THE IMPACT OF EXPENDITURE CATEGORY EXEMPTION ON THE INCIDENCE OF A RETAIL SALES TAX

THE IMPACT OF EXPENDITURE CATEGORY EXEMPTION ON THE INCIDENCE OF A RETAIL SALES TAX by Frederik Alonzo Judd IV A thesis submitted in partial fulfillment of the requirements for the degree of Master of Siene in Applied Eonomis MONTANA STATE UNIVERSITY Bozeman, Montana Marh 1987

i i APPROVAL of a thesis submitted by Frederik Alonzo Judd IV This thesis has been read by eah member of the thesis ommittee and has been found to be satisfatory regarding ontent, English usage, format, itation, bibliographi style, and onsisteny, and is ready for submission to the College of Graduate Studies. Date Chairperson, Graduate Committee Approved for the Major Department Date Head, Major Department Approved for the College of Graduate Studies Date Graduate Dean

iii STATEMENT OF PERMISSION TO USE In presenting this thesis in partial fulfillment of the requirments for a master's degree at Montana State University, I agree that the Library shall make it available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without speial permission, provided that aurate aknowledgement of soure is made. Permission for extensive quotation from or reprodution of this thesis may be granted by my major professor, or in his absene, by the Dean of Libraries when, in the opinion of either, the proposed use of the material is for sholarly purposes. Any opying or use of the material in this thesis for finanial gain shall not be allowed without my permission. Signature Date

iv ACKNOWLEDGMENTS I would like to take this opportunity to thank my major advisors Dr. Jeffrey LaFrane, Dr. Douglas Young, and Dr. Brue Beattie for their time, patiene, and enouragement during my work on this thesis and in related lass material. I would also like to give speial thanks to Dr. Mike Copeland for his helpful omments and to Rudy Suta for all the time and effort he put into aggregating the data set. Speial appreiation is expressed to my family and lassmates for their enouragement and patiene during my time spent at Montana State University.

v TABLE OF CONTENTS Po.ge APPROVAL I I I I I I I I I I I I I I I I STATEMENT OF PERMISSION TO USE..... ACKNOWLEDGMENTS I I I I I I I I I I. I TABLE OF CONTENTS. ' I I I I I LIST OF TABLES I. I I I. I I. I I. I I I I. I. I I. I I I LIST OF FIGURES.. ABSTRACT I I I I I I I I I I I I I I I I i 1 i i i iv v vii viii ix Chapter 1 INTRODUCTION I I I I I I I I I I I I. Statement of Purpose.......... Equity in Taxation..... A Coneptual Diffiulty.. Two Important Conepts Related to Tax Burden.. Tax inidene. Tax base... Some Additional Definitions... Overview.... Outline of Thesis. 1 2 2 2 3 3 4 4 5 7 2 ANNUAL VS LIFETIME INCIDENCE: PREVIOUS STUDIES.... A REVIEW OF 8 Annual Inidene... Lifetime Inidene.. History, Conepts, and Definitions.. Life-Cyle Based Studies... A Proxy for Permanent Inome. 9 11 11 13 17

vi TABLE OF CONTENTS-Continued Chapter Page 3 DATA, EMPIRICAL MODEL, ESTIMATION PROCEDURES AND PARAMETER ESTIMATES... 20 Data..........,...................... 20 Empirial Mod~l... 25 Seemingly Unrelated Regression... 27 Instrumental Variables... 28 Tobit Regression Analysis... 31 Heteroskedastiity... 31 INTERPRETATION OF MODEL RESULTS.... 47 Interpretation of Tobit Estimates... Impat of Expenditure Category Exemption on 48 the Inidene of a Retail Sales Tax... 51 Total Dollar Burden......... ~.. 61 5 SUMMARY, CONCLUSIONS AND IMPLICATIONS...... 66 Summary... 66 Con1us1ons..................................... 66 Impliations... 72 LITERATURE CITED. I. I I. I I I. I I I I I I I I. 74 APPENDICES I I... I I. I. I. I. I. I I. I I I, I I I I I.. 78 A: Family Charateristis in Data Set FINDAT... 79 B: Fortran Program 1... 81 C: The 54 Expenditure Categories in Data Set FINDAT...... 83 D: Fortran Program 2 I I I I I... 87 E: Fortran Program 3... I. 1.11. I 1 1. I I 1.. 94

vii LIST OF TABLES Table 1 2. 3. 4. The 41 Categories of Expenditures on Consumption Goods and Servies..................... Parameter Estimates and T-Ratios for the Permanent Inome Instrumenta 1 Variable.............,. Values of Log-Likelihood Funtion Under Different Assumptions of Heteroskedastiity......... Impat of Family Charateristis on Expenditures.... Page 23 30 34 36 5. Marginal Inome Effet on Expenditures and Share(l) for a Family Size of 2.7 at Different levels of Permanent Inome....................................... 53 6. Base($) and Base Share(X) at Different Levels of Permanent Inome for the Mean Family size--with and Without Exemptions... 68 7. Family Charateristis in Data Set FINDAT...... 79. a. The 54 Expenditure Categories in Data Set FINDAT..... 83

vi 1i LIST OF FIGURES Figure Page 1. Marginal Share (X) vs Permanent Inome: Food At Home... ~.... 56 2. Expenditure Shares (X) vs Permanent Inome...... 58 3. Marginal Share (X) vs Permanent Inome: Utilities... 59 4. Marginal Share (X) vs Permanent Inome: Presription Drugs... 60 5. Marginal Expenditures($) vs Permanent Inome...... 63 6. Total Expenditures($) vs Permanent Inome....... 64 7. Tax Base Share (X) vs Permanent Inome.......... 70 a. Tax Base($) vs Permanent Inome............. 71 9. Fortran Program 1..... 81 10. Fortran Program 2..... 87 11. Fortran Program 3.,.................... 94

ix ABSTRACT Questions of equity and onerns over an esalating defiit have fored the Montana State Legislature to seek alternative and/or additional ways to raise revenue. One suh proposal to raise revenue is a sales tax. Opposition toward a sales tax is based largely on the feeling that it is a regressive tax, and therefore distributes the burden unfairly. The purpose of this study is to determine the impat of expenditure ategory exemption on the inidene of a retail sales tax. The overall progressivity/regressivity of a retail sales tax is alulated, both with exemptions and without exemptions from the base of the tax. The model used in this study is an expenditure funtion that is quadrati in family size and permanent inome. Tobit regression analysis is used to derive maximum likelihood estimates for 41 expenditure ategories. From these tobit estimates, expenditure shares <proportion of expenditures relative to permanent inome) and the tax base share (proportion of total expenditures on those items inluded in the base relative to permanent inome) are alulated at different levels of perma~ent inome. Exempting those goods and servies that are a larger proportion of expenditures relative to permanent lnome for households in lower permanent inome brakets (suh as food purhased in groery and onviene st~res and utilities) inreases (dereases) the progressivity (regressivity) of a sales tax. A broad-based sales tax is regressive for households earning less than $5000 in permanent inome. From approximately $5000 to $25,000 a broadly-based sales tax is progressive. For those households earning $25,000 or more, the tax is slightly regressive to progressive. Exempting ertain expenditure ategories (Food at Home, Utilities, Telephone, Water and Other Publi Servies, Presription Drugs and Eduation) from the base makes the tax progressive for households whose permanent inome is $25,000 or less. From $25,000 to $60,000 the tax is slightly regressive. For households whose permanent inome is greater than $60,000, the sales tax is fairly proportional.

1 CHAPTER 1 INTRODUCTION Among the several issues involved in tax poliy, equity or fairness of the burden distribution is often a major onsideration. In the urrent tax reform debate in Montana this issue is often manifested onerning the propriety of a retail sales tax. Montana is one of only five states that does not have a retail sales tax. Over the years and in the urrent Montana tax reform debate the alleged regressivity of a sales tax is prominant in the disussion, espeially among those individuals and interest groups opposing the addition of a sales tax to Montana's tax system. Typial of the view held by many Montanans is that published in an editorial in the Bozeman.Daily Chronile, April 24, 1985: Still, the inome tax is the fairest tax. The inome tax is based on ability to pay. With study and minor reform, it an be the best hope for long-lasting tax poliy in the state. The sales tax is not as fair. Its tax rates are not adjusted aording to ability to pay; poor people are hit hardest. When a family making $10,000 a year buys a refrigerator it really needs, it pays the same tax as the family making $50,000. Beause they spend virtually all they earn, the poor would pay taxes on virtually all of their inome. Exlusions of essential purhases -- mediine and food are often mentioned-- does not hange the fundamentally regressive nature of the tax. It is probably not an exaggeration to say that the onventional wisdom in Montana is that retail sales taxes are undesirable, they are allegedly among the most regressive forms of in part, beause taxation. This thesis tests this onventional wisdom.

2 Statement of Purpose There are many advantages and disadvantages of alternative taxes; these often relate to matters of impat on eonomi growth, ost effetiveness of administration and ompliane, eonomi effiieny, ylial stability of revenue, and equity or fairness among other things (Musgrave and Musgrave, 1984, p.225), This study fousses on the general matter of equity as related to retail sales taxes. The purpose of this study is to examine the validity of the assertion that retail sales taxes are regressive and to assess the impat of ertain expenditure ategory exemptions on the inidene or "progressivity/regressivity" of a sales tax. Equity in Taxation One basi riterion for evaluating tax poliy is equity. There is general agreement that a tax system should be equitable. Most itizens feel that eah member of soiety should ontribute his/her fair share toward the burden of finaning publily-supplied servies. However, disagreement is ommonplae regarding what represents an equitable share. This is beause equitable taxation depends on ability to pay and on the benefits reeived from government outlays, relative to the tax payments, both of whih are diffiult to define and measure. A Coneptual Diffiulty The ability to pay riterion should reflet a household's eonomi apaity to onsume and save over its lifetime. Transitory flutuations in inome an substantially influene a household's eonomi apaity

3 from year to year. Aordingly, annual inome or total annual expenditures (on all goods and servies inluding major apital items suh as autqmobiles) are not good indiators of ability to pay. In this study household permanent inome is adopted as the ability to pay riterion. It is further assumed that a household's annual onsumption of non-durable goods and servies is an aeptable proxy for permanent inome. Two Important Conepts Related to Tax Burden Two ideas are partiularly germane in assessing the burden or who ultimately pays any tax, viz., a onrete idea of what is meant by tax inidene and tax base is essential. Tax inidene. Tax inidene is defined as the ultimate or final redistribution of inome due to the imposition of a tax. The final inidene of a tax is the burden plaed on individual households from taxes payed over their lifetime, net of lifetime benefits reeived from government expenditure programs. Ignoring benefits reeived, the distribution of the burden of a sales tax aross households depends on the breadth of the tax base (disussed later) and the market struture of expenditure ategories inluded in the base (disussed in Chapter 2). When.alulating the inidene of a partiular tax, the answer to who pays the tax, and who bears the burden are often different. One must look beyond those who are legally liable to find where the final burden lies. If taxes are olleted from business firms, the final burden will be traed to individual households as owners of the firm,

4 employees, produt. suppliers of other (nonlabor) inputs, or as onsumers of the Regardless of the type of tax or point of legal liability of the tax, the entire tax burden is ultimately borne by people. Tax base. The tax base is the subjet (items) upon whih the levy is formally imposed (Hellerstein, 1986). It is through the legislative proess that the tax base is ultimately defined. Exemptions from a tax base are often onsidered on grounds of stimulating eonomi ativity, equity, or politial lout of partiular interest groups. Assuming tax rates are held onstant, tax base has two impats. an inrease in the number of exemptions from a First, it narrows the taxable base resulting in a redution in the amount of revenue generated from the tax. The seond impat is a realloation of the burden of the tax. This realloation of burden may be intended to stimulate ertain types of eonomi ativity in hopes of attrating businesses to a partiular region or loation or to provide relief to households in l~wer permanent inome deiles on the grounds of equity. If exemptions are made from the base of a retail sales tax, the burden of the sales tax will be redistributed. If ategories suh as groery or drug purhases were exempt from the tax base, then the overall progressivity or inidene of the sales tax would hange. The diretion and magnitude of the hange would depend on how expenditure for these ommodities varies as a fration of permanent inome; for a given hange in permanent inome. Some Additional Definitions There are two onepts of equity having to do with ability to pay. The first is horizontal equity whih alls for equal treatment of households with the same level of ability to.pay. This implies that

5 households with the same level of permanent inome should ontribute an equal amount in taxes. On the other hand, vertial equity has to do with differential treatment of households aording to their ability to pay. Under this onept, households with higher levels of permanent inome should pay a greater amount of tax. The disussion of equity leads to the question how is the burden of a sales tax distributed relative to ability to pay. In other words how does the share (distribution) of taxes hange as a fration of permanent inome as permanent inome hanges. A regressive tax is one in whih the ratio of tax to permanent inome dereases as permanent inome inreases. A regressive tax plaes a greater share of the burden on households in lower permanent inome deiles. A progressive tax is one in whih the ratio of tax to permanent inome inreases as permanent inome inreases, while a proportional tax does not hange the tax to permanent inome ratio for a given hange in permanent inome. The assertion that a sales tax is regressive, implies that households in lower permanent inome deiles pay a larger fration of their total permanent inome in sales tax than do households in higher permanent inome deiles. As stated earlier the purpose of this study is to determine the validity of suh assertions inluding the sensitivity of the progressivity or regressivity of a sales tax to ertain expenditure ategory exemptions. Overview This study alulates the impat of expenditure ategory exemption on the. inidene of a retail sales tax. The data soure is

6 the "1982-1983 Interview Survey Publi Use Tapes", u.s. Department of Labor, Bureau of Labor Statistis. Family harateristis and expenditure ategories are generated for 3230 onsumer units (households). Examples of the 41 expenditure ategories are food onsumed at home, utilities and drugs. Annual expenditures on non-durable goods and servies is the proxy used for a household's level of lifetime or permanent inome. An instrumental variable is derived for this measu~e of permanent inome based on family harateristis suh as age of head of household, eduation, family size, reported inome, and family type. The expenditure ategories are regressed on a funtion that is. quadrati in family size and inome. The dependent variable (level of expenditures in a partiular ategory) is limited to a ertain range of observationsj therefore, heteroskedasti tobit regression analysis is used to alulate the relationship between different ategories of expenditures and permanent inome. Finally, total burden and measures of expenditure inidene are alulated. The total burden indiates the diretional hange of the dollar burden plaed on households for any expenditure ategory that is exluded from the base. It indiates how the total dollar burden hanges among households in different inome deiles for different family sizes. The inidene or progressivity that an expenditure ategory has on a sales tax is alulated. These measures of inidene are generated for different levels of permanent inome and different family sizes.

1 Outline of Thesis Chapter 2 presents seleted elements of the theory of tax inidene. The hapter fouses on those matters partiularly germane to assessing the inidene of a sales or onsumption tax relative to ability to pay. The differene between lifetime and annual inidene analysis is stressed. Rationale motivating a lifetime perspetive of tax inidene and the use of ~onsumption of non-durable goods as this study's measure of permanent inome is provided. A review of previous studies enables the reader to obtain a learer understanding as to why results differ rather dramatially depending on whether a lifetime or annual inome riterion is adopted. Empirial onsiderations are the topi of Chapter 3. The data soure and riteria used to aggregate household expenditures into different ategories are desribed. The empirial model is presented and defended, inluding disussion of means to orret for violations of desirable eonomi and statistial properties impliit in the problem and data set. Results are presented and disussed in Chapter 4; onlusions and impliations of the empirial findings are drawn. Finally, Chapter 5 briefly summarizes the results and impliations of the study.

8 CHAPTER 2 ANNUAL VS LIFETIME INCIDENCE: A REVIEW OF PREVIOUS STUDIES The reported inidene of a sales or onsumption tax varies among tax studies. The methodology used and assumptions made have signifiant impat on the results. One major differene among ontraditing tax studies is the measure used for eonomi apaity or ability to pay. The definiti~ns for regressivity and progressivity often impliitly assume annual inome as the metri against whih equity is judged. Not suprisingly, inome is the most often ited measure of ability to pay in different inidene studies. Most often, surveys olleting household statistis report annual inome. On the other hand, lifetime or permanent inome pertains to the permanent level of inome earned by a household over its lifeyle. (The permanent inome onept is further disussed in a subsequent setion.) The determination of final inidene of a tax requires the analysis of how government revenue is generated and expended. As previously stated, final inidene depends on taxes paid over a lifetime, net of lifetime benefits reeived. Diffiulty arises when estimating the benefits that a household reeives through government programs. The twin questions of how sales tax revenue will likely be distributed among alternative government programs and aross households are, for pratial purposes unanswerable (Browning and Johnson, 1979). This study looks at the burden and inidene of a sales tax. The burden of a sales tax is

9 defined as the total sales tax dollars paid by a household. The inidene of a sales tax is defined as the proportion (share) of inome that is the sales tax burden for the household. The benefits of government expenditures are ignored. This allows attention to be foused exlusively on the matter of tax inidene vis-a-vis ability to pay (or permanent inome). The purpose of this hapter is twofold. The first purpose is to motivate the use of permanent inome ai the preferred measure of a household's ability to pay. In so doing, literature is reviewed to present the differenes that annual versus permanent inome have on the alulation of inidene of a sales tax. Seondly, a rationale is presented for the permanent inome proxy utilized in the study. Assumptions made in this study are interspersed thoughout the hapter. Annual Inidene Annual inidene is the alulation of tax inidene using annual reported inome. Reent tax inidene studies that have alulated burden on the basis of annual inome found the sales tax to be regressive (Musgrave and Musgrave, 1984; and Pehman, 1985). In both studies, the total burden of the sales tax was assumed equal to the proportion of expenditure outlays subjet to the tax as a fration of annual reported inome. Total taxable expenditures, as a fration of annual inome, tend to derease as inome inreases. Therefore, assessing tax burden in proportion to taxable expenditure outlays on an annual basis leads to the onlusion that a sales tax is regressive.

10 Disagreement exists among tax analysts as to the extent to whih the tax burden falls in proportion to expenditure outlays. A sales tax an be passed forward to onsumers through higher pries, passed bak to fators of prodution (labor and apital), or a ombination of both. This study assumes that the burden of the sales tax is in diret proportion to expenditure outlays and thus is borne totally by onsumers. This is equivalent to saying that produt supply funtions are perfetly elasti or that produt demand funtions are perfetly inelasti for those items inluded in the taxable base. Either assumption alone an have a signifiant impat on the progressivity of a sales tax. However, to make the researh task manageable, perfetly elasti produt supply funtions are assumed. Serious questions revolve around the validity of tax inidene alulations omputed on an annual basis. Analysts note that a stronger, more plausible basis for analyzing the burden of a sales tax is permanent inome over the life yle of the household. Browning and Johnson (1979) note that annual data are biased in reported statistis. They point out that individuals or households in lower inome deiles may only be there for a short period of time (Browning and Johnson, 1979; pp. 24-25). Pehman (1985) motivates the above point by emphasizing that the effetive tax rates alulated in his study were based on inome data for a single year. Therefore, these rates may not be representati.ve of the tax burden a household faes due to unusually low (or high) inome in that year. Earnings an be unexpetedly low as a result of unemployment or illness. Pehman points out that a household often

11 ontinues to onsume at a level proportional to its longer run inome. Often, the share of taxes to inome is muh higher on an annual basis than when viewed over a longer time period. In onluding, Pehman suggests that the regressivity found in the lowest inome levels would be moderated, and possibly, eliminated if viewed from a life yle perspetive (Pehman, 1985; pp. 50-51). Lifetime Inidene History, Conepts, and Definitions Lifetime inidene is the alulation of tax inidene using permanent or life yle inome and onsumption. Muh of the theory used in life yle analysis today was introdued in the 1950s. The problems enountered in estimating a permanent relationship between household inome and onsumption dates bak to the 1930s, and possibly earlier. In 1936, John Maynard Keynes wrote of the relationship: The fundamental psyhologial law, upon whih we are entitled to depend with great onfidene both a priori from our knowledge of human nature and from the detailed fats of experiene, is that men are disposed, as a rule and on the average, to inrease their onsumption as their inome inreases, but not by as muh as the inrease in their inome (Keynes, 1936, p.96). When Modigliani and Brumberg (1954) first introdued the life yle hypothesis, they pointed out that if a onstant relationship between ' inome and onsumption ould be established, it would prove invaluable for eonomi analysis. Sin~e then, the life yle hypothesis has been empirially tested. The hypothesis has been both supported (Ando and Modigliani, 1963), and rejeted (White, 1978). Questions pertaining to the perfetion of apital markets have led towards relutany of

12 aeptane. Although~ the onlusions of a theory annot be rejeted based on the realism of its assumptions, skeptiism still exists. liquidity onstraints are imposed on households in redit markets. These onstraints an prevent households from onsuming at their optimal or permanent level during ertain periods of thei~ life. A similar theory to the Life Cyle Hypothesis has been advaned by Friedman (1957). Friedman argues that eah household has a measured level of annual reported inome (Y) and onsumption (C) and that these variables are the in turn sum of a permanent omponent (YP, CP) and a transitory omponent <~tt' ; 2 t> That is, ( 1 ) Yt = YP + ~lt Ct = CP + ~2t The permanent omponents of inome and onsumption are diffiult to desribe. Friedman (1957) suggests that permanent inome and onsumption depend on "those fators that the unit [inome produing or onsuming] regards as determining its apital value or wealth" [insertion added] (Friedman, 1957, p.21). Permanent Inome an be thought of as the level of inome whih a onsumer or household expets to reeive over a long period of time. It is this amount to whih it adjusts its permanent onsumption. Fators affeting the permanent omponent of both inome and onsumption are eduation, family size and personal ability. The transitory omponents (~lt' ; 2 t> represent flutuations in permanent inome and onsumption due to hane or aidental disturbane. An example on the inome side would be extremely low reported inome for a ow-alf operator due to drought or depressed attle pries. Similarly, if an individual were in a ar

13 aident and was laid up for six months, his I her transitory onsumption would be extremely large in absolute value. It is these transitory disturbanes on the permanent omponent that inorporate bias in annual reported inome and onsumption statistis. The life yle view and the related ideas of permanent inome and onsumption are aepted as maintained hypotheses for purposes of this study. This author subsribes to the ommonly held view that despite the ambiguities and methodolial/measurement problems posed by the life yle perspetive, it is a deidely more ompelling approah than is the annual inome approah. The oneptual diffiulties related to the underlying motivation for household onsumption behavior as well as the transitory omponent imbedded in inome data render the annual inome approah unquestionably more troublesome in ontrast. Life-Cyle Based Studies Several studies have been onduted using a life yle perspetive to determine the burden distribution of a sales or onsumption tax. The main diffiulty with life yle analysis is obtaining data that overs inome and onsumption over the life of a household. Many differenes exist between annual and lifetime data. Contrasting these differenes provides a learer understanding of the opposing results obtained from the two types of analysis. Davies, et al. (1984) summarize these ontrasting pointst 1) The inequality in the distribution of lifetime inome is smaller than for annual inome. Therefore, lifetime data show a smaller variane of personal inome tax rates amoung households when ranked by permanent data as opposed to annual data.

14 2) Transfer payments are less heavily onentrated in the bottom two deiles of the population, when viewed from a life yle rather than an annual perspetive. 3) The ratio of onsumption to inome varies less on a lifetime basis than on an annual basis (Davies, et al., 1984; pp. 640-641). Several studies that nave looked at the inidene of a sales tax given a lifetime or permanent inome perspetive have found the tax to be either slightly regressive or slightly progressive. The differene in the onlusions revolves around the assumptions made regarding bequests and the breadth of the tax base (Adams and Walker, 1977; Davies, et al., 1984; Davies, 1960). A sales or onsumption tax is (by definition) a proportional tax when it is assumed that all goods and servies are inluded in the tax base and that households leave no intergenerational transfers, either in the form of human apital or bequests. Adams and Walker (1977) onlude that if households leave no bequests, the burden is proportional aross all lifetime inome deiles. However, they found that non-zero bequests redue the perentage of lifetime inome that is taxed under a onsumption tax. If the share of bequests as a fration of inome is not equal aross all deiles, the tax is not proportional. Adams and Walker's onlusion is that if the share of bequests to inome inreases (dereases) as lifetime inome inreases, a onsumption tax is regressive (progressive). Davies, et al. (1984) onduted a similar study using a life yle simulation model to produe a set of lifetime tax inidene alulations for Canada. Annual inidene alulations were also estimated from the same data set. The purpose was to alulate and

15 ompare lifetime inidene of the Canadian tax struture to that of annual inidene of the same tax struture. The seond objetive was to ompare the robustness of annual and lifetime alulations. The major findings were 1) that tax struture is mildly progressive for annual and lifetime alulations and 2) that lifetime inidene alulations were more robust to different "shifting" assumptions than were annual inidene alulations. Another onlusion of Davies et al. is of partiular interest in the ontext of this study. That is,it was found that lifetime inidene of sales and exise taxes is muh less regressive than the annual inidene of the same tax alulated with the same data. The average lifetime sales and exise tax rate for Canadian households ranged from 15.0 in the lowest inome deiles to 12.4 in the highest inome deiles. This differs greatly from the average annual sales and exise tax rates whih ranged from 27.2 in the lowest deiles to 8.5 in the highest deile (Davies, et al., 1984). The extent to whih a broadly-based sales tax is regressive depends upon the atual distribution of bequests (as well as exemptions from the base to be disussed momentarily). Due to the lak of data, reliable estimates are not available. It is therefore assumed in this study that the share of intergenerational transfers (both human apital and bequests) as a fration of permanent inome is proportional aross all households. The lifetime inidene studies reviewed so far assume that the base is broadly defined. States that have a sales tax, without exeption allow for ertain exemptions from the base. Davies (1960) alulated

16 the inidene of a sales tax allowing for alternative tax bases and using four different inome onepts. The inome onepts used were gross (before tax) money inome, net (after tax) money inome, Fisher inome and permanent inome. Fisher inome is defined as "atual onsumption expenditures." An elastiity oeffiient was alulated to determine the inidene of a partiular tax base for a given onept of inome. If the elastiity of the base With respet to inome equalled one, the tax was said to be proportional. If the oeffiient was greater (less) than one, it was onluded that the tax base was progressive (regressive) (Davies, 1960). The Davies study looked at hypothetial tax bases that the Ohio State Legislature had not proposed, or had proposed and rejeted. The alternative tax bases inluded ategories ~uh as total onsumption, non-food onsumption, non-food onsumption and food sold in restaurants and total food onsumption. The results inidate that a sales tax is regressive under gross and net inome onepts, regardless of the base. However~ under the Fisher and permanent inome onepts, the sales tax was determined to range from slightly regressive to progressive depending on the breadth of the base. In every senario, Davies found that the exemption of food onsumed off the premises of the plae of sale inreased the progressivity of the base..it was also found that non-food exemptions allowed under the law inreased the progressivity of the base, but by a smaller magnitude than food exemptions (Davies,.1960, p. 944). The onlusion drawn from this literature, both life yle and annual varieties, is that the inidene and progressivity/regressivity

17 of a sales tax depend on a number of fators and assumptions impliit in the analyses. It is lear that the alulation of inidene will be affeted by the following fators: 1) whether a lifetime or annual time frame is aepted as the relevant perspetive; 2) assumptions regarding the nature of the markets (elastiities of supply and demand) for those goods goods and servies inluded in the base; and 3) the marginal share of and servies inluded in the tax base related to total expenditures (or onversely, of those goods and servies exempted from the base). A Proxy for Permanent Inome The data used in this study were generated from household surveys. The quarterly data were aggregated to provide household inome and expenditures for a single year. The transitory flutuations present in annual reported inome render annual inome an undesirable measure for inidene alulations. Therefore, permanent inome was the measure used to assess household ability to pay. Not only do researhers lak a omprehensive and extended time series data set on household expenditures and inome, but more importantly permanent inome by its very nature an not be known for existing households at any point in time. Thus, the "true" level of permanent inome for eah household is unknown. Fortunately, the Permanent Inome Hypothesis of freidman (1957) provid~s a means for deduing an estimate of household permanent inome. Freidman suggests that there is a linear relationship between permanent inome and onsumption and (as disussed previously) that urrent - inome

18 (onsumption) is given by permanent inome (onsumption) plus a transitory omponent. Formally, these relationships are CP = fjyp ( 2) Yt = YP + ~lt Ct = CP + ~2t where CP, YP, C, Y, and (~lt' ~ 2 t) are as defined for (1), E0; 1t> = 0, This study does not purport to test the Permanent Inome Hypothesis. Rather, the relationships between onsumption and inome in (2) are used to derive a proxy for permanent inome. Formal derivation and speifiation of the proxy variable is presented in Chapter 3; Barra (1984) points out that flutuations in permanent onsumption are muh greater due to hanges in permanent inome than due to hanges in temporary inome. If ~ household pereives its present level of inome as temporary, it will either save or dissave to maintain its onsumption patterns ommensurate with its desired level of permanent onsumption. Hall and Mishkin (1982) studied the sensitivity of onsumption to hanges in transitory inome. They found that the marginal propensity to onsume out of permanent inome was muh greater than for temporary inome. Stated alternatively from equation (2), Ct is a pre.ferred > Barra (1984) summarizes the empirial evidene on the'permanent Inome Hypothesis: More generally, statistial studies of onsumer spending over time indiate that the propensity to onsume out of permanent inome is large and not muh different from one (Barra, 1984, p. 95).

19 The relationship between permanent inome and onsumption suggests the use of onsumption as a proxy for permanent inome~ This study defines permanent onsumption as the annual expenditure on all nondurable goods and servies. Expenditures on durable goods are exluded from this measure. Bodkin {1959) notes that the element of savings in onsumption of durable goods would overestimate a household's permanent level of onsumption. However, he also notes that omitting annual servie flows from <previously and urrently aquired) durable goods underestimates permanent onsumption. Still, the definition of permanent onsumption would be overstated using total onsumption expenditures during years when onsumer expenditures on durables is rising (Bodkin, 1959, p.603). Therefore, expenditure on nondurable goods and servies was adopted in this study as a proxy for permanent inome (YP).

20 CHAPTER 3 DATA, EMPIRICAL MOpEL, ESTIMATION PROCEDURES AND PARAMETER ESTIMATES This hapter provides a desription of how the data set used in this study was generated from the seondary data soure. Criteria used to aggregate household expenditures are disussed. The empirial model is presented, and defended. Violations of assumptions of the lassial linear regression model and the methods used to drret for these violations are disussed. Data The data used in this study were generated from the "1982-1983 Interview Survey Publi Use Tapes" (U.S. Department of Labor, Bureau of Labor Statistis). The tapes present detailed data on inome and expenditures for approximately 16,000 households. Eah tape is divided into files whih represent quarterly data on reported inome, expenditures, and family harateristis by household. The data represents a random sample and are published in the Consumer Expenditure Survey: Interview Survey, 1982-83, Bulletin 2245. From these tapes, a data file was generated onsisting of 26 family harateristis and 52 ategories of yearly expenditures for eah of the 3230 households. The final data file inludes those households that started the interview in the first or seond quarter of 1982 or 1983. These four quarters are the earliest and latest dates that would

21 allow a household to start the survey and still report a full year's expenditure data before the termination date of the 82-83 tapes. The. reession in the fourth quarter of 1982 adds bias to reported expenditures on durable goods. The 3230 households were hosen in suh a manner to minimize the number of households that inluded data from the fourth quarter of 1982. Reported expenditures were in nominal terms. Thus, 1982 expenditures were inflated to 1983 pries when the statistial analysis was done. The inflator used was the ratio of the Impliit Prie Deflator for Personal Consumption Expenditures (IPD-PCE) from the first quarter of 1983 relative to 1982 (U.S. Department of Commere, Marh 1983, August 1983) IPD - PCE 83:1 IPD - PCE 82:1 The first step involved in generating the final data set was to read family harateristi information from the files BLS.INT.FMLY.08XX (XX represents the year and quarter of the interview, respetively). The family harateristi data inluded age and eduation of head of household, family size, and family type. An expliit breakdown of the family harateristis is presented in Appendix A, Table 7. The fortran program used to generate the family harateristis is presented in Appendix B (Figure 9). Findat onsists of one row of family harateristis and five rows of yearly reported expenditures for eah household. There are 54 expenditure ategories, inluding total expenditures and total expenditures on non-durable goods and servies. Forty-one of the

22 expenditure ategories.are used in the Tobit regression analysis. ategories omitted from the analysis do not represent expenditures Those for onsumption goods and servies that would possibly be subjet to the base of a sal,~ Household tax. expenditures are read from the files BLS.INT.MTAB.08XX. Those files ontain over 500 different lasses of expenditures. All but approximately four of these expenditure lasses (496) were ombined into more aggregate expenditure ategories. The resulting 41 ategories of expenditures on onsumption goods and servies differ mainly on the basis of whether the items represent durable or non-durable and/or luxury or neessity goods and servies. The 41 expenditure ategories are li~ted in Table 1. The breakdown of the lasses in eah of the 54 expenditure ategories found in Findat are presented in Appendix C, Table 8. The only modifiation made to the data at this stage is to those lasses that report redutions in mortagage prinipals. Catagories 8 and 52 ontain reported redutions in prinipal mortgages. These lasses are reported as negative expenditures in the survey. Therefore, the absolute value of these expenditure lasses is taken prior to aggregation in their perspetive ategories. The fortran progr~m used to aggregate household expenditures for a quarter is found in Appendix D (Figure 10). The third step is to aggregate quarterly household expenditures for a year. Those households who report zero expenditures on onsumption of non-durable goods for a single quarter are omitted from the data set. atagories 40, 41, and 42 represent expenditures on drugs, medial

23 Table 1. The 41 Categories of Expenditures on Consumption Goods and Servies. Category Category No. Desription No. Desription 1 Food at Home 21 Other Apparel 2 Food away from Home 22 Transportation Rental 3 Alohol 23 New Cars 4 Tobao 24 Other Transportation 5 Repair Material and 25 Used Cars Labor 26 Gasoline and Diesel 6 Building Material Fuel 7 Other Lodging 27 Vehile Parts and Fluids 8 Household Textiles 28 Auto Servies 9 Furniture 29 Transportation Fees 10 Floor Covering 30 Publi Transportation 11 Small Applianes 31 Presription Drugs 12 Large Applianes 32 Medial Supplies 13 Household Misellaneous 33 Medial Servies 14 Utilities 1 34 Insurane 15 Telephone 35 Reading Material 16 Water and Other Publi 36 Entertainment Equipment Servies and Supplies 17 TV and Radio 37 Entertainment Fees and 18 Household Domesti Admissions Servies 38 Entertainment Servies 19 Household Servies 39 Personal Care 20 Apparel 40 Eduation 41 Misellaneous Servies 1 Utilities = Fuel Oil +Gas (Bottled or Tank) + Coal + Wood and Other Fuel + Eletriity + Natural Gas.

24 supplies, and medial servies, respetively. Due to the wording of the interview questions, households ould report negative expenditures in the~e three ategories. If a household reeived reimbursement from an insurane ompany for medial servies paid for and rendered, the reimbursement is reported as a negative expenditure. Therefore, those three ategories are summed and set equal to zero if expenditures for the year are negative. The fortran program used to sum and merge quarterly expenditures with family harateristis is found in Appendix E (Figure 11). Finally, the four different files of family harat~ristis alled Findat. and yearly expenditures are merged into a single file Three additional modifiations are made to the data in Shazam. As previously stated, 1982 expenditures are inflated to 1983 pries. Seond, approximated property rental value is added to onsumption of non-durables (ategory 54). This is to aount for the amount of expenditure outlays for housing servies. It represents the onsumption of durable goods, whih is an important part of permanent onsumption. This value is equivalent to reported rental expenditures for families who live in rented housing. Third, ategories 17-22 are aggregated into the ategory, utilities. These ategories represent different soures of heating fuel and ele~triity. They are onsidered to be substitutes for eah other. If one soure of utility is taxed, the other sour~s are likely to be treated the same.

25 Empirial Model The model used in this study is an expenditure funtion. The funtion, whih is quadrati in family size and permanent inome, is 2 2 (3) eij = a 1 + dizj + rifj + ~iypj + BiYPjFj + W;YPj + ~ifj + Eij where (i = 1,2,3,...,41) (j = 1,2,3,...,3230) eij = expenditure on the ith ategory for the jth household, zj = vetor of family harateristis for the jth household, The Zj vetor is omprised of binary (0 or 1) variables as follows: A25 A35 A55 A65 AlOO OWNER RENTER EDELEM EDHIGH EDCOL EDGRAD H/W SINPAR OTHERFAM age of head of household <years) < 25, 25 < age of head of household (years) < 35, 35. < age of head of household (years) < 55, 55 < age of head of household (years) < 65, 65 < age of head of household (years), head 6f household owns housing, head of household rents housing, head of household is not high shool graduate, head of household is high shool graduate, head of household attended ollege (1-4yrs), put not a ollege graduate, head of household a is ollege graduate or greater, husband and wife family, single parent family, other type of family, Fj = family size for the jth household,

26 and YPj = permanent inome for the jth household, ij = stohasti disturbane on the ith expenditure ategory for the jth household. As previously stated, the proxy for permanent inome (YP) is onsumption of non-durable goods. The family harateristis inluded were those exogenous variables whih a priori appeared to be important in explaining a household's level of expenditure for different expenditure ategories. The variables family size and permanent inome were the most signifiant fators in determining the level of household expenditures for the different ategories. Equation (3) an be written as (4) or in matrix notation as (5) en= XPn +En (n = 1,2,3,...,41), where en is a (3230 x 1) vetor of total expenditures in the nth ategory; X is a (3230 x 7) matrix of independent variables (family harateristis, family size, and permanent inome); Pn is a ( 7 x 1) vetor of regression oeffiients; and En is a (3230 x 1) vetor of stohasti disturbanes.

27 Seemingly Unrelated Regression The ordinary least squares (OLS) estimates of the lassial linear regression model are unbiased and effiient under the following assumptions: (6) X is unorrelated with en, ( 7 ) E ( en ) = 0, (8) (Ik is the identity matrix (3230 x 3230), and (9) E ( e e' ) = 0 n P (n r p). Assumption (9) requires that the disturbanes from the different regression equations be unorrelated with eah other. In this study, violation of assumption (9) is likely. That is, many of the disturbanes on the 41 expenditure equations are likely to be orrelated with one or more disturbanes from the other expenditure equations. For -example, the disturbane on the equation for food onsumed at home is likely to be orrelated with the disturbane on the expenditure equation for food onsumed away from home. If the regression disturbanes are mutually orrelated then the ovariane (rrnp> is. This relationship between the disturbanes is what Kmenta (1971) refers to as "seemingly unrelated regression". Ordinary least squares estimates of regression oeffiients from seemingly unrelated regression equations are unbiased and onsistent. In general, OLS estimates are not effiient (Kmenta, 1971, pp. 519-520). However, Zellner (1962) proves that ordinary least squares estimates are

28 effiient, when eah of the seemingly unrelated regression equati 9 ns have exatly the same explanatory variables. Instrumental Variables The presene of an endogenous variable on the right hand side of equation (3) violates the onditions for onsisteny of the OLS estimator (Johnston, 1963). Correlation an exist between permanent inome and the disturbane from the same expenditure equation, i.e., E(YPtE. lj.. ) 0. This is due to the fat that onsumption of non-durable goods and servies is used as the proxy for permanent inome. The method used to provide onsistent estimators is instrumental A variable estimation. An instrumental variable (YPt> must fulfill two riteria: A 1) L(YPtEij) = 0 A (t. j) 2) L(YPtYPj). 0. A Criterion one states that the instrumental variable (YPt) must be unorrelated with the error term (Eij). The seond riterion states that the orrelation between the instrumental variable and the endogenous right hand side variable is not equal to zero. The greater A the degree of orrelation between ypt and ypj, the smaller is the variane of the instrumental variable estimator. For this reason, YPj is regressed on those exogenous variables that provide the greatest explanatory power. The model to derive the instrument variable is (j = 1,2,3,...,3230)

29 where = permanent inome for the jth household, = vetor of family harateristis for the jth household, where zj is defined as for equation (3), = family size for the jth household, = before tax inome for the jth household, and j = stohasti disturbane for the jth household. The ordinary least squares estimates for equation (11) are presented in Table 2. Substituting the instrumental variable derived from equation (9) into e quat i on ( 3 ), y i e 1 d s where (i = 1,2,3,...,41) (j = 1,2,3,...,3230) A A 2 A 2 Pij = ij + ~;(YPj- YPj) + B;(YPj- YPj)Fj + ~;(YPj- YPj). MFadden, Puig, and Kirshner (1977) prove that least squares estimates are onsistent, even with nonlinear funtions of the instrumental variable on the right hand side of the regression equation.

30 Table 2. Parameter Estimates and T-Ratios for the Permanent Inome Instrumental Variable. Family Charateristis Parameter Estimates (T-Ratio) INTERCEPT 6518.2 (13.037) z A25-1846.0 (-3.946) A35-1274.1 (-4.030) A55 809.78 (2.777) A65 1005.8 (3.367) OWNER -523.24 (-2.334) EDHIGH 1857.3 (7.546) EDCOL 2952.4 (10. 604) EDGRAD 4795.4 (16.777) SINPAR -2548.5 (-6. 181 ) OTHFAM -2225.4 (-8.366) YB 0.0362 2 YB (2.758) 0.106E-05 (9.556) F 1490.8 2 (6.511) F -95.145 (-3.614) FYB 0.303E-02 (1.058) R 2 = 0.4445

31 Tobit Regression Analysis Reported household expenditure data used in this study are, of ourse; non-negative. For many households, expenditures on durable goods during a year are zero. For example, expenditure ategories suh as ars and floor overing an have a large number of respondents reporting zero expenditures for any given year. This large onentration of observations at the lower limit of ertain expenditure ategories reates estimation problems. When this phenomenon is present the OLS estimator yields biased and inonsistent estimates. Tobin (1958) points out that when estimating the relationship between a limited dependent variable and exogenous variables, the onentration should be aounted for to avoid bias and inonsisteny in the OLS estimator. method employed in this study is alled Tobit Regression Analysis. The The Tobit proedure involves iterative maximum likelihood estimation on equation ( 12). Heteroskedastiity Assumption (8) of the lassial linear regression model requires that the variane of the disturbanes be onstant aross a 11 observations, i.e., (i = 1,2,3,...,41) (j = 1,2,3,...,3230). Violation of this assumption is prevalent in studies of this type. There tends to be greater variane in expenditures for households in higher inome deiles than for those in lower inome deiles. The result is heteroskedastiity whih violates assumption (8) and (13}.

The heteroskedati regression disturbane is written as 32 2 2 (14) E(e:ij) = <rij (i = 1,2,3,...,41) (j = 1,2,3,...,3230). That is, variane is not onstant aross j. Unfortunately OLS estimates are ineffiient with heteroskadasti disturbanes (Maddala, 1983). Maddala and Nelson (1975) report that a limited dependent variable model is both ineffiient and inonsistent if heterosk~dastiity is ignored. Thus it is important to ome to grips with this problem in this study. Four different assumptions of heteroskedastiity were made to identify the variane of the disturbane (Var(Eij)). The four different assumptions were: 1 ) 2 2 2 (T i j = YPjri (permanent inome squared x variane). 2) 2 2 (T i j = YPjri (permanent inome x variane). 3) 2 2 2 (T i j = F j r i (family size squared x variane). 2 2 4) (T i j = F j <r i (family size x variane). Heteroskedasti tobit regression analysis was used to estimate the parameters of equation (12). The values for the log-likelihood funtion for the four assumptions of heteroskedastiity were estimated and ompared to those from the homoskedasti model. These values are 2 2 2 reported in Table 3. The values for r 1 j = YPjri are greater for eah of the 41 expenditure equations than the values from the other four 2 speifiations of rij' This indiates that the variation of the disturbane is more likely due to the level of permanent inome than family size. However, it is extremely plausible that the inonsistent variane is due to a ombination of permanent inome and family size.