W2llllllllfllllm / 2 ‘““ LIBRARY Michigan State University This is to certify that the dissertation entitled ENERGY TAX CREDITS AND HOUSING IMPROVEMENT presented by MICHAEL JAMES WALSH has been accepted towards fulfillment of the requirements for PhD degree in Economics . /M Major professor nateMfi'? 2:9 /7 MCi where (private) MBi - DU{ til DFit*Pfte + st e’rT) i where: DU - change in utility as a function of changes in future income MCi - marginal cost of improvement 1 T - final date of occupancy for current household DFti - reduction in fuel use resulting from item i at time t - Fti - F o where F is fuel consumption in period t In the absence of item 1 Pft - fuel price in time t DSV1 - change in sales price of the residence resulting from the presence of the improvement t - time period subscript, r is the consumer's discount rate This is similar to approaches used by Isakson (1983), Johnson and Kaserme (1984) and Hirst and Goeltz (1984). This analysis assumes that any improvement increases the non-depreciating stock of energy capital for an indefinite period. Again, this approach ignores the increases in comfort and the social benefits which adoption of cOnservation equipment may imply. Presumably one could add a term to the .On ta 58 ’al: 951 'w L.I 20 account for ”public" benefits from energy savings to the marginal benefit expression to make it a more complete measure of private and public benefits (See Johnson and Raserme). Expression 5. indicates that the level of desirable investment rises (other factors held constant): 1) the lower the after-tax price of improvements ii) the greater is DF; the more fuel saved by a particular capital improvement iii) the higher is Pft; i.e. higher future fuel prices iv) the higher is sti; i.e. the higher the proportion of the value of reduced operating" expenses that are capitalized into the sales price of the residence v) the lower the discount rate applied to future reductions in fuel outlays vi) the larger the increase in utility as future income rises Conclusions 1) and iii) are essentially the same as the results of the static cost-minimization model. ggtg11§_p§;1bg§, a larger number of future periods of fuel savings makes more conservation improvement desirable. If, however, consumers believe that some portion of the value of weatherization is capitalized into the sales price of the residence (there is some evidence in support of capitalization, see Johnson and Kaserme) then the influence of expected home tenure on Optimum improvement depends on,the discount rate applied to that increase in resale value and the proportion of value believed to be capitalized into the home price. The tenure and capitalization factors are particularly relevant for analyzing the behavior of renters (those who directly pay their fuel bills and improvement costs). Because renters tend to stay in a particular dwelling for a shorter time than owner-occupants, an improvement made at the expense of the renter is 21 attractive only if it pays for itself very quickly. Also, the future increase in rent or enhanced marketability of a rental unit that may result from better energy efficiency will not benefit current renters at all. Another implication of 5. is that higher future fuel prices make it optimal to undertake more weatherization. Larger fuel price increases make larger weatherization improvements attractive for two reasons: an unimproved structure will be farther from the optimum mix of fuel and capital the larger the price increase, and an adaptive approach to predicting fuel price increases leads to expectations of even higher future prices and potential savings. This point may explain why many households waited until 1979 or later to install energy efficiency improvements. Between 1973 and 1979 real residential fuel prices rose 2.8% for electricity, 6.9% for natural gas and 8.25% for fuel oil. These were greatly exceeded by the increases of the three year period of 1979-1981 when prices rose 5.4% for electricity, 9.9% for natural gas and 19% for fuel oil (U.S. Department Of Energy, 1983). Conservation ‘measures which did not appear to be economically attractive before 1979 suddenly became economic when larger fuel price increases occurred and Suggested the possibility of even higher fuel price growth rates in the future. The result which causes monetary benefits from efficiency improvements is, of course, a reduction in fuel consumption. The magnitude of reduction depends on the level of pre-improvement fuel consumption. A.higher marginal product (fuel use reduction) of conservation devices increases the return on investment thus making these purchases more desirable. The proportionate reduction in fuel use 22 from adding, for example, three indhes of attic insulation, is larger the more poorly insulated is the structure before its addition. This reflects diminishing marginal productivity of structural weatherization as demonstrated in the following figures taken from engineering-cost analyses. heat flow .3 \ (Btu/hi. .2 per £8 per F .l temp. diff.) 0 T‘— 1 2 3 4 5 6 7 8 9 10 insulation thickness (inches) Figure 1 HEAT FLOW AS A FUNCTION OF INSULATION THICKNESS Source: U.S. Department of Agriculture, 1975 single Btu/hr. pane | 1050 I heat loss through fixed double| 519| windows (per 10 sq. ft.) trip1e|339 I Figure 2 HEAT FLOW THROUGH GLASS FOR SINGLE, DOUBLE AND TRIPLE PANE WINDOWS Source: Small Homes Council, Univ. of Illinois, 1979 23 A lower initial level of insulation implies a higher available marginal product for a given increase in the insulation level of a structure. This raises the value of the marginal benefit expression thus making weatherization investments more attractive. In summary, the hypothesis just developed is that changes in the amount of energy saving capital will be negatively correlated with initial levels of this capital stock. CONSTRAINED UTILITY MAXIMIZATION MODELS Consider a simple model of utility maximizing behavior in the consumption of home temperatures. Note that it is the demand for comfortable home temperatures that yields the derived demand for fuel and capital inputs. Just as the cost minimization model for temperature production dictates substituting capital for fuel when fuel prices rise, utility maximization prescribes substituting away from consumption of home heat towards other goods as the relative price of heat rises. Also, as depicted in Figure 3, the income effect of a fuel price increase shifts the heat vs. other goods budget constraint inward, thus forcing lower consumption of other goods as well (assuming "other goods” are normal goods). This increase in ”temperature" price results as the price of fuel inputs rises. A household optimizing in both consumption and production will "consume" less heat and, as suggested by cost minimization models, be less fuel intensive in producing heat. 24 other goods 00 \ \ MUD O \\\\\\\\ l \\—u p \ l \ a T. To temperature control Figure 3 "OTHER GOODS”/TEMPERATURE CONTROL INDIFFERENCE CURVES AS FUEL PRICE INCREASES Models that include both preferences and production are now examined. These are used later in the formulation of appropriate behavioral models for evaluating the influence of prices, income, policy and other factors on conservation capital adoption rates. Some of these models are found in the optimal housing maintenance literature and are adapted for the current purposes, while others were specifically developed for analysis of energy conservation investments. The household problem of how much to increase the stock of imbedded energy-related capital in a current residence is not fundamentally different from the problem of sustaining the right pace of overall housing maintenance and improvement. Any allocation of resources for upkeep or betterment of a dwelling is presumably done to provide future benefits in the form of higher housing quality ("utility" return on investment; more comfort etc.) lower "operating" costs (smaller fuel bills) and/or a higher resale price (pecuniary return on investment). The following analysis pursues this line of thinking in development of marginal conditions for optimum housing maintenance schedules. 25 In seeking to maximize the utility provided by their dwelling, households typically allocate improvement and maintenance expenditures over a wide variety of home improvements. Households can be assumed to maximize some combination of visual attractiveness, location, convenience and comfort from a dwelling subject to a housing cost constraint that includes "fixed" costs such as mortgage payments, operating costs and improvement expenses. Reducing the operating cost (fuel cost) portion in the cost constraint causes an outward shift of the heat/other goods isocost lines. Investments in weatherization may thus allow the household to attain a higher indifference surface in the future. As fuel prices rise, expenditures for energy efficiency have a greater marginal effect on shifting out (or avoiding an inward shift) operating cost isocost functions, thus making such expenditures more attractive compared to other improvement options. This change shifts the ”best" maintenance path toward investments in energy efficiency. Dildine and Massey (1974) and Sweeney (1974) formalize the above approach. They examine the problem faced by landlords in deciding the best strategy for maintaining rental units in order to maximize their net lifetime rent. When analyzing homeowner optimization related to housing consumption and investment, the problem becomes one of long run utility maximization of owner-occupied housing. The landlord's problem in the Dildine and Massey paper is to maximize after-cost rents, a discounted stream of per unit rents times the number of housing quality units minus operating and improvement costs (expenditures on the latter affect quality and gross rental value). This optimization is subject to a differential equation that 26 describes the time path of housing quality as a function of improvement inputs and quality depreciation rates. Similarly, Sweeney's approach considers optimum maintenance paths for a utility maximizing owner-occupant. The owner is assumed to maximize expression 6., economic surplus: T 6. U - f [W(Q) - C(M,Q,t)]e-rtdt 0 t + SV[Q(T). Tle'r - SV(QO.0) where W(Q) is the owner-occupant's willingness to forego other goods and services in order to consume housing services having quality Q. This "willingness to pay" is assumed to measure willingness net of current costs such as property taxes and heating bills. The other arguments in the objective function are: C(M,Q,t) - costs of maintenance as a function of: M, rate of maintenance, Q, housing quality t, time period and r - discount rate SV - sales value of dwelling T - final period Q0 - initial quality of the dwelling. The household is assumed to choose an optimum path of M and Q and would not purchase the dwelling unless U 2 0. If U < 0, another residence would be purchased or rented. The first order condition from the Hamiltonian optimization gives a maximization of surplus to the owner-occupant (willingness to pay minus costs plus revenue from the sale of the unit minus initial cost). The maintenance path M* is Optimal if the marginal cost of all M*(t) (the "quantity" of maintenance purchased in period t) equals its marginal contribution to the value of 27 the housing unit. This rule is the dynamic analog to the Optimum conservation investment rules derived earlier in the chapter. Investments in energy efficiency fit in this Optimization process by increasing Q, the quality of a dwelling (by making it more comfortable) or by reducing C, the cost of "maintaining" the dwelling. In either case the goal is presumably to increase economic surplus. These dwelling improvements and Operating cost reductions are compared with the costs Of making the improvements to yield the Optimum improvement path. As was found in other models, the Optimum quantity of improvement rises with reductions in the price of improvements or reductions in the discount rate, and increases as the marginal effect on quality or Operating costs rises or as the number Of time periods over which benefits are enjoyed increases. One novel but sensible result from this model is that energy efficiency investments which drastically reduce the visual attractiveness or increase the inconvenience of living in the home (reductions in Q) may be undesirable as these disadvantages might overwhelm the value the owner places on the resulting reduction in fuel bills. Alternatively, these problems may reduce the resale value of the residence. A recent paper by Karp (1984) uses a utility maximizing approach for explicit analysis Of consumer demand for insulation and fuel. The first stage of the two stage model determines the desired level of non-negative insulation upgrade. The second, done first, minimizes daily disutility of heating, a weighted sum Of discomfort from ”too cool” rooms and the cost Of heat. The second stage minimizes expression 7., daily disutility, with respect to X, fuel consumption. i: 28 d 24 7. u(X(t)) - f (w/2)(T* - T(t))dt + f cX(t)dt o o weighting parameter giving the dollar equivalent Of the disutility of the deviation of actual temperature from ideal temperature d - number of hours per day occupants are concerned about dwelling temperature where: w T* - ideal indoor temperature T(t) - actual indoor temperature setting c - cost of a unit of energy X(t) - rate of consumption of energy at time t subject to a temperature dynamics function approximated by: [A/RhVCp1Ta so T - Ta/T*. R1 - R0 + R' - thermal quality in the future period - initial thermal quality of the dwelling (R ) plus R' thermal improvement occurring in the current period "a" and "b" are utility parameters assumed to be less than one. The temperature control level in the "current" period is not included in the utility function because it assumed to have been chosen prior to the conservation improvement decision and is thus irrelevant to the choice of optimum thermal improvement. The first-order condition for °Ptimum R', thermal improvement, can be derived if the relationship ‘ 2This temperature control variable is similar to that described in Karp, (1984). 34 between fuel consumption and thermal quality is added to the model. A simple technical expression for (heating) fuel consumption along isotherm Ta is 12.3. 12. F - (Ta - E)Ah/R1 Thus heating fuel consumption rises with Ta, actual indoor temperature and A, area being heated (assumed exogenous here) and falls as external temperature (E) or thermal quality (R1) are higher. h is an exogenous physical parameter. The second derivative of F with respect to R is positive, implying diminishing marginal fuel use reductions as R is increased. When TT* is substituted for Ta, the partial derivative of F with respect to R1 is: 13. aE/aR1 - -(TT* - E)Ah/(R1)2 Expressions 14. and 15. are the first-order conditions for the choice variables R' and T. These are derived by computing the unconstrained maximum of U with respect to R' and T (budget constraints are implied in the Objective function). Because the maxima are computed by taking partial derivatives with respect to the choice variables, the influence of an increase in R on the optimum level of temperature control (aT/aR'), is ignored when the optimum increase in R is derived. 14. aU/aR' - ayoa‘l + bDY b'lrl‘b 1 (-Pf){-(TT*-E)Ah/(RO+R')2|To } - o 3The isotherm expression is derived from the temperature dynamics approximation described in Kreith and Black. 35 15. aU/aT - (l-b)DY1bT'b + DY b-lTl-b b 1 (-Pf)[T*Ah/(RO+R')] - 0 Expression 14. includes the utility reduction implied by a current period expenditure on R' and the utility increase implied by increased future period "other goods" consumption that result from the fuel savings as R is increased. The latter is the magnitude of fuel savings multiplied by P the price of fuel. (-P is also the derivative of net f’ f income with respect to fuel consumption). The second term of 14. expresses the utility of fuel savings resulting from an increase in R if T were held constant at T0 (the assumed level of current period temperature control). It is useful to rearrange 15. and express optimum future period temperature control as a function of R Expression 16. shows this 1' relationship: 16. optimum T - [(1-b)/T*]{Zl(Ro + R')/PfAh + E} Optimum future period temperature control is a positive function of the utility parameter for temperature control (l-b), gross income (21), the degree of thermal integrity (R1) and external temperatures, and is negatively related to the utility parameter of net income (b), fuel prices (Pf) and home size (A). Expression 16. indicates that the optimum value of T is an implicit function of R'. Also, the optimum value of R' depends on the chosen future level of T. Thus it is not possible to solve for a single expression to describe the optimum value for R'. In order to determine the direction of influence of energy tax credits, energy prices and other exogenous variables on the optimum amount conservation 36 improvement, it is necessary to take advantage of the fact that 14. and 15. are a pair of simultaneous equations that are both implicit functions. An approach described by Chiang (1974) is used to determine the signs of comparative static derivatives of optimum R' with respect to the exogenous variables of interest. THE GENERAL APPROACH Equations 14. and 15. are the specific expressions for aU/aR'and aU/ar. It is convenient to use their general forms in the derivation of the formulae for comparative-static derivatives of the optimum R'. Renaming l4. and 15. as F1 and F2 we have: 17. F : aU/aR' - (aU/aYo)(aYO/8R') + (aU/aY1)(aY1/6F)laF/8R'ITO} - o 18. F2: dU/aT - aU/BT + (6U/6Y1)(8Y1/6T) - 0 In order to explain the general approach, the partial derivative of optimum R' with respect to P the net-of-tax-credit price is now R! presented. The procedure requires that the other variables be held constant. If one takes the total differential of 17. and 18., sets all differentials except dP equal to zero and rearranges terms, we have: R 1 1 1 19. (as /aR')dR' + (8F /6T)dT - -(aF /8PR)dPR 2 2 2 20. (3F /8R')dR' + (6F /8T)dT - -(aF /8PR)dPR Dividing each side by dPR yields: 21. (aFl/aR')(dR'/dPR) + (aFl/aT)(dT/dPR) - -(aFl/6PR) 37 22. (an/aR')(dR'/dPR) + (an/aT)(dT/dPR) - -(aF2/6PR). These equations can be expressed in the general matrix form Ax-b which is: 23. aFl/aR' aFl/BT dR'/dPR -(8F1/8PR) 8F2/6R' aFZ/ar dT/dPR -(aF2/6PR) Assuming the determinant of the "A" matrix is positive as required by the second order conditions for a maximum, Cramer's rule indicates that the sign of dR'/dPR is the same as the sign of (-F1PR)(F2T) + (FZPR)(F1T). (Because the other exogenous variables are held constant, the derivatives dR'/dXi can be interpreted as partial derivatives. Thus those derivatives are hereafter labelled aR'/8X1.) Because F2PR is equal to zero and FZT is negative (it is the second derivative of U with respect to T) it is only necessary to determine the sign of F1 1 PR PR to sign 8R'/8PR. From 17., F is found to be: FIPR - (a-l)a(Zo-R'PR)8'2(-R')(-PR) + (-l)a(Zo-R'PR)a-1 Because a 0 26. Y - 0 ,if R' - 0. This approach yields a "qualitative" dependent variable that is a function of continuous and qualitative independent variables. The Linear Probability model is used to examine the linear relationship and degree of explanatory power of the "improvement"/"no improvement" specification of the conservation improvement model. Because the Linear Probability model has some well known difficulties, Logit estimates of the "improvement”/”no improvement” regression are also presented. RESULTS Table 8 shows results from Linear Probability regression estimation of expression 27. for three different samples. The dependent variable in 27. has a value of one for households that made any improvement and a 56 value of zero for households that did not make a conservation improvement. 27. where: (HID Yi - so + al(after-tax-price) + a2(income) + a3(future fuel price) + a4(yearmade) + a5(renter) + a6(age) + a7(HDD) + a8(CDD) + a9(sq ft of home) + a10(house) Y equals 1 for households who make a conservation improvement 0 0 for those who do not after- tax- -price- (1- t ) where t1 is the total available tax credit for household i. This is the after- tax- -price of spending $1 on conservation equipment. income - 1981 gross household income (in 1981 dollars) future fuel price - (current price)x(price growth rate of past four years) yearmade - an index of home newness; 0-pre-l940, (the "basis” level of dwelling age) 1-1940-50 2-1950-55 3-1955-60 4-1960-65 . 5-1965-70 6-1970-75 7-1976 8-1977 renter - 1 if household rents their current residence age - age of household head lflDD heating degree days cooling degree days sq. ft. of home - heated area of the residence hOuse - 1 for households that live in single-family dwellings Descriptive statistics of data used in these and later regressions are shown in Appendix D. Table 8 LINEAR PROBABILITY MODEL REGRESSION OF EXPRESSION 27. dependent variable - 1 if an improvement was made - 0 otherwise SAMPLE: independent variable: net-of-tax price income future fuel price year dwelling constructed renter age of hh head heating degree days cooling degree days sq. ft. of home "house" dummy N 2 adjusted R F-statistic (1) "WHOLE" .70 .14)** .0000012 .0000005)** .0023 .0013)* -.01 (.004)** -.28 (.02)** -.004 .0005)** .00004 .000006)** -.000033 (.000016)** .00004 .00001)** .17 .02)** 2911 .19 68 "WEST" (2) ONLY .13 .20) .0000010 .00000009) .01 .003)** .009 .007) .23 .04)** .0006 .001) .00005 .000009)** -.00002 (.00003) .00004 .00002)** .08 .046)* 787 .17 18 HOUSEHOLDS (3) . NON-"WEST" HOUSEHOLDS .64 (.74) .0000016 (.0000006)** .0003 (.001) -.009 (.005)* -.29 (.03)** -.005 (.0006)** .00002 (.000009)**. -.00008 (.00002)** .00003 (.00001)** .21 (.03)** 2124 .19 50 * : statistically significant at the 95% level of confidence ** :‘ statistically significant at the 99% level of confidence strong of the applie 039 ' ta indepe signs fuel ' singl likel :lima rente likel dwell Oldex are u the ' less ”701': head. house 58 With the exception of the net-of-tax price variable, theory strongly suggests negative or positive signs on the coefficients on each of the independent variables. Thus a two-tailed test of significance is applied to the coefficient on the net-of-tax price variable and a one-tailed test is applied to the others. The results in column (1) of Table 8 indicate that all the independent variables except the net-of-tax-price term have the expected signs. Households who have higher incomes, higher "expected" future fuel prices, older dwellings, larger dwellings, younger household heads, single-family units and who own their homes are, ceteris paribusu more likely to make a conservation improvement. Those who live in warmer climates, rent their dwellings and live in multi-family units (some renters live in single-family structures, some owners do not) are less likely to make an improvement. The negative coefficient on the "year of dwelling construction” variable indicates that households who live in older dwellings (those expected to have a lower initial thermal quality) are more likely to make an improvement. The negative coefficient on the "age of household head" variable indicates that older households are less likely to make an improvement. Households were also categorized as "young”, "middle-aged" and "older" depending on the age of the household head. When this form of the "age" variable was used, "young" households were still the most likely to make an improvement. The coefficient on the net-of-tax-price variable is posigixe and statistically significant in the "whole" sample regression. A negative coefficient would be evidence in support of the hypothesis that larger available tax credits stimulate conservation improvement activity. (A larger credit makes the after-tax-price term smaller). However, the s 50 fl Yale he “he ‘ 013g Veg Pro‘: risk SeFa hep $058 59 results from the "whole" sample regression indicate that households eligible for larger tax credits (primarily due to state of residence) are actually less likely to make a conservation improvement. 'When a dummy variable indicating the household lives in the Mountain or Pacific region ('west')°was substituted for the net-Of-tax price term in the "whole" sample ("west" and non-"west") regression, the coefficients on the other variables were essentially unchanged and the coefficient on the ”west" dummy was negagige and significant at the .01 level. The ”west" dummy performed just as well, with the same sign, as the tax credit variable. This suggests that the lower rates of conservation improvement among "west" households is a regional phenomenon that is spuriously correlated with relatively large conservation tax credits. Thus the aggregate trend that western region households were less likely to make a conservation improvement appears to hold even when the other relevant factors that are measured or proxied here are held constant. The lower rates of improvement among western households may reflect unmeasured differences in dwelling construction, expected home tenure or other important factors. To investigate the hypothesis that the estimated relationship for "west" households is different from the non-”west" households, Linear Probability regressions were also run on these two subsamples. The results are shown in the second and third columns of table 8. This separation yields results similar to the full sample regression, but the net-of-tax price term is not statistically significant in either of the subsample regressions. This result supports the contention that the 'net-of-tax price term in the "whole" sample is strongly correlated with some unmeasured characteristic common among western households. The ../_-1 IESl subs usir esti Bode reg: (\J C13 iv’her 6O explanatory power (R2) of each of subsample regression remains near that of the full sample. An F-test4 allows rejection (at the .01 level of confidence) of the hypothesis that the coefficients of the linear probability model regression of expression 27. are equal for the "west" and non-"west" subsamples. Because the estimates of the conservation improvement model are statistically different for the two regional subsamples, the results from additional regression analyses are reported for these subsamples only. To avoid the econometric problems inherent in an OLS regression using a binary dependent variable, the Logit technique was used to estimate the regressions discussed above. In the context of a Logit model, if the optimum increase in R for household 1 is labeled Y1*, a regression model of the relationship of interest is: 28. Y * - fi'Xi + u i i where the only observable value of Y * is Yi from 26.) (O or 1) and X i i aThe statistic to test the hypothesis that coefficients from regressions on two subsamples of data are different from each other is: [(RSSl+RSSZ) - RSSl]/k (RSSI+RSSZ)/(N + M - 2k) where: R88 are the residual sum of squares from each subsample regression, k is the number of regressors and N and M are the sample sizes of the two subsamples. is distributed Fk’ N+M-2k In each case that used this test statistic, the resulting F value was significantly significant at the 99% level of confidence, thus allowing rejection of the hypothesis that the coefficients in each subsample regression are equal. 61 is a vector of variables that influence Y1. Thus the probability that Yi equals one equals the probability that p'xi + 111 is greater than zero, or: 29. Prob(Y1-1) - Prob(ui > -fi'X . 1’ where F is the cumulative distribution function for u (Maddalla, 1986). The 8 vector is estimated by maximizing a likelihood function based on a binomial process for each Yi depending on the value of X for each household. The likelihood function is 30. L - n F(-p'x1) n [1 - F(-fi'Xi)] Yi-O Yi-l where F in the Logit model is the logistic distribution, i.e.: F(-fl'Xi) - 1/[1 + 8(fl X1’]. Table 9 shows results from Logit estimation of the "improvement"/ "no improvement" regression described by expression 27. for the two regional subsamples. Columns 1 and 3 show Logit coefficients estimated by an SPSS routine. Columns 2 and 4 show the partial derivatives of p, the probability of making an improvement, with respect to changes in each of the dependent variables. 62 TABLE 9 LOGIT ESTIMATES OF EXPRESSION 27. FOR ”WEST" AND NON-"WEST" HOUSEHOLDS DEPENDENT VARIABLE - l for households that made an improvement - 0 for households that did not make improvements SAMPLE: "WEST" HOUSEHOLDS NON-"WEST" ONLY HOUSEHOLDS 1 2 3 4 Logit aP/axi# Logit 8P/8Xi# coefficient coefficient net-of-tax-price .56 .209 1.55 .76 (-56) (2.08) income .0000021 .0000008 .0000037 .0000018 (.0000026) (.0000015)** future fuel price .032 .011 -.0018 -.00088 (.010)** (.0037) year dwelling -.025 -.0075 -.025 -.012 constructed (.013)** (.012)** renter -.79 -.30 -.78 -.387 (.15)** (.O8)** age of -.002 -.00092 -.013 -.006 household head (.002) (.001)** heating degree days .00014 .000053 .00005 .000025 (.00003) (.00002)** cooling degree days -.0001 -.000038 -.00023 -.00011 (.0001) (.00006)** sq.ft. of home .0001 .000038 .00005 .000025 (.00006)* (.00003)* "house“ dummy .36 .135 .62 .307 (-15)** (.09)** intercept 2.96 3.77 (,53)** (1.78)** .N 787 2124 Standard errors in parentheses * : statistically significant at the 95% level of confidence '** : statistically significant at the 99% level of confidence #=: evaluated at mean values of the independent variables 63 The increase in the likelihood of an improvement being made as a result of an increase in an independent variable, aP/axi calculated at the sample means of the X 's, is .38b1 for the "west" subsample (where bi is i the Logit coefficient of interest) and .494bi for the non-"west" subsample.S ° The Logit results are not greatly different from those of the Linear Probability regressions. The results for the "west" subsample indicate that residents of higher tax credit states are not more likely to make a conservation improvement than residents of states that have low or no conservation tax credits. Also, non-"west" households who are eligible for a larger tax credit do not appear to be more likely to make a conservation improvement, ceteris paribus. Because variation in tax credits among non-"west" households is primarily due to differences in federal tax filing status that was assigned to each household, and because that assignment process is only a rough approximation, less confidence is placed on the latter conclusion. As in the Linear Probability results, the age of household head (used to proxy expected tenure in the dwelling) is not statistically significant in the "west” Logit. If this result is not due to the smaller sample size being used, it suggests that the age of household head variable is not a good proxy for the underlying variable (expected home tenure) or that the underlying variable does not influence improvement activity in the west as it does elsewhere. 5SPSS uses the following specification for estimation of Logit coefficients: ln (p/l-p)/2 + 5 - X'fi. Thus the partial dgrivative of p with respect to X is: 28 exp[2X'fi-10]/(l + exp[2X'fi-10]) where 81's are SPSS Logit coefficients. (SPSS, 1986). The home ene coefficfi ofconf partici horove their 2 filter proper sigoii effeC‘ tredi were iIlptr “min: inte dist atti (the ear repr. Probe 1931, estim 64 When a dummy variable to indicate the household participated in a home energy audit was added to each of the above Logit regressions, its coefficient was positive and statistically significant at the 99% level of confidence. It is possible, however, that households who participated in an audit may have already been further inclined to make improvements and the audit supported that inclination or helped guide their spending. If the latter is true, the "audit" dummy acts as a filter that identifies those households that already had a higher propensity to make conservation improvements. Nevertheless, the significant positive coefficient does suggest that audits may effectively promote conservation improvement activity. To test the hypothesis that households eligible for a larger tax credit made "larger” improvements, two additional sets of regressions were estimated. Both utilize the "major"/"minor" categorization of improvements discussed above. It should be recognized that several "minor" improvements may actually yield a larger improvement in thermal integrity than a major improvement. Thus the "major"/"minor" distinction may not always accurately reflect a greater magnitude of improvement. The first approach using the "major"/"minor" ranking of improvement actions uses a scaled dependent variable to represent "no improvement" (the dependent variable is set equal to 1), "minor improvement" (-2) and “major improvement" (-3). Ordinary Least Squares estimation of this representation of the model has the same inherent problems as the Linear Probability model when a zero/one dependent variable is used (Amemiya, 1981, McKelvey and Zavoina, 1975). The appropriate technique for estimation when using an ordered qualitative dependent variable that can 65 have more than two values is a multinomial logit or probit. The latter is used here as computer software to estimate the model was available. The ordered multinomial approach assumes there is an underlying index 21 which, in the current case, describes the desired amount of conservation improvement for household 1. The only observed values of the dependent variable are l, 2 and 3. Thus the regression model: 31. 21 - a + 8x1 + :1 is estimated using Y a proxy for 2 where: i’ i’ 32. Y - 2 if pz 5 21 5 p1 where p1 and ”2 represent cut-off values for desired amounts of conservation improvement (Pindyck and Rubinfeld, 1981). A maximum likelihood routine for Probit estimation of the fi coefficient vector yielded the results shown in Table 10 for the two regional subsamples. The estimation technique normalizes the dependent variable so that the variance of 5 equals one and has a mean of zero. The second (lower) cut-off value (p2) is set equal to zero and p1 is estimated. 66 Table 10 MULTINOMIAL PROBIT ESTIMATES OF THE CONSERVATION INVESTMENT MODEL Dependent variable - 1 if no improvement was made - 2 if a "minor" improvement was made - 3 if a “major" improvement was made maximum likelihood estimates of the coefficients are shown, standard errors are in parentheses Sample: ”WEST" HOUSEHOLDS ONLY independent variable: net-of-tax-price income (in thousands) future fuel price year dwelling constructed renter age of household head heating degree days cooling degree days sq. ft. of home "house" dummy N -2 times log likelihood ratio ”1 ”2 **: statistically significant .11 .64) .004 .003) .03 .Ol)** -.03 (.025) .88 .l6)** .002 (.003) .0001 .00003)** -.0001 (.0001) .00009 .00007) .50 .18)** 787 162 .33 0 NON-WEST HOUS 2 (2. EHOLDS .4 3) .004 .001)** -.003 (.004) -.04 .01)** -.95 (.09)** .01 (.001)** .00006 .0003) -.0002 ( .00006)** .00007 .00003)** .62 .10)** 2124 431 .55 at the 99% level of confidence 67 As shown in Table 11, the multinomial probit results predict that in both regions, a household having the mean values for independent variables would not make a conservation improvement. However, when the effect of the error term is also included, the ”west" regression predicts that the probability that an "average" household would make a minor improvement is .35 and the probability of a major improvement is .17. The actual values among "west" households indicate that 68% made no improvement, 9.1% made minor improvements and 22.9% made major improvements. The probabilities of minor and major improvements for an "average" family outside the west region are slightly higher. (Actual values: 52.1% made no improvement, 18.5% made minor improvements and 29.5% made major improvements). In the second scenario, the household is assumed to own a single-family dwelling and has a $42,500 annual income (one standard deviation above the mean). The regression results for both regions predict such a household would make a minor improvement, and that the probability that a major improvement would be made is .45 (west) or .38 (non-west). There is a similar likelihood that such a household would make no improvement. Finally, a household that rents a dwelling in a multi-family structure and has a $15,000 income is predicted to make no improvement and is very unlikely to make minor or major conservation improvements. 68 Table 11 IMPROVEMENT ACTIONS PREDICTED BY MULTINOMIAL PROBIT RESULTS independent variable values: mean X's household owns dwelling, single-family structure, income - $42,500, all other X's at means household rents dwelling, multi-family structure, income - $15,000, other X's at means WESTERN HOUSEHOLDS p1 : 6326 “2 improvement actions: NON-WESTERN HOUSEHOLDS p1 : 6559 ”2 1 - no improvement 2 - minor improvement 3 - major improvement dependent variable - -.615 dependent variable - -.0706 predicted action - l prob(action - 2) - prob(-.615 + c ) > 0 - prob (normal 2 > .615) - .35 prob(action - 3) - prob(-.615 + :1) > .326 - .17 dependent variable - .196 predicted action - 2 prob(action - l) - prob (.196 + £1) < 0 - .42 prob(action - 3) - prob(.l96 + :1) > .326 - .45 dependent variable - -1.68 predicted action - 1 prob(action - 2) - prob(-1.68 + :1) > 0 - .046 prob(action - 3) - prob(-1.68 + :1) > .326 - .022 predicted action - 1 prob(action - 2) - prob(-.0706 + :1) > 0 - .47 prob(action - 3) - prob(-.0706 + 81) > .559 - .26 dependent variable - .26 predicted action - 2 prob(actibn - 1) - prob(.26 + £1) < 0 - .40 prob(action - 3) - prob(.26 + :1) > .559 - .38 dependent variable - -1.42 predicted action - l prob(action - 2) - prob(-1.42 + 8i) > 0 - .08 prob(action - 3) - prob(-l.42 + 8i) > .559 - .024 69 The final regression analysis to investigate whether households eligible for larger tax credits made larger conservation improvements uses a binomial Logit to estimate the influence of the independent variables on the likelihood of making a "major" improvement. In this case the dependent variable equals one if a "major" improvement was made and equals zero otherwise. Results from estimation of this Logit for the two regional subsamples are shown in Table 12. Logit coefficients from SPSS estimation are shown in columns 1 and 3, partial derivatives of the dependent variable with respect to independent variables are shown in columns 2 and 4. 70 TABLE 12 LOGIT REGRESSIONS OF "MAJOR" IMPROVEMENTS Dependent variable - 1 for households making "major" improvements - 0 otherwise SAMPLE: "WEST" HOUSEHOLDS NON-"WEST" ' ONLY HOUSEHOLDS 1 2 3 4 Logit 6P/8Xi# Logit aP/8X1# coefficient coefficient net-of-tax price 1.5 .435 3.33 1.29 (.62)** (2.4) income .0000044 .0000013 .0000042 .0000016 (.0000024)* (.0000015)** future fuel price .016 .0046 -.002 -.00094 (.010) (.004) year dwelling -.04 -.012 -.043 -.016 constructed (.024)* (.013)** renter -.70 -.20 -.85 -.33 ( 17)** (.10)** age of -.0015 -.00043 -.012 -.OO48 household head (.0032) (.001)** heating .00007 .00002 (.00004) .000015 degree days ' (.00003)** (.00002)** cooling -.00005 -.000014 .000003 -.0000012 degree days (.00011) (.00006) sq. ft. of home .00004 .000011 .00006 .000023 (.00006) (.00003)** "house" dummy .64 .186 .33 .131 (.23)** (.10)** intercept 2.33 1.9 (.58)** (1.9) N 787 2124 Standard errors in parentheses * : statistically significant at the 95% level of confidence ** : statistically significant at the 99% level of confidence # : evaluated at mean values of the independent variables FL SI 1% tile UL 71 At the mean values of the independent variables, the increase in the likelihood of a "major" improvement being made as a result of an increase in an independent variable can be calculated to be .289bi for the "west” sample (where b is the SPSS Logit coefficient) and .39lb i for the non-"west" subsample. (See footnote 5). i The net-of-tax price term for the western sample is again positive and in this case is statistically significant. Residents of western states that allowed relatively large tax credits were less likely to have made a ”major" improvement, ceteris paribus. The coefficient on the net-of-tax price term in the non-"west" is positive but is not statistically significant. For the "west" households the results for the other variables are essentially the same as those of the other regressions. In this specification, however, western households with higher incomes are significantly more likely to make a major improvement. For the non-"west" households, all variables except the net-of-tax price term, expected future fuel price and cooling degree days are statistically significant. An additional caveat is warranted when interpreting the net-of-tax price coefficients from all the reported regressions. Because the data used here only reflect improvement activity that occurred between mid-1980 and early 1982, improvement activity that occurred before this time period is ignored. It may be the case that those eligible for larger tax credits made improvements prior to this time period. Indeed, households eligible for larger tax credits may have made "major" improvements before the time period considered here, 72 thus they would be less likely to make a major improvement during the later time period. The data used are useful for a static cross-section analysis, but may yield invalid conclusions if the actions taken in earlier time periods are ignored. None of the results presented above provides evidence to support the hypothesis that households eligible for larger conservation tax credits are more likely to make conservation improvements or that they tend to make larger improvements. Indeed, residents of states that allow the largest tax credits are, ceteris paribus, less likely to make a major improvement. As discussed above, this result may be due to some unmeasured characteristics unique to households living in the west, but even when western households are isolated, those eligible for larger tax credits are not more likely to make a conservation improvement and do not tend to make larger improvements. Also, the econometric findings are consistent with the hypothesis that p, the tax credit perception accuracy factor, is less than one. It may be the case that the low rates of conservation improvement in western states prompted officials in those states to adopt a tax credit with the hope of stimulating conservation activity. The absence of evidence to support the hypothesis that larger tax credits lead to more conservation improvement activity suggests that p, the factor used to represent the accuracy of perception of available tax credits, is less than one. If the conclusion that tax credits do not influence improvement activity is correct but is not explained by the lack of perception of the credits, some other effect not considered here explains the above conclusions. 73 ADDITIONAL EVIDENCE Internal Revenue Service Statistics of Income figures from 1981 indicate that 4.2% of all tax returns had an energy conservation credit claim. The 1981 RECS summary document indicates that 33% of sample households made some kind of improvement in that year. Around 95% of improvement actiOns were eligible for a federal tax credit, so only 13% of eligible actions were claimed on the federal form. A similarly low proportion of actual claims to eligible claims occurred in 1983.6 Assuming the RECS survey was representative, it can be concluded that most taxpayers were unaware of the credit, did not find it worthwhile to file form 5695 ("Residential Energy Credit") or were not willing to file the "long” form (1040) in order to claim the credit. Although 19.6% of 1981 federal returns were not taxable, these were low income filers who were less likely to have made a conservation improvement, so this does not explain much of the difference between the proportions of improvement taxpayers and credit claim taxpayers. The average expenditure reported by those who did claim a credit was $600 to $700 in various years, far above the average expenditure reported by the U.S. Census Bureau.8 Two main reasons probably explain the differences between the expenditure levels reported by the Census Bureau and those reported to the IRS. First, taxpayers may have overstated their true expenditures on tax credit forms. 6Energy Information Administration, 1985. 7It is possible that some taxpayers had hit the ceiling for maximum federal credits allowed during the life of the program, but it is unlikely that enough households claimed the $2,000 year-to-year limit imposed by this ceiling, to explain the low claim rates discussed here. 8U.S. Bureau of the Census/U.S. Department of Housing and Urban Development, 1981. 74 The second reason for the difference is that credits tended to be claimed by those who spent more. As discussed above, the likelihood of claiming the credit (or citing it as a reason for improvement) is greater the larger its value; i.e. the larger the improvement. Because the magnitude of improvements (likelihood of making a "major" improvement) has a strong positive association with income, the benefits of the credit are skewed towards those having incomes above the median (see Table 13). Table 13 % OF ALL 1981 FEDERAL TAX RETURNS HAVING AN ENERGY CONSERVATION CREDIT CLAIM BY INCOME CATEGORY INCOME % WITH CONSERVATION CLAIM $1 - $5000 .2% $5001 - $10,000 1.1% $10, 001- $15, 000 2.1% $15,001 $20,000 4.0% $20,001 $25,000 6.3% $25,001 $30,000 7.3% $30,001 $40,000 9.7% $40,001 $50,000 9.8% $50,001 $75,000 11.2% $75,001 - $100,000 10.6% $100,001 - $200,000 9.2% $200,001 - $500,000 7.1% $500,001 - $1,000,000 5.1% > $1,000,000 4.1% overall proportion: 3.9% median AGI (approximate): $15,000 Source: Internal Revenue Service, Statistics of Income, 1981. The federal claim percentages are also useful for making interstate comparisons. Column 1 of Table 14 shows the percentage of households who claimed a federal energy conservation tax credit for states with 75 conservation credits or deductions and nearby, climate-similar states in 1981. Column 2 shows claim percentages adjusted so that all the claimed credits are assumed to be claimed by taxpayers who own their residences. Statewide average adjusted gross incomes are also shown because improvement activity and the likelihood of claiming a credit rise with income. 76 TABLE 14 PERCENTAGE OF ALL TAX RETURNS HAVING AN ENERGY CONSERVATION TAX CREDIT BY STATE FOR SELECTED STATES "Adjusted" proportion assumes all claims are taken by owner-occupants. ‘ (1) (2) (3) PROPORTION WITH STATE PROPORTION WITH CLAIMS ADJUSTED AVERAGE AGI CREDIT CLAIMS BY HOME OWNERSHIP Arizona ** 2.46% 3.61% $17,842 New Mexico 2.82% 4.14% $16,259 Texas 1.76% 2.73% $19,775 Oregon ** 3.75% 5.74% $17,412 Washington 4.61% 7.01% $19,701 California ** 2.08% 3.73% $19,817 Nevada 2.11% 3.54% $18,547 Colorado ** 6.52% 10.1% ’ $19,581 Utah 4.59% 6.48% $17,755 Nebraska 4.88% 7.14% $16,633 Idaho * 4.95% 6.88% $16,159 Montana * 4.23% 6.17% $15,891 Wyoming 2.52% 3.62% $20,460 North Dakota 3.78% 5.48% $16,370 Arkansas * 2.55% 3.62% $14,898 Oklahoma 3.18% 4.50% $18,555 Missouri 3.36% 4.83% $17,612 Indiana * 4.37% 6.08% $17,933 Illinois 4.86% 7.72* $19,924 Ohio 4.01% 5.86% $18,328 Massachusetts 6.41% 11.1% Rhode Island 5.81% 9.9% Connecticut 5.40% 8.4% National average: 4.17% 6.39% *: state allowed a tax credit for energy conservation expenditures **: state allowed a tax deduction for conservation expenditures Source: Internal Revenue Service, Statistics of Income, 1981. 77 Claim rates in Arizona and California are well below the national average and are not significantly different than rates in neighboring states where no state level tax incentives are available. The claim rate in Oregon is considerably below that of Washington although the significance of this difference is unclear as the mean ACT in Washington is well above that of Oregon. Claim rates in Idaho and Montana exceed those of their similar-climate neighbors even though the mean AGI in these two states is less than that of Wyoming and North Dakota. This difference is even greater if all credits are assumed to be claimed by owner-occupants. The claim rate in Colorado far exceeds that of its neighbors although the higher mean ACT in Colorado may explain part of this difference. Nevertheless, relatively high claim rates in Colorado, Idaho and Montana could be construed as some evidence that tax incentives have helped stimulate conservation improvement activity in these states. Another explanation for the results just presented is that conservation improvement rates are equal among the compared states, but availability of state tax incentives made taxpayers more aware of energy tax credits in general, thus making them more likely to claim the federal credit. If, however, the proportion of improvement households that made a credit claim is constant across states, residents of Colorado, Idaho and Montana did make more energy conservation improvements and this difference might be attributable to the presence of state tax incentives. In general, absolute and owner-adjusted claim rates were highest in New England, where a relatively high proportion of residences are heated with fuel oil, the fuel that had the largest price increase in the late seventies and early eighties. Comparisons of claim 78 rates in Arkansas and Indiana with those of their neighbors gives no indication that the availability of income tax deductions for conservation expenditures in those states have led to more widespread improvement activity. CONCLUSIONS Regression analysis indicates that the behavioral model developed in chapter two is useful for explaining conservation improvement activity, but indicates that fewer residents of high tax credit states made improvements. Comparison of the RECS survey data with IRS tax return data suggests that most households who made energy conservation improvements did not claim a federal tax credit. This, and the fact that claims are made by those spending relatively large amounts strongly suggests those who do claim a credit experience a windfall and claim the credit because it is more valuable, i.e., "because it was there". The absence of evidence to support the hypothesis that larger available tax credits lead to more widespread or more extensive energy conservation improvement activity should not be construed as evidence that "prices don't matter", i.e. that lower prices for conservation improvement do not lead to a greater quantity demanded. Rather, the evidence should be interpreted as an indication that tax credits are not effective in causing perceived net price reductions. That is, the lower net prices implied for a perfectly informed and eligible taxpayer do not represent price reductions for all taxpayers. Several possible explanations for this result are discussed in the next chapter. CHAPTER FOUR CONCLUSIONS AND POLICY IMPLICATIONS Survey evidence compiled by other researchers and reviewed in Chapter 3 indicates that only a small proportion of taxpayers understand the energy tax credit or state that its availability strongly influenced their decision to improve the energy efficiency of their dwelling. Similarly, among the RECS participants who made conservation improvements, only 9.6% cited tax credits as one reason for doing so. Econometric estimates of the influence of various factors on the likelihood of making a conservation improvement had fairly good explanatory power but indicate that conservation improvement activity is actually less extensive in states which allow income tax credits or deductions in addition to the federal credit. The latter result appears to be due to the fact that larger tax credits are available in western states where conservation improvement rates were far below the national average. It may be that shorter expected home tenures or better initial thermal quality of western homes (both variables were measured by highly imperfect proxies), or some other omitted factor common to western households or homes caused the lower conservation improvement rates. Even when western households are separated from the rest of the sample to allow for the differences in conservation behavior those households seem to exhibit, no discernible influence from the presence of state level tax credits can be identified. These findings and the other empirical evidence presented suggest that only a small percentage of conservation improvement activity, if any, has been caused by the availability of energy tax credits. To the extent that claimed tax credits did not cause improvements to be made, 79 abc abc eos rap Wm 3011. 1E9: This 8663 80 the tax savings (and revenue loss from government treasuries) generated by the credit programs were a windfall to taxpayers. As discussed in Chapter 3, the 1982 RECS data set does not report the extent of energy conservation improvement made on dwellings before September 1980. Thus the conclusion that larger tax credits cannot be shown to be associated with more widespread or extensive improvements only applies strictly to the time period covered by the 1982 RECS survey. Households eligible for a larger tax credit may have acted in response to the credits soon after (1978 or 1979) the credits became effective and would thus not report an improvement if they participated in a later survey. If that is the case the econometric evidence reported in Chapter 3 is less convincing because the true effects of the credits would have occurred before the time period considered here. Conversely, because the participants in the 1982 RECS were asked about improvements made since September 1980, the survey did inquire about improvement activity when (according to available evidence) it was most widespread. Because residential energy prices were rising more rapidly in 1980 than they had during the energy "crisis" of the 1970's, conservation improvement activity during 1980 was greater than any other year for which data are available. Survey evidence that unanimously concluded that energy tax credits were not effective for stimulating improvement activity was gathered at several different points in time. Thus the possibility that the 1982 RECS "missed" what really occurred seems less likely. There are several reasons that may explain why tax credits failed to stimulate conservation improvement activity. Households may have been unaware of the credits; this is true to some extent, as was found 81 in other studies. If one is aware of the credits, the time and effort involved in obtaining and filing tax credit forms reduces the net benefit of doing so. Because the price-reducing effect of a tax credit actually occurs several months after making an improvement (when tax forms are filed or tax returns received), taxpayers may not have considered a tax credit to truly represent a price reduction as they would a cut in the retail price. Also, the lack of complete understanding of the credits introduces uncertainty into the computation of the net-of-tax price of improvements, thus suggesting a further discounting of the value of the credit. Finally, while a tax credit reduces the net price of conservation improvements, the gross (retail) price of conservation materials increased much faster than the overall rate of inflation in the late seventies and early eighties.1 Thus, the effect of tax credits on the net relatize price of improvement materials may have been overwhelmed by retail price inflation. Sellers of conservation equipment may have raised prices as demand for this equipment increased. To the extent that the availability of tax credits contributed to the increase in demand for conservation materials, the credits benefitted sellers if the supply of conservation materials is less than perfectly elastic. It appears that tax credits caused only a very small fraction, if any, of the conservation improvements that occurred during the life of the tax credit program. A simple estimate of the total amount of fuel savings caused by conservation improvements installed from 1978 through 1985 is now computed. Various hypothetical values for the maximum value of fuel savings "caused" by the availability of energy tax credits are 1National Association of Home Builders, 1977, p. 2. 82 then computed. This allows determination of the required levels of "causation" needed to achieve various payback levels. The required levels of causation are then compared with the most extreme assumptions regarding the effect of the credits (i.e. that some improvement was caused by the availability of tax credits). The U.S. Department of Energy reports that 75% of households living in single-family dwellings (58 million of the total 83 million housing units in 1980) made some conservation improvement between 1978 and 1982. Nationwide improvement rates were falling quickly in 1981 and 1982 and most households who desired improvements probably made them prior to 1983, so the total proportion of improvement households from 1978 through 1985 (the life of the tax credit program) is probably around 80%. A reasonable estimate of the proportion of multiple-family housing units that received improvements is 20%. Keeping the analysis simple, 20 years of fuel savings for these 51.5 million households are applied against a heating and cooling fuel consumption base of 100 Mbtu/year at a weighted average price of $7.50 per Mbtu. Hirst, et. al., (1981b) estimated that the median proportion of energy savings due to conservation improvements was around 25% of pre-improvement energy consumption. Because they looked at more equipment types and did not adjust downward their savings estimate to reflect the "comfort buy-back"2 effect of lower marginal heat costs, their fuel savings estimate is probably too high. These adjustments and other sources of information regarding energy savings potential suggest a reasonable estimate for the effective proportion of energy saved by RECS 2see Hirst, et. al., 1984. 83 improvement households is around 15%. An average extent of improvement in the current study is approximately the energy-saving equivalent of the purchase an automatic thermostat and door and window caulking. Savings resulting from these improvements are probably closer to the 15% figure than to the 25% estimate. Using the estimates just discussed, the total value of savings in this scenario is: (20 years)x(51.5 million)x(100)x($7.50)x(.15) - $115.8 billion. If the $3 billion outlay of the federal conservation tax credit program "caused” 2.6% of this total savings to occur, the value of savings to households experiencing the savings would just equal the value of the tax expenditures allowed to tax credit claimants. This would be the case if 1.34 million households made a median improvement because the tax credit was available. The latter implies 4.8% of all federal tax credit claims over the life of the program (a total of 1.33 million or 167,000 claims per year) were made by taxpayers who made a median conservation improvement because the federal energy tax credit was available. Although the available evidence suggests the federal credit did not lead to this many median improvements, the 4.8% "causation" figure is not implausible as it is similar to the proportion of respondents in Petersen's survey (see Chapter 3) that said they definitely or probably would have spent less for improvements if the credit was not available. The 1.33 million total is also the approximate number of tax returns that had a conservation claim in 1982. Thus, if around one-eighth (12%) of all federal claims were made by house of ti disc: valor gene' {0:8 prog- COHS‘ 355T caus. valu. revi. fede' savi: 2mg Ofs high 53711 rave; Prese 84 households that would not have made a median improvement in the absence of the tax credit, the program would have achieved the "private payback" discussed above. If this is the case, the program may have simply subsidized energy savings for some taxpayers with an outlay of equal value by other taxpayers. Presumably the public policy goal of the tax credit program was to generate a positive externality by reducing energy consumption. The total value of externalities is the amount of savings caused by the program multiplied by the per unit public value of reduced energy consumption. If the public value of energy savings is 20% of the assumed market price of fuel, 13% of all savings would have to have been caused by the federal tax credit program to generate an "externality" value equal to the amount of tax expenditures. All the evidence reviewed in the current study indicate it is extremely unlikely that the federal tax credit program caused 13% of all the residential fuel savings that resulted from improvements made during the life of the program. Thus, even with the extreme assumption that 20% of the value of saved energy is a "public" benefit or positive externality, it is highly unlikely that the federal tax credit program caused enough energy savings to generate a payback to society equal to the amount of tax revenue that was redistributed by the tax credit program. OTHER POLICY IMPLICATIONS While a large amount of capital improvements for energy efficiency occurred during the late seventies and early eighties, evidence presented here indicates that improvements in rental housing by tenants were relatively rare. Thus direct grants, such as those financed by oil overcharge fines, and other programs to encourage landlords to improve CO: 85 the energy efficiency of rental units may be necessary if such improvements are considered a desirable public policy goal. Apparently renters who pay their fuel bills directly do not anticipate a high enough return on improvement expenditures and owners that include fuel costs in the rent do not fear the prospect of being unable to shift fuel costs to renters. If renters pay heating and cooling bills, an efficiently functioning market for rental housing would presumably force owners of energy inefficient units to either accept lower rents or insulate the dwelling if rents are to be sustained. Renters would avoid high rent apartments that have high utility bills, thus forcing the owner to reduce rents or improve the fuel efficiency of the dwelling. Although renters may seek information about past utility bills, that information does not fully describe the thermal quality of a dwelling because previous occupants may have had different levels of temperature control, used other appliances differently and may have experienced unrepresentative weather conditions. Thus renters typically do not have reliable information about the energy efficiency of a rental unit. The above considerations suggest that the market efficiency required to provide sufficient incentive for landlords to improve the energy efficiency of rental units is not likely to be present. Because renters tend to be lower income households, the absence of energy efficiency improvements in rental housing helps perpetuate the relatively high proportion of incomes that lower income people spend on fuel bills. Also, the presence of state and local taxes on heating and cooling fuel implies a regressive tax burden that for the most part remains so as rental unit energy efficiency improves only as new rental 86 units are constructed. The lack of efficiency improvements in rental housing also suggests that if reduction of the relatively high energy expenditures of lower income consumers is a goal, minimum standards for energy efficiency in new rental units or other policies may be necessary. Of course the costs of meeting such standards may end up being passed on to renters and the disproportionate burden they bear for energy-related expenses may not be alleviated. As mentioned in a note at the end of chapter two, it is not clear why purchases of new, more efficient furnaces and several other energy saving improvements were not eligible for the (federal) tax credit. If the goal was simply to save energy there is no obvious reason why these items should be excluded from the program. CONCLUDING COMMENTS While the RECS data set is not ideal for analysis of state-level variations in tax credits and fuel prices, it does provide a large and sufficiently detailed sample for examination of the economics residential energy consumption. Regional variations in energy .efficiency improvement activity were identified, and useful estimates of energy demand and other relationships can be generated by the data. It was necessary to also consider other data sources in order to support the findings based on the Residential Energy Consumption Survey. Although the designers of the survey wisely included questions about the reasons households made conservation improvements, more specific questions regarding the act of claiming state and federal tax credits would have made investigation of this issue easier and more conclusive. APPENDICES APPENDIX A: ANALYSIS OF COMPARATIVE STATIC DERIVATIVES OF THE OPTIMUM CONSERVATION IMPROVEMENT MODEL FROM CHAPTER 2. Total utility is defined to be (from expression 11.): a (1-b) b A-l U- Yo + DY1 T where: Y is current period gross income 2 minus expenditures for conservation improvement, P R', which is the net-of-tax price of a unit of multiplied by R', the "quantity” of R purchase in the current period. D is the discount factor, 1/(1+r) Y is future period gross income, Z , minus expenditures for fuel consumption, F(R1,T,E)Pf where: fuel consumption is a negative function of both R1, thermal integrity of the home in period 1, and E, external temperatures and is a q positive function of T, temperature control consumed in period 1. and: R - R + R', i.e. thermal integrity in the future period is the initial level of thermal quality plus R', the increase in R. T- temperature control in the future period, - * - ‘ * IT Tactuall/T where |T* - T 1‘ is the absolute value of the aiffgrence between "ideal" indoor temperatures and the one actually chosen, T . actual Consumers choose R' and T to maximize U. Because income constraints are incorporated into U, an unconstrained maximum of U with respect to the choice variables yields: A-2: F1 - aU/aR' - (aU/aYo)(aYo/3R') + (aU/aY1)(aY1/8F1)(aFl/aR'|T - o A-3: F2 - aU/ar + (aU/ayl)(aY1/ar) - o 87 88 where the l } term at the end of F1 represents fuel savings from the R' increase in R. The specific functions for F1 and F2 are: . l a-l b-l 2 A-4. F - aYo (-PR) + de1 (-Pf)[-TT*-E)Ah/R1 + (T*Ah/R1)(3T/3R')] - 0 b b b-l 1-b T' + bDY T (-Pf)(T*Ah/R1) - o . 2 A-5. F - (l-b)DY1 1 As discussed in Chapter 2, the optimum temperature control level in period 1 is an implicit function of R which is a function of R'. Thus implicit functions prevent the derivation of a single expression to represent the optimum value of R'. The qualitative influence of the various exogepous an? policy variables on optimum R' can be determined by treating F and F as a system of implicit functions. The sign of derivatives of o timum ' can be found by working through a total derivatives of F and F with respect to each exogenous variable and solving for the appropriate derivative which, for exogenous variable i is: l l i -F 1 F T : | -F2i FZT | A-6: gR'/di - I1 lI IFR FT: 2 2 I F R F T l where l | terms are determinants, Fn is the partial derivative of expression Fn with respect to choice ariable j and the determinant in the denominator can be assumed to be positive in fulfillment of second-order conditions for a maximum. Thus to determine the direction of influence that exogenous variable i has on the optimum increase in R, it is only necessary to determine the sign of: , 12 21 A-7. (-F i)(F T) - (-F i)(F T)' It was shown in Chapter 2 that F2 , the second derivative of U with respect to T, is negative. Because the derivatives of optimum R' with respect to the exogenous variables are partial derivatives, all other variables are held ionstang when signing the derivatives. Thus the partial aT/aR' in F and F can be removed from those expressions. 89 F1T can be shown to be: , 1 2 b-2 l-b A-8. F T - {PfAhbD/(Rl) }[(b-1)Y1 'r b-lT-b Pf(TT*-E)T*Ah/(Rl) + b-lTl-b (-(TT*-E)) + Y1 (l-b)Y1 (-T*)]. Thus it can be shown that FIT is positive. It was shown in Chapter 2 that the optimum increase in R' is a negative function of PR' The derivative of optimum R' with respgct to 20, curr nt period gross income, has the same sign as (-F )(F ) because (-F ) equals zero. - 20 T 20 From above: 1 , a-2 F 20 - (a-l)a[Zo-PRR ] (~PR). Because a<1 this expression is positive. Thus with F2 <0, the derivative of optimum R' with respect to current period gross income is positive if improvement expenditures do not exceed gross income. The influence of D, the discount factor, on optimum R' can also be found by examining only thg first half of A-7 because in equilibrium, the two components of A-5 (F ) sum to equal zero, thus making F equal to zero. To sign th derivative, it is necessary to sign -F . I? is clear from A-4 that F is positive. Thus 8R'/aD is positive. As r, the household's discount rate increases, D decreases, as D decreases optimum R' also decreases. Thus higher discount rates applied to the future imply lower optimum increases in R. The influence of I'a", the current period utility parameter on optimum R' can also be found by looking only at the first half of A-7. From A-4 it can be shown (and it is fairly obvious) that F is negative. Thus aR'/aa is negative, i.e. a larger weight on current period "net" income implies a smaller optimum conservation improvement. The sign of aR'/8P depends on the magnitude of each portion of A-7 because the first Half of the sum is positive while the second is negative. substantial manipulation of the relevant products of A-7 does not make it possible to clearly see the conditions under which the derivative would have a particular sign. As discussed in the text, an indeterminate sign of the influence of future fuel prices on optimum R' arises because a higher fuel price implies a lower optimum level of temperature control and the latter implies a lower optimum level of R. (In a single period utility-maximization model where temperature control is traded-off against net income, the optimum amount of R to have for that single period is a positive function of the amount of temperature control consumed.) The derivatives of optimum R' with respect to E, external temperatures and A, area of the dwelling, are also indeterminate and also do not yield identifiable conditions under which the derivative is signable. As E rises, the optimum level of R in a static model declines, but 90 optimum temperature control increases as E increases and the latter dictates a higher optimum level of R in a static model. The opposite holds for A. 91 APPENDIX B: IDENTIFICATION OF STATE OF RESIDENCE FOR RECS HOUSEHOLDS State of residence for each household was not reported in the RECS data. In order to assign the appropriate state energy tax credit or deduction to each household, it was necessary to indirectly identify residents of state where these policies apply. The states that were identified are: Arizona, California, Colorado, Idaho, Montana and Oregon, New Mexico, Washington and Wyoming were also identified. There were no Nevada residents in the sample. A census region identifier is included in the RECS data, so all residents of the above states were designated as "Pacific" (CA,OR,WA) or "Mountain“ region inhabitants. The Energy Information Administration (EIA) provided a list of the Primary Sampling Units (PSU's) (counties) from which RECS households were chosen. This information indicated the approximate number of households surveyed in each state and their location within each state. U.S. Weather Service data on actual heating- and cooling-degree days for weather stations in or near each PSU for 1981 are used for comparison with the relevant annual climate data reported in the RECS. The table B-l shows the steps and data used in the state identification process. TABLE B-l: STEPS USED IN STATE IDENTIFICATION PROCESS Residential Energy Consumption Survey Data Census region identifiers SMSA-City/SMSA-non-city/ non-SMSA location heating- and cooling-degree-days marginal electricity prices for three customer sizes and average electricity prices for each household average natural gas price for each household average fuel oil prices average LPG prices compared with.... list of sample locations (PSU's) U.S. Weather Service data at nearby stations in same time period (U.S Weather Service) marginal electricity prices for three customer sizes and average prices for local retail utilities ("Typical Electric Bills", January 1, 1982.) ' state level natural gas prices (U.S. DOE, State Energy Price and Expenditure Report, 1970-1982) state level fuel oil prices (U.S. DOE, State Energy Price and Expenditure Report, 1970-1982) state level LPG prices (U.S. DOE, State Energy Price and Expenditure Report) 93 APPENDIX C: RESULTS OF FUEL CONSUMPTION AND TAX CREDIT IMPORTANCE REGRESSIONS TABLE C-l Fuel Demand Regression Ordinary Least Squares regressions run on RECS households Dependent variable: natural logarithm of heating and cooling fuel consumption (in thousands of Btu's). INDEPENDENT VARIABLE COEFFICIENT (standard error) ln(square feet heated area) .46 (.02) ln(weighted fuel price adjusted -.61 for furnace efficiency) (.03) 1n (year made) (lower values of -.14 this variable imply older homes) (.01) ln(heating degree-days) .30 (.02) ln(cooling degree-days) .12 (.01) ln(income) .05 (.01) ln(number of household members) .15 (.02) ”house" dummy (- 1 for single- .09 family dwelling) (.02) All coefficients are statistically significant at the .01 level. N - 2941 adjusted R2 - .50 F - 373 94 TABLE C-2 Regression Results: Likelihood of citing tax credits as one reason for making an improvement Sample: households who made conservation improvements Dependent variable - 1 if the household cited the availability of a tax credit as one reason for making an improvement - 0 if tax credits were not cited VARIABLE LOGIT LINEAR PROBABILITY COEFFICIENT REGRESSION COEFFICIENT (std. error) (std. error) net-of-tax -4.48 -- price (1.65) income .75 .0000012 (.20) (.0000004) "major" (-1 if a major .44 .11 improvement (.07) (.02) was made) age of -1.05 -.0011 household (.42) (.0005) head ' "west" (-1 .04 for western -- (.018) region residents) all coefficients are statistically significant at the .01 level Logit variables are natural log transformations adjusted R2 -- .057 F-statistic -- 20.5 95 APPENDIX D: DESCRIPTIVE STATISTICS OF INDEPENDENT VARIABLES USED IN CHAPTER THREE REGRESSIONS Format: Means (Standard deviations) [minimum, maximum] Sample: Whole West Non-West Variable Annual Household $24,397 $24,121 $24,500 Income (18,087) (17,707) (18,228) (categorized [2,500, 100,000] [2,500, 100,000] [2,500, 100,000] raw data) Net-of-tax .822 .737 .853 price of conservation (.068) (.084) (.013) improvements [.61,l.06] [.61,l.0] [.80,1.0] Year Dwelling 3.45 3.67 3.36 constructed (2.07) (2.07) (2.06) (categorized [1,8] [1,8] [1,8] raw data) (See page 56) Age of 49.1 47.8 49.6 household head (17.0) (17.4) (16.8) [18,95] [18,93] [18,95] Square foot 1631 1469 1691 area of home (898) (815) (920) [151,7880] [240,6312] [151,7880] Future fuel 15.4 13.0 16.3 price ($/million (6.6) (4.4) (7.0) Btu) [3.3,47.3] [6.6,39.3] [3.3,47.3] Heating-degree . 4840 4876 4826 days (65° F (1998) (2118) (1952) base) [119,12664] [1185,12493] [119,12664] Cooling-degree 893 474 1048 days (70° F (782) (548) (799) base) [1,4618] [1,3522] [55,4618] % renters 21.2% 29.2% 18.2% % Living in single- 84.2% 81.7% 85.2% family dwellings BIBLIOGRAPHY Allen, C. 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