or other checks to verify respondent estimates. The conclusions 1x) be drawn from the correspondence tests that compare estimates for groups of counties include: - probit equation 2 predicts average percentage of burners fairly' well over' a wide range of county conditions, - equation (20) overpredicts average amount burned by woodburners for counties with high incomes and high p0pu1ation density, and underpredicts for counties with low income, - Model III overpredicts average fuelwood use Int 68% for counties with population density above 6000 per square mile. Model III predicts fairly well for counties with densities under 6000 persons per square mile. The specification of equation (20) needs to be improved to predict wood use at high densities. From comparisons of state level estimates we conclude that Model III under estimates total fuelwood use in states and counties if independent state survey results are correct. 73 Validation by Coherence Coherence among findings on what influences wood use behavior. How well does Model III agree with previous findings concerning the fuelwood use behavior of households? Three previous studies have evaluated the way various factors influence fuelwood use behavior.§2’ £2, £1 The elasticities of variables from these previous studies have signs which match the signs of elasticities for equations developed here (Table 11). The elasticities of the probability of woodburning - from probit equation 2 are compared to elasticities from Hardie's probit equation for individual households. Signs of elasticities match for variables found in both equations. Hardie does not include income in his model but uses "area heated" which is highly correlated with income. The elasticity for area heated is positive as is our elasticity for income in probit equation 2. The elasticities for amount burned by woodburners from equation (20) are compared to elasticities from Hardie's amount equation for individual households. Elasticity §§Lipfert. 1983. Residential fuelwood use in the United States. §2Frederich w. Lipfert et a_1_. 1984. Empirical analysis of residential wood bfirning impacts. An unpublished report for the Office of Policy Analysis, U.S. Environmental Protection Agency (Washington, D.C.) 36 p. élHardie and Hassan. 1984. An analysis of residential demand for fuelwood. 74 :uwmcow coflumfiaaom + + + woo: mo ouwua an wawa>aa ouwug Hosm woo::oz + + + + wzma amouom acouuom s u momma woo:~o=m + + oowua Hoam woo::oz + + + + + + mxmw oouwow wcwuoom +\« +\: n + oaoozm N Nana wwcwwcwm mmow chwwcwm :owuosoo Aflmcwwcwm fiowoz msow>oum :owums m mzow>oum canon: maofi>oum mwaocomso: ado nocusnwoo: woo: wcwcuzn meo: ofipmwum> uo>o wocusa unsos< you wocusp ucsos< comso: mo omaucoouom .HHH Howoz wcm AONV :omuwsco ucsoam .N :owumzco uwpoun aoum wcm mowwzum msow>oua eoum om: woo:~o=m mo mowquwumaHo mo mcwwm mo :omwuaasou wuwmoa ma oaoocw on uuoamou new: :ufiowumafimm .5» .Nn .a .wwaHm .wnwumo: owuuuofio pom o>wuwmon was mxmw oouwow wcwumon you o>wumwoc mm: xuwuHummao on» :owmou Hauucou :uuoz one you .mcowmou umoa you w:=om m“ was» ::o:m ma :mwm one .nNcmN .ag .woo:Ho=m you wcmsow mo mwmxamco :< .vwma .cammm: was owwumzm « : House: soon ago no one c « muoumo: Ham: ofluuuoum c c uflm uo: wouuzn c u muoumwwou amoum wow: ucoaamsuo mcwuoo: N mHHH «maawaam whoNV macawaam aoaaasua Macawaaw Howoz maow>oum :owaosom maow>oum uwnoum msow>oum meonomson ago nocnsnwoo: woo: wcwcnsn mwgon oanmwum> uo>o wocusn ucsoe< you weapon uczos< comso: mo owmucoupom ' A.w.u=ouv HH canny 76 signs match with the partial exception of income elasticity discussed below. Elasticities for equation (20) vary with population density and are shown in Table 12. Elasticities of amounts burned by woodburners are short term demand elasticities indicating how much fuelwood demand would change in the absense of entry and exit of households to woodburning. Short term demand elasticities are positive for heating degree days and for relative price of nonwood fuel both for Hardie's equation and equation (20). Hardie initially included income but found it had an insignificant coefficient, so, he excluded it from his amount equation. He retained the "area heated" variable which has a negative elasticity. Our proxy for "area heated" in equation (20) is income. Equation (20) has a negative elasticity for income for most combinations of income and population density. For these combinations wood is like an "inferior good" (less is used as income increases). But for higher income low density counties income elasticity is positive indicating fuelwood is a "normal good" (Table 12). Income elasticities' of ‘fuelwood use for the average woodburner vary from small positive values to negative values over income groups and population groups largely because of differences in the type of woodburning equipment the average woodburner is most likely to use and differences in woodburning purpose. In low density counties the average woodburner uses a stove and burns wood 77 mm. on. «N. mN. mN. Na. pm. me. afi. ca. h~. “w. hN. cm.~c Nm.~¢Hc.~c ~n.~¢ o~c- on. mN. vw. ca. no. am. am. am. am.c «0.: Hu.c Nm.c wow“ nN. 5H. wN. ea. we. mm. mm. mm. aN.c mn.c om.c mn.¢ haw ma. ma. ma. ma. ac. mm. mm. mm. no. cH.u h~.c on.c wa oN. «H. ma. ma. 5H. mm. mm. mm. ma. Ho. mH.o Nn.c mo.H AoNV one<=om om. No. we. cm.Hc oNo- ~v. OH. av. mm. u «can on. ca. mm. mm. a saw mN. ca. mm. mm. a mo wfi. hN. en. Hm. u mo.H haHV zoae<20m on. NH. ma. ao.H- ac< Away onawuaaom amouow ooumow oeoozm :owuofisqom ucoouom wcwumo: xuwmcow oHpmwum> xuczou :owuofiamom .mowuwmcow :owumfisaoa maowuo> so“: mowucsou pom .moanmwuo> wouuofiom ou uooamou saw: muocuanwoo: xn weapon ucsosm owmuo>a mo mowuwowumoamic.~fi canny 78 to provide much of his space heat. As we move to higher density counties the average woodburner is more likely to have a fireplace rather than a stove and is more likely to heat just part of his house or burn wood just for pleasure. In low density counties income elasticity moves from slightly negative to slightly positive. The move from negative to positive elasticity may be due to one or more factors: (1) higher income households may have larger houses to heat, (2) they may be more likely to heat entirely with wood, or (3) they may view greater woodburning as part of a life style to be desired. In higher density counties with low income the average woodburner is fairly likely to own a stove and burn wood for space heating. But, as average income increases, the average woodburner is more likeLy to use a fireplace just for pleasure. So as we move from low income to high income counties wood use by the average household goes down (income elasticity is negative). Equations (19) and (20) indicate that short term demand elasticities vary considerably with population density. For example, in higher density counties amount burned decreases much more rapidly in response to higher income. This might be interpreted as a greater sensitivity to inconvenience of wood use in high density areas. Unlike the increased response to changing income at high density, households decrease their response to heating degree day 79 changes at higher density. And, as we might expect, colder weather will increase a rural household's wood use more than an urban household's use. The short term response of households to change in forest availability (percent forest land) is greater for highly forested, middle density counties. Response is lowest for counties with little forest. These findings suggest increased access to forest land may increase average woodburning by the greatest percentage in highly forested, moderately populated rural counties. The short term response of woodburning households to increasing relative price of nonwood fuel increases sharply as county population density increases above 1800 persons per square mile. Even though woodburners in high density areas are responsive to relative nonwood fuel price changes, they are even more responsive to changes in income. In high density areas if income increases as fast as relative nonwood fuel price, fuelwood use by woodburners will decrease. But, in middle and upper income low density areas equal percentage increases in income and relative nonwood fuel price will cause an increase in woodburning. When probit equation 2 and equation (20) are combined as Model 111 both the entry/exit decisions and amount to burn decisions are included. Elasticities of amounts burned for Model III are long term fuelwood demand elasticities (Table 13). 80 v~.~ o¢.~ Na.” av. mN. ma. mo.H «H.H HH.H mN.H¢ on.~u wv.~s se.~a c~c- mm. m~.H nn.~ Nm. wN. mo. 0H.H o~.~ mN.H mH.¢ mn.¢ 50.: mm.a moan mo. cc.~ n~.H vm. wN. cc. m~.~ Hn.H o~.H on. ma. mn.s mo.c mama Hm. mm. ma. mm. w~. we. mH.H Hm.H w~.H om. we. Ho.c ov.c nae me. mu. an. be. mN. ca. 5H.H m~.H vN.H am. no. mg. ~v.u am me. no. mm. mm. nN. a“. mc.H a~.~ 5H.H om. me. HN. He.¢ mw.H HHH ammo: . . . .m. .MH H.m m.mH H.“H “._H cowam wcafi a aw Aaaaafiow cooav soaaaaw o>wumfiom amouom ooumow oaoucH cowuofiaaom vacuum: magnum: xuwmcow oapmwua> xucaou :owuaaaaom .momuwmcow cowumasnoq mzowum> new: mowucsoo pom .moanmwum> wouuofiom ou uuoamou new: mwaonomao: flaw uo>o xn wocuaa ucsosm owwuo>o mo xuwu«ummamuc.na enamh 81 The differences between short term and long term elasticities are smallest for percent forest land. This is due to the low entry/exit elasticity of .15 from probit equation 2 (Table 3). The small difference in elasticities implies that increasing access to forests/fuelwood will have the greatest influence on households that already burn wood. A change in household income has varying effects on the entry/exit and amount to burn decisions. The elasticity for entry/exit is .51 (at an income of $17,190); but for amount burned it varies at least from .15 to -2.54 (Table 12). The net long term elasticity is positive for most combinations of income and population density. Only at high densities or low incomes does overall woodburning decline with greater income. To the extent that annual heating degree days for an area do not persist at levels far from the mean, the main effect of changes in heating degree days will be to change the amount burned by woodburners. This degree of change is indicated by the short term elasticity which is .S to .6 except at-high population densities. If winter becomes persistently colder or warmer in an area the long term demand elasticity would be 1.1 to 1.3 (Table 13). 82 Long term elasticity with respect to relative price of nonwood fuel moves from less than one to greater than one as density increases. The elasticity is also much higher at lower relative prices where wood does not have as much price advantage. This means that increases in woodburning will be low in response to relative price increases to the extent that they occur in areas where wood already has a price advantage or where population density is low. When comparing the long term response of households to equal percentage increases in income and relative price at higher population densities, we find that the increase due to increased relative price exceeds the decrease due to increased income. This. means that overall wood use is likely to increase in densely populated areas as relative prices increase unless income increases at a faster percentage rate than relative price. Coherence between finding on what population density results in the most woodburning'per square mile. Lipfert t a}; constructed two single equation models to predict fuelwood use in individual counties.-S£’fl One purpose of these models was to estimate at what population density pollution from woodburning is greatest. His second, more detailed model, based on the same data as Model III §§Lipfert et 31. 1983. Residential fuelwood use in the United STates. flLipfert et a_1_. 1984. Empirical analysis of residential woodburning impacts. 83 estimated that wood use intensity is greatest at about 6000 persons per square mile (445 cords/sq. mi.). Model 111 estimates the highest wood use per square mile would be at 163,000 persons/sq. mi. This density is greater than for Manhattan (62,099 persons per sq. mi.). The estimate by Model III is too high given the finding in Table 8 that Model 111 overpredicts substantially for densities above 6000 persons per square mile. Lipfert's model gives a more realistic level of maximum use but does so by using a more rigid single equation model. Model III's more flexible form allows data from lower density counties to dominate determination of parameters in a way that causes overpredictions for the relatively few high density counties. In Model 111, the weight of observations in high density counties is not sufficient to cause the regression procedures to calculate parameters that predict wood use well at high densities. Validation by Pragmatic Uses How well does the model serve to guide or stimulate inquiry about fuelwood use behavior? This modeling effort raises a number of questions and conjectures worth further consideration in efforts to predict fuelwood use behavior. First, a household's fundamental view of the value of woodburning may differ depending on life styles predominant in various population density-income classes. Households in low' density areas with middle to high incomes view 84 fuelwood as a normal good. They want to use more of it as they become more affluent. Low income low density households and high density households consider some use of fuelwood to be desirable as they become more affluent, but, the desirable amount to be used goes down with increasing income. Second, Model 111 suggests availability of forest land increases fuelwood use. But we do not know what availability characteristics of forest land would cause more or less fuelwood use. What are the influences of public vs. private ownership, size of ownership, species, and management activities? Third, the probit equation in Model III predicts well, but the amount equation predicts amounts burned poorly for some counties. Can aggregate fuelwood use be predicted well with any equation using aggregate county characteristics, or are equations predicting individual household use needed for accuracy? There are a number of ways an aggregate model might be improved. - Use separate probit models to estimate the likelihood of use by oil, natural gas electricity and "other" fuel users - Use separate equations to predict amount burned by woodburners who use oil, natural gas, electricity or "other" fuels. 85 - Change the amount burned equation to allow greater change in the influence of variables at high population densities. - Change the amount burned equation to allow for a varying influence of income depending on both relative price of nonwood fuel and population density. The model developed here is pragmatic for researchers to the extent that the foregoing suggestions lead to better empirical models. The model will be pragmatic for local state or national officials to the extent that they use predictions of county fuelwood use given in the next section. V. IDENTIFYING COUNTIES WITH HIGH INTENSITY FUELWOOD USE Model 111 was used to estimate intensity of fuelwood use in each county in the continental U.S. Five measures of use intensity were used to rank counties. Tables 14-17 show the 10 counties in each of 9 regions which have the highest intensity use according to the following measures: - percent woodburners - amount burned per woodburning household - average amount burned over all households - amount burned per square mile of county. Information on population density of counties is included in the listings to show if a county has over 6000 persons per square mile and is therefore likely to have its wood use overpredicted. Counties ranking high in a particular intensity of use have certain characteristics in common. For example, counties with a high percentage of burners have small populations, low population density, high heating degree days for their region, substantial forest land and high relative price for nonwood fuel. It is somewhat surprising that these counties have low median incomes (except in the Pacific Northwest), since table 2 indicates percentage of burners increases with higher county income. In most 86 87 regions nonincome factors are most important in determining percent users in high use counties. The percentage of burners for the top 10 counties in each region ranges from a high of 86% in Mineral, Colorado to a low of 46% in Shannon, Missouri and Hampshire, West Virginia (Table 14). Counties with high amount burned per woodburning household are similar to those with a high percentage of woodburners. Forty-two of the 90 high percent user counties are also high amount burned counties. The high amount burned counties have more uniformly low income, more uniformly high percent forest land and more uniformly low population density. Amount burned per woodburner for the top 10 counties in each region ranges from a high of 6.01 cords in Hinsdale, Colorado to a low of 3.56 cords in Okanogan, Washington (Table 15). Counties with high use per household over all households are similar to those with high use under the previous two measures. In fact, fifty nine of the 90 counties with high use over all households are also on one of the previous two lists. Counties with high amount burned over all households are more uniformly low in population density than the previous two sets of counties. As for the preceding lists, they have low income, colder climate, substantial forest land and high relative price for nonwood fuel. 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This is because most fuelwood is cut by households themselves in their own counties. Three-quarters of all fuelwood is cut by households and half of these households d.-§2 Wood use in a travel less than 5.5 miles to cut woo county divided by forest area will give an indication of the harvest pressure on forest land. Estimates of percent forest land are not available for all counties or county equivalents listed by the Bureau of Census. For certain western states percent forest land is only available for groups of counties. For those cases averages were assigned to individual counties. In the east, a number of small cities are independent. In these cases percent forest land is set at 1%. In forming a table of counties with high use per square mile of forest, cities with one percent forest or with area less than 80 square miles have been excluded. Counties with higher forest use that meet these criteria have the following characteristics: - lower than median population density - lower than median percent forest land - higher than median income EQSkog and Watterson. 1983. Residential fuelwood use in 103 - contain larger cities. The two counties in each region with the highest forest use are shown in Table 19. A second more general way to identify where forest use is greatest is to estimate, for each state, the percent of fuelwood that comes from counties with high intensity forest use. To do this we first divided fuelwood use (40.5 million cords in 80-81) into intensity of forest use categories. Roughly equal amounts of fuelwood were consumed in counties with the following cords use per square mile of forest: (1) 0 to 40 cords per square mile of forest (2) 40 to 99 cords per square mile of forest (3) 99 to 306 cords per square mile of forest (4) more than 306 cords per square mile of forest Independent cities, or counties with only 1% forest land were placed in a 5th category. The first four categories contain 23% of U.S. fuelwood use each. The fifth category contains 8%. Table 20 shows which states have a relatively large fraction of fuelwood consumed in counties with high use per square mile of forest. The following states have 70% of their fuelwood coming from counties in categories 3 or 4: Connecticut, Indiana, Iowa, Maryland, Massachusetts, Nebraska, New Jersey, Ohio, Rhode Island, and thhington. These states are likely to have drain focused on fewer acres of forest land, possibly improving the prospects for 104 .mowucsoo mo nsouw e >om m> oumswummm <2 ~o> «escapee»; .om 22 mafifioeem mm mm 2°22 xmuuwmm <> xaou2<2 mm eN e<< 0222>2m<2 2> come>>xo=2 2> 2°22 ow << >~e >u22=o <2 xfioouoz mz n< Hue s<222<2 <2 xomofiee22 m2 <2 no> 2222.222; <2 >=onme22< <2 NN nnw «awesome 22 >>osomoeo2 <2 N moon <2o< eouN~ ofiopoon >2 o=><2 m2 N emee m>>o2<02222 22 22202202 m2 NH mmaN ecosgufim <2 22m N2 22mm omen cam >H e=<2>to2 2o 22. awwuooe a e m He Ne mo. avfluoam oo~ ac. .0.: am me no. oumzmaoa we an m an. uaowuuoccou we 2 ma Nn on. ovo>o~ou 5H en n~ 2H m om.H awcuomwfiau m cm as mm. mmmcmxu< em 0 cc mN. econ>>< NN mm ov me.“ m5onm~< 5 mm mN mN mN m.o< 4>>mcoucm .HmIOQGH .mfiwufiflou szfiw>wfiflw flw Om: Hmvhom MO xuwmcoucw 2n cowuoezmcou woozaosu fimwucowwmou mo moumawumo Ho>oH oueamcc.o~ edema 106 N2 2 22 N2. memoeo2 N 2N 2N 22 >2 N<. 22=omm22 n 2N NN <0. 2222mm2mm22 22 2N <2 2 o< Na. woomo==22 o< 0N a mN No.2 =2<2 an <2 <2 m>. «=2m2 a 2 N2 we N<. <=<2m2=o2 <2 22 N< <2 >2. >2u=2=u2 >2 NN <2 <2 2 eN. m2>22<22 2 22 2N 2N 22 <<.2 222222 2< 22 NN <2. 22222222 2 << 22 22 2 22.2 2222 <2 < N2 22. 222222 22222 2 >2 N< <2 2<.N 222222 222 22 2 2< <2 22. 222222 222 22 2< 22. >22222 222 <2 2N 2N 22. 222222222 222 2 <2 <2 oz <2 2< >2 2 2N. 22222222 Ameueo «cucucrcfine2uoszmeeu eumum Haney we ueoouoevuccccucctu 2e2222av Mmowuceeo ameuem eon :e2uqsamceu 222 <22 2222 <22 22 22 22 22 2< 2< <2 2 222252222 <2<22 22222e 2222 Aumeuem we 0225 oumsum >oq meneov xueseo e 22 em: vee32osm we xuwmeeucH A.v.u:ouv o~ oHAMH 108 .e23222222 22 umouem acouuon we oumswumo ca 02023 amouem e22222 :22: mowucaeu mouaaocu .umepem acoeueo we eumswumo e: o>2n can acevceqeve2 own 2222 memuwu moe:2ecaw 22 2< 22. 22222>2 < 2N 22 2222 2 22 <2 2 <2 22.2 2222222222 <2 <2 22 <2 <2.2 2222222> <2 N< 2N 22. 22222o> 22 22 22 2N 22. 222: 22 2 N 22 estimate use for small geographic areas (counties or groups of counties). The models which project fuelwood use well over many years and require projection of the fewest exogenous variables may be different than the models which estimate near term local use most accurately. One type of long term projection model that could estimate use for groups of counties is a two equation supply/demand model based on the increasing amount of fuelwood use data for states or survey units within states. Fuelwood prices for a standard fuelwood commodity might be obtained for from newspapers. This type of model could also include such potential fuelwood supply influences as the intensity of pulpwood harvest and 117 pulpwood prices in an area. An advantage of this type of model would be that fuelwood price would be endogenous. Nonwood fuel prices, income and other factors would be projected exogenously in order to make projections. There are a :number of ways the county level model developed in this study might be improved. These ideas may also help form small area models with different structures. A key notion used in the model developed here is that county characteristics have varying influence depending on population density. But, in less densely populated rural areas the fact that the households are rural may be all that is needed to characterize the influence of other variables. That is, the influence of income, prices and access to forests may not be much different over a wide range of rural population densities. For predominantly rural counties, use of population density as a modifier has the flaws that it (1) does not directly measure the predominance of rural households and (2) it distinguishes between lower and higher density "rural" areas, which may not be necessary. In more predominantly urban areas the influence of varying population density may be more important. If the modifying influence of both prevalence of rural or urban households and density in more urbanized areas cannot be included in one model, then counties with different degrees of urbanization might be modeled separately. 118 Another problem with the use of population density in the model is that fuelwood use per square mile is projected to increase to unrealistically high levels at high population densities. To prepare a model that would predict amounts burned well at high densities a sufficient sample of woodburners in high density locations is needed. If prediction at higher densities is important for assessing wood stove pollution then extra data collection in high density areas may be needed. If sufficient data is available, overprediction at high densities might be prevented by structuring an amount burned equation so fuelwood use per square mile must decrease beginning at a density to be determined by parameters in the model. This approach was taken in Lipferts' models. The probit equations used here could be improved by allowing the influence of income to vary with population density (or degree of urbanization). Although participation increases with income at all densities the increase in percent burners per unit increase in income is greater at lower densities. The probit equations used here estimate the probability of woodburning without determining whether a stove or fireplace is used. It was assumed that households estimate the difference in utility between burning and not burning by weighting economic factors in the same way regardless of whether they intend to burn wood in a stove or a 119 fireplace. It would be more realistic to assume economic factors are weighted somewhat differently in making the two decisions. This suggests that a multinomial logit or probit model might be used to predict percentage of stove users and percentage of fireplace users separately for a locality. Separate equations would be needed to estimate amounts burned. Such a model would require data for individual households (or possibly groups of households), on equipment used, amounts burned, and on county characteristics. These data might be provided by the trienneal Residential Energy Consumption Survey conducted by the Energy Information Administration (EIA) of the U.S. Department of Energy. It would be relatively easy to develop models which estimate individual household fuelwood use based on characteristics of the individual households using data from EIA surveys or the data used in this study. Although the models would identify the economic influences on individual household fuelwood use, they could not estimate local fuelwood use or project fuelwood use unless a sample set of households with their characteristics were available for each locality. Sets of sample households may become available from the 1980 Census of Population and Housing but they may not be grouped by units as small as counties. In order to project fuelwood use a sample set of households would have to be produced for the year and locality of the 120 projection. Regardless of whether projection or local use models are the target of research it will be important to link the influence of other wood harvesting and marketing activities (pulpwood and sawtimber markets) to fuelwood use and eventually to include well constructed fuelwood use models in larger models which predict prices and consumption in pulpwood and sawtimber markets. VII. APPENDIX - DATA SOURCES VII. APPENDIX - DATA SOURCES Probit Equations 1 and 2 The Residential Fuelwood Use Survey conducted by the U.S. Forest Service in 1981 interviewed 5506 households; 1874 had burned wood within the prior 24 months.-61 From respondents we learned (1) their county of residence, (2) whether or not they burned wood and (3) how much wood they burned during the preceeding 12 months. The survey was conducted from August through October, 1981. The probit model dependent variable was 0 or 1 depending on whether or not a household burned wood. The probit model independent variables were characteristics of the household's county of residence. These characteristics and their sources are as follows: Heating degree days: 40 year average heating degree day data by county (65 degree F basis), data tape from the Department of Energy (Mike Lawrence); 1981. Median household income (1979): Census of Population and Housing, 1980: Summary tape file 3C [machine-readable data file]/prepared by the Bureau of the Census -- 61Skog and Watterson. 1983. Residential Fuelwood use in the United States. p. C-3. 121 122 Washington: The Bureau [producer and distributor], 1982. (Table 69). Average nonwood fuel price: Prices for natural gas, fuel oil and electricity in "S/MMBtu input" were converted to "S/MMBtu output" by dividing by average conversion efficiencies of 61%, 66% and 100% respectively-91 Prices were weighted by the percent of households using each fuel as their main fuel in the county. Prices are from Los Alamos National Laboratory, 1980 Residential fuel price data base for solar heating market analysis. Percent of households using each fuel is from Census Summary tape file 3C (table 112). Average fuelwood price: Respondents from the 1981 Residential fuelwood use survey gave the prices paid for their most recent purchase of fuelwood. Prices per cord for respondents purchasing approximately one cord were averaged for urban and rural areas within nine regions. Average fuelwood price for a‘ county was estimated by weighting urban and rural prices for the region by the fractions of urban and rural population in the county. The source of fuelwood prices is the Residential fuelwood use, survey conducted by the U.S. Forest Service in 1981. The source of fractions of urban and rural households is the Census Summary tape file 3C (table 1). 22D.L. O'Neal. 1978. Energy and cost analysis of residential heating systems. ORNL/CON-ZS. (Oak Ridge, TN): Oak Ridge National Laboratory. 64 p. 123 Percent forest land: Forest land area and total land area for individual counties (or groups of counties in the West) is from the most recent forest survey reports for individual states published up to 1983 by USDA Forest Service Experiment Stations: Intermountain, Ogden, UT; North Central, St. Paul, MN; Northeastern, Broomall, PA; Pacific Northwest, Portland, OR; Pacific Southwest, Berkeley, CA; Rocky Mountain, Fort Collins, CO; Southeastern, Asheville, NC; Southern, New Orleans, LA. Population density: Calculated by dividing county population by county area. County population is from Census summary’ tape file 3C (table 1). County’ area is from: County and City Data tape, 1977; [machine-readable data file] prepared by the Inter-university consortium for Political and Social research, Ann Arbor, MI based on the County and City data book, 1977, published by the U.S. Bureau of the Census. (variables 11 and 12). Fraction of households using various types of heating equipment: Census Summary tape file 3C (table 111). Fuelwood Consumption Equations (18), (19) and (20) Fuelwood consumption. equations for ‘woodburning households were estimated using amount of fuelwood consumed by 1874 woodburning households interviewed for the Residential fuelwood use survey in 1981. Independent variables were the characteristics of the county where the household was located. 'Four of the five county variables 124 used are the same as for probit equations 1 and 2: median income for 1979, population density, heating degree days and percent forest land. Relative nonwood fuel price is the average nonwood fuel price for the county divided by the average fuelwood price for the county (see sources listed for probit equation variables). County Variables Used to Subdivide Households Tables 5 through 8 show percent of households burning wood and amount burned for households groups by county characteristic. Most of the county characteristics used to subdivide households are the same as variables used in the probit and fuelwood consumption equations. Two additional county variables are also used. Their sources are as follows: Percent rural population: Census Summary tape file 3C (table 1). Percent home owners: Census Summary tape file 3C (table 97). VIII . LITERATURE CITED VIII. LITERATURE CITED Brown, A. and Angus S. Deaton. 1972. Surveys in applied economics: models of consumer behavior. Economic Journal 328(82):ll4S-1235. Carlson, E. 1983. Smoke from wood becomes big polluter in northern U.S. Wall Street Journal. October 4. Deaton, Angus and John Muellbauer. 1980 Economics of Consumer Behavior. Cambridge University Press. 450 p. Esvelt, Terrence G. and Mark L. Roberts. 1980. The use of wood for residential space heating in the Pacific Northwest. Bonneville Power Administration, Portland, OR. Presented at solwest 80, Aug. 6, Vancouver, BC. 5 p. Field, D.B. 1982. Economic benefits from harvesting in forest management. pp. 67-81. In Proceedings of Fuelwood management and utilization seminar, Nov. 9-11, 1982. East Lansing, MI: Michigan. State 'University, Department of Forestry. 151p. Forrester, Jay W., and Peter M. Senge. 1978. Tests for building confidence in systems dynamics models. Massachusetts Institute of Technology, Alfred P. Sloan School of Management, Systems Dynamics Group paper D-2926-4. Cambridge, MA. Gill, John D. 1982. Wildlife and other multiple use considerations. pp. 106-109. In Proceedings of Fuelwood management and utilization seminar, Nov. 9-11, 1982. East Lansing, MI: Michigan State University, Department of Forestry. 151 p. Hardie, Ian W. and Aziz A. Hassan. 1984. An analysis of residential demand for fuelwood in the United States. Unpublished report to USDA Forest Service Northeastern Forest Experiment Station, Broomall, PA. 59 p. 125 126 Hardie, Ian W. and Paul F. Scodari. 1982. A model of residential demand for fuelwood. University of Maryland Department of Agriculture and Resource Economics Scientific Paper .A-330. College Park, MD. 61 p. Harris, Michael. 1980. The boom in wood use: promise or peril. American Forests 86(9):57-6O (September). Hartman, Raymond S. 1978. A critical review of single and interfuel substitution residential energy demand models. Massachusetts Institute of Technology Energy Research Lab Tech. Report MIT-EL-78-OO3. Cambridge, MA 121 p. Hartman, Raymond S. 1979. A generalized logit formulation of individual choice. Massachusetts Institute of Technology Energy Research Lab, Working Paper MIT-EL-79-010WP. Cambridge, MA. 28 p. Hauseman, John A. and D. A. Wise. 1978. A conditional probit model for qualitative choice: discrete decisions recognizing interde endence and heterogeneous preferences. Econometrica 46 2):403-406. Heckman, James J. 1976. The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. Annals of Economic and Social Measurement 5(4):153-16l. Heckman, James J. 1979. Sample selection bias as a specification error. Econometrica 47(1):153-6l. Henderson, Leslie. 1981. Greenbacks for green junk. American Forests 87(4):12-15 (April). Institute for Research on Poverty. 1984. Probit-version 6. An unpublished computer program. Madison: University of Wisconsin. Kaplan, Abraham. 1964. The Conduct of Inquiry. Scranton, PA: Chandler Publishing Company. 428 p. Lipfert, Frederick W.; Leonard R. Dupuis, Mary Daum, and Arnold Srackangast. 1984. Empirical analysis of residential woodburning impacts. An unpublished report to the Office of Policy Analysis, U.S. Environmental Protection Agency. Washington, D.C. 127 Lipfert, Fredrick W. and Jennifer L. Dungan. 1983. Residential fuelwood use in the United States. Science 219(25 March 82)1425-l427. Los Alamos National Laboratory. 1980 residential fuel price data base for solar heating market analysis. Unpublished data for 220 U.S. regions obtained from Fred Roach. Los Alamos, NM (1982). McCurdy, Dwight R. and John H. Burda. 1984. Highlights of wood for energy in Illinois 1982-1983. Carbondale, IL: Southern Illinois Univ., Dept. of Forestry. 21 p. Minnesota Dept. of Natural Resources - Forestry. 1981. Minnesota residential fuelwood demand, l979-80. Unpublished report. St. Paul (October) 9 p. Murphey, W.K.; J.G. Massey, P.R. Blankenthorn, and T.W. Bowersox. 1981. Some implications of using wood as a fuel. Southern Journal of Applied Forestry 5(1):l6-19 (February). O'Neal, D.L. 1978. Energy and cost analysis of residential heating systems. ORNL/CON-ZS. Oak Ridge, IN: Oak Ridge National Laboratory. 64 p. Perkey, Arlyn W. 1981. The New England fuelwood project. American Forests 87(8):13-15 (August). Seidl, Robert. 1980. Energy from wood: a new dimension in utilization. TAPPI 63(1):26-29 (January). Skog, Kenneth E. and Irene A. Watterson. 1983. Residential fuelwood use in the United States: 1980-81. ADA 131724. Springfield, VA: National Technical Information Service. 150 p. Skog, Kenneth E. and Irene A. Watterson. 1984. Residential fuelwood use in the United States. Journal of Forestry 82(12):742-747 (December). State of Connecticut Office of Policy Management - Energy Division. 1984. Residential wood energy users survey. Unpublished report. 17p. + appendix. Travis, Curtis C., Elizabeth L. Etnier and H. Robert Meyer. 1985. Health risks in residential wood heating. Environmental Management 9(3):209-216. 128 Tritton, Louise M. and Thomas C. Siccama. 1977. The fallacy of playing pick-up-sticks fuelwood. Connecticut Woodlands 42((4):17 (Winter). USDA Forest Service. 1982. An analysis of the timber situation in the United States. Forest Resource Report 23. Washington, D.C. 499 p. USDOE Energy Information Administration. 1983. Residential energy consumption survey: consumption and expenditures, April 1981 through 1982, part 2: regional data. DOE/EIA-0321/2(81), Washington, D.C.: U.S. Government Printing Office. USDOE Energy Information Administraiton. 1984. Estimates of U.S. wood energy consumption, 1980-83. DOE/EIA-034l(83), Washington, DC: U.S. Government Printing Office. 61 p. Van Hook, R. 1.; D. W. Johnson, D. C. West, and L. K. Mann. 1982. Environmental effects of harvesting forests for energy. Forest Ecology and Management 4:79-94. HICHIGRN STRTE UNIV. LIBRRRIES ||)llHHII"IIIIHWIWINIIHIHIHIIWIIlilil‘llllHl 31293106888468