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"Estimating Inequality Aversion"


Equity, Justice, Inequality, and Other Normative Criteria and Measurement, D630. Personal Income and Wealth Distribution, D310. Welfare Theory--General, 0240. National Wealth and Balance Sheets, 2240. Income Distribution, 2213.



The Atkinson Inequality Index is widely used, since it is based on parameters of the degree of preference for equality, sometimes referred to as ‘inequality aversion.’   This paper is the first attempt to empirically estimate that parameter (for the US economy).  Fifty years of income distribution and consumer confidence surveys allows estimates this Atkinson parameter of inequality aversion, using non-linear error-correction models. Consumer confidence appears to have become more sensitive to inequality since 1968. One can also show that about this time, inequality became less dependent on employment, and more correlated with the US stock market. Consumer confidence indexes are widely-used in spotting business cycle trends.  Thus, any added ability to understand changes in consumer confidence may be of practical importance.







Consumer Confidence and Income Inequality[1] (May, 2016)

James Stodder, Ph.D., Economics, West Hartford, CT 06119, USA




Introduction        The title to a piece in the Atlantic Monthly once asked, "If the GDP is Up, Why is America Down?" -- a question then exercising the minds of many political consultants. The authors (Cobb et. al., 1995) discount GDP for a number of social "bads", including inequality.  For this they used the maximin criterion, so that a nation's per-capita income is counted as just the income of its poorest members.  Since the poorest 20 percent of families earned an average of $19,093 in 1973, but $17,940 in 1994, both in 1994 dollars (US Census, 1996b), real income by this measure had fallen.

Many economists would object to the inflexibility of such maximin social accounting, but have been reluctant to offer anything specific by way of an alternative. Every society has a "revealed preference" for some Social Welfare Function (SWF), of course.  Those preferences are interesting, even after the Impossibility Theorem. As Sen (1999) notes in his Nobel lecture, impossibility demarcates the forms of social accounting that are possible and desirable, and to this end his own work provided an axiomatic basis.[2]  Even if consistent social preferences on distribution are theoretically possible, however, there is still an empirical question: does the public show any such consistency?  This paper finds that consistent estimates are possible, across several decades, for Atkinson's parameter of inequality aversion.

Atkinson (1970) counted it a virtue of his analysis that it forced "one's own" inequality values to be made explicit.  But preference relation also allows us to test the fit the public’s value parameters trace with their actual decisions.  As financial counselor uses prospective portfolio choices to gauge yield/security tradeoffs for an individual, economic history presents retrospective growth/equality tradeoffs to the public as a whole.   The public cannot replay history, but it can express preferences over its recent past through surveys of economic confidence.  Such surveys ask about recent changes in the economy, so on this level, preferences on distribution are stated only indirectly.  Inequality preferences can be inferred, however, if we can separate out growth from distributional effects.  Atkinson's index allows us to do this.

            This paper estimates the degree of inequality aversion directly, regressing consumer confidence against Atkinson's measure of inequality adjusted income.  Such inequality adjustment is now common in policy discussions.  Distributional weights are sometimes given by "reasonable" values for Atkinson's (1970) parameter of inequality aversion (Stiglitz, 1988: 272-74).  Similarly, Gini adjusted per-capita GDP is now used by the World Bank (1996a, 1996b) to measure developmental progress.   The degree of public support for such values is usually left as a political matter, however, outside the realm of economic analysis.  The following will show that it is possible to estimate these values empirically.

The paper is organized as follows.  Part I reviews the properties of the Atkinson index, and compares indexes of economic confidence to a formalization of inequality aversion based on risk aversion.  It is argued that such a fall in welfare should be reflected in a decline in surveyed values of economic confidence.  For an inequality (risk) averse Social Welfare Function (utility function), a rise in inequality  (risk) will decrease social welfare (expected utility), even without any fall in expected income.     Part II uses data on income distribution and surveys of consumer confidence to estimate Atkinson's parameter of inequality aversion.  Part III summarizes and discusses the findings.


I.   "Equally Distributed Equivalent" Income

From expected utility theory, Atkinson (1970) takes a SWF where the utility from income yi  to group i e(1, ..,I) is weighted by its portion of population, pi.  He defines a parameter of inequality aversion, e,  0  £  e  £ ¥+.  This determines yE [e], the equally distributed equivalent (EDE) value of average income to an inequality-averse society, just as the certainty equivalent evaluates a set of payoffs yi with probabilities pi to a risk-averse individual.  Assuming a constant-elasticity of marginal utility, these equivalent values are:

                        y E [e] = [ å i = 1 pi (yi)1-e ]1/ (1-e) ;      if e 1                      

                        y E [e] = exp[å i = 1 pln(yi) ] ;             if e = 1.[3]                                                          (1)


Note that if e = 0, then yE [e] is equal to the mean, y.  Atkinson wanted to compare inequality in 


countries with very different mean incomes (μ) so he focused on the relative inequality index


I[eº    1 -  y E [e] /μ .                                                                        (2)


Most uses of the inequality aversion parameter e have focused on I[e] rather than y E [e], but the latter is clearly a more comprehensive measure of economic welfare than inequality alone.  A consensus that welfare has gone up or down in some period can set upper or lower bounds on e if conditions are met for "order reversals" in welfare and inequality.  That is, if raising the level of e causes the ordering of two values of yE [e] in (1) to be reversed, this usually implies a parallel reversal of the two levels of measured inequality I[e] in (2) -- unless highly restrictive conditions are met on the progressivity of transfers between the two values of yi (Stodder, 1991).   With a time-series on economic confidence, however, e can be estimated more directly, as in the present paper. [4] 

            Consider a transfer between groups 1 and 2, with y1 £  y2.  Total differentiation of (1), with respect to y1 and y2, setting dyE = 0, yields the tradeoff between these two groups along a "social indifference curve" with slope                                                                         

dy1                   - (y1/y2)e        

                                     ──     =          ─────           .                                                                          (3)

                                    dy2                      p1/p2



This derivative has the useful interpretation of the minimum acceptable rate of  effective transfer from someone in the richer group 2 to one in the poorer group 1 when there are efficiency "leaks."  Rearranging (3), the minimum acceptable rate of effective total transfer for groups of possibly unequal size p1 and p2 is:                                                        

                                                p1dy1 / p2dy2   =   -( y1 / y2)e.                   (3')

This is a formalization of Okun's famous "leaky bucket" experiment (1975, pp. 91-95).  Okun considered transfers to the poorest p1 = 20 percent from the richest p2 = 5 percent, with y1/y2 = 1/9. If each member of group 2 gave up $400 (dy2 = -400) and the members of group 1 (4 times as numerous) got $100 each (dy1 = 100), there would be nothing leaking out of the bucket.  The left-hand side of (3') would then be -100 percent.  This minimally acceptable rate of effective transfer (MARET), 100 percent, implies that e = 0.  Short of such perfectly frictionless transfers, Okun said he would consider this transfer socially improving if no more than 60 percent of its value "leaked" away through inefficiency, for a MARET of 40 percent.    Okun's acceptance of -40 percent on the left hand side of (3') implies his inequality aversion reached a level of e = 0.417.      

This seems to be in line with what many consider modestly "progressive" preferences. The international comparisons of an OECD study use values between 0.5 and 1.0 (Atkinson et. al., 1995. pp. 22, 46).  Atkinson used values of e between 1.0 and 2.5 for his original paper (1970).  Stiglitz notes (1988, p. 274) that such values are considered reasonable in applied work.  The "reasonableness" of this range is supported by the empirical estimates to follow, which find a value of e around 2.0. 

It is worth noting, however, that these modest values appear quite "leak-tolerant" when illustrated by Okun's bucket.   If e is between 1.0 and 2.0, then where y1/y2 = 1/9, as in Okun's original thought experiment," then the MARET is between 11.1 and 1.2 percent.  Inequality of incomes is of course now much greater than when Okun was writing.  For any given parameter of inequality aversion e, preferences appear more “leak tolerant” as inequality itself increases.  In 1997 the ratio of the richest 5 percent compared to the poorest 20 percent of average family incomes was not 1/9, as in Okun’s time, but about 1/20 ($12,057 divided by $235,021 (US Census 1998b)).   Okun’s “reasonable” level of inequality aversion of e - derived as 1.0 to 2.0 – should therefore be willing to accept a MARET much lower than the 11 to 1 percent of his original bucket. Today’s inequality ratio would now give a MARET of 0.05 to 0.026 percent.

The classic analysis of risk aversion made it straightforward for Atkinson (1970) to argue that increases in inequality will usually lead to a reduction in social welfare, depending on the level of inequality aversion, e. At the same time, increases in any average income level(s) yi will also increase welfare. Atkinson's formulation allows us to estimate the level of inequality "discount" given by the parameter e, and also the degree to which changes in yi influence welfare.  If we can accept consumer confidence as a reasonable proxy for welfare, this opens-up an unexploited empirical opportunity: to estimate the terms of the social preference tradeoff between growth and inequality.


II.  Tests on Opinion and Distributional Data

Although the consumer confidence survey is a staple of modern business forecasting, few countries do regular distributional surveys.   A recent OECD survey (Atkinson et. al., 1995) shows only Italy, the UK, and the US as having unbroken annual series going back as far as the late 1960s.  The US Census Bureau may be unique in having annual distribution data going back to 1947.  These are grouped into 5 quintiles (groups of 20 percent each), from poorest to richest families, along with the richest 5 percent (Table F-3, 1998b). . Thus for equation (1) on y E [e], we can separate out n = 6 income groups, the first four quintiles, the top 5 percent, and the intervening 15 percent. 

 The Census Bureau also collects series by household income (Table H-3, 1998a), beginning in 1967.  The distributional data by households were not found to explain consumer confidence as well as the family distribution.  For this reason, and because the household series is twenty years shorter than the family series, the former are ignored in this paper.

The opinion surveys used here are the Consumer Confidence Index (CCI from the Conference Board of New York (1997), starting in 1967; and the Index of Consumer Sentiment (ICS) from the University of Michigan's Survey Research Center (1997), starting in 1952.[5]  These surveys are widely used by private companies trying to time the turning points in the business cycle.  From Figure 1 it can be seen that both indexes appear to be good at "hitting" the recessions as defined by the NBER (shown in gray) -- although how much predictive value they have is unclear from the annual data.  A careful study of the monthly data by Jason Braum of the Conference Board and Sydney Ludvigson of the Federal Reserve Bank of New York (1998) show that both series do have predictive value.

Sampling errors in these data bias estimated parameters, since they determine the chief independent variable in our model (4) below -- y [e], the EDE.  But because the size of errors in the distribution data is likely to be quite low compared to the variance in underlying population itself, bias is minimal.  Any bias, furthermore, understates the true coefficients to be estimated, so that results appear less significant than they really are.[6] 

I now estimate the parameters a, ß, g, d and e for the model 



(Confidence)t = a + ß( Growth in Distribution-Adjusted Income t)  + g(Change in Unemploymentt)                                         + d(Growth in Real Stock Market Value t)                                                          



where t = (1,...,T)                   is the time of the observation,


 Growth in Distribution-

  Adjusted Income t     is (yE [e]/yE-1[e]) - 1, the proportional change in yE [e], defined in (1),


 Change in Unemployment t   is the change in Unemployment, (Unemp- Unempt-1), 


 Growth in Real Stock Market Value t is the proportional change in the S&P 500 index of US )                   equities, inflation-adjusted to 1997 dollars,  (S&P t  / S&P t-1           ) - 1, and         


(Confidence)t              is one of several indexes of economic confidence.


Due to strong evidence of autocorrelation, equation (4) was estimated in a lagged form, with


estimation also required of the autocorrelation coefficient, r (rho):

         (Confidence)t  =  r(Confidence)t-1 + a(1-r)                                                                  (4')


     + ß(Growth in Distribution-Adjusted Income t - rGrowth in Distribution-Adjusted Income t-1)


            + g(Change in Unemployment t  -  rChange in Unemployment t-1)


     + d(Growth in Real Stock Market Value t - rGrowth in Real Stock Market Value t-1).                            


Along with (aggregate) personal income, unemployment is commonly assumed the chief factor influencing economic confidence.  Yet the estimates below show that, while important, it cannot account for the added explanation that equally distributed equivalent (EDE) income (yE[e]) provides for consumer confidence (as opposed to business confidence).  The parameter of inequality aversion, e, enters  yE [e] non-linearly in (1), so the estimation of (4') is by non-linear least squares.  This is equivalent to maximum likelihood estimation if the error term is normal. 

Other variables may effect economic confidence, but these are not available with sufficient regularity.  The value of accumulated housing wealth, for instance, is found by Acemoglu and Scott (1994) to influence British consumer confidence.  Britain's Central Statistical Office (1991) does regular surveys of wealth distribution, but the US Census bureau has surveyed median housing wealth only 4 times since 1984 (1996).  Other determinants of consumer confidence such as inflation (used by Acemoglu and Scott), or consumer debt-to-income ratios, were not significant when EDE real income, unemployment, and stock market wealth were included as regressors.

[Please Insert Table 1 about here.]

The first estimates in Table 1 are for the well-known Consumer Confidence Index, from the Conference Board of New York (1997).  Note the weak significance of the unemployment coefficient in the presence of distributional regressors, in regression [2].   The estimated e term, however, is virtually unchanged from regression [1], and only slightly less significant (still at the 1 percent level) after unemployment is included in [2]. When the unemployment and the stock-market regressors are added, either alone in [2] and [3] or in combination in [4], the R2 and log-likelihood terms are almost unchanged.  This is evidence of multicollinearity between unemployment, EDE income, and inequality aversion.

Next we compare the Gini Coefficient with the inequality index suggested by these parameter estimates centered around e = 2,  I[e = 2].  Recall from equations (1) and (2),

 y E [e] = y(1- I[e])  = [å i = 1 pi (yi)1-e ]1/ (1-e) ,

where y is mean family income. Thus y E [e=2] could be derived from a linear adjustment using I[e], and compared directly with the Gini Coefficient, G, in the adjusted yG = y(1- G).  This linear adjustment of real income with the Gini coefficient was characterized by Sen (1976, 1979) and now used by the World Bank (1996a, b).  

Given G and I[e], it is straightforward to estimate these linear adjustments of income as first-order autoregression (AR1) on a linear equation.  As can be seen from comparing regressions [4] and [5] in Table 1, y(1-Gini) is almost identical to  y(1 - I[e=2]) in the amount of variation in the CCI it explains.  This is remarkable, since the Gini is not derived from any empirical optimization. However, as will be seen in other comparisons of y G with an appropriately parameterized y E [e], the Gini is a robust estimator for consumer confidence.

Another such measure is the Index of Consumer Sentiment, collected by the University of Michigan's Survey Research Center (1997) since 1952, 15 years longer than the CCI.   As can be seen from Table 2, regressions [1] and [2], the estimate of e for the ICS is both far lower and less significant than it was for the previous CCI series, especially when other regressors are added. We see that e is not significantly different from zero in [2], once the unemployment and stock market terms are added. Similar results were obtained when adding either new variable by itself.

[ Please Insert Table 2 about here. ]

The non-linearity of the y E [e] (EDE income) equation (1) means that a low t-statistic on e in regression [1] dose not argue for the null hypothesis that e = 0.  The non-separability of e and ß (the coefficient on y E [e]) means that even though e appears not significantly different from zero, it may still work through ß to produce a log-likelihood significantly higher than it is when e = 0. If our basic equation (3) to be estimated were itself linear, we could test these linear restrictions with a standard F-test.  The non-linearity of (3), however, requires us to use a likelihood-ratio comparison between our restricted and unrestricted regressions. It can be seen that restricting e = 0 in regression [3] does not seriously reduce log-likelihood when compared with the unrestricted version [2] where e was estimated at 0.717.  The likelihood-ratio statistic comparing the restricted and unrestricted likelihoods of these equations has a Chi-squared (c2) distribution, with a significance of c2 (0.644, 1) = 0.4223, so the null hypothesis that the restriction (e = 0) is true can only be rejected at a 40 percent level of significance.  Thus the likelihood-ratio test points in the same direction as the t-test, and we assume that if e takes a single value, that value is zero.  This is equivalent to just using mean family income as the regressor.

This difference between the CCI and ICS estimates of e raises an interesting question, however.  Could the longer ICS series reflect a change in the underlying level of inequality aversion, as opposed to the changes since the early 1970s in inequality itself by most measures (Karoly, 1994)?  Could there have been a structural change in the relationship between inequality and the other regressors, unemployment and stock values?  This longer ICS series will allow us to investigate.

Regression [4] in Table 2 uses dummy variables to split the estimates of e into pre-1968 and 1968-or-after components, respectively.  In regressions where e was allowed to change its value, the unemployment term was insignificant. The inequality aversion term e in equation (4') is replaced with e68+/-, and broken into two time components,

e68+/-  º   (e68+) (D68+) + (e68-) (D68-),                                                    (5)

      where        D68+ = 1 if year ³ 1968, 0 otherwise;                                                                                           D68- =  1 if year < 1968, 0 otherwise.


As seen in Table 2's regressions [4] and [5], while the estimate of (e68-) is not significantly different from zero, that for (e68+) is significant at a value of slightly greater than 2.  Recall that this was about the value estimated for the post-1967 CCI series in Table 1   We can now test the hypothesis that there was a secular change in the value of e.   Regression [1] in Table 2 can be interpreted as a form of [4], but with the added linear restriction that e68+ = e68-.  The likelihood-ratio test on the restricted [1] and unrestricted versions [4] shows that this restriction causes a loss in likelihood that is significant at the 1.59 percent level -- while the estimated coefficients on e68+ is significant at a level of 0.2 percent.

Thus the null hypothesis, no secular change in the value of e, must be rejected.  Likelihood-ratio tests comparing the unrestricted (changing-e) [4] and [5] regressions with their restricted (unchanging-e) [1] and [2] versions, shows the restriction imposes significant losses in likelihood.

What could cause such a change in the underlying aversion to inequality?  One explanation would be a worsened growth-security tradeoff since the early 1970s.  The fact that the increase in inequality was matched by a lower rate of growth along with a decline in job security for much of the workforce (Uchitelle and Kleinfield, 1996), might cause people to reevaluate their basic expectations and induce higher level of inequality aversion.   This parameter shift would cause an increase in Atkinson's aversion-sensitive index of inequality (2), magnifying the rise in inequality shown by all the standard indexes over this same period (Karoly, 1994). 

            One need not accept such a "subjective" interpretation, however.  It is demonstrable that the basic relationship between income inequality on the one hand, and unemployment and the stock market on the other, has changed markedly since the late 1960s.  From Figure 2, we can see that before 1968, unemployment and the Gini coefficient of family distribution were moderately correlated, while afterwards they are basically independent.  The correlation from 1952 to 1967 was 30.9 percent, while from 1968 to 1997 it was only 6.64 percent.  But whereas unemployment became less correlated with inequality after 1968, stock market values became much more so.   Figure 3 shows this pattern.  In fact the S&P 500 was negatively correlated with the Gini coefficient from 1952 to 1968, at -30.3 percent, while from 1968 to 1997 its correlation was positive, at 65.4 percent. 

Obviously such correlation gives rise to problems of multicollinearity.  If the parameter of inequality aversion (e) did not explain consumer confidence in the absence of these other independent variables, this would be cause for serious concern.  The fact that it does have such explanatory power, with or without these other variables, lessens those concerns. 

Other years, such as 1974, have been put forward as a transition in inequality regimes (Greenwood and Yorukoglu, 1998).  Here, however, 1968 was the date that explained the most "switching" in parameters of inequality aversion.  More empirical work is needed before this conclusion can be sustained.

Comparing two linear adjustments in real income, by using the Gini coefficient, Y(1-Gini), and using I [e], Y(1- I [e]), it can be seen from the continuation of Table 2 that Gini-adjusted income explains a respectable amount of variation in regression [6], as compared to the "e-adjusted" real-income yE [e ] when e = 1.4517 in [1]. The coefficient b on the two distribution adjustments is income is very similar in equations [1] and [6], as is its significance, suggesting that the measures for I[e] and the Gini are indeed close. The log-likelihood ratio tests between regressions [1] and [6], and also between [7] and [2], reject the restriction that I[e] = Gini, at the 1 and 15 percent level respectively.[7] 

Recall, however, that we were unable to reject the hypothesis that e = 0, as seen in the statistically indistinguishable likelihoods of [2] and [3], by the log-likelihood ratio test.  Thus, while the Gini and the Atkinson measures of inequality are comparable, neither gives us much explanatory power if unchanging over time. When e was allowed to change its values over time, of course, in regressions [4] and [5], then the R2, adjusted R2, and the log-likelihood are all improved, compared to the Gini coefficient adjustments in regressions [6] and [7], respectively. What is surprising here is not that adjustments using two values of e outperform those using only the single standard of the Gini.  It is rather that the latter performs as well as it does.  (Note that no hypothesis comparing these regressions is tested here, but an F-test would be natural.)


III. Summary and Discussion

Almost 50 years of data on U.S. family income distributional and economic opinion are used to estimate Atkinson's parameter of inequality aversion, e.  From this estimate we can specify an index of inequality, and the equally distributed equivalent (EDE), or distribution-adjusted real family income.  The hypothesis that this distribution adjustment is not important for explaining consumer confidence; i.e., that e = 0, is rejected at the 5 percent level (see Table 1, columns 4 and 5).

In two independent surveys of consumer confidence, inequality aversion levels near e = 2 were estimated as statistically significant from the late 1960s up to 1997.  We test the hypothesis that there has been no increase in the public's underlying aversion to inequality since the early 1970s -- as opposed to the well-known rise in inequality itself by most conventional measures.  This null hypothesis of no change is rejected at 5 percent level of significance, using likelihood-ratio tests between restricted and unrestricted regressions (see Table 2, columns 4 and 5).  While levels of e close to 2.0 are estimated after the late 1960s, e does not appear to be statistically distinct from zero before then. 

There is clearly substantial correlation between unemployment, stock market values, and our measures of income distribution.  However, this correlation changes in strength, and even in sign, around 1968.  Unemployment is positively correlated with income inequality before this date, while the stock market is negatively correlated.  After 1968, the correlation between unemployment and inequality becomes much weaker, and that with the stock market becomes strongly positive. There is substantial multicollinearity within these periods, but it does not appear to greatly prejudice our basic conclusions.              A large increase in unemployment is sufficient to increase inequality, but it is not necessary.  The growth of US inequality over the 1993-98 boom makes this obvious.   Figure 2 shows that each of five pre-1974 unemployment "spikes" was associated with a similar spike in inequality.  Inequality also rose with the three post-1974 unemployment spikes, but rather than spiking itself, generally continued to climb.  In the most recent recession of 1990-92, however, there is some matching of unemployment and inequality spikes. 

[Insert Figures 3 and 4 about here.]


It is remarkable, and may also be practically useful, that the Gini coefficient (G) does so well at explaining both consumer and business confidence.  A distributional adjustment of real income (y) as  y(1-G),  is almost as good as an adjustment performed with the estimated index of inequality,  y(1-I[e]), when it comes to explaining confidence in a simple linear model.   From Figure 4, it is obvious that the Gini is highly correlated with this value of I[e] parameterized by measured inequality aversion (e).  The fact that the Gini is less sensitive to changes at the extremes of the distribution than many other measures of inequality (Atkinson, 1970), may lend it a certain conformity with the moderate center of popular opinion.   Whatever the causes, the practical importance of the Gini as a robust estimator of popular opinion demands further attention.

If aversion to inequality was indeed almost nonexistent from the early 1950s to the late 1960s, no large change in the US distribution of income would have been socially acceptable if it resulted in slower growth.  When growth slowed down in the early 1970s, however, and inequality nonetheless increased, any implicit "social contract" on distribution may have been nullified. Inequality aversion may well have increased.  Economists have measured these growth and inequality trends (Karoly, 1994), and debated their potential causes (Federal Reserve Bank of New York, 1995; Federal Reserve Bank of Boston, 1996).  The dynamic of social tension between the two, however, is left largely to political analysts like Kevin Phillips (1990).  Phillips compares current US economic culture to the "capitalist overdrives" of the 1890s and 1920s, both followed by powerful movements for income redistribution.

One has to consider the possibility that the aversion to inequality may be unstable.  Extensive experimental evidence shows that choices over lotteries routinely violate consistent von Neurman-Morgenstern (VNM) expected-utility (Machina, 1989; Stodder, 1997).  Anything that violates expected utility theory in individuals is not likely to aggregate into consistent VNM social preferences (Blackorby, Donaldson, and Weymark, 1997).   A changed social context might "frame" such reversals (Kahneman and Tversky, 1979).  Our estimates suggest, however, that inequality aversion has been stable over at least several decades.

Braum and Ludvigson (1998) find that both the Michigan and Conference board confidence surveys do have predictive power for US consumer spending.  A similar result is shown for the UK by  Acemoglu and Scott (1994).  The latter authors show that for the British case at least, the predictive power of consumer sentiment cannot be derived from other macro-economic aggregates.  (Their UK data do not include income distribution)  The possibility exists, therefore, that analysis of the type attempted here could be useful in macro-economic forecasting, especially if distributional surveys were done more regularly than just an annual basis. 

The fundamental purpose of the analysis in this paper, however, is to gauge public reaction to complex distributional outcomes.  Such questions are not easily asked in public opinion surveys. They may nevertheless be getting answered, if only indirectly.














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Table 2 (continued) : The Index of Consumer Sentiment (ICS) versus Distributed Real Family Income, as Adjusted by Inequality Aversion I[e] and the Gini Coefficient

                        Dependent Variable: Index of Consumer Sentiment (ICS), 1952 to 1994

Non-Linear Least Squares (Maximum Likelihood Iterative Technique)









     [1]  I thank William Bassett Jr. and Bhuvanesh Abrol for careful research assistance. Staff at the survey archives of the Conference Board of New York, the Survey Research Center at the University of Michigan, and the Social Science Library at Yale University were very helpful in obtaining data. Rensselaer's Beer Trust and the Lally School provided financial support.  Any errors are my own.

     [2]  Since a SWF must discard at least one of Arrow's axioms (1951), my own preference is to discard the axiom of universal domain.  Every human society marks some preferences as Aoff limits," and these get no (positive) weight in the social consensus.

     [3]  This precise parameter e = 1 is convenient for theoretical compactness.

     [4]  Such analysis could also use public opinion on inequality -- rather than confidence on the economy as a whole -- as its dependent variable.  Inequality attitudes, however, have not been surveyed regularly enough for time-series analysis. (See Kluegel and Smith, 1986.)  People's conscious opinions about inequality, furthermore, may not reflect their responses to real tradeoffs.

     [5] Surveys that ask about expectations of change in the economy,  such as the Expectations Index of the Conference Board, or the Expected Change in Business Conditions by the Michigan Survey Research Center, were not found to give significant estimates of e.  Slightly better are those asking about current business conditions, such as the Present Situation Index from the Conference Board or the Index of Current Business Conditions from Michigan. These were not found to give much explanatory power, however, when unemployment data were also used.

[6] Recent work by Braum and Ludvigson (1998) suggests that the Michigan confidence surveys, which have a much smaller sampling size, are less accurate as a predictor of business cycle trends.  Thus the problem of sampling errors is certainly more serious for this than for the Conference Board series. The estimates to follow actually give stronger evidence for inequality aversion when using the Conference Board series, so these errors are not a source of great concern in the present context.

[7] First-order serial correlation in regression [6] cannot be rejected at the 5 percent level, according to its Durbin-Watson statistic.  This is the only regression in this study showing serial correlation.  It is not of great concern in this case, however, because we are more concerned with the log-likelihood given by the Gini coefficient than by the estimated coefficients as such.