Land-use zoning in a local economy with optimal property taxes and public expenditures

Journal of Real Estate Finance and Economics, 1:373-391 (1988) �9 1988 Kluwer Academic Publishers

Land-Use Zoning in a Local Economy with Optimal Property Taxes and Public Expenditures

DENNIS R. HEFFLEY Department of Economics, The University of Connecticut

DANIEL P. HEWITI" Department of Economics, The University of Connecticut

Key words: zoning, property taxes, public expenditures, land rents, urban public finance.

Abstract

A three-sector, open-city framework is used to study the impact of changes in land-use zoning on a local economy. In addition to the customary direct supply effects, a rezoning prompts changes in local property.tax rates, public expenditures, and the location decisions of households and firms. Simu- lations are used to trace these general equilibrium adjustments. The final effects of a residential- to-commercial rezoning on crucial local economic variables, including residential and commercial site rents, property tax rates and the mix of public services, may contrast sharply with popular expectations based solely on a partial equilibrium analysis.

1. Introduction

The influence of land-use zoning changes on the character of a town is a con- troversial topic. Local proposals to open more land to business use, for example, lead to speculation on how this will affect residential and commercial land values, local property tax rates,-and the level and mix of public services. This study traces the direct and indirect effects of changes in land-use zoning on the economic con- figuration of a small open economy. Some of the direct effects of rezoning conform to popular beliefs. When local fiscal authorities are able to respond to such changes, however, and the mobility of households and firms is more complete, the final effects of a rezoning may be unanticipated.

A residential-to-commercial rezoning often is viewed as a way of increasing employment opportunities for local residents. Yet, if the town is small relative to the regional economy and households and businesses are mobile in the long run, employment gains are likely to be dissipated across neighboring towns) Under these circumstances, the primary potential benefits from the rezoning will consist of altered land values or added business property tax revenues. The latter, in turn, may permit an increase in public services to residents or a reduction in residential

374 DENNIS R. HEFFLEY AND DANIEL P. HEWlTT

property tax rates. The analysis here shows that land values, property tax rates and revenues, and public services do change, but not always as expected.

Interdependencies between zoning and fiscal decisions have been commonly acknowledged, but their specific relationship has not been thoroughly studied. In tax competition studies (e.g., Beck (1983), Gerber and Hewitt (1987a, b) and Wilson (1986, 1987)), optimal fiscal policies are examined when capital is mobile and residents are not. Zoning, in these models, is implicitly assumed to be entirely flexible; that is, a community is able to accommodate virtually any number of businesses it can attract. In studies based on the Tiebout model (e.g., Brueckner (1981), Hamilton (1975, 1976), Rose-Ackerman (1983), and Stiglitz (1983)), optimal fiscal policies are investigated with mobile residents. Rather than restricting land- use patterns, zoning is relegated to the role of filtering the type of residents that enter a community.

The zoning literature itself has tended to focus on the direct effects of zoning on land rents, housing prices, and the composition and size of the community. Results from different studies are not always comparable, due to differences in un- derlying assumptions (open vs. closed communities, municipal vs. metro- politan-wide zoning, etc.) and differences in the types of zoning considered. Grieson and White (1981) and Henderson (1985a, b) have done much to clarify our understanding of the different forms of zoning and the effects of these restrictions under various conditions, but even these studies do not fully account for the indirect effects of zoning through the fiscal mechanism. We refer to these and other studies of zoning in the course of our analysis. Section 2 presents a conven- tional partial equilibrium analysis of a residential-to-commercial rezoning. Sec- tion 3 specifies the general equilibrium model that is simulated in section 4. Sec- tion 5 offers some final remarks.

2. Direct effects of land-use zoning

A simple exposition of the direct effects of a zoning change illustrates the potential importance of fiscal reactions and migration in determining the final effects of the new zoning policy. The setting is a small suburban town with a fixed amount of land available for developed uses. To keep the analysis manageable, we consider two types of land-use, residential and commercial, and ignore the many forms of density zoning (minimum lot size, minimum unit size, height restrictions, frontage and set-back requirements, etc.) that delineate the subcategories within these broader land-use zones. 2 Land in this locality, although possibly different from land in other towns by virtue of its access to a regional center or a localized amenity, is assumed to be internally homogeneous except for the zoning designation of either residential or commercial.

Figure 1 depicts the markets for residential and commercial land within the town. Landowners, the suppliers of land to households and businesses, are

L A N D - U S E Z O N I N G IN A L O C A L E C O N O M Y 375

* r 2 = r

~ Z2 ~L~

z I >-

I

C tl C

Z2 z 1

residential ~ "~"_ -'I

l a n d

t o t a l area __ _

.R 1

R 2

IR u

Fig. 1. Partial equi l ibr ium analysis of the direct effects o f land-use zoning. Point A shows the unrestricted equi l ibr ium; point B determines the allocation of land that maximizes aggregate site rent. An initial zon ing policy (z 1, ZI) results in a commerc ia l site rent o f R 1, a residential site rent equal to the reservation site rent (rj = r), and v j acres of vacant residential land. The direct effect of an increase in Commer- cially zoned land, from Z 1 to Z 2, is to reduce the commercia l site rent toR 2 and, once vacant residential l and is exhausted, to increase the residential site rent.

assumed to have a constant reservation site rent of r dollars per acre. Positive values o f r may reflect either the utility value of vacant land or speculative motives of landowners. Residential and commercial users exhibit separate demands for this land, labelled d and D. 3 Associated marginal revenue curves are labelled m r

and MR. These demand and marginal revenue curves for each class of users are shown "face-to-face" in Figure 1, where residential and commercial site rents, r and R, are measured along the left and right vertical axes. Residential acreage is measured horizontal ly from left to right; commercial acreage is measured from right to left; and the length of the horizontal axis reflects the town's fixed total area zoned for developed u s e s . 4

Owners of land lease to the highest bidder in the absence of zoning restrictions, provided this dominant bid exceeds r. In the case depicted here, the unrestricted division of land between residential and commercial uses is determined by the in- tersection of demands at point A. Without zoning, equil ibrium residential and commercial site rents must equalize ( r , = R , ) . 5 But note that, contrary to popular interpretations of the doctrine of"highest and best use," the market's allocation of land to the highest bidder does not necessarily maximize aggregate site rent if the total area is constrained. The land split that maximizes aggregate rents in Figure 1

376 DENNIS R. HEFFLEY AND DANIEL P. HEWITT

occurs at point B, where residential and commercial marginal revenue (marginal aggregate site rent) curves intersect. Thus, even in the absence of land-use externalities, economic incentives for the town to regulate the land-use within its boundaries may exist. If zoning is adopted, unequal site rents for residential and commercial land should be expected.

Consider a town that currently follows a restrictive commercial zoning policy. An ample z, acres are zoned for residential use, but only Z~ acres are designated for commercial purposes. The supply of land in each submarket is nowL-shaped, perfectly elastic at the reservation site rent, r, up to the vertical zoning constraint, there becoming completely inelastic if zoning is enforced. 6 In Figure 1, this policy generates an equilibrium in the commercial land market at point C, where the Z, acres zoned for this use are fully utilized and the commercial site rent is R, dollars per acre. In the residential market, the equilibrium occurs at point E. The relative abundance of residential land under this initial zoning policy drives the equilibrium site rent (r,) down to r, and the actual usage of land for residential activity falls short of the z~ acres zoned for this purpose; v~ acres of residential land remain vacant. 7 The zoning constraint in this residential submarket is nonbinding in an economic sense, but it legally precludes owners of the vacant residential land from securing the higher commercial site rent (R0. The incentive for this subset of landowners to press for a rezoning is apparent.

Suppose that local authorities are persuaded to rezone a portion of the vacant residential land. The direct effect of this increase in commercially zoned land, from Z~ to some Z2 acres, is to reduce the equilibrium commercial site rent (R, < R~). Unless all vacant land in the residential market is rezoned, the equilibrium residential site rent is undisturbed (r_~ = r~ = r). A large enough shift in the zoning constraint (to the left of point E), though, would both eliminate any vacant residential land and boost the residential site rent.

The case depicted probably is not much at odds with circumstances in many smaller suburban towns, and the predictions of this direct analysis are generally consistent with popular notions about the effects of a residential-to-commercial rezoning. 8 Yet the final consequences of rezoning are less clear, especially if local fiscal behavior is introduced and the open nature of the local economy is considered.

Since property taxes are an important source of local revenue, a zoning change that alters land rents and the pattern of land use also affects the revenue yield of any particular set of tax rates. This, in turn, influences the level and even the mix of local public services. An ideal initial set of taxes and expenditures quickly may become suboptimal when local land markets respond to the rezoning. If fiscal authorities sense this need to modify policies and react to the new environment by altering tax rates and services, capitalization effects of these fiscal changes will shift the demand and marginal revenue curves shown in Figure 1. Consequently, r2 and R2 do not reflect the final equilibrium site rents under the new zoning pattern if "fiscal feedback" effects are considered?

Migration further complicates matters. If either the rezoning or the induced fis-

LAND-USE ZONING IN A LOCAL ECONOMY 377

cal changes alter the utilities of local residents or the profits of local firms, making them higher or lower than outside levels, entry or exit of households or firms can occur. Since the local market demand curves for residential and commercial land in Figure 1 are summations of the individual demands of households and firms, respectively, any change in the number of each type of agent causes additional demand shifts that again may affect conclusions about the ultimate impacts of rezoning.

Fiscal responses and relocation effects, prompted by the zoning change, could be illustrated in Figure 1, but the net results are complex and can best be evaluated with a model that integrates the economic behavior of the principal parties: households, businesses, and local government. We develop such a model in the following section. Then, in section 4, a numerical application of the model highlights the potential differences between the direct and the final consequences of a residential-to-commercial rezoning.

3. A model of the local economy

Complete analysis of local economic changes prompted by a rezoning requires a general equilibrium approach. Since this study focuses on how rezoning triggers tax and spending changes that influence final outcomes, the centerpiece of the analysis is a model of the local government's choice of property tax rates and public spending patterns. The local budget constraint and the town's existing zoning policy are incorporated, and nested within this model are two submodels that describe the long-run behavior of households and firms. When merged, the three models contain an array of endogenous elements: equilibrium site rents for residential and commercial land; residential and commercial property tax rates; the mix of expenditures on consumer-oriented and business-oriented public services; the equilibrium number of households and their demands for residential land, housing structure, and a composite consumption good; and the equilibrium number and scale of firms and their demands for commercial land, commercial structure, and a composite input. The zoning policy is parametric for comparative static purposes as well as for tractability. ~~ Because the household and business submodels provide information that fiscal authorities incorporate in their decisions, exposition of the local government model is simpler if the submodels are laid out first.

3.1. Households

The residential sector consists of an endogenous number, h, of similar, utility- maximizing households. UtiliW is a function of the household's consumption of residential land, l, housing structure, s, a composite (non-housing) private good, x, and the level of local expenditures on residential public goods, g. Household in-

378 DENNIS R. HEFFLEY AND DANIEL P. HEWlTI"

come,y, is fixed. The rental price or site rent of residential land, r, the rental price of structure, m, and the private good price, p. are exogenous to each household. Also, each household is subject to a property tax, t, that is imposed on its annual outlay for land and structure) l The level of public spending and the residential property tax rate are beyond the control of any one household. Later, however, g and t become endogenous variables in the government choice model. Given the household's decision to occupy a particular town, its behavior is characterized by the solution to the constrained maximization problem:

Max H(Ls, x,L) = u(l,s,x;g) + ~.[y - (1 + t)(rl + ms) - p x ] . (1)

Long-run behavior of the consumer is traced by using the resulting demands for land, structure, and the private good to obtain the indirect utility function, u*(y,r,m,p,g,t). Under an open-city assumption, households will enter or leave the town until u* matches the level attainable in other communities, ft. If non-land prices (m andp) are regionally determined, the local price of residential land ad- justs to meet the open-city condition. Solving the open-city condition for r yields r*(?t,y,m,p,g,t), the residential site rent consistent with household optimization and locational equilibrium.

Substituting r* back into the direct demand functions gives the household's long-run equilibrium behavior: l*(~,y,m,p,g,t), s*(~,y,m,p,g,t) and x*(~,y,m,p,g,t,). These behavioral functions are essentially compensated demand functions, with utility constant rather than income. The number of households that can be accom- modated depends upon the town's available supply of residential land. Ifz acres of land are zoned for this purpose and the constraint is binding (i.e., if r* > r), the number of households is h* = z/l*(K,y,m,p,g,t). Eventually this submodel of household behavior and a similar business submodel are imbedded in the primary model of local fiscal choice. The complexity of the full model hinders the derivation and analysis of general solutions, but by using specific forms we are able to demonstrate that the final effects of a rezoning may differ sharply from the direct effects outlined in Section 2.

Using a Cobb-Douglas utility function,

u(l,s ,x;g) = AUsOxVg ~, (2)

where ct,[~,y,SC (0,1) and 0 = (et + [3 + T) < 1, the procedure outlined above produces the following long-run demands of the typical household:

l* = [y~-~ + t)~/~]/Vgr/~O,

s* = ~y/Om(1 + t), (3)

x* = ~,y/Op,


where V = [A(1/O)~ > O. The equilibrium residential site rent, number of households, and revenue generated by the residential property tax a re

r* = [ay~ + t) ~+~1/~,

h* = [OzVgS/~y~~ + t)~/L (4)

j * = h*[t(r*l* + ms*) = t(1 + t)-~+~)/~zg6/~y~/~V(et + ~).

Several of the expressions in (3) and (4) reflect the influence of the open-city condition. The demands for structure and the composite consumption good, s* andx*, are standard Cobb-Douglas results. 12 In contrast, the demand for land em- bodies the open-city condition; l* may be thought of as the amount of land necessary to bring the household up to the required level of utility. If taxes are high or g is low, the household needs more land to reach ft. The influence of government policies on household demands and community equilibrium values is clear from (3) and (4). Residential site rent, for example, is positively related to g and negatively related to t: the familiar capitalization effects of local taxing and spending.

3.2. Businesses

The commercial sector consists of an endogenous number of firms, F, each with a common production technology. Each firm's output, X, is a function of its use of land, L, commercial structure, S, other inputs, N, and the level of a local commercial (or production) publi c good, G. ~3 Each firm maximizes profits, n, based upon the production technology, the output price, P, and the respective input prices: R, M, and W. A commercial property tax, T, is levied on property-related expenditures. In seeking profits, each firm solves the problem

Max ~(L,S,N) = PX(L,S,N;G) - (1 + T)(RL + MS) - WN. (s)

With normal assumptions about technology, the input demands derived from (5) can be used to construct an indirect profit function, n*(P, R, M,, W, G, T). If firms are mobile in the long run, another open-city condition will peg n* to some outside profit level, ~. This condition gives an equilibrium commercial site rent, R*(~, P, M, W, G, T), which can be used in the input demand functions to derive the firm's long-run behavior: L*(~,P, M, W, G, T),S*(~,P, M, W, G, T), and N*(~, P, M, W, G, T). The solution also provides at/equilibrium number of such firms, F* = Z/L*(~, P, M, W, G, T), where Z is the (binding) amount of land zoned for commercial use .

380 DENNIS R. HEFFLEY AND DANIEL P. HEWITF

Again, for the example in section 4, the production function is Cobb-Douglas with diminishing returns to scale and parametric G, or

X(L,S ,N, 'G) = BL~S*NqG ", (6)

where e,O,q,~ C (0,1) and f~ - (~ + ~ + q) < 1. The first-order and open-city conditions lead to the demands

L* = [if(1 + T)*/~]/G"/~(1 - f~)E,

S* = ~ff/(1 + T)M(1 - f~), (7)

N* = qff/W(1 - ~ ) ,

where E = {PB(q~/M)*(q/W)q[(1 - f~)/~] i-~} l/~ > 0. The equilibrium commercial site rent, number of firms, and commercial property tax revenues are

R * = [cEG"/~]/(1 + T) (~+*)/~,

F * = [ZG"/~E(1 - f~)]/(1 + T)* /~ ,

J* = F * [ T ( R * L * + MS*)] = T(1 + T)-c~+*)/~ZG~/~E(~ + q~).

(8)

The demands for structure and labor, S* and N*, are again the standard Cobb- Douglas results. The amount of land necessary for the firm to earn the required level of profits is represented by L*. This amount will be larger if T is high or G is low. Large values of T or small values of G can cause an outflow of firms and a reduction in commercial site rents. Given some amount of land zoned for such uses, Z, remaining firms must occupy larger parcels of the cheaper commercial land in order to earn the profits needed to stay.

The open-city device provides a compact way of describing the long-run behavior of households and firms in a local economy. Absent is a model of the choice of local tax and spending policies. Property tax rates (t,T) and levels of public spending (g, G) may be exogenous to any single household or firm, but in a general equilibrium model of the communi ty they are instruments of government policy. In the next subsection (3.3), we model this policy choice, incorporating the long-run behavior of households and firms, the need to balance the local budget, and the allocation of land associated with any particular zoning policy.

3.3. Local government

Land-use zoning normal ly is subject to irregular, discrete changes that are not easily reversed (e.g., the designation of a new industrial park). In contrast, fiscal

LAND-USE ZONING 1N A LOCAL ECONOMY 381

decisions are revised upward or downward annually, sometimes more frequently. For this reason, the model is constructed on the premise that the fiscal authority views the zoning policy as exogenous. The town's fixed area zoned for development is separated into z, the area zoned for residential use, and Z, the area zoned for commercial use. Given this zoning policy, the fiscal authority must limit its choice to tax/spending combinations (t, T,g, G) which balance the local budget. Within this budget, however, the property tax revenues generated by one sector need not be earmarked for services to that sector; i.e., cross-subsidization between sectors is permitted.

Various local government objectives have been proposed, but when both households and businesses are mobile, the number of reasonable choices is limitedJ 4 We assume that government adopts a fiscal package that maximizes aggregate site rent (ASR). M a x i m i z i n g A S R is equivalent to maximizing aggregate land value, an objective that has theoretical and empirical support in related studies.IS The goal of the local government can be summarized in the constrained maximazation problem

MaxASR( t ,T ,g ,G) = zr* + Z R * + 911"* + J * + I - - g - G], (9)

where I denotes exogenous sources of revenue; z and Z are parameters;~6 r* and j*, each a function ofg and t, come from the household submodel; and R* and J*, each a function of G and T, come from the business submodel. Since (9) incor- porates household and firm variables, it reflects government's recognition that its fiscal decisions will influence residential and business behaviorJ 7

The solution to (9) and the specific results from (4) and (8) produce the following guide to government policy:

t* = (a0/[3~)T*, (lOa)

g* = [(SVz)~y~ + t*)~] 1/1~-5), (10b)

G* = [(~EZ)~/(1 + T*)*] '/r (10c)

g* + G* = j * + J* + I. (10d)

Given the parameters of the household and business sectors and the zoning policy, this nonlinear system (10) defines a tax/spending menu (t*,T*~g*,G*) that maximizes aggregate site rent within the town. These optimal tax rates and public spending levels then can be substituted back into the behavioral functions of households and firms to obtain the final economic profile of the community. Any change in the zoning mix produces a new equilibrium.

Even using simple Cobb-Douglas forms for utility and production, a closed- form solution to (10) is not obtainable, though we are able to numerically compute a solution for any given set of parameters. 18 In the next section, we use this ap-

382 DENNIS R. HEFFLEY AND DANIEL P. HEWITT

proach to demonstrate that, even for a plausible set of parameters, the final effects of a residential-to-commercial rezoning may contradict the partial equilibrium analysis. Before considering the example, several results or properties of(10) may be of interest.

First, the notion that the property tax is a "benefit tax," equivalent to a user fee for local public services, has received strong support from a number of econo- mists. 19 By equation (10a), optimality in this model requires a proportional relationship between the two tax rates: t*/T* = (ct/[3)/(e/~). Absolute tax rates may vary with changes in other parameters of the model, but relative tax rates should be invariant if ct,[3,e, and 0 are constant. Equations (10b) and (10c) imply no similar proportional relationship between optimal expenditures on the two public goods, g* and G*. Since there is no fixed relationship between the level of taxes and the level of services for each group, the property tax cannot be viewed as a simple benefit tax. There must be overall balance in the budget (10d), but the sectoral components normally will not balance (i.e.,g* g:j* and G* ~ J*), even when there are no exogenous revenues (I = 0). If the property tax fails the benefit tax test for this specific model, it is difficult to see how the tax meets this test at a more general level.

A second related question is the issue of whether businesses should be taxed more heavily than residents. Households and firms are taxed on both land and structure, but land is the only limited factor in this model. Intuitively, if land is relatively more important than structure for households than it is for firms (i.e., (ct/ [3) > (e/0)), it will be optimal to tax residential land more heavily than commercial land, and vice versa. This logic is supported by (10a). If towns differ in the types of households and firms they contain, differences in the degree of tax discrimination across towns should be expected. Tax discrimination between land uses within a town and differences in the degree of tax discrimination across towns have led some state legislatures to impose "tax equalization" requirements and to press for uniform assessment practices. Communities which tax optimally, however, have an economic incentive to resist such measures, except in the rare case where ct/[3 = ~/~.

Finally, (10) illustrates the sensitivity of taxing and spending policies to zoning changes. It may appear that local taxes are independent of the zoning mix (z, Z); however, (10a) only indicates that relative tax rates are unaffected by zoning. Ab- solute tax rates are sensitive to zoning changes, as demonstrated by the simulations in section 4.

The dependence of spending levels on the zoning mix is more apparent from the mathematics (10b, c), but also more complex. For example, if~ > p, an increase in Z requires an increase in G* or T* to preserve the equality in (10c); one of these variables could decrease, but only if the increase in the other is sufficiently large. The fact that a higher value of Z might call for a larger outlay on commercial public services is not surprising. If the zoning constraint is binding in the commercial sector, relaxing this constraint initially reduces commercial site rents, in-


creases profits, and attracts additional firms, thereby raising the marginal local benefit of increasing G.

The fact that an increase in Z could lead to either an increase or decrease in T* and, by (10a), and increase or decrease in t* is more surprising and of particular interest. Residential-to-commercial rezoning is often "sold" to residents on prom- ises that residential tax rates will fall or that public services to residents will be en- hanced. Our example in the next section shows that it is possible, in a general equilibrium setting, for an increase in Z to simultaneously increase t* and reduce g*. In the face of such adverse effects, household utility can be preserved only by an exodus of some households and a reduction in residential land rents.

4. An example of the final effects of rezoning

Simulations based on plausible or empirically generated parameters have become more acceptable under the rubric of "computable general equilibrium" modeling, but, regardless of what we choose to call them, numerical examples ought to be in- terpreted cautiously. In addition to harboring all of the limitations of the model, simulation results are parameter specific and possibly quite sensitive to changes in these values. This degree of sensitivity, in itself, may be of considerable interest and not always evident from more general methods of analysis. In the end, however, simulations are more useful in disproving certain claims or preconcep- tions than in establishing general results.

We offer the following application of the model simply to illustrate that the final effects of a zoning change are quite complex; they need not contradict the predictions of a simple partial equilibrium analysis, but they do in the very reasonable example considered here. 2~ In almost all cases, the effects are more complicated than either the advocates or the opponents of a rezoning would have zoning of- ficials or the electorate believe.

Consider first some popular notions about a zoning change that allows more commercial development within a town that has a fixed amount of land available for developed uses. Abstracting from externality effects, a diversion of land from residential to commercial use might be expected to: (i) lower commercial site rents and increase, or at least not reduce, residential site rents; (ii) attract more firms~ and (iii) facilitate a reduction in the residential tax rate or an increase in the provision of public services to residents. Such intuition is generally consistent with the analysis in section 2. But the final effects of this rezoning may differ from the direct effects if households and firms can modify their consumption, production, and location decisions and if the local government is able to adjust its tax/ spending behavior to these new circumstances. The partial equilibrium analysis of zoning changes might stand if capitalization and migration effects were negli- gible; many empirical studies suggest they are not.

In establishing baseline parameters for our example, we try to construct a plaus-

384 DENNIS R. HEFFLEY AND DANIEL P. HEWIT'i?

ible economy by using 1980 data (Census, property assessment, fiscal reports, etc.) for a predominantly residential community: the coastal suburban town of Guil- ford, Connecticut. The Cobb-Douglas utility and production functions, (2) and (6), are convenient for this purpose, since each of the functional exponents corre- sponds to a household expenditure share or a factor cost share of business revenues. Aggregate data are used to estimate et,13,T,~,r and ~. The values of A, B, ~, and ~ are chosen to produce accurate benchmark levels ofh and F. The levels of p, m. P, M, and W are somewhat arbitrary but have no qualitative impact on the results. These parameters are listed at the top of Table 1. We make no strong claims about the accuracy of the parameters, but they are based on published data, look reasonable, and result in a baseline simulation that broadly resembles the community as it appeared in 1980. They also correspond well to simulation parameters adopted by Beck (1983), who cites other studies that use or offer empirical support for such values.

In 1980, approximately 10,650 acres were zoned for residential use and only 350 acres were zoned for commercial/industrial use, excluding public utilities. Only a small fraction (.08) of the land zoned for each use was listed as vacant and in prob- ability much of this vacant land was unsuitable for development; zoning apparen- tly was binding in both submarkets. The commercial zone might have been ex- panded without reducing the residential zone by incorporating "unzoned" forest or farmland areas. Our simulations, however, assume that any increase in the land zoned for one use reduces the land zoned for the other use (AZ = -Az). The con- version of an aging residential area to a shopping complex or industrial park is a common example of this zero-sum rezoning.

In addition to listing the common parameters, Table 1 contains equilibrium values for a sequence of simulations (SIM l, SIM 2 , . . . , SIM5) in which Z is allowed to change by 25-acre increments. Part A gives the zoning mix (z, Z), the optimal tax rates and spending mix (t*, T*,g*, G*), total government expenditures (g* + G*), revenues from residential (j*) and commercial (J*) property taxes, and aggregate site rent (ASR* = zr* + ZR*). Part B details critical values for the household and business sectors, including the number of agents (h* and F*), the site rent per acre (r* and R*), the average lot size (l* and L*), and the amount of structure per lot (s* and S*).

In square brackets, at the top of each part of Table 1, are our best estimates of actual 1980 values for some of the variables. The second line (SIM 1) gives the results for our baseline simulation. This initial simulation has 5,743 households residing in the community, each occupying 1888.4 square feet of structure on a 1.85 acre lot. Each household's average annual post-tax outlay on housing amounts to $5,708 or 23.1% [(ct + 13)/0] of household income; $778 of this amount is paid to the local government in property taxes. Given the equilibrium residential site rent ($825.5), the average 1.85 acre building lot would sell for about $15,300 to $30,600 if interest rates were in the 5-10% range. Records of a local realtor show that standard residential lots in Guilford sold for $16,000 to $29,000 in 1980.

On the commercial side of the baseline economy (SIM 1), 361 firms occupy the

Tab

le 1

. G

ener

al e

qu

ilib

riu

m s

imu

lati

on

s o

f zo

nin

g c

han

ges

.

Co

mm

on

par

amet

ers

Ho

use

ho

lds:

c~

= .

068,

[3

= .

151,

y =

.73

1, 8

= .

060,

A =

1.

0, m

=

1.8,

p =

1.

0, y

= 2

4760

, ~

=

1144

9.

Bu

sin

esse

s: a

= .

054,

~ =

.09

6, q

= .

750,

g =

.0

30,

B =

997

5, M

= 2

.0,

P =

1.

0, W

=

1500

0, ~

= 2

5000

. G

ov

ern

men

t: I

= 4

,992

,500

.

Zo

nin

g

Tax

rat

es a

nd

ex

pen

dit

ure

s C

om

mu

nit

y a

gg

reg

ates

Par

t A

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Z t*

T

* g*

G

* g*

+ G

* j*

J*

A

SR

*

(198

0 es

t.)

(106

50

350)

(

) (1

4028

071

8104

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386 DENNIS R. HEFFLEY AND DANIEL P. HEWI'IT

350 acres zoned for commercial use, giving an average lot size of .97 acres. The equilibrium land rent in this commercial sector ($11,640.2) is sharply higher than in the residential sector. At first glance, this differential appears to be "too large." Yet, if we calculate the typical firm's total land and structure costs [(1 + T)(RL + MS)] in SIM 1, and divide by the square feet of structure (10,024.2), we get an annual rental price for "commercial space," inclusive of land rents and property taxes, of $3.74 per square foot. Property rental listings from 1980 show that the annual lease price for commercial space in the Guilford area was roughly $3.00 per square foot. The large differential between r* and R* in the baseline simulation may be fairly accurate; the gap simply reflects the highly constrained supply of commercial land under 1980 zoning conditions.

A principal contention of this paper is that fiscal responses and migration effects prompted by a zoning change can substantially alter conclusions about the impacts of a rezoning on land rents, tax rates, public services, and other dimen- sions of the local economy. Immediately below the baseline simulation (SIM 1) is a simulation showing the direct effects of a 25-acre residential-to-commercial rezoning. The values for this simulation, labelled DIR and shown in parentheses, are generated by assuming that baseline values of the fiscal variables and the numbers of households and firms do not change. The results conform to the earlier analysis (section 2): residential site rents rise and commercial site rents fall. These changes, absent other adjustments, would improve the profits of existing firms (n = 25612 > ~) and lower the utility of existing residents (u = 11447 < ~). Not only will this prompt an entry of firms and an exit of households, but the local government will have an incentive to set a new menu of taxes and public services. The combined effects of these adjustments can be seen in the new long-run equilibrium (SIM 2).

Contrary to the direct effect, the commercial rezoning of 25 acres of residential land causes r* to fall (from $825.5 to $812.2) and R* to rise (from $11640.2 to $12693.9). Only part of this reversal of the direct impact is explained by the decrease in households (from 5,743 to 5,637) and the increase in firms (from 361 to 422). In fact, if only the open-city conditions were operative, the new values of r* and R* would not differ from the values in SIM 1. As conditions in the land submarkets change, however, the local government can increase aggregate site rents by altering property tax rates and the spending mix. Comparing SIM 2 and SIM 1 values, both tax rates have been cut, maintaining the proportional relationship between t* and T* in (10a). Changes in the spending mix are less evenhanded. Spending on the commercial public good (G*) rises by $456,048, but $166,331 less is spent on the residential public good (g*). In the commercial land market, both the reduction in T* and the increase in G* have positive effects on R*. These capitalization effects, together with the increase in the number of firms bidding for the land, are strong enough to offset the initial "supply effect" of the zoned increase in commercial land. Consequently, R* rises rather than falls. In the residential sector, the rezoning reduces the supply of land, initially causing r* to rise. This increase is reinforced by the reduction in t*, but both effects are swamped by the


reduction in g* and the number of households; residential land prices fall in the long-run, despite the smaller residential area.

The net changes between SIM 1 and SIM2 reflect the combined effects of the initial rezoning, induced fiscal changes, and open-city migration. By including the DIR simulation, in which the zoning mix is changed by fiscal policies and the numbers of households and firms are held constant, we already have isolated the direct supply effects of the rezoning. Additional adjustments between DIR and SIM 2 canbe decomposed into fiscal and open-city effects by including another in- termediate simulation that allows residential and business migration to restore utilities and profits to initial levels, ~ and ~, but still allows no fiscal response. Dif- ferences between DIR and this simulation, labelled NFR in Table 1, reflect the migration effects; the residual differences between NFR and SIM 2 are then ap- proximations of the fiscal effects. 2E Table 2 presents this decomposition of the net changes between SIM 1 and SIM 2 for endogenous variables of particular interest: residential and commercial site rents (r* and R*), residential and commercial property tax revenues (/'* and J*), the numbers of households and firms (h* and F*), and aggregate site rent (ASR*).

For the endogenous variables included in Table 2, open-city and fiscal effects work in the same direction, and often this is counter to the direct effect of the rezoning. It also is interesting to note that the fiscal effects can be considerably larger than the open-city effects. Since changes in tax rates and spending patterns may occur more quickly than migration, the potential importance of these fiscal effects suggests that the unanticipated results of a residential-to-commercial rezoning should not be dismissed as a curious product of exceptionally long- run adjustments.

Returning to the comparison ofSIM 1 and SIM2, the only "promise" to residents that has been fulfilled is the reduction in the residential tax rate. But even this "gain" may be short-lived. If the zoning authority continues to shift land from residential to commercial use, t* (and T*) may begin to rise rather than fall. In Table 1, this occurs for all simulations afterSIM3. In a general equilibrium setting, then, it is entirely possible for a residential-to-commercial rezoning to lower residential land values, reduce residential public services, and increase residential property tax rates. The open-city condition prevents utility from falling, but the "normal" level of utility 07) can only be maintained by the departure of some households.

These results may seem counterintuitive, yet they are entirely consistent with economic theory if capitalization effects and agent mobility are given full play. We hasten to add that the model omits a number of elements which make the results of a rezoning even less predictable. Employment effects on local income, positive or negative externalities between the residential and commercial sectors, congest- ible public goods, and endogenous zoning decisions would enrich the model but make it even more difficult to untangle the various effects of a zoning change. We plan to extend this model in a number of ways, selectively incorporating some of

388 DENNIS R. HEFFLEY AND DANIEL P. HEWITF

Table 2. Decomposition of the direct and indirect effects of a residential-to-commercial rezoning

changes in key endogenous variables

Ar* AR* A j* A J* Ah* AF* AASR*

Direct supply effects of AZ 1.943 -509.8 0 54640 0 0 99784

Indirect migration effects -1.943 509.8 -10492 104676 -13.49 25.80 170571

Indirect fiscal effects -13.326 1053.7 -74140 215033 -92.88 35.00 253536

Net effects -13.326 1053.7 -84632 374349 -106.37 60.80 523891

these elements. Appropriately modified, the framework also should be useful in studying the effects of other forms of zoning, tax equalization or uniform assessment requirements, public expenditure limits, intergovernmental grants, and other policies that hinge on the public and private responses of local economies.

5. Summary remarks

The nexus between zoning changes and the fiscal behavior of local government is obvious in any economy where the property tax is an important source of local revenue. Such links are acknowledged in the literature on zoning and on optimal local taxes and expenditures, but the relationships are often specified loosely or omitted in formal analyses. In examining the final effects of a residential-to- commercial rezoning, we show that these relationships are critical. Predictions of the standard partial equilibrium analysis (section 2) can be fully reversed when government tax and spending decisions are allowed to respond to the zoning change, and when residents and firms are able to enter or leave the community. An open-city general equilibrium model (section 3), incorporating the optimal tax and expenditure behavior of local government and the economic decisions of households and firms, is analyzed and then used to simulate the final effects of changes in the residential/commercial zoning mix of a suburban Connecticut town (section 4). Simulation results illustrate that it is entirely possible for a residential-to-commercial rezoning to raise commercial land rents, lower residential land rents, reduce the level of residential public services, and either reduce or increase the residental property tax rate. Capitalization and relocation are essen- tial elements of the story


Acknowledgments

T h e r e s e a r c h p r e s e n t e d i n t h i s p a p e r w a s f u n d e d , i n p a r t , b y a g r a n t f r o m T h e U n i -

v e r s i t y o f C o n n e c t i c u t R e s e a r c h F o u n d a t i o n . T h e a u t h o r s w i s h to t h a n k R o g e r

B a l l e n t i n e , J o h n C l a p p , R o b e r t G e r b e r , O s k a r H a r m o n , T o m M i c e l i , K a t h l e e n

S e g e r s o n , p a r t i c i p a n t s i n T h e U n i v e r s i t y o f C o n n e c t i c u t E c o n o m i c s C o l l o q u i u m ,

a n d t w o a n o n y m o u s r e f e r e e s f o r t h e i r h e l p f u l c o m m e n t s a n d a s s i s t a n c e .

Notes

1. The 1980 Census of Population contains interesting data on the difficulty that many communities face in appropriating local jobs for their residents. For example, in the 146 Connecticut townships with 1980 populations of 2,500 or more, the percentage of workers employed outside their town of residence ranged from 26.1 to 94.9, with a mean value of 69.0.

2. In practice, towns may have several types of zones (residential, commercial, industrial, and mixed-use) and each of these general zones may be further subdivided according to specific density zoning restrictions (e.g., residential land with a half-acre minimum lot size).

3. Throughout the paper we use lower case notation for the residential sector and upper case notation for the business sector. One exception is the reservation site rent, r, which applies to land in both sectors.

4. Grieson and White (1981, p. 283) use a similar device to consider the influences of zoning when there are externalities between two land uses.

5. The disparities between residential and commercial site rents in many communities suggest that land-use zoning does not merely follow or codify market outcomes.

6. This assumption of perfectly elastic supply up to the zoning constraint simplifies the exposition but can be easily relaxed to allow upward-sloping supply curves in each submarket. In either case, the zoning constraint causes each supply curve to become perfectly inelastic at some point.

7. The connection between zoning and vacant land has not been thoroughly explored. The example here illustrates that zoning may lead to land vacancy in a community where land would otherwise be fully utilized (recall the earlier discussion of point A in Figure 1). But it is important to note that vacancy can occur even in the unzoned case if the demand curves intersect at some site rent below the reservation level.

8. These short-run results are also compatible with the analysis of"fiscal zoning" by Ohl~, Weisberg, and White (1974, pp. 430-432) and Grieson and White's (1981, pp. 276-278) analysis of "allowable use" zoning.

9. Henderson (1985a, pp. 310-311; 1985b, pp. 115-116) considers capitalization effects associated with the "income" effect of minimum lot-size zoning, but not the capitalization effects that might ac- company zoning-induced changes in the tax/spending decisions of local government. Ohls, Weisberg, and White (1974, pp. 435-438) examine the relationship between zoning and the property tax rate, but public services are not explicitly treated and the assumed objective of voters (tax rate minimization) is somewhat unusual. Carpenter and Heffiey present spatial equilibrium models in which zoning (1981) and other types of land-use controls (1982) affect land values and, hence, property tax revenues. However, the property tax rate is exogenous, and public spending is not considered.

10. An interesting extension of this research would make zoning decisions, not just fiscal behavior, fully endogenous. The degree of separation of zoning and fiscal decisions varies across states and localities. In cases where these powers reside with the same body, a model with endogenous zoning and fiscal behavior has obvious applications. Even in cases where the decisions are made separately, endogenous zoning would permit an a'nalysis of the compatibility of various fiscal and zoning policies.

390 DENNIS R. HEFFLEY AND DANIEL P. HEWlTT

Interdependencies between these decisions, transmitted through local land markets, could result in suboptimal fiscal and zoning policies. If so, some mechanism for coordinating these policies could mutually enhance tile objectives of the two groups.

11. In practice, the traditional property tax base is the asset value of land and structure, which in turn depends upon the stream of net income associated with the housing services produced by these inputs. We avoid an extra layer of agents, namely developers or housing service producers, by having households directly consume the services of land and structure. This is a common device (e.g., Santerre (1985)), but the absence of an explicit market for housing services makes it difficult to calculate the asset value of a particular combination of land and structure and, hence, difficult to portray the property tax in a more realistic way. We think the distortion is relatively minor, and there is ample precedent for treating tile property tax as we have done here.

12. The relevant price in s* is the post-tax price, m (1 + t), since tile property tax in this model applies to structure as well as land.

13. The distinction between residential and commercial public goods, g, and G, is not always clear. To keep the analysis as general as possible and to capture the tension that exists in many communities over providing public funds for, say, education versus commercial infrastructure, we allow for separate goods, as in Beck (1983). Obviously the model could be recast to consider a public good that benefits both residents and businesses. In a similar way, we also allow for a classified property tax system. It would be easy enough to impose the restriction that tax rates on residential and commercial property be equal, but even in states where such requirements exist, effective tax rates on residential and commercial properties within a town often differ because of assessment practices.

14. For example, under open-city conditions, the local government can do little to alter the long-run utilities or profits of its present occupants. The difficulty of increasing employment opportunities for residents has been noted in Note 1 above.

15. See Stiglitz (1983), Sonstelie and Portney (1978), and Brueckner (1982, 1983). 16. This formulation of the problem assumes that the zoning constraint binds (i.e., no vacant land)

in each sector. Kuhn-Tucker methods could be used to consider vacant land cases, but this added complexity can be avoided by assuming a zero reservation price (r = 0) and market demand functions for residential and commercial land (as in the Cobb-Douglas case) which do not intersect the quantity axis.

17. There is ample evidence that local governments consider possible reactions to their fiscal decisions. Whether they anticipate the magnitude of the response as accurately as our model suggests is questionable. Yet, even if the local government initially misjudges this response, it seems likely that economic and political pressures would ultimately force a more accurate evaluation.

18. Though designed for dynamic simulations, the SAS procedure SIMNLIN also can be used to simulate static general equilibrium models of this sort.

19. See Zodrow and Mieszkowski (1983) and Hamilton (1975, 1976). 20. We have obtained qualitatively similar results using empirically generated parameters for

several other towns. 21. The decomposition would be exact for sufficiently small changes in the zoning mix. Our 25-acre

shift from residential to commercial represents a change in the zoning status of less than 1% (.0023) of the community's usable land; therefore, the decomposition procedure used here should be reason- ably accurate.

References

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Brueckner, Jan IC "Zoning and Property Taxation in a System of Local Governments: Further Analysis." Urban Studies 18 (1981), 113-120.


Brueckner, Jan IC "A Test for Allocative Efficiency in the Local Public Sector." Journal of Public Economics 19 (1982), 311-331.

Brueckner, Jan K. ~'Property Value Maximization and Public Sector Efficiency." Journal of Urban Economics 14 (1983), 1-15.

Carpenter, Bruce E. and Heffiey, Dennis R. "A Spatial Equilibrium Analysis of Flexible Zoning and the Demand for Development Rights." Environment and Planning A 13 (1981), 273-284.

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Land-use zoning in a local economy with optimal property taxes and public expenditures