# School lunch program participation.

School Lunch Program Participation

The National School Lunch Program (NSLP) is the largest of the Child Nutrition Programs administered by the United States Department of Agriculture's Food and Nutrition Service, both in terms of funding and number of children served. An average of 27 million children per day were served lunches through the NSLP in 1979. Following program changes and substantial funding reductions embodied in the 1980 and 1981 Omnibus Budget Reconciliation Acts (OBRAs), the number of lunches served dropped to 25.8 in 1981 and 22.9 million in 1982 (United States General Accounting Office 1984). The reductions in participation occurred despite the onset of a recession, which should have signaled an increase in participation. While such decreases in school lunch participation are of concern to hunger groups and legislators, the extent to which the OBRA legislation contributed to the participation decline is unknown. Closing that information gap is the specific focus of this research. More broadly, the objective is to determine what factors affect school lunch program participation and thereby inform future public policy.

The problem of obtaining accurate estimates of the determinants of NSLP participation has two dimensions. First, the effects of demographic and economic changes must be isolated to identify correctly the effects of specific program changes on participation. During the period under study, 1979-1981, school enrollments declined in many areas of the country and, as already noted, the economy headed into a deep recession. Second, required information regarding the number of students eligible for subsidized school lunches is not directly reported and must be estimated. The most suitable data for determining eligibility and for analyzing program participation are household-, student-, and school-level data. Unfortunately, high collection costs preclude frequent acquisition of such data.

The two-dimensional problem of obtaining an accurate picture of school lunch program participation is addressed by developing and implementing a two-stage model of county-level program participation in New York State. The data for New York counties are reasonably accessible and similar data should be available in other states. In the crucial first stage of the model, pre- and post-OBRA eligible populations are predicted by estimating poverty rates for each county. The second stage utilizes those predictions in an empirical model of county program participation designed to distinguish the effects of legislative changes from those associated with demographic, economic, and behavioral changes. Background material on the school lunch program and the OBRA legislative changes are presented first, followed by the empirical methodology, results, and conclusions, in turn.

THE NATIONAL SCHOOL LUNCH PROGRAM

The National School Lunch Program was established in 1946 with the passage of the National School Lunch Act. The primary objective of the legislation was to assist in providing adequate nutrition for the nation's school children. The Act established an entitlement to Federally subsidized nutritious lunches for all school children. The subsidies were considered an investment in the health, education, and future productivity of children throughout the nation. The 1946 Act also included funds for purchasing and distributing surplus farm commodities to schools. By incorporating this politically acceptable means for disposing of government-purchased agricultural surpluses, the appeal of the legislation was broadened.

The operation and funding of the lunch program evolved over the years. Currently, three different categories of lunches are served: free, reduced-price, and full-price. Lower-income students apply and eligibility is determined for the free or reduced-price lunches according to family size and income. All students are eligible for a full-price lunch. A Federal per-meal subsidy or reimbursement is provided to schools for all lunches. Free lunches receive the largest reimbursement, while full-price lunches currently receive a minimal reimbursement. Agricultural surplus commodities are provided in legislated amounts for schools to use in the preparation of all meals. The importance of the cash reimbursement rate has increased during the life of the program with a corresponding decline in the use of surplus commodities.

Schools are subject to a number of regulations concerning the type and amount of food they must serve in order to qualify for the program. The school lunch meal pattern, known as the Type A lunch, must include five items: "a specific amount of meat or meat alternate, two or more vegetables and/or fruits, whole grain or enriched bread or bread alternate, and fluid milk as a beverage" (United States Department of Agriculture, Food and Nutrition Service 1985). This combination of foods and the quantities stipulated is designed to satisfy one-third of the Recommended Daily Allowances (RDA) for school children. There is evidence that lower-income students depend on their school lunch for one-third to one-half of their daily calorie intake (Parker 1982).

OBRAs of 1980 and 1981 reduced funding for a number of social programs, including the school lunch program. OBRA 1981 reduced school lunch funding more than OBRA 1980, and, taken together, they account for significant changes in the program. Funding reductions were accomplished mainly by cutting the Federal per-meal reimbursements paid to schools for the full- and reduced-price lunches and by tightening the eligibility criteria for those families applying for subsidized meals. The major program changes are described in Table 1.

OBRA 1980 effectively tightened income eligibility criteria by substituting the poverty line definition used by the Office of Management and Budget (OMB) for that of the United States Department of Agriculture (USDA). As indicated in Table 1, OBRA 1981 simultaneously expanded free meal eligibility and constricted eligibility for reduced-price meals. More stringent income verification procedures also were established to determine the eligibility of applicants better.

Under prior legislation, reduced-price lunches had a maximum price of $0.20. Schools charging a price less than that maximum received an extra subsidy of up to $0.10 per reduced-price meal. New york State schools, taking advantage of this extra subsidy, charged eligible students $0.10 for reduced-price meals in 1979. With the elimination of this subsidy in OBRA 1980, the reduced-price lunch price increased to $0.20. To help schools accommodate OBRA 1981s simultaneous reductions in per-meal surplus commodity subsidies and in reimbursement rates, the maximum price allowed for reduced-price lunches increased to $0.40. For New York State schools, the price of a reduced-price lunch doubled from 1979 to 1980 and doubled again from 1980 to 1981.

Increases in lunch prices along with changes in nationwide eligibility criteria aroused fears that low-income children, dependent on school lunches for a substantial amount of their daily food requirements, would find themselves no longer eligible and face higher prices. A regulatory change coincident with the implementation of OBRA 1981 may have dampened the price increases associated with the legislation.

A change in the Code of Federal Regulations that govern the administration of the school lunch program nationwide shifted the program from a lunches served to a lunches offered system. Prior to the 1981-1982 school year, a lunch had to be served with all five items of the Type A lunch pattern. This is still the case for elementary school programs. Under the new regulations, all five items must be offered to older students, but they may refuse up to two of the items. The intent of the change was to reduce the likelihood of students discarding uneaten food items. (1) The elimination of such waste may have generated savings for school lunch operations at the same time as OBRA 1980-1981 reimbursement rate reductions increased lunch costs. Without this regulatory change, from lunches served to lunches offered, the increase in full-price lunch prices in the post-OBRA period may well have been higher than actually observed. While the determinants of school lunch prices are outside the focus of this study, the relationship between given prices and participation in the pre- and post-OBRA periods is explored. Unfortunately, the effects of OBRA reimbursement rate changes cannot be isolated from the effects of the regulatory change on lunch prices. Thus, if these estimates indicate a negative relationship between prices and school lunch program participation, as expected, the role of the two OBRAs may be somewhat understated in this regard.

THE TWO-STAGE PARTICIPATION MODEL

To meet the specific objective of identifying the impact of the OBRA 1980-1981 legislative changes on school lunch program participation, an empirical model of county-level participation for New York State is constructed. The model design reflects a pragmatic evaluation of the strengths and weaknesses of previous studies and the characteristics of available secondary data.

The data include county-level monthly average daily program participation (ADP), sociodemographic characteristics, economic indicators, and school lunch program parameters. The five New York City counties are excluded due to their size and uniqueness, leaving a total of 57 counties for analysis. The years 1979 and 1981 are used to represent the pre- and post-OBRA periods, respectively. Over that time frame, average daily participation in all three lunch categories declined in New York State. Descriptive statistics and sources for the data are presented in Table 2.

Analyses of participation in the national school lunch program completed in the early 1970s examined the effect of price on the number of participants or

on the participation rate (Braley and Nelson 1975; Nicholson 1973; West and Hope 1973). More recently, the 1977-1978 National Food Consumption Survey and the National Evaluation of School Nutrition Programs (NESNP) have been utilized for analyses of program participation and nutrient intake (Akin, Guilkey, and Popkin 1983; Akin et al. 1983; United States Department of Agriculture and System Development Corporation 1984). For the NESNP, data were collected on individual students, and weekly participation frequency was elaborately modeled as a function of program, school, family, and student characteristics.

Even though data are county-level rather than household-level, evaluation of the studies mentioned above led to two crucial design criteria for analysis. First, free, reduced-, and full-price lunch participation should be modeled separately rather than in combination, because lunch prices do differ and behavior may differ by category. Second, it is critical to identify the effect of OBRA income eligibility changes on the number eligible for lunches in each lunch category. Legislative redefinition of the eligible population may affect program participation very differently than changing other program parameters, such as lunch prices. Thus, predicting the number eligible for each lunch category is the necessary first stage of our two-stage recursive model of school lunch program participation.

Stage One: Predicting the Number of Eligible Students

The number of students eligible for a given lunch category depends upon the extent to which students' families fall within the relevant legislated poverty range. Over time, the poverty population changes as economic conditions change. Such changes along with changes in legislated eligibility criteria will cause shifts in the number of students eligible for school lunches.

To predict the number eligible for each school lunch category under pre- and post-OBRA eligibility criteria, we estimate county poverty rates for school-aged children given the relevant legislated eligibility criteria and 1980 county-level census data. The census reports 1979 income and income distribution information for school-aged children. Because the first OBRA changes occurred in 1980, we view 1979 as representative of the pre-OBRA setting. The pre-OBRA poverty rates are 125 percent of the poverty line for free lunches and 125 percent to 195 percent of the poverty line for reduced-price lunches. The census reports the number of children from ages 5 to 17, as well as the number of that total below 125 percent, 175 percent, and 200 percent of the poverty line by county. Thus, the pre-OBRA (1979) free lunch poverty rate is defined as

# of children 5 to 17 below 125 percent of the poverty line/# of children 5 to 17

and, after linearly interpolating between 175 percent and 200 percent of the poverty line, the pre-OBRA (1979) reduced-price lunch poverty rate is defined as

# of children 5 to 17 between 125 percent and 195 percent of the poverty line/# of children 5 to 17

The 1979 information is also utilized to generate the post-OBRA poverty rates for 1981, the first year in which both OBRA 1980 and 1981 were in effect. Thus, the post-OBRA poverty rate for free lunches is calculated as

# of children 5 to 17 below 130 percent of the poverty line/# of children 5 to 17

after appropriate linear interpolation. Likewise, the reduced-price lunch poverty rate is defined as

# of children 5 to 17 between 130 percent and 185 percent of the poverty line/# of children 5 to 17.

All four poverty rates are estimated as functions of variables that may explain differences in county income distributions, 1979 income per capita, 1979 unemployment rate, an indicator variable for rural, and the percent of county households with female heads. (2)

Because the dependent variables are poverty rates, a logit procedure is utilized. Specifically, a weighted least squares logit procedure was required, as noted by Pindyck and Rubinfeld, to account for heteroskedasticity (Pindyck and Rubinfeld 1976). The estimation results are presented in the top portion of Table 3. All variables have appropriate signs and all, except the unemployment rate and the percent female in both reduced-price equations, are significant.

To predict the number of students eligible to participate in the free and reduced-price lunch categories, the following general formula was utilized,

Predicted number eligible = Predicted county poverty rate X Actual county school enrollment.

The prediction of pre-OBRA free lunch eligibles utilized the coefficients from column (1) in Table 3, 1980 census data for the rural indicator and percent of households headed by females and actual 1979 values for county income per capita, unemployment rates, and enrollments for each county. The same data were utilized to predict the pre-OBRA reduced-price lunch eligibles combined with the column (2) coefficients. The prediction of post-OBRA eligibles utilized the coefficients from columns (3) and (4) in a similar fashion. However, because enrollments and economic conditions differed between the pre-OBRA (1979) and post-OBRA (1981) years, 1981 values for county income per capita, unemployment rates, and enrollments were used. The number of students eligible for paid lunches under pre- and post-OBRA conditions is simply calculated by subtracting the predicted numbers of students eligible for free and for reduced-price lunches from total enrollments for each county. Descriptive statistics regarding predicted eligibles are provided in the bottom portion of Table 3. These predicted variables, free, reduced-price, and full-price eligibles, are among the important explanatory variables for explaining participation in stage two.

Stage Two: Estimating the Determinants of Participation

The data are a pooled time-series (1979, 1981) cross-section (counties). Three linear equations are specified and estimated with Ordinary Least Squares (OLS), one for each of the lunch categories. In each equation the dependent variable is county average daily participation (ADP). Three versions of each free, reduced-price, and full-price lunch program participation equation were estimated and statistically compared in order to select the appropriate model for analysis and determine whether the behavior of participants changed between the pre- and post-OBRA periods. The three models are (Johnston 1984):

MODEL I:

[Mathematical Expression Omitted]

MODEL II:

[Mathematical Expression Omitted]

MODEL III:

[Mathematical Expression Omitted]

where Y indicates the dependent variable; i indicates the intercept term; X indicates the other explanatory variables; a and B are the coefficients associated with the explanatory variables, respectively; u is an error term; and the subscripts are for the years 1979 and 1981, respectively.

We selected the explanatory variables ([X.sub.79] and [X.sub.81]) based upon our literature review and the characteristics of available county-level data. The number eligible for school lunches (predicted in stage one) is included to isolate the effects of changes in eligibility criteria on participation. (3) Beyond its effect on eligibility, deflated income per capita should play a role in the decision to have a school lunch. Urbanization (percent urban) is included because urban areas may have more lunch options such as eating out or going home. The unemployment rate, race (percent black), and female head of household (percent) are expected to have unique relationships to participation. They also reflect differences in a county's income distribution not specifically captured by income per capita. The unemployment rate is a measure of the economic health of a community. Because female-headed and black households tend to be at the lowest end of the income distribution, a higher percentage of female-headed or black households in a county will indicate a more serious degree of poverty. An education variable (percent college) is specified because individuals with college degrees, on average, have higher earning potentials. A family with at least one college educated adult may well be eligible to receive free or reduced-price lunches, but they may be more likely to view their current financial situation as temporary and not apply for subsidized lunches. Also, more highly-educated parents may believe they are more capable of providing a nutritious meal than the school lunch program. The amount charged for a full-price lunch is included, but we could not specify the reduced-price lunch prices of $0.10 and $0.40 for 1979 and 1981, respectively, because within each year there was no price variation.

Descriptive statistics for the variables are presented in Tables 2 and 3. The expected signs of the coefficients in the full-price, reduced-price, and free lunch equations are presented in Table 4. As indicated therein, the signs of the coefficients for the free and reduced-price equations are expected to be similar, although the magnitudes may well differ.

For all lunch categories, the statistical tests for structural change reported in Appendix A indicate that Model III is the most appropriate. That is, the slopes and intercepts taken together do differ between 1979 and 1981. This suggests a shift in participation behavior between the pre- and post-OBRA years. The tests cannot, however, distinguish between two possible sources of changes in behavior. In the free-lunch category, for example, the eligible set included children

with family incomes less than 125 percent of the poverty line in 1979 and less than 130 percent of the poverty line in 1981. Significant differences in behavior between the two years, therefore, could be observed because the eligible sets differ, because actual behavior changed, or both.

PARTICIPATION RESULTS

The regression results from Model III are reported in Table 5. In the free lunch equation, the variables that significantly affect participation, either positively (+) or negatively (-), in both years are number eligible (+), income per capita (-), and percent black (+). The coefficients significantly affecting reduced-price lunch participation are number eligible (+) and deflated income per capita (-) in both years and percent college (-) in 1979. The significant coefficients in the free and reduced-price equations had the expected signs.

The full-price equation deviated from expectations for some variables. Full-price lunch program participation in both years is significantly affected by number eligible (+), unemployment rate (-), percent urban (+), and income per capita (-). Percent black (+) and percent college (-) are significant only in 1979 for full-price lunches. The significant negative coefficients for per capita income suggest that school lunch participation is perceived to be an inferior good by those required to pay the full price. The positive coefficients for percent urban are contrary to expectation. Rather than providing more lunch choices, highly urbanized schools may limit alternatives by adopting closed campus policies that restrict students to the campus during lunch periods. Expectations regarding the relationship between percent black and full-price lunch participation also were not met. One possible explanation for the significant positive coefficient is that blacks may reside in urban, segregated neighborhoods and face higher prices for food and other goods, making school lunches a more attractive alternative.

The coefficients for the number eligible deserve further attention because they raise some interesting policy questions. The number eligible coefficients represent the change in the number participating with respect to a change in the number eligible. In the free lunch equation these coefficients are 0.96 and 0.84 in 1979 and 1981, respectively. These are quite a bit larger than the respective coefficients in the reduced-price equation, 0.19 and 0.22. Furthermore, the coefficients on number eligible in the full-price equation 0.31, in 1979 and 0.25 in 1981, are also larger than those of the reduced-price equation. The significance tests reported in Appendix B support the hypothesis that these coefficients are significantly different across all of the lunch categories.

The small size of the number eligible coefficients in the reduced-price category may arise for a variety of reasons. Students eligible for reduced-price lunches may not always be able to afford the school lunch even at a reduced charge. These students are not as poor as those eligible for free lunches, yet they must still apply for reduced-price status and possibly experience welfare stigma. While the effort required to apply for meals and the possible stigma experienced are transaction costs for both free and reduced-price lunch categories, the benefit of receiving a lunch free of charge is greater than the benefits of receiving a reduced-price meal do not sufficiently outweigh the transaction costs to yield a relationship between eligibility and participation at least as large as that found in the full-price category. To encourage a stronger relationship between reduced price eligibility and participation either the transaction costs must be lower (easier application procedure or decreased welfare stigma) or benefits higher (a lunch at a lower price).

ANALYSIS OF RESULTS

To measure the effects of the OBRAs on participation, legislative factors must be isolated from economic and demographic factors. This objective is accomplished by simulating 1981 school lunch participation for hypothetical "what if" situations. For example: What if the 1979 income criteria had been in place in 1981? Four specific questions are posed. What is the effect on participation of (1) the decline in enrollments from 1979 to 1981, (2) the OBRA change in income criteria from 1979 to 1981, (3) the change in economic conditions from 1979 to 1981, and (4) the change in full-price lunch prices from 1979 to 1981? The first three questions are addressed for each of the lunch categories. Some of the hypothetical variables for the simulation required prior calculation. (4)

The simulation results are illustrated in Table 6. Therein, the + (-) indicate that actual 1981 participation was higher (lower) than would have been the case if the hypothetical 1979 condition prevailed. For example, actual 1981 average daily participation was lower for all three lunch categories than would have occurred if school enrollments had remained at the higher 1979 levels.

The simulation highlights three important aspects of school lunch program participation in New York State. First, the reduction in the school age population was the major reason for the decline in total school lunch program participation across the state from 1979 to 1981, reducing participation by 6.7 percent. The decline in economic conditions and increases in full-price lunch prices reduced total participationw less, by 1.3 and 3.3 percent, respectively. Second, aggregating across all lunch categories, the OBRA income eligibility changes had the only positive effect, increasing school lunch participation by 3.1 percent. Third, the simulations reveal important differences in the patterns of participation response to changes in explanatory variables across lunch categories.

In the free lunch category, the decline in economic conditions and changes in income eligibility criteria increased participation by 4.7 and 11.8 percent, respectively, between 1979 and 1981. The picture for the reduced-price lunch category differs in one important aspect: the shifts in income eligibility criteria apparently reduced participation by 29.6 percent. As shown in Table 1, the legislative intent was to reduce the number eligible for reduced-price lunches, shifting some to free and others to full-price lunches. It is not clear, however, that narrowing eligibility for reduced-price lunches was expected or intended to reduce participation substantially among those who continued to be eligible for those lunches. The magnitude of this effect may be partially explained as the researchers were not able to capture or isolate the fact that reduced-price lunch prices quadrupled between 1979 and 1981. The impact of price increases for full-price lunches between the two years was captured. The associated decrease in participation in that category was 5.5 percent. The effects of the other simulated changes on full-price lunch participation mirror the pattern present in the aggregates, which should not be surprising given the relatively large weight of full-price participation in the totals.

SUMMARY AND IMPLICATIONS FOR THE FUTURE

School lunch program participation declined for all lunch categories in New York State and nationwide between 1979 and 1981. Between those years, enrollments decreased, the economy headed into a recession, and the 1980 and 1981 Omnibus Budget Reconciliation Acts were implemented. With a broad objective of determining what factors affect school lunch program participation, an empirical model is developed for isolating the impact of legislated program changes from the effects of demographic and economic factors. Reasonably accessible secondary data for New York State are used in this study. Similar data should be available in other states.

The two-stage model allows the separation of factors affecting eligibility (legislation, economic conditions, enrollments) from factors affecting lunch participation (student, family, school, and program characteristics). By first predicting the number eligible, a complete analysis of the effect of OBRA income criteria changes on lunch participation is possible because the relationship between the predicted number eligible and participation is clarified. In addition, by estimating and simulating free, reduced-price, and full-price lunch participation separately, crucial comparisons across the lunch categories are possible.

Such comparisons of the estimation results generate two important findings. First, school lunch participation is an inferior good, regardless of lunch category. The extent to which participation is viewed as inferior is strongest for full-price lunches. Second, the relationships between the predicted number eligible and lunch participation differ significantly across lunch categories. The effect of eligibility on participation is greatest in the free category, not an unexpected result. However, the effect of eligibility is greater for full-price than for reduced-price participants. The transaction costs (application procedure and welfare stigma) involved in obtaining a reduced-price meal apparently do not outweight the benefit of a lower-priced meal for many of the potential participants. This suggests that to increase participation in this category either price should be lower or transaction costs smaller.

Comparisons of the simulation results yield interesting policy conclusions regarding the past and policy implications for the future. With respect to the past, the information gap regarding the impact of the OBRAs on school lunch program participation may be closed. The results show that the impact of the income eligibility criteria changes were positive in the aggregate, increasing total program participation by 3.1 percent, despite the large percentage reduction in reduced-price lunch participation. While some students were made ineligible for reduced-price lunches, the gains in free lunch participation were more than twice the losses in reduced-price participation. Given that the simulated reduction in reduced-price participation may also reflect the large price increase for reduced-price lunches permitted under OBRA, the OBRA legislative changes to the school lunch program had a positive overall effect on the well-being of low-income students in New York State.

The decline in participation between 1979 and 1981 by New York State students in all school lunch categories should be attributed to factors other than the OBRA. The simulation showed that the major cause for this decline was the reduction in the school aged population. This has implications for the future for New York State and, perhaps, the nation. Even though birth rates are declining, the "Baby Boom" generation is now in prime child-bearing years. That, continued immigration, and other demographic assumptions yielded a forecast of increasing school enrollment through the year 2000 with little change thereafter (Bovier and Briggs 1988). If so, participation in all components of the school lunch program is likely to increase. Given fiscal stress at all levels of government the added program costs may be problematic, at least in the decade to come.

APPENDIX A

Tests of Structural Change

The notation and general forms for the structural change tests reported in the table that follows are:

Notation:

RSS1 = Residual sum of squares, Model I RSS2 = Residual sum of squares, Model II RSS3 = Residual sum of squares, Model III n = Number of observations k = Number of explanatory variables

(1) Model I against Model II tests for differential intercepts in the two years. The test statistic is

[F.sub.calc] = RSS1 - RSS2/RSS2/(n - k - 1) | [F.sub.table] (1, n - k - 1)

(2) Model II against Model III tests for differential slope coefficients in the two years. The test statistic is

[F.sub.calc] = (RSS2 - RSS3)/(k - 1)/RSS3/(n - 2k) | [F.sub.table] (k - 1, n - 2k)

(3) Model I against Model III tests for differential regressions (slopes and intercepts). The test statistic is

[F.sub.calc] = (RSS1 - RSS3)/k/RSS3/(n - 2k) | [F.sub.table] (k, n - 2k)

Our specification assumes a common error term, undifferentiated by year. The impact of departures from this assumption on the significance level of the Chow test has been explored by Schmidt and Sickles (1977). They show that when sample sizes for the two periods under comparison are equal, as is true in our case, wide differences in the variances for the two periods will have a very minor effect on the significance level. For example, given sample size [n.sub.1] = [n.sub.2] = 25 and one variance one hundred times the other, the true significance level is .059 compared to the nominal level of .05. Because [n.sub.79] = [n.sub.81] = 57 and the largest ratio of estimated variance is 2.25 in our case we feel comfortable with the assumed homoskedastic error structure.

APPENDIX B

Comparing Eligibility Coefficients Across Lunch Categories

A procedure for comparing regression coefficients from different groups when the ratios of the population variances are unknown has been outlined by James (1951). To pairwise test the difference in the magnitude of the number of eligible coefficients to the free, reduced-price, and full-price equations the general hypothesis is:

(1) [H.sub.0]: [b.sup.1] = [b.sup.2].

The statistic is

(2) h = [summation] [w.sub.i.(b.sup.i).sup.2] - ([summation] [w.sub.i.b.sup.i]).sup.2/w,

distributed chi-square with n degrees of freedom, where n equals the number of coefficients being compared. If h is greater than the critical value, [H.sub.0] is rejected. The following are defined:

(3) [w.sub.i] = 1/var([b.sup.i]) and

(4) w = [summation] [w.sub.i].

For our tests in the following table, the chi-square critical value is 3.84 with one degree of freedom at [alpha] = .05.

(1) The discussion of the regulation change is based on a conversation with Richard Reed in September, 1985, before he retired from his post as Chief, Bureau of School Food Management, Department of Education, New York State.

(2) Other variables were explored and rejected. In particular, percent black was originally included but later rejected because it confounded the effect of percent female householder.

(3) The specification of a two-step recursive system, with the number eligible calculated from estimates for the poverty rate (from stage one) entering as explanatory variable in the relevant stage two participation equation, presumes that poverty rates are uncorrelated with the error term of the participation equation. That is, we assume that people do not become poor specifically to gain eligibility and hence participate in the school lunch program.

(4) Enrollments and income criteria do not appear as direct variables in the participation equations but are incorporated into the predicted number eligible variable. Economic conditions are reflected in the participation equations in two ways, directly as explanatory variables (deflated income per capita and unemployment rate) and indirectly because the predicted number eligible is a function of the economic indicators. For details regarding the exact simulation method see Appendix X of Zucchino and Ranney (1987).

REFERENCES

Akin, J. S., D. K. Guilkey, and B. M. Popkin (1983), "The School Lunch Program and Nutrient Intake: A Switching Regression Analysis," American Journal of Agricultural Economics, 65(3): 477-485.

Akin, J. S. et al. (1983), "Demand for School Lunches: An Analysis of Individual Participation in the School Lunch Program," Journal of Human Resources, 17(2): 213-230.

Bovier, L. F. and V. M. Briggs, Jr. (1988), The Population and Labor Force of New York: 1990 to 2050, Washington, DC: Population Reference Bureau, Inc.: 42.

Braley, G. A. and P. E. Nelson, Jr. (1975), "Effect of a Controlled Price Increase on School Lunch Participation: Pittsburgh 1973," American Journal of Agricultural Economics, 57: 90-96.

James, G. S. (1951), "The Comparison of Several Groups of Observations When the Ratios of the Population Variances Are Unknown," Biometrika, 3a: 324-329.

Johnston, J. (1984), Econometric Methods, 3rd edition, New York, NY: McGraw-Hill Book Company: 207-225.

Nicholson, R. H. (1973), "Some Economic Aspects of the National School Lunch Program in North Carolina," Economic Information Reports, Number 32, July.

Parker, L. (1982), The Impact of Child Nutrition Budget Cuts: A Look at the States and Selected School Districts, Washington, DC: Food Research and Action Center: 26.

Pindyck, R. S. and Rubinfeld, D. L. (1976), Econometric Models and Economic Forecasts, New York, NY: McGraw-Hill Book Company: 97-98.

Schmidt, P. and R. Sickles (1977), "Some Further Evidence on the Use of the Chow Test Under Heteroskedasticity," Econometrica, 45(5): 1293-1298.

United States Department of Agriculture, Food and Nutrition Service, Office of Governmental Affairs (1985), National School Lunch Program.

United States Department of Agriculture and System Development Corporation (1984), "National Evaluation of the School Nutrition Programs," The American Journal of Clinical Nutrition, 40(2) (August).

United States General Accounting Office (1984), Participation in the National School Lunch Programs, Report to the Chairman, Committee on Agriculture, Nutrition, and Forestry, United States Senate, Washington, DC: 19.

West, D. A. and R. A. Hoppe (1973), "Pricing and Participation Rates in the National School Lunch Programs in Washington Public School Districts," Washington Agricultural Experiment Station Bulletin, 784 (October).

Zucchino, L. and C. Ranney (1987), School Lunch Program in New York State, A. E. Res. 87-19, Department of Agricultural Economics, Cornell University, July.

Christine K. Ranney is an Associate Professor at Cornell University, Ithaca, New York, and Lori Zucchino is a former graduate student in the Department of Agricultural Economics at Cornell.

The authors would like to thank W. Keith Bryant and Jim Reschovsky for their insightful comments.

The National School Lunch Program (NSLP) is the largest of the Child Nutrition Programs administered by the United States Department of Agriculture's Food and Nutrition Service, both in terms of funding and number of children served. An average of 27 million children per day were served lunches through the NSLP in 1979. Following program changes and substantial funding reductions embodied in the 1980 and 1981 Omnibus Budget Reconciliation Acts (OBRAs), the number of lunches served dropped to 25.8 in 1981 and 22.9 million in 1982 (United States General Accounting Office 1984). The reductions in participation occurred despite the onset of a recession, which should have signaled an increase in participation. While such decreases in school lunch participation are of concern to hunger groups and legislators, the extent to which the OBRA legislation contributed to the participation decline is unknown. Closing that information gap is the specific focus of this research. More broadly, the objective is to determine what factors affect school lunch program participation and thereby inform future public policy.

The problem of obtaining accurate estimates of the determinants of NSLP participation has two dimensions. First, the effects of demographic and economic changes must be isolated to identify correctly the effects of specific program changes on participation. During the period under study, 1979-1981, school enrollments declined in many areas of the country and, as already noted, the economy headed into a deep recession. Second, required information regarding the number of students eligible for subsidized school lunches is not directly reported and must be estimated. The most suitable data for determining eligibility and for analyzing program participation are household-, student-, and school-level data. Unfortunately, high collection costs preclude frequent acquisition of such data.

The two-dimensional problem of obtaining an accurate picture of school lunch program participation is addressed by developing and implementing a two-stage model of county-level program participation in New York State. The data for New York counties are reasonably accessible and similar data should be available in other states. In the crucial first stage of the model, pre- and post-OBRA eligible populations are predicted by estimating poverty rates for each county. The second stage utilizes those predictions in an empirical model of county program participation designed to distinguish the effects of legislative changes from those associated with demographic, economic, and behavioral changes. Background material on the school lunch program and the OBRA legislative changes are presented first, followed by the empirical methodology, results, and conclusions, in turn.

THE NATIONAL SCHOOL LUNCH PROGRAM

The National School Lunch Program was established in 1946 with the passage of the National School Lunch Act. The primary objective of the legislation was to assist in providing adequate nutrition for the nation's school children. The Act established an entitlement to Federally subsidized nutritious lunches for all school children. The subsidies were considered an investment in the health, education, and future productivity of children throughout the nation. The 1946 Act also included funds for purchasing and distributing surplus farm commodities to schools. By incorporating this politically acceptable means for disposing of government-purchased agricultural surpluses, the appeal of the legislation was broadened.

The operation and funding of the lunch program evolved over the years. Currently, three different categories of lunches are served: free, reduced-price, and full-price. Lower-income students apply and eligibility is determined for the free or reduced-price lunches according to family size and income. All students are eligible for a full-price lunch. A Federal per-meal subsidy or reimbursement is provided to schools for all lunches. Free lunches receive the largest reimbursement, while full-price lunches currently receive a minimal reimbursement. Agricultural surplus commodities are provided in legislated amounts for schools to use in the preparation of all meals. The importance of the cash reimbursement rate has increased during the life of the program with a corresponding decline in the use of surplus commodities.

Schools are subject to a number of regulations concerning the type and amount of food they must serve in order to qualify for the program. The school lunch meal pattern, known as the Type A lunch, must include five items: "a specific amount of meat or meat alternate, two or more vegetables and/or fruits, whole grain or enriched bread or bread alternate, and fluid milk as a beverage" (United States Department of Agriculture, Food and Nutrition Service 1985). This combination of foods and the quantities stipulated is designed to satisfy one-third of the Recommended Daily Allowances (RDA) for school children. There is evidence that lower-income students depend on their school lunch for one-third to one-half of their daily calorie intake (Parker 1982).

OBRAs of 1980 and 1981 reduced funding for a number of social programs, including the school lunch program. OBRA 1981 reduced school lunch funding more than OBRA 1980, and, taken together, they account for significant changes in the program. Funding reductions were accomplished mainly by cutting the Federal per-meal reimbursements paid to schools for the full- and reduced-price lunches and by tightening the eligibility criteria for those families applying for subsidized meals. The major program changes are described in Table 1.

OBRA 1980 effectively tightened income eligibility criteria by substituting the poverty line definition used by the Office of Management and Budget (OMB) for that of the United States Department of Agriculture (USDA). As indicated in Table 1, OBRA 1981 simultaneously expanded free meal eligibility and constricted eligibility for reduced-price meals. More stringent income verification procedures also were established to determine the eligibility of applicants better.

Under prior legislation, reduced-price lunches had a maximum price of $0.20. Schools charging a price less than that maximum received an extra subsidy of up to $0.10 per reduced-price meal. New york State schools, taking advantage of this extra subsidy, charged eligible students $0.10 for reduced-price meals in 1979. With the elimination of this subsidy in OBRA 1980, the reduced-price lunch price increased to $0.20. To help schools accommodate OBRA 1981s simultaneous reductions in per-meal surplus commodity subsidies and in reimbursement rates, the maximum price allowed for reduced-price lunches increased to $0.40. For New York State schools, the price of a reduced-price lunch doubled from 1979 to 1980 and doubled again from 1980 to 1981.

Increases in lunch prices along with changes in nationwide eligibility criteria aroused fears that low-income children, dependent on school lunches for a substantial amount of their daily food requirements, would find themselves no longer eligible and face higher prices. A regulatory change coincident with the implementation of OBRA 1981 may have dampened the price increases associated with the legislation.

A change in the Code of Federal Regulations that govern the administration of the school lunch program nationwide shifted the program from a lunches served to a lunches offered system. Prior to the 1981-1982 school year, a lunch had to be served with all five items of the Type A lunch pattern. This is still the case for elementary school programs. Under the new regulations, all five items must be offered to older students, but they may refuse up to two of the items. The intent of the change was to reduce the likelihood of students discarding uneaten food items. (1) The elimination of such waste may have generated savings for school lunch operations at the same time as OBRA 1980-1981 reimbursement rate reductions increased lunch costs. Without this regulatory change, from lunches served to lunches offered, the increase in full-price lunch prices in the post-OBRA period may well have been higher than actually observed. While the determinants of school lunch prices are outside the focus of this study, the relationship between given prices and participation in the pre- and post-OBRA periods is explored. Unfortunately, the effects of OBRA reimbursement rate changes cannot be isolated from the effects of the regulatory change on lunch prices. Thus, if these estimates indicate a negative relationship between prices and school lunch program participation, as expected, the role of the two OBRAs may be somewhat understated in this regard.

THE TWO-STAGE PARTICIPATION MODEL

To meet the specific objective of identifying the impact of the OBRA 1980-1981 legislative changes on school lunch program participation, an empirical model of county-level participation for New York State is constructed. The model design reflects a pragmatic evaluation of the strengths and weaknesses of previous studies and the characteristics of available secondary data.

The data include county-level monthly average daily program participation (ADP), sociodemographic characteristics, economic indicators, and school lunch program parameters. The five New York City counties are excluded due to their size and uniqueness, leaving a total of 57 counties for analysis. The years 1979 and 1981 are used to represent the pre- and post-OBRA periods, respectively. Over that time frame, average daily participation in all three lunch categories declined in New York State. Descriptive statistics and sources for the data are presented in Table 2.

Analyses of participation in the national school lunch program completed in the early 1970s examined the effect of price on the number of participants or

on the participation rate (Braley and Nelson 1975; Nicholson 1973; West and Hope 1973). More recently, the 1977-1978 National Food Consumption Survey and the National Evaluation of School Nutrition Programs (NESNP) have been utilized for analyses of program participation and nutrient intake (Akin, Guilkey, and Popkin 1983; Akin et al. 1983; United States Department of Agriculture and System Development Corporation 1984). For the NESNP, data were collected on individual students, and weekly participation frequency was elaborately modeled as a function of program, school, family, and student characteristics.

Even though data are county-level rather than household-level, evaluation of the studies mentioned above led to two crucial design criteria for analysis. First, free, reduced-, and full-price lunch participation should be modeled separately rather than in combination, because lunch prices do differ and behavior may differ by category. Second, it is critical to identify the effect of OBRA income eligibility changes on the number eligible for lunches in each lunch category. Legislative redefinition of the eligible population may affect program participation very differently than changing other program parameters, such as lunch prices. Thus, predicting the number eligible for each lunch category is the necessary first stage of our two-stage recursive model of school lunch program participation.

Stage One: Predicting the Number of Eligible Students

The number of students eligible for a given lunch category depends upon the extent to which students' families fall within the relevant legislated poverty range. Over time, the poverty population changes as economic conditions change. Such changes along with changes in legislated eligibility criteria will cause shifts in the number of students eligible for school lunches.

To predict the number eligible for each school lunch category under pre- and post-OBRA eligibility criteria, we estimate county poverty rates for school-aged children given the relevant legislated eligibility criteria and 1980 county-level census data. The census reports 1979 income and income distribution information for school-aged children. Because the first OBRA changes occurred in 1980, we view 1979 as representative of the pre-OBRA setting. The pre-OBRA poverty rates are 125 percent of the poverty line for free lunches and 125 percent to 195 percent of the poverty line for reduced-price lunches. The census reports the number of children from ages 5 to 17, as well as the number of that total below 125 percent, 175 percent, and 200 percent of the poverty line by county. Thus, the pre-OBRA (1979) free lunch poverty rate is defined as

# of children 5 to 17 below 125 percent of the poverty line/# of children 5 to 17

and, after linearly interpolating between 175 percent and 200 percent of the poverty line, the pre-OBRA (1979) reduced-price lunch poverty rate is defined as

# of children 5 to 17 between 125 percent and 195 percent of the poverty line/# of children 5 to 17

The 1979 information is also utilized to generate the post-OBRA poverty rates for 1981, the first year in which both OBRA 1980 and 1981 were in effect. Thus, the post-OBRA poverty rate for free lunches is calculated as

# of children 5 to 17 below 130 percent of the poverty line/# of children 5 to 17

after appropriate linear interpolation. Likewise, the reduced-price lunch poverty rate is defined as

# of children 5 to 17 between 130 percent and 185 percent of the poverty line/# of children 5 to 17.

All four poverty rates are estimated as functions of variables that may explain differences in county income distributions, 1979 income per capita, 1979 unemployment rate, an indicator variable for rural, and the percent of county households with female heads. (2)

Because the dependent variables are poverty rates, a logit procedure is utilized. Specifically, a weighted least squares logit procedure was required, as noted by Pindyck and Rubinfeld, to account for heteroskedasticity (Pindyck and Rubinfeld 1976). The estimation results are presented in the top portion of Table 3. All variables have appropriate signs and all, except the unemployment rate and the percent female in both reduced-price equations, are significant.

To predict the number of students eligible to participate in the free and reduced-price lunch categories, the following general formula was utilized,

Predicted number eligible = Predicted county poverty rate X Actual county school enrollment.

The prediction of pre-OBRA free lunch eligibles utilized the coefficients from column (1) in Table 3, 1980 census data for the rural indicator and percent of households headed by females and actual 1979 values for county income per capita, unemployment rates, and enrollments for each county. The same data were utilized to predict the pre-OBRA reduced-price lunch eligibles combined with the column (2) coefficients. The prediction of post-OBRA eligibles utilized the coefficients from columns (3) and (4) in a similar fashion. However, because enrollments and economic conditions differed between the pre-OBRA (1979) and post-OBRA (1981) years, 1981 values for county income per capita, unemployment rates, and enrollments were used. The number of students eligible for paid lunches under pre- and post-OBRA conditions is simply calculated by subtracting the predicted numbers of students eligible for free and for reduced-price lunches from total enrollments for each county. Descriptive statistics regarding predicted eligibles are provided in the bottom portion of Table 3. These predicted variables, free, reduced-price, and full-price eligibles, are among the important explanatory variables for explaining participation in stage two.

Stage Two: Estimating the Determinants of Participation

The data are a pooled time-series (1979, 1981) cross-section (counties). Three linear equations are specified and estimated with Ordinary Least Squares (OLS), one for each of the lunch categories. In each equation the dependent variable is county average daily participation (ADP). Three versions of each free, reduced-price, and full-price lunch program participation equation were estimated and statistically compared in order to select the appropriate model for analysis and determine whether the behavior of participants changed between the pre- and post-OBRA periods. The three models are (Johnston 1984):

MODEL I:

[Mathematical Expression Omitted]

MODEL II:

[Mathematical Expression Omitted]

MODEL III:

[Mathematical Expression Omitted]

where Y indicates the dependent variable; i indicates the intercept term; X indicates the other explanatory variables; a and B are the coefficients associated with the explanatory variables, respectively; u is an error term; and the subscripts are for the years 1979 and 1981, respectively.

We selected the explanatory variables ([X.sub.79] and [X.sub.81]) based upon our literature review and the characteristics of available county-level data. The number eligible for school lunches (predicted in stage one) is included to isolate the effects of changes in eligibility criteria on participation. (3) Beyond its effect on eligibility, deflated income per capita should play a role in the decision to have a school lunch. Urbanization (percent urban) is included because urban areas may have more lunch options such as eating out or going home. The unemployment rate, race (percent black), and female head of household (percent) are expected to have unique relationships to participation. They also reflect differences in a county's income distribution not specifically captured by income per capita. The unemployment rate is a measure of the economic health of a community. Because female-headed and black households tend to be at the lowest end of the income distribution, a higher percentage of female-headed or black households in a county will indicate a more serious degree of poverty. An education variable (percent college) is specified because individuals with college degrees, on average, have higher earning potentials. A family with at least one college educated adult may well be eligible to receive free or reduced-price lunches, but they may be more likely to view their current financial situation as temporary and not apply for subsidized lunches. Also, more highly-educated parents may believe they are more capable of providing a nutritious meal than the school lunch program. The amount charged for a full-price lunch is included, but we could not specify the reduced-price lunch prices of $0.10 and $0.40 for 1979 and 1981, respectively, because within each year there was no price variation.

Descriptive statistics for the variables are presented in Tables 2 and 3. The expected signs of the coefficients in the full-price, reduced-price, and free lunch equations are presented in Table 4. As indicated therein, the signs of the coefficients for the free and reduced-price equations are expected to be similar, although the magnitudes may well differ.

For all lunch categories, the statistical tests for structural change reported in Appendix A indicate that Model III is the most appropriate. That is, the slopes and intercepts taken together do differ between 1979 and 1981. This suggests a shift in participation behavior between the pre- and post-OBRA years. The tests cannot, however, distinguish between two possible sources of changes in behavior. In the free-lunch category, for example, the eligible set included children

with family incomes less than 125 percent of the poverty line in 1979 and less than 130 percent of the poverty line in 1981. Significant differences in behavior between the two years, therefore, could be observed because the eligible sets differ, because actual behavior changed, or both.

PARTICIPATION RESULTS

The regression results from Model III are reported in Table 5. In the free lunch equation, the variables that significantly affect participation, either positively (+) or negatively (-), in both years are number eligible (+), income per capita (-), and percent black (+). The coefficients significantly affecting reduced-price lunch participation are number eligible (+) and deflated income per capita (-) in both years and percent college (-) in 1979. The significant coefficients in the free and reduced-price equations had the expected signs.

The full-price equation deviated from expectations for some variables. Full-price lunch program participation in both years is significantly affected by number eligible (+), unemployment rate (-), percent urban (+), and income per capita (-). Percent black (+) and percent college (-) are significant only in 1979 for full-price lunches. The significant negative coefficients for per capita income suggest that school lunch participation is perceived to be an inferior good by those required to pay the full price. The positive coefficients for percent urban are contrary to expectation. Rather than providing more lunch choices, highly urbanized schools may limit alternatives by adopting closed campus policies that restrict students to the campus during lunch periods. Expectations regarding the relationship between percent black and full-price lunch participation also were not met. One possible explanation for the significant positive coefficient is that blacks may reside in urban, segregated neighborhoods and face higher prices for food and other goods, making school lunches a more attractive alternative.

The coefficients for the number eligible deserve further attention because they raise some interesting policy questions. The number eligible coefficients represent the change in the number participating with respect to a change in the number eligible. In the free lunch equation these coefficients are 0.96 and 0.84 in 1979 and 1981, respectively. These are quite a bit larger than the respective coefficients in the reduced-price equation, 0.19 and 0.22. Furthermore, the coefficients on number eligible in the full-price equation 0.31, in 1979 and 0.25 in 1981, are also larger than those of the reduced-price equation. The significance tests reported in Appendix B support the hypothesis that these coefficients are significantly different across all of the lunch categories.

The small size of the number eligible coefficients in the reduced-price category may arise for a variety of reasons. Students eligible for reduced-price lunches may not always be able to afford the school lunch even at a reduced charge. These students are not as poor as those eligible for free lunches, yet they must still apply for reduced-price status and possibly experience welfare stigma. While the effort required to apply for meals and the possible stigma experienced are transaction costs for both free and reduced-price lunch categories, the benefit of receiving a lunch free of charge is greater than the benefits of receiving a reduced-price meal do not sufficiently outweigh the transaction costs to yield a relationship between eligibility and participation at least as large as that found in the full-price category. To encourage a stronger relationship between reduced price eligibility and participation either the transaction costs must be lower (easier application procedure or decreased welfare stigma) or benefits higher (a lunch at a lower price).

ANALYSIS OF RESULTS

To measure the effects of the OBRAs on participation, legislative factors must be isolated from economic and demographic factors. This objective is accomplished by simulating 1981 school lunch participation for hypothetical "what if" situations. For example: What if the 1979 income criteria had been in place in 1981? Four specific questions are posed. What is the effect on participation of (1) the decline in enrollments from 1979 to 1981, (2) the OBRA change in income criteria from 1979 to 1981, (3) the change in economic conditions from 1979 to 1981, and (4) the change in full-price lunch prices from 1979 to 1981? The first three questions are addressed for each of the lunch categories. Some of the hypothetical variables for the simulation required prior calculation. (4)

The simulation results are illustrated in Table 6. Therein, the + (-) indicate that actual 1981 participation was higher (lower) than would have been the case if the hypothetical 1979 condition prevailed. For example, actual 1981 average daily participation was lower for all three lunch categories than would have occurred if school enrollments had remained at the higher 1979 levels.

The simulation highlights three important aspects of school lunch program participation in New York State. First, the reduction in the school age population was the major reason for the decline in total school lunch program participation across the state from 1979 to 1981, reducing participation by 6.7 percent. The decline in economic conditions and increases in full-price lunch prices reduced total participationw less, by 1.3 and 3.3 percent, respectively. Second, aggregating across all lunch categories, the OBRA income eligibility changes had the only positive effect, increasing school lunch participation by 3.1 percent. Third, the simulations reveal important differences in the patterns of participation response to changes in explanatory variables across lunch categories.

In the free lunch category, the decline in economic conditions and changes in income eligibility criteria increased participation by 4.7 and 11.8 percent, respectively, between 1979 and 1981. The picture for the reduced-price lunch category differs in one important aspect: the shifts in income eligibility criteria apparently reduced participation by 29.6 percent. As shown in Table 1, the legislative intent was to reduce the number eligible for reduced-price lunches, shifting some to free and others to full-price lunches. It is not clear, however, that narrowing eligibility for reduced-price lunches was expected or intended to reduce participation substantially among those who continued to be eligible for those lunches. The magnitude of this effect may be partially explained as the researchers were not able to capture or isolate the fact that reduced-price lunch prices quadrupled between 1979 and 1981. The impact of price increases for full-price lunches between the two years was captured. The associated decrease in participation in that category was 5.5 percent. The effects of the other simulated changes on full-price lunch participation mirror the pattern present in the aggregates, which should not be surprising given the relatively large weight of full-price participation in the totals.

SUMMARY AND IMPLICATIONS FOR THE FUTURE

School lunch program participation declined for all lunch categories in New York State and nationwide between 1979 and 1981. Between those years, enrollments decreased, the economy headed into a recession, and the 1980 and 1981 Omnibus Budget Reconciliation Acts were implemented. With a broad objective of determining what factors affect school lunch program participation, an empirical model is developed for isolating the impact of legislated program changes from the effects of demographic and economic factors. Reasonably accessible secondary data for New York State are used in this study. Similar data should be available in other states.

The two-stage model allows the separation of factors affecting eligibility (legislation, economic conditions, enrollments) from factors affecting lunch participation (student, family, school, and program characteristics). By first predicting the number eligible, a complete analysis of the effect of OBRA income criteria changes on lunch participation is possible because the relationship between the predicted number eligible and participation is clarified. In addition, by estimating and simulating free, reduced-price, and full-price lunch participation separately, crucial comparisons across the lunch categories are possible.

Such comparisons of the estimation results generate two important findings. First, school lunch participation is an inferior good, regardless of lunch category. The extent to which participation is viewed as inferior is strongest for full-price lunches. Second, the relationships between the predicted number eligible and lunch participation differ significantly across lunch categories. The effect of eligibility on participation is greatest in the free category, not an unexpected result. However, the effect of eligibility is greater for full-price than for reduced-price participants. The transaction costs (application procedure and welfare stigma) involved in obtaining a reduced-price meal apparently do not outweight the benefit of a lower-priced meal for many of the potential participants. This suggests that to increase participation in this category either price should be lower or transaction costs smaller.

Comparisons of the simulation results yield interesting policy conclusions regarding the past and policy implications for the future. With respect to the past, the information gap regarding the impact of the OBRAs on school lunch program participation may be closed. The results show that the impact of the income eligibility criteria changes were positive in the aggregate, increasing total program participation by 3.1 percent, despite the large percentage reduction in reduced-price lunch participation. While some students were made ineligible for reduced-price lunches, the gains in free lunch participation were more than twice the losses in reduced-price participation. Given that the simulated reduction in reduced-price participation may also reflect the large price increase for reduced-price lunches permitted under OBRA, the OBRA legislative changes to the school lunch program had a positive overall effect on the well-being of low-income students in New York State.

The decline in participation between 1979 and 1981 by New York State students in all school lunch categories should be attributed to factors other than the OBRA. The simulation showed that the major cause for this decline was the reduction in the school aged population. This has implications for the future for New York State and, perhaps, the nation. Even though birth rates are declining, the "Baby Boom" generation is now in prime child-bearing years. That, continued immigration, and other demographic assumptions yielded a forecast of increasing school enrollment through the year 2000 with little change thereafter (Bovier and Briggs 1988). If so, participation in all components of the school lunch program is likely to increase. Given fiscal stress at all levels of government the added program costs may be problematic, at least in the decade to come.

APPENDIX A

Tests of Structural Change

The notation and general forms for the structural change tests reported in the table that follows are:

Notation:

RSS1 = Residual sum of squares, Model I RSS2 = Residual sum of squares, Model II RSS3 = Residual sum of squares, Model III n = Number of observations k = Number of explanatory variables

(1) Model I against Model II tests for differential intercepts in the two years. The test statistic is

[F.sub.calc] = RSS1 - RSS2/RSS2/(n - k - 1) | [F.sub.table] (1, n - k - 1)

(2) Model II against Model III tests for differential slope coefficients in the two years. The test statistic is

[F.sub.calc] = (RSS2 - RSS3)/(k - 1)/RSS3/(n - 2k) | [F.sub.table] (k - 1, n - 2k)

(3) Model I against Model III tests for differential regressions (slopes and intercepts). The test statistic is

[F.sub.calc] = (RSS1 - RSS3)/k/RSS3/(n - 2k) | [F.sub.table] (k, n - 2k)

Our specification assumes a common error term, undifferentiated by year. The impact of departures from this assumption on the significance level of the Chow test has been explored by Schmidt and Sickles (1977). They show that when sample sizes for the two periods under comparison are equal, as is true in our case, wide differences in the variances for the two periods will have a very minor effect on the significance level. For example, given sample size [n.sub.1] = [n.sub.2] = 25 and one variance one hundred times the other, the true significance level is .059 compared to the nominal level of .05. Because [n.sub.79] = [n.sub.81] = 57 and the largest ratio of estimated variance is 2.25 in our case we feel comfortable with the assumed homoskedastic error structure.

APPENDIX B

Comparing Eligibility Coefficients Across Lunch Categories

A procedure for comparing regression coefficients from different groups when the ratios of the population variances are unknown has been outlined by James (1951). To pairwise test the difference in the magnitude of the number of eligible coefficients to the free, reduced-price, and full-price equations the general hypothesis is:

(1) [H.sub.0]: [b.sup.1] = [b.sup.2].

The statistic is

(2) h = [summation] [w.sub.i.(b.sup.i).sup.2] - ([summation] [w.sub.i.b.sup.i]).sup.2/w,

distributed chi-square with n degrees of freedom, where n equals the number of coefficients being compared. If h is greater than the critical value, [H.sub.0] is rejected. The following are defined:

(3) [w.sub.i] = 1/var([b.sup.i]) and

(4) w = [summation] [w.sub.i].

For our tests in the following table, the chi-square critical value is 3.84 with one degree of freedom at [alpha] = .05.

(1) The discussion of the regulation change is based on a conversation with Richard Reed in September, 1985, before he retired from his post as Chief, Bureau of School Food Management, Department of Education, New York State.

(2) Other variables were explored and rejected. In particular, percent black was originally included but later rejected because it confounded the effect of percent female householder.

(3) The specification of a two-step recursive system, with the number eligible calculated from estimates for the poverty rate (from stage one) entering as explanatory variable in the relevant stage two participation equation, presumes that poverty rates are uncorrelated with the error term of the participation equation. That is, we assume that people do not become poor specifically to gain eligibility and hence participate in the school lunch program.

(4) Enrollments and income criteria do not appear as direct variables in the participation equations but are incorporated into the predicted number eligible variable. Economic conditions are reflected in the participation equations in two ways, directly as explanatory variables (deflated income per capita and unemployment rate) and indirectly because the predicted number eligible is a function of the economic indicators. For details regarding the exact simulation method see Appendix X of Zucchino and Ranney (1987).

REFERENCES

Akin, J. S., D. K. Guilkey, and B. M. Popkin (1983), "The School Lunch Program and Nutrient Intake: A Switching Regression Analysis," American Journal of Agricultural Economics, 65(3): 477-485.

Akin, J. S. et al. (1983), "Demand for School Lunches: An Analysis of Individual Participation in the School Lunch Program," Journal of Human Resources, 17(2): 213-230.

Bovier, L. F. and V. M. Briggs, Jr. (1988), The Population and Labor Force of New York: 1990 to 2050, Washington, DC: Population Reference Bureau, Inc.: 42.

Braley, G. A. and P. E. Nelson, Jr. (1975), "Effect of a Controlled Price Increase on School Lunch Participation: Pittsburgh 1973," American Journal of Agricultural Economics, 57: 90-96.

James, G. S. (1951), "The Comparison of Several Groups of Observations When the Ratios of the Population Variances Are Unknown," Biometrika, 3a: 324-329.

Johnston, J. (1984), Econometric Methods, 3rd edition, New York, NY: McGraw-Hill Book Company: 207-225.

Nicholson, R. H. (1973), "Some Economic Aspects of the National School Lunch Program in North Carolina," Economic Information Reports, Number 32, July.

Parker, L. (1982), The Impact of Child Nutrition Budget Cuts: A Look at the States and Selected School Districts, Washington, DC: Food Research and Action Center: 26.

Pindyck, R. S. and Rubinfeld, D. L. (1976), Econometric Models and Economic Forecasts, New York, NY: McGraw-Hill Book Company: 97-98.

Schmidt, P. and R. Sickles (1977), "Some Further Evidence on the Use of the Chow Test Under Heteroskedasticity," Econometrica, 45(5): 1293-1298.

United States Department of Agriculture, Food and Nutrition Service, Office of Governmental Affairs (1985), National School Lunch Program.

United States Department of Agriculture and System Development Corporation (1984), "National Evaluation of the School Nutrition Programs," The American Journal of Clinical Nutrition, 40(2) (August).

United States General Accounting Office (1984), Participation in the National School Lunch Programs, Report to the Chairman, Committee on Agriculture, Nutrition, and Forestry, United States Senate, Washington, DC: 19.

West, D. A. and R. A. Hoppe (1973), "Pricing and Participation Rates in the National School Lunch Programs in Washington Public School Districts," Washington Agricultural Experiment Station Bulletin, 784 (October).

Zucchino, L. and C. Ranney (1987), School Lunch Program in New York State, A. E. Res. 87-19, Department of Agricultural Economics, Cornell University, July.

Christine K. Ranney is an Associate Professor at Cornell University, Ithaca, New York, and Lori Zucchino is a former graduate student in the Department of Agricultural Economics at Cornell.

The authors would like to thank W. Keith Bryant and Jim Reschovsky for their insightful comments.

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Author: | Zucchino, Lori; Ranney, Christine K. |
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Publication: | Journal of Consumer Affairs |

Date: | Dec 22, 1990 |

Words: | 5672 |

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