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Unformatted text preview: 624 SEPTEMBER 1981 THE AMERICAN ECONOMIC RE VIEW close accord with prior expectations based
on neoclassical economic theory. In doing so,
we have not had to suppress untidy results,
the picture is a remarkably consistent one. It
is this consistency which motivated the tests
of the Slutsky-substitution effect reported in
the next section. Although the theory allows
the labor supply curve to be of any shape,
and even permits increases in consumption
with increases in effort price (a Giffen good)
over portions of the choice space, there is no
ambiguity regarding the sign of the Slutskysubstitution effect.
This is not to say that the psychologists
who conducted the experiments surveyed
support a maximizing model of the type
employed here. In fact some of them explicitly reject this approach (see Herrnstein
and Vaughan, also Allison et al.). We will
return to the question of competing explanations of the data following the consistency
tests reported below.
II. Experimental esign
Figure 1 provides a graphical representation of the experimental design. Subjects start
out working at wage rate wl, with the level of
free income F1, set equal to zero (budget line
OA). The income-leisure choice bundle, represented by point X, is observed. Subjects are
then given a positive level of nonwage income F2, and wages decreased to w2until the
quantity of labor supplied reaches its previous level, Rx. Should this point be reached,
wages revert to their original level wl.
The new budget line, OBXA, provides an
exactly compensated wage rate decrease relative to the original choice point X. Convexity
of the indifference curves, or simple consistency of choices in terms of revealed preference theory, requires that the new choice
point lie somewhere on the interval BX of
the new budget line. Choice point Y illustrates one of many possible consistent
choices. The new budget line OBXA involves
a Slutsky-compensated wage change, and the
interval R X-Ry measures the magnitude of
the Slutsky-substitution effect.
Following establishment of stable choice
behavior under the new budget line, free
income F2 is reduced to zero with wage rate =
INCOME C =
F=NONWAGE A RX Rz Ry 0
WORK=R FIGURE 1 w2 maintained throughout the work period.
This new budget line OD is parallel to the
BX portion of the compensated wage rate
line. In this way we can isolate and directly
measure the effect of nonwage income F2 on
The sequence of budget line manipulations
shown in Figure 1 was repeated at a number
of different wage rates. In this way we can
test for consistency of choices at different
wages and observe the shape of the labor
supply schedule and the associated demand
for income schedule. Given this design we
can also decompose changes in labor supplied (RX -Rz) into their component Slutsky-substitution effects and income effects. (7) (RX-RZ) )(Rx
changein laborsupplied = -Ry )
effect + (Ry-Rz)
+ incomeeffect This enables us to identify changes in the
magnitude of the income and substitution
effect along different segments of the labor
supply schedule. For example, we can determine whether the backward-bending portion of the labor supply schedule is due to a
decreasing substitution effect, an increasing
income effect or some combination of the
two. VOL. 71 NO. 4 BA TTALIO ETA L: INCOME-LEISURE TRADEOFFS 627 TABLE 1- SLUTSKY-COMPENSATEDHANGESIN LABOR SUPPLY
C Wage Rates
Correlation |100 _~~~~~~ Workd |50+ 200 r
44 4680 ?free 4286 197 200+
?2free 400 40+
-e 4540 2855 ~ 3657 1486 Coefficient -.91
Subject 47 Change 4636 Percent
Work 5839 48 2889 4249 6648 (3. 19) b 37 4173 4144 (5.23)
3686 c7ab 2659 2475 38 51 1685 59 c 2950 Pren
Work 6908 c Change 2171 95 99 d
Subject 4089 458 (5.41) b 11 37 (5.50)
328 6162 5290 1065 4905 1097 4027 3932 -.
Subject 49 Change 5834 Percent
Work 4225 95
5343 3808 80
2914 5375 -95 78
3596 -.96 b
3877 4756 4846f 98b (6.94) 4008 -.84
Subject 50 Change Percent
in Work 2429 45
(5.07) Percent 72.5 Change (5-09)b in Work 1779 879 33
(5.42) 838 18 b 61.5 17- 2333
(3.88) (50)(.1(36)194 .84 721.5
(1.93) 15.8 48.0
a (2.23) a (1-94) Note: t-statistics are shown in parentheses.
aSignificant at 10 percent level.
bSignificant at 5 percent level.
'Significant at I percent level.
dMean for the last 5 days under each condition.
'Percent change =(wo - w /wo) X 100 where wo and w1 measure work during the baseline and compensated wage
change periods respectively.
fSubject 50 was originally inconsistent under this condition. While the size of the substitution effect
does not correlate well with baseline labor
supply, there is a strong negative correlation
with respect to wage rates for all subjects.
This negative correlation holds for both the
absolute size and percentage change in labor
lowest to the highest wage rate. Similarly, small tstatistics are found in comparing baseline labor supply
with absolute changes in work, although the power of
these tests are low due to the sample size. supplied. Since the percentage change in wage
rates is the same amount at each point, this
implies that both the absolute size and elasticity of the (Slutsky) substitution effect decrease with increases in real wage rates.
Table 2 shows the effect of free income on
labor supply at each of the wage rates for
which data are available. In all cases the
addition of free income, holding wage rates
constant, results in a reduction in total labor
supplied; leisure (not working) is a normal SEPTEMBER 1981 THE A MERICAN ECONOMIC RE VIE W 628 TABLE 2-EFFECTS OF FREE INCOMEON
LABOR SUPPLIED TABLE 3-LABOR SUPPLY AND DEMAND FOR INCOME Labor
100 + free
200 + free
50 + free
100 + free
50 + free
100 + free
200 + free
4756 Change in
in Workd 24.0 -1777b -98 43.0 -4483b -96 73.0 - 2800b -65 179.4 -801b 47 -22 48 49
29.0 - 2030b -41 69.4 -1590b -27 133.0 -2734b -40 166.4 -2962b -45 31.8 -4751b -94 53.0 -5097b
-4193b -79 167.2 -878b -18 27.2 -1619b -36 54.0 -1747b -33 95.0 -1498b -28 -748b -16 Supplieda Income
387.0 -83 95.8 Wage
800 Subject 50 193.6 aSignificant at 5 percent level.
bSignificant at 1 percent level.
cMean for last five days under each condition.
dPercent change=w, -wo/wo X 100 where wI and wo
measure work with and without free, respectively. good in this environment. Here, too, we find
empirical regularities in that for three of the
four subjects (47, 49, and 50) the absolute
size of these income effects decreases at the
higher real wage rates. More striking still is
the steady decrease in the percentage change
in work as real wages increase, even though
the absolute amount of free consumption
increases with real wages too." This suggests
'Free income as a percentage of maximum income earnings is approximately constant, or decreases slightly aMean for last five days under each condition. a strong interaction effect between wage rates
and nonwage income in labor supply response, a point we return to shortly.
Free income also results in an increase in
total consumption (free plus earned) holding
wage rates constant for 15 of 16 observations. Under the conditions of this experiment consumption is a normal good too.
Table 3 draws together data from Tables 1
and 2 to show labor supply and demand for
income schedules with no free income. For
all subjects labor supply increases up to wage
rate 100-200, after which it tends to bend
back on itself, results consistent with data
reported from other experiments. The data
also rule out explaining the positive substitution effects of Table 1 as a simple response
to decreases in wage rates; the wage change
part of the Slutsky-compensated changes
tends, by itself, to increase labor supply over
the backward bending portion of the curve.
The data in Table 3 also show demand for
income increasing uniformly with increases
in real wage rates (decreases in effort price).
This provides yet another confirmation of
with increases in real wage rates, hardly enough to
account, by itself, for the diminishing impact of free on
labor supply. ...
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