The impact of changing state economic conditions on public school enrollments

Sock-Econ Plan. Sri., Vol. 13. pp 265-273 0 Pergamon Press Ltd., 1979 Printed in Great Britam

THE IMPACT OF CHANGING STATE ECONOMIC CONDITIONS ON PUBLIC SCHOOL ENROLLMENT% ROBERT P. HAGEMANN Bureau of Labor Statistics, U.S. Department of Labor, Washington, DC 20212, U.S.A.

and THOMAS J. ESPENSHADE Florida State University, Tallahassee,

FL 32306, U.S.A.

(Received 18 May 1978; revised 10 October 1978) Abstract-In this paper we present an economic-demographic regression model for projecting grades 1-12 public school enrollments. The proposed model is tested using data from the State of Florida. The results strongly support the hypothesis that state economic conditions are important determinants of 1-12 public schoolenrollments.One of the most evident policy iniglications of the results is that enrollment projections should be tied into state econometric forecasting models and should be produced as an integral part of a wider array of economic outputs.

In making projections of primary and secondary school enrollments, it is customary to consider the educational sector in a vacuum. For instance, after surveying 122 mathematical models of the educational sector, the Organization for Economic Cooperation and Development concluded that “the absolute maority of models surveyed represents the education sector by itself, that is, without establishing explicit links with any external sector” ([l], p. 58). The purpose of this paper is to demonstrate that this is an erroneous tendency. In particular, we show that a state’s changing economic conditions are important determinants of its public school enrollments at grades one to twelve,” and that neglect of such economicdemographic linkages can lead to significant projection errors. As a starting point in the development of a new method of projecting lst-12th grade public school enrollments, we propose two hypotheses which are tested empirically below. First, we hypothesize that, ceteris paribus, when the economy of a given region is performing at better-than-normal levels, enrollments in grades 1-12 will rise primarily as a result of increased net in-migration; conversely, in years characterized by abnormally poor business conditions, enrollments will either decline or remain relatively unaltered. It is further hypothesized that in grades 10-12, marginal students (i.e. marginal with respect to their desire to remain enrolled)

withdraw from school when the economic climate is favorable and remain enrolled when economic conditions worsen, ceteris paribus. For the purpose of testing these hypotheses and developing a more theoretically based projection method, we focus our attention on Average Daily Membership (ADM) data at grades 1-12 in Florida’s public schools. Excluded from the analysis are kingergarten, adult education and vocational programs, as well as enrollments in community colleges and the state university systems. The remainder of the paper is organized as follows. Jn Section 1 we briefly review the existing method of projecting public school enrollments in Florida, and note some general historical relationships between enrollment changes and the state’s economic condition. Section 2 turns to the development of a new methodology for projecting aggregate public school enrollments in grades 1-12. In Section 3 we present the emprical results. Section 4 provides some concluding remarks.

tThe views expressed are those of the authors and do not reflect the policies of the Bureau of Labor Statistics or the views of other BLS staff members. “We have not included kindergarten in the analysis of this paper because of its peculiarities, in Florida as well as in most other states. First, kindergarten attendance is not compulsory in Florida. Second, only recently have public schools in Florida been required to provide kindergarten instruction. The result has been a fairly rapid rise in kindergarten enrollments. For instance, the ratio of kindergarten to first graders has risen from 0.04 in 1%344 to 0.89 in 1975-76. For a detailed analysis of projecting kindergarten in a similar methodological vain as presented here for grades l-12, see Hagemann[Zl. bit is roughly equivalent to a five-year average of single-year progression ratios. 265

1. THE NEED FOR A REVISED

METHODOLOGY

In Florida at the present time, projections of statewide enrollments in each grade 1-12 are provided by the Office of Educational Facilities (School Facilities) of the Department of Education. The method is basically of a “curve fitting” nature, which uses a five-year average grade progression ratio to determine the following year’s enrollments. For instance, to project enrollments in second grade in 1976, average daily membership (ADM) figures in second grade in school years 1971-75 are summed and divided by the sum of first grade ADM’s in school years 1970-74. Since second graders in year! are members of the same birth cohort as first graders in year t_l, the above calculation represents a five-year progression ratio.b The observed ADM’s in first grade in 1975are then multiplied by the computed ratio to obtain the expected number of 1976 second grade ADM’s. Underlying the School Facilities’ averaging procedure is the desire to minimize random fluctuations in observed ADM’s. However, if trendsexist in single-year grade progression ratios or if school enrollments are systema-

266

R. P. HACEMANN and T. J. ESPENSHADE

tically related to underlying economic conditions, this averaging procedure is unwarranted and may lead to faulty predictions. As a preliminary indication of the extent to which enrollments are intluenced by non-random forces, consider Table 1. In the left portion are shown the annual percentage changes in ADM ratios in grade l-12, where such ratios are computed by dividing ADM’s in grade i in a given school year by the corresponding figure in grade i - 1 in the previous school year.’ On the right are the annual percent changes in three economic indicators: nondurable and durable consumption, and nonfarm investment in Florida. The data span the period 1965-75. Note that the ADM ratios in all grades l-12 declined in 1970, a year of relatively sluggish economic activity, as suggested by the behavior of the economic indicators. On the other hand, there were marked increases in the ADM ratios in grades l-9 from 1971 to 1973, associated with a recovery in all three economic indicators, especially durable consumption and nonfarm investment. In the most vibrant years, 1972 and 1973, the ratios in grades 10-12 declined markedly. Lastly, in 1974, which witnessed another decline in economic activity, the ratios in grades l-10 all declined, while those of 11th and 12th grades increased. Viewed in terms of broad aggregates, these data suggest that the levels of ADM’s at each grade may not be random, but instead are systematically related to various social and economic conditions in the state. Accurate enrollment projections should therefore be based on a procedure which incorporates those forces which operate to alter the annual size of each grade cohort in the public school system. In this paper, multiple regression techniques are used to assess the quantitative effects of the underlying forces which may theoretical cause variations in each grade’s cohort. 2.

THE DETERhfMANTS GRADE

OF FIRST TO TWELFI’H

PROGRESSION

Promotion and nonpromotion

Extensive literature exists on the determinants of school progression.’ Inasmuch as promotion and nonpromotion reflect the net effects of socio-economic characteristics of the state population, quality and quantity of school inputs, and explicit public policy such as “social promotion”, variations over time in such factors can be expected to generate trends in retention rates.’ Thus, in seeking to account for the variation over time of GPR’s at grades 1-12, allowance must be made for the annual grade-specific rates of promotion and nonpromotion. Promotion and nonpromotion may impact a grade progression ratio in a given year in two ways. First, a proportion of the students in grade i in year t will have been members of the previous grade in the previous year. The greater the proportion of students in grade i - 1 in year t - 1 promoted to i in year I, other things 7 bemg equal, the larger will be the GPR of grade i in year t. Second, those students who fail to be promoted from grade i in year t - 1 will, other things being equal, 7 reappear in grade ! m year l. The higher the proportion of students in grade i in year t - 1 not promoted, the larger will be the GPRin grade iTyear t. Since inclusion of separate &Cables-for promotion and nonpromotion in the same regression equation would likely result in multicollinearity between the two, a net promotion variable was constructed which would account for the joint effect on each GPR of both promotion from the previous grade and retention in the same grade. The net promotion rate variable associated with any GPR was formulated by adding the number of students in the previous grade (i- - 1) in the previous year (t - 1) who were promoted to grade i to the number of students in the same grade (i) in in-year t - 1 who were not promoted to grade &I, then dividinghe sum by total enrollment in grade -i - 1 in year t - 1 and multiplying by 100. The larger is net promotion, the higher we expect the GPR to be, ceteris paribus.

RATIOS

We begin by defining a grade progression ratio (GPR) as the level of enrollments in grade 1 in a given year divided by the level of enrollments in grade 7i - 1 in the previous year. For first grade, resident state buths in year t - 6 are used as the denominator.“ In any given school year, there are twelve GPR’s computed as just described. With n years of enrollment data, we obtain a time series consisting of Y n - 1 annual observations on each grade’s progression ratio. Each grade progression ratio is assumed to be a function of a set of economic and demographic factors, each of which operates to inflate or deflate the GPR in each school year. The remainder of this section is devoted to a discussion of these potential influences. ‘For grade 1, ADMratios were computed by dividing observed first grade ADM’sin the given school year by resident births six years earlier. ‘?his assumes that the proportion of six year old first graders remains fairly constant over time. Also the practice of linking GPR’sto annual changes in the explanatory variables implicitly assumes that changes in these ratios are confined largely to the preceding year. However, the size of this birth cohort may in fact have been altered during the longer interval between birth and age six. ‘See, for example, Coleman et al. [3], Nam et nl. [4], Conhsk[S], Masters[6] and Tuckman[‘l]. ‘Retention is used here as synonymous with nonpromotion.

Interstate migration

Migration to Florida has, for the past several decades, contributed substantially to the growth rate of the population. In fact, interstate migration has had an increasingly positive effect on the population growth rate. For instance, for the period 1970-75, migration accounted for 93.7% of the total change in Florida’s population, compared to a 63.1% contribution during the l%Os ([2], p. 38). The significance of migration to our problem is clear; migration to the state increases public school enrollments if the migrants consist of parents with school-age children who are enrolled in public schools. Although migration to Florida tends to affect the older age groups most heavily, estimates of the age distribution of migrants to the state between 1970 and 1975 indicate that age groups 5-9 and 10-14, which were expected to decline independently of migration, were heavily influenced by it. The age group 10-14 actually increased by 21.4% while the group 5-9 declined by only 4.7% instead of 17.6% had migration been zero. In the 15-19 year age group, whereas the increase due to natural increase exclusive of migration would have been ll.O%, the actual growth was an estimated 39.4% ([2], pp. 3940). In accounting for migration’s impact on each GPR, however, one encounters the problem of data limitations; annual age distributions of migrants are unavailable.

1

z: -1:63 2.08 2.44 0.10 -2.28 -0.81

-0.31 0.11 0.42

2

0.20 0.60 0.20 0.20 0.89 -1.75 1.89 0.68 0.10 -2.97 -0.53

3

5

0.30 0.00 rl.20 0.60 -0.20 0.50 0.30 0.10 0.50 0.20 -1.40 -1.68 1.20 1.52 1.78 1.20 1.38 0.58 -2.04 -2.32 0.30 -0.40

4

0.30 0.50 -0.20 0.60 0.30 -1.58 0.60 0.90 0.79 -2.64 0.50

-0.38 0.67 -0.76 0.38 -0.48 -1.24 0.19 0.77 0.77 -3.23 0.88 0.62 1.24 -0.71 2.26 -0.20 -0.81 1.62 1.40 1.97 -3.19 1.00

8 0.10 0.41 0.20 1.12 0.40 -0.50 2.83 0.49 0.98 -1.36 0.98

9 0.42 0.94 -1.24 1.78 -0.51 -0.41 2.07 -1.73 -0.41 -0.42 2.08

10

-X -0:56 0.79 -2.80 -0.35 1.97 0.68

-0.45 0.56 -1.11

11 -0.11 0.22 -0.89 -0.11 -1.01 -0.57 -0.57 -4.12 -1.00 0.36 2.64

12

The time periods correspond only approximately. since the percent changes in ADM ratios correspond to school years (eg. 1965 figures for school grades refer to the change from 1964-65 to 1965-66), while the economic indicators are from actual years. There is thus some overlap. For general ourposes, this is not too critical.

Percentages not calculable because data far previous years were unavailable.

*

NC

4529.9 5078.8 5553.1 7083.7 8581.0 9909.9 10761.6 11559.9 13035.4 14593.9 15657.1 12NF2 9:34 27.56 21.14 15.49 8.59 7.42 12.76 11.96 7.29

2739.0 2890.0 2972.8 3528.2 4069.6 4402.2 4977.7 6186.3 7743.8 7287.7 6801.8 5.51 2.87 18.68 15.35 8.17 13.07 24.28 25.18 -5.89 -6.67

NC

CONSUMPTION kon-Durable Durable Amount % Change Amount % Change

ratios and Economic Indicators*

ADM ratios were obtained from "Preliminary Forecasts for 1977-78 of FTE's at K-12 in the Public Schools: State of Florida," by Thomas J. Espenshade et.al., (Septelrber, of the 1976): Table 3. The economic data were extracted from the EconGirReport Governor: Florida, (August, 1976): Table 12, p. 81.

-3.03 -0.09 -0.09 -0.28 0.83 -1.46 0.09 1.39 2.29 -1.43 -1.72

SOURCE:

;z 1970 1971 1972 1973 1974 1975

1965 1966 1967

YEAR __--

SCHDOL GRADE 6 7

Table1.AnnualpercentchangeinADM

2258.8 2439.3 2518.6 3014.4 3874.6 4361.4 5002.9 6789.1 8748.0 9620.7 8678.4

7Ni9 3:25 19.69 28.54 12.56 14.71 35.70 28.85 9.98 -9.79

NON-Farm INVESTMENT Amount % Change

268

R. P. HACEMANN and T. J. ESPENSHADE

Indeed, were such data available, determining the effects of migration on public school enrollments would be a relatively straightforward matter. Circumvention of these data deficiencies, not their neglect, is the major objective underlying the methodology developed in this paper. The approach adopted here derives from the theoretical and empirical determinants of interstate migration. While people migrate for varied and often complex reasons, some generalizations are possible.’ In a 1966 issue of Current Population Reports, an effort was made to determine the reasons why people moved between March 1962 and March 1963[10]. One of the dominant findings was that interstate migration is generally related to employment factors. For 18-64 year olds, 69.4% of the “between-state” moves were for job-related reasons, while only 3.9% were for housing reasons; 12.7% were for family status adjustments; and 13.1% for “other reasons” ([lo], p. 9). Further support for the economic motivation in interstate migration is found in numerous studies in which migration is viewed in a “push-pull” context.” That is, interstate migration is . . . interpreted largely as a function of man’s response to situations of economic stress and push factors.. . , and pull factors relating to economic opportunities elsewhere, amenity differentials, etc. ([8], p. 55). Rising income and falling unemployment tend to attract migrants, while falling income and rising unemployment induce out-migration. Since variations in economic conditions in Florida may be expected to generate corresponding variations in annual rates of migration, each grade’s progression ratio can be linked directly to the economic determinants of migration. The problem, then, is to select the appropriate predictors of interstate migration. Since previous research has emphasized income and employment as significant determinants, we have chosen two such measures. Theoretically, one would at first consider some per capita measure of income to be most relevant, since migration is an individual decision. The draw back to median or per capita income in aggregate models of migration, however, is that such measures tend to conceal income changes in particular industries or occupa-

tions. Since migration flows are likely to be induced by income changes in thriving industries and occupations, per capita measures which may conceal such changes are deemed inappropriate. Also on theoretical grounds one might argue that income in Florida relative to the sending region is a more accurate specification of the income-incentive to migrate. Again, the level of aggregation in the present study suggests that such an approach would be unsuccessful. Since the region of origin of migrants is defined here as the remainder of the U.S., relative income would fail to reflect the regional differences within the U.S. itself.’ The measure which we have selected as a proxy for the income-incentive to migrate is the percentage deviation (with a one-year lag) from the long term trend of real aggregate Florida personal income.’ Positive (negative) deviations from the trend should be associated with higher (lower) rates of net in-migration and, hence, with positive (negative) changes in each grade’s progression ratio. Income alone, however, is not the sole economic determinant of interstate migration. Employment opportunities also influence a migrant’s decision to move. Thus, some measure of the condition of the labor market must be used to account for the separate effect of employment prospects on the rate of in-migration. As a measure of the employment conditions in the state, we have selected the annual overall rate of unemployment in the state.k Lower (higher) levels of unemployment, reflecting a favorable (unfavorable) labor market, should attract (discourage) migrants in the labor force ages, and hence be associated with higher (lower) levels of each GPR.’ Dropout rate

Economic theory tells us that an important cost of schooling is represented by the foregone earnings that could be obtained from full-time employment.” As the opportunity cost of schooling rises (falls), the dropout rate of post-sixteen year-olds should correspondingly rise (fall), ceteris paribus. Such variations over time in the dropout rate will in turn generate changes in the upper-secondary grade progression ratios. As in the case of migration, accurate data on dropout gFor two excellent surveys of the literature,see Shaw[8], and rates are not available, which necessitates the use of an Greenwood[9]. appropriate proxy variable. In addition, since both *See, for example, Gallaway et al.[ll], Raimon[lZ], migration and the dropout rate may affect (in opposite MeInnis[13],Fabricant[14]and Gallaway[lS]. directions) enrollments of post-sixteen year olds, a proxy ‘When per capita income in Florida and relative per capita that would capture the effect of the dropout rate inincome were alternatively used in the regressions, neither dependently of the influence of migration is desirable. measure performed satisfactorily. Since, in the short-run, the greatest cause of school‘The deviation is lagged for two reasons. First, potential leaving is likely to be the opportunity cost of schooling, migrants are likely to at first make observations of conditions at a the approach taken here is to link the 10-12 grade potential destination, and then decide whether or not to migrate. progression ratios directly to trends in such costs. Second, failure to lag income can lead to serious simultaneous equation bias, since incoming migrants increase aggregate Initial attempts to capture separate effects of migration demand, which in turn has a positive effect on income (see and the dropout rate, through the use of specific Greenwood[9]). measures of the trend in the opportunity cost of school‘See the research referenced in footnotes g and h. ing,” proved unsuccessful. This is due in large part to the ‘Other climatic and environmental factors which have been correlation between the income and employment varifound to be important determinants of cross sectional variations ables used to account for migration’s influence on the in interstate migration can be neglected in the present time-series GPR and proxies for the trends in the opportunity cost analysis. of school. Favorable economic conditions for potential “See Schultz[l6], Becker[l7], Parsons[lb], Schweitzer[l9] migrants also imply relatively favorable opportunities for and Edwards[ZO, 211. teen-agers who are considering dropping out before “As proxies for the trend in the opportunity cost of schooling, graduation. we used: (1) The percentage deviation from the long term trend The decision was therefore made to use variables in retail and wholesale trade; and (2) the annual unemployment which measure the net effects of both migration and the rate of 16-19 year olds for the US., the latter not being available for Florida. dropout rate on the upper secondary GPR’s. Specifically,

The impact of changing state economic conditions on public school enrollments

the percent deviation of real aggregate personal Florida income from its trend, over the course of the two school years spanned by each GPR was used as a predictor of the net effects of migration and the dropout rate on 10-12 grade progression ratios. The percent deviation was not lagged for these grades, on the assumption that postsixteen year old high-schoolers are free to withdraw at any time during the scholastic year. As a proxy for the net employment effects (of migration and the dropout rate) on 10-12 grade progression ratios, the average rate of unemployment in Florida during the school years covered by each GPR was used. Other factors There remain a number of additional factors which might be influential in causing variations in grade progression ratios. First, any GPR might be reduced as a result of deaths to members of the grade cohort. However, not only are death rates extremely low among the school-age population, but there is little annual variation in such death rates, and hence there is likely to be negligible explanatory power attributable to mortality. Second, while school attendance in Florida is mandatory between ages seven and sixteen, some students may be compelled to withdraw temporarily from school due to critical illness. But, as with mortality, dropouts for medical reasons are likely to remain a relatively constant proportion of each age group. While epidemics would render such a conclusion erroneous, medical advances in the field of immunization have reduced the likelihood of widespread diseases to a minimum. Thirdly, the mobility of students between the public and private educational sectors represents an additional potential cause of variation in GPR’s. More precisely, a changing rate of net private-to-public school migration could generate fluctuations in the public school GPR, everything else constant. However, lack of appropriate private school data precludes the inclusion of this factor in the regression equations. 3.EMPIRICAL RESULTS

On the basis of the discussion in Section 2, two separate regression specifications are proposed: one for grades l-9, and a second for grades 10-12. The estimating equation for grades l-9 is: e,’ =pO+p,INC,

tP2FU, t&NP,

t u1

“ADM’s are used as a measure of enrollments in all grades l-12 for a number of reasons. First, it avoids the problem of double-counting, since a student may not be a member of two different schools at the same time. Second, ADM’s provide a continually varying measure of enrollments, since students may add to or subtract from the membership. And third, the construction of a historical series of GPR’s mandates definitional consistency throughout the sample period. Again, ADM’s provide such compatibility from year to year. Data on Average Daily Membership were extracted from various issues of [22]. PData on persona1 income and unemployment rates were obtained from the Department of Administration of the State of Florida. The authors are grateful to William James. @Promotion and nonpromotion rates were obtained from various issues of [23]. ‘There were thus 12 observations at grades 2-12. For first grade, there were only 9 observations, spanning the period 1%768 to 1975-76. There was an apparent structural shift in 1966 (see Hagemann[2]) which warranted a discarding ‘of first grade observations from 1963-64 through 1966-67. “This section of the paper has been significantly improved over its earlier version. The authors wish to thank an anonymous referee for the insightful suggestions.

269

where e,i = for first grade, the ratio of ADM’s in first grade in school year _tdivided by resident births in year t_6; for grades 2-9, e,’refers to the ratio of ADM’s in grade i in year _tdivided by ADM’s in grade i - 1in year r_1;O ZNC, = the percentage deviation from the trend in real aggregate personal income in Florida, lagged by one school year;p FU, = the overall Florida unemployment rate during school year 1; NP, = the “net promotion” rate associated with grade i in school year _t4i = grades 1,2,. . . (9; and U, = a random error term. From the earlier discussion, p,, and ps are expected to be greater than zero, while pz should be negative; the sign of POis ambiguous. The specification of the 10-12 grade regression equations is similar to that of l-9grades, excepting for a change in the time span of the economic variables: e,’ = POf PJNC, t p2FlJ1 t psNPr t uI where e,’and NP, are as deened for grades l-9; INC, = the percentage deviation from the trend in total real income, computed over both school years spanned by e,i; FU, = the overall rate of unemployment in Florida averaged over the two school years spanned by ei; i = grades 10-12; and u, = a random error term. We expect /33to be positive. However, since ZNC and FU are simultaneous proxies for the effect of state economic conditions both on migration to Florida and on the high school dropout rate, and since these effects work in opposing directions, the signs of /I1 and /J2are, a priori, ambiguous. We have no expectations about the sign of &+ Empirical results The regression equations were estimated from data

beginning with the academic year 1963-64 and ending with 1975-76.’ The results are shown in Table 2. In general, the hypotheses receive strong empirical support. the regression specifications explain from 50 to 98% of the variation in 1-12 grade progression ratios. At the lqwer grades (l-9), the percentage deviation of personal income from the trend is properly signed in every grade except ninth, and is statistically significant in 6 of these. Trend deviations in income are positively correlated with enrollments at grades 1-9. The unemployment rate has the expected negative sign in 7 of the equations, and is statistically significant in a majority of these cases. Decreasing unemployment is associated with increasing enrollments at l-9. The net promotion variable is properly signed in all grades 1-9, and is significant in 6 of these. At the higher grades (lO-12), unemployment continues to have a negative influence on grade progression ratios. However, positive deviations of Florida personal income from its historical trend are now associated with declines in GPR’s at the two highest grades, suggesting perhaps that the negative dropout rate effect dominates the positive migration effect. Predictive ability of the model”

Although the empirical results strongly support the hypothesis that economic conditions are significant determinants of enrollment trends, will the proposed methodology yield more accurate projections than can be obtained from the School Facilities method? Whether or not the incorporation of quantitative estimates of the forces which influence enrollment trends is preferable to an averaging procedure depends, of course, upon the relative predictive accuracies of each method.

270

R. P.

HAGEMANNand T. J. ESPENSHADE

In order to assess the relative predictive abilities of the two methods, we have made both ex ante and ex post projections of ADM’s, by grade, and compared the performances of each method. We discuss first the ex ante projections, and turn next to the ex post comparisons. .Ex anre projections were made for only one academic year, 1976-77, for which there were observed Full-Time Equivalents. These were converted to make actual enrollments comparable to the _projections.’ Next, “School Facilities” projections were obtained by applying the averaging procedure, discussed in Section 1, to observed ADM’s in the preceding years.” Lastly, the regression estimates described above were used to predict each grade’s progression ratio in 197677, and these were then multiplied by observed ADM’s in the preceding grade in school year 1975-76 to obtain projections of ADM’s in each grade in 1976-77.” As with most regression-based forecasting procedures, some or all of the exogeneous variables are not known with certainty, and must first be forecasted in order to obtain forecasts of the endogenous variable.” For income and the un-

employment rate forecasts were obtained from data contained in Economic Report of the Governor: 1977 Economic Forecasts [26].” For the net promotion rate, for which no forecasts could be found, extrapolations were required. Scattergrams for each grade suggested that no precise trend existed in the net promotion rates. Even splitting the net rate into its two components (see Section 2) provided no solution. Although a parabola would fit each separate component of most grades’ net promotion rate, such functions yielded unreasonable predictions. Therefore, rather than making any assumptions regarding promotional trends, the sample period mean of each grade’s net promotion rate was used in the projections. The ex ante projection errors (in percentages), for each grade and the total 1-12, are shown in the last column of Table 3 (School Facilities method) and Table 4 (Regression method).Y In order to facilitate comparison, we have affixed a superscript “L” to the School Facilities errors which are lower in absolute value than the corresponding ones in Table 4. While the regression method yields a substantially more accurate ex anfe projection for the total l-12 (0.27% vs - 1.13%) than does the averaging procedure, on a grade by grade basis the same ‘The conversion was performed in the following manner: conclusion cannot be drawn. The regression method performs better in six of the first seven grades, while the ADM$_,, = FTE;w, X$& averaging procedure yields more accurate projections in all other grades. “That is, School Facilities ADM projections for 1976-77were It is surprising, given the rather convincing evidence obtained as follows: from the regression results, that the proposed methodology fails to significantly out-perform the averaging procedure. However, as noted earlier, this could result from model mis-specification or inaccuracies For grade 1, the second term in brackets was obtained by in the forecasts of the independent variables. As summing resident births from I%5 to 1%9. the resultant ratio Stekler[24] points out, in order to evaluate the model in was then multiplied by resident births in 1970to obtain first grade the absence of errors in the values of the independent ADM’s in 197677. variables, one should consider ex post forecasts.’ We “That is, ADM’s from the regression method for 1976-77were therefore computed ex post projections of ADM’s in obtained as follows: each grade for the school years 1970-71 to 1975-76, using 1 each method. The percentage errors are shown in the ADM;c,, = ADMS;!,ex GPRjc,, first six columns of Table 3 (School Facilities method) where CiPR& refers to the predicted grade progression ratio. and Table 4 (Regression method). The School Facilities For grade one, ADM& was replaced by resident births in 1970. ex post projections were obtained by using observed “This, indeed, represents a limitation of a regression approach ADM’s in the necessary earlier years. For the regression to projecting enrollments. To the extent that forecasts of the method projections, the actual values of the independent independent variables are subject to error, projection inac- variables were used to predict the grade progression curacies may result from errors either in the model itself or in ratios. These were in turn applied to the observed ADM’s incorrect forecasts of the exogenous variables. Thus, projections in the preceding grade at 7t - 1 in order to obtain the obtained from the regression approach will only be as good as projections. As for the comparison of ex ante projection the forecasts of the independent variables, assuming, of course, errors, we have affixed a superscript “I,” to the School that the model is appropriately specified. Ex post forecasting errors, on the other hand, will reflect Facilities errors which are lower in absolute value than model mis-specification alone, since values of the independent those generated by the regression method. Of the 72 variables are known with more certainty. For a more detailed individual grade projections over the period 1970-71 to discussion of these issues, see, for example, Stekler[24] and 1975-76, the regression method generated smaller errors Intrilligator[25]. than did the averaging procedure in 55 (76.4%) of the ‘A detailed description of the procedure used to obtain the cases. Looking at the performance of each method at the forecasts of these exogenous variables can be found in aggregate level (bottom row) the regression method perHagemann ([2], chap. IV). forms better in four of the six years. Also, note that in YThe percentage errors were computed according to the fol- each year the regression method yields smaller errors in lowing formula: a majority of the grades. Percentage Error =

ADM’- ADM’x loo ADM

where ADM’ refers to observed ADM’s in grade i, and ADti refers to predicted ADM’s in grade i. ‘It would have been preferable to perform an ex post forecast for a year preceding the sample period, but the necessary ADM data were not available.

4. CONCLUSION consequences of failing to project primary and secondary school enrollments accurately at the state level are all too easily imaginable: congested or half-filled classrooms, shortages or surpluses in educational personnel, and dilapidated and obsolete equipment. The implications for the quality of education are obvious. The

The impact of changing state economic conditions on public school enrollments

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ho

“,,

ma

0

”

da

“a

r: ~

R. P. HAGEMANNand T. J. ESPENSHADE

272

Table 4. Ex oost and ex an& oroiection errors: Regression Method (Numbers Bue Er P

IT

x Ante

Grade /il970-71 11971-72 11972-73 I1 II I I 1

II -0.53

-0.32

0.16

1

974-75

L975-76

976_77

0.83

-0.19

0.17

0.29

2.14

L

II 2

0.17

I

2.04

0.66

-0.90

0.76

1.14

I

1.24

-0.26

-0.25

0.10

-0.15

-0.41

0.08

0.73

-0.75

0.81

0.87

-0.33

0.65

0.61

-0.50

0.51

0.84

-0.46

0.16

0.37

-0.64

0.66

1.01

-0.47

0.15

0.81

-0.76

0.68

-0.38

-0.01

0.20

0.53

-1.22

1.22

3.44

0.40

0.87

-0.01

-0.06

0.26

-0.26

-3.73

II -0.78

1.24

-0.37

0.08

-0.37

-.ll

-1.01

-0.25

-0.18

0.28

-0.23

-4.24

-0.04

-0.09

-0.44

0.10

-5.26

0:35

0.35

-0.47

0.40

0.27

II -1.11

II 3

II -0.35

4

II -1.24

II

I

II 5

II -1.38

II 6

II -0.79

II 7

II -0.75

II 8

II -1.31

II 9

II

II 10

II 11

11 -0.67

0.98

12

II -0.12

1.31

II

II ' 'otal I I -0.74 -12 II

Lpositive

error

I

I I 0.27

L

L enotes

an underestimate;

In this paper, we have proposed a new method for projecting state-level public school enrollments at grades 1-12. The empirical results strongly support the hypothesis that enrollment trends are very sensitive to changing state economic conditions. Comparison of the ex post (and ex ante, in part) performance of the School Facilities and Regression Methods suggests the superiority of the latter. It must be admitted that the shortage of degrees of freedom represents a shortcoming of the empirical results. Additional years of evidence are needed before conclusively declaring the regression approach the superior method. Nevertheless, the implications of the results presented in this paper are clear. Enrollment projections should be removed from the “demographic vacuum” within which they are commonly obtained. Forces which are assumed random, and thus “smoothed out” in an averaging procedure, are clearly systematic, and must be quantified. Since most states rely on econometric forecasting models to anticipate future state economic conditions, we suggest that enrollment projections be tied into these models and be produced as part and parcel of a wider array of economic outputs.

3. J. S. Coleman et al., Equality of Educational Opportunity. U.S. Government Printing Office, Washington, D.C. (1966). 4. Charles R. Nam, A. Lewis Rhodes and Robert Herriott, School retention by race, religion and socioeconomic status. J. Human Res. 3, 171-90 (1967). 5. John ConIisk, Determinants of school enrollments and school performance. J. Human Res. 4, 140-57 (1%8). 6. Stanley H. Masters, The effect of family income on children’s education: some findings on inequality of opportunity. J. Human Res. 4, 158-75 (1%8). Howard P. Tuckman, High school inputs and their contribution to performance. J. Human Res. 6, 490-509 (1971). R. Paul Shaw, Migration theory and Fact. Bibliography Series No. 5. Regional Science Institute, Philadelphia (1975). Michael J. Greenwood, Research on internal migration in the United States: a survey. J. Econ. Literature 13, 397-433 (1975). 10. U.S. Department of Commerce. Bureau of the Census. Current Population Reports. Population Characteristics. Reasons for moving: March 1%2-March 1%3. Series P-20, No. 154. U.S. government Printing Office, Washington, D.C. 22 August, 1%6. I

1: Acknowledgemenfs-This research was supported by the Department of Education, State of Florida, Contract No. 770016, and by the Board of Regents STAR Project RS-176. The authors wish to thank Professors Howard Tuckman, Charles Nam, and Mickey Burnim for their helpful suggestions at various stages of research. We are also grateful to an anonymous referee for some valuable suggestions.

1.

14. 15.

REFERENCES 1. Organization for Economic Cooperation and Development. Mathematical Models for the Education Sector: A Survey. O.E.C.D., Paris 1973. 2. Robert P. Hagemann, An economic-demographic regression model for projecting K-12 public school enrollments: the case of Florida. Unpublished Ph.D. dissertation, Florida State University, 1977.

16. 17. 18.

L. E. Gallaway, R. F. Gilbert and P. E. Smith, The economics of labor mobility: an empirical analysis. Western Econ. J. 5, 211-223 (1967). Robert L. Raimon, Interstate migration and wage theory. Rev. Econ. Statist. 44, 428-438 (1%2). M. McInnis, Provincial migration and differential economic opportunity. In: Migration in Canada (Ed. by L. 0. Stone), D.B.S., Ottawa (1%9). Ruth A. Fabricant, An expectational model of migration. J. of Reg. Sci. 10, 13-24 (1970). L. E. Gallaway, Interindustry Labor Mobility in the United States 195769. Research Rep. No. 18, Social Security Administration. U.S. Government Printing Office, Washington, D.C. (1%7). Theodore W. Schultz, Capital formation by education. J. Polit. Economy 68,571-583 (l%O). Gary S. Becker, Human Capital. Columbia University Press, New York (1%4). Donald 0. Parsons, The cost of school time, foregone earnings, and human capital formation. J. Polk Economy 82, 251-266 (1974).

The impact of changing state economic conditions on public school enrollments 19. Stuart 0. Schweitzer, Occupational choice, high school graduation, and investment in human capital. .I. Human Res. 6, 321-332. 20. Linda Nasif Edwards, The economics of schooling decisions: teenage enrollment rates. .I. Human Res. 10, 153-173(1975). 21. Linda Nasif Edwards, School retention of teenagers over the business cycle. J. Human Res. 5, 20&208 (1969). 22. Florida Department of Education. Annual Principals’ Report. Selected issues, 1%3-75. 23. Florida Department of Education. Promotion and NonPromotion in Florida Public Schools, Division of Elementary

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and Secondary Education, Research Reps. Selected issues, 1%3-75. 24. H. 0. Stealer, Forecasting with econometric models: an evaluation. Econometrica 36,437-463 (1968). 25. Michael D. Intrihigator, Econometric Models, Techniques and Applications. Prentice-Hall, Englewood Cliffs, New Jersey (1978). 26. Florida Department of Administration. Economic Report of the Governor: 1977 Economic Forecasts. Tallahassee. Jan. 1977.