The demographic cycle and optimal schooling choices.

I. Introduction

Several studies using U.S. data have documented that individuals in large birth cohorts have experienced temporary or permanent reductions in labor market earnings [4; 11; 15; 16; 17; 20]. It has also been suggested that cohort size is important in making schooling decisions [1]. In fact, some have argued that individuals react to their position in the demographic cycle by adjusting their schooling decisions [8; 10;17;19].

Instead of examining the effects of the demographic cycle on either earnings or schooling, in this paper we construct a model that enables us to estimate the effects of the demographic cycle on both earnings and schooling. The structural link between the schooling choice equation and the labor market earnings equations also permits us to address the question of the optimality of individuals' schooling decisions.

Another contribution of this study is the use of the Korean data, since little is known about the effects of cohort size and demographic cycles outside the United States. Dooley [9] examines earnings differences across birth cohorts in Canada, Bloom, Freeman, and Korenman [7] look at the issue of generational crowding in a few O.E.C.D. countries, and Behrman and Birdsall [3] consider cohort size effects on earnings of Brazilian males. However, it is not known whether cohort size affects earnings in the same way outside these countries and whether individuals respond in a similar fashion to their positions in the demographic cycle.

In earlier studies, identification of demographic effects has been achieved by the upswing (and subsequent downswing) in birth rates caused by the post-World War II baby boom. Similarly, the baby boom in Korea that started in the 1950s after the Korean conflict offers an untapped opportunity to examine the effects of a demographic cycle on schooling and labor market outcomes.

II. Model

The basic model for this study consists of a set of three earnings equations for different schooling completion levels and a criterion function for schooling completion. The earnings equations are specified as

(1) [W.sub.j] = [X.sub.j][[Beta].sub.j] + [u.sub.j] = c, h, l,

where W is the wage, X is a vector of wage determinants such as cohort size and experience, and c, h, and I refer to college graduates, high school graduates, and the less than high school group.[1] The subscript i denoting each individual is omitted for simplicity.

An individual's choice of one of the three schooling groups is determined by the equation below:

(2) S = Y[Alpha] + f([W.sub.c], [W.sub.h], [W.sub.l]) + [u.sub.s],

where S is the level of schooling, the W's are expectations of future earnings and Y is a vector of variables other than future earnings that are likely to influence a person's schooling decision. According to equation (2), individuals consider expected returns to an additional level of schooling, which is a function of expected wages at different schooling levels, [W.sub.c] through [W.sub.l]. In the case of a binary choice such as the college enrollment decision after high school, as in Willis and Rosen [21], the functional form off(.) in equation (2) would simply be ([W.sub.c] - [W.sub.h]). The final form of the schooling equation for this study includes two expected return variables in order to accommodate three schooling levels:

(3) S = Y[Alpha] + [[Delta].sub.1] ([W.sub.c] - [W.sub.h]) + [[Delta].sub.2] ([W.sub.h] - [W.sub.l]) + [u.sub.s].

Estimation of the model follows the steps summarized below.

Step 1. Equation (3) is estimated excluding the expected return variables using the ordered probit technique:

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [Y.sup.*] includes measures of the demographic cycle, national income during the schooling years, and region, all of which can be assumed to have affected the schooling choice. These estimates are used in the self-selection correction of the wage equation below.

Step 2. Estimation of the wage equation (1) requires a self-selection correction because individuals in each group have non-randomly chosen that schooling level. Therefore, each equation would be estimated based on a self-selected sample. In the college graduate group, for example, the wage equation estimated using the self-selected sample would be

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [micro] is a limit value in an unobserved continuous scale at which the college graduate group and high school graduate group are separated. The ordered probit estimation in Step 1 produces the estimate of [micro]. The parameter estimates of equation (1) based on a self-selected sample will be biased unless the last term in equation (5) is zero.

Consistent OLS estimates of equation (1) can be obtained by including a selection correction term, [Lambda], as below:

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(7) [[Lambda].sub.j] = [Phi] ([[micro].sub.j] - [Y.sup.*][[Alpha].sup.*)] - [[Phi]([[micro].sub.j + 1] - [Y.sup.*][Alpha].sup.*])] - [[Phi]([[micro].sub.j] - [Y.sup.*][[Alpha].sup.*])],

and E(v) = 0.

The notation j + 1 denotes a schooling category which is one level higher than [j.sup.2] Thus,

(8) [[Lambda].sub.c] = [[Phi]([micro] - [Y.sup.*][[Alpha].sup.*])]/ [1 - [Phi] ([micro] - [Y.sup.*][[Alpha].sup.*]),

[[Lambda].sub.h] = [[Phi](- [Y.sup.*][[Alpha].sup.*]) - [Phi]([micro] - [Y.sup.*][[Alpha].sup.*]) - [Phi](- [Y.sup.*][[Alpha].sup.*)], and

[[Lambda].sub.l] = [- [Phi]([Y.sup.*][[Alpha].sup.*])]/ [1 - [Phi]([Y.sup.*][[Alpha].sup.*)].

Step 3. The structural parameters [Alpha] and [Delta]s in equation (3) are recovered by using predicted wages at different schooling levels as estimates of expected future earnings and re-estimating the equation.(3) The predicted wages at each schooling level are generated using the wage equation parameter estimates, individual (or cohort) specific values of the X's known at the time of the schooling choice such as demographic cycle and region, and mean values for all of the other variables such as experience, tenure and firm size.[4]

The model structure described above has several advantages:

1. The estimation of the schooling choice equation allows us to observe behavior in response to the individual's position in a demographic cycle.

2. The ordered probit estimation technique permits an examination of choices involving more than two schooling levels.

3. The selection corrected estimation of wage equation for each schooling level group yields consistent estimates of the effects of the demographic cycle that are conditioned on schooling choice. It also allows us to examine the optimality of schooling choices.

III. Data and Results

Data

The data for this study are drawn from the 1991 Korean Occupational Wage Survey (OWS). The OWS is the most comprehensive and representative source of labor market data available in Korea. Since the Korean census data do not include individual earnings information, the OWS data are the most widely used in labor market analyses.

The data are collected and compiled by The Ministry of Labor on individuals employed by firms with at least ten workers. The surveyed firms are selected by stratified sampling based on industry, region, and firm size [14]. The original data tape contains more than 400,000 observations. The represented individual worker information includes gender, age, educational attainment, occupation, and experience. Most importantly, the data provide complete earnings information which is recorded in detailed categories such as regular monthly payments, overtime payments, and yearly amount of bonus.

A ten percent random sample of the original data set was drawn and the final sample used consists of 28,833 male workers from age 16 to 53 in nonfarm occupations. Only male workers are included to focus on demographic cycle effects. Workers older than 53 are not included due to the lack of national income information during their schooling years, which is necessary for the estimation of the model.

Summary Statistics

Table I provides means and standard deviations of variables for each of the three schooling level groups. In fact, the main structure of Korean school system comprises six-year elementary school, three-year middle school, three-year high school, and either two-year junior college or four-year college.(5) Actual years of education are unavailable in the OWS. In our three schooling categories junior college graduates and college graduates are grouped together, the middle category consists of those with a high school diploma including those who did not finish college, and all those with less than a high school diploma are included in the lowest schooling group.

Table 1. Table of Means (Selected Variables)

Group                      Variable                        Mean

ALL (Schooling Equation)   FCOH                          0.06424
n = 28,833                 PCOH                         -0.08094
                           NI                            0.47979
                           REGION2                       0.36968
                           REGION3                       0.10155
                           REGION4                       0.13713
                           RC ([W.sub.c] - [W.sub.h])    0.22823
                           RH ([W.sub.h] - [W.sub.l])    0.08118

College Graduates          W                             8.63521
 n= 9,525                  FCOH                          0.06240
                           PCOH                         -0.08302
                           EXP2                          0.24042
                           EXP3                          0.25995
                           TENURE                        5.3267
                           [Lambda]                     -1.0277

High School Graduates      W   8.203780.44994
n= 13,454                  FCOH                          0.05962
                           PCOH                         -0.07737
                           EXP2                          0.23718
                           EXP3                          0.27962
                           TENURE                        5.5242
                           [Lambda]                     -0.16297

Least Schooling            W                             8.08564
n= 5,854                   FCOH                          0.07785
                           PCOH                         -0.08577
                           EXP2                          0.24838
                           EXP3                          0.38504
                           TENURE                        6.1242
                           [Lambda]                     -1.2977

Group                      Standard Deviation

ALL (Schooling Equation)        0.07036
n = 28,833                      0.06901
                                0.28487
                                0.48273
                                0.30206
                                0.34400
                                0.04383
                                0.02232

College Graduates               0.47797
n= 9,525                        0.06547
                                0.07026
                                0.42736
                                0.43863
                                4.9797
                                0.25169

High School Graduates           0.44994
n= 13,454                       0.07103
                                0.06864
                                0.42537
                                0.44883
                                5.2564
                                0.30225

Least Schooling                 0.42488
n= 5,854                        0.07468
                                0.06735
                                0.43211
                                0.48665
                                5.5605
                                0.28369

FCOH and PCOH are the sizes of the future (or following) and past (or preceding) cohorts respectively. They are constructed as follows:

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

FCOH is the natural log of the relative size of five future cohorts to five current cohorts, and PCOH is the natural log of the relative size of five preceding cohorts to five current cohorts. In general, upswing (or pre-peak) cohorts will have larger FCOH and smaller PCOH; the opposite will be true for downswing cohorts. Figure 1 shows the plots of FCOH and PCOH, along with the actual demographic cycle. Demographic data used to construct measures of cohort size and the demographic cycle are obtained from the Demographic Yearbook [18] published by the United Nations.

[Figure 1 ILLUSTRATION OMITTED]

Per capita real national income (NI) and region are included in the schooling equation as the variables other than expected future income that are likely to influence schooling choices. Unfortunately, the Occupational Wage Survey does not include individual-specific family background measures. NI will partially capture income effects and account for the long term trend in economic development. It is an average of per capita real national income figures (in million 1980 won) for the six years when the survey respondent either attended or would have attended middle school and high school. The data on national income and the price level used to convert NI to real terms were obtained from the Economic Statistics Yearbook published by The Bank of Korea [2].

Regional differences in wages and education levels are captured by a series of dummy variables. REGION2 is for Seoul, REGION3 is for Pusan, the second largest city in South Korea, and four other major cities are represented collectively by REGION4.

W is the natural log of the hourly wage which is obtained by dividing regular monthly salary by regular monthly working hours.

EXP2 and EXP3 are interval dummy variable for experience. EXP2 represents five to nine years of experience in the current occupation, and EXP3 is for 10 years or more (0-4 years is the omitted category). The OWS data provide the experience variable only in categories. The data, however, do have information on tenure. The TENURE variable is the actual number of years with the current employer. Experience and tenure variables are interacted with cohort size variables in the wage equations to allow their effects to vary over the demographic cycle.

There are two sets of variables not shown in Table I that are included in the wage equation estimation. MEDIUM and LARGE are firm size dummy variables representing 500 to 999 employees and 1,000 or more employees (10-499 is the omitted category). Also included in the wage equations are five dummy variables representing six occupation categories.(6)

Identification of the wage equations is achieved through both the nonlinearity in the creation of [Lambda] and the exclusion of NI from the wage equations. While national income when an individual was young may affect schooling decisions, it is assumed not to affect current wages.

Schooling Adjustment

The first stage parameter estimates in Table II show positive effect of FCOH and negative effect of PCOH on schooling. Over a demographic cycle, this result indicates a relatively larger amount of formal schooling by upswing (pre-peak) cohorts compared to downswing cohorts of similar size. The size and signs of the two coefficients can also be used to predict relative schooling amounts for peak and trough cohorts. Holding constant the size of future and past cohorts, the first stage estimates imply an increase in own cohort size raises the level of schooling completed.(7)

Table II. Schooling Equation Estimates

Explanatory Variable         First Stage
Constant                      0.1192
FCOH                          0.3016 (2.49)(**)
PCOH                          1.4735 (12.91)(***)
NI                            0.8854 (31.09)(***)
REGION2                       0.6102 (40.28)(***)
REGION3                      -0.1707 (5.95)(***)
REGION4                      -0.0236 (1.11)
RC ([W.sub.c] - [W.sub.h])
RH ([W.sub.h] - [W.sub.l])

n                                 28,833
Log-likelihood                   -28,607
[Chi square]                       3,063(***)

Explanatory Variable         Structural Equation
Constant                     -0.1027
FCOH
PCOH
NI                            0.8854 (31.09)(***)
REGION2                       0.4143 (18.69)(***)
REGION3                      -0.5067 (10.88)(***)
REGION4                      -0.0855 (3.88)(***)
RC ([W.sub.c] - [W.sub.h])    0.7045 (8.26)(***)
RH ([W.sub.h] - [W.sub.l])    4.1045 (7.03)(***)

n                                   28,833
Log-likelihood                     -28,607
[Chi square]                         3,063(***)

Asymptotic t-statistics in parentheses.

(***) significant at .01 level.

(**) Significant at .05 level.

Falaris and Peters [10] obtained similar results to those found in the Table II -- ". . . individuals on the upswing of a demographic cycle get significantly more schooling than those on the downswing."(8) It may be argued that our results are also consistent with the prediction of Wachter and Wascher [19]. The pre-peak cohorts, according to Wachter and Wascher, would make heavier human capital investment in order to get onto a 'fast track' which will make them compete with smaller preceding cohorts, and which will also allow greater distance between themselves and the larger following cohorts. The post-peak cohorts, on the other hand, would not be as motivated to acquire costly education which would only make them compete with more crowded preceding cohorts. Falaris and Peters, however, dispute the timing hypothesis of Wachter and Wascher because the larger amount of schooling by upswing cohorts may actually be an indication of delayed entry to the labor market.

National income has a positive and significant effect on level of schooling completed. It is not surprising that as incomes have increased, so have schooling levels.

The second column of Table II contains the structural estimates of schooling completion. In these estimates, cohort size and the position on the demographic cycle affect schooling choice through their influence on predicted future wages. The positive estimated effect of RC on schooling completion suggests that as predicted college wages increase relative to high school wages, so do schooling completion levels. The same result holds for RH, that is, schooling completion levels are positively affected by increases in the predicted wage of high school graduates relative to those with less than a high school education.

Cohort Size and Earnings

Table III presents the least squares estimates of the wage equations given in the expression (6). The t-statistics shown in the table are asymptotic t-statistics that are calculated taking into account the fact that one of the regressors, A, is estimated.(9)

Table III. Wage Equation Estimates

Variables       College               High School

Constant         6.7002                7.7133
FCOH             0.3383 (0.59)         0.7565  (7.55)(**)
PCOH            -1.6978  3.94)(***)   -0.6511  (6.40)(***)
EXP2            -0.0649 (0.91)        -0.0108  (0.75)
EXP3            -0.0325 (0.28)         0.0178  (0.79)
FCOH*EXP2        1.0170 (1.42)         0.2015  (1.22)
FCOH*EXP3        1.0694 (0.80)         0.6964  (3.57)(***)
PCOH*EXP2       -0.4479 (0.65)        -0.2592  (1.68)(*)
PCOH*EXP3       -0.2844 (0.33)        -0.3639  (1.84)(*)
TENURE           0.0923 (6.05)(**)     0.0830 (25.56)(***)
TENURESQ        -0.0031 (4.41)(***)   -0.0022 (14.69)(***)
FCOH*TENURE     -0.1806 (1.18)        -0.1943  (6.00)(***)
FCOH*TENURESQ    0.0034 (0.46)         0.0056  (3.88)(***)
PCOH*TENURE      0.3064 (2.14)(**)     0.1273  (3.70)(**)
PCOH*TENURESQ   -0.0129 (1.80)(*)     -0.0044  (2.71)(***)
OCCUP2           0.3191 (5.87)(***)    0.2425 (18.49)(***)
OCCUP3           0.5469 (8.15)(***)    0.6265 (29.24)(***)
OCCUP4           0.2342 (4.37)(***)    0.1814 (24.40)(***)
OCCUP5           0.1040 (0.92)         0.0564  (1.93)(*)
OCCUP6          -0.2084 (1.82)(*)     -0.1417 (10.64)(***)
REGION2          0.4876 (5.19)(***)    0.0652  (4.25)(***)
REGION3         -0.1918 (2.91)(**)    -0.1432 (13.21)(***)
REGION4         -0.0380 (0.80)        -0.0387  (4.33)(**)
MEDIUM           0.1023 (3.19)(**)     0.0996 (11.88)(***)
LARGE            0.1497 (5.48)(***)    0.1807 (26.12)(***)
[Lambda]         0.9213 (4.37)(***)    0.1217  (4.57)(***)

n                      9,525                 13,454
[R.sup.2]               .54                    .57

Variables       Least Schooling

Constant         7.8387
FCOH             0.6457  (4.47)(**)
PCOH            -0.5907  (4.07)(***)
EXP2             0.1256  (5.17)(**)
EXP3             0.2130  (7.40)(***)
FCOH*EXP2       -0.2288  (1.10)
FCOH*EXP3       -0.0414  (0.18)
PCOH*EXP2       -0.0630  (0.28)
PCOH*EXP3        0.2624  (1.05)
TENURE           0.0358  (7.29)(*)
TENURESQ        -0.0005  (2.36)(***)
FCOH*TENURE     -0.0771  (1.72)(*)
FCOH*TENURESQ    0.0030  (1.30)
PCOH*TENURE      0.0303  (0.65)
PCOH*TENURESQ   -0.0006  (0.26)
OCCUP2           0.2853  (4.02)(***)
OCCUP3           0.7190  (9.26)(***)
OCCUP4           0.1439  (6.06)(***)
OCCUP5           0.0344  (0.41)
OCCUP6          -0.2326 (14.02)(***)
REGION2          0.0184  (0.91)
REGION3         -0.2083 (14.16)(***)
REGION4         -0.0488  (3.72)(***)
MEDIUM           0.1575 (12.14)(***)
LARGE            0.1788 (15.60)(***)
[Lambda]         0.0975  (2.80)(***)

n                      5,854
[R.sup.2]              .42

Asymptotic t-statistics in parentheses.

(***) Significant at .01 level.

(**) Significant at .05 level.

(*) Significant at .10 level.

The presence of interaction terms makes it difficult to see the wage effects of cohort sizes directly from Table III. Therefore, Table IV reports the full wage effects, i.e., the partial derivatives of the dependent variable with respect to each of the cohort size variables. The partial derivatives are evaluated at sample means of the experience and tenure variables, and the standard errors are calculated using the covariance matrix of coefficient estimates. There is a significant wage depressing effect of larger past cohorts for all three school groups. An increase in the size of future cohorts has a positive and significant effect on wages in the high school and the least schooling groups.

Table IV. Effects of Cohort Size on Wage

Group             Effects   Mean      Standard Error   t-statistic

College           FCOH       0.0800   0.2831           0.283
                  PCOH      -0.9304   0.2113           4.403(***)
High School       FCOH       0.2513   0.0488           5.148(***)
                  PCOH      -0.3696   0.0496           7.455(***)
Least Schooling   FCOH       0.3056   0.0721           4.241(***)
                  PCOH      -0.3618   0.0723           5.006(***)

(***) Significant at .01 level.

The positive significance of FCOH and negative significance of PCOH together indicate a clear wage advantage of the upswing cohorts over the downswing cohorts. Berger [6, Figure 1] reports similar results. Among college graduates, he finds that pre-peak cohorts have higher earnings than for post-peak cohorts over the entire range of experience levels in his sample.

The coefficient for the selection correction variable [Lambda] is positive and significant in all three schooling groups. From the construction of the variable shown in (8), [[Lambda].sub.c] and [[Lambda].sub.l] are greater than and less than zero, respectively. The sign of [[Lambda].sub.h] depends on the sign of its numerator, and cannot be determined a priori. From the Table I, however, we see that the mean value of [[Lambda].sub.h] is less than zero. Since each observation in this study has three schooling categories to choose from, interpreting the selection coefficients becomes slightly different from the more common two category case. Perhaps the best way to see the selection effects is examining the mean earnings of the observations in alternative choices. For instance, the mean wage earnings of high school graduates had they chosen to acquire a college degree would be

(11) E([W.sub.c]|[X.sub.h], 0 [is less than or equal to] S [is less than or equal to] [micro]) = [X.sub.h][[Beta].sub.c] + [[Delta].sub.cs] [Lambda].sub.h],

where [[Delta].sub.cs] is the selection coefficient estimate for the college group and [[Lambda].sub.h] is the mean selection correction variable for high school graduates.

Table V contains the actual mean wages of each group and the predicted mean wages in the other two schooling levels had they chosen them, calculated based on the estimates in Table III and group mean values of the regressors, including the selection correction variable. Aside from a small difference between the high school and the least schooling predicted wages for high school graduates, the results show that the actual average wage of the members in each schooling group is higher than what it would have been had they made alternative schooling choices. This result is consistent with optimal individual schooling adjustments in response to their position on the demographic cycle.

Table V. Mean Wages in Alternative Schooling Choices

Current Group      Had They Chosen      Mean Wages

College            College              8.6352
                   High School          8.5572
                   Least Schooling      8.5694

High School        College              7.1739
                   High School          8.2038
                   Least Schooling      8.2362

Least Schooling    College              6.0510
                   High School          8.0192
                   Least Schooling      8.0856

IV. Conclusions

Recent studies have recognized the influence of the demographic cycle on formal schooling decisions. Building on these studies, we examine the effect of the demographic cycle on schooling decisions and earnings in Korea. While a couple other studies have looked at cohort size effects in Brazil and some O.E.C.D. countries, this study is the first to our knowledge to examine demographic cycle effects outside of this group of countries. Schooling levels are structurally linked to wages through the estimation of a schooling choice equation. This equation permits the estimation of cohort size effects on wages, conditioned for endogenous schooling choices. The linkage of the schooling equation and the wage equations also allows for an examination of the optimality of observed schooling choices by individuals.

It is found that post-peak cohorts choose relatively less formal schooling compared to pre-peak cohorts. Within schooling groups, post-peak cohorts also appear to have lower earnings. The results of the structural probit estimation and a comparison of selectivity corrected wages at alternative schooling levels both suggest that individuals make optimal decisions in selecting formal schooling levels.

The result that post-peak cohorts invest in less formal schooling and earn less than pre-peak cohorts is consistent with the U.S. findings of Falaris and Peters [10] and Berger [6]. Thus, it appears that the effects of the demographic cycle on schooling choices and earnings in Korea are similar to those found in the United States. (*) The authors thank John Garen and an anonymous referee for helpful comments on an earlier version of the paper. This research is supported partly by the Wasmer research grant of John Carroll University.

(1.) See the Summary Statistics subsection for detailed explanations of the schooling level categories.

(2.) The threshold value which separates high school group from the least schooling group is set to 0 by ordered probit estimation method. The threshold values in equation (8) are, from bottom to top, [infinity], 0, [micro], [infinity].

(3.) The estimation method used here follows Maddala [13, 234-56].

(4.) The assumption implicit in this approach is that individuals form their future wage expectations knowing the wage structure at each schooling level, their position in the demographic cycle, and their region. (While region at the time of the schooling choice is not available, it is most likely highly correlated with current region.) In addition, we want to evaluate wages at the same point in the career because we are attempting to proxy differences in future expected earnings at the three schooling levels with the three predicted wages. We do not want to mix differences in experience and tenure across the sample into the estimation. Therefore, we evaluate all three schooling levels at the sample means for experience and tenure variables. For cohort size interactions with experience and tenure, we use the mean values for experience and tenure and the individual's values for the cohort variables. We assume that the individual has no specific expectations about the other determinants of future earnings so we also predict earnings using the mean values of the remaining variables in the model (e.g., occupation, firm size). Finally, we do not use the selection variables in calculating predicted wages for the structural probit estimation. The approach used in developing the predicted wages for the structural probit is similar to that used by Berger [5] in the structural estimation of college major choice.

(5.) See Kwark and Rhee [12] for a discussion of the Korean educational system and a treatment of educational wage differences in Korea.

(6.) The occupation categories are, 1 (omitted) -- laborers, machine operators, 2 -- professional, technical workers, 3 -- administrative, managerial workers, 4 -- clerical workers, 5 -- sales workers, 6 -- service workers.

(7.) The own cohort size effect, holding constant the size of future and past cohorts, can be calculated in the following manner. Ignoring the variables other than the demographic cycle, the reduced form schooling equation can be written as

S = .30161n[P(+5)/P(5)] - 1.47351n[P(-5)/P(5)]

where P(+5) refers to the five future cohorts, P(-5) refers to the five past cohorts, and P(5) refers to the five surrounding or "own" cohorts. Rearranging,

S = .30161n[P(+5)] - .30161n[P(5)] - 1.47351n[P(-5)] + 1.47351n[P(5)].

Thus the partial effect of a change in S due to a change in ln[P(5)] (i.e., own cohort size) is -.3016 + 1.4735 = 1.1719. In other words, increases in own cohort size, holding constant future and past cohort sizes, leads to an increase in the level of schooling completed.

(8.) Falaris and Peters [10,566]. since their definitions of "future cohort sizes, and "past cohort size" are more exactly "size of own cohort in relation to future cohorts" and "size of own cohort in relation to past cohorts", respectively, their regression results report signs that are opposite to the results in this paper. The implications of the results in the two papers, however, are consistent.

(9.) The computation of asymptotic covariance matrix followed Maddala [13, 254-56].

References

[1.] Ahlburg, Dennis E., Eileen M. Crimmins, and Richard A. Easterlin, "The Outlook for Higher Education: A Cohort Size Model of Enrollment of the College Age Population, 1948-2000." Review of Public Data Use, November 1981, 211-27.

[2.] The Bank of Korea. Economic Statistics Yearbook. Seoul: The Bank of Korea, various issues.

[3.] Behrman, Jere R. and Nancy M. Birdsall, "The Reward for Good Timing: Cohort Effects and Earnings Functions for Brazilian Males." Review of Economics and Statistics, February 1988, 129-35.

[4.] Berger, Mark C., "Cohort Size and the Earnings Growth of Young Workers: A Reexamination of the Evidence." Journal of Political Economy, June 1985, 561-73.

[5.] --, "Predicted Future Earnings and Choice of College Major." Industrial and Labor Relations Review, April 1988, 418-29.

[6.] --, "Demographic Cycles, Cohort Size, and Earnings." Demography, May 1989, 311-21.

[7.] Bloom, David E., Richard B. Freeman, and Sanders D. Korenman, "Labour Market Consequences of Generational Crowding." European Journal of Population, May 1988, 131-76.

[8.] Connelly, Rachel, "A Framework for Analyzing the Impact of Cohort Size on Education and Labor Earnings." Journal of Human Resources, Fall 1986, 543-62.

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