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BattalioetalSlides - 624 SEPTEMBER 1981 THE AMERICAN...

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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. D 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 = P X,Y,Z CHOICEOINTS INCOME 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 labor supply. 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 ) Slutskysubstitution 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 ~2f ee 44 4680 ?free 4286 197 200+ 40e 800 ?2free 400 40+ -e 4540 2855 ~ 3657 1486 Coefficient -.91 Subject 47 Change 4636 Percent Changee 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 Changee 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 Change Work 4225 95 5343 3808 80 2914 5375 -95 78 3596 -.96 b (4.77) -2 3877 4756 4846f 98b (6.94) 4008 -.84 Subject 50 Change Percent Change Average Values Change in Work 2429 45 433117(2.23) 3962b (5.07) Percent 72.5 Change (5-09)b in Work 1779 879 33 3188 (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 Wage Rates Subject 47 50+free 50 100 + free 100 200 + free 200 400+ free 400 Subject 48 50 + free 50 100 + free 100 200+free 200 400+free 400 Subject 49 50 + free 50 100 + free 100 200 + free 200 400+free 400 Subject 50 50+free 50 100+free 100 200+free 200 400+free 400 Free Workc Incomec 44 1821 197 4680 1486 4286 2856 3657 2889 4919 4249 5839 4174 6908 3686 6648 328 5079 1065 6162 1097 5290 4027 4905 2914 4533 3596 5343 3877 5375 4008 4756 Change in Workc Percent Change 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 Earneda 1821 4680 4286 3657 4540 4918 5839 6908 6648 4144 5078 6162 5290 4905 3932 4533 5343 5375 4756 4846 9.4 47.2 85.7 .145.8 362.9 25.3 61.7 106.0 196.1 316.2 24.5 58.1 137.3 266.0 331.2 22.6 53.7 107.5 190.3 387.0 -83 95.8 Wage 50 100 200 400 800 50 100 200 400 800 50 100 200 400 800 50 100 200 400 800 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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