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# Advanced Seminar Policy and Administration PPA 810

Syracuse

GPA 3.52

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This 15 page Class Notes was uploaded by Harmon Price on Wednesday October 21, 2015. The Class Notes belongs to PPA 810 at Syracuse University taught by John Yinger in Fall. Since its upload, it has received 43 views. For similar materials see /class/225666/ppa-810-syracuse-university in OTHER at Syracuse University.

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Date Created: 10/21/15

State Aid in the Budget Constraint Class Notes JY 22107 These notes discuss the impact of state aid on a household s budget constraint This impact is the key to studying the impact of state aid on the demand for local public services The notes focus on education because that is Where state aid is most Widely used and Where the principles are clearest but the basic analysis applies to other types of state aid too LumpSum Aid The household budget constraint YZPH2VZPH2 1 The community budget constraint With aid per pupil A ES I A 2 Combining the two constraints gives YZPHES A 3 This equation can easily be rearranged to be YAZPH 1315 4 This leads to the rst big insight about aid which is that it is just like income except that it is weighted by taX share The reason for this is that the impact of 1 of aid on the median voter depends on her taX share that is on how much it saves her in taxes This was first pointed out by Oates see his book Fiscal Federalism This is an equivalence result 1 time taX share of aid has an impact on a voter s budget constraint and hence on her choice of S that is equivalent to 1 of income But there are two important extensions 1 The impact of aid is difficult to estimate due to its nonlinearity Remember the multiplicative demand function that is so common in the literature Replacing Y with the left hand side of 4 gives us SKYA9 T1M K YA j6MC 5 We can replace income with augmented income and estimate this equation but only by assuming that the equivalence theorem holds We cannot test this theorem this way that is we cannot determine whether the elasticity is the same for Y and taxshareweightedA 2 Estimates of the impact of aid resoundingly reject Oates equivalence theorem VI7 of aid has a much bigger impact on the demand for local public services than does 1 of income This is known as the ypaper effect money sticks where it hits So how can we estimate the ypaper effect First rewrite the augmented income expression V AV YA7Y177 6 Then plug this expression into the demand equation 5 take logs and use the approximation 1n1a 2 a 1115 111K 6111Y1 11111013 1nS lnK61nY 61nl ylnTP 7 1 A V nS lnK61nY6Y7JlnTP Now all we have to do is add a term for the ypaper effect say f and estimate 111S111K 61nY 6f ylnTP 8 The ypaper effect is the ratio of the coef cient of the aid variable to the coef cient of the Y variable Note One also could add a ypaper effect to equation 5 and estimate it with nonlinear techniques Why does the ypaper effect exist Nobody really knows For some reason voters treat money that comes directly into the public budget differently than money that comes in through their own budget even after correcting for the taXshare effect Some kind of illusion is at work but nobody in my opinion has been able to pin it down The person who does will be famous Matching Aid We can also add matching aid which supplements local revenue to the community budget constraint There are two ways to set this up One way is to express the matching rate as the state share of total spending mSSL where S stands for state and L stands for local In this case the denominator equals total spending less block grant aid A that is states do not supplement their own block grant aid with a match In a community budget constraint we write ES A1 mzV 9 which when combined with the individual budget constraint lead to YZPHES A1 m 10 So now the taxprice term has a third component TP MC1 mj 11 The other approach is to express the matching rate as the ratio of state aid to local revenue m SL With this approach the rate really is a match how much state aid is provided for each local dollar With this approach we write ES 71mA 12 and the individual budget constraint becomes 1mquotlt YZPHES A 13 So you can see that the two matching rates are related l m 14 However the matching rate is expressed raising the matching rate lowers the tax price and stimulates spending This leads to a widely known theorem A matching rate is thought to have a bigger impact on the demand for public services than an equal cost block grant A matching rate has a substitution effect as well as an income effect so it stimulates a larger shift toward the subsidized activity A corollary is that a matching grant does not raise the utility of the median voter as much as does a block grant because it does not strictly follow her preferences The diagram supporting this comes from intermediate microeconomics and in particular from comparing the consumption impact of a price subsidy with that of an equalcost income subsidy Recall that the demand for public services tends to be inelastic This applies to matching grants as well as to tax shares or marginal cost But few studies estimate price elasticities for matching grants The reason is that matching grants mess up state budgets Their cost depends on the decisions of recipient governments and therefore is hard to predict Legislatures can handle predicting revenues but they hate to have to predict spending A strange puzzle Because of this uncertainty legislatures usually make matching grants closedended They match only up to a certain spending level And then they make the cap so low that most recipients hit it In effect this step transforms the matching grant into a block grant But a few studies have estimated price elasticities for matching grants and found them to be in the same ball park as price elasticities based on tax shares or marginal costs In other words response to a matching grant is inelastic One well known implication of this is that one should not expect the demand response to be much greater with a matching grant than with a block grant With a small substitution effect the two grants have a similar impact on demand But with the ypaper effect this may not go far enough The theorem ignores the ypaper effect which only affects block grants So it might be true that a block grant is more stimulative than an equalcost matching grant This topic is ripe for further research Interaction between Block and Matching Aid For some reason the literature has missed a key implication of this set up if some block grant aid already exists and the question concems the impact of additional aid Because matching grants alter the value of block grant aid to the median voter it is not at all clear the matching grants have a greater stimulative effect even if the price elasticity is large Rearrange the budget constraint we wrote down earlier and add a ypaper effect YfA1 mZPHES1 m 15 So the augmented income term has m in it and so of course does the price term Moreover the impact of m on the income term has the opposite sign from its impact on the price term The higher the matching rate the lower the value of existing block grant aid for the median voter and the lower her demand for public services Grants and Ef ciency One nal twist on this story arises because grants affect ef ciency A higher block grant leads to less ef ciency through the augmented income term A higher matching grant leads to less ef ciency through the taxprice term Thus both types of grants not only have direct impacts on demand but also have offsetting indirect impacts on demand through ef ciency Both types of grants have less impact on service quality if not on spending than one would think because they undermine ef ciency and thereby boost the effective tax price for a voter Moreover if the indirect impact of matching grants is greater than the indirect impact of block grants the standard theorem could be reversed One nal implication of the link to efficiency Which is not proved formally here is that When ef ciency is omitted from the demand equation the estimated income and price elasticities Will pick up both the direct and indirect effects through efficiency and therefore cannot be interpreted as standard income and price elasticities In fact the true income and price elasticities Will generally be larger than the estimated ones Types of Aid to Education There are 2 main types of aid to education 3 if you count ad hoc foundation grants and power equalizing grants Power equalizing grants are also called guaranteed tax base grants GTB Foundation Grants Most states use a foundation grant for some of their education spending It is also the form most Widely discussed for recent reforms in most states including New York With a foundation grant aid per pupil to district j equals a foundation spending level per pupil E minus what the district could raise at what is presumed to be a fair taX rate t This revenue equals t multiplied by the district s property tax base per pupil Thus the standard formula for a foundation grant is AjE IVJ 16 This formula does not recognize cost variation but this is easily added A J SC J tV 17 NW 39 gtlt ASTJ IV Note that it is not appropriate to multiply the entire aid expression the rst line of 19 by weighted pupils This would link pupil weights to property values which makes no sense A lowvalue district should not get less aid because it has more weighted pupilsll One important decision is whether to make I required If it is not required as in New York and many other states then a troubled district is unlikely to reach the foundation spending level because some of the aid it receives will be devoted to a tax cut The City of Syracuse is a good example Power Equalizing Grants GTB A power equalizing grant GTB is based on the philosophy that the amount of money a district spends on education should depend only on the rate at which it is willing to tax itself not on its tax base It is used in three or four states In symbols 15th 18 Now since spending equals aid A plus the local contribution tjVj we can also write EjAjthjth or AjtjV VJ 19 Combining this with equation 21 gives the nal form for aid namely 20 Comparing this with equation 19 reveals that GTB aid is similar to foundation aid except that it is based on actual spending not foundation spending which is a policy parameter Equation 23 also reveals that GTB aid is a form of matching aid in which the state share of the total the expression in parentheses also m increases as a district s property value declines Powerequalizing grants were introduced at about the same time as the Serrano decision in California which was the first major case to throw out a state s education finance system At the time these grants were thought to satisfy the criterion of wealthneutrality which is said to exist when there is no correlation between wealth and spending or better performance and which was part of the Serrano decision Another way to put it is that with wealth neutrality a regression of spending performance on wealth will have a zero slope A GTB grant was thought to do this because it seems to say that spending does depend on district wealth In a wellknown article Feldstein showed that this is not the case The impact of a powerequalizing grant on performance depends on the behavioral response to the matching rate which is much higher for poorer districts It would be an amazing coincidence if this behavioral response exactly produced wealth neutrality Feldstein also found that a GTB grant went past wealthneutrality to a negative slope Bill and I nd that it moves toward wealthneutrality but does not go past it If the behavioral response is known one can build it into the grant to get wealthneutrality Alternatively one can put in a parameter and adjust it over time until wealth neutrality is achieved Finally Bill and I show that it is possible to add costs to a GTB grant In this case the cost index simply goes into equation 23 21

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