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http://clevelandfed.org/research/workpaper/index.cfm Best available copy Working Paper 8101 THE WELFARE IMPLICATIONS OF ALTERNATIVE UNEMPLOYMENT INSURANCE PLANS b y Mark S. Sniderman Working papers o f t h e Federal Reserve Bank o f Cleveland a r e p r e l i m i n a r y m a t e r i a l s , c i r c u l a t e d t o s t i m u l a t e d i s c u s s i o n and c r i t i c a l comment. The views expressed h e r e i n a r e t h o s e o f t h e a u t h o r and n o t n e c e s s a r i l y t h o s e o f t h e Federal Reserve Bank o f Cleveland o r of t h e Board o f Governors o f t h e Federal Reserve System. A p r i l 1981 R e p r i n t e d September 1982 Federal Reserve Bank of Cleveland http://clevelandfed.org/research/workpaper/index.cfm Best available copy THE WELFARE IMPLICATIONS O F ALTERNATIVE UNEMPLOYMENT INSURANCE PLANS by !?lark S. Sniderman* A recent survey of and extension t o research on the topic of unemployment insurance (UI) by Tope1 and Welch (1980) focuses on the issue of UI financin g .' In particular, following Becker (1972), they a r e interested in the influence of the experience-rating provisions of the American UI system on a f i r m ' s layoff policy. They suggest t h a t a more complete model of both firms and workers would be a f r u i t f u l endeavor, and two e f f o r t s of t h i s type have been made by Azariadis (1979) and Brown (1980).' This paper investigates a pe- numbral issue in the UI financing l i t e r a t u r e : the relationship between experience rating, public and private UI systems, and individual welfare. A public insurance system can never be perfectly experience-rated i f the government desires people w i t h different layoff probabilities to hold identical insurance policies. A corollary proposition i s t h a t a private insurance system, i f information i s perfect, would always feature fully- rated plans, b u t the characteristics of these plans may f r u s t r a t e other public policy transfer or maintenance). l y a l l previous research points out the moral he UI system, there has been l i t t l e attention uced by government introduces t h i s issue irm i s tantamount to the firm t o the vagaries of the business cycle. *Mark Sniderman i s an economic advisor, Federal Reserve Bank of Cleveland. The author wishes to thank Douglas Hough for helpful comments. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Firms may be willing t o bear t h i s exposure when UI i s part of an impliclt labor contract with i t s employees, and employees likewise may be willing to pay f o r the risk shifting through wage adjustments (Azariadis (1975), Baily (1977a), (1977b). However, for some firms, the degree of exposure necessary t o insure a l l workers legally may contribute to insolvency. Incomplete experience rating i s one method of achieving risk-pooling among firms posure of high-turnover firms. and limits the ex- Incomplete experience rating i s a form of market intervention by government for the benefit of high risk firms and employees. Incomplete experience rating i s contro- versial where UI i s concerned,in part because of the adverse incentives i t provides firms and employees. A great deal i s known about the distribution of the turnover risk ex ante than i s the case in many other insurance markets. For example, Munts and Asher (1980) show that construction, manufacturing, and agriculture a r e most likely t o be subsidized and t h a t trade, finance, insurance, and real estate are most often the subsidizing industries. Part I . Basic Model The basic model follows the one developed f o r competitive insurance markets by Rothschild and S t i g l i t z (1976). An individual has an income of W i f he i s f u l l y employed f o r some period, and an income of W-d i f he suffers a layoff.3 The individual can insure himself against t h i s layoff by paying a premium a,I t o an insurance company, in return for which a net benefit of a3 i s paid in the event http://clevelandfed.org/research/workpaper/index.cfm Best available copy of layoff. The vector a = ( a l , a 2 ) denotes the insurance contract. Preferences f o r income in the two s t a t e s of nature a r e given by the the expected u t i l i t y function: where U(.) describes preferences f o r money income, W1 = W ( n e t income), W2 = W probability. - - al, d + a 2 ( n e t income), and p i s t h e layoff All individuals a r e identical except f o r t h e i r layoff p r o b a b i l i t i e s , and a l l a r e r i s k averse (U" < 0). Contracts a r e sold by risk- neutral, expected-profit-maximizing insurance companies. Mhen contract a i s sold t o an individual with layoff probability p, the contract i s worth: t o the individual and, (3 n(a, P) = (1 - p)al - P a2 t o the insurance company. zero expected p r o f i t s . insurance ( i.e. , Free entry and perfect competition require In equilibrium, individuals have complete they expect the same income whether l a i d off or not) purchased a t a c t u a r i a l odds. 4 x (1 - Suppose a f r a c t i o n firms and a fraction of a l l individuals work f o r high turnover A ) work f o r low-turnover firms. If layoffs w i t h i n firms o f each type a r e random, then individuals can be c l a s s i - f i e d as high- and low-risk types purely on the basis of t h e i r employand low-, and average-risk probabilities ment a f f i l i a t i ~ n . High-, ~ http://clevelandfed.org/research/workpaper/index.cfm Best available copy a r e denoted by: pH, pL ( p H > p L ), and d = h p H +(1 - A ) p L . Rothschild and S t i g l i t z (1976) demonstrate that in t h i s type of market, with imperfect information, there cannot be an equilibrium in which both groups of individuals purchase the same insurance contract (pool ing equil i b r i urn) .6 They further establ i sh t h a t even when high-and low-risk types purchase separate contracts, an equilibrium may not e x i s t (separating equilibrium). A diagram, which will be used in various forms throughout the paper, c l a r i f i e s the 7 basic model (see Figure 1). The point E represents expected income i n each of the two s t a t e s of the world. The EH l i n e has slope H (1 - p ) l o H ; i t represents a l l actuarially f a i r contracts f o r high- risk individuals (or firms). The EL l i n e has slope ( 1 and an analogous interpretation. - The slope of EF i s ( 1 p L )/p L - pip). Sol id 1ine indifference curves depict high-risk individuals and dashed 1ine indifference curves depict low-risk individual s . In contrast w i t h Rothschild and S t i g l i t z , I am interested in examining an insurance market in which the accident (layoff) proba b i l i t i e s are known by customers, insurance companies, and the government. In the case of UI, t h i s point of view i s legitimate. F i r s t , the moral hazard f o r the employee to extend his unemployment spell i s not being considered here, so only the occurrence of a layoff i s important. Furthermore, the employment and layoff policies of f i r y s tend t o be related more t o industry type and size than t o http://clevelandfed.org/research/workpaper/index.cfm Best available copy http://clevelandfed.org/research/workpaper/index.cfm Best available copy other variables, and information of t h i s type i s easy t o obtain. 8 Fi nal l y, going concerns have a known track record regarding t u r n overs that result in UI benefits paid. Future layoffs cannot be perfectly predicted, of course, b u t relative layoff rates among firms a r e likely to be f a i r l y constant over time. Over short periods of time, the actual layoff rates f o r high- and low-risk firms may d i f f e r from p H and p L , b u t over more lengthy periods (such as several years) the distributions of layoff rates are assumed t o have means of p H and p L The variances of these firm layoff rates are important, . and they will be discussed more f u l l y in Part 11. The two contracts a and 6 ( i n Figure 1 ) are the separating equilibrium contracts sold respectively to high- and low-risk firms by private insurance companies. Although both high- and low-risk individuals are f u l l y insured, low-risk individuals pay less per dollar of benefit received, and they receive larger benefits i n the event of a layoff. There i s evidence that private insurance companies, i f they could have written unemployment insurance pol icies in the 1920s, woul d firm. offered group plans with premiums varying by industry and riables , pol i c i e s r e also re such as a and B could result. Private insurers would not be confined t o issuing only contracts a and B , b u t they would r e s t r i c t themselves to policies on or "below" the EH and EL lines. Free entry presumably would guarantee that a l l private policies actually appear on the EH and EL l i n e s , and that in f a c t policies a and B result. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Part 11. Government Intervention Suppose the government would require t h a t the benefit payments of insurance companies must be identical among a l l policyholders whose conditional income i s represented by E in Figure 2 , regardless of t h e i r layoff probability. policy + Some insurance companies might s e l l t o a l l individuals and earn zero-expected p r o f i t s . Hig r i s k individuals would be b e t t e r would become worse off. Companies p find t h a t another company, s e l l i n g u t o low-risk individuals ( a 2 = business. ividuals and T ~ ) , The 4 policy i s viable and low-risk types in the proport separating equilibrium S = ( a , This descripti issues associated w T) of A and ( I - A). The dominates the pooling e q u i l i b r uminates some e United States. Various i n t e r e s t groups were interested in different goals; some wanted high benefits, others wanted limited l i a b i l i t y , others wanted one national plan. Disagreement over the form of UI insurance t o be established by s t a t e governments in the 1920s could be construed as disagreement over whether S or 4 was the b e t t e r social policy. Policies of type S, i t was argued, encouraged employers t o reduce layoffs ( i n e f f e c t , pivoting the EH l i n e u p toward the EL l i n e ) . Other s t a t e s argued f o r pooling plans l i k e 4 on the grounds t h a t S 10 did n o t represent t r u e insurance. http://clevelandfed.org/research/workpaper/index.cfm Best available copy http://clevelandfed.org/research/workpaper/index.cfm Best available copy The debate over whether plans l i k e S represent t r u e insurance and risk pooling r e l a t e s to the d i v e r s i f i a b i l i t y of the unemployment risk. The Rothschi ld-Stigl i t z model applies t o diversifiable r i s k s , a broader class than the class of independent r i s k s . l1 Tope1 and Welch concede t h a t "...the primary force militating against the provision of firm-financed UI i s probably the high correlation in the timing of unemployed spells f o r workers. "I2 To the extent t h a t layoffs are correlated among covered workers, "insurance" plans merely serve the purpose of transferring the lending and borrowing a c t i v i t i e s of employees t o t h e i r employers.13 Tope1 and Welch provide evidence that in the United States the uninsurable portion of total risk i s so large as t o " strain the solvency of private UI programs. "I4 The covariance of firm-layoff r a t e s over time and with other firms thus i s crucial t o 1) the s i z e and composition of the pool of f i m s required of a diversifiable UI plan, and 2) whether such a UI plan i s true insurance (guarantees stipulated benefits) o r i s a reserve fund t h a t pays out until i t i s depleted. 15 The equilibrium plans S and 4 i n Figure 2 a r e both true insurance plans i f the d i v e r s i f i a b i l i t y of the layoff risks i s sufficient to guarantee solvency of the insurer. neither one may be viable. The policies a and different insurance companies. T In actual practice, may be marketed by Since information i s perfect, s e l f - B u t the market f o r one of these policies 16 may be too t h i n to guarantee solvency f o r the insuring company. selection i s not an issue. Similarly, @ may not prove t o be a solvent policy ex post; a firm http://clevelandfed.org/research/workpaper/index.cfm Best available copy can s e l l Q in the ex ante c o r r e c t (zero-expected p r o f i t ) r a t i o between the two risk c l a s s e s and s t i l l have a d e f i c i e n t number ,of policyholders (and/or d e f i c i e n t c a p i t a l ) t o guarantee solvency. The d i v e r s i f i a b i l i t y of the layoff r i s k s i s , of course, not related t o the government requirement t h a t a l l UI plans pay identical bevefits t o a l l policyholders. unregulated markets. This problem would e x i s t in completely However, i t i s unlikely t h a t s t a t e governments would permit undercapitalized underwriters t o operate within t h e i r borders .I7 Private insurers may perceive the 1imi t s of d i v e r s i f i c a t i o n , even where reinsurance i s possible, as preventing t h e i r participation i n any UI market, even i f benefit payments a r e very low. However, governments could guarantee "thick" markets, f o r example,by assigning a s u f f i c i e n t number of diverse policyholders t o each insurer so t h a t the probability of inso!vency would be considerably reduced. In the 1irni t , t h i s law-of-large-numbers approach might iniuly a monopoly insurance system, public o r private. A public monoooly UI system provides governments with the opportunity t o s e t Senef it 1eve1 s , tax r a t e s , and e l i gi bi 1i t y requi rements in accordance w i t h other public goals. the - compulsory UI system. Governments may choose t o o f f e r S or + as Theycould a l s o e l e c t t o earn negative- expected p r o f i t s by t r a n s f e r r i n g income from general tax r e c e i p t s t o UI r e c i p i e n t s . The current UI program in the United States operates as a t r a n s f e r system i n ways other than inter- industry t r a n s f e r s . Covered workers a r e subsidized by the general public when the UI system http://clevelandfed.org/research/workpaper/index.cfm Best available copy borrows from the U.S. Treasury. Whether or not high-income workers subsidize low-income workers i s not clear.18 Of course, any deliberate transfer system of t h i s s o r t i s inconsistent with true insurance principles ( i .e. , a perfectly experience-rated system). 19 I t i s possible t h a t high-and low-income individuals would be better off under such an income-transfer program than i f there were no UI a t all. Consider the situation of two large groups of people, d i s t i n guished from one another by income class (see Figure 3 ) . Assume i n i t i a l l y that each income class has the same proportion of high- and low-risk individuals. The example shown in Figure 3 i s one in which those i n the high-income group (E2 i n i t i a l point) have twice as much income in each s t a t e of the world as those in the low-income group ( E l i n i t i a l point). Assume further t h a t the government s e t s a UI benefit level equal to one-half of (W1 tracts m shows that policies ml and - W2) Then government- e BIBl or B2B2. m2, Inspection which meet the benefit criterion and are pooling e q u i l i b r i a , benefit only the high-ri sk individuals of each income clas improve the welfare of a l l low-income in- di vi dual s whi 1e ing the benefit c r i t e r i o n , say through policy T-, being sold to both high- and low-risk, low-income individuals, me individuals must subsidize the negative-expected-profit 20 forms. Either a l l high- r , on the B2Be l i n e , or they http://clevelandfed.org/research/workpaper/index.cfm Best available copy http://clevelandfed.org/research/workpaper/index.cfm Best available copy purchase a policy l i k e e , near the line. The Y policy respects the proportional - benefit c r i t e r i o n b u t severely punishes the highincome, low-risk individuals. lot The policy greatly improves t h e i r 8 b u t violates the proportional-benefit c r i t e r i o n . policy, located in the area formed by Y, s p i r i t of a compromise. m2, e , and An intermediate a2, i s in the The actual choice of a subsidy i s partly a function of arithmetic (the number of high-income individuals in the society) and partly of p o l i t i c s (which risk class among the highincome group i s rendered more worse o f f ) . In the American UI system, benefit replacement i s typically proportional to a ceiling income, a t which point the benefit increases no further. If the group of high-income individuals contained a larger proportion of low-risk individuals than the group of low-income individuals, i t might be possible t o (1) s a t i s f y the proportional -benefi t rule f o r both income groups and ( 2 ) subsidize expected losses of the low-income group while not making anyone worse o f f . the p This situation would a r i s e when l i n e f o r high-income individuals in Figure 3 i s very close t o the L2 line. Then a policy l i k e w makes positive-expected p r o f i t s , i s on the B2B2 l i n e , and makes no high-income individuals worse off. A The expected u t i l i t y function ( V ) that underlies the argument i l l u s t r a t e d in Figure 3 generates homothetic expansion paths ( i .e., the slopes of ULl a t El and UL2 a t Ep are equal). The logarithmic uti 1i t y function, which displays constant relative r i s k aversion of unity, yields an expected u t i l i t y function w i t h a homothetic expansion path. When the expansion paths are not homothetic, i t may http://clevelandfed.org/research/workpaper/index.cfm Best available copy be possible to improve the welfare of both high- and low-risk highincome individuals, while a t the same time subsidizing the low-income individuals. The situation i s i l l u s t r a t e d in Figure 4. Low-income individuals receive a policy l i k e II on the BIBl l i n e , while highincome individuals receive a policy l i k e 0, which improves t h e i r position relative to E2 (regardless of risk type). Notice t h a t the slope of UL1 a t El no longer equals the slope of UL2 a t E2. Part 111. Conclusion A proper concern of s t a t e governments i s the solvency of UI plans operating within s t a t e jurisdictions. Perfectly experience- rated private UI plans are likely t o structure premiums and indemn i t i e s differently than public UI plans, partly because public plans are less concerned about solvency. Public plans in principle can be perfectly experience-rated, b u t such plans would entail different costs per dollar of insurance f o r high- and low-risk individuals. Though economically j u s t i f i a b l e , these differences may be d i f f i c u l t to defend pol i t i c a l ly. Yet, once governments attempt t o provide "adequate" benef i t s , o r "proportional " benefits , perfect experience rating must be replaced by some pooled-equilibria-contracting pattern. A monopoly UI system based on pooling (imperfect experience rating) forces some people t o purchase less than optimal insurance coverage, while others may purchase more than i s optimal. http://clevelandfed.org/research/workpaper/index.cfm Best available copy http://clevelandfed.org/research/workpaper/index.cfm Best available copy FOOTNOTES: 1. The authors a r e unconcerned with the relationship between UI benefit payments and job search a c t i v i t y . I ignore t h i s issue as we1 1 . 2. Azariadis (1970) provides an example of how a f u l l y experiencerated plan can support an employment level larger than i s socially optimal ; f o r an unrated system, the benefit level can be chosen t o yield the socially desirable employment level (see pp. 18-22). Brown's model shows t h a t severance pay and labor mobility a r e important factors i n the f i r m ' s layoff policy and the nature of the optimal contract. In other words, layoff duration i s known with certainty. The employee moral hazard i s disregarded. As a r e s u l t of equations 1 , 2 , and 3 , the following conditions hold: n(o,p) = 0 + ap/ol = (1 - p)/p W2) = slope of actuarial odds l i n e PI = (1 - P)/P when W1 = WE. uals among firms causes no problems as long a s X i s fixed. 6. Equilibrium i s of the Cournot-Nash type: no equilibrium contract ected p r o f i t s , and there i s no non-equilibrium contract t h a t earns a non-negative p r o f i t , i f offered. 7. This diagram comes d i r e c t l y from Rothschild and S t i g l i t z (1976), hough subsequent modifications do n o t . i l i e n (1980) provides evidence that the range of average rehire g manufacturing industries i s quite variable ( p . 28). http://clevelandfed.org/research/workpaper/index.cfm Best available copy FOOTNOTES (cont ' ) 9. James (1947) recounts the attempts of t h e Metropolitan Life Insurance Co. t o obtain permission t o w r i t e UI p o l i c i e s from t h e New York S t a t e Assembly. In the Metropolitan plan benefits would depend on wages, employment tenure, and unemployment duration. See pp. 226-31. 10. Under t h e Wisconsin plan, each employer's l i a b i l i t y was limited t o the reserves s e t aside in a fund. minimum b e n e f i t . surance. There was no guaranteed This plan was decried a s not being t r u e in- Some s t a t e s , such a s Ohio, believed t h a t minimum b e n e f i t s could be guaranteed by pooling plans. For a more general description of t h e h i s t o r i c a l and l e g i s l a t i v e history of UI, see Nelson (1969) and Haber and Murray (1966). 11. Rothschild and S t i g l i t z (1976), p. 631, footnote 4. 12. Tope1 and Welch (1980), p. 355. 13. This i s l i k e l y t o be desirable from the employees' viewpoint, because t h e firm has comparative advantages i n these practices. Furthermore, firms can d i v e r s i f y more completely than employees. 14. 15. Tope1 and Welch (1980), 7 . 356. Suppfemental unemployment benefit funds i n the automobile and s t e e l i n d u s t r i e s a r e examples of such reserve funds. 16. The s t a t e of Michigan recently considered revoking the s e l f insurance s t a t u s of Chrysler Corporation i n t h e s t a t e workmen's compensation program, because of the f i r m ' s potential insolvency. See "Chrysler Must Buy Workers' Insurance, Says S t a t e of Michigan," Wall S t r e e t Journal, December 26, 1980, p.3. http://clevelandfed.org/research/workpaper/index.cfm Best available copy FOOTNOTES (con ' t ) 17. Again, the experience of Metropolitan Life i s instructive. The New York State Senate Insurance Committee was concerned that Metropolitan Life policyholders would be exposed t o too much risk i f the company were permitted to offer UI. See James (1947), pp. 226-31. 18. There i s not much evidence on t h i s point. The range of benefit maxima in s t a t e UI programs (50 to 79 percent of average wages) suggests t h a t an intra-program transfer e x i s t s . B u t taxes are collected on only the f i r s t $6,000 of each employees1 earnings, suggesting a higher tax incidence on low-income workers. Of course, the tax exemption of UI benefits means that high-income beneficiaries require fewer before-tax dollars than low-income beneficiaries t o be on equal footing a f t e r tax. Feldstein (1974) reports that the distribution of benefits i s similar to the distribution of income for the general population. On t h i s basis, he argues t h a t the poor do not benefit much from UI. My interest i s only in transfers among covered workers. 19. Practical matters, however, apart from an income -transfer motive, might lead to an insurance system with the ex post characteristic of income transfer. These practical considera- tions include employer and employee moral hazards and imply coinsurance f o r certain groups of people. 20. Assuming, of course, that the entire UI program i s &sisned to be ac tuarial l y sound. http://clevelandfed.org/research/workpaper/index.cfm Best available copy REFERENCES Azariadi s , Costas. (1975). " Impl i c i t Contracts and Underemployment E q u i l i b r i a ,"Journal of P o l i t i c a l Economy, vol . 8 3 , pp. 1182-1202. "Impl i c i t Contracts and Related Topics: Azariadis, Costas. (1979). A Survey." Processed. University of Pennsylvania, Department of Economics, CARESS Working Paper No. 79-17. Baily, Martin Neil. (1977a). "Unemployment Insurance a s Insurance f o r Workers," I n d u s t r i a l and Labor Relations Review, vol. 30, pp. 495-504. Baily, Martin Neil . (1977b). "On t h e Theory of Layoffs and Unemployment ," Econometrica, vol. 45, pp. 1043-63. Becker, Joseph M. (1972). Experience Rating i n Unemployment Insurance : An Experiment i n Competitive Socialism. Baltimore and London: Johns Hopkins University Press. Brown, James N . (1980). "How Close t o an Auction I s t h e Labor Market? Employee Risk Aversion, Income Uncertainty, and Optimal Labor Contracts." Processed. National Bureau of Economic Research Working Paper No. 603. Fel d s t e i n , Martin. (1974). "Unemployment Compensation : Incentives and D i s t r i b u t i o n a l Anomalies." Adverse National Tax J o u r n a l , vol. 27, pp. 231-244. Haber , W i 11iam, and Merri 1 Murray. (1966). t h e American Economy. James, Marquis. (1947). Growth. New York: Homewood, 111.: Unemployment Insurance in Richard D. Irwin Co. The Metropolitan Life: Viking Press. A Study in Business http://clevelandfed.org/research/workpaper/index.cfm Best available copy REFERENCES c o n ' t L i l i e n , David M. (1980). "The Cyclical Pattern of Temporary Layoffs i n United S t a t e s Manufacturing," Review of Economics and S t a t i s t i c s , vol. 62, pp. 24-31. Munts , Raymond, and Ephraim Asher. (1980). "Cross- Subsidies Among I n d u s t r i e s from 1969 t o 1978," Unemployment Compensation: Studies and Research, vol. 2, pp. 277-97. Nelson, Daniel . (1969). 1915-1935. - Madison: Unempl oyment Insurance : The American Experience, University of Wisconsin Press. Rothschild, Michael, and Joseph S t i g l i t z . (1976). "Equilibrium i n Competitive Insurance Markets: An Essay on t h e Economics of Imperfect Information," Quarterly Journal of Economics, vol. 90, pp. 629-49. Tope1 , Robert, and F i n i s Welch. (1980). "Unemployment Insurance: Survey and Extensions, " Economica , vol . 47, pp. 351-79.
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