Electoral College reform and the distribution of voting power DOUGLAS H. BLAIR*

1. Introduction The issue of Electoral College reform arises anew whenever the prospect of a close popular vote threatens to elect a minority president or a close Electoral College vote threatens to send the election to the House of Representatives. The matter reappeared this year in Congress. 1 A critical ingredient in the evaluation of alternative reform plans i~ an understanding of the consequences of these proposals for the distribution of voting power among demographic groups in the electorate. Until recently, however, advocates and opponents of the Electoral College have argued their cases in a virtual empirical vacuum on this question. Nearly every geographic and demographic group can Fred support among political scientists, journalists, or politicians for each of two propositions: that replacement of the existing election method will both increase and decrease that group's ability to infiuence the outcome of the electoral process. 2 This essay first surveys briefly the existing empirical techniques for estimating power discrepancies across groups. Then an alternative approach to measuring voter power under the Electoral College is described and the resultant estimates are presented.

2. Earlier voting power studies The distribution of voting power under the Electoral College has been estimated using several power indices. The first attempt to measure the power of individual voters was undertaken by Banzhaf (1968). 3 Under the assumption that all coalitions of voters are equally likely, he calculated the probability that a voter in a given state could by changing his or her vote reverse the outcome of the election. That is, a voter's power is the likelihood that the voter is in a position to alter the way his or her state's electoral votes will be cast and that this shift will reverse the outcome in the * Department of Economics, University of Pennsylvania. Gerald Kramer suggested this problem to me and has contributed several helpful discussions. Charles Rosen expertly programmed and executed the simulation. I am grateful also for the assistance of Len Champney, Eileen Mauskopf, Nell Sheflin and Jim Wheeler. I am responsible for remaining errors. Public Choice 34 (1979) 201-215. All rights reserved.

Copyright © 1979 Martinus Niihoff Publishers by, The Hague/Boston/London.

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D.H. Blair

Electoral College. 4 Banzhaf himself was well aware of the principal shortcoming of his measure (and the similar Shapley-Shubik [1954] index), conceding that: A critical distinction must be drawn between inequalities in voting power which are built into the system (e.g. the old county unit system in Georgia or the distribution of votes in the Electoral College) and those which result either from the free choice of citizens as to the use of their voting power (e.g. the political impotence of a Republican in a sofidly Democratic state) or from factors outside the legal rules governing the p r o c e s s . . . The voting power measured here is that inherent in the system (1968, p. 307).

Thus, however suitable such measures as the Banzhaf index might be for such purposes as aiding courts in making reapportionment decisions,s they are silent on the real-world, short-run consequences of electoral reform for various interest groups. Yunker and Longley (1975, 1976) were the first investigators to employ power indices to test hypotheses about the distribution of power among demographic groups other than residents of states of varying size. The groups they considered were based on divisions of the electorate by region, race and ethnicity, occupational status, and type of residential area. The coalition-formation model used by Yunker and Longley was precisely Banzhaf's assumption that all coalitions are equiprobable. The questions they sought to answer were of the folowing form: given that all combinations of voters are equally likely, what is the probablity that, say, a randomly selected black voter is a critical member of a winning coalition? Such probabilities were estimated for fifteen groups by calculating weighted averages of Banzhaf values across states using as weights the state populations of each group. Yunker and Longley have at least posed the parochial question of the effects in practice of Electoral Colege abolition. But they have not taken into account any of the many complications of actual political experience like variations in voter turnout and interparty competitiveness across states. They have only explored the implications of the skewed distribution of members of a particular class across states whose residents possess varying amounts of 'formal power' conferred exclusively by the structural properties of the electoral system. Their equiprobability assumption would lead them to conclude that left-handed voters would be the most advantaged group under the Electoral College if they all lived in California and New York. They would do so even if right-handed Republicans in both states were cohesive majority blocs that always denied left-handed voters any opportunity to pivot in an actual election. The most elaborate study of the consequences of electoral reform for the voting power of population groups has been carried out by Spilerman and Dickens (1975). No explicit power indices were calculated in their re-

Electoral College reform and the distribution of voting power 203 search. Instead, using voting patterns of various social groups at the county level in the 1960 election as a base, they posited several proportional changes in the percentage partisan vote of one demographic group at a time. They then observed the sensitivity of the electoral vote total to these changes under five alternative electoral procedures. Importantly, they have taken some account in their analysis of the probabilities with which actual coalitions form in presidential elections. Thus they explicitly recognize that the likelihood of a voter's pivotality depends on the way the votes of others are distributed, a complication ignored in earlier research. Two broad criticisms of Spilerman and Dickens' study may be made. The first is that they have abandoned the power index approach completely in favor of a sensitivity analysis whose results are quite difficult to compare with earlier conclusions. It is only possible to construct power measures of the probability-of-effective~iefectionform from their data ffadditional information about the probability distribution of votes is available. In addition, serious questions may be raised about their decision to examine a single election and, given that decision, their choice of the 1960 election. They are forced to assume that 1960 turnout and party loyalty rates for each social group are stable, long-run values and not peculiar to the candidates and issues of the day. No estimates of the covariance of party voting rates of pairs of groups are calculated or used. While these objections would be valid for any single election, 1960 was an especially atypical year. 6 3. Some alternative power indices At least two alternative measures of the power of voting groups under direct election and the Electoral College may be calculated which suffer less than the existing estimates from the defects just discussed. 7 The first index is the probability that a member of a given demographic group is critical to the success of a winning coalition. In contrast with the Banzhaf and earlier estimates, the probability model of coalition formation for this measure has been derived from survey data on the five presidential elections between 1956 and 1972. Earlier elections were omitted because of data acquisition problems and the remoteness of.these elections from current political realities. The model recognizes that electoral coalitions do not consist of precise unions of demographic groups; each group in the electorate is assumed to be able to turn out varying numbers of its members to the polls and to ensure only partial loyalty to a particular candidate. The Democratic and Republican votes for each group studied as percentages of voting-age population were taken to be random variables with a multivariate normal distribution. Votes for candidates of other parties were ignored, that is, taken to be abstentions. These variables were assumed to be constant across states for each group in each election. From this assumed stable distribution of presidential-party preferences, a set of 10,000 simulated election returns was generated. Each of these sets of voting percentages was the aggregated

204

D.H. Blair

according to the Electoral College and direct election procedures, employhag data on the voting-age populations of each state. The resultant returns were then examined to calculate the frequency with which a group could reverse the outcome by reducing the number of votes it cast for the winner by 100,000, distributed across the states in proportion to the group's state populations, and casting these votes for the loser; This frequency is then proportional to the desired marginal-probability power measure for each group. We can express formally the nature of these calculations. Let nsi = 1970 voting-age population of group i in state s.

N• e$

--

~nsi, the national voting-age population of group L s electoral votes assigned to state s. proportion of group i's voting-age population voting for the Democratic candidate in the/th simulated election. proportion of group i's voting-age population voting for the Republican candidate in the/th simulated election.

o(x) =

1 ifx > 0 0 i f x < 0.

ds/ ¸ --

~'i ~D ns i _ ~i" ~il nsi ' the Democratic plurality in state s in election ]; dsi may, of course, be negative.

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~, e s o(dsi), the number of electoral votes received by the 8 Democrat in election/. ~. e s o ( - Clsl), the number of electoral votes received by the $ Republican in election ].

EO=

e s o(dst - lO0,O00nsi/Ni), the number of electoral votes which the Democrat would receive if 100,000 fewer members of group i voted Democratic than in election/, with that decrease distributed across states in proportion to the state populations of group i.

E'~i i = 8

e s O(ds/ + lO0,O00nsi/Ni) , the number of electoral votes which the Democrat would receive if 100,000 more members of group i (distributed as in the previous definition) voted Democratic than in election ].

Electoral College reform and the distribution o f voting power E'Rii =

205

F~ e s a ( - dsi - lO0,O00nsi/Ni),the Republicanelectoralvote " defined similarly. analogous to E'Dii" E "Rii is

The probability that a randomly chosen member of group i is in a position to reverse the outcome of the Electoral College balloting is then approximately proportional to the calculated:

vi =

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I

.

Etl

t

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O(ERi - EDi ) o(. Dii - ERii)] Any simulation which resulted in a tie at either the state or Electoral College level was discarded and repeated. Unlike its predecessors, the power index calculated here can be directly connected with candidates' campaign strategies by a straightforward economic argument. Suppose that each candidate has a fixed resource budget for persuading undecided voters; assume for simplicity that expenditures Ei dkected toward group i influence only that group. Then under suitable regularity conditions a candidate seeking to maximize the subjective probability of his or her election P will have allocated campaign resources so that: aP aP for all i, / ;

aE i

aE;

that is, the marginal effects on the probability of election of expenditures on different groups should be equal. Letting xi denote the plurality received by the candidate in question, we can express such derivatives as:

aP

aP

ax i

aE t ax i aE i Now axi/aEi is simply the vote-productivity of an expenditure on group i, while aP/Dxi = vi, the candidate's subjective probability of effective defection from a winning coalition by a member of group i. If the candidate forms his or her subjective probabilities on the basis of recent historical patterns of coalition formation, then vi is just the sort of power index we have calculated. The first order conditions given above may thus be rewritten: a ~ / a E i = v___i axi/aE i v/ At the optimal allocation, the ratio of expenditures' vote-productivities should equal the ratio of the power indices. Of the three methods of estimating power valuations in large voting procedures which have been used in earlier studies, only Monte Carlo

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D.H. Blair

estimation, first used in this context by Mann and Shapley (1960), was feasible for the problem at hand. Generating functions for the Shapley/ Shubik and Banzhaf indices have been given by Mann and Shapley (1962) and Brams and Affuso (1976) respectively, but none is available for the present problem. Recent work by Owen (1972, 1975) on multilinear extensions could only with great difficulty be applied to the estimation of these valuations. The task of numerical integration necessary in a problem of these dimensions would be extremely complex. The electorate in each state was divided into nine disjoint and jointly exhan~tive groups using two tripartite divisions. One division is along lines of race and nativity and parentage, into blacks, nonblack persons of foreign stock, and native whites. 'Persons of foreign stock' is a census category including persons who were born abroad and persons at least one of whose parents was born abroad. This group serves as an admittedly imperfect proxy for ethnic voters. Comprehensive data on the ethnic groups relevant to the electoral power hypotheses discussed here are unavailable in the requisite detail in the census reports. Catholic voters would be a more suitable substitute than persons of foreign stock, but unfortunately inquiries about religion are no longer included in census questionnaires. Each of these groups is further divided along residential lines, into central-city and noncentral-city residents of metropolitan areas, and nonmetropolitan residents. Those groups will be referred to hereafter as ~rban', "suburban', and 'nonmetropolitan', although it is recognized that in fact urbanized areas lie in all three sectors and that substantial parts of metropolitan areas (which are defined as collections of counties) are quite rural in character. For about half the states, state populations of voting-age persons in each of the nine groups were tabulated directly from the One-in-Ten-Thousand subsample on computer tape of the 15 Percent State Public Use Sample of the 1970 Census. Because of the confidentiality requirements of the Bureau of the Census, residential characteristics of persons in the remaining states are not fully reported due to the small size of some subgroups. For these states, total group populations taken from the published census reports were multiplied by the national proportions of persons of voting age in each residential class. The voting behavior of the nine demographic groups was estimated using data gathered by the Survey Research Center of the University of Michigan in national surveys taken shortly before and after each presidential election. The sample sizes in these surveys were far too small to expect them to be representative at the state level. As a result, it was not possible to estimate separately the voting behavior of the nine groups within states. One consequence of the inability to disaggregate further either the survey data or the census data, aside from the inherent oversimplification of voting behavior it entails, is that it precludes analysis of any reform proposals other than direct election.

Electoral College reform and the distribution of voting power 207 It was not possible to tabulate the voting behavior of the survey respondents in precisely the same nine categories used in the census data. No difficulties arise on the race-and-nativity dimension, but the residence categories do not in every survey make clear whether the respondent resided in a metropolitan area and, if so, in a central city. Consequently, the 'urban' votes counted in each survey were those reported by residents of the central cities of the twelve largest metropolitan areas and of places with a population of 50,000 or more outside these twelve areas. 'Suburban' voting behavior was estimated using the responses of the noncentral-city residents of the twelve largest SMSAs, rather than all such areas. The votes reported by all other respondents were used to estimate the electoral behavior of the 'nonmetropolitan' category. A difficulty which frequently arises in election surveys is the over-reporting by respondents both of the act of voting and of voting for the winner. An adjustment procedure described by Frederick Mosteller (1968) was used to take account of these two types of error. The procedure is an iterative method which transforms the raw contingency table compiled from the survey data into a table with marginal distributions consistent with aggregate election returns while preserving the strength of association among variables (cf. Axelrod, 1972). The adjusted survey data on voting behavior in the five elections are presented in Table 1. The simulated elections yielded frequency distributions of both the total electoral vote and the popular vote in each state. From these data the probability that a shift of 10,000 votes cast for the Electoral College winner in a given state to the loser would reverse the Electoral College outcome was calculated. This number yields an approximation of the likelihood that a voter in a given state is critical to the success of a winning coalition, and makes possible a test of Electoral College bias for or against large states. A byproduct of these calculations is a second measure of power for each of the nine demographic groups which was first proposed by Douglas Rae (1969); his index is the probability that a voter in a given group belongs to a winning coalition. Formally, in the notation set out earlier in this section, the Rae index for a member of group i under the Electoral College is given by: 10,000 n

Ri(EC) = j~=l [n~ij°(EDi- ERJ) + ~ij°(ERi-EDi)]/IO'O00

The Rae index for a member of group i under direct election is: 10,000 ,-~ Ri(DE) = ~ [n~io(Nds/)+~i/o(- Zsd/)]/lO,O00 ]= 1 " s No explicit estimates of this index have been published for the Electoral College procedure under any assumptions about coalition formation probabilities, a

208

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Electoral College reform and the distribution o f voting power

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4. Power estimates The results of the probability-of-criticalness power calculations for the nine groups are presented in Table 2 for the Electoral College. 9 The raw probabilities, weighted by national group populations, were used to calculate a national mean power value; the table's entries are proportions of this average. By definition, of course, this measure of power is equal to one for all voters under the direct election procedure. From these nine values eight more were calculated for selected groups consisting of unions of three or more of the original groups.

Table 2. Probability-of-criticalness power index. Group

Power as proportion of national average

Central city native white . . . . . . . . . . . . . . . . . . . Central city black . . . . . . . . . . . . . . . . . . . . . . . . . Central city foreign stock . . . . . . . . . . . . . . . . . . . Suburban native white . . . . . . . . . . . . . . . . . . . . . Suburban black . . . . . . . . . . . . . . . . . . . . . . . . . . Suburban foreign stock . . . . . . . . . . . . . . . . . . . . Nonmetropolitan native white . . . . . . . . . . . . . . . . . Nonmetropolitan black . . . . . . . . . . . . . . . . . . . . . Nonmetropolitan foreign stock . . . . . . . . . . . . . . . . Central city . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suburban . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonmetropolitan . . . . . . . . . . . . . . . . . . . . . . . . . Native white . . . . . . . . . . . . . . . . . . . . . . . . . . . Black . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Foreign stock . . . . . . . . . . . . . . . . . . . . . . . . . . . Metropolitan . . . . . . . . . . . . . . . . . . . . . . . . . . . Minorities (blacks and persons of foreign stock) . . . . . . . . . .

1.052 909 1.001

1.154 940 1.093 807 960 930 1.013 1.130 833 1.003 927 1.029 1.074 996

As the table reveals, these calculations suggest the existence of substantial disparities in voting power across groups under the Electoral College. The most advantaged group, suburban native whites, has 43 percent more power than nonmetropolitan native whites, the least advantaged group. The conjectures of Bickel (1971), Sayre and Parris (1970) and others of advantages accruing to metropolitan areas under the Electoral College seem to be borne out. Voters in such areas have nearly 29 percent more power than nonmetropolitan residents. But within metropolitan areas, the locus of

210

D.H. Blair

power is decidedly not where Bickel and Sayre and Pards believed it to be. It is the suburbs which are most likely to be pivotal. Voters of foreign stock have power indices larger than the national average only in the suburbs. Blacks are consistently across residential areas disadvantaged by the Electoral College; their least powerful subset is the central city component. This finding supports Peirce's claim (1968, p. 283) that blacks would be better off able to pool their electoral resources at the national level under direct election. Rae indices for the nine demographic groups are presented in Columns 1 and 2 of Table 3 for both the direct election and Electoral College procedures. Despite the substantially different nature of the two measures of power, the Rae index results are broadly similar to those of Table 2. The third column shows the percentage change in each group's Rae index which would occur if the Electoral College were replaced with direct election. The likelihood that the choice made by a randomly-selected black voter would be elected would rise by about 3 percent. For persons of foreign stock, this probability would increase by a fractiori of 1 percent. Only native whites would be disadvantaged by the institution of direct presidential election, although their power loss would be quite modest. No substantial differences in the Rae index appear across residential groups, as column 3 makes clear. Comparisons of Rae index values within column 1 or 2 are misleading indicators of intergroup power differences because much of the variation across groups is due to differences in participation rates. We can correct for these variations by dividing the columns by the mean participation rate for each group, which is derivable from Table 1. That is, we assume that the proportions of votes actually cast by members of each group reflect the preferences of the group as a whole. (Recall, however, that third-party votes are treated in this analysis as abstentions.) Columns 4 and 5 contain the results of this adjustment. To facilitate intergroup comparisons, each of these numbers has been divided by a population-weighted average power value; these values may be found in columns 6 and 7. Under either electoral procedure, blacks and noncentral-city persons of foreign stock have Rae indices below the national average. The disparity between the least and most-advantaged groups (central-city blacks and suburban native whites, respectively) is 58 percent under the Electoral College and 52 percent under direct popular election. Figure 1 consists of voting-age populations of states plotted against the frequency with which a swing of 10,000 votes in that state from the national Electoral College winner to the loser would reverse the election outcome. As this diagram suggests, there is no simple analytic relationship between these two variables. A chi-square test leads to acceptance of the null hypothesis of independence of the two variables at the standard significance levels.

Electoral College reform and the distribution of voting power

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Voting Age Population of State in Millions Figure 1. Relationship between power and state size.

5. Conclusion The empirical f'mdings of this essay suggest that suburban native whites, the most economically advantaged of the nine demographic groups, also wield the most political power in the selection of the president under either of two power measures. They further indicate that this power would be diminished by abolition of the Electoral College. Blacks, on the other hand, the least economically advantaged of the groups, are shown to have belowaverage voting power under the Electoral College procedure according to each index; they would gain power under direct election. It would seem to be no very strenuous normative leap for an egalitarian to conclude that electoral reform is in order. Three caveats should be borne in mind while taking this plunge, how-

Electoral College reform and the distribution o f voting power

213

ever. The first concerns the robustness o f the model. Most o f the simplifications underlying the coalition-formation model have already been pointed out. At least one, however, has not: the assumption implicit in the Raeindex calculations that candidate behavior, and hence group voting patterns, would not be appreciably affected b y changes in the m e t h o d o f election. Secondly, even if this model succeeds in capturing each group's current voting behavior, it is hazardous to forecast with it political realities over the likely constitutional life o f any reform amendment. Issues and alliances will doubtless change, as will the distribution o f demographic groups across states. Finally, Bickel has defended the Electoral College on the ground that its supposed bias in favor o f urban and minority groups counterbalances the 'interests that have a more rural, nativist, and Protestant orientation . . . [which] have tended to dominate Congress." (1971, p. 7.) Can we simply insert into Bickel's argument our evidence that minority groups are advantaged b y direct election and invert his conclusion on the same balance-ofpower grounds? We cannot do so with certainty, at least without undertaking a parallel investigation o f the biases o f Congress, a task which is doubtless vastly more complex than the undertaking reported here.

Notes 1.

See S.J. Res 1, 95th Congress, 1st Session. 2. For a sample of the conventional wisdom, see Longley and Braun (1972, Chapter 4). 3.

An earlier study by Mann and Shapley (1960) sought to quantify the bias introduced by the unit-rule and constant-two-votes provisions of electoral law and practice. They treated the Electoral College as a fifty-player weighted majority game and calculated Shapley-Shubik power indices (see Shapley and Shubik [ 1954] ) for the states themselves. The power indices of individuals were not computed. 4.

Yunker and Longley (1976) review and update Banzhaf's findings. 5. The Banzhaf index has been equated by a court with the legal clef'tuition of voting power; see lannucci v. Boardof Supervisors, 20 N.Y. 2d 244 (1967). 6.

Catholics in 1960 voted Democratic in vastly greater numbers than usual; their 82 percent support of Kennedy was 25 percent higher than its five-election average in the 1950s and 1960s. For another example, voter turnout in large central cities was 10 percent higher in 1960 than its five-election average. See Axelrod (1972, p. 14). 7. All of these measures, as well as the Banzhaf and Shapley-Shubik indices, share a common lattice-theoretic property which is examined in Blair (1976).

214

19.1t. Blair

8, Under the Banzhaf assumption of equiprobable coalitions, it is well known that the Rae index r bears a simple relation to the Banzhaf index b: r = (1 + b)/2. Thus Rae indices under Banzhaf probabilities can readily be computed from published Banzhaf indices. (See, e.g. Yunker and Longley [1976] .) However, this identity fails to hold under alternative coalition formation assumptions such as those used in this paper. To see this, consider the case of a citizen in a dictatorship who happens always to agree with the dictator. Since he is never pivotal (under any coalition formation assumption, including equiprobability) his Banzhaf index is zero. Nevertheless his Rae power is unity, since he always gets what he wants.

9. Of the 10,000 simulated elections, the number of elections which could be reversed by a 100,000-vote defection by a demographic group ranged from 79 for nonmetropolitan whites, the least-advantaged group, to 113 for suburban whites.

References Axeltod, R. Where the Votes Come From: An Analysis of Electoral Coalitions, 19521968.' American Political Science Review 66 (1972), pp. 11-20. Banzhaf, J.F., llI. 'One Man, 3.312 Votes: A Mathematical Analysis of the Electoral College.' ViUanova LawReview 13 (1968), pp. 303-46. Bickel, A.M. Reform and Continuity. New York: Harper and Row, 1971. Blair, D.H. 'On a Class of Power Measures for Voting Rules.' Discussion Paper No. 361, Department of Economics, University of Pennsylvania, 1976. Brams, S., and Affuso, P. 'Power and Size: A New Paradox.' Theory and Decision 7 (1976), pp. 29-56. Longley, L.D., and Braun, A.G. The Politics o f Electoral College Reform. New Haven: Yale University Press, 1972. Lucas, W.F. 'Measuring Power in Weighted Voting Systems.' Technical Report No. 227, Department of Operations Research, Cornell University, 1974. Mann, I., and Shapley, L.S. 'Values of Large Games IV: Evaluating the Electoral College by Monte Carlo Techniques.' RAND Research Memorandum RM-2651, 1960. and 'Values of Large Games VI: Evaluating the Electoral College Exactly.' RAND Research Memorandum RM-3158 PR, 1962. Mosteiler, R. 'Association and Estimation in Contingency Tables.' Journal o f the American StatisticalAssoeietion 63 (1968), pp. 1-28. Owen, G. 'Multilinear Extensions of Games.' Management Science 18 (1972), pp. 6479. Owen, G. 'Evaluation of a Presidential Election Game.' American Political Science Review 69 (1975), pp. 947-953. Peirce, N.R. The People's President. New York: Simon and Schuster, 1968. Rae, D.W. 'Decision-Rules and Individual Values in Constitutional Choice.' American Political Science Review 63 (1969), pp. 40-56. Sayre, W.S., and Parris, LH. Voting for President: The Electoral College and American Political System. Washington: Brookings, 1970. Shapley, L.S., and Shubik, M. 'A Method for Evaluating the Distribution of Power in a Committee System?American Political Science Review 48 (1954), pp. 787-792. Spilerman, S., and Dickens, D. 'Who Will Gain and Who Will Lose Influence Under Different Electoral Rules.' American Journal o f Sociology 80 (1975), pp. 443-471. U.S. Department of Commerce. Bureau of the Census. United States Census o f Popula-

Electoral College reform and the distribution of voting power 215 tion: 1970, Vol. 1, Characteristics o f the Population. pts. 1-52. U.S. Department o f Commerce. Statistical Abstract o f the United States 1974. Washington: GPO, 1975. Yunker, J.H., and Longley, L.D. q'he Biases o f the Electoral College: Who is Really Advantaged?' in D.R. Matthews, ed., Perspectives on Presidential Selection. Washington: Brookings, 1973. and ~ 'The Electoral College: Its Biases Newly Measured for the 1960s and 1970s.' Sage Professional Papers in American Politics, 3, 04-031. Beverly Hills and London: Sage Publications, 1976.

THE QUARTERLY REVIEW OF ECONOMICS AND BUSINESS Vol. 19

Autumn 1979

No. 3

ARTICLES

E m p l o y m e n t and Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . loan Robinson Focusing the Catastrophic Illness Debate . . . . . . . . . . Howard Birnbaum, Naomi Naierma~, Michael

Schwartz, and Douglas Wilson Empirical Cost Curves and the Production-Theoretic Short R u n : A Reconciliation . . . . . . . . . . . . . . . . . . . . . . Timothy P. Roth T h e Estimation of Tenure-Specific Depreciation,/ R e p l a c e m e n t Rates U s i n g Housing Quality Measures for the US, 1950-70 . . . . . . . . . . . . . . . . . Wilhelmina A. Leigh Industry Effects and the D e t e r m i n a n t s of Beta . . . . . . . . . . . . . . . . . . . . Frank ]. Fabozzi and Jack Clark Francis A Study of Industry Location from Pooled Time-Series and Cross-Section Data: T h e Case of C o t t o n Textile Mills . . . . . . . . . . . . . . . . . . . . Hui S. Chwag H i d d e n Preferences for Developing Countries: A Note on the U S I m p o r t Valuation Procedure . . . . . . . . . . . . . . . Andrzej Olechowski and Alexander ]. Yeats T h e I m p a c t of N O W Accounts on Savings and L o a n Behavior and Performance . . . . . . . . . . . . . . . . . . B. G. Hartzog, .Ir. BOOKS RECEIVED

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