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D . degree in Economics /—.’/' yajor professor Date 61/16/9’5 MS U is an Affirmative Action/Equal Opportunity Institution 0 —1Z77 1 LIBRARY Michigan State L University PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or botoro date duo. DATE DUE DATE DUE DATE DUE ll MSU Is An Affirmative ActioNE qual Opportunity Institution czbtmmpma-pJ PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE: THEORETICAL INSIGHTS AND THEIR EMPIRICAL RELEVANCE BY Kelvin Robert Utendorf A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1993 ABSTRACT PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE: THEORETICAL INSIGHTS AND THEIR EMPIRICAL RELEVANCE BY Kelvin Robert Utendorf This dissertation examines the behavior of precautionary saving in the presence of unemployment insuranceu Given that others have found that precautionary saving could account for fifty percent of the aggregate life cycle capital accumulation in the United States, any factor which influences private precautionary saving has a potentially large effect on capital accumulation and future productivity growth. In chapter one, a precise link is developed between precautionary saving and unemployment insurance. A theoretical model is presented in which risk averse agents save as a precaution against the possibility of future unemployment. Two different types of unemployment insurance schemes are examined: a forced-saving plan with characteristics similar to those found in the 0.8. unemployment insurance system; a pay-as-you-go plan.possessing attributes similar to unemployment insurance systems found throughout much of the rest of the world. Precautionary saving is shown to be decreasing in the level of unemployment insurance benefits, and in fact is replaced by unemployment insurance benefits by more than one-to- one in the forced-saving model. Chapter two extends the theoretical model by giving agents the ability to borrow or lend. Previous work on precautionary saving assumes that loan markets are closed so that saving is the only means of intertemporal consumption smoothing. Opening credit markets provides agents with a second method of transferring resources across time periods. The addition of a forced-saving unemployment insurance plan is shown to harm non-covered workers by increasing the interest rate they must pay to borrow. Chapter three tests the relationship between unemployment insurance and precautionary saving using panel data from the National Longitudinal Surveys of men. Wealth-based measures of precautionary saving are regressed on an unemployment insurance generosity index and other determinants of precautionary saving. Precautionary saving is generally found to be positively related to the generosity of unemployment insurance, especially for unionimembers, whichrmay indicate that a greater than optimal portion of wages are replaced by unemployment insurance benefits. Copyright by KELVIN ROBERT UTENDORF 1993 This dissertation is dedicated to my parents, Robert and Agnes Utendorf, whose constant love and support enabled me to complete it. ACKNOWLEDGMENTS Writing a dissertation is a long, arduous process. Without the aid, support, and encouragement of many individuals, I never would have finished mine. Although words seem inadequate to express the extent of my appreciation, I am happy to have this opportunity to thank some of the people who played a part in my graduate education. I would not be writing these words were it not for my dissertation committee chair, Professor Rowena Pecchenino. Without her advice, her prodding, her patience, her experience, and her wisdom I could not have finished this work. Even though she was very busy with her own work and responsibilities, she always found time to listen to my problems, to answer my questions, to suggest improvements for the numerous drafts of this dissertation, and to offer words of encouragement. II mm forever indebted to her for the time and effort she has given to me and to my work. .Thank you, Rowena! I have also had the good fortune of working closely with the other two members of my dissertation committee, Professors Paul Menchik and Larry’ Martin, whose guidance and. direction have been invaluable in completing this dissertation. They spent many hours working with me on drafts of this work and provided many valuable comments and suggestions. I have learned much from them and have benefitted greatly from their knowledge and advice. In addition, I would like to express my gratitude to Professors Jeffrey Wooldridge, Jack Meyer, and Dan Hamermesh who read parts of this dissertation and offered many helpful suggestions. There are so many other people, both professors and graduate students, who have been important to me as I progressed through the Ph.D. program at Michigan State University; I am.especially grateful to my good vi friends Tony (Black Sox) Creane and Steve (Dream Team) DeLoach who have provided many hours of needed distraction from the rigors of the dissertation process and much good advice along the way. I also want to express appreciation to my fellow PADsters at the Institute for Public Policy and Social Research, Andrea Ranval, Dian Xashawlic, and Donna Anderson, who, in addition to providing computer facilities and financial support for the past two years, helped me to smile even when things seemed to be crashing all around me and provided a nearly infinite stream of encouraging words. No one has given me more encouragement and support than my best friend and confidant Margie Tieslau. Margie has shared in all of my victories and picked me up after all of my defeats. She helped me get through many, many rough times by listening to my problems and offering sound advice. Simply put, without her friendship, I probably would not have gotten my Ph.D. Margie, YOU ARE!!! Finally, to my family, THANK YOU!! Without the love and support of the 'Utendorf Clan," I would not have enjoyed the success that I did throughout graduate school. My mother and father have always offered their unconditional support and love, without which I would not have had the courage to undertake the Ph.D. process. The rest of my family, too, have always given me their full support, even though my workload often prevented me from participating in family events. This support has been invaluable to me. vfi TABLE OF CONTENTS L I ST or TABLE 5 O O O O O O O O O O O O O O O O O O 0 LIST OF FIGURES O O O O O O O O O O O O O O O O O O 0 CHAPTER I: 1. 2. 5. 6. PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE: A SIMPLE THEORETICAL MODEL . . . . . . . Introduction . . . . . . . . . . . . . . . The Model . . . . . . . . . . . . . . . . . The Agent's Problem . . . . . . . . . . . Comparative Statics on Precautionary CARA . . . . . . . . . . . . . . . The Forced-Saving Unemployment Insurance Model The Forced-saVing MOdGl e e e e e s e e s The Optimal Tax Rate in the Forced-Saving Model Precautionary Saving in the Forced-Saving Model The Pay-As-You-Go Unemployment Insurance Model The Optimal Tax Rates in the Pay-As-You-Co Model Model Precautionary Saving in the Pay-As-You-Go Comparative Statics on Precautionary Saving couCIUSj-on O O O O O O O O O O O O O O O 0 APPENDIX 1A 0 O O O O O O O O O O O O O O O O 0 REFERENCES 0 O O O O O O O O O 0 0 O O O O O 0 Saving 0 O O O O O 0 CHAPTER II: PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE 1. 2. 3. 4. 5. 6. MODEL WITH FUNCTIONING CREDIT MARKETS . Introduction . . . . . . . . . . The Extended Model Without Unemployment Insurance . The Agent' s Problem . . . . . . . . . The Forced-Saving Unemployment Insurance OCM Model The Optimal Tax Rate in the Forced-Saving OCM Model The Pay-As-You-Go Unemployment Insurance OCM Model Optimal Tax Rates in the Pay—As-You-Go OCM Model Comparing the Various Models . . . . . . . canoluaion O O O O O O O O O O O O O O O 0 APPENDIX 2A 0 O O O O O O O O O O O O O O O O 0 APPENDIX 23 . . . . . . . . . . . . . . . . . . APPENDIX 2C 0 O O O O O O O O O O O O O O O O 0 REFERENCES 0 O O O O O O O O O O O O O O O O O \Iiii xii U'IUH I-' 89 93 CHAPTER III: 1. Introduction 2. Data . 3. Index of Unemployment Insurance Generosity 4. Empirical Specification . . . . . . . . . . Cross-section Analysis . . . . . ... . . Panel Data Analysis . . . . . . . . . . . 5. Regression Results . . . . . . . . . . . . . . Cross-section Cross-section Cross-section Fixed-Effects Fixed-effects 6. Estimation Problems and Precautionary Saving Behavio Inadequate Measures of Precautionary Saving . . . Precautionary Savings Satiation Point . . . Liquidity Constraints . . . . . . . . . . . Data Problems . . . . . . . . . . . . . . . Precautionary 7. Conclusions . PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE: EHPIRICAL TESTS O C O O O O C O O C O O O O O I 0 APPENDIX 3A . . APPENDIX 38 . . APPENDIX 3C . . REFERENCES . . Results for the Savings Equatio s Results for the Saving Equations Regressions by Union Membership . Panel Regression Results . . . . . Panel Regressions by Union Membershi Saving Levels May Be Very Low oeoseefl'ueoooeeeoooo ix 96 96 100 104 106 106 108 110 110 116 119 120 123 124 124 125 125 126 127 127 130 160 164 166 TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE 1.1 2.1 3A.1a 3A.1b 3A.2a 3A.2b 3A.3a 3A.3b 3A.4 3A.5 3A.6 3A.7a 3A.7b 3A.8a 3A.8b 3A.9a 3A.9b 3A.10 3A.11 3A.12 3A.13a 3A.13b 3A.14a LIST OF TABLES Comparative Static Results for Precautionary Saving Comparative Static Results for Precautionary Saving LOGIT RESULTS USING SAVl, . . . . . . . . . . . . . REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAVl, LOGIT RESULTS USING SAV2‘ . . . . . . . . . . . . . REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAV2t LOGIT RESULTS USING SAV3, . . . . . . . . . . . . . REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAV3, REGRESSION RESULTS FROM DISSAVERS USING DSAVI O O O O O O O O O O O O O O O REGRESSION RESULTS FROM DISSAVERS USING DSAV2 . . . . . . . . . . . . . . . REGRESSION RESULTS FROM DISSAVERS USING DSAV3 C O O O O O O O O O O O O O O REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAVI‘ REGRESSION RESULTS FROM SAMPLE WITH NEGATIVE DSAV1‘ REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAV2, REGRESSION RESULTS FROM SAMPLE WITH NEGATIVE DSAV2, REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAVB‘ REGRESSION RESULTS FROM SAMPLE WITH NEGATIVE DSAV3, AGGREGATE SAVINGS REGRESSION RESULTS FOR 1966 UNION vs 0 NON-UNION O O O O O O O O O O O O O O O O AGGREGATE SAVINGS REGRESSION RESULTS FOR 1971 UNION vs . NON-UNION . O O O O O O C O O O O O O O O SAVING REGRESSION RESULTS FOR PERIOD 1966-69 WHEN SAVING IS POSITIVE, UNION vs. NON-UNION . . . . . . LOGIT RESULTS USING SAV1" PERMINC>$SOOO (1976 S's) REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAV1t PERMINC>$SOOO (1976 s I 8) e e e e e s e e e e e e s LOGIT RESULTS USING SAV2u PERMINC>$SOOO (1976 S's) SAMPLE WITH BOTH SAVERS AND SAMPLE WITH BOTH SAVERS AND SAMPLE WITH BOTH SAVERS AND 24 75 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE 3A.14b 3A.15a 3A.15b 3A.16a 3A.16b 3A.17a 3A.17b 3A.18a 3A.18b 33.1 33.2 33.3 33.4 3C.1 REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAVZ. PERMINC>$SOOO (1976 S's) . . . . . LOGIT RESULTS USING SAV3" PERMINC>$SOOO (1976 5") REGRESSION RESULTS FROM SAMPLE WITH PERMINC>$SOOO (1976 S's) . . . . . REGRESSION RESULTS FROM SAMPLE WITH PERMINC>$SOOO (1976 S's) . . . . . REGRESSION RESULTS FROM SAMPLE WITH PERMINC>$SOOO (1976 S's) . . . . . REGRESSION RESULTS FROM SAMPLE WITH PERMINC>$SOOO (1976 S's) . . . . . REGRESSION RESULTS FROM SAMPLE WITH REGRESSION RESULTS FROM SAMPLE WITH PERMINC>$SOOO (1976 S's) . . . . . REGRESSION RESULTS FROM SAMPLE WITH FIXED-EFFECTS PANEL REGRESSIONS . . FIXED-EFFECTS PANEL REGRESSIONS, FAMILY INCOME GREATER THAN $5000 . FIXED-EFFECTS PANEL REGRESSIONS, NOT UNION MEMBERS . . . . . . . . . FIXED-EFFECTS PANEL REGRESSIONS, UN I ON MEMBERS 0 C O C O C O O O O 0 INDEX OF UNEMPLOYMENT INSURANCE GENEROSITY xi POSITIVE SAV3‘ POSITIVE DSAV1( NEGATIVE osav1t POSITIVE DSAV2( NEGATIVE DSAVZ‘ POSITIVE DSAV3t NEGATIVE DSAV3, RESPONDENTS WITH RESPONDENTS WHO ARE RESPONDENTS WHO ARE 151 152 153 154 155 156 157 158 159 160 161 162 163 164 Figure 1 Figure 2 LIST OF FIGURES xii CHAPTER I: PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE: A SIMPLE THEORETICAL MODEL CHAPTER I PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE: A SIMPLE THEORETICAL MODEL 1. Introduction A great deal of theoretical and empirical work studies the effects of unemployment insurance (01) on various aspects of worker behavior. Topics such as duration of unemployment, rate of unemployment, the intensity of job search, and acceptable reservation wage have all been linked in various ways to the existence of unemployment insurance.‘ In addition, increases in the level of provision of unemployment insurance benefits have been shown theoretically to lead to decreases in the level of private saving.2 Presumably, agents change their saving behavior in these models because unemployment insurance benefits alter the need for self-insurance, or’precautionary saving, although.previous work has failed to make explicit that connection. Any program which has an effect on precautionary saving has a potentially large effect on aggregate life cycle capital accumulation. Hall and Mishkin (1982) and MaCurdy (1982) find that consumers face substantial uncertainty about lifetime resources which could lead to large levels of precautionary savings. Zeldes (1989) states that precautionary saving could account for a substantial portion of the capital accumulation in the U.S. while Skinner (1988, p. 238) argues that "precautionary savings are therefore calculated to be substantial, accounting for up to 56 percent of aggregate life cycle capital accumulation.” An unemployment insurance program which decreases precautionary saving could therefore have a tremendous impact on capital accumulation, particularly if "forced" saving under the auspices of the government is '80:, for example, papers by Foldstcin (1974, 1975), Chapin (1971), Ehrenburg and Oaxaca (1976), Baily (1978), and Fleming (1978). ’36: Baily (1978) and Flemming (1978). 2 not as efficient in producing capital as is private saving. With high administration costs and an emphasis on "low-risk” investments, saving in a governmental program may lead to lower capital accumulation and lower potential for future growth than would private saving. Unlike previous work in the unemployment insurance or precautionary savings literatures, this chapter specifically explores the link between precautionary saving and unemployment insurance. I present a theoretical model which can.be solved for an exact level of precautionary saving under two different types of unemployment insurance schemes: one with characteristics similar to those found in the U.S. unemployment insurance system, a second possessing attributes similar to unemployment insurance systems found throughout much of the rest of the world. Within the framework of the U.S. model, I find precautionary saving is decreasing in the level of unemployment insurance benefits, and in fact may be replaced by unemployment insurance benefits by more than one-to-one. The theoretical model provides testable hypotheses for an empirical examination of precautionary saving and unemployment insurance. This chapter is arranged as follows. Section two describes the basic*model before the introduction of unemployment insurance and provides a solution to the agent's problem. I also derive an expression for precautionary saving and detail the reaction of precautionary saving to changes in the parameters in section two. Section three introduces a forced-saving unemployment insurance scheme as well as the optimal unemployment insurance taxes for the model. I describe a pay-as-you-go unemployment insurance tax and disbursement scheme and solve for the optimal unemployment insurance taxes under that scheme in section four. Section five explores the reactions of precautionary saving in the models presented to changes in the parameters. Section six concludes the chapter by discussing possible extensions and by presenting testable hypotheses for the empirical work found in chapter three. 2. The Model In the base model% a. finite-horizon (two-period) economy is populated by N two-period lived agents. In any period i=1,2, pN agents receive a high endowment, em, at the beginning of the period, where p, assumed to be constant across periods, is the probability of receiving the high endowment. The remaining (1-p)N agents receive a low endowment, em, at the beginning of period i. All agents receive utility from consumption in each period of their lives. An agent maximizes expected, discounted life-time utility with complete knowledge of her first-period endowment but without knowing her second-period endowment. An agent with a high first-period endowment, in other words one who begins life ”employed,” solves the following problem: 2 max 81;: 61" U14 (€1.11) (1) -1 subject to Period 1: en, . on + s“, Period 2: e“ + 11813 = can (2) 920 + r1313 3 C20 where ij,U for high endowment (employed) or low endowment (unemployed), respectively, Elie the first-period expectations operator, be[0,1) is the subjective discount rate, cm is the second-period consumption level of an agent who receives a high second-period endowment while cu,is the second- period consumption level for an agent who receives a low second-period endowment, am is the amount saved by a high-endowment agent in the first period, and r, is the gross rate of return on savings. Throughout this chapter it is assumed that loan markets are closed, prohibiting agents from borrowing against future income. Thus, saving is the only avenue ’I‘his model is similar to the model used by Leland (1968). 4 available to agents who desire to smooth consumption.‘ The additively- separable utility function is assumed to be thrice differentiable, with U'()zO, U"(y50, and U'"()>O.s An agent with a low first-period endowment, an agent who begins life ”unemployed,” solves a very similar problem, maximizing (1) subject to 1 Period 1: em s on + Sm Period 2: e23 + 118“, = on (3) 320 I r1310 3 C20 where sw represents the first-period savings of an unemployed agent and the other variables are as defined above. The agents can take advantage of the very simple storage technology present in the economy if they so choose. An agent who saves slj in period one, jsE,U, receives rqf(su) in period two, where, for simplicity, it is assumed that f(su)=su. As stated earlier, :3 is the gross rate of return on savings in the economy. The use of a storage technology, rather than a production technology with capital and labor, allows for a sharper focus on the topics of precautionary saving, unemployment insurance, and the relationship, if any, between the two. An agent whose preferences are represented by a utility function exhibiting constant absolute risk aversiod‘ (CARA) will engage in precautionary saving behavior since such a functionrmeets the requirements set out in Leland (1968). The CARA functional form given by _ '1 'Y¢1.5 Um‘cm) ’ 7e ' (4) is used throughout this dissertation. Although it might be argued that the reaction to risk generated by this type of utility function is ‘Nearly all models which examine precautionary saving assume either explicitly or implicitly that loan markets are closed. Relaxing the closed loan market assumption is examined in chapter two. sGiven the additive separability of the model, a positive third derivative of the utility function is sufficient for the existence of precautionary saving. Leland (1968) proves that a positive third derivative of the utility function is sufficient for the existence of precautionary saving under weaker assumptions. “The Arrow-Pratt measure of absolute risk aversion is R(x)=(-U'(x)/U '(x)), where an agent is considered to be risk averse, risk seeking, or risk neutral as R(x))O, R(x) <0, or R(x)=0, respectively. 5 somewhat unrealistich,‘the CARA-type utility function is used heavily in the literature to portray risk-averse behavior. By using a CARA utility function, the results in this chapter can be more readily compared to previous work in the field. The other functional form used in the precautionary saving literature, the constant relative risk aversion (CRRA) utility function, does not allow for closed-form solutions for saving or for precautionary saving and is therefore less satisfactory for this type of study. Furthermore, the exponential utility function used can be thought of as belonging to the increasing relative risk aversion (IRRA) class of utility functions. IRRA utility functions are considered to be more realistic than the CRRA utility functions by Arrow (1974), Pratt (1964), and others. Therefore, although the exponential utility function may belong to the less reasonable CARA class of utility functions, it also is a member of the IRRA class of utility functions and as such merits attention. The Agent's Problem An agent who receives a high endowment in the first period of life solves the following problem“, in which the equations of (2) have been substituted into (4): max -1 e '1‘.u"'1')_ 62 e -Y(°2E.t1.u) _ 6 (l-p) e -Y(.30’I1lu) I 31; Y Y Y (5) The first-order condition for the above maximization problem is -8 «('13-'18) +0pI16 '1 (023*1181.) +6 (l'p)11e “7(920‘t1'1l) = 0 . ( 6 ) Equation (6) is the very familiar condition which indicates that an agent's utility is maximized.where her marginal rate of substitution (MRS) is equal to the marginal rate of transformation (MRT) she faces in the economy. The agent's MRS is equal to the ratio of her marginal utility 7Arrow, Pratt, and others have argued that utility functions which exhibit decreasing absolute risk aversion (DARA) are more realistic. However, DARA utility functions tend to be much less tractable than are the CARA utility functions. Pratt (1964) gives examples of DARA utility functions. 'An agent ”unemployed" in the first period solves a similar problem, maximizing (4) with respect to the constraints given in (3). 6 from first period consumption to the linear combination of her possible marginal utilities from consumption in the second period. The MRT in the economy is simply Or” the subjective discount rate times the rate of return to saving. The second-order condition for utility maximization, 'Ye '7 "“""’ “(6pr e 7 ‘°“"""’ ~76 (1 -p) 1136 '“"°"1'“’ < o ( 7 ) holds for all risk-averse agents, i.e. those for whom Y>0. Precautionary saving by an agent in this model, undertaken because of uncertainty with regards to future income, is the difference between the level of saving by the agent under uncertainty and the level of saving under certainty, sm-sfi;. Equation (7) can be solved explicitly for the level of saving under uncertainty by the employed consumer, sm, which is given by _ 1 -1e _ -ye 3:: ’ mllnwrl) +ye13+ln(pe "+(1 p)e “0] . (8) Saving under uncertainty by an agent unemployed in period one is found in a similar fashion to be = _l___ 81" y(1+r,) [1n(brl)+yem+ln(pe"”'+(1-p)e"°’°)] . (9) For reasonable values of :3, i.e. less than a 200% rate of return to storage, slU as given by (9) would be negative. The unemployed agent in the first period would like to borrow but is unable to do so. Since storagermust be non—negative, an agent unemployed in period one saves zero and consumes all of her endowment when facing uncertain second-period income. Throughout the dissertation, certainty means that an agent knows with probability one that her income in the second period will be the expected value of her random second-period income. In the model without an unemployment insurance scheme, the expected valwe of second—period income is pem+(1-p)ew. under certainty, therefore, saving by an agent employed in period one is c 1 918 = Wiln(ari)+yeis'7(pezs+(1‘p)eau)l - (10) Similarly, saving under certainty by an unemployed agent in the first period is given by 1 8c = — IU 7(1+I1) [1n(6r1) +Ye10-Y(pezg+(1-p)ezu)] - (11) Again, for reasonable values of r,, the expression for sf” in (11) is negative, meaning the unemployed agent saves nothing in the first period. Precautionary saving by an employed agent in the base model with no unemployment insurance scheme is PS?“ 1 = firs-[1116* 1(Pe;g+(1"P)ezai] : (12) 1 where for simplicity 6 . pe'teu 4, (1_p)e'\'ezu ) 0. Precautionary saving, as given in (12), will be positive as long as the high endowment in the second period is greater than the low endowment in the second period, a condition which I assume throughout the chapter. Aggregate precautionary saving in this model is the summation of the precautionary saving by the employed agents only. Since the unemployed agents do not save anything, they do not save as a precaution against an uncertain future. Aggregate precautionary saving is therefore P8P"! = 'Y—(‘J%T)—[ln£+ Y(pezg+ (1-1)) 620)] - (13) Comparative Statics on Precautionary Saving Under CARA Differentiating the expression for aggregate precautionary saving (13) with respect to the parameters of the model (r,, p, e25, and em) yields the following comparative static results 8P8?“ ,_ pN(1-p) (1_ e'g'w) < 0 1+1 1:900: 1 _ g (14) EEEEL__:=_EEE(1—£ilig)) 0 392s 1 +r1 i and 8 a1>s','°"1r . pN(-1nezu)) < o 1 y(1+r1)’ ‘1'”-8'7030 (15) BPS?“ _ 4111517 (peas+(1‘p)°sa+pL2—_T—— +Twas-92:70] < T I v (1+11) 7 > o The effect of a change in the coefficient of absolute risk aversion on precautionary saving is not shown. In models with agents whose preferences satisfy the von Neumann-Morgenstern axioms, the coefficient of risk aversion is constrained to be related to the reciprocal of the elasticity of intertemporal substitution.’ Any effects on precautionary saving which come about from changing Y may be a reflection of changing elasticity of intertemporal substitution rather than changing risk aversion.” In the certainty model with no unemployment insurance plan in place, for example, increasing 7 causes saving to fall, which reflects the strength of the intertemporal substitution effect. Given the difficulty of separating the intertemporal substitution effect from the risk aversion effect, nothing definitive can be said about the effect of changing ‘Y on precautionary saving in this framework. Therefore, the effect of changes in the coefficient of absolute risk aversion are left unexplored throughout the rest of the chapter. That precautionary saving is negatively related to low second-period endowment and positively related to high second-period endowment, as shown by the inequalities of (14), may at first seem counter-intuitive. However, increasing e2E while holding everything else constant increases the variability of second-period income in this model. This increased variability causes a risk-averse agent to increase her level of precautionary saving. Similarly, decreasing e20 will increase the ’l'hc elasticity of intertemporal substitution for consumption between any two time periods s and t is given by -U’(c,) /U’(c,) d(c,/ct) C./C, dlU’(c,) /U’(c,_)] a (ct) "' i"See papers by Wei] (1990), Farmer (1990), Selden (1978, 1979), Kreps and Porteus (1979), and Johnsen and Donaldson (1985) for theoretical and empirical evidence of this difficulty. 9 variability of second-period income, which in turn means that precautionary saving increases in the model. The first inequality in (15) shows that precautionary saving and the rate of return to storage in the economy are inversely related. This is true despite the fact that the effects of changes in the rate of return on total saving under uncertainty and on total saving under certainty are generally indeterminate without strong conditions on the parameters. Increasing the rate of return to saving allows an agent to provide an adequate "buffer” against variations in income with a lower level of precautionary saving. The agent is able to attain some desired "self- insurance coverage” goal with lower levels of precautionary saving, thus giving the inverse relationship between precautionary saving and the rate of return to storage. The reaction of precautionary saving to changes in the probability of receiving the high endowment in the second period cannot be determined as shown by the second expression of (15). For an individual agent, increasing the probability of receiving the high endowment, or of being “employed," decreases the variability of income in the second period of life, which in turn reduces the need to save for precautionary reasons. However, increasing p increases the number of agents engaging in precautionary saving which counters the effect of individual agents reducing precautionary saving. 3. The Forced-Saving Unemployment Insurance Model Two different types of unemployment insurance (UI) funding and disbursement schemes are examined in this section and the next. The first of these, a "forced-savings” plan, has two characteristics similar to the 01 system which exists in the United States.” In order to be eligible to receive unemployment benefits in the United States, one is generally required to have worked for some minimum specified time at some minimum "For a thorough discussion of the unemployment insurance system in the U.S. see Hansen and Byers (1990). 10 wage level prior to the period of unemployment. Also, the UI system in the U.S. was originally designed to be "trust fund” type system in which the individual states built up large enough fund balances in the U.S. Treasury during periods of low unemployment to weather periods of high unemployment. In this system, unemployment insurance is often seen as a form of forced saving in which the money paid into the fund for agent A is disbursed to agent A should she experience unemployment in a future period. Both of the properties described above are captured in the model of unemployment insurance in this section. The second model of unemployment insurance, presented in the next section, more closely resembles UI systems which exist in countries such as Great Britain'2 in that it has a "pay-as-you-go" funding scheme. Perhaps more properly termed "social insurance," one is not required to have prior work experience to qualify for the 01 benefits in this system. In addition, current payments into the system by the employed are immediately disbursed to the unemployed in the period.'3 In this type of system, the idea of unemployment insurance as forced saving is absent. The second model of unemployment insurance incorporates both features of the pay-as-you-go UI system. The Forced-Saving Model This model encompasses two aspects of the 01 system present in the U.S.: (1) only unemployed agents in the second period who were employed in the first period are eligible to receive benefits, and (2) payments made by employed agents in the first period are placed in an interest- earning fund from which disbursements are made to those unemployed agents 11See, for example, Reubens (1990), McLaughlin, Millar, and Cooke (1989), or Beenstock and Brasse (1986) for details on the assistance available to the unemployed in Great Britain. l3Great Britain actually has two programs for the unemployed. One program pays unemployment benefits out of a fund created by employer and employee contributions. Benefits are paid out of this fund to the eligible unemployed for a maximum of one year. The second program is a means-tested income support program for the unemployed which is of unlimited duration payable to people sixteen years and older who are not working full-time and whose income from all sources falls below established standards. Prior work experience is not necessary to receive income support benefits. M°Laughlin et al. ( 1989) report that over 60% of the unemployed claimants receive income support nflusdnndunmwmpbmmaubawfit 11 in the second period who were previously employed. Agents who were unemployed in period one, i.e. those without a "work history," are not eligible to receive unemployment insurance benefits in period two. In the first period, the endowments of employed agents are taxed at rate’tqs[0,l].“ Given that there are pN employed agents in the economy in period one each receiving the high endowment of em, the total tax revenue generated for the unemployment insurance fund is pNtlem. This tax revenue is placed in a trust fund held by a "government" whose sole function is to collect, hold, and disburse the 01 tax revenue. It is assumed that the government has access to the same storage technology available to individual agents, meaning monies in the fund earn a gross rate of return r“ During period two, therefore, erfiaem is available for disbursement to the unemployed of the period.” Of the pN agents employed in the first period, l-p will be unemployed in the second. Therefore, p(1-p)N agents will be eligible to receive 01 benefits during the second period of their lives, implying a per capita disbursement of r,’c:,e,,.:(l-p)’l to those who are eligible. The addition of this unemployment scheme does not affect the budget constraints of the agent who is unemployed in the first period of life. Being unemployed, such an agent would pay no 01 tax in the first period and would not be eligible to receive 01 benefits in case of unemployment in the second period since she would not meet the prior-work requirement. Therefore, agents who begin life unemployed are constrained by (3) and solve the same type of problem as they solved in the model with no unemployment insurance plan. These agents do not save under either certainty or uncertainty and therefore are not precautionary savers. “It is generally true that employees do not, in the strictest sense, pay an unemployment insurance tax in the U.S. However, much of the burden of such a tax falls on wage earners. Furthermore, if their total wages include benefits paid for by their employers, then an unemployment insurance tax can be considered a tax on employees' total wages. Such a tax on total wages is similar to the endowment tax of the model. "The rather trivial government budget constraint is that the tax revenues collected in period one multiplied by the gross rate of return on trust fund monies must equal the unemployment insurance disbursement in period two. 12 The budget constraints faced by the agent employed in the first period become Period 1: sun-ti) - on + s“ Period 2: e" + 1'18“ - on (15) 920 " Ilt1818(1-p) '1 I 131913 = C20 where the variables are as defined above or as defined in section two. The agent employed in period one now receives a smaller first-period net endowment and, if unemployed in the second period, receives the unemployment insurance payment of rfiqem(1-p)“. Under the assumption of constant absolute risk aversion, an agent facing the constraints in (16) would solve the following problem max -1 e -'(.1' (1"t1) -.u) _ 62 e -1 (.3..I1.u) 8n Y Y (17) .. 6 (1-2) e '7(920‘riciers(1'P)-l‘ri'is) T where the constraints have been substituted into the utility function. Performing the above maximization yields the following first-order condition _e .Y(.1.(1-t1)'.u) "(.u§tl.1') +bprle (18) +5 (1-13) 116 ”7(OW*IIC;Oa(1—p) 4:31.“) = O which shows that the optimal level of period-one saving by an employed agent is that which equates her marginal rate of substitution with the marginal rate of transformation she faces in the economy. The second- order condition for utility maximization holds for all Y >0 (i.e. , all risk averse agents). Solving (18) for the optimal level of saving under uncertainty, em, yields = ln(5r1)+ye13(1-t1)+ln'i’ y(1+r,) u (19) where Y . pe “an" (1_p) e -1(e,uar1t,eu(1-p)-ll . 13 The Optimal Tax Rate in the Forced-Saving Model In order to determine the optimal tax rate t” the optimal consumption allocations" must be determined by solving a constrained social planner’s problem. A social planner in the forced-saving model is only concerned with maximizing the lifetime welfare of agents employed in the first period because the unemployment insurance redistribution scheme in this system deals only with those who are employed during the first period. A planner, therefore, maximizes the expected lifetime utilities of the agents employed in ‘the first period subject to feasibility constraints. The planner maximizes the following function _-;LN e we“ _ 6212}, e ~1cu _ Op (lY-p) N e we” (20) subject to the feasibility constraints chn+pNsu+pNs ‘ a pNelg ppNC“ " ppNeZE+ppNIISIE (21) er-rfllfic,u = Pll'PlNezu+P(l-PlN11813+PN11$' where all variables, except s2, are as defined earlier. s' is the per capita saving by the planner set aside solely for payment to the unemployed in period two, and is therefore equivalent to the tax payments made by the employed in period one, i.e. s'==taem. The constrained social planner's problem presented above captures the forced-saving aspect of this UI system by ignoring the unemployed of the first period, since they do not qualify to receive unemployment insurance benefits, and by placing the saving undertaken for the second-period unemployed, s‘, in a fund which grows at the rate of storage available in the economy. Only those agents employed in period one but unemployed in period two are eligible to receive unemployment insurance payment from the fund, as indicated by the third feasibility constraint in (21). Solving the constrained social planner's problem given above yields the following first-order conditions which can be solved for sIE and 62 The solution implies that the planner I‘Optirnal in the sense that these allocations maximize the expected, lifetime utilities only of the agents employed in the first period. The planner is unable to affect the welfare of those agents unemployed during the that period given the constraints of the system being examined. 14 81‘: _ e -'(.lI-.13-..) ... 6px). 6 ’1 (Osa‘xs'u) - '1» 0 +6(1_p)rlefl(.n.11.u*(1 P) :1. ) = o (22) 8 . g - e -1(.13-.1E-..’ + 611 e "Y(Om‘11lu‘(1-p) -tr1. .) 8 O allocates resources so as to eliminate the second-period income uncertainty for an employed agent.‘1 The planner reduces the first-period incomes of all employed agents by an amount large enough to just equate the income received by an agent unemployed in the second period (low endowment plus unemployment insuranceidisbursement) with the income of the agent employed in the second period (high endowment). d'is given by the following 8 . = (828-820) (l-p) I1 . (23) meaning the optimal tax, t}, under the forced-saving UI plan is e = (623-620) (1.13) I1911: (24) The’optimal tax in this model is therefore increasing in the second-period high endowment, decreasing in the second-period low endowment, decreasing in the probability of employment, decreasing in the rate of return to the unemployment insurance trust fund, andidecreasing in the first-period high endowment. Precautionary Saving in the Forced-Saving Model Certainty, as described in section two, means that an agent knows with probability one that she will receive the expected value of her random second-period income. Under the forced-saving plan, the expected value of second-period income is pe25+(1-p)ezu+t.r,e,g. In the second period, an agent is employed with probability p, in which case she receives em, or she is unemployed with probability 1-p and receives the "This analysis assumes that the planner is restricted to an interior optimum. 1f second-period income disparity isgnatmmmfliuflnhmeu:hqpcmdmmmmugnwnhfiomrnnmimmnopmfintwo,hnmwtwtm:uuedmtfimb period income is not great enough to eliminate period-two income uncertainty without taxing away all of the first- period endowment. Given slow endowment growth, however, such a situation will not arise. 15 low endowment of en,plus the unemployment insurance benefit (provided she was employed in period one) of tgqem(1-p)“. Using this definition, the agent's saving with second-period certain income in the forced-saving model is given by s" = 1n(5:1) +ye13(1-t1(1+rl)) -y(pe23+(1-p)ew) (25) IE Y(1+I1) ' Using equations (19) and (25), the optimal level of precautionary saving for an agent employed in the first period in the forced-saving model is found by subtracting s& from sm to obtain the result PS, = 1n! +Yt111e13 TY (1)6234- (11)) 620) I! 1 (1+1,) . (25) where T'is as defined earlier in this section. Precautionary saving will be positive under this definition of certainty as long as t,¢t}.“ Since there is no precautionary saving by unemployed agents, aggregate precautionary saving in the forced-saving model is given by ps’ = pN(lnY +Yt1rlein +7 (Pezg*(1'p)ew)) ' 1(1+I,) (27) Comparative statics for precautionary saving in the forced-saving model are contained in section five. A comparison of equation (27) with the equation for the level of aggregate precautionary saving without unemployment insurance, equation (13), yields the following proposition: Proposition 1: There exist tax rates such that the introduction of a forced-saving unemployment insurance scheme promotes lower levels of precautionary saving than found in the model with no unemployment insurance scheme. Any tax rate less than the optimal tax rate will cause Psf to be less than Psfow. Proof: As shown by equations (1A.3) and (1A.4) in Appendix 1A and footnote 18, the figure on the following page approximates the relationship between precautionary saving in the model with no unemployment insurance scheme and precautionary saving found in the forced-saving model. For all values of t.l less than ”P8: =0, its minimum, at t,=t‘ and is equal to P5,?0m at t.=0. Over the range [0, t', ), P8,;: is decreasing in t., while over the range (t’, , 1), P83 is increasing in t.. At t,=1, PSé= again falls (discontinuously) to zero as the agent is unable to save because all of her income is being taxed away. 16 the optimal tax rate 63 PS: is less than Psfom. In addition, for some values of t1 greater than t', P8: is less than PSI‘OUI. The exact value of t. at which PS," becomes the greater of the two depends on the parameter values chosen. PS 8 PS 3 s I x. 6 PS 3 s . 0 * 1 t t, 1 Figure 1 Q.E.D. Thus, in the forced-saving model of unemployment insurance, imposing an unemployment insurance tax generally reduces the level of precautionary saving undertaken by agents below that found in a model with no 01 plan. At the optimal tax level, public saving in the form of forced saving completely eliminates precautionary saving due to uncertain future employment for those eligible for the unemployment insurance plan. This has a potentially important empirical implication in that if the unemployment taxes imposed on firms in the U.S. are near "optimal“ levels, then it certainly could be the case that the decreased impact of future income uncertainty has greatly reduced the levels of precautionary saving, possibly making it very difficult to detect empirically. 17 4. The Pay-As-You-Go Unemployment Insurance Model Two features of the type of 01 systems present in much of the world (other than in the U.S.) are captured in the following model: (1) unemployed agents are not required to have a prior work history to be eligible to receive benefits, and (2) the system is funded in a pay-as- you-go method in that taxes collected from the employed agents in period one are disbursed to the unemployed agents in period one, and similarly for period two. The endowments of agents employed in the first or second periods are taxed at the rates t.| or t,, respectively, where tutae[0,1]. Given that there are pN employed agents who are each receiving em in period one, the total tax revenue collected for unemployment insurance purposes in period one is pNtlem. Similarly, the total tax revenue generated for unemployment insurance use in period two is pNtzem. The tax revenue is collected by a government whose only function is to gather and disburse the UI tax revenue in each period.” In each of the periods, (1-p)N agents will be unemployed and therefore will be eligible to receive 01 benefits, meaning there is a per capita disbursement of p(1-p)”tnmg to agents unemployed in the first period and a per capita disbursement of p(1-p)"t2e25 to unemployed agents in the second period. The budget constraints faced by an agent employed in the first period become Period 1: emu-ti) = Cu: + SIB Period 2: cull—t2) + 1191, = C2: (28) 920 1’ p(1-p)‘1t2e23 + 11313 2 C20 where the variables are as defined earlier. An agent unemployed in the first period faces the following budget constraints "The government budget constraint requires that tax revenues collected in any specific period equal unemployment hmumwedhmmummmuhrmMJxfimi 18 Period 1: em + p(1-p)'1t1en - cm + Sm Period 2: sun-ta) + rlsm - c3, (29) em + p(1-p)'1t,eu + r18“, s cm . An employed agent receives a smaller net endowment in the first and second periods and an unemployed agent receives an.unemployment insurance payment to supplement her low'endowment during her period(s) of unemployment. The transfers from employed to unemployed in the pay-as-you-go model are intraperiod transfers rather than interperiod transfers characteristic of the forced-saving model. Under the assumption of constant absolute risk aversion, an agent employed in the first period solves the problem max '1 e ‘7‘91sl1't1)"1s) _ 62 e ”7(92sl1't2)‘t1'tsl 813 Y 7 (30) _ 0 (1-2) 8 -v(emrp(1-p) "taezvranl 7 where the budget constraints given in (28) have been substituted into the utility function. Solving the above maximization problem yields the first-order condition ..e -'(.ll(1-t1) "u’ ... bprle -1(e23(1-t2)‘t1.13) 31 + 6 (1-p) Ile -1‘.3v*p(1'p) -1t393'irllu) = 0 ( ) which shows that the optimal level of saving in the first period by an employed agent is that which equates her marginal rate of intertemporal substitution with the marginal rate of transformation she faces in the economy. The second-order condition for maximization holds for all risk averse agents. Solving (31) for the optimal level of saving under uncertainty yields a = lnlbr1)+ye13(1-t1)+ln0 18 7(17'11) (32) where n . p6 '79ssu'ts) ... (1 _p) e 'Y(°zu‘P(1'P)-1tz°zs) Solving a similar problem for an agent unemployed in period one gives the 19 following expression for em __ ln(6r1) +y(em+p(1-p)'1t1eu) +1nO 310 ’ y(1+r1) (33) When facing uncertain second-period incomes, employed agents will save if < ln (6110) + yen 34 7313 ( ) t:1 which is also a sufficient condition for unemployed agents to save nothing in period one.‘'0 If the first-period tax on employed agents is great enough so that 121 > -(1-p)(yem+ln(8110)) I (35) 713913 then employed agents in period one would save nothing while the unemployed would be savers.” The Optimal Tax Rates in the Pay-As-You-Go Model Determining the optimal tax rates, t, and t2, in the model requires solving the social planner's problem relevant to this framework for the optimal consumption allocations. Unlike in the forced-saving unemployment insurance scheme, under which the planner is unable to affect the utility of those initially unemployed, in the pay-as-you-go plan, the planner allocates resources so as to maximize the welfare of all agents in each time period. Thus, the planner under this UI system is not limited to only interperiod transfers as in the forced-saving unemployment insurance system. Once the optimal consumption allocations are obtained, a tax scheme which brings about those optimal allocations is determined.from the budget constraints and the maximizing saving choices. ”A necessary condition for the first-period unemployed to demand "negative" storage is < -(l-P)(ve.u+ln(6r.0)) ‘flpm , which is satisfied if (34) holds. h 2'(35) is sufficient to cause employed agents to desire to borrow, but they are prohibited from negative storage. 20 The social planner maximizes the following function 'ENe-ycu_ (l-p)Ne-ycm_ pre‘chs- 5(1-p)Ne-ycn (36) Y Y Y Y subject to the feasibility constraints chu+ (1 -p) Ncm+pNsu+ (1 -p) New . pNeu+ (1 -p) New (37) chn+ (1-p)Ncw = pNe23+ (1 -p)New+pN1:1sm+(1-p)N:rlsm in order to determine the optimal consumption allocations for this economy. Solving the constrained maximization problem given above yields the following first-order conditions cu: pNe "7°“ —J.pN = 0 pre "7°" - 1%! = O 1 cm: (1-p)Ne"°‘°-A(1—p)N = 0 6(1-p)Ne""”"-).(;;M = o 1 03': (38) C20: from which it can be shown that the social planner allocates resources so that C ‘C 13 10 (39) can = C2!) - The equalities in (39) show that the planner under the pay-as-you-go systemt equates the marginal utility of consumption (and given the functional form, actual consumption) in both periods across states. In the forced-saving scheme of the previous section, the constrained planner equates only the marginal utility of consumption from period two across states since in that system the planner is unable to allocate resources to those initially unemployed. The optimal tax rate for each period may be determined by finding that t" i-l,2, using the budget constraints (28) and (29), which brings about the equalities given in (39). The optimal tax rates for the pay-as- you-go model of unemployment insurance are similar in form to the optimal tax rate from the forced-saving model and are given by the following tel = (ell-e10) (l-p) (40a) 913 and 21 e _ (323-320) (1.1)) 3 '- —-———— . 40b e“ ( ) In both periods, these rates are increasing in own-period high endowment, decreasing in own-period low endowment, and decreasing in the probability of being employed, p. In the pay-as-you-go model, the rate of return to storage plays no role in the unemployment insurance taxation process because tax revenues collected in period one are immediately disbursed to the unemployed in period one and there is no "funding” involved in the process. Also in the pay-as—you-go model, the tax rates do not depend on the parameter values present in the other period, i.e. tn does not depend on any period-two parameters. This is not the case for the forced-saving model in that, due to the interperiod nature of the forced-saving scheme, the ratio of the endowment difference in period two to the employed endowment in period one plays an important part in determining the level of the optimal tax. Precautionary Saving in the Pay—As-You-Go Model As with the previous two models, certainty in the pay-as-you-go model again signifies that an agent knows with probability one that she will receive the expected value of her random second-period income. In the pay-as-you-go model, an agent will be employed with probability p in the second period, in which case she receives e25(1-t2), or will be unemployed with probability (l-p) in the second period, meaning she receives the low endowment e2U plus the unemployment insurance benefit (whether employed or unemployed in period one) p(l-p)"t2ezg. The expected income she receives with probability one in the second period is therefore pen(1-t2)+(1-p)ew+ptzem. The level of saving under certainty by an employed agent, sfg, is given by 3,, = 111(611)+Y(e13(1-t1)-pe23-(1-p)ew) 1! Y (1+I1) (41) Saving by an agent unemployed in period one when facing second-period income certainty is 22 8° _ 111(611) +y(em+p(1-p)'1t1)eu-peu-(1-p)e20) m - Y(l+11) (42) If t,.is such that both t1 < 1n(br1) ‘Y(pe:,;1:1-p)ezu) Help. (43) and t1 < -(1'P)[1n(6rL-y(pen+(1—p)ejl) +1619] ' (44) ypen then an agent employed in period one will save while an unemployed agent in period one, who would like to dissave but cannot, saves nothing. If the inequalities in (43) and (44) are reversed, the roles of saver and non-saver are reversed. Precautionary saving by an employed agent when (43) and (44) are true22 is the difference between total saving under uncertainty, (32), and total saving under certainty, (41), and is given by , __ 1n0+y(peu+(1-p)ezu) 93, “1+!” , (45) where (I is as defined earlier in the section. Precautionary saving by an employed agent will be greater than zero as long as tzst; (and t,¢l).23 Since the unemployed agents, when (43) and (44) hold, are saving zero, aggregate precautionary saving in this case is pN(1n0 +7 (pen + (1-p) 620)) P .. PSI Y(1+I1) (employed) . (46) When (43) and (44) do not hold, precautionary saving by an unemployed agent is again given by (45). Aggregate precautionary saving when only the unemployed are saving is (1-p) N(1n0 +7 (pen + (1-p) 620)) 93’ = ' y(1+r,) (unemployed) . (4?) Comparative static results on the versions of precautionary saving given 22Note that if t, is such that (43) is true, then (34) will also be true. ”P8; is minimized (=0) at t, = t5. At t, = 0, P8; = P330"! , over the range [0, t5), precautionary saving is decreasing in t, and positive, and in the range (t; , 1] precautionary saving is increasing in t2 and positive. 23 by (46) and (47) are contained in section five. As in the forced-saving model, comparisons of equations (46) and (47) with the equation for precautionary saving in the>model with no unemployment insurance yield the following proposition: Proposition 2: There exist tax rates such that the introduction of a Proof: pay-as-you-go unemployment insurance scheme promotes lower levels of precautionary saving than found in the model with no unemployment insurance scheme. Any tax rate less than the optimal tax.rate will cause P8: to be less than Psfm”. As seen from (1A.16) and (1A.17) in Appendix 1A and footnote 23, the figure below approximates the relationship between precautionary saving in the model with no 01 system and P8: when the employed agents are saving. For all t2e(0, t; ) , precautionary saving in the pay-as-you-go model is less than that in a model with no 01 scheme. The value of t5 greater than the optimal tax rate at which P8: becomes greater than Psi“) U' depends on the parameters of the model. Since aggregate precautionary saving by unemployed agents is less than that by employed agents in the pay-as-you-go model, the above argument also holds in the case of unemployed saving. PS Figure 2 9.3.0. 24 5. Comparative Statics on Precautionary Saving This section presents and discusses the comparative static results for the three models of precautionary saving given in this chapter: the model without an unemployment insurance scheme, the forced-saving model, and the pay-as-you-go model. Table 1.1 below summarizes the comparative static results on aggregate precautionary saving for the various models.“ Table l . 1 Comparative Static Results for Precautionary Saving' rl P 928 3w tlelE t:2 rs?“ - 2 + - N /a N/A ?2 +2 _2 _2 PS' (employed) - +5 _. +5 N/A ,5 , _4 +4.7 _4 _4 PS, (unemployed) - ?, _. +5 N/A +5 'Blocks with N/A inside indicate that either the expression for precautionary saving does not contain that variable or that the variable is examined jointly with another variable (i.e., t1 and e"I were examined as one variable, he“, in the instances where they always appeared together). Any assumptions used to sign a partial derivative are noted and explained in the other footnotes below. All signs are determined underthe assunption that pamnretu values are such that the applicable precautionary saving is non-negative. A question mark indicates a partial derivative whose sign is indeterminate. 11ft, is less than the optimal tax rate, tf. ’lf tI is greater than the optimal tax rate, tf. ‘Ift, is less than the optimal tax rate, t; ’lft, is greater than the Optimal tax rate, Q. ‘lft, is greaterthan t; but less than l-p. 7!! t, is greater than l-p. When the 01 tax rate is below its optimal value in the case of the forced-saving model, and for all tax rates in the other models, precautionary saving is inversely related to the rate of return to storage. In the forced-saving model, increasing rl has three effects: (1) substitution: saving, including precautionary saving, is more attractive since the same investment now yields a relatively higher return; (2) “The complete derivations for the comparative static results are given in Appendix 1A. 25 income a: since a lower level of precautionary saving provides the same level of 'insurance»coverage,' precautionary saving tends tondecrease; and (3) income b: a higher rate of return means a larger disbursement to the unemployed, reducing the need for precautionary saving. For the forced- saving model, income effects (2) and (3) dominate so that precautionary saving and r‘ are inversely related. In the pay-as-you—go model, there is no effect (3). The income effect given by (2) alone, however, dominates the substitution effect, again implying an inverse relationship between precautionary saving and the rate of return to storage. Proposition 3: A change in the rate of return to storage in the economy causes a smaller response in precautionary saving in the pay-as-you-go model than in the model without an unemployment insurance scheme when parameter values are such that PSItI in the forced-saving model, an increase in the probability of being employed in the second period actually increases the individual agent's desired precautionary saving and this, combined with the increase in the number of employed agents, causes an increase in aggregate precautionary saving. The agent insures herself against the possibility of being employed if the tax rate is high enough because with t,>t:, her income would be higher were she to be unemployed. At high unemployment insurance tax rates (high relative to the optimal rate), an increasing unemployment rate may therefore actually decrease aggregate precautionary saving in an economwaith a forced-saving 01 plan. When the employed are saving in the pay-as-you-go plan, the analysis of the effects of a change in p on precautionary saving is similar to that given for the forced-saving plan. However, in the case of first-period UI tax rates great enough that the unemployed become savers in the pay-as- you-go plan, the relationship between p and aggregate precautionary saving changes. When p increases, there are fewer unemployed savers which means lower levels of aggregate precautionary saving due to effect (3) above. The individual agents still react to changes in the probability of being employed in the second period as they did in the no insurance and forced 27 saving models. If t2t'i, i=1,2, precautionary saving is positively related to the second-period low endowment because an increase in em in that situation causes an increase in income disparity which drives the agents to increase their precautionary saving. One can think of e2U as a basic, subsistence level of service available to all agents. Any increase in aid from 28 programs such as welfare, AFDC, or a national health care plan reduces the need for agents to undertake precautionary saving (if unemployment insurance tax rates are below the optimal rates) to protect against job loss since programs like the above will suffice to maintain an agent's life. As indicated by the models, increasing such aid could decrease the level of precautionary saving by an agent. Proposition 4: A change in second-period endowments causes a smaller magnitude change in precautionary saving in the forced- saving model than in the model with no unemployment insurance. Proof: To show that proposition 4 holds for e2E in the case of the forced-saving model vs. the no 01 model, it must be shown that the partial derivative in the no insurance case is larger than that in the forced-saving model (since precautionary saving is positively related to em). This will be true if T<€, which can easily be shown. In the low second-period endowment case, the partial derivative in the no insurance model will be smaller than in the forced-saving model (and hence larger in magnitude) if the term 111t1elg(1-P)'1 is non-zero. Q.E.D. An increase in em or a decrease in e2U causes a larger increase in precautionary saving in'thexmodel without an unemployment insurance scheme than in the forced-saving model. Thus in an economy in which expected wages are quickly increasing or quickly decreasing, according to this model one would expect to find higher levels of precautionary saving if there were no unemployment insurance scheme. If future labor income is expected to be highly variable, the presence of unemployment insuranceemay actually hinder capital accumulation in the aggregate. The second-period tax on endowments is found only in the pay-as-you- go model. Whether the level of precautionary saving is positively or negatively related to changes in.td depends on whether ta is greater than or less than the optimal tax rate in the economy. At a high enough tax rate (i.e., at a tax rate greater than the optimal tax rate), so much income is being transferred from the employed to the unemployed in the second-period that an agent facing the saving/consumption decision in the 29 first period*would save to insure herself against the possibility of being employed in the second period. Further increases in the tax rate beyond the optimal rate would induce further precautionary saving on the part of an agent. For tax rates smaller than the optimal tax rate, increasing the tax rate towards the optimal rate would decrease the income uncertainty faced by an agent during the second period and would therefore lead to a decrease in precautionary saving. Precautionary saving is inversely related to the amount of unemployment insurance tax paid in the first period, tlem, in the forced- saving model if t,t,'. Increasing tea has two effects: (1) it decreases the resources available to the agent for consuming and saving in the first period; and (2) it leads to higher 01 disbursements in the second period. In both cases, effect (1) reduces the level of precautionary saving undertaken by an agent under the assumption that saving and precautionary saving are normal goods. If tpt{, then increasing tqlcauses a widening of the income disparity in period two and causes an agent to desire higher levels of precautionary saving. In this case, effect (1) and effect (2) conflict, with effect (2) dominating, so that the net result of an increase in t. if t.>tf is an increase in precautionary saving. One failing of this simple model is that it does not distinguish clearly between the tax effects and the disbursement effects of unemployment insurance in the forced-saving model since all monies collected by the government in the'model are disbursed to unemployed agents. In the 1980's in the 0.8. we observed a period during which the taxes collected for unemployment insurance increased while the levels of benefit provision fell. In part this was an attempt by states to replenish their 01 fund accounts held by the U.S. Treasury after the periods of high unemployment during the late 1970's and early 1980’s. A richer model which allowed for greater independence between 01 tax levels and benefit levels, however, 30 might not allow for the clear exposition afforded by the present framework. Proposition 5: There exist tax rates t,less than the optimal tax rate such that an increase in t,e,5 leads to a proportionately greater decrease in precautionary saving in the forced- saving model. Proof: In the forced-saving model, the partial derivative of precautionary saving with respect to tle"; will be less than -1 if c1< (63"°30H1’p)- 11’ 1 “1+2!" (48) I191: 711313 p(1+211)-(1+I1) which means tl must be less than the optimal tax rate. If the right hand side of the inequality above is greater than zero, then there exist feasible values for t, for which the statement in proposition 5 holds. The right hand side of the inequality will be greater than zero if P(1+211) p(1+211) - (1+r1) e 7 (‘as'°as) (49) which depends on the parameter values chosen. However, there are certainly reasonable values for em and en,for which (49) could be true, meaning a feasible t, exists for which (48) is a true statement. 9.3.0. Thus, it is possible for 01 benefits to "more than replace" precautionary saving in the forced-saving model, which has definite policy ramifications. If greater capital accumulation is desired in order to spur investment, the forced-saving model presented here indicates that an increase in unemployment insurance benefits could be counterproductive. Therefore, even in the unlikely event that "saving" with the government produces capital as efficiently as private precautionary saving, the levels of precautionary saving could still decrease in the aggregate because of this more than one-to-one offset, with the end result being a reduction in capital growth and a deterioration in the infrastructure of the country. 31 6. Conclusion This chapter presents two different models of unemployment insurance in a simple framework. In both models, one a forced-saving plan with features common to the 01 system found in the U.S., the other a pay-as- you-go plan with characteristics found in unemployment insurance schemes found in other parts of the world, the reactions of precautionary saving to changes in various parameter values are derived. The level of precautionary saving is found to be inversely related to the level of unemployment insurance benefits provided if the unemployment insurance tax rate is less than the optimal tax rate and directly related to the level of 01 benefits provided otherwise. Furthermore, 01 benefits are found to replace precautionary saving by more than one-to-one in the forced-saving model for certain feasible 01 tax rates. In chapter three, both of the above effects will be tested empirically. In addition, tests will be done to determine whether the relationships between precautionary saving and the probability of being employed and between precautionary saving and the rate of return in the economy found in this chapter can be shown empirically. Besides the empirical chapter, chapter two presents an extension to the model used in this chapter. Nearly all of the work on precautionary saving (including this chapter) assumes that loan markets are closed, meaning the only avenue available for consumption smoothing is saving. In chapter two, the model is extended by opening loan markets to allow agents to borrow against future incomes and the effect this has on precautionary saving is examined. APPEND I X 1A 32 APPENDIX 1A Derivatives for the Forced-Saving Model Aggregate precautionary saving in the forced-saving model is given by pN(1n‘P +7t1r1eu +7 (pen + (1-p) 92(1)) P where a -7.“ - " 1’ pa +(1 p)e 7" (114.2) I‘ ' eart"r1‘:1e1s(«1-'F’) -1 ' Propositiqp l utilizes (1A.3) and (1A.4), which examine the relationship between PS, and t” in order to show the relationshiplbetween precautionary saving in the forced-saving model and precautionary saving in the model with no unemployment insurance scheme. The optimal tax rate tf is the solution when (1A.3) is set equal to zero, and given that g}A.4) is always greater than or equal to zero, is the minimum point for P8, in the P8,, t, plane. BPS: = erle13(1 _ e ’1') (1A. 3) 3t1 14’:1 ‘P a’ps: . pN‘rrieig e '7" _ e '2" ‘ (1a. 4) (1A.S) through (1A.9) give the partial derivatives of P8: with respect to rt! 322! 920! PI and ttelE: 3:: = -pN(ln‘P+7tlrlem+7(pe,E+(1-p)e20)) 2 1 7(1+II) (1A.5) + pNt1e13(1 _ e'Yll) 1+1:1 ‘l’ 3P8: 2N( e'Y‘aa) = - 15.6 ‘39—“ Lu“ 1 T ‘ ’ BPS: = pN(1-p)(1_e"") (IA-7) 3e” 1+11 \ Y 33 aps‘.’ _ N $- Wfln? +Ytlrlell *7 (Pest: + (1'9) 630)] (1A. 8) . we... - «1 W" a» w") . mean- .20, 7 (1+II) Y 1H5: 3P3: er1( e -1“) = - 1A. 9 a—W _1+1:1 l T ( ) Derivatives for the Pay-As—You-Go Model Aggregate precautionary saving when the employed agents are saving in the pay-as-you-go model is given by pN(1nO + 7 (pen + (1 -p) 82:9) ps‘.’ = “1+1 ) (employed) (1A.10) l where . .7033 (1 ‘t3) _ ~13 0 pe +(1 p)e (“'11) a) - ew+p (1-p)‘1t,e,3 (1A.12) through (1A.16) give the partial derivatives of PS}, for the employed agents with respect to the parameters r“ em, ew, p, and t,: 898: _ pN(-1n0-7(pe23+(l-plewl) - 1a.12 5’ 7 (1+11) 2 ( ) @358: pzN ( (l-tz) e-"Ml-t’) +t2e 4”) = - 1a.13 3' 1‘11 1 O ( ) 36—3“: M[ e-..) = - 113.14 20 1+11 1 Q ( ) 393’ N W e -8 39. . 7(1+rl) [1n0*Y(Peza+(1-p)ew)]+__(13_;1_ml (1A.15) + pNie -7033(1-ta) — (1 +Yt2623+Yp(1-p) -1t2923) e -7") Y (“11) 0 3P3: - P’Nezx(e "°u‘1"=’ -e"“) (la. 16) 3E, ' (1mm 34 Proposition 2 makes use of (1A.16) above and (1A.17) below in order to determine the relationship between PS, and t2. This information is then used to contrast precautionary saving in the pay-as-you-go model with precautionary saving in the model with no unemployment insurance plan. Setting (1A.16) equal to zero and solving for t, yields t;, and since the expression in'(la.l7) is always non-negative, t; is the minimum point for PS, in the PS, , t2 plane. 3'98: _ Yp’Neix (e ““1"” no <1-p) '1 e 'W) at: (1 +11) 0 p=ne2.(e-"=-“-t=’ -e-w’) (1 +1.) 03 Aggregate precautionary saving when the unemployed agents are saving in the pay-as-you-go model is given by (11>) 11(an + y (pen + (1-p)em)) P = ps, “1+1” (unemployed) (1A. 18) (1A.19) through (13.23) give the partial derivatives of PS: for the unemployed agents with respect to the parameters r” e25, e2”, p, and t2: aps: _ (1-p)N(-1n0-y(pe23+(1-P) 620)) _ (1A.19) 3E1 7(1+I1)2 2:82 = p<11:rz>)N(1- ‘1-t2>e""";""’”26"“) ' (11mm 23 l 1 P - e aps. = n(1-2)3(1_e v ) (1A.21) an 1+:1 0 aps’ _N (1-p)Ne -e ap- . 7(1+r1)[1n°+7(pe23*(1'p)920)]+ 151:3 2U) (1A 22) + (1-p) pN(e ""‘”"‘" - (1 +vtzen +19 (HP) "9923) 6‘ "'“) y(1+r1)0 3982 = p(1-p)Nezg(e"°””"”-e"°) (15.23) Y2 (1+rl)0 35 REFERENCES Abel, A. and O. 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Topel, R., 1990, "Financing Unemployment Insurance: History, Incentives, and Reform," in unemployment Insurance: The Second Half-Century, Madison, WI: The University of Wisconsin Press, pp. 108-35. Vroman, W., 1990, Unemployment Insurance Trust Fund.Adequacy in the 1990s, Kalamazoo, MI: W. E. Upjohn Institute for Employment Research. Weil, P. , 1990, "Nonexpected Utility in Macroeconomics, " Quarterly Journal of Economics, 105:29-42. 37 Zeldes, S. , 1989, “Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," Quarterly Journal of Economics, 104:275-98. CHAPTER II: PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE IN A MODEL WITH FUNCTIONING CREDIT MARKETS CHAPTER II PRECAUTIONARY SAVING AND UNEMPLOYMENT INSURANCE IN A MODEL WITH FUNCTIONING CREDIT MARKETS 1. Introduction This chapter extends the model of precautionary saving and unemployment insurance developed in chapter one by incorporating a functioning credit market into the economy. Previous work in the area of precautionary saving, including chapter one of this work, assumes that credit markets are closed, meaning the only avenue open to agents who desire to shift resources from one period to another is through some form of saving. The opening of credit markets provides another avenue for agents to transfer wealth between periods. In particular, in the models of this chapter, the unemployed can borrow against future income in order to smooth their consumption path. Some might argue that those who are unemployed would have great difficulty borrowing against anticipated future income. However, there are many examples of this phenomenon in the world.‘ This chapter examines three models of precautionary saving in an economy in which agents both can store and can borrow or lend as a way to transfer resources from one period to the next: a model with no unemployment insurance plan, a forced-saving plan with characteristics similar to the unemployment insurance system found in the United States, and a pay-as-you-go plan which has similarities to unemployment insurance plans throughout the rest of the world. Two main ideas come out of this work. The first is that when the rate of interest in the loan market is equal to the rate of return to ‘Consider, for example, the ease of a graduate student who, upon learning that he or she has a new job lined up after completion of the Ph.D., purchases a new car with the expectation that future income will suffice to make the payments. This is certainly a case in which borrowing by an unemployed individual is used to smooth consumption. 38 39 storage in the economy, aggregate precautionary saving in each of the models with functioning credit markets is identical to aggregate precautionary saving in the models without functioning credit markets-- only the portfolio of saving instruments changes. When loan markets open up, agents who would be limited to storing in a’ model without credit markets are able to lend and therefore divide their saving between lending and storage. The second main idea to come out of this chapter is that the addition of a forced-saving unemployment insurance plan, while directly financed by the agents who are covered by the plan and who might benefit from the plan, costs those agents who are not covered by the plan in the form of higher interest rates in the economy. In a sense, public borrowing under the guise of an unemployment insurance system "crowds out” private borrowing, making it more expensive for those agents not covered under the plan, the borrowers in the model, to smooth consumption. In addition, this increase in the interest rate in the loan market further aids those covered by the forced-saving plan since they are the lenders in the model and receive a higher return to their lending. This chapter is arranged as follows. Section two describes the basic model without an unemployment insurance plan but with the functioning credit market extension. In section three I introduce the forced-saving unemployment insurance scheme into the model and.examine the problem of deriving the optimal unemployment insurance tax in this framework. I describe the pay-as-you-go unemployment insurance plan and solve for the optimal unemployment insurance taxes in section four. Section five examines the reactions of precautionary saving in the models presented to changes in the parameters. The final section concludes the chapter. 2. The Extended Model Without Unemployment Insurance The model in this chapter is similar to the model presented in chapter one except that in the economy presented in this chapter credit 40 markets are open, providing an additional method (besides storage) for agents to shift resources from one period to another. This open credit market (OCM) economy is a finite-horizon (two-period) economy populated by N two-period lived agents. In any period i, where isl,2, pN agents receive a high endowment, em, at the beginning of the period, where p, assumed to be constant across periods, is the probability of receiving the high endowment. The remaining (1-p)N agents receive a low endowment, em, at the beginning of period i. All agents receive utility from consumption in each period of their lives. An agent maximizes expected, discounted life-time utility with complete knowledge of her first-period endowment but without knowing her second-period endowment. An agent with a high first-period endowment, in other words one who begins life ”employed," solves the following problem: 2 "‘2’! 2,; °"‘ ”1.: «c1.» «1) -1 subject to Period 1: 91: = c“ + s", + 11, Period 2: 923 + 1:1813 + x1113 = on 920 + I1311: + X111: 3 C20 (2) C13! C23! C20! 513 2 0 where j-E,U for high endowment (employed) or low endowment (unemployed), respectively, E,is the first-period expectations operator, be[O,1] is the subjective discount rate, c28 is the second-period consumption level of an agent who receives a high second-period endowment while cu,is the second- period consumption level for an agent who receives a low second-period endowment, am is the amount stored by a high-endowment agent in the first period, r,is.the gross technological rate of return on storage, xlis the gross interest rate paid by borrowers to lenders for the privilege of borrowing, and 1m is the amount the agent lends or borrows in period one. An agent with a low first-period endowment, an agent who begins life “unemployed," solves a very similar problem, maximizing (1) subject to 41 Period 1: em - cm + 810 + 110 Period 2: e" + 1181,, + x11“, - on 920 I r18m * xilw ' can (3) C10! C23! C20! 910 2 0 where s“, represents the first-period storage of an unemployed agent, where 1w represents the borrowing or lending of the unemployed agent in the first period, and where the other variables are as defined above. The credit market operates through a “bank" which facilitates all lending and borrowing transactions at no cost to the individual agents”. An agent who borrows 1,1 in period one, j=E,U, repays the bank either xllIJ or all of her second-period assets (endowment plus any savings), whichever is smaller. An agent who lends llj to the bank in period one receives x,lu in period two as payment for the use of her funds. It is assumed that agents do not default on loans, meaning xllU0), while 15, is the amount borrowed (dissaved) in equilibrium by an agent unemployed in the first period and facing uncertain second-period income. To prevent the possibility of default by agents borrowing in the first period, it is assumed that the following condition holds 1+x' e“ < 610+ .1920 . (13) x1 It is easily seen that there exist parameter values for which this condition is satisfied. Throughout the chapter, certainty means that an agent knows with probability one that her income in the second period will be the expected value of her random second-period endowments. In the model without an unemployment insurance scheme, the expected value of second-period income is pem+(1-p)enp Under certainty, therefore, the level of 1m chosen by an employed agent in the first period is fl = 7(1_1+X;)—[1n(ax1) +Ye1B-Y (peg; +(1-p)e20)] ' (14) Similarly, under certainty an agent unemployed in the first period chooses 1lu such that c - 10 - fi[ln(bx1)+yeIU-y(pezx+ (1-p)e20)] . (15) Loan market clearing again requires that le,E+(l-p)Nl,U-0. Substituting into this expression for 1,5 and l“J from (14) and (15), 45 respectively, and solving the resulting expression for x, gives the following market clearing interest rate in the certain second-period income case x” = e -1(p(eu-eu) 9(1-9) (Om-0:0” ( 16) 1 C ' The equilibrium expressions for lending and borrowing in the certainty case are found by substituting if into (14) and (15) to obtain 1;: ' fileis-ew] (17) and 1i?) ' filew'els] ' (18) Again, to guarantee that borrowers do not default on the loans they incurred in period one, the following condition is assumed to hold .C 1 +x1 e“ < 610+ e2U . (19) Did" In equilibrium, the interest rate in the loan market is greater when the agents face certain second-period income than when they face uncertainty about the endowment they will receive in period two. For lenders this means that in equilibrium they lend (save) more when faced with uncertain second-period incomes than when they know with certainty what their second-period incomes will be. In equilibrium, borrowers take out larger loans in an uncertain world than in a certain one. Precautionary saving in the model with no unemployment insurance scheme in the case where ryew. In equilibrium, the loan market must clear which again implies that lending must equal borrowing in the aggregate, i.e. that PN1:E+(1'P)N1w'°- Substituting into this market clearing condition the expression for 1w given in (22) and solving for 1”; gives the following expression for lending by an agent employed in period one '(1' ) ' ‘as - ' ‘20 11s ‘ mflnwrlhyemdnme ' +(1 p)e ' )] (24) which is greater than zero given that the expression in brackets is negative. In the case of rfi3X” an employed agent facing second-period income uncertainty chooses a combination of storage and lending such that the first order condition (6a) holds with equality. Together, storage and lending must satisfy the condition (from (6a)) that 1 81"? 113 = —__Y (1+r1) [ln(br1) +yeu+1n (pe '7‘“+(1-p)e""°)] . (25) Given (24) and (25), storage by the employed agent in the first period is _ 1 31s - Wflnwrltl +pye13+(1-p)vem] (26) where z ' 9923+(1‘P)920 ° Notice that total saving by the employed agent when faced with second 48 period income uncertainty is given by (25) since saving is the combination of the amount stored by the agent and the amount the agent lends. This expression is identical to the expression for storage in the model of chapter one where the agent did not have the opportunity to lend. For the employed agent, opening the credit market simply alters the distribution of her portfolio of saving instruments. With certain second-period income of the formlgiven in the borrowing and lending only case earlier in this section, an agent unemployed in the first period maximizes utility by borrowing so that 1 c = —_ 10 7(1+I1) [1n(brl) +yew-y(pe23+ (1-p)ew)] - (27) This identical to the agent's choice when rp ewl] (29) which means that the employed agent, when facing income certainty in period two, chooses storage in the first period such that Bis ' Wflnwrl) +py(e13-e23) +y(1-p) (em-e20” - (30) Again it is important to note that total saving by an employed agent with certain second-period income in this case is given by (29). 49 Precautionary saving in the rpm case by an employed agent is the difference»between saving under uncertainty given by (25) and saving under certainty as given by (29): PS?“ ' rfi'irjflnt +1(pe,,+ (1-p)ew)] - (31) This is identical to the precautionary saving choice by an employed agent in the model without open credit markets. While an employed agent in the model in this chapter may have a different selection of saving instruments in her savings portfolio, she chooses a mixture of those savings instruments such that her level of precautionary saving is identical to that of the agent who has only storage as a means of saving as in the models presented in chapter one. For the same reasons given earlier in this section, dissaving in the form of borrowing by the unemployed in period one cannot generate precautionary saving behavior» So although dissaving by agents unemployed in period one decreases aggregate saving in the model, it has no effect on aggregate precautionary saving in the) model. Therefore, aggregate precautionary saving when rpnxlin this model is given by P813101 .3 WEI—13D“: I Y (peas + (l-p) ezu) ] ‘32) A comparison of this result with those from the unemployment insurance models is contained in section five. 3. The Forced-Saving Unemployment Insurance OCM Model This section introduces into the OCM. model the forced-saving unemployment insurance scheme presented in chapter one in which employed agents pay into a fund and are required to have been employed in period one to qualify for unemployment insurance benefits in period two. Since this unemployment insurance scheme was thoroughly discussed in chapter one, this section will be limited to presenting it in the context of a model with a functioning credit market. 50 In the first period, the endowments of employed agents are taxed at rate t,s[0,1] . Given that there are pN employed agents in the economy in period one each receiving the high endowment of em, the total tax revenue generated for the unemployment insurance fund is pNtlem. This tax revenue is placed in a trust fund held by a "government” whose sole function is to collect, hold, and disburse the UI tax revenue. It is assumed that the government has access only' to the storage technology available to individual agents, meaning monies in the fund earn a gross rate of return r" Government trust funds, such as the unemployment insurance trust fund, are often prohibited from investing in high rate of return, riskier assets. The restriction in this model that the government is limited to earning only the rate of return to storage captures this effect. During period two, therefore, er.t,e.E is available for disbursement to the unemployed.of the period.7 Of the pN agents employed in the first period, 1-p will be unemployed in the second. Therefore, p(l-p)N agents will be eligible to receive UI benefits during the second period of their lives, implying a per capita disbursement of r,t,e,E(l-p)“ to those who are eligible. The budget constraints and the choice problem facing agents who are unemployed in period one are identical to those faced by these agents in the model with no unemployment insurance. Since they will have had no ”work history," if they are again unemployed in the second period they will not be eligible for unemployment insurance benefits, so for them the forced-saving plan is nonexistent. An agent employed in period one faces the budget constraints Period 1: sun-ti) =- on + an + 11,, Period 2: on + r1818 + x1113 = c3, (33) 920 I 11313 " x1113 + I1t1613(1-p)’1 = can cut C23! Czuv 818 2 0 where all variables are as defined above or in section 2. There are only 7The rather trivial government budget constraint is that the tax revenues collected in period one multiplied by the gross rate of return on trust fund monies must equal the unemployment insurance disbursement in period two. 51 two differences between the budget constraints presented in (33) and those presented in (2) in section 2: (1) agents are taxed at the rate t, in period one to build the unemployment insurance fund; and (2) if employed in period one but unemployed in period two, the agent receives the unemployment insurance benefit of r,t.e,E(1-p)'l in addition to the low endowment and whatever savings she may have undertaken in period one. An agent who is employed in the first period solves the following problem m 16 -1(eu(1-t1) and“) '126 -1(euor,snox,ln) 51st 113 7 7 (34) _ 0 (1 -2) e -y (ew+r1s“+x,lu+r,t,en(1-p) ") Y in which the constraints from (33) have been substituted into (4). Because of the non-negativity constraint 9,520, the first-order conditions for the above maximization problem are the Kuhn-Tucker conditions .6 «(.u(1-tx) -.n‘lu) + aprle -7 (.3.’!x.uPX113.) a (35a) + 6(1-p)r1e "“w“z'x-"‘tlx-"m'n‘l’w ’ so, =0 if 9,, >0 and _e ’1(.y.(1't1) "u‘11.) + bpxle '7 (03.011.u*X311.) (35b) + O (1 'P) X18 -1 (‘30.rl'u'x111lIritsenu'p) i) = 0 where (35a) is the Kuhn-Tucker condition obtained from the partial differentiation of (34) with respect to s”; and (35b) is the partial derivative of (34) with respect to 1.5} As in the model with no unemployment insurance, (35a) and (35b) imply that rISxI so that it is again necessary to consider two possible cases. Case 1: r, a“, 1“ Y Y (70) _ 0 (1-2) e -1(ewrrxsumllurp(l-p)"t,e,.) I Y in which the constraints from (68) have been substituted into (4), subject ”Again, the government budget constraint is rather trivial. Tax revenues collected by the government in any specific period must equal unemployment insurance disbursements by the government in that period. 61 to the non-negativity constraint slgzo. The first-order conditions for the above maximization problem take the form of the following Kuhn-Tucker conditions -e -y(o,,¢1-c,)-u,,-1,.) + bprle -y(o,.(1-c,)o:,nnox,1,.) 4 (71a) +5(1_p)Ile'Yim923'u0t11ufip(1'p) :30“) SO, =0 if 813 )0 -6 'Y(.u(1‘t1) -.u-11.) + 6px1e ’7 (.a(1‘ta, .tg.n’x:1u) _, mm + 5 (1_p) xle-v(eu¢r,suoxllnvp(1-p) taeu) =0 where (71a) and (71b) are the partial derivatives of (70) with respect to a“; and 1.3, respectively.‘1 An agent unemployed in period one facing uncertain period-two income solves a similar problem, maximizing (where the budget constraints in (69) have been substituted into (4)) max -1 e -1 «mop(1-pr1c,o,.-am-1mr _ 5p e -y(ou(1-c,)+z,a,,ox,1m) 910' 110 Y Y (72 ) _ 0 (1 '2) e -1(smartsmoxllmsp(1-p)"t,enl ' subject to the non-negativity constraint sluzo. The Kuhn-Tucker conditions for the unemployed agent’s problem are _e 'Y(.30’9(l'p)-lt1.3."1o‘lxu) + 6px e 'Y(.;'(1‘ta’ OI‘.10*X1110) 1 . (73a) +b(1-p)r1e '7(°'°"1"°"‘*11°'p(1"’ ‘3‘“) so, =0 if 310 >0 _e '7(.1099(11,-xt101."1u‘13u) + bpxle ’1(.u(1't3) ’r1'10,x1110) (73b) . a (1-p) x1e ""assurance(”New = o where (73a) and (73b) are the partial derivatives of (72) with respect to s“, and 1“,, respectively. As in the previous models in this chapter, (71a) and (71b) and (73a) and (73b) imply that r,5x,, so that there are two possible cases to consider. Case 1: r, ew(1-p)+ . e2U (employed) . (80b) 3‘1 Certain second-period income for the pay-as-you-go model is defined as pe73(1-t2)+(1-p)(ew+p(1-p)°'t2ezg). Under certainty, an employed agent in the pay-as-you-go»model with only borrowing and lending chooses 1m such that is = Y—(lt—xjflnwxl)+ye13(1-t1)-y(pe23+ (1-p)ezu)] . (81) In a similar fashion, an agent unemployed in the first period in this model selects 1w so that :0 = filln (6x1) +7 (610*P(1‘p)-1t1913) -7 “3923* (l—p) 620)] (82) when facing certain period-two income. The equilibrium borrowing and lending only interest rate under certainty in the pay-as-you-go model is “For the employed, (79) means they will be lenders in period one. Reversing the inequality in (79) causes the employed in period one to be borrowers because so much of their endowment is being taxed away. 64 -1(p(eu-e,.) 0(1-9) (em-en) ) x? = e (83) 6 where the expressions for I; and 1;,from (81) and (82), respectively, have been substituted into the loan market clearing condition, with the resulting equation solved for xf. The equilibrium interest rate in this case is identical to that found in the r, 913 (33) then an unemployed agent in the first period will be a lender and will generate precautionary saving of 1 1 - PS: - p(1+x;- 1+x;°)[ew'eis(1't1'P) (l-p) 1] ' (89) Again, the expression for precautionary saving from (89) is non-negative given the condition on t.l in (88) and aggregate precautionary saving is 1 1 - Psi - p(l-p)l~{1+x;- 1+x;c)[°10'°13(1't1-p) (l-p) 1] (unemployed) - (90) Precautionary saving as given in (87) and (90) is compared to the results from the other models in section five. Case 2: r,8x, When risxl, agents who would lend in the r1 -(1-p) (yew+ln(br10)) , (92) YPe1s then roles of borrower and lender would be reversed.“ -(1- X70 +1110! 0)) ”A necessary condition for the first-period unemployed to be borrowers is t, < p w ' , which is satisfied if (91) holds. we... “(92) is sufficient to cause employed agents to desire to borrow, but they are prohibited from negative storage. 66 If (91) is true, then an unemployed agent, when faced with uncertain period-two income, chooses l“J as given in (75) (with.xq replaced by rd. The assumption _ 7(1+ri)eso (1- )‘1t e > 1p p 1 1s 11p -yem-ln(6r1) -ln0 (93) ensures that she will not default on her loan. Substituting for l.U from (75) into the loan market clearing condition and solving for lending by the employed in period one yields 41-2) 1370-111.) 18 [1n(5:,) +y(ew+p(1-p)'1t1eu) +1no] - (94) It can be seen from (71a) that under uncertainty an employed agent, when (91) is true, chooses a combination of storing and lending such that 1 81". 113 = —_Y (1+II) [1n(5110)+ye13(1-t1)] . (95) (95) gives the total saving by an employed agent if (91) is true. Subtracting (94) from (95) gives storage by an employed agent when facing second-period income uncertainty in the pay-as-you-go model of a“ - 'py(_]:_l+r-IT[In(6:10) +y(pe13+ (113)910” ' (96) Inga similar manner to the analysis above, if (92) is true, then an employed agent faces such a high unemployment insurance tax in period one that she becomes a borrower, with the amount she borrows being identical to the amount in (74) (withzn replaced by r”. An assumption similar to (93) guarantees that the employed borrower does not default on her loan. Using this expression for 1m in the loan market clearing condition and solving for 1w yields 110 *- 7(”$531+“)[mung +ye13(1-t1) +1no] (97) which is the equilibrium level of lending by the unemployed in period one if (92) holds. Since lending and storage (total saving) by an unemployed agent in period one must be such that 1 3"”1‘” . mhnwrfl +Yt;, the equilibrium interest rate reacts less strongly to changes in em and em than when t2t,' has an indeterminate» effect on aggregate precautionary saving' while an increase in eu,when ty>t§ actually causes precautionary saving to fall as the effect described in (1) above dominates. If unemployed agents are the lenders under the pay-as-you-go scheme, the reaction of precautionary saving to changes in em and em is, for the most part, the reverse of what it was when the employed were lenders, given the tax rates. With the exception of the forced-saving plan, aggregate precautionary saving reacts to changes in the second-period high endowment and the second-period low endowment in the same fashion in the r,t; , precautionary saving is positively related to the second-period low endowment because an increase in en,in.that situation causes an increase in income disparity which drives the agents to increase their precautionary saving, giving an overall increase in precautionary saving when combined with the interest rate effects. For the forced-saving plan, changing either em or em has an indeterminate effect on aggregate precautionary saving. Increasing em, for example, leads to an increase in the variance of second-period endowments which by itself would lead to an increase in precautionary saving. However, increasing e25 also increases the equilibrium loan market interest rate which again has the opposite effect on precautionary saving of (l) and (2) above. The combined outcome of these effects is an indeterminate reaction to changes in an; by aggregate precautionary saving. A similar argument may be made for the reaction of precautionary saving in the forced-saving plan to changes in en” An increase in the first-period unemployment insurance tax rate increases aggregate precautionary saving in the pay-as-you-go model when the unemployed are the lenders (savers), decreases precautionary saving in the pay-as-you-go model when the employed are the lenders, and has indeterminate effects on precautionary saving in the forced-saving model. In the pay-as-you-go model, changing tI affects precautionary saving through a simple income effect. Increasing tl decreases the after-tax income of the employed in period one, meaning, if they are the savers in the economy, that they have less ability to save. For the unemployed when they are the savers in the economy, an increase in t1 increases their unemployment insurance benefits and permits them to increase their saving. For the forced-saving plan, the effect on precautionary saving of changing tl is unclear. Increasing the first-period unemployment insurance tax rate decreases the ability of the employed in the first period to lend 80 (save). In addition, increasing t. increases the unemployment insurance benefit in the second period which decreases the income disparity faced by the agent, decreasing her desire to engage in precautionary saving. Finally, increasing t, increases the equilibrium loan market interest rate which affects saving the reverse of effects (1) and (2) above. The net result is that without making specific assumptions about parameter values, one cannot determine what happens to precautionary saving when t, changes. The second-period.tax on endowments is found only in the pay-as-you- go model. Precautionary saving, when r,ta¢l-0rder Conditions: 0C)! Itodel with Forced-Saving 01 Plan :2: Becond partials (and cross partial) of (34) with respect to s"; and 1,5 82.: we " - yéprge “ - 76 (1-p)rfe "‘ (2A. 7) .131133 -ye " - 76px 1xle " - v6 (1-p) lele “' (2A.8) 1? where All expre 5288i Above 2A.9 whicl Seco: The I are Vhe: A11 EXP: EESE (5.1 83 13.: ~16"-ybpx§e“-yb(1-p)x§e"‘ (2L9) where ¢ " Y‘°n(1't1)'313'113) ‘ ‘ Yiess+r13u+x111fl _ (2A.10) " ' Y(320+119u+x1113+r1t19u(1"Pr1) A J., 1 three expressions in 2A.7-2A.9 are negative. Note that the expressions take the same form as those in 2A.1-2A.3 above, so that the He ssian matrix of second partials takes on the same form as that in 2A.S ’mve. The determinant of the Hessian formed by the expressions in 2A.?- 23 .9 is (bpy’e"e" + 6 (1—p)yze"e"‘) (XI-r1)2 (2A.11) wh job is non-negative, meaning the second-order conditions for utility maximization in the forced-saving model are satisfied. 8-cond-Order Conditions: OCH Hodel with Pay-As-You-Go 01 Plan The second partials (and cross partial) of (70) with respect to s"; and l”; are 8%,: ~16 “ - ybpxie “ - yb (1-p) Ife "' (215- 12) 813113: -ye “ - ybprlxle “ - 76(1-p)rlx1e "' 4 (2A. 13) 1:3: -ye “ - ydpxfie ‘1 - yb(1-p)x§e "' (2A. 14) where C ' Y(e13(1-t1) '313'113) es: - y(e,3(1-t3) +rlsm+x11n) (2A.15) "I "' Y (920 +11513 +3111: + tzezsp (1 _p)-1) :11 three expressions in 2A.12-2A.l4 are negative. Note that the xI’li‘cssions take the same form as those in 2A.1-2A.3 above, so that the a‘iiian matrix of second partials takes on the same form as that in 2A.S VG. The determinant of the Hessian formed by the expressions in 2A.12- (633126484 + 6 (1-p)yze"e ") (XI-1:1)2 (2A.16) which is non-negative, meaning the second-order conditions for utility “utilization in the pay-as-you-go model are satisfied. APPEND I X 2 B 84 APPENDIX 28 Derivatives for the OCH ttodel with Ho 01 Plan Aggregate precautionary saving in the extended model without an unemployment insurance plan when r,— = (l-2p)N[eu-ew]A 6 fl, (8 ~70“ _ e 'Yeau + {Y (e13 -810) ) +P(1‘p)N[e1B—e1ul 6(1+x;)2£2 (23.2) +P(1-p)N[e -e ] ewflq'Yieis'eza) *7 (610-820)) 13 10 6(1+x;0)2 whore A - 1 - 1 1+X; 1+xi° " ' “pew <1-p)em> ” . 7(p623+ (1-p) 820) 3983”“ q, M T = P(1-p)NA+[e -e ] ype _ ype 23.3 is [ 18 1o [6£(1+X;)2 5(1+x;°)2 ( ) 8P3?!” (1_ ) '3 (1_ ) -'+“ T'pu-pm -A+[ -e 1 L p e _L p 6 23.4 m ( 613 w 5((1+XI)2 6(1+x;°)3 ( ) 8P3? DI - '“'V°as -s+|t T =p(1-p)N[e -e ] 1138 + ype 23.5 3' 13 w [5€2(1+x{)3 6(1+x;°)= ( ) 3P3)?“ _ (1_ ) ““1030 _ we): x—‘Pil-p)N[e -e ] Y P e +Y(1 p)e 28.6 20 18 10 ( 6{2(1+X;)z 5(1+x;c)2 ( ) mti‘ltives for the DC)! Forced-Saving Model Ag93-‘Ogate precautionary saving in the OCM forced-saving unemployment “‘“rance model when r,f covered to uncovered employment across states. 105 The index number for each state is calculated according to the following: index = (%)trt(%)tloooo, where A - total benefit payments B - total covered wages and salaries mean covered unemployment rate state covered unemployment rate A - number of covered employees E - total state employees The term A, the total of all benefit checks issued during a year, varies directly with any liberalization or tightening of benefit provisions. B represents the earnings of those people working in covered employment and controls for differences in size and wages among states. States with the same benefit ratio, A/B, given that they face the same unemployment rates, provide their covered employees with the same value of insurance coverage regardless of differences in state size, wage levels, and legal provisions. In order to compensate for differing unemployment rates across states, the above index measure is adjusted by scaling it to an average covered unemployment rate for the years under study. The scaling factor is the mean covered unemployment rate for the five years under study, 3.32%, divided by the actual covered unemployment rate in a specific state during a given year. Finally, the measure is modified by multiplying the first two components described above by the ratio of the covered employment in a state during a given year to the total employment in that state that year. The inclusion of the term A/E makes the index a true’measure of generosity for all workers in the sense that in order for a state to have a "high” index number, that state must provide both relatively large benefit payments per dollar of covered wages and salaries and it must provide those unemployment insurance benefits to»a relatively large portion of its work force. 106 The index is a cardinal measure of the generosity of unemployment benefits for each state and for the District of Columbia. The actual numbers used to formulate the index for each of the states for the years 1966, 1969, 1971, 1976, and 1981 are contained in Appendix 30. Data for calculating the indices are taken from the U.S. Statistical Abstract and f roar the Handbook of Labor Statistics. 4 - Empirical Specification The theoretical model of consumer saving behavior in the U.S. with an unemployment insurance scheme in place shows precautionary saving to be a function of income, of the probability of being employed in the next period, of the rate of return to saving, of the level of unemployment benefits, and of the degree of absolute risk aversion exhibited by the consumer." Because previous attempts to empirically establish the existence of precautionary saving have varied as to their success, I Proceed with my analysis in two distinct directions. Cross-section Analysis The first method I use to test for the existence and strength of the above relationships is a cross-section analysis utilizing the following basic estimating equation savt = p, + pzpsammc + B3PERMINCSQR + B‘VARINC + (350mmt + BsJURATt + 7’1, + et (1) Where t represents the year of the cross section and where PERMINC, PERMINCSQR, VARINC, and JURAT, are as defined in section two. SAV, is one Of six possible wealth measures, SAV1,, SAV2,, SAV3,, DSAV1,, DSAV2,, or DSAV3,. For each of the savings measures SAV1,, SAV2,, and SAV3,, five different cross sections corresponding to the years 1966, 1969, 1971, 1976, and 1981 are analyzed. Four cross sections are available for analysis for the saving measures DSAV1,, DSAV2u and DSAV3, because they \ "1 present these results in chapter one. 107 represent variations in liquid asset holdings from one year of the study to the next. UINDx,is the index of unemployment insurance benefit generosity as calculated from the formula given in section three. This index varies both from state to state, since different states provide different levels of benefits to their unemployed workers, and from year to year for each state, since over time, due to legal modifications and/or changing economic conditions, benefit generosity'within a state fluctuates. In the cross-section analysis, consumers in states with more generous unemployment insurance provision levels (a higher UINDX, number) should save less than similar individuals in states with less generous unemployment insurance programs because of the effects of unemployment insurance on precautionary saving. 1'! is a vector sum of additional exogenous variables intended to control for characteristics other than those presented above which may affect the level of saving undertaken by someone in the panel. These additional variables include DRACE, UNION, AGE” TENCJ" NC" SPOUSEINC,and MD" all of which were defined in section two. A two-stage regression process is used to analyze the versions of equation (1) which use the savings measures as dependent variables.‘2 An investigation of the data shows that a significant number of individuals in the panel reported holding zero liquid assets. The percentage of those who reported having no deposits in financial institutions (SAVLfO) ranged from a low of 39% in 1976 to a high of 46% in 1969. For the broader measure of liquid asset holdings (SAVZQ, the percentage reporting zero holdings ranged from 37.5 percent of the respondents in 1971 to 40 percent in 1969. Significantly smaller percentages of respondents reported zero or negative net real wealth holdings, ranging from 19% in 1966 to 14% in ”This is the "hurdle" method proposed by Cragg (1971). He originally proposed this method as a means of modelling the demand for durable goods by consumers but argued that it is applicable to any situation in which "there is an event which at each observation may or may not occur. If it does occur, associated with it will be a continuous, positive random variable. If it does not occur, this variable has zero value.” Cragg (1971, p. 829) 108 1981. The first stage of the regression process involves using a logit model to distinguish between the savers and the nonsavers in the panel.” The logit model indicates which traits increase the probability of an individual holding some positive level of saving. The second stage in the analysis of (1) involves running either OLS or weighted least squares on those observations for which the savings measures are positive. Because of the large range of reported values for PERMINC, it is possible that the error terms from OLS in this second stage might be heteroscedastic. A Breush-Pagan test is conducted for each of the regressions and if the null of homoscedasticity is rejected, weighted least squares is used to ensure that correct standard errors are reported.“ To analyze (1) when the saving measures DSAVl" DSAV2u and DSAV3,are used as dependent variables, a similar procedure to that outlined above is used. The saving measures assume positive, zero, or negative values as individuals save, maintain a constant level of liquid asset holdings, or dissave, respectively, over the period in question. A.logit model is again used in the first stage, this time to distinguish the zero savers from those who have saved or dissaved over a period. As before, the second stage involves running OLS or weighted least squares, depending on the outcome of a Breush-Pagan test, on those observations for which the saving measure non-zero. The results for the cross-section analyses conducted are reported in section five. Panel Data Analysis The second method I employ makes use of the panel aspects of the data by extending in both the individual and the time dimensions. The model estimated, similar to equation (1), is given by the following "Nothing in the data indicates the true nature of the'distn'bution of the error terms. Using a probit model in place of the logit model does not change the results in any qualitative or quantitative way. "The weighted least squares procedure is performed in the following way. The natural logarithms of the squares of the residuals from an 01.8 regression are regressed on the OLS variable set. The exponentiated fitted values from this regression are then used as weights on the variables. OLS is then run on these weighted observations. 109 35V“ ' “r *’ x1e“ + “1: (2) where i indexes the individuals, t indexes the time periods, a,represents those effects fixed for an individual over time, 1, represents those k variables which vary over individuals as well as over time, and u, is an error term. I chose to estimate a "fixed-effects" panel model because there is no reason to assume that the q's will be uncorrelated with K... I also assume that the parameters are fixed across individuals and time and that the errors are i.i.d. For ease of computation, I first differenced equation (2) rather doing a fixed-effects estimation, both of which eliminate the fixed-effect component of the error term. .After first differencing, the specific form that equation (2) takes for estimating is SAVu-SAVu,1 = (31 + pzwamsmcit-Fwsmcnq) + B, (LABINCSQR,,-LABINCSQR,,-1) + 55 (REAL INTit-REAL INT1t_1) (3) "‘ Be‘JURATtt'JURATit-r) + (zus'zue-r.) Bk "’ uit-uit-l where 1,, represents additional exogenous variables included in the various regressions, and the other variables are as explained above. Note that variables which are constant over time, such as PERMINC and VARINC, are not included in a fixed-effects panel regression because it is not possible to estimate the coefficients of time-invariant regressors. Thus, real labor income, FAMLABINC, is used to capture the effects of income on the saving decision. Besides the possible efficiency gain which comes from estimating the model with more information, using the entire panel should allow me to examine the saving behavior of individuals over time. Specifically, as the index of unemployment insurance generosity changes within states over time, we should observe an inverse relationship between those unemployment insurance‘generosity changes and the level of precautionary saving desired by individuals. We should observe analogous effects for the other variables as they change over time. 110 5. Regression Results The results from the regressions described in the previous section are presented below. The tables dealing with the cross-section analysis of accumulated savings, contained in Appendix 3A, are paired, with the first table (designated a) in the pair containing the results from the logit regressions and with the second table (designated b) containing the corresponding OLS or weighted least squares results. Each pair of tables presents the results for the five years used in the study. Also contained in Appendix 3A are the OLS or weighted least squares regression results for the saving equations.” The results from the fixed-effects panel regressions, which are presented in Appendix 38, are examined after the discussion of the cross-section results. Cross-section Results for the Savings Equations The empirical results for the regressions using the entire sample with accumulated savings as the dependent variable are presented.in.Tables 3A.1a through 3A.3b in Appendix 3A. The Breush-Pagan (B-P) statistics reported in Table 3A.1b (as well as in the other tables) are those for the unweighted OLS regression in question, while the coefficients and t- statistics presented in Table 3A.1b (and the others) are either those for the OLS regressions if the B-P test shows little evidence of heteroscedasticity or those for the weighted least squares regressions if the B-P test indicates that heteroscedasticity may be a problem. Given the logit results presented in Tables 3A.1a, 3A.2a, and 3A.3a, it seems fair to conclude that the higher a respondent's permanent income, the greater the probability of the respondent having deposits in financial institutions, as all of the coefficients on PERMINC for the liquid savings measures are positive and statistically significant while three of the five regressions on the illiquid savings measure show significant and positive coefficients on PERMINC. It also seems evident that the l"’l'l're logit results for the saving regressions are available from the author upon request. They are very similar to the logit regressions for the savings equations in sign and statistical significance. 111 relationship between asset holdings and income is nonlinear since the coefficients on PERMINCSQR are in nearly all cases statistically significant. For the liquid savings measures, it is generally the case that the higher the index of unemployment insurance generosity, UINDX, the higher the probability of having accumulated savings. An increase in the generosity of unemployment insurance may decrease the probability that the respondent held wealth in illiquid assets, as shown by Table 3A.3a, although in only two of the five regressions is the coefficient statistically different from zero. Tables 3A.1a, 3A.2a, and 3A.3a also indicate that: (1) having an income-earning spouse (SPOUSEINO-1), if anything, increases the probability of having accumulated savings; (2) the greater the income variability, VARINC, the lower the probability of the respondent having accumulated savings; (3) the higher the job-specific unemployment rate, in general, the lower the probability of having accumulated savings; (4) the greater the age of the respondent, the higher the probability of having accumulated savings; (5) the greater the number of children (N0), the lower the probability of having accumulated savings; (6) the longer the respondent had worked at the same job (TENCJ), the higher the probability of having accumulated savings; (7) black respondents (DRACE-1) had a much lower probability of having accumulated savings than did white respondents; and (8) union members (UNION-1) exhibited a much lower probability of having accumulated savings than did respondents who were not members of a labor union. The coefficients on UINDX, VARINC, and JURAT seem to run counter to what would be expected if consumers were saving for precautionary reasons. However, it must be kept in mind that these regressions only distinguish between those respondents who have accumulated savings and those who do not. Agents who have experienced periods of unemployment in the past or who have highly variable incomes may have had to ”pay the bills” using their accumulated savings during an unemployment spell or a low income stretch, thus decreasing their level of accumulated savings. 112 Tables 3A.1b, 3A.2b, and 3A.3b present the results from the weighted least squares regressions for the three savings.measures under examination conditional on accumulated savings being positive. The regressions in these tables show demonstrate the nonlinearity of the relationship between accumulated savings and permanent income in this data, especially the regressions for SAV2,and SAV3" The results with respect to UINDx in Tables 3A.1b, 3A.2b, and 3A.3b would seem to indicate that the higher the index of unemployment insurance generosity, the greater the accumulated savings for those with positive levels of accumulated savings." For the three tables, only those coefficients‘which are positive are statistically significant» Given that on average a 51 increase in weekly benefits translates into an increase in UINDX of about 2.5 points”, every additional $1 of weekly unemployment insurance benefit meant nearly $90 dollars of additional passbook savings by respondents in 1966 who had accumulated savings and nearly $658 dollars of additional net wealth. One possible explanation for this result is that the savings measure used might not be a good proxy for precautionary savings. If agents set aside a specific dollar amount for precautionary reasons, say the equivalent of three months income, and maintain that as a minimum level of savings, then any fluctuations in accumulated savings above that dollar amount may not accurately reflect changes in precautionary saving behavior. If a positive relationship» between unemployment insurance benefit generosity and savings does exist, the results from the chapter one would imply that the unemployment insurance tax rate in the U.S. may be greater than the optimal tax rate. "Regressions using the separate components of the unemployment insurance generosity index were run to determine if any individual component was more important than the others with regards to the results on the UINDX variable. The results from these regressions showed no consistent pattern on the coefficients of the three components of the index in terms of sign or statistical significance. For some years, the benefit ratio was important in determining the level of savings by the respondents in the surveys while for other years the covered unemployment rate seemed to be more important in determining the level of savings. Since there is no individual component of the generosity index which consistently determined the level of savings, the index itself seems to be the better overall determinant in the level of savings. The individual component regression results are available from the author. "This varies from state to state depending on the level of the average weekly benefit in that state. The figure used is an average for all the states. 113 The coefficients on JURAT are small in value and are generally not statistically significant for the regressions which use the liquid savings measure as the dependent variables, meaning that for this sample of individuals, changes in the job-specific unemployment rate affect liquid savings very little. Table 3A.3b shows, however, that net wealth is negatively related to the job-specific unemployment. rate (at least for all years other than 1981). There are two possible reasons for the lack of a statistical relationship between JURAT and the two liquid savings measures. It is conceivable that for these individuals, most of whom have been working at the same job for long periods of time, the unemployment rete represented by JURAT does not accurately represent the unemployment possibilities they face. If that is the case, then changes in JURAT would not affect SAVl or SAV2 in any systematic way. A second possible reason might be that because of their long job times, the subjective Probabilities of these individuals being unemployed may be so low that they save little as a precaution against future unemployment. The negative, statistically significant relationship between JURAT and net Walth could indicate that respondents who face relatively high unemployment rates may have experienced frequent periods of unemployment, Prohibiting them from building up assets in the form of homes, autos, etc. Finally, the negative coefficients on JURAT in all three tables, although in many of the cases not statistically significant, could be the result of BOlf—selection on the part of respondents in that those more willing to a(Heept the risk of a job in a field with higher unemployment rates would also be those less likely to save for precautionary reasons." The coefficients on SPOUSEINC, a dummy variable indicating whether tlhe spouse of the respondent had any wage or salary income, may indicate the existence of precautionary saving behavior. Without a precautionary ‘aving motive, one would expect that having a working spouse would translate into higher levels of family savings if saving is a normal good. I‘Skinner (1988) also recognized that this may be a problem when categorizing the income risk faced by individuals according to the job they possess. 114 For: the regressions depicted in Tables 3A.1b, 3A.2b, and 3A.3b, the only coefficients on SPOUSEINC which are statistically significant are negative in sign, with the exception of the 1981 regression using SAV3 as the dependent variable. For the respondents in this data set, having an income-earning spouse corresponds to lower levels of accumulated savings, conditional upon accumulated savings being positive, perhaps because of a - decreased demand for precautionary saving. The coefficients on VARINC seem to indicate that variance of income explains little if any of the variation in the level of accumulated eevings for those who have accumulated savings since the coefficient is statistically significant in only three of the fifteen regressions in the three tables. When statistically significant, the coefficients on VARINC are negatively signed which may indicate that these respondents simply are not able to accumulate wealth as effectively when their income exhibits lerge fluctuations. The coefficients on AGE in nearly all of the regressions in the three tables show that the level of accumulated savings is positively related to the age of the respondent. The older the participant in the Durvey, other things equal, the higher the level of accumulated savings. The length of time on the current job, TENCJ, was included as a tOQressor to capture the possibility that long job tenure represented greater job security and therefore less risk of income drops due to unemployment, meaning that if a precautionary saving motive were operative One might expect there to be an inverse relationship between savings and 30b tenure. Tables 3A.1b, 3A.2b, and 3A.3b reveal, however, that the Coefficients on TENCJ are most often positive, and in none of the 1‘Ogressions are they negative and statistically significant, meaning that the longer the time on the current job, the more the respondent had in Qccumulated savings. It is likely that the coefficients on TENCJ again reflect a self-selection process in action. Individuals with long job histories may also be individuals with a greater predisposition towards 3aving, causing TENCJ to fail to detect precautionary saving behavior. 115 The greater the number of children in the home, the lower the level of savings, especially liquid savings, as can be seen by examining the coefficients on NC in the regressions in Tables 3A.1b, 3A.2b, and 3A.3b. The expense involved in feeding, clothing, and caring for children evidently reduces the ability of consumers to accumulate liquid savings. The relationship is much less strong between net wealth and NC. Those with children living with them may be more likely to also be homeowners and may be accumulating wealth in the form of home equity, which may offset the effects of having children on other assets. The coefficients on the durmny variable for race, DRACE, are negatively signed and highly statistically significant for the regressions presented in all three tables. For this sample, non-white males had average accumulated liquid savings up to $4800 less, depending on the saving measure used, and on average up to $60,000 less in net wealth, than did white males, everything else constant. The NLS did intentionally oversample blacks with nearly thirty percent of the respondents in the Olimple being black. Average PERMINC for the black respondents was nearly $6000 lower than that for the white respondents, so it is very likely the case that the black respondents simply were unable to save as much as their white counterparts. The coefficients on UNION in Tables 3A.1b, 3A.2b, and 3A.3b are, for the most part, negatively signed, large in magnitude, and statistically .1gnificant, indicating that union members accumulate significantly less .Qvings, both liquid and illiquid, than do those not in labor unions. One Possible explanation for this effect could be that unions provide more income security both in the form of greater job security and in higher unemployment insurance benefit provision should layoffs occur, thus decreasing the need for precautionary saving by union members since income Variability is reduced. Separate regressions were run for union members find for those not in unions with the results reported later in this Sect ion . 116 For the most part, being married reduced the accumulated liquid savings for the respondents in the survey, conditional on savings being positive, as shown by the coefficients on MD in Tables 3A.1b and 3A.2b in Appendix 3A. On the other hand, Table 3A.3b indicates that being married generally led to greater levels of illiquid asset holdings. For the liquid savings measures, it may be that MD is capturing the same type of effect as the regressor N0, namely that it is more expensive for two people to live than one, and that those in the survey who were married were unable to save as much as their unmarried counterparts. It could be that the married dummy is capturing the effects of having a spouse with income which are not captured by the variable SPOUSEINC. If the spouses of the respondents had significant sources of income other than wage and salary income, then perhaps MD captures a precautionary saving effect similar to that indicated by SPOUSEINC. An outside income source (other than labor income) would make family income less volatile, reducing the need for precautionary savimg. The positive relationship between net wealth and being married may indicate that net wealth is not a good proxy for precautionary savings. MD may simply be picking up the fact that married couples tend to accumulate assets in the form of homes, cars, and other such illiquid wealth in place of more liquid assets. Cross-section Results for the Saving Equations Tables 3A.4 through 3A.9b in Appendix 3A give the results for the regressions using a measure of saving as the dependent variable. Tables 3A.4 through 3A.6 present the regression results for DSAVl, DSAV2, and DSAV3, respectively, when the dependent variables are comprised of both savers and dissavers. As the low values for the F-statistics and the R- squares indicate, these variables do a poor job of explaining why both savers save as much as they do and dissavers dissave as much as they do, given that they either save or dissave. Because it might be the case that the same model does not adequately explain the behavior of both savers and dissavers, a variation of the hurdle method was used which distinguishes between the three groups, 117 dissavers, zero savers, and savers. In the first stage of the process, a multinomial logit model is used to differentiate between those who dissave, those who save, and those who choose zero saving over a period. The second stage of the process involves running separate OLS (or weighted least squares) regressions on those with positive saving and those with negative saving. Tables 3A.7a through 3A.9b present the saving regression results.‘9 The 'a' portion of the table gives the regression results conditional on saving being positive over the period in question while the ”b" portion of the table presents the results conditional on saving being negative over the period. A test to determine the equivalence of the "a” and "b" regressions (whether or not the samples come from the same population) overwhelmingly rejects the hypothesis that the coefficients in the "a" and 'b' regressions are equal.20 For this sample, it seems that saving and dissaving should be modelled in different ways. Tables 3A.7a, 3A.8a, and 3A.9a in Appendix 3A show the weighted least squares regression results conditional on saving in a period being positive. As with the regressions dealing with accumulated savings, the regressions on saving in Tables 3A.7a, 3A.8a, and 3A.9a generally indicate that there is a nonlinear relationship between saving and the family unit's permanent income. The coefficients on UINDX in Tables 3A.7a, 3A.8a, and 3A.9a again generally seem to indicate that a more generous unemployment insurance plan results in increased saving by those who save. Where the coefficients on UINDX are statistically significant, they show a positive relationship between the unemployment generosity and saving. As stated earlier, given the theoretical work in chapter one, this may be an I’l'he multinomial logit regression results are similar to the logit regression results given in tables 3A.1a, 3A.2a, and 3A.3a in terms of signs and statistical significance of the coefficients. These results are available upon request. ”A Chow test was used to determine whether or not the two samples came from the same population in each of the regression pairs. The F—statistics from the Chow tests were all greater than 50 meaning, with the critical value being less than 2 in all cases, that the null hypotheses of equivalence of coefficients between the various pairs of ngnedmuisauflynmwud. 118 indication that the unemployment insurance tax rate (and therefore the UI benefits) is too high. The coefficients on VARINC are positive for the most part in Tables 3A.7a, 3A.8a, and 3A.9a which might indicate precautionary saving on the part of the respondents. However, in all cases but one the coefficients are not statistically different from zero. As is the case with the regressions dealingHwith accumulated savings, the variance of income seems to play little role in determining the amount of saving undertaken during a period. The coefficients on JURAT provide little evidence for or against the existence of precautionary saving in the regressions detailed in tables. In the twelve regressions in these three tables, in only four regressions is the coefficient on JURAT statistically significant, three times negatively so. A job-specific unemployment rate for workers in specific job categories may not be a good proxy for the perceived unemployment probabilities faced by these respondents. Overall, little can be said about the effects of the unemployment rate on the level of precautionary saving using these data in a cross-section analysis. The results for the effect of having an income-earning spouse on saving behavior may provide evidence of precautionary saving behavior. Tables 3A.7a and 3A.8a show that for the periods 1966-69 and 1969-71 for the narrow saving measure and for all four periods for the broader liquid saving measure, families with two incomes saved less than families with only one income (conditional on saving being positive). One possible explanatiOn is that given in the discussion of the accumulated savings regressions: two-income households have a lower probability, in general, of drastic income decreases and hence have a lower demand for precautionary saving. The coefficients on SPOUSEINC for the last two regressions in Table 3A.7a may indicate that as older respondents retire, only those with working spouses are able to add to very liquid savings. The regressions in Table 3A.9a show that a working spouse seems to have very little impact on saving in the form of illiquid asset accumulation. 119 The results for the other variables in the saving regressions in Tables 3A.7a, 3A.8a, and 3A.9a are very similar to those for accumulated savings given in Tables 3A.1b, 3A.2b, and 3A.3b and the discussions there about the reasons behind the results apply here as well. The coefficients on AG! in the regressions in Tables 3A.7a, 3A.8a,_and 3A.9a for the most part show that the older the respondent, the more he saved in a period. Similarly, the longer the respondent has been on the job (the larger TtMCJ), the greater the saving undertaken by the respondent on average. The greater the number of children at home (the greater NO), the lower the saving undertaken by the average respondent. Non-white respondents generally saved a great deal less than did white respondents in any given period. For the saving regressions, a married respondent seemed to save less than a non-married respondent in the form of liquid assets. The coefficients on MD in Table 3A.9a would seem to indicate that being married had very little effect on saving in the form of illiquid assets for the respondents in the survey. In general, union members saved less than non-union members in the form of illiquid assets and in SAVZ-type QIIOtI s Cross-section Regressions by Union Membership Whether or not a respondent is a member of a labor union may play a role in the precautionary saving decision process. Frequently, labor unions provide unemployment insurance benefits beyond those provided by a state, may ensure that their members are provided health care, and may provide for greater job security for their members. If union members are the beneficiaries of such programs, they may exhibit different saving behavior than their non-union counterparts. A comparison of the two groups indicates that union.members have substantially higher labor income on average, although their family permanent income is only about $300 per year greater than that of the average non-union member. Also interesting is the fact that for the five years of this data set, union members consistently reported very liquid asset holdings (deposits in banks and savings 8 loans) only sixty percent, on average, of those of the typical 120 non-union member. In order to'examine this aspect of precautionary saving behavior more closely, separate regressions were run for those who were members of a union and for those who were not union members. Selected results for the regressions on these two groups are reported in Tables 3A.10 through 3A.12 of Appendix 3A.2| The regressions of the saving(s) measure on the independent variables conditional on saving(s) being positive, show that job tenure may be viewed differently by the two groups in this sample when the decision about how much to save is made. For non-union members, the coefficients on TENCJ were positive and generally statistically significant, indicating that longer job tenure for non-union workers meant, on average, higher levels of saving(s). For union members, the coefficients on TENCJ were never statistically significant. There also may be some difference between union members and non- union members with respect to the generosity of unemployment insurance. More often than not, for union members the coefficients on UINDX are positive, statistically significant, and larger in magnitude than the corresponding coefficients on UINDX for non-union members. Given the results from the theoretical work, this empirical result may be evidence that labor unions replace a larger-than-optimal portion of a laid-off worker's income. The fact that union members generally had lower asset holdings than did non-union members may indicate that union members perceived themselves to be at lower risk of loss of income due to unemployment because of their union membership and thus chose to save less. If this is the case, then increased union membership may lead to decreased precautionary saving. Fixed-Effects Panel Regression Results The tables in Appendix 33 present the results from various regressions using the fixed-effects panel data model. Table 33.1 in "Regression results for the other years are available from the author upon request. The logit regressions by union membership for all of the years in the study are also available. 121 Appendix 38 shows the regression results for all six measures of saving(s), SAVl, SAVZ, SAV3, DSAVl, DSAV2, and DSAV3, and provides some evidence as to the existence of precautionary saving behavior. The coefficients on the variable SPOUSBIMC are negative (although not statistically significant) for the liquid saving(s) measuresq meaning that respondents with income-earning spouses generally had lower levels of accumulated savings and that they saved less over any given period. As explained in the cross-section analysis parts above, this could come about because of a reduced demand for precautionary saving due to lower family income uncertainty. For the illiquid measure of saving(s), the coefficients on SPOUSEINC are positive but are not statistically significant. This may be another indication that net wealth is not a good proxy for precautionary savings. Also indicative of the possible existence of precautionary saving behavior are the coefficients on the regressor TENCJ in Table 33.1. Negative (although again not statistically significant) in three of the four regressions on the liquid saving(s) measures, the coefficients on TENCJ show that a longer time on the current job results in a lower level of accumulated savings. One reason for this might be that a longer time on the job translates into greater job security, lower income uncertainty, and a therefore a reduced need for precautionary saving on the part of the respondents in the surveys. Similarly, for the more liquid saving(s) measures SAVl and DSAVl, the positive and statistically significant coefficients on JURAT in Table 38.1 of Appendix 33 reflect the fact that the greater the probability of being unemployed, as measured by the unemployment rate, the higher the level of accumulated savings and the higher the amount of saving each period. This makes sense in a world in which the individuals are saving for precautionary reasons against some potential income loss. In three of thetother four regressions, the coefficients on JURAT are positive, though not statistically significant, giving further evidence of behavior one would expect if the respondents were saving for precautionary reasons. 122 The coefficients on UINDx in Table 33.1 are all positive but not significantly different from zero. The fact that the coefficients are positive could be an indication that the unemployment insurance tax rate is greater than the optimal tax rate. However, given the fact that the coefficients are not statistically significant, the generosity of unemployment insurance provision would seem to have little effect on the saving(s) behavior of those in the sample. Again, it is not clear whether this accurately reflects the lack. of any substantial link. between precautionary saving behavior and the provision of unemployment insurance or whether, since I have not distinguished between the covered and non- covered respondents, my data are insufficient to detect the link. As stated earlier in the discussion of the cross-section results, it may also be the case that this group of individuals, with their generally long job tenures, may face such low personal probabilities of unemployment that changes in the generosity of 01 benefits have little effect on their saving(s) behavior. Time dummies D1, DZ, and D3 were used in regressions for each of the savings measures to determine if any effects outside the model which changed over time had an impact on saving(s) behavior, and given the results in Table 33.1, it is clear that the respondents had larger accumulated savings balances as they aged. It also seems clear that the respondents saved less in any one period as they aged, given the coefficients on DD2 and D33 in the regressions using the saving variables of the last three columns. In conjunction with the large magnitude of the coefficients on REAL INT, the reported rate of return to asset holdings adjusted for inflation, the coefficients on 31, D2, and D3 for the accumulated savings regressions could also be detecting the effects of the liberalization of the banking laws in the 1970's. The saving environment changed greatly over the years 1966 to 1981, with the late 1970's and early 1980's being a period of high interest rates and diversification in banking services, enabling those who desired secure investments to obtain high rates of return on bank instruments such as certificates of deposit. 123 As in the cross-section analysis, the coefficients on PAMLABINC and LABIMCSQR provide evidence that the relationship between a family's labor income and its saving(s) is nonlinear for those in this data set. The coefficients on the variables MC and MD are not statistically significant for the saving(s) regressions of Table 33.1, although the positive coefficient on the number of children for the regressions is somewhat curious. The cross-section results indicate that saving is negatively related to the number of children in the household. This is a strong, consistent result of the cross-section analysis. It is not clear why saving(s) should increase with the number of children unless some sort of ”saving for the children's future” is occurring. Fixed-effects Panel Regressions by Union Membership Tables 33.3 and 33.4 of Appendix 33 show the results of splitting the sample into respondents who are in a labor union and respondents who are not members of a labor union, respectively. The regressions for those not in labor unions for the most part show a nonlinear relationship between income and saving(s). This is not the case for those respondents who*were members of labor unions as clearly seen in Table 33.4 of Appendix 33. Also interesting are the coefficients on UINDX for the respective groups. For the non-union respondents, changes in the generosity of unemployment benefits seem to have little affect on saving(s). However, for those respondents who were union members, the regressions in Table 33.4 indicate that the more generous the unemployment insurance benefits, the higher the level of saving(s). This might be evidence that for union members, unemployment insurance benefits are greater than some optimal benefit level. In this case, the theoretical model of chapter one indicates that a positive relationship between precautionary saving and unemployment insurance benefits is to be expected. One final difference between the panel regressions run on union members versus those run on non-union.members involves the coefficients on JURAT. The coefficients on JURAT for the liquid saving(s) measures SAVl 124 and DSAVl for non-union respondents are positive and statistically significant, while none of the coefficients on JURAT for those respondents who were union members are statistically significant. This might indicate that the possibility of future unemployment causes the non-union members to engage in precautionary saving against some probability of future income loss, while union members can rely more heavily on their union to provide for them during bouts of unemployment. In summary, the results of the fixed-effects panel regressions show a limited relationship between the generosity of unemployment insurance provision and precautionary saving; There is some evidence that for union members, precautionary saving and unemployment insurance generosity may be positively related. These regressions do, however, seem to indicate the presence of precautionary saving behavior on the part of the respondents in the survey. Section six discusses reasons for the difficulties encountered in determining the relationship between precautionary saving and unemployment insurance generosity. 6. Estimation Problems and Precautionary Saving Behavior As the previous section detailed, there appeared ‘to be limited evidence from the regressions run for the existence of a link between precautionary saving and the generosity of unemployment insurance benefits. Furthermore, signs of precautionary saving behavior were detected, but in many cases these signs were based on coefficients which were not statistically significant or whose signs fluctuated from regression to regression. Below I detail some of the possible reasons for these problems. Inadequate Measures of Precautionary Saving The proxies used in this chapter may not accurately represent precautionary saving. To accurately perform this type of analysis, what is needed is a survey asking the respondents exactly how much of their ”saving" dollar is set aside for precautionary reasons, howrmuch for their 125 retirement, howrmuch for the new car they wish to buy, etc. Unfortunately such data, to my knowledge, do not exist. The researcher is left to try to control for as many variables affecting saving behavior as possible in the hopes of being able to distinguish between the reasons for saving, a task which proves to be very difficult. All of the empirical studies to date have struggled with the question of how to represent precautionary savings. Most have opted to try to detect consumption fluctuations brought about by changes in some variable representing the risk faced by consumers. These previous empirical studies have met with little success, indicating either that precautionary saving behavior does not exist or that their measure of precautionary savings was flawed. I make use of reported liquid asset holdings data in the belief that any precautionary savings would. be held in liquid form so that it would. be readily accessible. It is possible that since precautionary savings may actually be some fraction of actual asset holdings, my measures may be detecting saving forces at work other than the precautionary saving forces I had hoped to detect. Precautionary Savings Satiation Point If consumers set aside some fixed amount in a "rainy-day fund” and the amount in this fund stays relatively constant, then fluctuations in income, interest rate, unemployment insurance provision, etc. will not have any detectable effects on precautionary savings. Any changes in savings brought about by changes in these variables would not reflect changes in precautionary savings, and thus coefficients may not be statistically different from zero. Liquidity Constraints Another possible reason for the failure to find strong evidence of precautionary saving behavior and to find a link between unemployment insurance benefits and precautionary savings may be that some of the respondents in the surveys were liquidity constrained. If they needed every dollar of income simply to meet day-to-day living expenses, those 126 surveyed would have been unable to save for any reason, let alone for precautionary reasons. In order to test for the possibility of liquidity constrained behavior, I eliminated all households with permanent income of less than $5000 and less than $10000 (in 1976 dollars) and reran the main regressions presented in section five. The results for regressions in which households with permanent incomes of less than $5000 have been eliminated are presented in Tables 3A.13a through 3A.18b in Appendix 3A for the cross-section regressions and Table 33.2 in Appendix 33 for the panel regressions.n Even though this resulted in the elimination of up to half the observations in some of the regressions, the results are nearly identical in terms of signs, magnitudes, and the statistical significance of the coefficients to the results of section five. The fact that eliminating respondents who may be liquidity constrained had little effect on the detection of precautionary savings behavior corroborates the same finding by Dynan (1991). Data Problems In addition to the above problem in defining precautionary savings, there are problems particular to the NLS data set I use. Ideally, I would have savings data (as well as the other data) for at least every year over a five or ten year period. The fact that I have "snapshots" of savings behavior at two- to five—year intervals, while better than having simply one year of cross-sectional data, allows for large, and quite possibly important, intraperiod fluctuations in savings which I am unable to detect. Perhaps the main problem with the data set is that these respondents may have very low perceived probabilities of being unemployed in the future because of their ages and job tenures, meaning changes in the generosity of unemployment insurance benefits would have very little practical impact on them. If they feel with near certainty that they are z’l‘l'te results for regressions in which households with permanent incomes of less than 510,000 have been eliminated are available upon request. 127 not going to be unemployed in the prior to retirement due to layoff, for example, they may not alter their saving behavior in any way in response to a small change in UI benefit levels. Precautionary Saving Levels May Be Very Low Given all of the social safety nets in today's society, it may be the case that people simply do not save a great deal for precautionary reasons. Auto insurance, health insurance, life insurance, unemployment insurance, food stamps, welfare, and other "assistance” programs may have eroded the perceived need for precautionary saving to the point where the levels of precautionary saving are indistinguishable from zero empirically. So even though people may have an inclination to save for an uncertain future, the need to do so is not there because of the programs mentioned above. 7. Conclusions This chapter empirically tests the link.between precautionary saving and the generosity of unemployment insurance provision. In order to do this, I develop an index of unemployment insurance benefit generosity for each state. Using this index and data from the National Longitudinal Surveys of Mature Men for the years 1966, 1969, 1971, 1976, and 1981, I test for the above link using two distinct methods: (1) I perform separate cross-section analyses for each of the years listed above, using six different liquid asset measures and various sets of regressors in a two-stage process; (2) I use a fixed-effects panel regression model to analyze the six liquid asset measures in both the individual and the time dimensions. I find some evidence of a link between precautionary savings and unemployment insurance benefit generosity. In the cases in which the coefficients are statistically significant, more often than not they indicate the existence of a positive relationship between unemployment insurance and precautionary saving. This positive relationship between 128 precautionary saving and unemployment insurance seems especially evident in the case of union members, which may be an indication that 01 benefit provision levels by labor unions are greater than optimal. In part, the difficulty in finding definitive evidence of the link in the whole sample may be due to the fact that the respondents in this sample are generally at a point in their careers at which their perceived probability of being unemployed in the near future is very low. If this is the case, changing unemployment insurance benefit generosity will have very little, if any, effect on them since they do not anticipate ever needing to use it. My regressions do show some evidence of the existence of precautionary saving, unlike the results of Skinner (1988), Kuehlwein (1991), or Dynan (1991). I find that the levels of liquid asset holdings are generally lower for respondents in the survey who have an income- earning spouse. The risk of complete income loss faced by two-income households is lower than that faced by a single-income household and the empirical results indicate that this reduced risk leads to lower levels of saving, presumably because of lower levels of precautionary saving. Also, the levels of liquid asset holdings are in some cases found to be inversely related to tenure on the current job. If long job time can be equated. with job security and hence with a decrease in income uncertainty, then the negative relationship between length of job tenure and saving levels may be an indication of precautionary saving behavior. Finally, I find a positive relationship between the job-specific unemployment rate faced by the respondents and the level of savings for some of the regressions. Higher saving in the face of higher unemployment rates is behavior typical of a consumer engaging in precautionary saving behavior. The fact that this work finds no evidence that increasing unemployment benefit provision reduces the level of savings is especially meortant given the evidence uncovered of precautionary saving behavior on the part of the respondents in this sample. If the respondents were not saving for precautionary reasons, one would not expect changes in 129 unemployment insurance benefits to affect savings since the precautionary component of savings would be absent. However, given the empirical evidence that these respondents are engaging in precautionary saving behavior, the lack of empirical evidence of an inverse relationship between savings and unemployment insurance is more robust. Given the potential significance of saving in terms of capital accumulation and economic growth, it is important to determine if (and the extent to which) programs such as unemployment insurance, health insurance, worker's compensation, and the host of social welfare programs have decreased consumer saving by decreasing the demand for precautionary saving. This chapter represents the first attempt to determine empirically the extent to which unemployment insurance programs affect precautionary saving behavior. """l .u—«w «M 1 . APPENDIX 3A LOGIT RESULTS USING Ski/1,l 130 APPENDIX BA TABLE 3A. 1a _ — 1966 1969 1971 1976 1981 .00020 .00019 .00017 .00012 .00015 P‘““‘"° (12.056) (10.475) (9.46) (5.159) (4.973) -2.7e-09 -2.68e-09 -2.48e-09 -1.4e-09 -2.1le-09 P’R“INCSQR (-7.813) (-7.312) (-6.846) (-2.461) (-3.579) 0130: .0053 .0091 -.0030 .0069 .0132 (1.400) (2.242) (-.888) (1.387) (2.419) vaarnc -7.36e-10 -l.85e-09 -9.01e-10 -2.29e-09 -6.81e-09 (-.932) (-1.954) (-1.084) (-2.354) (-2.817) as: .0266 .0273 .0311 .0100 .0227 (2.315) (2.188) (2.511) (.597) (.937) -.0051 .1190 -.0786 .1792 .6862 SP°USEINC (-.054) (1.154) (-.771) (1.362) (3.360) (-4.182) (-3.653) (-4.657) (-.949) (-.494) rsuca .0116 .0138 .0065 .0074 .0106 (2.756) (3.274) (1.653) (1.650) (1.738) oases -1.052 -1.072 -1.066 -1.163 -1.295 (—10.462) (-9.64) (-9.912) (-8.778) (-6.372) -.1248 -.2469 -.0142 -.1275 -.2045 "RIO“ (-1.339) (-2.459) (-.142) (-.996) (-1.082) (-1.671) (-1.515) (-1.327) (-.048) (-2.638) -.0444 -.0922 -.0280 .0115 -.0208 JURAT (-l.825) (-2.734) (-1.421) (.562) (-.786) cows -2.524 -2.751 -1.870 -1.582 -2.795 (-3.668) (-3.491) (-2.366) (-1.387) (-l.611) 085 2962 2482 2552 1613 766 L°° -1623 95 -1385 51 —1435 93 -897 92 -422 38 ersLIaoon ' ° ° ' ' chi2 650.45 515.27 418.63 263.51 158.82 't-matimics are given in parentheses beneath the coefficient values. 131 TABLE 3A.1b REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAV1.‘ ‘ 1 H 1966 1969 1971 1976 1981 PER“I"° (.037) (.895) (.605) (-3.060) (.994) 3.65e-06 3.78e-06 5.62e-06 ..000025 8.08e-06 9““INCSQR (1.407) (1.250) (1.312) (3.475) (.510) (4.190) (1.264) (1.327) (-1.032) (-1.474) vaarnc 8.22e-07 -3.92e-06 2.64e-06 -.000011 -.000019 AG: 181.40 216.81 204.80 -162.07 343.24 (6.561) (6.401) (4.471) (-2.211) (1.773) -633.13 -528.35 -986.90 826.82 -2658.26 SP°USEIN° (-3.448) (-2.372) (-2.965) (1.641) (-2.491) so -80.27 -99.51 -448.68 -704.50 -914.03 (-2.772) (-1.766) (—3.600) (-4.725) (-3.844) rssca .0250 28.24 10.04 84.82 .4578 (.003) (2.655) (.753) (4.073) (.011) cases -2051.27 -2152.10 -2138.44 -3351.31 -4098.36 (-9.949) (—9.178) (-6.713) (-7.405) (-4.674) UNION -546.92 -788.93 —833.01 1298.2 -2041.63 (-2.848) (—3.349) (-2.398) (2.370) (-1.878) as -767.14 -3117.90 -1652.92 48.15 4142.01 -10.09 -14.65 -76.07 -100.42 78.03 JURAT (-.242) (-.225) (-1.270) (-1.558) (.533) cons —6561.51 -5918.77 -5432.49 18389.97 -18048.69 (-3.671) (-2.441) (-2.008) (3.979) (-1.311) 08s 1871 1549 1670 1071 488 r-srar 54.77 51.46 52.62 36.61 12.79 8-9 80.452 82.872 54.782 32.023 44.652 |t-matisties are given in parentheses beneath the coefficient values. 2Sigm'ficara at the .001 level, so weighted least squares results reported. ’Sigru'ficam at the .005 level, so weighted least squares results reported. LOGIT RESULTS USING SAVLl 1966 132 TABLE 3A. 23 1976 lt-statistics are given in parentheses beneath the coefficient values. 1969 1971 1981 .00021 .00024 .00020 .00015 .00017 9’3“!“c (10.320) (12.028) (10.113) (5.751) (5.478) -2.35¢-09 -3.31e-09 -2.58e-09 -l.67e-09 -2.40e-09 P'R“I"°S°R (-4.775) (-8.321) (-6.219) (-2.532) (-3.947) urunx .0051 .0074 -.0008 .0074 .0146 vanrnc -7.49e-10 -2.736-09 -1.356-09 -2.86e-09 -6.09e-09 (-.789) (-2.731) (-1.468) (-2.769) (-2.599) ass .0259 .0266 .0379 .0041 .0136 (2.127) (1.985) (2.861) (.235) (.542) .0011 .0337 -.1446 .1941 .7979 SP°USBI"° (.011) (.303) (-1.322) (1.405) (3.675) (-5.189) (-3.518) (-3.231) (-1.042) (.361) wanes .0204 .0160 .0106 .0124 .0132 (4.524) (3.538) (2.521) (2.629) (2.050) Danes -1.051 -1.082 -1.082 -1.131 -1.336 (-10.202) (-9.507) (—9.793) (-8.324) (-6.488) euros -.1088 -.1995 -.0782 -.1754 -.3377 (-1.090) (-1.829) (-.729) (-1.304) (-1.716) as -.2110 -.2496 -.2196 -.1852 -.7579 (-1.308) (-1.426) (-1.329) (-1.023) (-2.870) JURAT (-2.030) (—3.488) (-1.777) (.554) (-.727) cons -2.400 -2.609 -2.450 -1.276 -2.317 (-3.302) (-3.100) (-2.904) (-1.073) (-1.284) ' 038 2962 2482 2552 1613 766 LOG -1479 02 -1236 47 -1295 99 -836 76 -394 28 ersnraooo ° ' ° ' ' chi2 732.83 604.40 493.71 293.91 174.61 I. IA. ' ’ 133 TABLE 3A.2b REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAVZ‘l 1966 1969 1971 1976 1981 -.1130 -.3965 .2175 -1.013 1.451 P‘RRINC (-.629) (-1.656) (.905) (-4.052) (2.273) .00001 .00002 .00001 .00005 -.00002 P‘R“INCSQR (1.882) (2.825) (1.188) (4.407) (-.667) 43.98 92.69 19.91 -3.61 6.33 ”INDX (2.470) (4.549) (1.195) (-.166) (.127) -.00003 -.00001 8.88e-06 7.51e-06 -.00006 V‘RINC (-1.700) (-.611) (.595) (.248) (-.574) (4.981) (6.856) (5.602) (-.750) (2.040) -1247.11 -1429.90 -2192.88 478.17 -273.32 SP°°SEINC (-2.894) (-2.814) (-4.498) (.757) (-.168) no -140.07 -292.78 -438.14 -881.78 -622.75 (-1.143) (-2.053) (-3.160) (-4.293) (-1.432) -l3.08 26.52 66.67 69.66 .4180 T'NCJ (-.568) (1.106) (3.226) (3.046) (.007) naacs -3153.36 -2811.72 -2690.77 -4378.92 -3957.57 (-6.837) (-5.418) (-s.172) (-7.606) (-2.238) auras -1380.08 -888.92 -2343.55 922.85 -5409.64 (-3.020) (-1.651) (-4.551) (1.274) (-3.056) an -5052.13 -2747.19 -3512.32 344.07 3118.64 (-5.018) (-1.613) (-3.376) (.416) (1.541) JURAT -162.82 -113.29 -10.03 -188.34 444.19 (-1.509) (-.662) (-.105) (-2.168) (1.832) cons -5796.03 -22414.09 -14745.62 16609.77 -51634 (-1.663) (-4.952) (-3.418) (2.666) (-2.194) 038 2029 1710 1805 1131 s19 r-srar 46.64 38.91 65.55 36.09 12.46 R-square .2312 .2296 .3223 .2956 .2425 8-9 33.072 229.482 332.482 88.222 24.863 _ ‘t-matistics are given in parentheses beneath the coefficient values. 3Significant at the .00l level, so weighted least squares results reported. ’Significant at the .025 level, so weighted least squares results reported. LOGIT RESULTS USING SAVB.l 134 TABLE 33. Ba 1966 1969 1971 1976 1981 I .00016 .00020 .00018 .00009 .00014 P‘R“I"° (5.436) (5.524) (3.618) (1.089) (1.210) -1.78¢-O9 -2.286-09 -1.26e-09 4208-09 3.300-09 P'R“INCSQR (—2.170) (-2.215) (-.727) (1.125) (.664) (-1.939) (-2.176) (-1.312) (.731) (-.378) (-.769) (-1.149) (.221) (-1.404) (-3.231) as: .0174 .0424 .0438 .0634 .0690 (1.039) (2.186) (2.123) (2.174) (1.672) .0227 -.1488 -.2521 .1578 .0669 SPOUSEINC (.153) (—,900) (-1.426) (.627) (.179) no -.0514 -.0622 -.0520 -.0556 .2002 (-1.577) (-1.461) (-1.248) (-.807) (1.124) .0366 .0305 .0321 .0259 .0297 TENCJ (5.491) (4.405) (4.524) (3.086) (2.513) I DRACE -1.286 -1.113 -1.144 -1.192 -1.020 (-9.376) (-7.153) (-6.989) (-5.647) (-3.375) UNION -.4030 -.7378 -.3410 -.7199 -.9204 (-2.810) (-4.482) (-1.947) (-3.052) (-2.701) an .5743 .8128 .6697 1.019 .6949 (3.116) (4.020) (3.227) (4.378) (2.070) -.1352 -.1621 -.0604 -.0586 .0097 JURAT (-4.086) (-3.410) (-1.930) (-1.675) (.219) cows .5531 -.8734 -1.332 -3.439 -4.232 (.563) (-.731) (—1.022) (-1.736) (-1.389) 088 2962 2482 2552 1613 766 LOG -864 79 -678 49 -627 39 -363 94 -175 11 erannooo ' ° ' ' ° ch12 442.32 358.85 309.28 270.28 122.73 ‘t—iatinics are given in parentheses beneath the coefficient values. PE PE 135 TABLE BA . 3b REGRESSION RESULTS FROM SAMPLE WITR POSITIVE SAV3,‘ r 1966 1969 1971 1976 1981 P'R“I"° (.660) (-3.042) (.747) (-4.105) (-2.821) 7.796—06 .00011 .00003 .00015 .00023 P‘R“INCSQR (.345) (3.860) (1.363) (6.714) (3.678) (4.110) (3.860) (3.661) (-1.277) (-.804) .00003 -.00014 .000030 -.00006 -.00036 V‘RINC (1.210) (-2.554) (1.757) (-.993) (-1.505) as: 589.42 947.58 207.07 -417.38 2544.03 (2.878) (3.785) (1.117) (—2.064) (4.192) -1450.09 -5071.38 -4551.89 -8090.59 11736.03 SP°°SEINC (-.867) (-2.834) (-3.012) (-5.639) (2.152) NC 213.04 -374.00 -601.31 -294.45 -1007.96 (.617) (-.744) (-1.416) (-1.147) (-.718) rune: 194.42 -51.85 .2650 120.19 -47.11 (2.432) (-.585) (.004) (1.818) (-.208) DRACE -9094.41 -12787.1 -12166.57 -17927.26 -27199.18 (-5.783) (-7.105) (-8.696) (~10.614) (-4.304) UNION —4177.99 -5727.57 -8794.80 -5186.03 -7629.97 (-2.254) (-2.361) (-4.770) (—2.723) (-1.479) “D —2645.41 10103.03 7755.48 5829.46 -13036.71 (-1.020) (2.944) (2.638) (2.248) (-2.351) JURAT -1500.48 -2363.03 -768.46 -60.10 1557.45 (-4.106) (-4.313) (-3.086) (-.253) (2.338) cons -17316.77 -38826.22 5951.86 73427.62 -75300.1 (-1.463) (-2.562) (.507) (5.518) (-1.748) 08s 2607 2210 2318 1463 695 r-srnr 66.12 81.52 129.93 107.10 27.99 R-square .2489 .3254 .4229 .4899 .3479 8-83 51.36 379.46 363.93 93.78 62.13 ‘ 't-natistics are given in parentheses beneath the coefficient values. 3All are significam at the .001 level, so weighted least squares results reported. 136 TABLE 3A.4 anennssxou RESULTS rnou SAMPLE WITH BOTH SAVSRS AND DISSAVERS USING DSAV1| 1966-69 1969-71 1971-76 1976-81 PERMINC .1517 .1269 -.9032 .5991 pannxncsoa -3.8e—06 -5.3e-06 '.00003 -9.So-06 (-1.648) (2.792) (.651) (.012) VIKINC 1.20-06 -.00001 9.80-07 -.00002 (.271) (1.831) (-5.592) (3.097) SPOUSEINC .875 -294.84 2188.44 '572.73 (.005) (-1.122) (7.360) (-1.053) NC '21.62 -203.84 '262.85 172.38 (-.759) (-2.039) (-4.256) (2.226) TENCJ 1.86 '38.19 '4.021 -37.08 (.207) (-3.236) (-.312) (-1.542) DRACE '144.86 '138.47 '2327.40 '1157.36 UNION '68.85 427.94 1807.53 '869.18 MD '188.41 709.78 903.92 '766.34 (-.390) (1.227) (1.818) (-.887) JURAT -40.16 -141.71 '186.97 '120.01 CONS '238.17 '4567.65 17270.67 -17210.84 (—.157) (-2.330) (7.866) (-3.077) 038 1970 1771 1627 1001 P-STRT 1.69 5.62 19.14 4.21 R-aquare .0111 .0399 .1336 .0525 B-Pz 65.01 46.93 44.74 80.48 ‘t-natistics are given in parentheses beneath the coefficient values. 3All are sigm'fieam at the .001 level, so weighted lean squares results are reported. REGRESSION RESULTS 137 TABLE 3A.5 USING DSAVZ' PROM SAMPLE WITH BOTH SAVERS AND DISSAVERS 1966-69 1969-71 1971-76 1976-81 PERMINCSQR -2.1o-07 -2.20-06 8.50-06 -8.3o-06 (-.039) (-.537) (.833) (-.747) VBRINC -8.3e-08 -4.9e-06 .00002 -.00003 (-.007) (—.592) (1.044) (-.929) AG! 65.12 121.43 69.36 139.54 (1.505) (3.244) (.902) (1.53) SPOUSEINC '532.69 '476.32 356.94 -286.72 NC -92.98 -72.17 -104.41 112.81 (-1.226) (-1.485) (-.708) (1.314) -8.66 '29.02 13.54 '20.85 (-.578) (-2.432) (.580) (-.850) -506.38 '720.52 -1692.38 '1903.34 (-1.634) (-2.656) (-3.188) (-3.149) 300.87 '308.16 -326.57 ‘6.547 (.878) (-1.101) (-.449) (-.009) 2.133 675.90 1462.25 -834.22 (.002) (1.021) (1.269) (-.733) 37.39 '85.29 '125.22 “79.83 (.444) (-1.175) (-1.203) (-.922) '3408.94 '5760.06 -1214.63 '7302.29 H (-1.354) (-2.680) (-.241) (-1.197) 2079 1860 1690 1026 1.80 4.99 5.55 1.79 .0377 .0339 .0413 .0403 133.06 370.14 257.73 231.16 't-latinics are given in parentheses beneath the coefficient values. 3All are significam at the .001 level, so weighted least squares results are reported. 138 TABLE 3A.6 REGRESSION RESULTS rnou SAMPLE WITH 80TH SAVERS AND DISSAVERS USING 0SAV3‘ l 1966-69 1969-71 1971-76 1976-81 PERMINC -.2663 .6354 -.3171 1.028 (-.872) (1.810) (-.522) (2.003) PERMINCSQR .00002 -.00002 .00003 -.00001 (1.990) (-1.367) (1.242) (-.645) UINDX 24.42 55.98 -105.94 50.11 (.849) (1.662) (-2.24) (.991) VARINC -.00002‘ 8.66-06 2.48-06 .00003 (—1.363) (.366) (.102) (.529) AG! 264.09 -50.23 -.6651 194.51 (2.91) (-.494) (-.004) (1.053) SPOUSEINC -1898.71 -520.06 2218.98 1432.19 (-2.785) (-.662) (1.708) (1.053) NC -149.06 -281.12 376.43 598.67 (-1.035) (-1.374) (1.023) (1.634) (.073) (-.173) (.308) (.581) DRACE —2251.41 542.91 -4760.31 -3707.63 (-3.021) (.649) (-3.682) (-1.968) UNION -2217.67 1028.32 -638.18 -1597.96 (-2.684) (1.040) (-.363) (-1.026) MD 2038.31 834.93 1096.40 -1147.29 (1.722) (.624) (.532) (-.511) JURAT -384.62 29.87 -139.49 69.94 (-2.408) (.131) (-.S75) (.295) CONS -8704.50 -4460.45 12755.35 -17944.23 (-1.646) (-.699) (1.175) (-1.426) 038 2603 2259 2006 1231 P-STAT 9.87 4.88 8.17 4.41 R-aquara .0472 .0275 .0506 .0449 8-p2 267.85 483.20 155.26 77.18 It-datistics are given in parentheses beneath the coefficient values. 3All are significant at the .001 level, so weighted least squares results are reported. 139 TABLE 3A.7a REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAVIJ l:__ 1969-71 1976-81 1966-69 1971-76 (4.314) (.326) (-7.677) (-2.132) PERMINCSQR -S.188-06 1618-06 .000054 .000019 (-2.032) (.303) (6.507) (1.590) UINDX 7.835 86.38 57.30 -5.39 VABINC 8.233-07 -.000019 .000013 9.213-06 AGE 142.93 66.30 -352.04 360.72 (5.655) (1.166) (-6.779) (2.687) SPOUSEINC -404.68 -777.569 2780.85 3959.70 (-2.232) (-1.902) (6.215) (4.635)‘ NC -107.27 -329.38 -630.27 -117.87 . (-2.376) (-1.992) (-6.7S9) (-.698) TENCJ 26.80 -24.72 19.05 -50.78 (2.930) (-1.484) (1.029) (-1.428) DRACE -1100.94 -1741.85 -2947.69 -S411.49 (-6.698) (-4.55) (-7.277) (-7.018)= UNION -937.71 1077.10 1100.00 4829.23 (-4.444) (2.680) (1.822) (6.555) an -1277.69 -2096.60 433.41 1980.50 (-1.353) (-3.937) (.591) (1.360); JURAT -123.33 216.86 -304.71 2.187 (-2.882) (2.051) (-3.723) , (.014) CONS -5176.00 -4642.42 28359.97 -16803.66 (-3.227) (-1.569) (8.945) (-1.934) OBS 1063 1073 996 513 P-STAT 35.67 29.03 42.41 34.60 R-aquare .3063 .2626 .3593 .4736 B-P 33.912 26.293 43.432 53.302 73 't-ntistics are given in parentheses beneath the coefficient values. ’Sigru'ficam at the .001 level, so weighted least squares results are reported. ’Sigrificam at the .01 level, so weighted least squares results are reported. 140 TABLE 3A.7b REGRESSION RESULTS FROM SAMPLE WITH NEGATIVE DSAVI: _ 1966-69 1969-71 1971-76 1976-81 PERKINC .1335 -.0546 -.2883 .2310 (1.360) (-1.280) (-4.056) (1.014) PERMINCSQR -4.69-06 '2.83-07 -3.2e-06 -.00002 (-1.242) (-.259) (-1.4S9) (-1.757) UINDX -21.33 -10.79 17.66 -2.37 (-2.059) (-1.205) (2.093) (-.108) VARINC -7.89-06 2.76-06 -1.89-06 .00001 (-2.541) (1.120) (-.433) (.610) AGE -104.80 -66.56 -68.92 66.90 (-3.564) (-2.193) (-2.089) (.648) SPOUSEINC 368.66 466.84 1342.05 21.63 (1.565) (2.156) (4.255) (.031) NC 29.00 131.00 416.66 547.80 (.799) (3.287) (1.668) (3.932) TENCJ 5.67 -40.18 -2.75 -111.92 (.567) (-3.636) (-.264) (-3.619) DRACE 1942.84 1072.15 1225.46 1336.83 (8.372) (4.747) (4.033) (2.122) UNION -122.13 77.47 1184.21 942.73 MD 616.52 1707.26 1422.03 -10.04 (.899) (1.657) (1.283) (-.012) JURAT 62.85 101.54 -41.88 200.12 CONS 1779.35 669.81 338.53 -9315.91 (.992) (.332) (.153) (-1.477) 038 907 698 631 488 P-STAT 26.41 24.16 26.75 13.75 R-Iquare .2774 .3143 .3601 .2734 B-P 31.112 28.902 30.672 22.593 — ‘ 1t-natiuies are given in parentheses beneath the coefficient values. 2Significant at the .001 level, so weighted least squares results are reported. ’Signifieant at the .05 level, so weighted least squares results are reported. 141 TABLE 3A.83 REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAV2: 1966-69 1969-71 1971-76 1976-81 PERMINC .2469 .0705 1.559 -1.583 PERMINCSQR -2.64e-06 5.490-06 -.00002 .00008 UINDX 55.37 55.82 -40.66 25.83 (3.580) (3.723) (-.902) (.235) VARINC .00001 4.329-06 4.650-06 3.128-06 (.999) (.716) (.321) (.106) AGE 361.97 139.82 574.85 274.17 (6.053) (2.872) (3.339) (.765) SPOUSEINC -1077.37 -606.52 ~2812.47 -6448.93 (-2.658) (-1.649) (-2.062) (-2.433) NC -111.86 -127.56 -955.39 -318.25 (-1.027) (-1.320) (-2.059) (-.293) TENCJ 18.18 8.79 53.30 292.16 (.934) (.567) (.975) (3.162) DRACE '1395.58 -1487.97 '2779.28 -4539.09 (-3.480) (-4.260) (-1.558) (-1.246) UNION -876.35 -409.63 -4966.66 -5210.87 (-2.007) (-1.111) (-3.703) (-2.029) MD -1885.95 -2361.98 '2587.32 -7546.40 (-1.572) (-3.540) (-1.058) (-1.723) JURAT 1.372 '45.51 -492.23 8.59 (.012) (-.429) (-1.793) (.020) CONS -17804.6 -6038.40 -29236.96 2286.76 (-5.144) (-2.133) (-2.586) (.090) 088 1157 1111 999 523 P-STAT 24.05 31.87 11.96 23.85 R-Iquare .2146 .2739 .1270 .3594 8'? 130.162 317.522 21.183 154.862 — m lt-datistitu are given in parentheses beneath the coefficient values. 1Sigru'firzarl at the .001 level, so weighted least squares results are reported. ’Not signifieam at the .05 level, so ordinary least squares results are reported. 142 TABLE 3A.8b REGRESSION RESULTS FROM SAMPLE WITH NEGATIVE DSAV2: r —- I 1966-69 1969-71 1971-76 1976-81 PERMINC .2654 .0859 -.3194 2.5213 PERMINCSQR -7.7e-06 -.00001 46.90-07 -.00008 (-1.261) (-1.968) (-.051) (-4.677) UINDX '16.88 -22.81 -19.20 53.24 VARINC .00002 '3.59-06 -1.60-06 -.00013 (2.102) (-.630) (-.238) (-2.160) AGE -146.31 -78.04 -309.54 738.28 (-2.886) (-2.642) (3.576) (4.177) SPOUSEINC -219.18 427.09 ’146.74 '6190.78 (-.544) (1.579) (-.243) (-4.502) NC -6.92 120.72 570.61 335.99 (-.071) (2.379) (1.942) (.805) TENCJ 5.70 '30.16 -1.34 '201.71 (.329) (-2.704) (-.055) (-4.579) DRACE 2246.06 1240.88 2248.18 2641.06 (6.174) (5.002) (2.755) (2.071) UNION '2.55 132.85 3357.56 '1022.52 (-.006) (.498) (4.068) (-.549) ND 1629.08 1117.98 6316.75 '3648.74 (1.977) (1.102) (4.350) (-2.153) JURAT 109.17 128.80 '11.74 _ 32.62 CONS 1065.05 1957.33 8768.36 '58551.8 (.356) (1.024) (1.410) (-5.163) OBS 922 749 691 503 F-STAT 21.30 23.29 29.10 26.05 R-square .2335 .2915 .3582 .4087 B-P 23.703 121.562 197.702 22.133 J 't-uatinics are given in parentheses beneath the coefl'rcierl values. ’Sigm'ficarl at the .001 level, so weighted least squares results are reported. ’Significarl at the .05 level, so weighted least squares results are reported. 143 TABLE 3A.9a REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAV3J 1966-69 1969-71 1971-76 1976-81 (-2.682) (.515) (2.335) (-.151) PERMINCSQR .00005 .00001 -4.180-06 .00005 (3.616) (1.017) (-.271) (2.155) (1.821) (5.352) (-1.366) (1.768) VARINC '7.308-06 2.439-06 .00002 .00037 (-.407) (.182) (.577) (4.028) AGE 418.57 67.49 135.42 400.46 (3.363) (.650) (.394) (2.166) SPOUSEINC 23.74 -133.26 '6408.25 469.87 NC 285.25 '99.77 683.20 89.87 TENCJ 123.81 105.04 225.25 111.17 I (2.491) (2.458) (2.041) (1.451) DRACE -4299.25 -2090.89 '8587.14 '9721.94 (-4.948) (-2.582) (-2.543) (-5.063) UNION -4373.23 '1417.47 '12945.74 '1312.88 (—4.425) (-1.326) (-4.720) (-.848) ND 527.65 '2525.62 299.38 2125.30 JURAT -824.94 147.31 '689.82 129.84 CONS '4821.28 -7569.63 11056 '20417.59 (-.681) (-1.235) (.495) (-1.347) OBS 1633 1348 1285 747 F-STAT 55.30 47.27 10.07 32.14 R-unare .3074 .3152 .0868 .3627 8'? 219.802 62.822 19.663 46.542 _ 'm‘ .’ —x mus—.— I"'..'..‘L'; ‘t-‘atistics are given in parentheses beneath the coefficient values. zSiglificarl at the .001 level, so weighted least squares results are reported. ’Not significant at the .05 level, so ordinary least squares results are reported. 1r»— 144 TABLE 3A.9b REGRESSION RESULTS PROM SAMPLE WITH NEGATIVE DSAV3J I... 1966-69 1969-71 1971-76 1976-81 PERMINC -.3007 -.6239 1.962 -.3653 (-.876) (-1.185) (1.224) (-1.346) PERMINCSQR .00001 2.69-06 -.00007 3.99-07 UINDX -27.63 -91.96 -655.54 -32.03 (-.777) (-2.232) (-8.132) (-.717) VARINC .00004 .00002 .00001 .00011 (1.533) (1.130) (.260) (3.561) AGE 78.40 -513.14 -1476.97 103.93 (.710) (-3.448) (-3.952) (.646) SPOUSEINC -2047.4 505.35 6202.55 2317.29 (-2.073) (.504) (1.955) (1.724) NC -603.56 204.22 -1096.29 -601.86 (-2.874) (.757) (-1.240) (-.619) TENCJ -27.37 139.86 191.91 -27.14 (-.516) (2.855) (1.310) (-.453) DRACE 5273.51 1398.08 20762.5 335.91 (5.418) (1.355) (6.783) (.310) UNION -1318.72 4843.31 1587.26 3842.23 (-1.147) (3.694) (.362) (2.291) MD 1568.62 1343.54 -2100.76 -4181.49 (1.283) (.544) (-.470) (-2.340) JURAT 701.29 575.25 -1155.75 -470.76 (3.453) (1.859) (-2.207) ' (-2.925) CONS -12278.81 22325.43 100474 -6111.48 (-2.057) (2.394) (3.770) (-.621) OBS 970 911 721 484 F-STAT 26.87 28.44 18.84 24.88 R-square .2674 .2916 .2570 .4072 B-P2 29.0 353.0 85.80 3 . 0 1 3 54 't-datistics are given in parentheses beneath the coefficient values. 3All are significam at the .001 level, so weighted least squares results are reported. 145 TABLE 3A. 10 AGGREGATE SAVINGS REGRESSION RESULTS FOR UNION vs . NON-UNION”-3 1966 SAv1 SAv2 SAv3 N-U U N-U U N-U U -.349 .1735 -.466 .1592 1.95 .231 PnnuINC (-2.84) (.834) (-1.98) (.807) (3.67) (.208) .00002 -19-06 .00004 29-06 -.00002 .00005 PREMINCSQR (4.39) (-.145) (3.86) (.322) (-.76) (1.52) UINDX 15.00 17.80 .0092 39.38 284.29 179.19 (.896) (1.52) (.003) (3.12) (3.829) (1.59) VARINC 46-07 -3e-06 -.00003 -6o-06 .00004 .00001 AGE 309.51 91.38 400.26 87.97 1063.62 1198.1 (5.60) (2.26) (4.805) (1.785) (4.857) (3.39) -773.27 -452.90 -3028.6 -618.92 -13469 -3368.7 SP°USEINC (-1.93) (-1.84) (-4.57) (-2.28) (-5.37) (-1.18) "c -286.71 -257.73 -410.80 ~323.52 -1561.1 -1807.9 (-2.56) (-6.54) (-1.89) (-8.15) (-3.68) (-2.36) TENCJ 31.74 -2.29 31.51 -14.64 763.36 80.22 (1.33) (-.157) (.795) (-.964) (7.91) (.611) “D -4081.0 -1079.6 -2878.8 ~2021.3 9070.8 -2120.1 (-4.50) (-.284) (-1.94) (-.409) (2.63) (-.418) i JURAT -173.39 58.41 -2s4.26 93.26 -895.72 -777.61 CONS -6402.9 -3582.0 -8618.6 -3485.2 -61321 -54323 (-2.09) (-.771) (-1.79) (-.616) (-5.11) (-2.37) OBS 1147 724 1236 793 1612 995 P-STAT 41.58 29.79 36.25 31.08 87.67 6.57 R-squsro .2871 .3148 .2456 .3042 .3759 .0626 B-P 48.98 36.49 23.48 27.52 32.72 17.41‘ _ 'N-U signifies respondents not in a union while U represents those who are union members. at-statistics are given in parentheses beneath the coefficient values. ’Weighted least squares results reported unless otherwise indicated. ‘Ordinary least squares results reported because of low B-P statistic. 146 TABLE 3A.11 UNION vs . NON-UNIONW AGGREGATE SAVINGS REGRESSION RESULTS FOR 1971 SAv1 SAv2 SAv3 N-U U N-U U N-U U I -.7966 .4393 -.4715 .3110 -1.20 .094 PER“I"° (-5.46) (2.50) (-1.63) (2.048) (-1.60) (.115) .00003 -7o-06 .00004 6a-06 .0001 .00005 93““I"CSQR (5.62) (-1.21) (3.748) (1.01) (3.26) (1.65) UINnx 38.35 73.53 22.85 37.72 344.12 203.7 (2.13) (4.41) (.848) (2.149) (4.90) (3.01) VARINC .00001 .00002 .00002 -3e-07 -.00009 4e-06 AGE 290.38 162.60 430.07 288.82 648.90 344.44 (3.41) (2.55) (3.896) (4.74) (2.08) (1.44) -947.30 -387.49 -3591.7 -1289.1 -13378 -3489.2 SPOUSEI"C (-1.34) (-.92) (-4.08) (-3.05) (-3.97) (-2.18) NC -531.80 -245.39 -467.26 -380.97 -3023.2 -1432.2 (-1.93) (-2.98) (-1.55) (-4.69) (-4.76) (-3.53) TENCJ 86.77 -3.23 121.51 -2.75 771.40 -26.49 up 3947.1 -3714.3 817.68 -4002.5 13252 3989.1 (4.58) (-1.66) (.588) (-3.16) (1.62) (.802) JURAT 91.70 102.59 -94.71 -30.52 -1765.3 -923.09 (.787) (1.22) (—.546) (-.394) (-4.00) (-3.01) CONS -13352 -11345 -18227 -13732 -23347 -13770 (-2.73) (-2.76) (-2.70) (-4.05) (-1.14) (-.898) OBS 1011 659 1093 712 1408 910 P-STAT 45.78 27.50 42.35 32.39 93.21 83.66 R-equare .3349 .3182 .3010 .3370 .4233 .5059 B-P 36.60 28.40 207.67 27.13 219.93 22.75 I .32 '~“Q.‘?. U- '..¥ .‘5 . 'N-U signifies respondents not in a union while U represents those who are union members. at-statistics are given in parentheses beneath the coefficient values. ’Weighted least squares results reported unless otherwise indicated. 1r_..-. SA 147 TABLE 3A.12 SAVING REGRESSION RESULTS FOR PERIOD 1966-69 WHEN SAVING IS POSITIVE UNION vs . NON-UNION'JJ" DSAVl DSAV2 DSAV3 ‘1 N-U U N-U U N-U 111 .2347 .3083 .2739 .0658 ~1.50 -1.37 PERMINC (3.351) (1.40) (1.52) (.195) (-2.54) (-1.45) -16-06 -56-06 20-06 80-06 .00008 .00003 ”"1“qu (-.425) (-.579) (.289) (.867) (3.55) (.758) UINDX -.4061 10.52 20.49 15.61 174.68 269.34 VARINC .00003 -20-06 .00005 -4e-06 -80-06 -.00006 (3.451) (-.433) (3.76) (-.41) (-.23) (-1.46) AGE 88.39 188.89 189.00 365.97 639.15 -248.43 -219.17 -55.49 -1659.2 -607.51 -1862.2 6627.0 spouszmc (-.753) (-.175) (-3.14) (-.67) (-1.14) (4.27) NC -72.70 -205.06 -88.45 -617.01 -124.59 663.58 TENCJ 57.48 16.08 101.03 .3432 578.96 128.86 (3.035) (1.05) (4.79) (.009) (5.828) (1.62) MD -1127.0 -1773.5 -1858.6 -1437.9 7306.0 195.62 JURAT -85.50 -117.18 -122.26 169.94 -797.77 -1762.9 CONS -3165.9 -8702.9 -8561.5 -16558 -31671 17119 (-1.68) (-2.06) (-2.40) (-2.38) (-2.58) (1.15) OBS 634 429 681 476 979 654 F-STAT 25.76 19.88 28.83 3.47 42.25 27.47 B—square .3126 .3435 .3213 .0694 .3244 .3197 B-P 21.18 21.75 80.43 6.765 153.41 26.23 I 'N-U signifies respondents not in a union while U represents those who are union members. ’t-datistics are given in parentheses beneath the coefficient values. ’Weighted least squares results reported unless otherwise indicated. ‘Results of regressions conditional upon saving being negative available upon request. ’Ordinary least squares results reported because of low B-P statistic. II- 148 TABLE 3A.13a LOGIT RESULTS USING SAVIJ PERMINC> $5000 (1976 s ' s) — l a 1966 1969 1971 1976 1981 .00019 .00020 .00017 .00012 .00015 PER“I”° (10.121) (9.593) (8.195) (4.165) (4.308) -2.556-09 -2.79e-09 -2.44e-09 '-1.33e-09 -2.1e-09 PER“I"CSQR (-6.702) (-7.018) (-6.131) (-2.049) (-3.230) UINDX .0053 .0083 -.0040 .0102 .0135 vAnINc -7.6le-10 -1.83e-09 -9.06e-10 -2.24e-09 -6.8e-09 (-.966) (-1.939) (-1.090) (-2.312) (-2.804) AGE .0306 .0316 .0343 .0038 .0039 (2.567) (2.445) (2.662) (.215) (.157) -.0087 .0952 -.0882 .1540 .6864 SP°USEINC (-.089) (.908) (-.848) (1.138) (3.314) NC -.0968 -.1112 -.1430 -.0619 -.0458 (-3.609) (-3.431) (-4.354) (-1.175) (-.436) TENCJ .0089 .0116 .0034 .0067 .0013 (1.980) (2.610) (.809) (1.375) (1.764) DRACE -1.013 -1.088 -1.020 -1.169 -1.269 UNION -.1647 -.2640 -.0397 -.1410 -.2076 (-1.755) (-2.601) (-.394) (-1.089) (-1.086) MD -.2786 -.2427 -.2244 -.0974 -.8272 (-1.591) (-1.312) (-1.272) (-.493) (-2.925) -.0414 -.0754 -.0251 .0191 -.0256 JURAT (-1.642) (-2.155) (-1.236) (.898) (-.936) CONS -2.597 -3.015 -1.911 -1.368 -1.474 (-3.570) (-3.625) (-2.294) (-1.120) (-.819) 088 2747 2326 2388 1484 710 L0“ -1521 72 -1300 90 -1345 74 -818 60 ~392 44 LIKELIHOOD ° ° ' ' ' ch12 469.06 418.58 315.63 201.82 124.87 ‘t-Natistics are given in parentheses beneath the coefficient values. 149 TABLE 3A.13b REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAV1,l PERMINC>$SOOO (1976 5'!) - — 1966 1969 1971 1976 1981 -.0912 .1626 .6125 .2110 -.0211 933“!"C (-.958) (1.301) (3.389)) (1.130) (-.035) 6.719-06 1.450-06 -.00001 3.096-06 .000018 PER“I"CSQR (2.024) (.337) (-1.704) (.457) (.916) UINDX 37.21 14.71 3.933 15.44 -62.95 (4.162) (1.522) (.385) (1.122) (-2.078) 4.29-07 -4.76e-06 5.22.-06 -5.48.-06 -.00001 V‘RINC (.114) (-1.009) (.497) (-2.023) (-1.267) as: 170.63 255.88 193.42 176.13 611.88 (5.852) (6.978) (4.216) (2.411) (2.593) -668.50 -611.75 -1624.81 541.91 -2368.14 SPOUSEINC (-3.556) (-2.618) (—4.842) (1.284) (—2.166) NC -98.54 -86.53 -439.58 -739.18 -1266.81 2.751 21.18 26.57 17.19 28.55 Tnnca (.273) (1.805) (1.993) (.970) (.613) DRACE -2083.76 -2078.08 -1744.68 -2222.92 -4077.09 (-9.775) (-8.707) (-5.646) (-5.795) (-4.362) UNION -532.72 -1011.47 -971.49 -708.08 -1888.89 (-2.683) (-3.822) (-2.825) (-1.s48) (-1.696) “D -214.35 -4036.96 -2335.03 1219.67 4299.82 (-.174) (-1.456) (-2.697) (1.701) (3.411) 6.580 -20.26 -60.54 165.38 70.38 JURAT (.147) (-.306) (-1.001) (2.712) (.436) cons -6035.43 -7728.78 -7533.23 -10748.58 -29398 (-2.931) (-2.210) (-2.432) (—2.198) (-1.721) 08S 1820 1505 1615 1023 469 F-STAT 53.03 49.37 54.99 43.09 12.21 R—square . 2761 . 3008 . 3085 . 3568 . 2583 B-P 77.902 81.122 53.132 31.203 42.912 I-" |t-statiuics are given in parentheses beneath the coefficient values. ’Significant at the .001 level, so weighted least squares results reported. ’Significant at the .005 level, so weighted least squares results reported. 150 TABLE 3A.14a LOGIT RESULTS USING SAv2J PERMINC>$SOOO (1976 S's) 1966 1969 1971 1976 1981 .00019 .00025 .00019 .00015 .00019 P'R“I"° (7.891) (10.872) (8.501) (4.951) (5.285) -2.06e-09 -3.44e-09 -2.486-09 -1.76e-09 -2.73.-09 PERMINCSQR (-3.516) (-7.915) (-5.356) (-2.388) (-4.050) "INDX .0044 .0061 -.0021 .0099 .0169 (1.070) (1.336) (-.553) (1.802) (2.826) V‘RINC -8.26e-10 -2.72a-09 -1.36o-09 -2.79e-09 -6.26o-09 (-.869) (-2.723) (-1.477) (-2.723) (-2.674) as: .0318 .0319 .0425 .0017 —.0091 (2.497) (2.284) (3.065) (.092) (-.346) -.0012 .0047 -.1547 .1671 .7535 SP°USEINC (-.011) (.042) (-1.383) (1.173) (3.420) NC -.1263 -.1106 -.o955 -.0695 .0566 (-4.520) (-3.250) (-2.822) (-1.281) (.529) TENCJ .0185 .0134 .0074 .0112 .0113 (3.809) (2.774) (1.648) (2.202) (1.694) DRACE -1.015 -1.098 -1.036 —1.106 -1.240 UNION -.1488 -.2197 -.1075 -.1875 -.3444 (-1.479) (-1.992) (-.993) (-1.379) (-1.728) “D -.1831 -.2484 -.2387 -.2863 -.8427 (-1.012) (-1.289) (-1.295) (-1.390) (-2.876) -.0473 -.1095 -.0351 .0197 -.0267 JURAT (-1.754) (-2.916) (-1.605) (.870) (-.932) (-3.266) (-3.224) (-2.813) (-1.021) (-.624) 088 2747 2326 2388 1484 710 L°° -1372 67 -1152 22 -1206 24 -758 03 -364 72 LIKELIHOOD ' ' ° ° ° ch12 623.32 472.13 361.64 221.62 137.98 .. .u—--- s- al. a I 4 a ; \ lt-Iatinics are given in parentheses beneath the coefficient values. 151 TA8L8 3A.14b REGRESSION R8SULTS PROM SAMPLE WITH POSITIVE SAv23 PERMINC> 55000 (1976 s ' a) _ 7 I 1966 1969 1971 1976 1981 I -.3058 -.4934 .6732 .4002 1.771 Pznxluc (-1.174) (-1.s73) (2.190) (1.199) (1.890) .00002 .000027 -5.29e-06 ‘ 3.309-06 -.00003 PERKINCSQR (1.993) (2.496) (-.498) (.258) (-.801) UINnx 51.95 98.55 19.67 28.96 30.05 (2.775) (4.796) (1.203) (1.492) (.569) -.00002 -.00001 .00001 6.456-06 -.00006 Vfinluc (-1.215) (-.657) (.705) (.247) (-.528) as: 294.06 525.43 351.20 256.91 1153.83 (4.256) (6.833) (5.007) (2.652) (2.706) -1311.32 -1369.40 -2423.05 -394.10 -777.33 SP°USEINC (-2.955) (-2.685) (-4.983) (-.713) (—.449) No -148.56 -262.76 -388.08 -965.41 -529.49 (-1.185) (-2.161) (-3.022) (-5.175) (-1.156) Tnnca (-.398) (.570) (3.246) (.844) (.713) DRACE -3172.36 -2779.67 -2670.37 -3555.87 -3716.12 (-6.564) (-5.449) (-5.368) (-6.921) (-1.902) UNION -1350.35 -1039.37 -2364.92 -1816.64 -5389.09 MD -5683.96 -3539.18 -3462.90 1163.80 1650.90 (-4.745) (-1.623) (—3.589) (1.451) (.660) -187.85 -95.86 32.94 95.44 -22.159 Junar (-1.S85) (-.549) (.346) (1.152) (-.081) CONS -3712.47 -21401.53 -16206.48 -15208.71 -80341.11 (—.886) (-4.036) (-3.450) (-2.291) (-2.729) OBS 1972 1665 1749 1080 497 P-STAT 41.65 37.59 63.09 38.14 11.49 R-square .2165 .2283 .3209 .3172 .2358 B-P 32.543 230.772 330.212 83.812 24.05‘ It-statistics are given in parentheses beneath the coefficient values. ’Significau at the .001 level, so weighted least squares results reported. ’Significarl at the .005 level, so weighted least squares results reported. ‘Sigm'ficarl at the .025 level, so weighted least squares results reported. LOGIT RESULTS USING SAv3J PERMINC> $5000 (1976 S ' s) 152 TABLE 33. 158 ‘7 I I 1966 1969 1971 1976 1981 .00019 .00024 .00024 .00013 .00004 P‘R“I"° (5.809) (6.133) (5.011). (.874) (.173) -2.506-09 -3.09o-09 -2.800-09 2.736-09 6.936-09 P‘Rnlncsqa (-3.307) (-3.477) (-2.158) (.480) (.829) UINnx -.0124 -.0148 -.0120 .0047 -.0044 (-2.033) (-2.160) (-1.959) (.498) (-.433) VARINC -7.86e-10 -2.020-09 4.490-10 -2.336-09 -1.13e-08 (-.585) (-1.187) (.194) (-1.191) (-3.128) AG: .0108 .0518 .0528 .0634 .0319 (.582) (2.450) (2.321) (1.847) (.674) —.0281 -.1076 -.2849 .2629 -.0097 SP°USEINC (-.185) (—.621) (-1.537) (.959) (-.024) (-1.309) (-1.347) (-1.460) (-1.067) (1.036) TENCJ .0312 .0215 .0203 .0180 .0294 (4.118) (2.820) (2.625) (1.828) (2.178) DRACE -1.430 -1.200 -1.128 -1.288 -.9275 (-9.654) (-7.232) (-6.335) (-5.394) (-2.790) UNION -.4211 -.7509 -.3619 -.7153 -1.034 (-2.854) (-4.438) (-2.011) (~2.912) (-2.894) “D .4425 .6858 .4267 1.039 .9707 (2.205) (2.984) (1.748) (3.864) (2.546) -.1172 -.1532 -.0532 -.0602 -.0050 JURAT (-3.208) (-2.944) (-1.559) (-1.545) (-.100) CONS .8715 -1.484 -1.725 -3.393 -1.231 (.791) (-1.121) (-1.186) (-1.407) (-.345) OBS 2747 2326 2388 1484 710 Loc -744 85 -596 79 -546 83 -294 37 -144 30 LIKELIHOOD ° ' ° ' ° ch12 354.05 293.94 227.75 200.39 88.40 ‘t-astistics are given in parentheses beneath the coefficient values. 153 TABLE 3A. 15b REGRESSION RESULTS FROM SAMPLE WITH POSITIVE SAv3J PERMINC> $5000 (1976 s ' a) 1966 1969 1971 1976 1981 I -1.6614 -2.391 1.206 -1.615 1.002 P‘R“I“° (-1.880) (-2.214) (1.432) (-2.097) (.620) .00008 .00011 6.579-06 .00013 .00004 P33“INCSQR (2.382) (2.952) (.218) (4.742) (.728) UINnx 284.83 614.93 145.82 28.06 208.84 (4.123) (7.931) (3.249) (.505) (1.768) VIKING .00002 -.00013 .000023 —.00010 .00026 (.841) (-2.393) (1.345) (-1.583) (1.602) AGE 626.51 1035.15 304.97 364.24 541.44 (2.686) (3.840) (1.519) (1.486) (1.049) -665.75 -5353.10 -4715.60 -7676.17 5713.43 SPOUSEINC (-.360) (-2.863) (-2.816) (-4.784) (1.448) NC 510.31 -118.90 —537.95 -113.03 -318.65 (1.313) (-.220) (-1.290) (-.352) (-.309) TENCJ 157.99 -67.89 15.19 199.34 621.04 DRACE -9252.60 -12855.36 -11764.37 -18132.21 -33576.59 (-5.540) (-7.081) (-8.076) (-11.072) (-8.S77) UN10N -5163.29 -7131.22 -8511.95 -10951.33 -17472.31 (-2.534) (-2.663) (-4.267) (-5.033) (-4.316) “D -6003.23 9507.97 9093.57 10542.53 17060.3 JURAT -1659.25 -2307.68 -9s7.86 281.34 -949.27 (-4.079) (-4.090) (~3.574) (.994) (-1.988) CONS -2684.83 -44507.74 -4486.63 10739.65 -17195.95 (-.181) (-2.572) (-.338) (.635) (-.444) 088 2459 2099 2199 1373 657 r-STAT 61.91 75.97 116.06 101.43 41.36 R-aquare .2476 .3213 .4084 .4923 .4550 8-21 48.69 369.84 354.48 88.83 62.09 ‘t-datilics are given in parentheses beneath the coefficient values. ’All are significam at the .001 level, so weighted least squares results reported. 154 TABLE 3A.16a REGRESSION RESULTS PROM SAMPLE WITH POSITIVE DSAVI,l PERMINC>$SOOO (1976 s 'a) 1966-69 1969-71 1971-76 1976-81 PERMINC .2694 .9624 .4125 -1.747 (2.766) (4.203) (1.924) (-4.125) PERMINCSQR -4.63e-06 -.000026 -1.886-06 .00006 (-1.379) (-3.012) (-.224) (3.588) UINDX 9.92 58.92 -43.57 -28.03 VARINc 2.900-07 -.00002 -3.96e-07 -3.79e-06 7“ (.075) (-1.726) (-.039) (-.282) AGE 160.74 53.26 89.20 267.42 ‘ r (5.101) (.950) (2.003) (1.831) SPOUSEINC -432.01 -1154.66 -702.84 4313.22 (-2.308) (-3.291) (-2.099) (4.872) , Nc -114.11 -270.28 -436.41 -61.96 g (-2.356) (-1.933) (-6.823) (-.356) L TENCJ 23.23 6.48 -32.89 3.13 (2.123) (.424) (-2.395) (.072) DRACE -1192.11 -363.25 -729.87 -6013.30 (-6.617) (-1.067) (-2.537) (-7.109) UNION —1037.11 -1353.47 ~301.64 5036.24 (-4.204) (-3.471) (-.805) (6.739) MD -1993.41 -1100.80 147.73 1858.74 (-1.481) (-1.497) (.256) (1.007) JURAT -128.76 -149.65 -101.50 -25.68 CONS -5224.90 -8002.14 -558.05 -2930.83 (-2.311) (-2.203) (-.182) (-.288) 088 1032 1041 959 498 r-STAT 35.35 23.42 36.27 37.67 R-square .3108 .2285 .3326 .5024 B-P 32.922 26.443 43.252 51.342 't-uatiaies are given in parentheses beneath the coefficient values. ’Significam at the .001 level, so weighted least squares results are reported. 1Significam at the .01 level, so weighted least squares results are reported. 155 TA8LE 3A.16b REGRESSION RESULTS FROM SAMPLE WITH NEGATIVE OSAV1J PERMINC> $5000 (1976 S ' a) 1966-69 1969-71 1971-76 1976-81 I PERMINC .3659 -.0984 -.3349 -.0762 (-2.279) (.824) (-1.972) (-.577) UINDX -19.21 -8.81 19.33 '37.26 VARINC -.00001 2.79-06 '5.53-06 3.29-06 (-4.434) (1.169) (~1.103) (.237) AGE -116.04 -68.20 '68.34 '64.29 (-3.573) (-2.043) (-1.596) (-.748) SPOUSEINC 401.31 554.36 1420.95 673.29 (1.617) (2.654) (4.223) (1.248) NC 13.06 132.65 412.85 667.67 (.317) (3.044) (1.623) (6.898) DRACE 2075.46 990.59 1035.91 1182.18 (8.441) (4.338) (3.258) (2.359) UNION '186.48 66.23 921.10 2364.92 (-.781) (.275) (2.516) (4.648) MD -241.90 559.89 2208.79 -606.68 (-.243) (.305) (1.874) (-.890) JURAT 40.90 104.52 -23.60 78.27 (.750) (1.747) («.353) (1.000) CONS 1527.50 2012.38 196.39 2475.70 (.709) (.740) (.065) (.440) OBS 875 671 604 456 F-STAT 29.58 22.07 34.52 18.57 R-Square . 3085 . 3037 . 4316 . 3527 I B-P 30.012 28.582 30.502 24.123 lt-‘atistics are given in parentheses beneath the coefficient values. zSignificarn at the .001 level, so weighted least squares results are reported. ’Significam at the .025 level, so weighted least squares results are reported. 156 TABLE 3A.17n REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAV2: PERMINC> $5000 (1976 S ' a) _ — I 1966-69 1969-71 1971-76 1976-81 I PERMINC .1522 .7127 .0683 -1.669 PERMINCSQR 2.788-07 -.00002 .00001 .00006 (.034) (-1.841) (1.061) (3.699) (4.281) (3.731) (-3.002) (1.493) VARINC .00002 3.603-06 .00002 .00001 (1.379) (.569) (1.710) (3.648) AGE 376.89 146.59 90.56 166.16 (6.027) (3.063) (1.547) (1.276) SPOUSEINC -921.12 -946.21 -373.75 2346.08 (-2.234) (-2.731) (-.821) (2.534) NC '107.53 -117.83 '352.01 56.16 (-1.036) (-1.218) (-3.432) (.200) TENCJ 23.98 13.58 -30.95 22.59 (1.232) (.924) (~1.671) (.507) DRACE '1266.52 -1129.69 -1704.40 -6613.49 UNION -989.76 -1208.08 124.83 3687.97 (-2.213) (-3.257) (.254) (4.626) MD -2663.43 -1065.48 335.51 357.59 (-1.728) (-1.629) (.389) (.064) JURAT 41.21 -139.40 -143.92 160.54 (.330) (-1.313) (-1.965) (.850) CONS -18252.19 -11109.33 1531.21 '1109.28 (-4.473) (-3.446) (.387) (-.106) OBS 1124 1078 960 506 P-STAT 25.90 33.16 19.04 31.93 R-aquare .2325 .2882 .2072 .4571 8-P 130.162 313.912 21.603 150.892 ‘I--- ‘t-Iatistics are given in parentheses beneath the coefficient values. 'Significam at the .001 level, so weighted least squares results are reported. ’Significam at the .05 level, so weighted least squares results are reported. 157 TA8LE 3A.17b REGRESSION RESULTS PROM SAMPLE WITH NEGATIVE DSAV2: PERMINC>$SOOO (1976 S's) F l — 1966-69 1969-71 1971-76 1976-81 (.307) (.416) (.284) (-.901) PERMINCSQR '1.3B-06 '9.70‘06 ".00002 “4.30-06 (-.161) (-1.217) (-1.132) (-.563) (-1.865) (-1.798) (-1.257) (-1.506) VARINC .00003 -5.20-06 2.18-06 .00001 AGE -166.02 -96.64 '271.05 24.37 (-3.243) (-2.866) (-2.865) (.343) SPOUSEINC '13.76 294.95 '253.62 94.66 (-.035) (1.022) (-.352) (.212) NC '117.32 125.42 560.76 920.19 (-1.029) (2.260) (1.914) (6.152) TENCJ 12.61 -20.94 -.1877 5.23 (.688) (-1.609) (—.007) (.296) DRACE 2156.03 1086.12 3112.55 569.28 (5.645) (4.260) (3.103) (1.228) UNION 68.06 60.71 4124.05 3328.53 (.162) (.194) (4.774) (5.226) ND 845.87 1287.46 6948.03 '457.17 (.976) (.727) (4.554) (-.692) JURAT 56.56 155.54 '194.54 113.82 (.612) (1.960) (—1.246) (1.701) CONS 4904.23 2577.47 4022.88 '4381.39 OBS 887 722 665 472 F-STAT 21.31 20.06 28.41 21.35 R-square .2407 .2689 .3616 .3768 _ 3 2 2 3 B P 23.42 120.07 197.90 25.35 It-statistics are given in parentheses beneath the coefficient values. aSignificam at the .001 level, so weighted least squares rewlts are reported. ’Significam at the .025 level, so weighted least squares results are reported. 158 TABLE 3A.188 REGRESSION RESULTS FROM SAMPLE WITH POSITIVE DSAV3,| PERMINC> $5000 (1976 $ ' B) 1966-69 1969-71 1971-76 1976-81 (-3.559) (1.276) (2.394) (-.384) PERMINCSQR .00008 -2.918-06 -.00001 .00006 UINDX 55.71 204.65 '139.31 101.35 (1.641) (5.837) (-1.489) (1.524) VARINC -5.07e-06 6.758-06 .00002 .00039 AGE 375.32 38.75 128.90 415.37 (2.857) (.320) (.357) (1.843) SPOUSEINC 337.39 -865.51 -6610.13 -2856.40 (.396) (-1.041) (~2.334) (-1.585) TENCJ 102.98 97.05 183.13 45.72 (2.033) (2.035) (1.567) (.534) DRACE -4358.48 '753.00 “7934.98 -8880.73 (-5.048) (-.841) (-2.200) (-4.510) UNION -4492.32 -1845.80 -13035.07 92.79 (-4.449) (-1.479) (-4.633) (.047) MD -66.56 2654.33 1757.72 6914.24 (-.031) (1.342) (.319) (.528) JURAT -849.53 '66.06 '688.80 '133.80 CONS 3914.08 '15026.9 10828.40 '22201.50 (.487) (-1.899) (.447) (-1.106) OBS 1524 1281 1218 704 F-STAT 52.84 41.53 9.23 32.39 R-aquare .3125 .2986 .0842 .3787 8-P 209.552 60.592 18.273 44.492 't-statistics are given in parentheses beneath the coefficient values. zSignificam at the .001 level, so weighted least squares results are reported. ’Not significam at the .05 level, so ordinary least squares results are reported. 159 TABLE 3A.18b REGRESSION RESULTS PROM SAMPLE WITH NEGATIVE 08Av33 PERMINC>$SOOO (1976 S's) 1966-69 1969-71 1971-76 1976-81 PERMINC .0449 -1.153 2.153 -.5259 (.083) (-1.811) (1.270) (-1.897) PERMINCSQR -2.4e-06 .00002 ' -.00008 2.56-06 UINDX 56.32 -105.42 -668.10 -25.47 VARINC .00005 .00002 .00003 .00008 (1.662) (1.399) (.647) (2.597) AGE -25.05 -427.63 -1030.06 -72.75 (-.189) (-2.804) (-3.007) (-.452) SPOUSEINC -3116.91 389.26 5215.49 38.92 (-2.876) (.392) (1.788) (.031) NC -470.23 385.88 -724.57 1494.93 (-1.977) (1.617) (-1.031) (1.527) TENCJ 24.92 174.69 19.20 -14.80 (.413) (3.631) (.147) (-.262) DRACE 5866.36 1184.45 9957.92 863.59 (5.684) (1.168) (3.889) (.844) UNION -2138.87 6182.44 5825.89 6168.06 MD 2382.63 1663.50 -1676.23 -2485.22 (1.917) (.485) (-.475) (-1.287) JURAT 601.01 445.59 -391.60 -224.05 CONS -14408.57 20681.15 76066.79 1554.90 (-1.812) (2.034) (3.064) (.140) OBS 895 843 671 436 F-STAT 22.68 28.48 16.06 27.45 R-square .2505 .3084 .2409 .4576 B-P 27.833 346.812 80.182 32.792 . J‘”J'“.d. lt-uatistitn are given in parentheses beneath the coefficient values. 1Significarn at the .001 level, so weighted least squares results are reported. ’Significam at the .01 level, so weighted least squares results are reported. APPENDIX 38 ..ril‘ 160 APPENDIX 3B TABLE 38.1 FIXED-EFFECTS PANEL REGRESSIONS"2 ENTIRE SAMPLE 8Av1 8Av2 SAv3 08Av1 DSAV2 08Av3 -.0159 .2342 -.603 -.0142 -.1613 -1.469 "“L‘31"° (-.402) (2.209) (-2.79) (-.164) (-.720) (-3.12) 1.370-06 1.028-07 8.049-06 3.269-06 .000014 .00004 L‘BI"CSQR (2.362) (.066) (2.551) (2.417) (3.977) (5.83) -17.262 -1501.35 1432.03 -258.67 -3155.66 1162.02 SP°USEINC (-.040) (-1.297) (.607) (-.280) (-1.326) (.232) UINnx 23.40 40.797 94.699 53.570 24.495 119.94 (1.240) (.809) (.921) (1.552) (.275) (.642) NC 254.346 220.61 85.579 481.61 45.840 1-597.42 TENCJ -22.330 -64.626 96.21 -27.632 64.093 .892 (-1.077) (-1.166) (.852) (-.723) (.651) (.004) M0 117.732 -1616.4 3575.39 1518.55 358.527 1180.60 (.123) (-.633) (.687) (.733) (.067) (.105) JURAT 217.564 103.25 314.561 437.27 -125.57 265.346 (2.654) (.471) (.704) (2.887) (-.322) (.324) REAL INT 4071.54 4773.36 5989.34 3985.60 3976.13 4102.60 (12.426) (5.447) (3.355) (7.315) (2.833) (1.391) 001 13972.4 17503.1 23858.58 (11.443) (5.360) (3.587) . 002 937.208 2931.84 -509.508 -8054.3 -8300.9 -14759 (2.160) (2.526) (-.216) (-7.301) (-2.921) (-2.47) 003 4929.5 5717.03 6274.31 1103.26 -613.30 1674.34 (7.992) (3.466) (1.867) (1.626) (-.351) (.456) cons -326.45 -815.52 4004.93 -6358.1 -6083.81 -8561.s (-1.184) (-1.106) (2.667) (-6.195) (-2.301) (-1.54) 088 5961 5961 5961 3436 3436 3436 P-STAT 17.06 4.52 3.34 8.67 5.44 6.24 R-Square .0333 .0090 .0067 .0271 .0172 .0197 1t-statistics are given in parentheses beneath the coefficient values. 3Age and the time dummies, D1, D2, and D3, are collinear, so age is dropped from the regressions. ’For the regressions on saving, DSAVl, DSAV2, and DSAVS, D1 is collinear with D2 and D3 and is dropped from the regression. 161 TABLE 38.2 FIXED-EFFECTS PANEL REGRESSIONS"2 RESPONDENTS WITH FAMILY INCOME GREATER THAN $5000 8Av1 8Av2 SAv3 08Av1 DSAV2 OSAV3 "“LABI"° (—.563) (1.188) (-.844) (-1.525) (-1.748) (-3.04) 1.576-06 -3.9e-07 5.470-06 5.199406 .00001 .00005 L‘BINCSQR (2.798) (-.228) (1.652) (3.897) (3.628) (5.766) -161.58 -1642.2 -2535.60 -65.112 -1218.9 -3957.3 SP°USEINC (-.386) (-1.278) (-1.026) (-.074) (-.455) (-.748) UINOx 24.91 38.52 70.237 57.31 107.88 160.393 (1.312) (.661) (.627) (1.684) (1.045) (.786) (1.758) (.571) (.831) (.792) (-.409) (-.201) TENCJ 17.74 -15.09 186.50 27.10 36.35 122.52 Mb -979.36 -2183.9 1704.57 -1511.6 -2848.79 2657.04 JURAT 138.45 148.12 479.36 353.08 409.33 965.31 (1.734) (.605) (1.019) (2.145) (.923) (1.101) RRAL INT 3872.8 4965.7 7475.99 3845.1 4441.2 7241.82 (11.96) (5.001) (3.917) (7.289) (2.774) (2.289) 001’ 13066.2 18105 28148.4 (10.86) (4.905) (3.967) 002 735.06 3104.1 781.80 -7378.3 -9384.3 -19440 (1.685) (2.32) (.304) (-6.825) (-2.860) (-3.00) DD3 4806.8 6202.09 8547.3 1709.06 -1111.0 -232.20 cons -266.37 -799.90 2806.4 -6331.0 -7420.5 -13001 (-.965) (-.945) (1.724) (-6.379) (-2.463) (-2.18) 088 4801 4801 4801 2724 2724 2724 R-aquaro .0414 .0067 .0068 .0391 .0133 .0254 It-stati‘ics are given in parentheses beneath the coefficient values. 2Age and the time dummies, D1, D2, and D3, are collinear, so age is dropped from the regressions. ’For the regressions on saving, DSAVI, DSAV2, and DSAV3, D1 is collinear with D2 and D3 and is dropped from the regression. 162 TABLE 38.3 PIXEO-EEEEGTS PANEL REGRESSIONS"2 RESPONDENTS WHO ARE NOT UNION MEMBERS F SAv1 SAv2 SAv3 OSAV1 DSAV2 OSAv3 ’““LABI"° (.343) (2.191) (-2.417) (.154) (-.236) (-2.45) 1.56e-06 7e-08 .00001 3.586-06 .00002 .00005 LABINCSQR (1.91) (.031) (2.265) (1.955) (3.205) (4.908) 47.74 -2161.01 2131.89 -118.84 -4937.42 2379.7 39°”S‘INC (.072) (-1.162) (.567) (-.083) (-1.284) (.297) "INDX 6.06 31.60 71.91 43.18 21.07 141.39 (.217) (.405) (.456) (.834) (.152) (.491) NC 346.32 253.37 ~14.49 798.23 -40.67 -830.46 (1.431) (.375) (-.011) (1.586) (-.030) (-.296) TENCJ -19.75 -75.75 91.47 -15.87 103.00 -84.569 (-.642) (-.881) (.527) (-.281) (.681) (-.269) ND 569.07 -1907.0 5483.02 2987.63 1538.13 809.39 (.397) (-.476) (.677) (.990) (.190) (.048) JURAT 280.67 140.04 486.27 571.42 -316.80 295.42 (2.338) (.417) (.717) (2.569) (-.532) (.238) REAL INT 4618.85 5418.24 7000.0 4464.35 4236.64 5113.43 (9.259) (3.886) (2.485) (5.336) (1.892) (1.097) 001’ 15862.1 20329.9 30185.4 (8.511) (3.903) (2.868) 002 916.43 3843.07 666.94 -9161.7 -9272.7 -19972 (1.403) (2.105) (.181) (-5.431) (-2.054) (-2.13) DD3 5479.88 6194.18 8575.79 1071.32 -1511.50 2720.05 (5.937) (2.401) (1.645) (1.066) (-.562) (.486) CONS -283.24 -1120.45 4018.11 -7206.50 —6638.87 —11772 (-.679) (-.961) (1.705) (-4.561) (-1.57) (-1.34) 088 3706 3706 3706 2138 2138 2138 P-STAT 10.58 3.21 2.35 5.61 4.14 4.85 R-unare .0332 .0103 .0076 .0282 .0210 .0245 ‘t-statistics are given in parentheses beneath the coefficient values. ’Age and the time dummies, D1, D2, and D3, are collinear, so age is dropped from the regressions. ’For the regressions on saving, DSAVl, DSAV2, and DSAV3, D1 is collinear with D2 and D3 and is dropped from the regression. 163 TABLE 38.4 FIXED-EFFECTS PANEL REGRESSIONS"2 RESPONDENTS WHO ARE UNION MEMBERS SAVI 8Av2 SAv3 08Av1 DSAV2 DSAV3 -.0820 -.0209 -.1500 .0173 .0672 -.1814 ’““L‘3I"° (-2.14) (-.452) (-1.191) (.842) (.652) (-.603) 5.770-07 -1.6e-07 1.850-06 -2.90-07 -1.50-06 4.60-06 ”“31"CSQR (1.002) (-.236) (.979) (-.187) (-.824) (.862) 1.693 -32.26 -165.29 -405.58 -14.35 -686.17 SP°USEINC (.005) (-.074) (-.139) (-.553) (-.016) (-.270) UINDX 53.07 69.23 97.78 77.72 60.01 61.86 (3.159) (3.408) (1.771) (2.671) (1.735) (.613) NC 90.04 150.48 157.56 91.04 129.22 -395.32 (.699) (.966) (.372) (.356) (.425) (-.466) TENCJ -21.94 -28.09 70.76 -51.11 -12.34 102.40 MD -662.44 -1247.93 1083.01 -1915.64 -24os.46 3378.84 (-.802) (-1.249) (.399) (-1.035) (-1.093) (.526) JURAT 93.07 55.56 -179.79 156.16 168.41 -336.27 REAL INT 3102.10 3710.35 4420.99 3218.00 3709.66 2854.24 (11.195) (11.072) (4.853) (7.342) (7.119) (1.879) 001’ 10727.3 13165.2 13448.3 (10.439) (10.593) (3.981) 002 1026.48 1602.42 -2631.31 -6244.89 -7325.48 1-7573.6 (2.733) (3.527) (-2.131) (-6.957) (—6.864) (-2.43) 003 4088.74 5238.44 2188.77 1324.13 1250.42 -353.20 (7.586) (8.037) (1.235) (2.277) (1.808) (-.175) CONS -363.05 -376.46 4458.43 -4843.30 -5530.00 1-2497.9 (-1.532) (-1.313) (5.721) (-5.879) (-5.646) (-.875) 088 2255 2255 2255 1298 1298 1298 r-STAT 13.84 12.41 5.10 6.66 5.79 1.20 Lit-square .0690 .0623 .0266 . 0539 .0472 . 0101 It-statistics are given in parentheses beneath the coefficient values. 2Age and the time dummies, D1, D2, and D3, are collinear, so age is dropped from the regressions. ’For the regressions on saving, DSAVl, DSAV2, and DSAV3, D1 is collinear with D2 and D3 and is dropped from the regression. APPEND IX 3C Ly 164 APPENDIX 3C TABLE 3C.1 INDEX OF UNEMPLOYMENT INSURANCE GENEROSITY ......- ...—....r Stat. UIN0x66 UINDX69 UINDX71 UIN0x76 UINnxa1 ALAS 56.5 56.7 66.3 71.0 69.5 ALAS 41.9 40.1 41.9 51.2 61.4 ARIz 57.8 54.2 54.9 66.9 65.4 E ,‘ ARE 59.7 65.1 67.3 64.4 79.8 I CAL 82.0 78.0 78.1 75.3 74.2 COLO 66.7 65.4 60.0 65.6 81.8 CONN 81.7 104.7 123.7 100.2 94.4 ‘ DEL 96.5 78.0 88.1 112.8 107.5 _”g. 0.0. 57.3 62.0 70.0 76.3 62.2 i ‘ PLA 40.8 41.4 42.5 74.4 66.0 GA 56.4 57.6 60.0 74.4 76.6 HAWAII 97.4 81.0 107.9 111.4 113.0 IDAHO 73.2 69.7 67.8 59.9 82.2 ILL 70.6 67.0 74.0 79.8 113.3 IND 61.2 59.0 64.0 64.1 74.0 IOWA 63.4 71.7 77.5 99.5 123.8 KAN 67.4 72.5 71.5 79.6 106.9 KY 53.5 58.1 62.7 71.4 93.6 LA 63.1 74.9 71.1 67.5 107.5 MAINE 51.3 60.6 66.7 71.7 89.5 MD 71.9 77.5 81.4 77.5 81.6 MASS 81.2 81.9 99.2 82.7 85.2 MICH 65.0 69.9 72.4 69.4 85.8 MINN 55.1 65.9 74.7 96.5 116.7 I MISS 47.8 48.3 51.2 53.5 68.3 MO 52.1 53.9 61.2 66.5 77.1 MONT 55.7 52.3 53.7 65.6 88.5 NEB 66.6 62.3 71.5 76.9 89.9 NEV 82.7 66.7 76.8 81.5 101.4 N.H. 58.5 61.4 80.4 74.1 90.4 165 TABLE 3C.1 INDEX OF UNEMPLOYMENT INSURANCE GENEROSITY (con't) .L *1. State UIN0x66 UIN0x69 UIN0x71 UIN0x76 UINDX81 N.J. 76.8 88.9 99.9 85.4 103.1 N.MEX 53.5 49.0 53.1 49.5 61.7 N.Y. 77.9 77.9 86.6 73.4 71.3 N.CAR 57.7 58.4 66.2 85.4 89.2 N.0AR 76.4 57.0 50.9 74.6 107.7 OHIO 60.1 65.2 67.6 87.7 101.1 OKLA 42.1 45.0 52.3 59.3 77.2 OREG 62.1 62.5 62.6 65.2 91.0 PA 63.9 70.7 75.8 92.5 111.3 8.1. 86.8 93.2 103.5 91.7 97.0 S.CAR 65.3 68.7 73.7 74.8 77.8 8.0AR 48.3 95.0 43.5 65.9 89.9 TENN 54.1 59.5 62.6 63.1 77.0 TEx 51.6 54.9 59.2 53.1 66.8 UTAH 62.9 58.9 61.2 67.5 92.5 VT 62.4 67.9 83.6 77.0 88.7 VA 53.7 53.1 62.2 80.8 95.3 WASH 53.7 53.3 89.8 56.5 87.3 W.VA 41.2 41.8 45.8 55.9 87.4 WIS 80.7 78.1 81.7 84.3 105.5 WYO 63.5 80.8 77.1 81.2 124.2 166 REFERENCES Baily, M., 1978, “Some.Aspects of Optimal Unemployment Insurance," Journal at Public Economics, 10:379-402. Barsky, R., Mankiw, N. and S. Zeldes, 1986, ”Ricardian Consumers with Keynesian Propensities," American Economic Review, 76:676-91. Beenstock, M. and V. 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