# Interpersonal comparisons and labor supply: an empirical analysis.

I. Introduction

In a 1985 American Economic Review article, Robert Frank explored how patterns of spending behavior are affected when household's make interpersonal comparisons with respect to some goods but not others.(1) Following Fred Hirsch (1976) Frank uses the term "positional good" to refer to those goods whose value is significantly affected by interpersonal comparisons. When such comparisons are important, it can be shown that spending on nonpositional goods will be sacrificed so that spending on positional goods can be increased.

But what kinds of things fall into each category? By necessity, many things fall into the nonpositional category simply because they are not easily observed by other people. An example is savings. In other cases where the good is observable, the answer is less clear cut. A good example is leisure. Frank's hypothesis is that leisure is a nonpositional good -- its consumption often being sacrificed so that an individual can attain the income needed to increase the consumption of other positional goods. However, such a treatment of leisure runs counter to the more widely held view made famous in 1899 by Thorstein Veblen that individuals strongly care about how their level of leisure compares with that attained by others. A variety of empirical evidence supports the treatment of savings as a nonpositional good.(2) However, despite the vast empirical literature on labor supply, little serious empirical work has been directed towards testing the importance of interpersonal comparisons in the valuation of leisure time.(3)

The argument behind Frank's treatment of leisure is that important outcomes in a person's life are often determined by relative standing in the consumption hierarchy. Frank (1985a) argues that the family that rushes out to buy a home computer for its children because others in the neighborhood have done so need not be viewed as being irrationally obsessed with keeping up with the Joneses. Most families want their children to have access to good jobs and other opportunities in life, and few fail to recognize that such opportunities depend very strongly on their ability to keep pace with community consumption standards. This ability, in turn, depends not on how much the family saves for retirement, but on how much it spends today. It also depends in large part on how many hours of work the household supplies in the labor market.

While shifting income from savings to consumption may help in the quest for relative standing, getting ahead in the consumption hierarchy is ultimately a question of getting ahead in the income hierarchy, and getting ahead in the income hierarchy is in part a function of how many hours are worked.(4) In such circumstances the choice between additional income or more leisure can be likened to a prisoner's dilemma. If everyone makes a move towards more work, position in the income distribution remains unchanged, and so the pursuit of self-interest leads the players away from the most preferred outcome. Frank (1985a) argues that one of the reasons the overtime pay premium evolved was to provide a way out of this prisoner's dilemma. Such a pay premium creates a disincentive for firms to offer workers the chance to sacrifice leisure for extra income.

To support the hypothesis that leisure is a nonpositional good, Frank focuses on the prediction of the positional goods model which says that if consumption decisions could be made cooperatively (i.e., if households acted as if their rank was fixed in advance), demand for nonpositional goods will be higher than when households behave noncooperatively (i.e., when households act as if their own spending does not alter the spending of others). Frank cites the finding that over the period 1967-72, union workers devoted a larger share of total compensation to paid vacations than similarly situated non-union workers as support for the above prediction.(5) His reasoning is that while both union and non-union firms can facilitate collective decision-making among its members, unions are better positioned to implement meaningful agreements because of the closer personal association between coworkers brought on by the longer job tenure and larger workforce that characterizes employment at union firms. In addition, the union's administrative framework may make it easier to exchange information and thereby implement collective agreements. While Frank's interpretation of this difference between union and non-union compensation packages is plausible, a more direct test of the hypothesis that leisure is a nonpositional good seems in order.(6)

Such a test is also warranted because Veblen's original view that the relative level of leisure is important still has its proponents. Two papers by Laurence Seidman exploring the implications of relative standing concerns have included concern for relative leisure along with concern for relative consumption as a significant feature of the model (i.e., leisure is treated as a positional good).(7) In principle, the proper treatment of leisure in such relative standing models is simply an empirical question -- but one that is necessary to settle. Seidman's (1987) exploration of the tax consequences of relativity concerns underscores the importance of knowing the correct treatment of leisure. The optimal tax response to the externalities created by relative standing concern varies considerably depending on whether people are concerned with relative leisure and relative consumption, or just relative consumption. For example, in Seidman's very first example, the optimal income tax rate on the highest ranked person is one-third if relative leisure is disregarded, while it falls to zero if people care equally about relative income (or consumption) and leisure.

II. Labor Supply When Consumption and Leisure Rank Matter -- The Cobb-Douglas Case

To integrate concern for interpersonal comparisons into the traditional labor supply model, consider an individual that is faced with a maximization problem of the form(8)

Maximize U = |a.sub.1~ln(C) + |a.sub.2~ln(L) + |a.sub.3~ln|R(C)~ + |a.sub.4~ln|R(L)~ (1)

subject to

pC + wL = wT + V = Z, (2)

where |a.sub.1~, |a.sub.2~, |a.sub.3~, |a.sub.4~ |is greater than~ 0, and

C = composite consumption commodity,

L = leisure hours,

p = price of the composite consumption commodity,

w = price of leisure (wage rate),

T = total time available,

V = non-labor income,

Z = full income,

U = utility,

ln = natural logarithm,

R(C) = consumption rank,

R(L) = leisure rank.

R(C) and R(L) are the terms of interest in the utility function. They reflect how an individual's consumption level and leisure hours rank relative to other members of a comparison group, with zero being the lowest rank and one the highest. If C and L are continuous variables, and the probability density function associated with C or L can be represented by f(x), then R(X) represents the cumulative distribution function and is defined as

|Mathematical Expression Omitted~

where |X.sub.0~ represents the minimum level of consumption or leisure in the population.

If interpersonal comparisons in general are a significant determinant of utility, the value of the parameter associated with at least one of the rank terms in equation (1) must be comparable to the values of the parameters associated with C and L.(9) How the values of |a.sub.3~ and |a.sub.4~ compare, however, is the important question. Frank's hypothesis that leisure is a nonpositional good implies that the value of |a.sub.3~ would be large relative to |a.sub.4~, while Veblen's original view would be represented by a small value of |a.sub.3~ relative to |a.sub.4~. Intermediate cases like those explored by Seidman would be represented by relatively equal values of |a.sub.3~ and |a.sub.4~.

If each individual takes f(C) and f(L) as given, the marginal utilities (MU) of leisure and consumption are given by the equations

M|U.sub.L~ = |a.sub.2~/L + |a.sub.4~/R(L) f(L), (4)

M|U.sub.C~ = |a.sub.1~/C + |a.sub.3~/R(C) f(C). (5)

The marginal rate of substitution of leisure for consumption can then be written as

MR|S.sub.L for C~ = M|U.sub.L~/M|U.sub.C~ = C||a.sub.2~ + |a.sub.4~|E.sub.RL~~/L||a.sub.1~ + |a.sub.3~|E.sub.RC~~, (6)

where |E.sub.RX~ = Xf(X)/R(X) and equals the elasticity of rank with respect to X (X = C or L). Individuals will participate in the labor force provided the MRS when evaluated at the point where L equals T is less than the real wage rate (w/p). For unconstrained persons that participate in the labor force, the MRS of L for C exactly equals w/p. Solving this equality simultaneously with the budget constraint yields the leisure demand (labor supply) schedule.

To see the type of labor supply functions predicted by each extreme of the model, start by assuming |a.sub.4~ = 0. Such a parameter choice is most consistent with Frank's hypothesis that leisure is a nonpositional good. For simplicity assume that f(C) follows a uniform density over the interval (10,000; 10,000K) where K is any large number.(10) Even with these assumptions, the conditions for utility maximization do not yield explicit solutions for L and C. The marginal utility of leisure is now given by the expression |a.sub.2~/L and so the marginal rate of substitution of L for C becomes

MR|S.sub.L for C~ = M|U.sub.L~/M|U.sub.C~ = |a.sub.2~CR(C)/L||a.sub.1~R(C) + |a.sub.3~Cf(C)~. (7)

In equilibrium this expression should equal the real wage (w/p). Assuming the uniform density mentioned above, and assuming the values of the other utility function parameters, as well as the price level (p), are equal to one, L can be isolated on the left side of the equilibrium condition with C being the only variable on the right side. Solving the budget constraint so that C appears on the left side and L on the right side, this system of two equation and two unknowns can be solved iteratively by most popular spreadsheet programs. The resulting labor supply schedules for various values of non-labor income are shown in Figure 1.

Despite the restriction of the Cobb-Douglas form, note that the introduction of the consumption rank term is powerful enough to generate labor supply functions that are downward sloping. Those at the lowest end of the wage distribution respond to their lack of relative standing in the consumption distribution by working as many hours as possible. The possibility of such a result was anticipated earlier by James Morgan (1968) and (1979).

To illustrate the labor supply schedules associated with the other extreme of the model, assume |a.sub.3~ = 0. Such a parameter choice would be most consistent with Veblen's original hypothesis that high relative leisure is an important source of status.(11) For simplicity assume that f(L) is distributed uniformly on the interval (2920, 8760).(12) The marginal utility of consumption is now given by the expression |a.sub.1~/C and so the marginal rate of substitution of L for C becomes

MR|S.sub.L for C~ = M|U.sub.L~/M|U.sub.C~ = |a.sub.1~LR(L)/C||a.sub.2~R(L) + |a.sub.4~Lf(L)~. (8)

In equilibrium this expression should equal the real wage (w/p). Assuming the uniform density mentioned above, and assuming the values of the other utility function parameters, as well as the price level (p), are equal to one, C can be isolated on the left side of the equilibrium condition with L being the only variable on the right side. Solving the budget constraint so that L appears on the left side and C on the right side, this system of two equation and two unknowns can be solved iteratively by most popular spreadsheet programs. The resulting labor supply schedules for various values of non-labor income are shown in Figure 2.

When concern for leisure rank is included in the utility function, the labor supply schedules maintain the positive slope associated with the Cobb-Douglas form. The increase in the MRS that accompanies the inclusion of the leisure rank terms serves mainly to reduce the level of hours supplied relative to the amount associated with a standard Cobb-Douglas function that excludes interpersonal comparisons.

Additional predictions of the model can be seen if both |a.sub.3~ and |a.sub.4~ are allowed to be greater than zero and the marginal rate of substitution in equation (6) is set equal to the real wage (w/p). From this equilibrium expression it is easy to isolate an expression for total spending on consumption (pC). Taking this expression and substituting into the budget constraint given by equation (2), it is possible to rearrange the terms into the following expression

wL/wT + V = |a.sub.2~ + |a.sub.4~|E.sub.RL~/|a.sub.1~ + |a.sub.2~ + |a.sub.3~|E.sub.RC~ + |a.sub.4~|E.sub.RL~. (9)

This equation says that the share of full income devoted to leisure expenditures is inversely related to the elasticity of consumption rank and positively related to the elasticity of leisure rank. However, with the wage held constant and non-labor income negligible or constant, the equation also says that leisure hours are inversely related to the elasticity of consumption rank and positively related to the elasticity of leisure rank.

For equation (9) to yield any testable predictions, however, these elasticities must be linked to an exogenous variable. This can be done by first noting that in any group where the minimum values of C and L are greater than zero, and the values of the respective density functions evaluated at those minimum points are greater than zero, the rank elasticities will be decreasing as rank increases. However, if everyone has the same preferences, and assuming the level of consumption and full income are positively related, rank in the consumption distribution is ultimately determined by the level of full income (Z) available to each household.(13) Because the rank term raises the perceived payoff to consumption now, each household sees the potential for gain by increasing consumption, but because everyone does the same, the final ranking is ultimately determined by the full income available to each household. The same is true for rank in the leisure distribution provided the wage level is held constant. Without a constant level of wages, one can not be assured of a positive relationship between full income and leisure.

Given that the positive relationships between C and Z and L and Z do exist,(14) it follows that, for persons with similar levels of non-labor income, rank in each distribution is ultimately determined by rank in the wage distribution. Of course, with the wage rate held constant, to study the effect of differences in wage rank, the variation in rank must come from looking across different groups of the population.

Changing wage rank with the level of the wage constant will reduce both of the elasticities in equation (9). How the left side of the equation changes, which in turn indicates how L changes (since everything else on the left side of the equation is constant), depends on the relative magnitudes of the utility function parameters -- along with the initial values of the rank elasticities and the amounts by which the elasticities change. Allowing the elasticities to vary together, and employing the rule for the differential of a quotient, we can write the total differential for equation (9) as

dL = (|a.sub.1~|a.sub.4~ + |a.sub.3~|a.sub.4~|E.sub.RC~)d|E.sub.RL~/|(|a.sub.1~ + |a.sub.2~ + |a.sub.3~|E.sub.RC~ + |a.sub.4~|E.sub.RL~).sup.2~ - (|a.sub.2~|a.sub.3~ + |a.sub.3~|a.sub.4~|E.sub.RC~)d|E.sub.RC~/|(|a.sub.1~ + |a.sub.2~ + |a.sub.3~|E.sub.RC~ + |a.sub.4~|E.sub.RL~).sup.2~. (10)

Assuming for simplicity that |E.sub.RC~ and |E.sub.RL~ are initially the same, that the elasticities change by the same amount, and that |a.sub.1~ and |a.sub.2~ are constant and equal to one, then |a.sub.3~ |is greater than~ |a.sub.4~ implies dL |is greater than~ 0 as wage rank increases, while |a.sub.4~ |is greater than~ |a.sub.3~ implies dL |is less than~ 0 as wage rank increases (recall that the elasticities are inversely related to wage rank).

Taken together, equations (9) and (10) say that if interpersonal comparisons are important, wage rank should be an important determinant of across group variations in the supply of labor hours -- with the direction of the variation depending on whether individuals are more concerned about relative consumption or relative leisure. The following propositions will therefore guide the interpretation of the empirical evidence presented in the next section:

Proposition 1: If interpersonal consumption or leisure comparisons are an important determinant of individual utility, when comparing the labor supply of working individuals with similar levels of non-labor income, hours supplied should be more similar when classified by wage rank than by the level of wages.

Proposition 2: At any given wage level, if wage rank is positively related to hours supplied, this suggests that concern for relative leisure dominates the concern for relative consumption (|a.sub.4~ |is greater than~ |a.sub.3~ in equation (1)). On the other hand, if wage rank is negatively related to hours worked, this suggests that concern for relative consumption dominates the concern for relative leisure (|a.sub.3~ |is greater than~ |a.sub.4~ in equation (1)).

III. Empirical Evidence on Work Hours and Wage Rank

A. Analysis of Morgan's Data

One of the few labor supply studies that has the potential to shed any light on the effect of relative standing in the wage distribution is Morgan, et al. (1966). Morgan compares a sample of employed male family heads aged 25-64 (who were not self-employed businessmen or farmers) in 1959 with a similar sample collected in 1964. In general, earnings growth over the period means that remaining in the same wage group would push the typical person in that group downwards in the wage distribution. The framework suggested in this paper in turn predicts that such a change in position would lead to a change in hours supplied. In addition to the average hours worked each year by the individuals in each wage category, Morgan's study provides data on the percentage of individuals in each wage category. The wage rank variable was then constructed by cumulating the percentages in each category starting with the lowest wage category. The wage, wage rank, and hours data are presented in Table 1.

Referring back to Propositions 1 and 2, the data in Table 1 suggest that interpersonal comparisons are important, and that the primary concern of individuals over this time period was interpersonal consumption comparisons. Figures 2 and 3 are designed to help draw out these conclusions. Figure 2 shows the level of hours plotted against the wage level for each year, while Figure 3 shows the level of hours plotted against the wage rank for each year. Note that the data generally confirm the hypothesis that hours are more similar when classified by wage rank. The downward slope of the schedules together with the fact that at any given wage, the higher ranked group seems to work less, suggest that concern for relative consumption dominates the concern for relative leisure (|a.sub.3~ |is greater than~ |a.sub.4~ in equation (1)).

B. Analysis of Current Population Survey Data

An alternative way to hold the level of wages constant and still generate differences in wage rank is to compare behavior across different geographic groups. To complement the analysis of the Morgan data, a more extensive analysis was conducted using data from the March 1988 Current Population Survey (CPS). This survey contains information on key variables such as hours worked, wages, income levels, and most importantly, indicates detailed geographic locations. In this section comparisons of the type conducted earlier are made across states.

The sample used in the comparisons consisted of all individuals between the ages of 25 and 64 who worked for pay in the year preceding the survey and who were not constrained in their choice of hours due to illness.(15) Hours supplied were computed by multiplying weeks worked in the previous year by hours per week worked in the previous year. The wage rate was computed by dividing total wage earnings by hours worked. All wage rates were adjusted for regional price differences.(16) Individuals in each state were then placed into one of eight wage categories and the frequencies in each category, along with the average hours worked by the individuals in that category, were computed. The wage rank variable was computed by converting the frequencies in each wage category to percentages and then cumulating those percentages starting with the lowest wage category. Labor supply and wage rank data for three states, Alaska, Michigan, and North Carolina, are presented in Table 2. These states make for a good comparison because each contains a large number of observations and their wage distributions differ significantly.(17)

While Table 2 shows a strong relationship between wage rank and hours supplied, the data can perhaps best be interpreted by considering Figures 5 and 6. Figure 5 plots hours against wages for each state, while Figure 6 plots hours against wage rank for each state. Since there are many low wage workers in North Carolina, a worker earning, for example $8.00 per hour, would have a higher wage rank in North Carolina than in Michigan. The rank in Michigan would, in turn, be significantly higher than the rank in Alaska, a state with many high wage workers. Therefore, Figure 5 shows that at any given wage level, the workers with higher wage rank work more hours. All three schedules are also upward sloping. Both of these results are different from that found in the Morgan data. Most importantly, however, Figure 6 reveals that when hours are plotted against wage rank, hours supplied in each of the three states are very similar at any given wage rank. Recall that for the Morgan data, grouping by wage rank also led to more similarity in hours worked.

Taken together the comparisons supports the TABULAR DATA OMITTED general notion that wage rank, and hence interpersonal comparisons, are an important determinant of the supply of labor hours. However, the CPS data, unlike the 1959 and 1964 Morgan data (as well as the data on union compensation packages collected over the period 1967-72), suggest that interpersonal comparisons with respect to leisure matter more than the comparisons made with respect to consumption levels (i.e., |a.sub.4~ |is greater than~ |a.sub.3~ in equation (1)). It is interesting to note that the data supporting the opposite weighting of rank terms all come from a much earlier time period.

To see if the results suggested by Figures 5 and 6 hold across all fifty states, a simple regression analysis was carried out using the data from Table 2 along with similarly constructed data for the other 47 states and the District of Columbia. With eight wage categories per group, these fifty one groups created a total of 408 observations. The equation estimated was:

Hours = |B.sub.0~ + |B.sub.1~ Wage + |B.sub.2~ |Wage.sup.2~ + |B.sub.3~ Rank + |B.sub.4~ |Rank.sup.2~ + |B.sub.5~ D1 + . . . + |B.sub.12~ D8, (11)

where Hours = annual hours worked(18) (1938.3),

Wage = wage level (11.25),

Rank = wage rank (59.9),

D1 = New England dummy variable (0.12),

D2 = Mid-Atlantic dummy variable (0.06),

D3 = West North Central dummy variable (0.14),

D4 = South Atlantic dummy variable (0.18),

D5 = East South Central dummy variable (0.08),

D6 = West South Central dummy variable (0.08),

D7 = Mountain dummy variable (0.16),

D8 = Pacific dummy variable (0.10), (mean values of the variables in parentheses).

The squared terms were included to capture the non-linearities suggested by Figures 5 and 6. Dummy variables for each of the Census Bureau's nine census divisions were included to capture any across the board differences in hours due to unspecified regional characteristics. These regional characteristics could potentially be correlated with the level of wages or wage rank and so, if omitted, make it appear that the source of the supply differences is the wage level or the wage rank.(19) The variables D1 through D8 all represent departures from the behavior associated with the East North Central group of states, which includes Michigan. OLS estimates of the parameters and standard t-statistics for the null hypothesis that a particular parameter value equals zero are shown in Table 3. The purpose of the regression again was not to estimate a state of the art labor supply function, but simply to verify if the basic patterns seen in Figures 5 and 6 held across all the states in the sample.

The results correspond very closely to those found earlier in Figures 5 and 6. The rank term plays an important role in explaining hours supplied even when wages are held constant. The estimated coefficients on the squared terms are consistent with the graphs. The coefficient on the rank term is relatively large and well-measured as indicated by the t-ratio. The positive effect of the wage level stems from the inclusion of the absolute levels of consumption and leisure in the original utility function. Even the signs on the dummy variables are consistent with the information in Figure 6. Note that in this figure, at any given rank, Alaska (in the Pacific division) tends to be inexplicably below the Michigan plot, while at the same time, North Carolina (in the South Atlantic division) tends to run slightly above the Michigan schedule. This pattern is consistent with the negative sign on the D8 (Pacific) variable and the positive sign on the D4 (South Atlantic) variable -- the only regional dummy variables that are well-measured as indicated by the size of the t-ratios.

So far the analysis has ignored the effect of non-labor income (V) on hours supplied. Technically, however, the predictions concerning the relationship between hours supplied and wage rank require that non-labor income be held constant. For example, if individuals with high wage rank were to save at a higher rate,(20) they would accumulate wealth faster and earn more interest. More interest income, in turn, usually means more leisure is consumed, and so the individual supplies fewer hours in the labor market. While such a connection could help to explain in part the pattern that is observed in Morgan's data, there would have to be an inverse relationship between an individual's wage rank and the level of non-labor income in order to explain the pattern seen in the CPS data.

Table 4 represents a reworking of the hours and wage rank comparisons, this time breaking the samples into high and low non-labor income groups. Non-labor income was computed by summing all sources of income other than wages. The resulting totals were adjusted for regional price differences in the same manner as the wage rates. Only the Michigan and North Carolina samples are compared since the Alaska sample was smaller -- and so dividing it would leave only a few observations in some wage categories.(21)

The data in Table 4 indicate that leisure is a normal good, but more importantly, they also show that controlling for non-labor income does not eliminate the effect that wage rank has on hours supplied. This is clear if one looks at Figures 7 and 8.

In Figure 7 significant differences exist between all the curves. The variation between the schedules for a particular state, however, is presumably due to differences in non-labor TABULAR DATA OMITTED income. In Figure 8 when hours are plotted against rank, the schedules having the same non-labor income now appear close together, even though they represent different states. The separation between the two sets of schedules can now clearly be attributed to non-labor income. Controlling for differences in non-labor income does not eliminate the similarity between labor supply behavior that is observed when individuals are classified according to wage rank.

IV. Conclusions

Models of consumer behavior which allow for interpersonal comparisons have differed considerably in their treatment of leisure. Veblen's early writings pointed to the importance many societies place on relative leisure standing. Gradually, however, interest in the consequences of concern for relative leisure faded as more scholars focused on the effects of concern for relative consumption standing. Undoubtedly, both concerns weigh on some consumers, while neither concern may exert a significant influence on others. The question that remains is whether these concerns exert enough influence on enough consumers to show up statistically, and if so, which of the concerns receives relatively more weight in the minds of most consumers?

In this paper a simple consumer choice model was presented to illustrate the general empirical implications of each view when taken to its extreme. In each case, the model suggests a correspondence between an individual's wage rank and hours supplied. The direction of the relationship, however, depends on whether the consumer is more concerned with relative leisure or relative consumption. The data surveyed in this paper unambiguously support the notion of a correspondence between hours supplied and wage rank. However, there remains some ambiguity with respect to the direction of the relationship. While data from the late 1950's and mid 1960's seems to support the view that relative consumption is the primary concern, evidence from the 1988 Current Population Survey suggests that concern about relative leisure is still an important influence in the labor supply decision. Taken together, the evidence suggests that perhaps the ongoing race for positional consumption goods has resulted in a renewed interest in the social significance of leisure time.

Notes

1. See also Frank's (1985) book.

2. For empirical evidence relating directly to Frank's positional goods model, see Kosicki (1987b) and (1988) and Frank's book (1985b). Other important empirical support can be found in Duesenberry (1949), Easterlin (1973), and Menchik and David (1983). For a survey of the cross-section evidence relating to the influence of interpersonal comparisons on saving, see Kosicki (1987a).

3. Opinions on this subject in the popular arena also vary widely. In a Time magazine essay, Michael Kinsley (1990) writes that "We've come a long way in the century since Thorstein Veblen wrote about 'conspicuous' or even 'honorific leisure' as a way of displaying social status. 'Gosh, you must have nothing at all to do all day,' would not be considered a compliment." A similar argument was made as early as 1959 by Vance Packard in the book The Status Seekers. Packard argues that the tremendous growth in leisure time that has accompanied productivity increases has resulted in a situation where "leisure has lost most of its potency as a status symbol". However, an alternative view was presented by reporter Carrie Dolan (1992) in The Wall Street Journal. In the article she quotes Watts Wacker, executive vice president of Yankelovich Clancy Shulman, Inc. concerning a survey done by the firm. According to Mr. Watts, the survey suggested "The biggest status symbol today is being able to say you have nothing to do" and that what people wanted most was to be able "to hang out and not account for productivity".

4. Of course it is also a function of the wage rate, and so as Frank (1985a) points out, the quest for relative consumption standing may result in the deliberate choice of jobs with undesirable nonpecuniary characteristics.

5. This finding is reported by Freeman (1981).

6. Killingsworth's extensive (1983) survey of the labor supply literature acknowledges that the notion of individual labor supply decisions being affected by the behavior of persons outside the family "has not been analyzed extensively, and its potential implications remain largely unexplored".

7. See Seidman (1987) and (1988-89). Layard (1980) also briefly mentions the possibility of such a model but does not pursue its implications.

8. The Cobb-Douglas form results in a tractable model. The form is employed in the context of the choice between consumption and savings by Frank (1985b), and Kosicki (1987b) and (1988), but also in the relative standing model by Seidman (1988-89) in which utility is a function of consumption and leisure. Here the Cobb-Douglas form has been transformed by the natural logarithm function. Felder (1988) used the Cobb-Douglas form to explore the implications for the labor supply schedule of introducing a subsistence level of consumption. To the extent that the subsistence level is socially determined, Felder's work is complementary to that undertaken here.

9. With the Cobb-Douglas utility function, only the relative magnitudes of the utility parameters are important.

10. Actually, f(C) is an endogenous expression that results from the simultaneous choice of L and C, but such a treatment is beyond the scope of this paper. A similar assumption is made with respect to the function f(L) when generating labor supply functions associated with the other extreme of the model. For any variable X that is distributed uniformly on the interval |X.sub.0~ to K|X.sub.0~, f(X) = 1/(K|X.sub.0~ - |X.sub.0~) and R(X) = (X - |X.sub.0~)/(K|X.sub.0~ - |X.sub.0~). The ratio f(X)/R(X) is then given by the simple expression 1/(X - |X.sub.0~).

11. This case is characterized as an "extreme" form of Veblen's hypothesis since a careful reading of Veblen suggests he also appreciated the importance of relative consumption standing. Winston (1965), who makes a similar point, cites as supporting evidence Veblen's quote that "A life of leisure is the readiest and most conclusive evidence of pecuniary strength, and therefore of superior force; provided always that the gentleman of leisure can live in manifest ease and comfort".

12. The maximum time T was set at 24 hours times 365 days a year. Minimum leisure time was set at 8 hours a day times 365 days a year.

13. This positive relationship between C and Z can be verified by looking at the consumption data that is simultaneously generated in producing the simulations presented in Figures 1 and 2.

14. The latter relationship is clear from Figures 1 and 2 since leisure increases as V (and hence Z) increases.

15. Because the sample consists of only those who worked for pay in the preceding year, the comparisons may suffer from some degree of sample selection bias.

16. See the price indices for 1987 available in the Statistical Abstract of the United States: 1990, Table 763. Computing the wage rate by dividing total wage earnings by hours worked potentially creates a spurious negative correlation between hours and the wage rate if there are measurement errors in the hours data. Hence the analysis is slightly biased towards finding the type of relationship seen in the Morgan data. In general the results presented are very insensitive to any exclusions from the total sample or to the particular variable definitions that are employed.

17. A large number of observations helps to ensure that the wage rank computations reflect the wage distribution in that area.

18. Throughout this analysis it is assumed that individuals are not constrained in their choice of hours so that hours supplied and hours worked are the same.

19. Persistent unexplained regional differences in labor force participation rates are cited by Browne (1990).

20. For evidence on the relationship between income rank and savings rates, see Kosicki (1987b).

21. For the same reason, a regression analysis like the one presented in Table 3 was not performed on this data. Once the sample was also split on the basis of non-labor income, many states had only a few observations in each wage category, thus calling into question the reliability of the wage rank variable.

References

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Current Population Survey, March 1988 |machine-readable data file~ / conducted by the Bureau of the Census for the Bureau of Labor Statistics. Washington: Bureau of the Census |producer and distributor~, 1988.

Current Population Survey, March 1988 Tape Technical Documentation / prepared by the Data User Services Division, Data Access and Use Staff, Bureau of the Census. Washington: The Bureau, 1988.

Duesenberry, James. Income, Saving, and the Theory of Consumer Behavior. Cambridge: Harvard University Press, 1949.

Dolan, Carrie. "Lazy Days of Summer? No, Year Round" The Wall Street Journal 219 (February 7, 1992):A4.

Felder, Joseph. "The Supply of Wage Labor, A Subsistence Level of Consumption, and Household Production -- The Cobb-Douglas Case." The American Economist 22 (Spring 1988):10-18.

Frank, Robert H. Choosing the Right Pond: Human Behavior and the Quest for Status. New York: Oxford University Press, 1985a.

-----. "The Demand for Unobservable and Other Nonpositional Goods." American Economic Review 75 (March 1985b):101-116.

Freeman, Richard B. "The Effect of Unionism on Fringe Benefits." Industrial and Labor Relations Review, 34 (July 1981):489-501.

Hirsch, Fred. Social Limits to Growth. Cambridge: Harvard University Press, 1976.

Killingsworth, Mark, R. Labor Supply. Cambridge: Cambridge University Press, 1983.

Kinsley, Michael. "You Must Be Very Busy." Time 136 (August 20, 1990):82.

Kosicki, George. "A Note About Savings as a Nonpositional Good." Eastern Economic Journal 14 (July-September 1988):271-276.

-----. "The Relative Income Hypothesis: A Review of the Cross Section Evidence." Quarterly Journal of Business and Economics 26 (Autumn 1987a):65-80.

-----. "A Test of the Relative Income Hypothesis." Southern Economic Journal 54 (October 1987b):422-434.

Layard, Richard. "Human Satisfactions and Public Policy." Economic Journal 90 (December 1980):737-49.

Morgan, James, N. "Hours of Work by Family Heads: Constraints, Marginal Choices, and Income Goals." In Five Thousand American Families -- Patterns of Economic Progress (Volume VII), pp. 65-99. Edited by Greg J. Duncan and James N. Morgan. Ann Arbor: University of Michigan, 1979.

-----. The Supply of Effort, the Measurement of Well-Being, and the Dynamics of Improvement," American Economic Review 58 (March 1968):31-39.

-----, Sirageldin, Ismail, and Baerwaldt, Nancy. Productive Americans. Ann Arbor: University of Michigan, 1966.

Packard, Vance. The Status Seekers. New York: Pocket Books, 1959.

Seidman, Laurence, S. "Relativity and Efficient Taxation." Southern Economic Journal 54 (October 1987):463-74.

-----. "The Welfare Cost of a Relativistic Economy." Journal of Post Keynesian Economics 11 (Winter 1988-89):295-304.

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George Kosicki

Associate Professor, Department of Economics, College of the Holy Cross, Worcester, MA 01610.

In a 1985 American Economic Review article, Robert Frank explored how patterns of spending behavior are affected when household's make interpersonal comparisons with respect to some goods but not others.(1) Following Fred Hirsch (1976) Frank uses the term "positional good" to refer to those goods whose value is significantly affected by interpersonal comparisons. When such comparisons are important, it can be shown that spending on nonpositional goods will be sacrificed so that spending on positional goods can be increased.

But what kinds of things fall into each category? By necessity, many things fall into the nonpositional category simply because they are not easily observed by other people. An example is savings. In other cases where the good is observable, the answer is less clear cut. A good example is leisure. Frank's hypothesis is that leisure is a nonpositional good -- its consumption often being sacrificed so that an individual can attain the income needed to increase the consumption of other positional goods. However, such a treatment of leisure runs counter to the more widely held view made famous in 1899 by Thorstein Veblen that individuals strongly care about how their level of leisure compares with that attained by others. A variety of empirical evidence supports the treatment of savings as a nonpositional good.(2) However, despite the vast empirical literature on labor supply, little serious empirical work has been directed towards testing the importance of interpersonal comparisons in the valuation of leisure time.(3)

The argument behind Frank's treatment of leisure is that important outcomes in a person's life are often determined by relative standing in the consumption hierarchy. Frank (1985a) argues that the family that rushes out to buy a home computer for its children because others in the neighborhood have done so need not be viewed as being irrationally obsessed with keeping up with the Joneses. Most families want their children to have access to good jobs and other opportunities in life, and few fail to recognize that such opportunities depend very strongly on their ability to keep pace with community consumption standards. This ability, in turn, depends not on how much the family saves for retirement, but on how much it spends today. It also depends in large part on how many hours of work the household supplies in the labor market.

While shifting income from savings to consumption may help in the quest for relative standing, getting ahead in the consumption hierarchy is ultimately a question of getting ahead in the income hierarchy, and getting ahead in the income hierarchy is in part a function of how many hours are worked.(4) In such circumstances the choice between additional income or more leisure can be likened to a prisoner's dilemma. If everyone makes a move towards more work, position in the income distribution remains unchanged, and so the pursuit of self-interest leads the players away from the most preferred outcome. Frank (1985a) argues that one of the reasons the overtime pay premium evolved was to provide a way out of this prisoner's dilemma. Such a pay premium creates a disincentive for firms to offer workers the chance to sacrifice leisure for extra income.

To support the hypothesis that leisure is a nonpositional good, Frank focuses on the prediction of the positional goods model which says that if consumption decisions could be made cooperatively (i.e., if households acted as if their rank was fixed in advance), demand for nonpositional goods will be higher than when households behave noncooperatively (i.e., when households act as if their own spending does not alter the spending of others). Frank cites the finding that over the period 1967-72, union workers devoted a larger share of total compensation to paid vacations than similarly situated non-union workers as support for the above prediction.(5) His reasoning is that while both union and non-union firms can facilitate collective decision-making among its members, unions are better positioned to implement meaningful agreements because of the closer personal association between coworkers brought on by the longer job tenure and larger workforce that characterizes employment at union firms. In addition, the union's administrative framework may make it easier to exchange information and thereby implement collective agreements. While Frank's interpretation of this difference between union and non-union compensation packages is plausible, a more direct test of the hypothesis that leisure is a nonpositional good seems in order.(6)

Such a test is also warranted because Veblen's original view that the relative level of leisure is important still has its proponents. Two papers by Laurence Seidman exploring the implications of relative standing concerns have included concern for relative leisure along with concern for relative consumption as a significant feature of the model (i.e., leisure is treated as a positional good).(7) In principle, the proper treatment of leisure in such relative standing models is simply an empirical question -- but one that is necessary to settle. Seidman's (1987) exploration of the tax consequences of relativity concerns underscores the importance of knowing the correct treatment of leisure. The optimal tax response to the externalities created by relative standing concern varies considerably depending on whether people are concerned with relative leisure and relative consumption, or just relative consumption. For example, in Seidman's very first example, the optimal income tax rate on the highest ranked person is one-third if relative leisure is disregarded, while it falls to zero if people care equally about relative income (or consumption) and leisure.

II. Labor Supply When Consumption and Leisure Rank Matter -- The Cobb-Douglas Case

To integrate concern for interpersonal comparisons into the traditional labor supply model, consider an individual that is faced with a maximization problem of the form(8)

Maximize U = |a.sub.1~ln(C) + |a.sub.2~ln(L) + |a.sub.3~ln|R(C)~ + |a.sub.4~ln|R(L)~ (1)

subject to

pC + wL = wT + V = Z, (2)

where |a.sub.1~, |a.sub.2~, |a.sub.3~, |a.sub.4~ |is greater than~ 0, and

C = composite consumption commodity,

L = leisure hours,

p = price of the composite consumption commodity,

w = price of leisure (wage rate),

T = total time available,

V = non-labor income,

Z = full income,

U = utility,

ln = natural logarithm,

R(C) = consumption rank,

R(L) = leisure rank.

R(C) and R(L) are the terms of interest in the utility function. They reflect how an individual's consumption level and leisure hours rank relative to other members of a comparison group, with zero being the lowest rank and one the highest. If C and L are continuous variables, and the probability density function associated with C or L can be represented by f(x), then R(X) represents the cumulative distribution function and is defined as

|Mathematical Expression Omitted~

where |X.sub.0~ represents the minimum level of consumption or leisure in the population.

If interpersonal comparisons in general are a significant determinant of utility, the value of the parameter associated with at least one of the rank terms in equation (1) must be comparable to the values of the parameters associated with C and L.(9) How the values of |a.sub.3~ and |a.sub.4~ compare, however, is the important question. Frank's hypothesis that leisure is a nonpositional good implies that the value of |a.sub.3~ would be large relative to |a.sub.4~, while Veblen's original view would be represented by a small value of |a.sub.3~ relative to |a.sub.4~. Intermediate cases like those explored by Seidman would be represented by relatively equal values of |a.sub.3~ and |a.sub.4~.

If each individual takes f(C) and f(L) as given, the marginal utilities (MU) of leisure and consumption are given by the equations

M|U.sub.L~ = |a.sub.2~/L + |a.sub.4~/R(L) f(L), (4)

M|U.sub.C~ = |a.sub.1~/C + |a.sub.3~/R(C) f(C). (5)

The marginal rate of substitution of leisure for consumption can then be written as

MR|S.sub.L for C~ = M|U.sub.L~/M|U.sub.C~ = C||a.sub.2~ + |a.sub.4~|E.sub.RL~~/L||a.sub.1~ + |a.sub.3~|E.sub.RC~~, (6)

where |E.sub.RX~ = Xf(X)/R(X) and equals the elasticity of rank with respect to X (X = C or L). Individuals will participate in the labor force provided the MRS when evaluated at the point where L equals T is less than the real wage rate (w/p). For unconstrained persons that participate in the labor force, the MRS of L for C exactly equals w/p. Solving this equality simultaneously with the budget constraint yields the leisure demand (labor supply) schedule.

To see the type of labor supply functions predicted by each extreme of the model, start by assuming |a.sub.4~ = 0. Such a parameter choice is most consistent with Frank's hypothesis that leisure is a nonpositional good. For simplicity assume that f(C) follows a uniform density over the interval (10,000; 10,000K) where K is any large number.(10) Even with these assumptions, the conditions for utility maximization do not yield explicit solutions for L and C. The marginal utility of leisure is now given by the expression |a.sub.2~/L and so the marginal rate of substitution of L for C becomes

MR|S.sub.L for C~ = M|U.sub.L~/M|U.sub.C~ = |a.sub.2~CR(C)/L||a.sub.1~R(C) + |a.sub.3~Cf(C)~. (7)

In equilibrium this expression should equal the real wage (w/p). Assuming the uniform density mentioned above, and assuming the values of the other utility function parameters, as well as the price level (p), are equal to one, L can be isolated on the left side of the equilibrium condition with C being the only variable on the right side. Solving the budget constraint so that C appears on the left side and L on the right side, this system of two equation and two unknowns can be solved iteratively by most popular spreadsheet programs. The resulting labor supply schedules for various values of non-labor income are shown in Figure 1.

Despite the restriction of the Cobb-Douglas form, note that the introduction of the consumption rank term is powerful enough to generate labor supply functions that are downward sloping. Those at the lowest end of the wage distribution respond to their lack of relative standing in the consumption distribution by working as many hours as possible. The possibility of such a result was anticipated earlier by James Morgan (1968) and (1979).

To illustrate the labor supply schedules associated with the other extreme of the model, assume |a.sub.3~ = 0. Such a parameter choice would be most consistent with Veblen's original hypothesis that high relative leisure is an important source of status.(11) For simplicity assume that f(L) is distributed uniformly on the interval (2920, 8760).(12) The marginal utility of consumption is now given by the expression |a.sub.1~/C and so the marginal rate of substitution of L for C becomes

MR|S.sub.L for C~ = M|U.sub.L~/M|U.sub.C~ = |a.sub.1~LR(L)/C||a.sub.2~R(L) + |a.sub.4~Lf(L)~. (8)

In equilibrium this expression should equal the real wage (w/p). Assuming the uniform density mentioned above, and assuming the values of the other utility function parameters, as well as the price level (p), are equal to one, C can be isolated on the left side of the equilibrium condition with L being the only variable on the right side. Solving the budget constraint so that L appears on the left side and C on the right side, this system of two equation and two unknowns can be solved iteratively by most popular spreadsheet programs. The resulting labor supply schedules for various values of non-labor income are shown in Figure 2.

When concern for leisure rank is included in the utility function, the labor supply schedules maintain the positive slope associated with the Cobb-Douglas form. The increase in the MRS that accompanies the inclusion of the leisure rank terms serves mainly to reduce the level of hours supplied relative to the amount associated with a standard Cobb-Douglas function that excludes interpersonal comparisons.

Additional predictions of the model can be seen if both |a.sub.3~ and |a.sub.4~ are allowed to be greater than zero and the marginal rate of substitution in equation (6) is set equal to the real wage (w/p). From this equilibrium expression it is easy to isolate an expression for total spending on consumption (pC). Taking this expression and substituting into the budget constraint given by equation (2), it is possible to rearrange the terms into the following expression

wL/wT + V = |a.sub.2~ + |a.sub.4~|E.sub.RL~/|a.sub.1~ + |a.sub.2~ + |a.sub.3~|E.sub.RC~ + |a.sub.4~|E.sub.RL~. (9)

This equation says that the share of full income devoted to leisure expenditures is inversely related to the elasticity of consumption rank and positively related to the elasticity of leisure rank. However, with the wage held constant and non-labor income negligible or constant, the equation also says that leisure hours are inversely related to the elasticity of consumption rank and positively related to the elasticity of leisure rank.

For equation (9) to yield any testable predictions, however, these elasticities must be linked to an exogenous variable. This can be done by first noting that in any group where the minimum values of C and L are greater than zero, and the values of the respective density functions evaluated at those minimum points are greater than zero, the rank elasticities will be decreasing as rank increases. However, if everyone has the same preferences, and assuming the level of consumption and full income are positively related, rank in the consumption distribution is ultimately determined by the level of full income (Z) available to each household.(13) Because the rank term raises the perceived payoff to consumption now, each household sees the potential for gain by increasing consumption, but because everyone does the same, the final ranking is ultimately determined by the full income available to each household. The same is true for rank in the leisure distribution provided the wage level is held constant. Without a constant level of wages, one can not be assured of a positive relationship between full income and leisure.

Given that the positive relationships between C and Z and L and Z do exist,(14) it follows that, for persons with similar levels of non-labor income, rank in each distribution is ultimately determined by rank in the wage distribution. Of course, with the wage rate held constant, to study the effect of differences in wage rank, the variation in rank must come from looking across different groups of the population.

Changing wage rank with the level of the wage constant will reduce both of the elasticities in equation (9). How the left side of the equation changes, which in turn indicates how L changes (since everything else on the left side of the equation is constant), depends on the relative magnitudes of the utility function parameters -- along with the initial values of the rank elasticities and the amounts by which the elasticities change. Allowing the elasticities to vary together, and employing the rule for the differential of a quotient, we can write the total differential for equation (9) as

dL = (|a.sub.1~|a.sub.4~ + |a.sub.3~|a.sub.4~|E.sub.RC~)d|E.sub.RL~/|(|a.sub.1~ + |a.sub.2~ + |a.sub.3~|E.sub.RC~ + |a.sub.4~|E.sub.RL~).sup.2~ - (|a.sub.2~|a.sub.3~ + |a.sub.3~|a.sub.4~|E.sub.RC~)d|E.sub.RC~/|(|a.sub.1~ + |a.sub.2~ + |a.sub.3~|E.sub.RC~ + |a.sub.4~|E.sub.RL~).sup.2~. (10)

Assuming for simplicity that |E.sub.RC~ and |E.sub.RL~ are initially the same, that the elasticities change by the same amount, and that |a.sub.1~ and |a.sub.2~ are constant and equal to one, then |a.sub.3~ |is greater than~ |a.sub.4~ implies dL |is greater than~ 0 as wage rank increases, while |a.sub.4~ |is greater than~ |a.sub.3~ implies dL |is less than~ 0 as wage rank increases (recall that the elasticities are inversely related to wage rank).

Taken together, equations (9) and (10) say that if interpersonal comparisons are important, wage rank should be an important determinant of across group variations in the supply of labor hours -- with the direction of the variation depending on whether individuals are more concerned about relative consumption or relative leisure. The following propositions will therefore guide the interpretation of the empirical evidence presented in the next section:

Proposition 1: If interpersonal consumption or leisure comparisons are an important determinant of individual utility, when comparing the labor supply of working individuals with similar levels of non-labor income, hours supplied should be more similar when classified by wage rank than by the level of wages.

Proposition 2: At any given wage level, if wage rank is positively related to hours supplied, this suggests that concern for relative leisure dominates the concern for relative consumption (|a.sub.4~ |is greater than~ |a.sub.3~ in equation (1)). On the other hand, if wage rank is negatively related to hours worked, this suggests that concern for relative consumption dominates the concern for relative leisure (|a.sub.3~ |is greater than~ |a.sub.4~ in equation (1)).

III. Empirical Evidence on Work Hours and Wage Rank

A. Analysis of Morgan's Data

One of the few labor supply studies that has the potential to shed any light on the effect of relative standing in the wage distribution is Morgan, et al. (1966). Morgan compares a sample of employed male family heads aged 25-64 (who were not self-employed businessmen or farmers) in 1959 with a similar sample collected in 1964. In general, earnings growth over the period means that remaining in the same wage group would push the typical person in that group downwards in the wage distribution. The framework suggested in this paper in turn predicts that such a change in position would lead to a change in hours supplied. In addition to the average hours worked each year by the individuals in each wage category, Morgan's study provides data on the percentage of individuals in each wage category. The wage rank variable was then constructed by cumulating the percentages in each category starting with the lowest wage category. The wage, wage rank, and hours data are presented in Table 1.

Referring back to Propositions 1 and 2, the data in Table 1 suggest that interpersonal comparisons are important, and that the primary concern of individuals over this time period was interpersonal consumption comparisons. Figures 2 and 3 are designed to help draw out these conclusions. Figure 2 shows the level of hours plotted against the wage level for each year, while Figure 3 shows the level of hours plotted against the wage rank for each year. Note that the data generally confirm the hypothesis that hours are more similar when classified by wage rank. The downward slope of the schedules together with the fact that at any given wage, the higher ranked group seems to work less, suggest that concern for relative consumption dominates the concern for relative leisure (|a.sub.3~ |is greater than~ |a.sub.4~ in equation (1)).

TABLE 1 Comparison of Hours Across Wage Distributions Wage Rank Average Hours Wage Group 1959 1964 1959 1964 $ |is less than~ 1 6 6 2357 2489 $1-2 30 22 2263 2290 $2-3 67 51 2142 2296 $3-4 87 76 2083 2134 $4-5 94 88 2011 2082 $|is greater than~ 5 100 100 2180 2031 Source: James N. Morgan, et al., Productive Americans, p. 43.

B. Analysis of Current Population Survey Data

An alternative way to hold the level of wages constant and still generate differences in wage rank is to compare behavior across different geographic groups. To complement the analysis of the Morgan data, a more extensive analysis was conducted using data from the March 1988 Current Population Survey (CPS). This survey contains information on key variables such as hours worked, wages, income levels, and most importantly, indicates detailed geographic locations. In this section comparisons of the type conducted earlier are made across states.

The sample used in the comparisons consisted of all individuals between the ages of 25 and 64 who worked for pay in the year preceding the survey and who were not constrained in their choice of hours due to illness.(15) Hours supplied were computed by multiplying weeks worked in the previous year by hours per week worked in the previous year. The wage rate was computed by dividing total wage earnings by hours worked. All wage rates were adjusted for regional price differences.(16) Individuals in each state were then placed into one of eight wage categories and the frequencies in each category, along with the average hours worked by the individuals in that category, were computed. The wage rank variable was computed by converting the frequencies in each wage category to percentages and then cumulating those percentages starting with the lowest wage category. Labor supply and wage rank data for three states, Alaska, Michigan, and North Carolina, are presented in Table 2. These states make for a good comparison because each contains a large number of observations and their wage distributions differ significantly.(17)

While Table 2 shows a strong relationship between wage rank and hours supplied, the data can perhaps best be interpreted by considering Figures 5 and 6. Figure 5 plots hours against wages for each state, while Figure 6 plots hours against wage rank for each state. Since there are many low wage workers in North Carolina, a worker earning, for example $8.00 per hour, would have a higher wage rank in North Carolina than in Michigan. The rank in Michigan would, in turn, be significantly higher than the rank in Alaska, a state with many high wage workers. Therefore, Figure 5 shows that at any given wage level, the workers with higher wage rank work more hours. All three schedules are also upward sloping. Both of these results are different from that found in the Morgan data. Most importantly, however, Figure 6 reveals that when hours are plotted against wage rank, hours supplied in each of the three states are very similar at any given wage rank. Recall that for the Morgan data, grouping by wage rank also led to more similarity in hours worked.

Taken together the comparisons supports the TABULAR DATA OMITTED general notion that wage rank, and hence interpersonal comparisons, are an important determinant of the supply of labor hours. However, the CPS data, unlike the 1959 and 1964 Morgan data (as well as the data on union compensation packages collected over the period 1967-72), suggest that interpersonal comparisons with respect to leisure matter more than the comparisons made with respect to consumption levels (i.e., |a.sub.4~ |is greater than~ |a.sub.3~ in equation (1)). It is interesting to note that the data supporting the opposite weighting of rank terms all come from a much earlier time period.

To see if the results suggested by Figures 5 and 6 hold across all fifty states, a simple regression analysis was carried out using the data from Table 2 along with similarly constructed data for the other 47 states and the District of Columbia. With eight wage categories per group, these fifty one groups created a total of 408 observations. The equation estimated was:

Hours = |B.sub.0~ + |B.sub.1~ Wage + |B.sub.2~ |Wage.sup.2~ + |B.sub.3~ Rank + |B.sub.4~ |Rank.sup.2~ + |B.sub.5~ D1 + . . . + |B.sub.12~ D8, (11)

where Hours = annual hours worked(18) (1938.3),

Wage = wage level (11.25),

Rank = wage rank (59.9),

D1 = New England dummy variable (0.12),

D2 = Mid-Atlantic dummy variable (0.06),

D3 = West North Central dummy variable (0.14),

D4 = South Atlantic dummy variable (0.18),

D5 = East South Central dummy variable (0.08),

D6 = West South Central dummy variable (0.08),

D7 = Mountain dummy variable (0.16),

D8 = Pacific dummy variable (0.10), (mean values of the variables in parentheses).

The squared terms were included to capture the non-linearities suggested by Figures 5 and 6. Dummy variables for each of the Census Bureau's nine census divisions were included to capture any across the board differences in hours due to unspecified regional characteristics. These regional characteristics could potentially be correlated with the level of wages or wage rank and so, if omitted, make it appear that the source of the supply differences is the wage level or the wage rank.(19) The variables D1 through D8 all represent departures from the behavior associated with the East North Central group of states, which includes Michigan. OLS estimates of the parameters and standard t-statistics for the null hypothesis that a particular parameter value equals zero are shown in Table 3. The purpose of the regression again was not to estimate a state of the art labor supply function, but simply to verify if the basic patterns seen in Figures 5 and 6 held across all the states in the sample.

The results correspond very closely to those found earlier in Figures 5 and 6. The rank term plays an important role in explaining hours supplied even when wages are held constant. The estimated coefficients on the squared terms are consistent with the graphs. The coefficient on the rank term is relatively large and well-measured as indicated by the t-ratio. The positive effect of the wage level stems from the inclusion of the absolute levels of consumption and leisure in the original utility function. Even the signs on the dummy variables are consistent with the information in Figure 6. Note that in this figure, at any given rank, Alaska (in the Pacific division) tends to be inexplicably below the Michigan plot, while at the same time, North Carolina (in the South Atlantic division) tends to run slightly above the Michigan schedule. This pattern is consistent with the negative sign on the D8 (Pacific) variable and the positive sign on the D4 (South Atlantic) variable -- the only regional dummy variables that are well-measured as indicated by the size of the t-ratios.

Table 3 Regression Results Using CPS Data by State Variable Coefficient t Ratio Constant 1263.7 37.3 Wage 53.9 4.6 |Wage.sup.2~ -1.73 -4.2 Rank 9.91 6.1 |Rank.sup.2~ -0.062 -4.7 D1 19.6 1.1 D2 10.4 0.5 D3 5.4 0.3 D4 62.4 3.8 D5 13.4 0.6 D6 11.8 0.6 D7 -31.4 -1.8 D8 -37.7 -2.1 Observations = 408 |R.sup.2~ = .82

So far the analysis has ignored the effect of non-labor income (V) on hours supplied. Technically, however, the predictions concerning the relationship between hours supplied and wage rank require that non-labor income be held constant. For example, if individuals with high wage rank were to save at a higher rate,(20) they would accumulate wealth faster and earn more interest. More interest income, in turn, usually means more leisure is consumed, and so the individual supplies fewer hours in the labor market. While such a connection could help to explain in part the pattern that is observed in Morgan's data, there would have to be an inverse relationship between an individual's wage rank and the level of non-labor income in order to explain the pattern seen in the CPS data.

Table 4 represents a reworking of the hours and wage rank comparisons, this time breaking the samples into high and low non-labor income groups. Non-labor income was computed by summing all sources of income other than wages. The resulting totals were adjusted for regional price differences in the same manner as the wage rates. Only the Michigan and North Carolina samples are compared since the Alaska sample was smaller -- and so dividing it would leave only a few observations in some wage categories.(21)

The data in Table 4 indicate that leisure is a normal good, but more importantly, they also show that controlling for non-labor income does not eliminate the effect that wage rank has on hours supplied. This is clear if one looks at Figures 7 and 8.

In Figure 7 significant differences exist between all the curves. The variation between the schedules for a particular state, however, is presumably due to differences in non-labor TABULAR DATA OMITTED income. In Figure 8 when hours are plotted against rank, the schedules having the same non-labor income now appear close together, even though they represent different states. The separation between the two sets of schedules can now clearly be attributed to non-labor income. Controlling for differences in non-labor income does not eliminate the similarity between labor supply behavior that is observed when individuals are classified according to wage rank.

IV. Conclusions

Models of consumer behavior which allow for interpersonal comparisons have differed considerably in their treatment of leisure. Veblen's early writings pointed to the importance many societies place on relative leisure standing. Gradually, however, interest in the consequences of concern for relative leisure faded as more scholars focused on the effects of concern for relative consumption standing. Undoubtedly, both concerns weigh on some consumers, while neither concern may exert a significant influence on others. The question that remains is whether these concerns exert enough influence on enough consumers to show up statistically, and if so, which of the concerns receives relatively more weight in the minds of most consumers?

In this paper a simple consumer choice model was presented to illustrate the general empirical implications of each view when taken to its extreme. In each case, the model suggests a correspondence between an individual's wage rank and hours supplied. The direction of the relationship, however, depends on whether the consumer is more concerned with relative leisure or relative consumption. The data surveyed in this paper unambiguously support the notion of a correspondence between hours supplied and wage rank. However, there remains some ambiguity with respect to the direction of the relationship. While data from the late 1950's and mid 1960's seems to support the view that relative consumption is the primary concern, evidence from the 1988 Current Population Survey suggests that concern about relative leisure is still an important influence in the labor supply decision. Taken together, the evidence suggests that perhaps the ongoing race for positional consumption goods has resulted in a renewed interest in the social significance of leisure time.

Notes

1. See also Frank's (1985) book.

2. For empirical evidence relating directly to Frank's positional goods model, see Kosicki (1987b) and (1988) and Frank's book (1985b). Other important empirical support can be found in Duesenberry (1949), Easterlin (1973), and Menchik and David (1983). For a survey of the cross-section evidence relating to the influence of interpersonal comparisons on saving, see Kosicki (1987a).

3. Opinions on this subject in the popular arena also vary widely. In a Time magazine essay, Michael Kinsley (1990) writes that "We've come a long way in the century since Thorstein Veblen wrote about 'conspicuous' or even 'honorific leisure' as a way of displaying social status. 'Gosh, you must have nothing at all to do all day,' would not be considered a compliment." A similar argument was made as early as 1959 by Vance Packard in the book The Status Seekers. Packard argues that the tremendous growth in leisure time that has accompanied productivity increases has resulted in a situation where "leisure has lost most of its potency as a status symbol". However, an alternative view was presented by reporter Carrie Dolan (1992) in The Wall Street Journal. In the article she quotes Watts Wacker, executive vice president of Yankelovich Clancy Shulman, Inc. concerning a survey done by the firm. According to Mr. Watts, the survey suggested "The biggest status symbol today is being able to say you have nothing to do" and that what people wanted most was to be able "to hang out and not account for productivity".

4. Of course it is also a function of the wage rate, and so as Frank (1985a) points out, the quest for relative consumption standing may result in the deliberate choice of jobs with undesirable nonpecuniary characteristics.

5. This finding is reported by Freeman (1981).

6. Killingsworth's extensive (1983) survey of the labor supply literature acknowledges that the notion of individual labor supply decisions being affected by the behavior of persons outside the family "has not been analyzed extensively, and its potential implications remain largely unexplored".

7. See Seidman (1987) and (1988-89). Layard (1980) also briefly mentions the possibility of such a model but does not pursue its implications.

8. The Cobb-Douglas form results in a tractable model. The form is employed in the context of the choice between consumption and savings by Frank (1985b), and Kosicki (1987b) and (1988), but also in the relative standing model by Seidman (1988-89) in which utility is a function of consumption and leisure. Here the Cobb-Douglas form has been transformed by the natural logarithm function. Felder (1988) used the Cobb-Douglas form to explore the implications for the labor supply schedule of introducing a subsistence level of consumption. To the extent that the subsistence level is socially determined, Felder's work is complementary to that undertaken here.

9. With the Cobb-Douglas utility function, only the relative magnitudes of the utility parameters are important.

10. Actually, f(C) is an endogenous expression that results from the simultaneous choice of L and C, but such a treatment is beyond the scope of this paper. A similar assumption is made with respect to the function f(L) when generating labor supply functions associated with the other extreme of the model. For any variable X that is distributed uniformly on the interval |X.sub.0~ to K|X.sub.0~, f(X) = 1/(K|X.sub.0~ - |X.sub.0~) and R(X) = (X - |X.sub.0~)/(K|X.sub.0~ - |X.sub.0~). The ratio f(X)/R(X) is then given by the simple expression 1/(X - |X.sub.0~).

11. This case is characterized as an "extreme" form of Veblen's hypothesis since a careful reading of Veblen suggests he also appreciated the importance of relative consumption standing. Winston (1965), who makes a similar point, cites as supporting evidence Veblen's quote that "A life of leisure is the readiest and most conclusive evidence of pecuniary strength, and therefore of superior force; provided always that the gentleman of leisure can live in manifest ease and comfort".

12. The maximum time T was set at 24 hours times 365 days a year. Minimum leisure time was set at 8 hours a day times 365 days a year.

13. This positive relationship between C and Z can be verified by looking at the consumption data that is simultaneously generated in producing the simulations presented in Figures 1 and 2.

14. The latter relationship is clear from Figures 1 and 2 since leisure increases as V (and hence Z) increases.

15. Because the sample consists of only those who worked for pay in the preceding year, the comparisons may suffer from some degree of sample selection bias.

16. See the price indices for 1987 available in the Statistical Abstract of the United States: 1990, Table 763. Computing the wage rate by dividing total wage earnings by hours worked potentially creates a spurious negative correlation between hours and the wage rate if there are measurement errors in the hours data. Hence the analysis is slightly biased towards finding the type of relationship seen in the Morgan data. In general the results presented are very insensitive to any exclusions from the total sample or to the particular variable definitions that are employed.

17. A large number of observations helps to ensure that the wage rank computations reflect the wage distribution in that area.

18. Throughout this analysis it is assumed that individuals are not constrained in their choice of hours so that hours supplied and hours worked are the same.

19. Persistent unexplained regional differences in labor force participation rates are cited by Browne (1990).

20. For evidence on the relationship between income rank and savings rates, see Kosicki (1987b).

21. For the same reason, a regression analysis like the one presented in Table 3 was not performed on this data. Once the sample was also split on the basis of non-labor income, many states had only a few observations in each wage category, thus calling into question the reliability of the wage rank variable.

References

Browne, Lynn E. "Why Do New Englanders Work So Much?" New England Economic Review (March/April 1990): 33-46.

Current Population Survey, March 1988 |machine-readable data file~ / conducted by the Bureau of the Census for the Bureau of Labor Statistics. Washington: Bureau of the Census |producer and distributor~, 1988.

Current Population Survey, March 1988 Tape Technical Documentation / prepared by the Data User Services Division, Data Access and Use Staff, Bureau of the Census. Washington: The Bureau, 1988.

Duesenberry, James. Income, Saving, and the Theory of Consumer Behavior. Cambridge: Harvard University Press, 1949.

Dolan, Carrie. "Lazy Days of Summer? No, Year Round" The Wall Street Journal 219 (February 7, 1992):A4.

Felder, Joseph. "The Supply of Wage Labor, A Subsistence Level of Consumption, and Household Production -- The Cobb-Douglas Case." The American Economist 22 (Spring 1988):10-18.

Frank, Robert H. Choosing the Right Pond: Human Behavior and the Quest for Status. New York: Oxford University Press, 1985a.

-----. "The Demand for Unobservable and Other Nonpositional Goods." American Economic Review 75 (March 1985b):101-116.

Freeman, Richard B. "The Effect of Unionism on Fringe Benefits." Industrial and Labor Relations Review, 34 (July 1981):489-501.

Hirsch, Fred. Social Limits to Growth. Cambridge: Harvard University Press, 1976.

Killingsworth, Mark, R. Labor Supply. Cambridge: Cambridge University Press, 1983.

Kinsley, Michael. "You Must Be Very Busy." Time 136 (August 20, 1990):82.

Kosicki, George. "A Note About Savings as a Nonpositional Good." Eastern Economic Journal 14 (July-September 1988):271-276.

-----. "The Relative Income Hypothesis: A Review of the Cross Section Evidence." Quarterly Journal of Business and Economics 26 (Autumn 1987a):65-80.

-----. "A Test of the Relative Income Hypothesis." Southern Economic Journal 54 (October 1987b):422-434.

Layard, Richard. "Human Satisfactions and Public Policy." Economic Journal 90 (December 1980):737-49.

Morgan, James, N. "Hours of Work by Family Heads: Constraints, Marginal Choices, and Income Goals." In Five Thousand American Families -- Patterns of Economic Progress (Volume VII), pp. 65-99. Edited by Greg J. Duncan and James N. Morgan. Ann Arbor: University of Michigan, 1979.

-----. The Supply of Effort, the Measurement of Well-Being, and the Dynamics of Improvement," American Economic Review 58 (March 1968):31-39.

-----, Sirageldin, Ismail, and Baerwaldt, Nancy. Productive Americans. Ann Arbor: University of Michigan, 1966.

Packard, Vance. The Status Seekers. New York: Pocket Books, 1959.

Seidman, Laurence, S. "Relativity and Efficient Taxation." Southern Economic Journal 54 (October 1987):463-74.

-----. "The Welfare Cost of a Relativistic Economy." Journal of Post Keynesian Economics 11 (Winter 1988-89):295-304.

United States Bureau of the Census. Statistical Abstract of the United States: 1990 (110th edition) Washington, DC, 1989.

Veblen, Thorstein. The Theory of the Leisure Class. New York: The Modern Library, 1899 (reprinted 1934).

Winston, Gordon C. "Income and the Aggregate Allocation of Effort." American Economic Review 55 (May 1965):375-85.

George Kosicki

Associate Professor, Department of Economics, College of the Holy Cross, Worcester, MA 01610.

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Author: | Kosicki, George |
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Publication: | American Economist |

Date: | Mar 22, 1993 |

Words: | 6632 |

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