Week-15

THOMAS DERNBURG, KENNETH STRAND AND JUDITH DUKLER**

A Pararaetric Approacli to Labor Force Projection

RECENT research has established beyond a reasonable doubt that labor force participation is positively associated with the degree of tightness in the labor market.^ Alfred Telia's time-series studies indicate that if the unemployment and labor force totals for 1962 had been corrected for what is generally denoted as "hidden unemployment," the civilian unem- ployment rate would have been 8.5 per cent as opposed to the official rate of 5.6 per cent.^ The TeUa figure of 8.5 per cent is identical to the revised "low full employment gap" unemployment rate calculated by Demburg and Strand, who found that labor force participation fiuctuates both as the result of withdrawal of "discouraged workers" and as the result of the entry into the labor force of "additional workers" in response to deteriorating business conditions.^ The discouraged worker efiFect was found to dominate to such an extent that over the period 1953-1962 the loss of 100 jobs was associated with net withdrawal from the measured labor force of between 44 and 51 workers.

The report that contains the most recent Bureau of Labor Statistics labor force projections includes an attempt to assess the impact of changes in em- ployment on unemployment and labor force participation.* It was found tiiat

" The authors are, respectively, Professor of Economics, Oberlin College; Economist, Man- power and Social Affairs Directorate, OECD, Paris; and graduate student in economics. Univer- sity of Michigan.

1 The research for this article was supported by a grant from the Brookings Institution and a Ford Foundation Public Affairs Grant to Oberlin College.

2 Alfred Telia, "The Relation of Labor Force to Employment," Industrial and Labor Rela- tions Review, XVII (April, 1964), 454-469, and "Labor Force Sensitivity to Employment by Age, Sex," Industrial Relations, IV (February, 1965), 69-83.

3 Our original estimates were based on aggregate labor force and employment data and are reported in Kenneth Strand and Thomas Demburg, "Cyclical Variation in Civilian Labor Force Participation," Review of Economics and Statistics, XLVI (November, 1964), 378-391. The re- vised estimates, based on an age-sex breakdown, are reported in "Hidden Unemployment 1953- 1962; A Quantitative Analysis by Age-Sex," American Economic Review, LVI (March 1966) 71-95.

* Sophia Cooper and Denis F. Johnston, "Labor Force Projections for 1970-80," Monthly Labor Review, LXXXVIII (February, 1965), 129-140.

46

Labor Force Projection / 47

over the period 1947-1962 a decline in the level of unemployment of 100,000 would, on the average, be associated with a rise in labor force participation of 60,000.

Finally, the findings of the various time-series studies cited above have been supported by a cross-section analysis of large metropolitan areas by Bowen and Finegan.^ Their research reveals strong negative correlations between labor force participation rates of various specific groups in the population and unemployment rates in these metropolitan areas.

Projection of futxire labor force changes has always been a hazardous and diflBcult task. The problem becomes even more complicated when it is rec- ognized, as recent findings have shown, that labor force participation rates at any one time are determined by short-run economic, as well as demo- graphic, factors. In addition to the fact that the technical task of projecting becomes more difficult, the analyst is now faced with the uncomfortable realization that if policy planners act on the projection, an incorrect projec- tion may become a self-fulfilling prophecy.

Labor force projections are made in order to estimate the manpower potential of the future and to calculate the ntimber of jobs required in order to achieve full employment at that time. If an analyst extrapolates the actual labor force participation rates of a period of less than fuU employment, he will be projecting the depressed labor force participation rates that arise in such a period rather than the labor force participation rates that would have been observed had the economy been at full employment. Moreover, be- cause cyclical changes in participation rates vary widely among the several subgroups of the population, the projections will not only underestimate total labor force, but wiU, in addition, give a seriously distorted picture of the composition of the full employment labor force.

Alternatively, if the projections do in fact provide an accurate representa- tion of futiare labor force potential, they may nevertheless be in error when compared with the actual recorded values if the economy is at less than fuU employment during the projected year. In this case, the projections will appear to be "wrong." The analyst, however, will have done his job properly, even though he is not very likely to receive much credit for having done so.

Our purpose in this paper is to present projections of the civilian labor force for 14 age and sex groups for the years 1970, 1975, and 1980, allowing for short-term variations, as well as long-term trends, in labor force partici- pation rates. Put differently, the projections reported in this paper are

^W. G. Bowen and T. A. Finegan, "Labor Force Participation and Unemployment," in A. M. Ross, editor. Employment Policy and the Labor Market (Berkeley and Los Angeles: Uni- versity of California Press, 1965).

4 8 / THOMAS DERNBXJRG, KENNETH STRAND AND JtFDITH DtTKLER

based on the presumption that observed participation rates in an economy characterized by the presence of substantial imemployment are not suitable data points for purposes of extrapolation. The major substantive conclusions are the following: Recent low participation rates are primarily the product of slack economic conditions rather than of long-term demographic changes. Because the BLS full employment projections are based on data refiecting these slack conditions, they xmderestimate the full employment labor force of the future. Moreover, since participation in the different groups varies enormously vdth. respect to the degree of responsiveness to changes in labor market tightness, the projected composition of the potential labor force is seriously distorted.

Projections of the Civilian Population The population projections that are used in the present study

are the same as those utilized by the BLS in its most recent report. These data are based on the Series B population projections of the Census Bureau.®

The Census Bureau population projections include the armed forces. Because our concern is with the civilian population and the civilian labor force, we adjust the estimates by assviming, as does the BLS, that the armed forces will continue to remain at their 1964 level of 2,739,000. Although the recent build-up in the size of the armed forces renders this estimate cur- rently incorrect, it is nevertheless appropriate to retain it because our pvir- pose is to compare our estimates wiih those of the BLS. The total 2,739,000 is distributed among the 14 age-sex groups on the basis of the average pro- portions that prevailed between 1959 and 1962. The data in Table 1 therefore represent Census Bureau population projections roughly adjusted to elim- inate the armed forces and thereby to provide estimates of the civiKan population.

Procedure As was pointed out earHer, projections that are derived by

extrapolation of observed participation rates will fall short of the mark if these observed rates refiect labor force participation in a less than fully employed economy. It is therefore necessary to adjust the observed rates in such a way that the adjusted rates vdll serve as estimates of what t i e actual rates would have been had the economy been at fuU employment. We in- tend, therefore, to derive "full employment labor force participation rates" and to use these, rather than the observed rates, to make our projections.

6 "Projections of the Population of the United States by Age and Sex: 1964-1985," Current Population Reports, Series P-25, No. 286, U.S. Bureau of the Census (Washington, D.C.: 1964).

Labor Force Projection / 49

For present purposes we define "low full employment" as a situation that obtains when the overall civilian unemployment rate is 4 per cent and "high fuU employment" as a situation associated with a 3 per cent civilian unem- ployment rate.

TABLE 1

CrvnjAN POPULATION PROJECTIONS

(Thousands)

Age and Sex

Male 14-19 20-24 25-34 35-A4 45-54 55-64 65 and over

Female 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Totals Male Female Both sexes

1970

11,182 7,565

11,817 10,902 11,222 8,754 8,385

11,293 8,471

12,671 11,689 12,060 9,741

11,186

69,834 77,118

146,952

1975

12,124 8,553

14,834 10,673 11,312 9,282 8,923

12,213 9,434

15,573 11,386 12,193 10,558 12,248

75,703 83,604

159,307

1980

12,350 9,338

17,562 12,101 10,690 9,771 9,606

12,351 10,218 18,223 12,766 11,435 11,279 13,481

81,418 89,751

171,169

For any specific group in the population, the ratio of the group's level of labor force participation to total population may vary because of seasonal, cyclical, secular, and random causes. In order to capture and isolate these separate effects we specify:

(1) {f) = a,,

where Li and P* represent labor force and population in group i, and E, X, and P are the aggregate values of civilian employment, exhaustion of unem- ployment compensations, and adult civilian population respectively. The subscript t dates the variables, and m specifies the month of the year. The term eit, finally, is a random error component which, henceforth, is ignored in the notation. Note should be taken of the circumstance that the dependent variables of the study are t i e labor force participation ratios, Li/P, rather

5 0 / THOMAS DERNBtlRG, KENNETH STRAND ANB JUDITH DUKLER

than the group speeifie labor foree partieipation rates, Li/Pi.'' The raw data are unadjusted for seasonal variation and eover the 146 months, November 1952 to Deeember 1964, inelusive.

Sinee we utilize the non-seasonally adjusted data as reported by the BLS. we allow for seasonal variation by means of 12 zero-one dummy variables that permit the intereept of the regression equation to shift with the month of the year. The method may be thought of as one that generates a separate estimating equation for eaeh month. The slope eoeflBeients remain the same while the intereept term varies with the month of the year.

Cyclieal effects are presumed to be of two types and are represented by the presence of the employment ratio, E/P, and the exhaustions ratio, X/P, as independent variables. The employment ratio is our measure of labor market tightness. If the data support the discouraged worker hypothesis, according to which economie adversity causes workers to become discoiu-- aged and to leave the labor force, the an coefficients will be positive. The exhaustion of unemployment compensations measures pressure on additional workers to enter the labor force. Therefore, if the data support the addi- tional worker hypothesis, the an coefficients will also be positive. It should be observed that the exhaustions ratio enters Equation 1 with a two-month lead. The reason for this is that the pressure on additional workers to enter the labor force begins prior to the actual exhaustion of imemployment com- pensation payments to the primary worker. Thus, the pressure on additional workers to enter the labor force in month t is not reflected in the exhaus- tions data until month t+2. It appears, therefore, that it is the expectation of the exhaustion of compensations, rather than the actual event, that in- fluences additional worker behavior.

Long-range, or secular, factors that affect the labor force participation ratio are also of two types. If the composition of the population changes so that group i represents a larger fraction of the population, the labor force participation ratio for the group wiU increase. For this reason, relative popu- lation, Pi/P, is added as an independent variable. The participation ratio will also change if there are long-term changes in habits and tastes. Such long-term changes would be reflected in a trend, and these effects are there- fore presumed to be captured by the variable

"^ To avoid confusion, we denote any quantity that represents a per cent of total adult civilian population a "ratio," whereas quantities that are divided by group specific population totals are denoted as "rates." The choice of Li/P as the dependent variable is a matter of con- venience which facilitates the subsequent aggregation process.

8 The variable 1/P has several advantages over other possible means of allowing for trend. It builds an assymptotic relationship into the behavior of Lt/P and thereby appropriately bounds the dependent variable. More important, however, is that its insertion as a separate independent variable avoids the problem that spurious correlation between E/P and Li/P may ofiierwise result from changes in P. For a discussion of these and other technical details the reader may wish to consult Demburg and Strand, "Hidden Unemployment. . . ."

Labor Force Proiection / 51

The results are reported in Table 2. The first column of the table presents the average values of the intercept terms. The last column reports the co- efficients of determination adjusted to eliminate explanation attributable to seasonal variation. The intervening columns contain the regression coeffi-

TABLE 2

E Q U A T I O N 1: REGRESSIO f̂ C O E F F I C I E N T S , STANDARD E R R O R S ,

AND C O E F F I C I E N T S O F D E T E R M I N A T I O N

Age and sex

Male

14-19

20-24

25-34

35-44

45-54

55-64

65 and over

Female

14-19

20-24

25-34

35-44

45^4

55-64

65 and over

ami

-.0816

.0025

-.0063

-.0068

-.0034

-.0019

-.0907

-.0769

-.0161

.0034

-.0143

-.0439

-.0341

-.0056

(2) a.i

.1279 (.0179) .0499 (.0111) .0028" (.0049)

-.0025" (.0040) .0200 (.0050) .0086" (.0073) .0745 (.0064)

.1157 (.0127) .0426 (.0096) .0561 (.0102) .0918 (.0107) .0918 (.0100) .0676 (.0092) .0574 (.0060)

(3) â i

.9761 (.0310) .6318 (.1772) .0049' (.0919)

-.0008° (.0795) .3678 (.1062) .5292 (.1559) .8649 (.1239)

1.1355 (.2376) .6925 (.2001) .8641 (.1935) 1.2425 (.2236) 1.1271 (.2122) .4515 (.1821) .7058 (.1156)

(4) aai

1,434" (1,007)

- 2,491 (664) 1,446 (592) 45"

(258) 404 (79)

1,281 (302) 5,163 (151)

719" (784)

-1,769 (158)

-6,514 (1,523)

-3,532 (380)

-6,708 (222)

-5,131 (242)

-1,947 (457)

(5) ati

.4231 (.0834) .6070 (.0721) .8917 (.0355) 1.0624 (.0454) .8212 (.0396) .6415 (.2441) .4638 (.0535)

.4033 (.0667) .6106 (.0360) .5537 (.0792) .3553 (.0922) 1.0478 (.0507) .9668 (.1142)

-.0489" (.0569)

(6) R2

.6525

.9709

.9986

.9932

.9118

.8355

.9768

.8143

.8160

.9298

.6119

.9827

.9664

.6363

" Not statistically signiBcant at the S per cent level.

cients. The values in brackets beneath the coefficients are their respective standard errors. As can be seen from inspection of the table, the data are consistent with both the discouraged and the additional vî orker hypotheses in 11 of the 14 groups. The results conform to expectation: participation is virtually autonomous for men in the central age groups, but fluctuates with business activity for all female groups and for young and old males.

A fall in employment lowers participation directly through the discour-

5 2 / THOMAS DERNBURG, KENNETH STRAND AND JUDITH DUKLER

aged worker effect and raises participation indirectly via the additional worker effect as reflected by a rise in the exhaustions ratio. Consequently, it is necessary to add an equation to explain the exhaustion ratio, and thereby to ascertain the net effect on participation of a change in employment. Since the level of unemployment compensation exhaustions depends on the history of past unemployment (or employment) levels, we spedfy the distributed lag fimction:

which, for the 146-month period covered by the data, was estimated to be:

(2a) (j)=b,,,- .004904 (^) + .9000 (fj + 7J.6of|). ^ ^ ' (001753r^'-' (0326r^'-' (314)^^''

The standard error of estimate is .000103; the coeflBcient of determination, adjusted to eliminate explanation due to seasonal variation, is .9300; and the average intercept value is .00218.

In order to utilize these equations to make labor force projections, we must find a way to eliminate the effects of both seasonal and cyclical varia- tion. The procedure through which this is accomplished is outlined in the following five steps:

Stef 1: Seasonal variation can be eliminated by converting the equations that predict monthly labor force and exhaustions ratios into annual average relationships. This can be done by aggregating Equations 1 and 2 over con- secutive 12-month periods beginning with January.

12

where, a,. = - i ^ , ( f ) ^ = - A ^ , etc.

This aggregation procedure has the effect of flying the floating monthly inter- cepts as constants and it converts the variables into annual average values. The subscript t now dates the beginning of the seventh month of the year, and it will, henceforth, be thought of as dating the year.

Step 2: In Equation 1 the exhaustions ratio leads by two months and there are one-period lags of the employment and exhaustions ratios in

Labor Force Projection / 53

Equation 2. Since we are now dealing with, annual averages and since our concern in this paper is with long-range projections, these monthly lags may properly be ignored. Consequently we rewrite Equation 2b as:

p)< l-b.,

and by substituting this expression in equation lb, and again ignoring lags, obtain:

(3)

where.

The coe£Bcient, An, is what we may call the net stationary derivative of a change in group labor force participation with respect to a change in em- ployment. It represents the change in participation that would restilt from a change in £ / P if aU reactions occiured instantaneously, and it combines the discouraged worker effect and the offsetting additional worker effect. The values of these coefiBcients are reported in column 1 of Table 3. It is instructive also to convert these derivatives into elasticities. These elastici- ties are reported in column 2. Inspection of the table shows that the respon- siveness of labor force participation with respect to changes in total employ- ment is U-shaped with respect to age—high for yoimg and old persons and low for the central age groups. For males in the central age groups the re- sults are not statistically significant and participation in these groups must be regarded as independent of the level of economic activity in the short run.®

Female participation is generally more responsive to changes in employ- ment than is male participation in the corresponding age group; the chief

9 The only result that does not conform to initial expectation is in the male 55-64 age group, where participation appears to increase as the labor market grows slack. A possible ex- planation for Qiis is that recession causes early retirees to retum to the labor market. Another possibility is that recession causes workers in this age group to postpone retirement in order to assist hard-pressed relatives.

5 4 / THOMAS DERNBURG, KENNETH STRAND AND JUDITH DUKLER

TABLE 3

STATIONARY DEWVATTVES AND ELASTicrrrEs OF GROUP SPECIFIC LABOR FORCE

PARTICIPATION W I T H RESPECT TO CHANGES IN AGGREGATE EMPLOYMENT"

Age and Sex

Male 14-19 20-24 2 5 - ^ 35-44 45-54 55-64 65 and over

Female 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Totals Male Female Both sexes

Net derivative of participation with respect

to employment

.080

.019

.003" - . 0 0 3 "

.002 - . 0 1 7

.032

.060

.009

.014

.031

.037

.046

.023

.116

.218

.334

Elasticity of participation with respect to

employment

1.608 .325 .016"

- . 0 1 5 " .014

- . 1 7 9 .881

1.721 .216 .214 .394 .500

1.077 1.794

.163

.630

.317

« Elasticities have been computed hy multiplying derivatives hy the ratio of average value of total employment to group labor force participation over the period covered hy the data.

^ Not statistically significant at the 5 per cent level.

exception to this rule is the 20-24 group. In absolute terms a rise in employ- ment of 1,000 w ôuld be accompanied by an increase in male participation of 116 and an increase in female participation of 218. Thus the total rise in labor force participation would be 334 vv̂ hich imphes that unemployment vŝ ould fall by only 666.

Step 3: The third step is to aggregate the 14 Equations 3 in order to ob- tain the aggregate labor force participation ratio. The result is:

for convenience, may be rewritten:

The coeflBcient Bi represents the net total stationary derivative of labor force participation with respect to employment. As can be seen in Table 3 its value is .334.

Labor Force Projection / 55

Step 4: Full employment is defined as a situation which obtains when the aggregate annual civilian unemployment rate equals a fuU employment criterion value, 4. FuU employment therefore exists whenever:

Substitution of this "criterion function" into Equation 4 provides the esti- mated aggregate full employment labor force participation ratio:

(̂ ) \P/, l-B,(l-u) Equation 5 is the expression that permits us to determine projected total

full employment labor force merely by deciding on a suitable full employ- ment criterion unemployment rate and by substituting projected total popu- lation and relative population in the equation. This procedure therefore not only adjusts observed data points for the absence of full employment but generates the total labor force projections themselves. Unlike most projec- tion procedures, moreover, the method provides a means of checking the projections against the ultimate outcome. If, for example, it turns out that in 1970 population and its distribution are somewhat different from the pro- jected values and if the unemployment rate differs from the criterion rate, the actual population values and the actual unemployment rate may be substituted into Equation 5 and the resulting predicted labor force partici- pation ratio may be compared vdth the actual ratio for 1970.

Step 5: The final step is to take the aggregate projections and to distribute the totals over the 14 age and sex groups. Since we have derived the pro- jected full employment participation ratio, (L/Pjt", we may calculate the associated employment ratios, (E/P)t**, simply by multiplying the aggregate participation ratio by (1-u). The projected aggregate employment ratio may then be substituted back into the 14 Equations 3, along with projected popu- lation and relative population, in order to obtain the group specific labor force projections.

The results for 1970, 1975, and 1980, utilizing 4 and 3 per cent civilian unemployment rates as f uU employment criteria, are reported in Tables 4, 5, and 6, respectively. Included in the tables are three sets of projections by the BLS, which are reported in order to provide benchmarks for comparison with our results. A glance at the totals in the bottom row of the tables im- mediately brings to light the presence of sizeable discrepancies between our projections and those of the BLS. Our low fuU employment total exceeds the current BLS projections by 1.2 nuUion for 1970,1.5 million for 1975, and

5 6 / THOMAS DERNBtJRG, KENNETH STRAND AND JUDITH DtTKLER

TABLE 4

CIVILIAN LABOR FORCE PROJECTIONS FOR 1970 (Thousands)

BLS D-S-D

Age and sex

Male 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Female 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Totab Male Female Both sexes

Previous

5,075 6,531

11,450 10,604 10,658 7,716 2,704

3,174 3,854 4,896 5,465 6,553 4,313 1,360

54,738 29,615 84,353

Interim revised

4,711 6,368

11,267 10,618 10,758 7,584 2,284

3,322 3,927 4,710 5,508 6,604 4,108 1,195

53,590 29,374 82,964

TABLE 5

Current

4,705 6,410

11,340 10,535 10,658 7,383 2,108

3,400 4,255 4,885 5,550 6,673 4,267 1,091

53,139 30,121 83,260

Low full employment

4,491 6,482

11,289 10,431 10,726 7,276 1,716

3,286 4,451 5,503 5,897 6,867 4,735 1,305

52,411 32,044 84,455

High full employment

4,591 6,506

11,292 10,428 10,729 7,254 1,756

3,361 4,461 5,521 5,935 6,913 4,794 1,333

52,556 32,316 84,872

CIVILIAN LABOR FORCE PHOJECTIONS FOR 1975 (Thousands)

BLS D-S-D

Age and sex

Male 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Female 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Totals Male Female Both sexes

Previous

5,437 7,367

14,400 10,545 10,850 8,178 2,871

3,368 4,299 6,068 5,473 6,812 4,779 1,589

59,648 32,388 92,036

Interim revised

5,115 7,152

14,193 10,360 10,923 8,088 2,380

3,628 4,359 5,881 5,457 6,879 4,546 1,331

58,211 32,081 90,292

Current

5,130 7,275

14,243 10,308 10,743 7,790 2,087

3,733 4,853 6,115 5,577 7,022 4,826 1,205

57,576 33,331 90,907

Low full employment

4,752 7,427

13,925 10,079 10,871 7,599 1,322

3,468 5,093 7,489 6,183 7,037 5,569 1,547

55,975 36,386 92,361

High full employment

4,862 7,452

13,928 10,076 10,874 7,575 1,367

3,549 5,104 7,508 6,226 7,084 5,632 1,579

56,134 36,682 92,816

Labor Force Projection / 57

sex

Male 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Female 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Totals Male Female Both sexes

CIVILIAN LABOR

BLS current

5,285 8,008

16,867 11,689 10,152 8,179 2,096

3,826 5,368 7,338 6,381 6,803 5,337 1,340

62,276 36,393 98,669

TABLE 6

FORCE PROJECTIONS FOR 1980 (Thousands)

Low full employment

4,699 8,230

16,300 11,497 10,429 7,906 1,015

3,328 5,619 9,317 7,044 6,272 6,299 1,765

60,077 39,641 99,718

D-S-D

High full employment

4,817 8,257

16,304 11,494 10,433 7,881 1,063

3,417 5,631 9,337 7,090 6,325 6,366 1,799

60,248 39,965

100,213

1.2 million for 1980. In order to identify the sources of these discrepancies, it is important first to imdertake a brief review of the difiFerent BLS pro- jections.

BLS Projections In 1959 the BLS pubhshed labor force projections for 1965,

1970, and 1975." The projections were subsequently revised dovmward in light of the fall in participation rates since 1960.̂ ^ Recently a third set of projections has been published which revises the estimates for 1970 and 1975 and adds projections for 1980.̂ ^ The BLS projections, which are re- ported in Tables 4,5, and 6, difiFer from the published BLS figures because of the deduction of the armed forces estimates. For purposes of identification, the 1959 BLS projections are labelled "previous"; the 1962 revisions are labelled "interim revised"; and the latest set is denoted "current."

An inference that may reasonably be drawn from the BLS reports is that the differences in the projections reflect the changing thinking of the BLS

10 Population and Labor Force Projections for the United States, 1960-1975, Bureau of Labor Statistics Bulletin 1242 (Washington, D.C.: 1959).

11 Sophia Cooper, "Interim Revised Projections of U.S. Labor Force, 1965-75," Special Labor Force Report, No. 24, Bureau of Labor Statistics (Washington, D.C.: 1962).

12 Cooper and Johnston, op. cit.

5 8 / THOMAS DERNBURG, KENNETH STRAND AND JUDITH DtJKLER

technicians about the question of the sensitivity of labor force participation to changes in employment. The interim revised projections are lower than the previous projections. This circumstance is partly attributable to changes in Census Bureau population projections. However, the most important reason for the revisions was the ". . . greater declines than previously antici- pated in labor force participation rates of young men and men aged 65 and over." ̂ * The adjustments seem, therefore, to have been based on the assump- tion that these more rapid declines in participation rates were long range and demographic in character. Had this not been the case, there would have been little justification for the changes. In tihe words of the 1962 report:

Labor force participation rates for yoiing persons have been declining for a long time. This has resulted from the continuing shift of population from farm to city . . . ; it has also reflected the rising proportion in school... .^*

The decline in participation was therefore not regarded as related to high unemployment and diminishing job opportunities. In the same report we read:

The labor force participation rates for men aged 65 and over have declined more rapidly in the last several years than was anticipated in the earlier projections on the basis of long-term reductions. . . . The 1956 break in pattern was followed by a drop of 2.5 percentage points in 1957 which can be associated with amendments in the Social Security Act. . . .̂ ^

But not apparently with tbe worst of the postwar recessions which began in that year.

These citations clearly indicate that the BLS based its interim revised projections on actual participation rates rather than on full employment participation rates. The BLS was, in effect, projecting the depressed partici- pation rates of a less than fully employed economy.

The 1965 BLS report represents a welcome turnabout even though there is considerably more form than substance to the revisions. We are now in- formed in the case of married women that

. . . the level of labor force participation among this group is to some extent a function of the availability of the desired type of job. The same situation obtains with respect to young persons still in school.̂ *'

Moreover,

The rates for some teenage groups no longer in school have been declining in

13 Cooper, "Interim Revised Projeetions. . . ," p. 1. 14 Ibid., p. 3. 15 Ibid., p. 8. 1* Cooper and Johnston, op. cit., p. 130.

Labor Force Projection / 59

recent years, possibly because they have been discouraged by growdng compe- tition for the limited number of entry jobs.̂ ^

And finally,

. . . some of the reduction in labor force activity in ages over 60 may represent in- voluntary withdrawal from the labor force because of difiBculties in finding jobs in the last few years. . . . The decline in labor force partieipation rates since 1957 for men in ages 60 and over was [therefore] reduced by 20 percent before the trend was extrapolated.^^

These citations indicate that the BLS has begun to recognize the need to allow for the efiFects of short-term variations in labor market tightness in making its projections. We contend, how^ever, that the attempt up to the present has not been adequate. Projected participation among men 60 and over is adjusted upward by an arbitrary percentage; and certain teen-age youths are assigned their 1955-1957 participation rates. Furthermore, it is not explained how adjustments were made for women even though it is exphcitly recognized that job opportvmities act as an important determinant of labor force participation. In summary, according to the BLS report:

. . . the projections made in this article more nearly represent a four percent unem- ployment situation. The 1955-57 experience was used as a guide for those age groups whose labor force participation rates appear to be constant except for some sensitivity to the economic situation. For age groups whose labor force participa- tion rates have been rising or falling consistently throughout the postwar period, it was assumed that past trends vwll continue but at a slower rate. These trends, however, were adjusted where it appeared that they might have been dampened in recent years by reduced job opportunities.^*

The last section of the latest BLS report is devoted to an explicit attempt to relate employment and unemployment to labor force participation. Utiliz- ing quarterly data beginning with the fourth quarter of 1947 and ending with the third quarter of 1963, it was found that a decline in the level of imemployment of 100,000 would cause labor force participation to rise by 60,000.^" Unfortunately, no attempt was made to use this result in making the projections or to calculate and utilize group specific derivatives. The analysis is presented as an afterthought and is used to suggest how the pro- jections, for the labor force as a whole, would have to be revised if a 3 per cent unemployment rate were to materialize in a projected year.

" Ibid., p. 136. 18 Ibid., pp. 136-137. (Our brackets.) " Ibid., p. 138. 20 Since this implies that the associated increase in employment is 160,000, the derivative

of labor force participation with respect to employment is .375. This value equals the derivative calculated by us for the period 1947-1962 (see Strand and Demburg, "Cyclical Variation. . . ," p. 383) and slightly exceeds our value (reported in Table 3) of .334 for the 1953-1964 period.

6 0 / THOMAS DERNBTJRG, KENNETH STRAND AND JUDITH DUKLER

Comparisons Since the BLS "current" projections are held "more nearly [to]

represent a foxir percent unemployment situation," the relevant comparison is between that series and our low full employment estimates. The bottom row of Tables 4, 5, and 6 shows the BLS total labor force projections to be below our figures by sizeable amounts. For 1970 the discrepancy is 1,195,000; for 1975 it is 1,454,000; and for 1980 it is 1,049,000. Although the BLS cur- rent revision is in the right direction over the "interim revised" projections, it is clear that the adjustments are not nearly large enough.

The overall totals obscure ever-widening discrepancies between the male and female totals. The BLS male projections exceed ours by 727,000, 1,601,- 000, and 2,199,000 for 1970, 1975, and 1980 respectively. This progressive divergence between the male projections is, however, offset by a progressive divergence in the opposite direction for females of 1,923,000, 3,055,000, and 3,248,000 respectively. Thus we find that in 1975 and 1980 the female fuU employment labor force may be 3,000,000 more than is presently anticipated by the BLS. However, since the BLS male projections exceed ours, the difference for the labor force as a whole falls to between 1 and 1.5 million.

To what are these enormous discrepancies attributable? We contend that the short-run employment elasticity of labor force participation has been substantially underestimated by the BLS. Since this elasticity is much higher for females than for males, the BLS female projections err on the low side. To facihtate examination of this hypothesis it is useful to compute the ratio of our projected labor force to BLS current projections and to compare these ratios with our computed employment elasticity of participation. The results are reported in Table 7, where it can be seen that in most cases in which the BLS projections exceed ours, the employment elasticity of participation is low and, when the BLS projections faU below ours, the elasticity is high. The overall elasticity for males is only .16 and the projections, except in the youngest and oldest groups, match fairly well. However, for females the elasticity is .63, which coincides with discrepancies in the total projections ranging from 6 per cent to 9 per cent for the years under consideration. As can be seen by comparing the ratios and elasticities for the individual groups, it is, in general, true that the higher the employment elasticity of participa- tion, the lower is the BLS projection relative to our own.

Nevertheless, there are several cases which do not conform to the ratio- elasticity rule. For males 14r-19 the elasticity is much higher than for males 20-24; yet for the 20-24 group our projections exceed the BLS, whereas the opposite is the case for those 14—19 years. The BLS expHcitly recognizes that

Labor Force Projection / 61

labor market tightness plays an important role in determining participation in the 14^19 and in the 65 and over groups. It would appear, however, that the BLS has gone too far in attributing declining participation in these groups to job scarcity.

RATIO OF

Age and sex

Male 14r-lQ 20-24 25-34 3 5 ^ 4 45-54 55-64 65 and over

Female 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Totals Male Female Both sexes

TABLE 7

Low FULL EMPLOYMENT LABOR FORCE TO BLS

1970 '

.95 1.01 .99 .99

1.01 .99 .81

.97 1.05 1.13 1.06 1.03 1.11 1.20

.99 1.06 1.01

CxnVHENT

1975

.93 1.02 .98 .98

1.01 .98 .63

.93 1.05 1.22 1.11 1.00 1.15 1.28

.97 1.09 1.02

PROJECTIONS

1980

.89 1.03 .97 .98

1.03 .97 .48

.87 1.05 1.27 1.10 .92

1.18 1.32

.96 1.09 1.01

PROJECTIONS

Employment elasticity of

participation

1.61 .33 .02*

—.02" .02

- . 1 8 .88

1.72 .22 .21 .39 .50

1.08 1.79

.16

.63

.32

* Not statistically significant at the S per cent level.

For the male 20-24 group our estimates exceed the BLS projections by 1, 2, and 3 per cent respectively. As can be seen from the elasticity value of .33, labor market tightness is an Important determinant of participation in the group, although this fact does not seem to have been taken into account in the BLS estimates.

In general, we may say that the BLS male projections come close to our own where participation is not affected by labor market tightness; our pro- jections exceed theirs when participation is responsive to labor market tight- ness and this is not recognized as important by the BLS; and our projections faU short of the BLS estimates when the BLS takes explicit account of short- run economic conditions.

The ratio-elasticity rule works out reasonably well for the individual female groups. The highest elasticity is in the 65 and over group, which is also the group in which the excess of our projections over the BLS values is

6 2 / THOMAS DERNBURG, KENNETH STRAND AND JUDITH DUKLER

greatest. An odd result appears in the 14-19 group, where, despite a high elasticity, our projections fall short of the BLS values. The strangest results appear in the 25-44 groups, where, even though the elasticities are relatively low, the discrepancies between the projections are very large. This is partic- ularly true of the 25-34 group, where our projections exceed the BLS esti- mates by 13, 22, and 27 per cent respectively. The fact that the discrepancy rises from 1970 to 1980 suggests that here, in part, the diflFerences are due to the way trend is projected. In Table 2, we see that the regression coefficient of participation on the reciprocal of population for this age-sex group is negatively greater than any other an coefficient with the exception of the female 45-54 group. This means that the female 25-34 group has shown a stronger secular increase in full employment participation than almost any other group. Despite the similarity in the secular rise of the full employment participation ratio of the 25-34 and 45-54 groups, the BLS's projected 1960-1980 percentage increase in the participation rate of the 25-34 group of 13 per cent (from 35.8 to 40.3) is much lower than the projected increase of 21 per cent (from 49.3 to 59.5) of the 45-54 group. Moreover, the relative population of the 25-34 group is going to increase rapidly over the period. On the basis of the population projections, the increase between 1962 and 1980 will be about 61 per cent, whereas the projected increase in total civilian population is expected to be about 35 per cent. Therefore, if our analysis is correct, the BLS projections fall short not only because of the underestimation of the employment elasticity of participation but also be- cause of underestimation of the rising trend of participation at full employ- ment.

In summary, the projections reported in this paper exceed BLS estimates by margins of 1.2, 1.5, and 1.1 million in the projected years. These diflFer- ences obscure ever-widening diflFerences between the male and female totals. The BLS projections appear not to have taken adequate account of the eflFect of labor market tightness on participation of males 20-24 and for all female groups, except those 14^19. The BLS appears to have erred in the opposite direction in the case of males 14-19 and 65 and over and females 14^19. The most perplexing diflFerence is that for the female 25-34 group, where the 1980 discrepancy of 1,979,000 (27 per cent) accoimts for 61 per cent of the diflFerence of 3,248,000 in the female totals. In the case of this group, as well as the 35-44 group, it appears that the rising trend in full employment par- ticipation, as well as the employment elasticity of participation, has been underestimated by the BLS.

Labor Force Projection / 63

Projected Participation Rates The absolute values of projected labor force direct attention

to total manpower potential and to total future employment requirements. However, the absolute values obscure the underlying determinants of labor force participation. It is therefore useful to examine the trends in participa- tion rates and relative population that tinderhe the absolute values.

The aggregate full employment labor force participation ratio is the sum of the individual group ratios. Therefore, if there is a change in the projected aggregate participation ratio, the source of the change may be traced to changes in the group specific participation ratios. Furthermore, a group specific ratio may change because the fraction of the total population (rela- tive population) in the group changes, or because of long-run behavioral changes. The eflFect of relative population may be observed by examining relative population trends, and the long-run behavior changes are reflected in changes in the group specific participation rates. Since the full employ- ment labor force participation ratio, (Lt/Pj*, is the product of relative popu- lation, (Pi/P), and the full employment labor force participation rate, (Li/Pi)", these eflFects can easily be segregated.

In Table 8 these measures are presented in order to make possible a closer examination of the factors that determine future labor force participa- tion. For purposes of comparison, we provide low full employment estimates for 1960 along with the projected low full employment values for 1970, 1975, and 1980. We concentrate, in the main, on the 1960-1980 comparison.

In the bottom row of Table 8 it may be noted that the projections imply a steady increase in the full employment participation ratio between 1960 and 1980. The source of the increase is a rise of .038 (from .194 to .232) for women, which more than oflFsets a decline for men of .032 (from .383 to .351). Thus the trend of rising full employment participation that marked the fifties seems likely to continue into the future.

Inspection of the inciividual male groups shows a relatively stable par- ticipation ratio for males 14-19. Although there is a decline in the projected participation rate, possibly reflecting more widespread school attendance and the continuing decline of agricultural employment, this decline is oflFset by an increase in projected relative population in this group. In the 20-24 group there is an enormous 45 per cent increase in the projected participa- tion ratio, which is almost entirely attributable to increasing relative popula- tion. In the 25-34 group, the participation ratio rises from .083 to .095. This projected increase occurs despite a dechne in the projected participation

6 4 / THOMAS DERNBUBG, KENNETH STRAND AND JUDITH DUKLER

rate. The rise in relative population in this group will swamp the effect of the declining participation rate. For the remaining male groups we project size- able declines in the participation ratios. In the 35-54 groups the decline is attributable both to falling participation rates and to declining relative pop-

TABLE 8

Low FULL EMPLOYMENT LABOR FORCE PARTICIPATION RATIOS, RELATIVE POPULATION, AND

LABOR FORCE PARTICIPATION RATES

Age and sex

Male 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Female 14-19 20-24 25-34 35-44 45-54 55-64 65 and over

Totals Male Female Both sexes

I960

.028

.033

.083

.089

.078

.052

.019

.020

.021

.034

.044

.043

.025

.007

.383

.194

.577

Participation ratios 1970

.031

.044

.077

.071

.073

.050

.012

.022

.030

.037

.040

.047

.032

.009

.357

.218

.575

1975

.030

.047 .087 .063 .068 .048 .008

.022

.032

.047

.039

.044

.035

.010

.351

.228

.580

1980

.027

.048

.095

.067

.061

.046

.006

.019

.033

.054

.041

.037

.037

.010

.351

.232

.583

Relative 1960

.064

.038

.086

.091

.081

.060

.056

.065

.046

.094

.099

.086

.065

.069

.476

.524 1.000

1970

.076

.051

.080

.074

.076

.060

.057

.077

.058

.086

.080

.082

.066

.076

.475

.525 1.000

population 1975

.076

.054

.093

.067

.071

.058

.056

.077

.059

.098

.071

.077

.066

.077

.475

.525 1.000

1980

.072

.055

.103

.071

.062

.057

.056

.072

.060

.106

.075

.067

.066

.079

.476

.524 1.000

I960

.445

.877

.974

.977

.958

.866

.339

.304

.466

.360

.440

.502

.383

.107

.805

.370

.577

Participation rates 1970

.402

.857

.955

.956

.956

.831

.205

.291

.526

.434

.505

.569

.486

.117

.751

.416

.575

1975

.392

.868

.939

.944

.961

.819

.148

.284

.540

.481

.543

.577

.528

.126

.739

.435

.580

1980

.380

.881

.928

.950

.976

.809

.106

.269

.550

.511

.552

.548

.559

.131

.738

.442

.583

ulation, whereas ia the 55 and over groups the stabiHty of relative population suggests that the contLnuiag projected fall in the participation ratio is mainly the consequence of a continuation of a trend towards earlier retirement and the continuing decline of overall agricultural employment.

On the basis of our projections we expect the share of the fuU employ- ment labor force represented by 14^19 year old women to remain stable. Large increases however are expected in the 20-24 and 25-34 groups. These increases are the product both of rising participation rates and rising relative population. In the 20-24 group the increase is largely due to population changes, whereas in the 25-34 group the major source of the increase is a rising participation rate. In the 35-44 and 45-54 groups we project a slight decline in the participation ratios. In both cases, projected participation rates continue to increase, but the effect is more than offset by declining relative population. For females 55-64 we project a large relative increase in the full

Labor Force Projection / 65

employment participation ratio between 1960 and 1970. The increases, how- ever, taper oflF thereafter. As can be seen from the constancy of relative popu- lation, this increase is attributable to changes in the participation rate and therefore, presumably, to long-term changes in habits and tastes. The par- ticipation rate for females 65 and over will show some increase as both relative population and participation rates rise.

At the bottom of Table 8 it may be observed that relative population for males and females at large will remain constant. It is tempting therefore to attribute all changes in the participation ratios to changing habits and tastes. However, as we have seen, there wiU be very sizeable relative population shifts within the male and female groups and these shifts wiU play an impor- tant part in determining the course of the total male and female participa- tion ratios.

High Full Employment and Projected Requirements In recent years we have come to regard a 4 per cent imemploy-

ment rate as our full employment target. The Council of Economic Advisers describes the target as "interim." Less optimistic economists, however, think it may be permanent. One reason for this pessimistic attitude is the belief that relative structural unemployment has grown worse. Technical progress, it has been argued, has marched ahead at such a rapid pace that the skills of otir working population are being rendered obsolete at an accelerated pace. Accordingly, a larger fraction of the potential working force is structurally unemployed and such unemployment is not susceptible to cure through expansion of demand.

If it really is true that it is now more difficult to reduce tmemployment than in the past, another possible explanation for this circumstance is that the composition of the labor force has changed in such a way as to render the expansion of employment potentially more costly in terms of increases in the levels of costs and prices. In comparing the year 1954 with 1962 we found that, if the imemployment rate had been exactly 4 per cent in both of those years, 36 per cent of the unemployed would have been men between the ages of 25 and 54 in 1954, whereas by 1962 this fraction would have been reduced to 19 per cent.̂ ^ In short available additional manpower has become progressively more heavily concentrated at the extremes of the age spectrum and among women.̂ ^

This development imphes that in the full employment labor force there has been a rise in the relative importance of age and sex groups which may

21 D e m b u r g and Strand, " H i d d e n Unemployment. . . ." 22 This circumstance is noted also by Telia, "Labor Force Sensitivity. . . ."

6 6 / THOMAS DERNBtmG, KENNETH STRAND AND JUDITH DUKLER

be comparatively less employable. Put differently, there has developed a growing shortage of men in the central age groups and a relative surplus of everyone else, and this may very well be one of the reasons why it may be more difficult to expand employment to satisfactory levels at present than during the early postwar years.

If this thesis possesses any merit, the very factors that render the reduc- tion of the unemployment rate below 4 per cent difficult at present ought, eventually, to operate to make such a reduction much easier in the future. As population continues to grow, the proportion of males in the central age groups will increase relative to the total population. In Table 9 it can be seen

TABLE 9

ACTUAL 1962 AND PROJECTED RELATIVE POPULATION FOR SELECTED GROUPS

Male 25-54 20-54 25-64 20-64 AU male

1962

25.0 28.8 30.9 34.8 47.5

1970

23.1 28.2 29.1 34.2 47.5

I97S

23.1 28.5 28.9 34.3 47.5

1980

23.6 29.0 29.3 34.7 47.6

that population trends will gradually be reversed. Although the relative number of males 25-54 will continue to decline for the next several years, the trend wiU have reversed itself prior to 1980 even though the proportion in this group will remain below the 1962 level. For males 20-54, the trend wiU be reversed prior to 1975 and, by 1980, relative population in this group will exceed the 1962 level. Similarly, the trend for males 20-64 vidU reverse itself prior to 1975; and for all males the reversal will take place prior to 1980.

There is a second consideration which suggests that it may be possible once again to regard a 3 per cent unemployment rate as the appropriate fuU employment target. A permanent acceleration in the rate of technical prog- ress might permanently raise the fraction of the labor force that may be said to be structurally unemployed. This could mean that the structural unem- ployment problem would remain with us more or less permanently in the absence of selective labor market policies. On the other hand, the necessary adaptations to a change in the composition of the labor force are not per- petual, but rather in the nature of once-for-all changes, since it is obviously not possible for the relative number of females or old persons in the labor force to increase indefinitely.

The point may, perhaps, be clarified by borrowing a leaf from the pages

Labor Force Projection / 67

of neoclassical growth economics. The long-run equilibrium rate of output growth is a function of the rate of population growth, the elasticity of output with respect to the stock of capital, and the rate of technical progress. An increase in the rate of technical progress wiU permanently raise the growth rate. On the other hand, an increase in the ratio of investment to income, such as would be brought about by a rise in the savings ratio, can raise the growth rate only temporarily, but in the long run the growth rate can be expected to revert to its original equihbrium level. To raise the growth rate steadily by increasing the savings ratio would require the investment frac- tion of income to become steadily larger and this is not possible, any more than it is possible for a particular group to become an ever-increasing frac- tion of the labor force.

These considerations imply that the economy ought sooner or later to be able to adapt to a change in the age-sex composition of the labor force. It is likely, for example, that employment substitution between men and women will become less imperfect over time. In addition, growing national aware- ness of the importance of education may produce improvements in the train- ing and therefore the employability of young persons. Finally, the provision of additional social services may make it possible for an increasing fraction of elderly workers to move from the ranks of the discouraged workers into voluntary retirement.

If the difficulties in reducing imemployment that have been caused by the changing composition of the labor force are reversible, the 4 per cent unemployment target may be too tinambitious as a guide to the future. If this is the case, the projector of manpower cannot simply adopt today's full employment criterion and base his projections on that criterion. He must consider also the appropriateness of that criterion for the future.

With these considerations in mind, we tum to the high full employment projections that are reported in the last columns of Tables 4, 5, and 6. The high full employment projections exceed the low full employment projec- tions by 417,000, 455,000 and 495,000 for 1970, 1975, and 1980 respectively. When compared with the BLS totals, the diflFerences become 1,612,000, 1,909,000, and 1,544,000 respectively. Most of the discrepancy between the high and low fuU employment estimates is, of course, to be found in the female totals where we observe increases of 272,000, 296,000, and 324,000, while the corresponding male increases are 145,000, 162,000, and 171,000, and are concentrated in the 14^19 and 65 and over groups.

In case it be thought that a short-fall in fuU employment labor force pro- jection of only about half a million is not so large as to render the proper selection of a full employment criterion unimportant, it should be empha-

6 8 / THOMAS DERNBURG, KENNETH STRAND AND JUDITH DUKLER

sized that the associated dijBFerences in job requirements are enormous. If total labor force in 1970, 1975, and 1980 equals the projected low full em- ployment values and the unemployment rate stands at the 4 per cent cri- terion, the associated employment levels would be 81,077,000, 88,667,000, and 95,729,000 respectively. On the other hand, if labor force totals corre- spond to the projected high full employment values and the unemployment rate stands at the 3 per cent criterion, the employment totals would be 82,326,000, 90,032,000, and 97,207,000. The additional jobs that could be had by moving to a 3 per cent unemployment rate would therefore be 1,249,000,1,365,000, and 1,478,000 respectively. Consequently, even though the projected labor force differences between high and low full employ- ment may be only half a million, the f ailiure to achieve a 3 per cent unem- ployment rate would mean by 1980 that about 1.5 million jobs would be lost. The number of lost jobs would be even greater if actual labor force happened to coincide with the BLS estimates, while full employment labor force coincided with our high, or for that matter our low, full employment estimates.