The elusive flypaper effect

JOURNAL OF URBAN ECONOMlCS 30, 310-328 (1991) The Elusive PAUL Hamilton Received Flypaper GARY College, July 23,1989; Effect WYCKOFF* Clinton, revised New York 13323 December 28, 1989 The flypaper effect is the common empirical result that lump-sum intergovernmental grants stimulate more local government spending than increases in private income which are theoretically equivalent. In this paper, four of the best-known explanations of the fiypaper effect are tested, using data from Michigan school districts. None of these explanations are confirmed by the data. The cause of the flypaper effect is likely to be much more deeply rooted in the nature of local o 1991 Academic PMS, IX. decision-making than is currently recognized. I. INTRODUCTION The flypaper effect is a well-known anomaly in empirical studies of local government expenditure behavior: compared to the effect of private income on government spending, lump-sum intergovernmental aid causes a disproportionately large increase in spending. Money in the private sector, from private income, tends to stick like flypaper to the private sector, and not be taxed away. Money in the public sector, from intergovernmental aid, tends to stick in the public sector and get spent there. The exact meaning of the word “disproportionate” in the previous definition depends upon the model of local expenditure determination being used. In general, it means that the effect of lump-sum aid exceeds that anticipated by the model. In the most popular model of Iocal public choice, the median voter model, lump-sum aid affects spending by altering the voter’s effective income. Since the median voter can vary local public spending to suit his tastes, his share of lump-sum aid becomes a fungible asset which can be used for public or private purposes, and which therefore ought to be included in his total income. For example, if the median voter decides to use his share of lump-sum aid for private consumption, he directs that the aid be used entirely to lower local taxes, and his after-tax income rises by the amount of the lump-sum aid times his tax share times the community’s share of expenditures under any matching *I thank Tom Means and the referee for helpful 310 0094-1190/91 Copyright All rights $3.00 0 1991 by Academic Press, Inc. of reproduction in any form rcservcd. comments THE ELUSIVE FLYPAPER EFFECT 311 grants. In the median voter model, then, a flypaper effect occurs when increases in this share of lump-sum aid have a larger effect on spending than increases in the median voter’s private income. Almost every study of local public finance concludes that flypaper effects do occur (for a review of such studies, see Fisher [5] and Gramlich [6]). Although it may seem that, the flypaper effect is a minor detail in our understanding of local public choice, it is likely to be a central question in research on the process of public expenditure at all levels of government. Lump-sum intergovernmental grants represent one of the few observable exogenous variables affecting real-world public finance decisions. For this reason, it is possible to construct consistent models of their effects, and to test those models. Other public finance variables, such as the price of public goods, income in the community, and population, are endogenous variables which both influence and are influenced by public expenditure decisions. Hence, several theoretical relationships between these variables are consistent with the data. Testing with these variables is difficult, and progress in these areas is problematic. Lump-sum intergovernmental aid, therefore, represents one of the best available opportunities to understand public finance decision-making. In this paper I test four of the best-known explanations of the flypaper effect: the arguments of Megdal [9] and Moffitt [ll] that econometric misspecification is the cause of the flypaper effect; the position of Hamilton [7] that omitted variables create the flypaper effect; the suggestion by Courant et al. [2] and Oates [13] that voters use the average price of public goods as a proxy for their marginal price; and the explanation of Filimon et al. [31 that voters are unaware of the existence of intergovernmental aid. No test of Hamilton’s hypothesis has ever been performed. Moffitt and Megdal provide econometric tests of their theories, but there is no comparison of their models with competing explanations. Filimon et al. compare only their model and the fiscal illusion models of Courant et al. and Oates. Moreover, the Moffitt, Megdal, and Filimon et al. tests were performed with different, specialized data sets making interpretation of the results difficult. For example, Moffitt uses state level spending on AFDC for his dependent variable, and Filimon et al. use spending for school districts in Oregon. To sort out the flypaper effect and with it the nature of local public decision-making, a comprehensive test of all these models with the same data set is needed. Based on the tests below, none of these theories hits the mark-the cause of the flypaper effect eludes these authors. Each of these authors suggests a “disease” which might be responsible for the “symptom” of flypaper effects. But I find in each case that either the patient does not have this disease (the data rejects the model) or the patient has the 312 PAUL GARY WYCKOFF private goods expenditure ity's share of matching grant education expenditure FIG. 1. The bias created by using OLS with closed-end matching grants. disease but it is not the cause of this particular symptom (correcting for the problem does not reduce the flypaper effect). Section II below tests the Moffitt-Megdal and Hamilton models. Section III does the same for the fiscal illusion models. Section IV offers some concluding comments. II. FLYPAPER EFFECTS DUE TO ANALYST ERROR The theoretical literature on flypaper effects can be broken into two categories. In the first group, including the Moffitt-Megdal and Hamilton models, the analyst is fooled into erroneous conclusions about the flypaper effect by failure to recognize an important feature of the problem. Most of these explanations are confined to particular grant types, expenditure categories, or institutional situations. a. The Mo#itt-h4egdal Model i. The nature of the analyst’s error. In the case of closed-end matching grants, Moffitt [ll] and Megdal [9] argue that contemporaneous correlation between the error term and the price and income variables of an OLS equation have led to an observed flypaper effect. Figure 1 illustrates the source of the problem. Under a closed-end matching grant, the community receives matching money up to some expenditure limit E*. Up to this limit, the price to the community is reduced by the matching rate. Above the limit, the price THE ELUSIVE FLYPAPER 313 EFFECT again returns to its original level. The grant has only an income effect, and is usually classified as lump-sum. Now suppose a community has characteristics such that, given the functional form of the equation employed by the analyst, the community should locate at point A on the diagram. But suppose instead that, due to errors in observing the community’s output, or administrative and bureaucratic errors in carrying out the wishes of the community, we observe the community at point B. The analyst records the community as having the price and income associated with point B, and the estimation procedure registers an error component for this community. This means that the error term and the price and income variables are correlated, since communities like this one which have large error terms also have low price and income terms. As a result, the 0L.S estimates are inconsistent. ii. Michigan’s aid to school districts. Michigan’s state aid system during the 1978-1979 school year represents an ideal test of the Moffitt-Megdal model. Because of the unusual aid system employed, all school districts faced the nonlinear budget constraint discussed by these authors. General school aid consisted of a lump-sum component of $274 per pupil and a matching component in which the state share depended upon the level of assessed value per pupil (measured by SEVPP-state equalized value per pupil) in the community. Matching aid per pupil was set equal to ($40,000-SEVPP) times the tax rate of the school district. As the expenditures of the district increased, state matching continued until the community reached a tax level of 30 mills (one mill equals one one-thousandth of the taxable value of property). This system resulted in two budget constraints for these districts, depending upon their level of SEVPP. For districts with less than $40,000 SEVPP, state aid lowered the price of education up to the 30 mill limit. At low tax rates, the school district contributed (tax rate) (SEVPP) (pupils), with the state contributing (tax rate) (40,000-SEVPP) (pupils). The “price” of a dollar of education was therefore (tax rate) (SEVPP) (pupils) [tax rate* SEVPP + (tax rate) (40,000-SEVPP)] = SEVPP/$40,000. * pupils (1) Beyond 30 mills, the community financed additional spending on its own; state aid was lump-sum and equaled (0.03[$40,000-SEVPP] + $274) per pupil. The budget set faced by these districts was convex but included a kinked budget constraint, as depicted in Fig. 2. For districts above $40,000 SEVPP, the same formulas applied, but they had different effects. The school district still got $274 per pupil in 314 PAUL GARY WYCKOFF private goods expenditure education (.03[40,000+274])pUpilS= 1474*pupi1s expenditure FIG. 2. The convex case. lump-sum aid, but it received negative matching aid. The district continued to pay SEVPP/$40,000 for extra dollars of school spending, but this ratio was now bigger than one. The extra dollars were “taxed away” by the state in the form of reduced state aid. This effect lasted until the aid reached zero; the district did not have to pay any “tax” to the state. Thus, at the point where -274 = (tax rateX$40,000-SEVPP), aid was zero, and private goods expenditure = -SEvPP/40,00 +elope = -1 m education SEVPP-40,000 FIG. 3. The concave case. expenditure THE ELUSIVE FLYPAPER EFFECT 315 the budget line became the same as under no state financing. The result is the nonconvex budget set depicted in Fig. 3. iii. Estimation technique. The biases inherent in ordinary least-squares estimation under this aid scheme were avoided by using the nonlinear procedure suggested by Wales and Woodland [17].l They reasoned that the difficulty with OLS is that, by determining price and income according to the observed position of the community on the budget constraint, the analyst runs the risk of observing the community’s position incorrectly, or that the community errs in trying to achieve its optimal position. These problems create a specification error which leads to correlation between the error term and the price and income variables. Wales and Woodland’s solution to this problem is to assign points to segments according to the community’s predicted demand, since this represents demand free of the error term. By freeing price and income of their correlation with the error term in this way, the bias caused by OLS regression is eliminated. This sorting of communities by predicted demand was performed by a nonlinear least-squares iterative technique. In each round, parameter values were selected and communities were assigned to segments based on their predicted demand under these parameters. Using the price and income terms associated with these segments, the sum of squared residuals was then calculated. The machine searched and selected the final parame‘Megdal [lo] presented Monte Carlo evidence that suggests that maximum likelihood estimation gives the most desirable results for this estimation problem. However, as pointed out by Moffitt [12], under certain circumstances nonlinear least-squares estimates are equivalent to maximum likelihood estimates. Moffitt distinguishes between heterogeneity error, which arises because individuals have differences in their utility function, and optimization or measurement error, which arises because the decisionmaker fails to achieve his utility maximizing point or because the investigator measures the optimum point incorrectly. In the case of optimization or measurement error only, nonlinear least-squares and maximum likelihood estimates are equivalent. Moffitt further points out that the two types of error can be distinguished by examining the clustering of the data around the kink points. Optimization or measurement error tends to spread points evenly around the constraints, while heterogeneity error tends to bunch points around the kink points in the convex case (Fig. 2) and disperse points away from the kink in the concave case (Fig. 3). An examination of the data revealed no indication of heterogeneity error. One hundred thirty-eight school districts in our sample faced a convex budget constraint, and only one of those districts was on the kink. Further, only eight districts were within one mill of the 30-mill kink. In the concave case, no bunching away from the school district’s limit of 274/(40,000SEVPP) occurred. There was a bimodal distribution, but the trough between the peaks occurred well below the limit. Although there were only three observations in the range from 16 to 4 mills below the kink, there were 16 observations in the interval from 4 mills below the kink to 8 mills above the kink. 316 PAUL GARY WYCKOFF ters so as to minimize the total sum of squares. To avoid the “Tiebout bias” inherent in using metropolitan data (see Rubinfeld et al. [KY]), all school districts within SMSAs were deleted from the sample. iv. Results. Table 1 presents a comparison of estimates using OLS and the Wales and Woodland procedure. Table 2 presents variable definitions. Four of the variables deserve special mention. First, following the median voter literature, the price variable is the median voter’s tax share times the community’s share of the costs under matching grants. Second, following Tumbull [16] I have added the median voter’s share of lump-sum aid (as described above) to his private income in order to determine his total effective income Z. Third (and fourth), while median household income would be the appropriate measure of private income, only median fumi/y income was available for these school districts. Accordingly, I added the ratio of families to unrelated individuals (HSRATIO) and the percentage of population 16 and up (PC16UP) to account for differences in the composition of households across school districts. Neither variable, however, had a significant coefficient. The two sets of estimates in Table 1 are close. In no case are the differences in values in the two regressions statistically significant; for example, the 0.171 value for the OLS regression for the income term is within one standard error of the 0.207 value for the nonlinear regression. More interesting, using the Moffitt-Megdal approach does not appear to “fix” the flypaper effect; in fact, it increases it. I measured the flypaper effect by including the variable INCRATIO in both regressions. This is the ratio of the voter’s lump-sum aid share to his total effective income. If there is no flypaper effect, the composition of income should not matter, so this variable should have a zero coefficient; if flypaper effects exist, the coefficient should be positive. Table 1 shows that correcting the inconsistency of OLS estimates increases the coefficient on INCRATIO from 1.301 to 2.079, and makes the coefficient significant. There is no doubt that Moffitt and Megdal have pointed out the theoretically correct way to estimate demand functions in the face of closed-end matching grants, but their correction does not explain the flypaper effect. b. The Hamilton Model In the case of police protection and education, Hamilton [7] argues, private income represents both a pool of resources for consumption and a surrogate for certain unobserved factors in the production of local public goods. In education, for example, increased income in a community makes possible increased spending on schools, but it also reduces the expenditure levels necessary to reach a given level of learning on the part of pupils, since educational studies show that children from families with higher THE ELUSIVE FLYPAPER 317 EFFECT TABLE 1 Comparison of OLS and Nonlinear Least-Squares Regressions OLS results Variable LNP LNZ PCBLACK PCKOS PCK611 PCKNPUB PCCLGRAD PCNONHS PCFEMALE PCRTRDI PCAGE65 PCUNEMP PCIRANSF LNENRL LNPPB LNCICH INCRATIO CATAID HSRATIO PC16UP n = 202 R2 Nonlinear least-squares results Estimate (std. error) - 0.153* (0.033) 0.171” (0.062) 0.630* to.1751 -0.148 (0.104) - 0.059 (0.096) 0.074 (0.072) 0.663* (0.255) - 0.200* (0.100) - 0.031 (0.239) 0.239 (0.149) - 0.370 (0.209) - 0.306* (0.109) - 0.823* (0.395) -0.186* (0.032) - 0.048* (0.015) 0.414* (0.064) 1.301 (1.1821 6.127E-04* (6.412505) 4.486E-03 (3.312E-03) 0.108 (0.158) ,704 Variable LNP LNZ PCBLACK PCKOS PCK611 PCKNPUB PCCLGRAD PCNONHS PCFEMALE PCRTRDI PCAGE65 PCUNEMP PCTRANSF LNENRL LNPPB LNClCH INCRATIO CATAID HSRATIO PC16UP n = 202 R* Estimate (std. error) - 0.186* (0.033) 0.207* (0.0621 0.607* to.1711 -0.146 (0.102) - 0.036 (0.094) 0.049 (0.070) 0.534* CO.2491 - 0.203* (0.097) - 0.092 CO.2341 0.254 (0.146) - 0.422* (0.204) - 0.309* (0.1071 - 0.646 (0.383) -0.216* (0.031) - 0.047* (0.015) 0.415* (0.0631 2.079* (0.584) 6.015E-04* (6.254E-05) 4.579E-03 (3.253E-03) 0.143 (0.154) .718 Nore. Dependent variable in both regressions is log of general expenditures, 1978-1979. *Indicates variable is statistically significant at the 5% level. PAUL GARY WYCKOFF 318 TABLE 2 Variable Definitions LNP LNZ PCBLACK PCK05 PCK61 PCKNPUB PCCLGRAD PCNONHS PCFEMALE PCRTRDI PCAGE65 PCUNEMP PCTRANSF LNENRL LNPPB LNCTCH INCRATIO CATAID HSRATIO PC16UP logarithm of tax price. Tax price is equal to the voter’s tax share (median house value/taxable property value in community) times the community’s share of expenditures under matching aid logarithm of total income, defined as Z = median family income in community + p * G, where G is lump-sum aid and p is tax price percentage of population that is black percentage of population aged 0 to 5 percentage of population aged 6 to 11 percentage of population in nonpublic schools percentage of population that graduated from college percentage of population that did not graduate from high school percentage of population that is female percentage of population that is retired or permanently disabled percentage of population aged 65 and over percentage of population that is unemployed percentage of population receiving AFDC or food stamps logarithm of enrollment in school district (1977-1978) logarithm of 1977-1978 enrollment/number of school buildings logarithm of county average teacher’s salary (1977-1978) =p*G/Z categorical aid ratio of families to unrelated individuals percentage of population age 16 or more Note. Sources: US Census Bureau, “1970 Censuses of Population and Housing”; Michigan Department of Education, Bulletin 1014, “Michigan School Districts Ranked by Selected Financial Data, 1978-79.” income and educational levels learn more rapidly than other children. Thus, as income increases, expenditure increases may be held down by the fact that children from higher-income homes require fewer educational resources to achieve a given level of educational achievement. This effect again causes lump-sum aid to have a greater expenditure effect than income increases. Table 3 contains a test of the Hamilton hypothesis that missing variables cause the flypaper effect. In the table is a comparison of regressions with and without many of the variables deemed important by Hamilton: age, sex, race, education level, unemployment rates, and welfare recipient rates. There may be missing variables not included in this list, but it certainly includes the crucial variable-educational level of the commu- THE ELUSIVE FLYPAPER 319 EFFECI TABLE 3 Comparison of Regressions With and Without Socioeconomic Variables Without extra variables Variable LNP LNZ LNENRL LNPPB LNCTCH INCRATIO CATAID HSRATIO Estimate (std. error) -0X33* (0.035) 0.296” (0.050) - 0.201* (0.034) - 0.048* (0.016) 0.455* (0.063) 1.491* (0.613) 5.143E-04* (4.779E-05) l.O18E-03 (3.482E-03) n = 202 R2 With extra variables Variable LNP LNZ PCBLACK PCKOS PCK611 PCKNPUB PCCLGRAD PCNONHS PCFEMALE Estimate (std. error) -0.186* (0.033) 0.207* (0.062) 0.607* (0.171) -0.146 (0.1021 - 0.036 (0.094) 0.049 (0.070) 0.534* (0.249) - 0.203* (0.097) - 0.092 (0.234) 623 PCRTRDI PCAGE65 PCUNEMP PCTRANSF LNENRL LNPPB LNCTCH INCRATIO CATAID HSRATIO PC16UP 0.254 (0.146) - 0.422* (0.204) - 0.309* (0.107) - 0.646 (0.383) - 0.216* (0.031) - 0.047* (0.015) 0.415* (0.063) 2.079* (0.5841 6.015E-04* (6.254E-05) 4.579E-03 (3.253E-03) 0.143 (0.154) II = 202 R2 .718 Note. Dependent variable in both regressions is log of general expenditures, 1978-1979. *Indicates variable is statistically significant at the 5% level. 320 PAUL GARY WYCKOFF TABLE 4 Correlation of INCRATIO with Socioeconomic Variables Variable Correlation with INCRATIO PCBLACK PCKOS PCK611 PCKNPUB PCCLGRAD PCNONHS PCFEMALE PCRTRDI PCAGE65 PCUNEMP PCTRANSF PR16UP - 0.015 0.276 0.290 0.004 -0.111 - 0.035 - 0.029 - 0.201 - 0.289 0.028 0.114 - 0.172 nity-which Hamilton suggested was a cause of the flypaper effect in education. To account for possible bias in the price and income terms, the nonlinear approach of Moffitt and Megdal was employed in estimating both equations. These additional socioeconomic variables help explain expenditure levels in these communities. An F test of the hypothesis that these additional explanatory variables are irrelevant rejects the hypothesis at the 1% level. But these additional variables do not help to explain the flypaper effect. First, the coefficient on INCRATIO is increased, not reduced, when we move to the more complete model. Second, as Table 4 shows, the correlation coefficients between INCRATIO and the socioeconomic variables are small-the largest absolute value is less than 0.3. This suggests that the flypaper effect is unlikely to fade away with the inclusion of these omitted variables. III. FLYPAPER EFFECTS a. The Courant-Gramlich-Rubinfeld-Oates DUE TO VOTER (CGRO) ERROR Model i. The nature of the voter’s error. In the second fiscal illusion group of flypaper effect theories, the voter is fooled by grants into making erroneous estimates of his effective income and the price of public goods. Courant et al. [2] and Oates [13] argue that the typical voter has little information about the extent of grants to his community. Accordingly, the voter estimates the unknown marginal cost of public goods using other known variables. By taking the ratio of his tax payments to total expenditures in the community, the voter can determine the average cost of public goods and use this as an approximation for their marginal cost. When THE ELUSIVE FLYPAPER EFFECT 321 lump-sum aid is present, however, the use of this proxy causes the voter to err in his estimate of marginal cost. If lump-sum aid is initially used to finance additional expenditure, total expenditure increases while the median voter’s tax payments remain unchanged, thus driving down the average price of public goods and leading the voter to mistakenly demand more public goods. Because of this fiscal illusion, these writers argue, lump-sum aid has a price as well as an income effect and we should not expect the aid to have an expenditure impact that is equivalent to the effect of an income increase. ii. Estimation. The most precise specification of the CGRO model of flypaper effects is given by Oates [131. Oates employs the following formal system: E=T+A P = T/E p=mP E = alYa2pa3 where E is the T is the A is aid P is the p is the Y is the m is the (budget constraint) (formation of price to community) (formation of price to the median voter) (median voter’s demand function), (2) (3) (4) (5) expenditure of the community, community’s combined tax payment, to the community (of all types), price of the community, price to the median voter, median voter’s income, and median voter’s tax share. In this system, the voter first estimates the marginal price to the community by looking at the average price of public goods. He then multiples this figure by his tax share to get the price to him. p is then incorporated into his demand function to determine the median voter’s optimal output of public goods, and political competition ensures that this is the output realized by the community. Unfortunately, because of the log-linear demand function, it is not possible to solve this system explicitly for E. It is possible, however, to formulate the following two-equation simultaneous system: In E = a,/(1 + a3) + [a,/(1 + a,)]lnY + [a,/(1 + a,)](lnm + 1nY) (6) T=E-A (7) Table 5 shows the results of two-stage least-squares estimation of (6) and (7) using the Michigan school district data, when several additional socioeconomic variables have been added to the equation. (Since the voter 322 PAUL GARY WYCKOFF TABLE 5 The CGRO Model Variable LNM + LNT LNY PCBLACK PCKOS PCK611 PCKNPUB PCCLGRAD PCNONHS PCFEMALE PCRTRDI PCAGE65 PCUNEMP PCTRANSF LNENRL LNPPB LNCTCH HSRATIO PC16UP Estimate (std. error) - 0.322* (0.048) 0.416* (0.076) 1.493* (0.192) - 0.334* (0.1221 0.007 (0.111) 0.212* (0.084) 0.801* (0.290) - 0.389* (0.1181 - 0.438 (0.275) 0.337 co.1751 - 0.275 (0.242) 0.244* (0.106) - 0.270 (0.442) - 0.397* to.0491 - 0.062* (0.017) 0.723* (0.0761 1.856E-03 (3.833E-03) - 0.224 (0.1791 Fl = 202 R2 .596 Note. All variables defined in Table 2, except: LNM + LNT = the sum of the logarithms of the voter’s tax share (median voter’s house value/total property value in community) and the total tax revenue of the community; LNY-logarithm of median family income in the community. Dependent variable is log of general expenditures, 1978-1979. *Indicates variable is statistically significant at the 5% level. THE ELUSIVE FLYPAPER EFFECT 323 is unaware of the effect of aid on income and marginal price in the fiscal illusion models, the nonlinear specification of Moffitt and Megdal is unnecessary.) Although the estimates of the price and income elasticities of demand are plausible, R2 is significantly less than in Table 1, suggesting that the model does not fit the data well. iii. Testing the CGRO model. Since the CGRO model is not a special case of any more general model in this paper, a formal test of the CGRO hypothesis is difficult. However, both the CGRO and Moffitt-Megdal models can be considered special cases of the following theoretical model: In E = b, + b,ln(Y + b,nmG) + b,[ln m + b4 In II + b, ln( T/E)] + b, incratio + b, categorical aid, (8) where, as before, additional socioeconomic variables have been omitted, G stands for lump-sum aid, and n stands for the local government’s share of expenditures under any matching grants. Under the CGRO assumptions, b,, b,, b,, and b, are all zero and b, equals one, while under the Moffitt-Megdal model, b, and b, are zero while b, and b4 equal one. Equation (8) would be extremely difficult to estimate as a general case. Not only is it nonlinear, but the estimation technique must account for both the endogeneity of n and G (as Moffitt and Megdal insist) and the simultaneity of E and T (as required by CGRO). However, the purpose of estimating (8) would be to find the unrestricted sum of squared residuals to perform an F test on the CGRO restrictions. This suggests that we might use the Moffitt-Megdal model as a stand in for (8). Since the Moffitt-Megdal case is a restricted form of (81, its sum of squared residuals must be larger than that of (8). Therefore, using the Moffitt-Megdal model as a stand-in works in &or of the CGRO model, because the difference in the sum of squared residuals will be smaller. If an F test using the Moffitt-Megdal stand-in rejects the CGRO model, an F test using (8) would also reject CGRO.’ *Proof: The appropriate F statistic is given by (SSRQ - SSR,)(n - Q) ’ SSE&Q - K) where: SSRe is the regression sum of squares for the unrestricted model, SSR, is the regression sum of squares for the restricted model, n is sample size, Q is the number of parameters in the unrestricted regression, SSEp is the error sum of squares in the unrestricted regression, and K is the number of parameters in the restricted regression (see Kmenta [8]). Since the Moffitt-Megdal model is a restricted form of the unrestricted model, it must have a smaller 324 PAUL GARY WYCKOFF Using this procedure, the CGRO restrictions are rejected. The F statistic is 15.395, while the appropriate cutoff value is 3.17 at the 1% level. Therefore, it is extremely unlikely that the CGRO model is correct. As an additional check on incomplete fiscal illusion, average tax rates were added to the Moffitt-Megdal specification (including all the variables in Table l), again using two-stage least-squares to account for simultaneity. (As explained above, due to the complexity of the estimated equation, the Wales-Woodland procedure could not be employed, but its use appears to have little influence on the results.) In this case the coefficient on average tax rate, although significant, was of the wrong sign. It should have the same sign as the coefficient on the median voter’s tax share. Also, the inclusion of average tax rate increased, rather than decreased, the coefficient on INCRATIO. b. The Filimon-Romer-Rosenthal (FRR) Model Filimon et al. [3] suggest another stronger variant of these voter ignorance theories. In their version, voter ignorance about aid and expenditure levels is combined with budget-maximizing bureaucrats. Voters in their model are unaware of the existence of intergovernmental grants, and they calculate the marginal cost of public goods by estimating their share of taxes in the community. Moreover, because of voter misinformation, the bureaucrat can find ways to pad the budget without altering the voters’ perceived level of output. Intergovernmental grants, then, do not alter the voter’s perception of his budget constraint. This leaves the bureaucrat free to use these “hidden” resources to expand his budget through hidden expenditures. In the FRR model, then, intergovernmental aid must be eliminated from the price and income terms of the equation, and $1 of intergovernmental aid (of whatever type) expands the budget by $1. In Table 6, a simple test of this hypothesis is performed, using the log-linear specification. Intergovernmental aid appears only in the term LNTOTAID. The effect of intergovernmental aid is much more modest than predicted by FRR. Differentiating the FRR specification gives: dE/d( aid) = (coefficient The upper on LNTOTALAID)* end of the confidence interval E/( aid). for the coefficient (9) on SSRO and a larger SSEQ than the unrestricted model. Hence its use biases the numerator downward, the denominator upward, and the F statistic downward, and biases our test toward the conclusion that there is no significant difference between the CGRO and unrestricted models. THE ELUSIVE FLYPAPER TABLE 6 The Romer-Rosenthal Variable LNM LNY LNTOTAID PCBLACK PCKOS PCK611 PCKNPUB PCCLGRAD PCNONHS PCFEMALE PCRTRDI PCAGE65 PCUNEMP PCT RANSF LNENRL LNPPB LNCTCH HSRATIO PC16UP n = 202 R2 EFFECT Model Estimate (std. error) -0.142* (0.031) 0.224* (0.071) 0.044* (0.020) 1.128” (0.207) -0.159 (0.127) 0.040 (0.118) 0.089 (0.087) 0.479 (0.338) - 0.214 (0.121) - 0.350 (0.290) 0.224 (0.183) - 0.240 (0.255) 0.210 (0.113) 0.444 (0.489) -0.201* (0.032) - 0.044* (0.018) 0.551* (0.076) - 1.644E-03 (4.002E-03) - 0.162 (0.188) .544 Note. All variables defined in Tables 2 and 5, except: LNTOTAID = log of total aid to the community. Dependent variable is log of general expenditures, 1978-1979. *Indicates variable is statistically significant at the 5% level. 325 326 PAUL GARY WYCKOFF LNTOTAID is 0.084. When multiplied by the sample mean for E/(aid) of 3.632, the estimated derivative is just 0.305, implying a strong rejection of the FRR specification. VI. CONCLUSION There are other explanations of the flypaper effect in the literature. These explanations are not tested in this paper, but for the most part they do not apply to the circumstances faced in this study. For example, Chernick [l] developed an explanation of flypaper effects when project grants are included in the lump-sum aid category, but project grants are not present in the lumps-sum aid variable in the regressions below. Romer and Rosenthal [14] developed a second theory which blames flypaper effects on the institutional arrangements for approving the bureaucrat’s budget in some states, in which the budget drops to a state-mandated reversion level if the bureaucrat’s proposed budget is not approved. Therefore, this second Romer-Rosenthal explanation of flypaper effects is confined to a limited set of circumstances. The Michigan school districts in this study faced a more complex set of institutional arrangements in which the reversion level was not likely to have a significant effect.3 Similarly, Fisher [4] has noted that tax effort requirements in revenue sharing formulas can cause a flypaper effect, but Michigan school districts do not receive revenue sharing of this type. The skeptical reader might argue that all of the results above relate only to the case of Michigan school districts at this particular time. There is no guarantee, of course, that Michigan school districts are not unusual, and that these four theories do not have relevance for other circumstances. ‘Michigan property tax laws require voter approval of property tax rates, and there are state-mandated “allocated” millage rates if the voters refuse to approve a specific tax rate. But the situation is more complicated than the simple binary choice analyzed by Romer and Rosenthal. First, in Michigan, additional higher tax requests are separated from requests to renew the existing millage. Hence the typical voter has a three-part, rather than two-part, choice: he can vote for the additional millage and the renewal, he can vote for the renewal only, or he can vote against both proposals. This complicates the analysis. Furthermore, the allocated millage is typically so low (less than one-third of current tax rates) that few voters are likely to find it attractive, so the choice for most voters is between the existing millage and a new, higher proposed tax rate. Second, tax approvals are for varying periods of time. Voters approve the term of the tax rate as well as its amount at the time of voting. Tax rates can be approved for an indefinite period, but most referenda are for less than 5 years duration. This means that the voter and the bureaucrat must introduce future expectations of each other’s demands into their thinking. Third, a sequence of elections is common in Michigan. After the initial proposal is defeated, school boards can go back to the voters for a second, a third, or even a fourth time. Hence voters know that the alternative to defeating the school boards proposal is not the state-mandated reversion level, but rather approving a later, smaller proposal from the school board. All these factors reduce the influence of the state-mandated reversion on the expenditures of the school district. THE ELUSIVE FLYPAPER EFFECT 327 But the skeptic’s position requires the simultaneous conjunction of a number of unlikely factors. If flypaper effects are caused by different factors in different places and times, why do these effects show up so consistently and so significantly in empirical studies? If a number of factors were involved, surely the empirical results on flypaper effects would be more mixed than we observe. This problem is particularly severe since many of the explanations of flypaper effects-such as those of Moffitt and Megdal and Hamilton-relate only to particular types of grants of particular types of public goods. How can these particular explanations account for the nearly universal phenomenon of flypaper effects? The data are more consistent with the idea that the flypaper effect is caused by a single factor which is imbedded much more deeply in the process of local government decision-making than is currently acknowledged. Only through such a consistent factor could the strength and universality of flypaper effects be easily explained. The nature of this factor has eluded the authors of these four theoretical explanations. In a previous article in this journal (Wyckoff [IS]), I suggested that bureaucracy might be such a deeply imbedded factor. My explanation included two components: (1) a bureaucrat who sought to increase the size of his budget or “pad” it with unnecessary expenses; and (2) a voter whose alternative to living with a particular bureaucracy was to move to a new jurisdiction. The flypaper effect occurs because of an asymmetry in the voter’s bargaining position with bureaucrats under lump-sum aid and increases in income. A lump-sum aid increase stays with the jurisdiction if the voter moves, so the voter’s bargaining position is not enhanced by the aid. An income increase, on the other hand, would be moved to the new jurisdiction if the voter gets fed up with the bureaucracy, so it increases the value of the voter’s threat to leave. This difference in threat value holds down spending in the income increase case but not in the lump-sum aid case, creating a flypaper effect. It must be admitted, however, that testing for these more deeply imbedded factors is more difficult than testing for the explanations offered above, because there is no way to correct for or isolate the factor. If flypaper effects are caused by the use of the wrong econometric technique, we can simply use the right technique, see if that eliminates the problem, and attribute the flypaper effect to econometric causes if it does. But the only way to correct for bureaucratic influence is to find a jurisdiction without that influence, which presumably would be difficult. In the future, then, tests of the causes of flypaper effect will probably be accomplished only indirectly, through testing for the presence of other empirical implications of the underlying models. For example, in two papers (Wyckoff [18, 1911, I showed that the theoretical implications of 328 PAUL GARY WYCKOFF bureaucratic influence are consistent with the empirical behavior of local governments. In this way, the debate about the flypaper effect is likely to merge into the more general debate about who controls the local fist. REFERENCES 1. H. A. Chemick, An economic model of the distribution of project grants, in “Fiscal Federalism and Grants-in-Aid” (P. Mieszkowski and W. H. Oakland, Eds.), The Urban Institute, Washington, DC (1979). 2. P. N. Courant, E. M. Gramlich, and D. L. 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