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Land Taxation in Philadelphia:
A General Equilibrium Analysis

Mary Braun



[A University of Pennsylvania Research Paper, 2003. Reprinted with permission by the author. The mathematical equations contained in the original paper could not be reproduced in this format and have been omitted. Additonally, Appendixes and References are omitted from the original. Researches interested in the subject should contact the author for a version of this paper in Microsoft Word]


Abstract


Although economists generally agree that land value taxation is economically efficient, only a handful of U.S. municipalities have ever implemented a land tax. The relative rarity of this type of taxation makes it difficult to predict how land tax reform effects local economies. Research on this type of taxation typically involves examining the impact modest land tax reforms have had on small Pennsylvania towns, or using general equilibrium modeling to examine radical land tax reforms. This paper uses a small-open economy general equilibrium model to estimate the nature and the magnitude of economic change resulting from modest land tax reform. The model is calibrated to resemble Philadelphia's current fiscal and economic climate. Two different types of tax reform are examined, (1) Philadelphia's Real Estate Tax is modified so that revenues generated by taxing property structures equal revenues generated by taxing land, and (2) the tax burden is shifted from the Wage Tax onto the Land Tax. The model found that in Philadelphia, modest land tax reform resulted in significant jobs creation and population growth. Thus, when compared to other revenue alternatives, land value taxation can act as a strong economic stimulant.


I am indebted to Robert Inman and Andrew Haughwout, without their help, this paper would not have been possible. All errors and oversights are my own.

Table of Contents


  • 1. Introduction
  • 2. The Need for a Change in Philadelphia's Tax Structure
    2.1 The City Controller's Tax Structure Analysis Report
  • 3. What is Land Value axation
    3.1 What do Critics Say about the Land Value Tax?
    3.2 What do Proponents of Land Value Taxation Claim?
  • 4. Empirical Research on Land Value Taxation in Pennsylvania
  • 5. General Equilibrium Modeling and Land Taxation
    5.1 Open and Closed Case for Property Tax Reform (Tideman)
    5.2 Prospects for Land Rent Taxes in State and Local Tax Reforms (Nechyba)
    5.3 A General Equilibrium Analysis of Land Taxation in NYC (Haughwout)
  • 6. The Need for New Research Analyzing Policy Proposals in Philadelphia
  • 7. Modeling Philadelphia's Economy (Haughwout & Inman)
  • 8. Model Modifications and Simulations
    8.1 Modifying the Model
    8.2 First Policy Proposal
    8.3 Second Policy Proposal
  • 9. Results
  • 10. A Word of Caution
  • 11. Conclusion
  • 12. Appendixes
  • 13. References


Introduction


Land is unique because, no matter how much you tax it, the supply will never change. This makes it possible to levee a tax on land rents without changing people's production decisions and stifling economic progress. When compared to most other types of taxation, a land tax is both more efficient and more equitable. Land taxation is more equitable because it recaptures for society the portion of property value that is derived from the community rather than from the property owner's labor. Additionally, there are both theoretical and empirical reasons to believe that replacing more distortionary taxes with a land value tax would help stimulate the economy.

In Philadelphia, there is ongoing debate both among policy makers and city residents about the relative merits of land value taxation. Much of this debate was generated by a series of policy proposals laid out in the City Controller's Tax Structure Analysis Report. Because this type of taxation is relatively unknown, and because most land tax municipalities in the United States are quite small, there exists some uncertainty about the ways in which the economy of a large city, like Philadelphia, would respond to land tax reform. Although several general equilibrium models have been used to examine the impact of dramatic land tax reform, no research has been done which explores the consequences of adopting a modest land tax reform, like the one proposed by the City Controller. My research is designed to fill this void.

This paper is organized as follows: Section 2 establishes the fact that, in Philadelphia, there is a great need for tax reform. This section also contains a brief summary of the policy proposals put forth in the City Controller's Tax Structure Analysis Report. In Section 3 there is an in-depth analysis of land value taxation. Section 4 provides an overview of empirical research done on land value taxation in Pennsylvania. In section 5, three prominent general equilibrium models used to analyze the impact of land value taxation are discussed. Section 6 establishes the fact that there is a need for new research explaining how a city like Philadelphia would be effected by modest land tax reform. Section 7 contains an overview of Andrew Haughwout and Robert Inman's general equilibrium model. A modified version of their model is used in this paper to analyze the impact land value taxation would make on Philadelphia's economy. Section 8 describes how the original model was modified and what simulations were conducted. The results of these simulations are presented and discussed in Section 9. Section 10 contains information about the limitations of general equilibrium modeling and offers a word of caution about interpreting the results.


2. The Need for a Change in Philadelphia's Tax Structure


Philadelphia reached its population peak in 1950 at 2.1 million and since that time roughly a quarter of Philadelphia's population has left the city. Since the 1950's the tax burden on those who remained dramatically increased. This occurred because the wealthy and middle class moved out of the city at a faster rate than the poor and because the city's budget did not decreased as rapidly as the population did. An increased demand for city services and a lack of fiscal discipline on the part of elected city officials lead to increased per capita city spending. Year after year as the tax base shrunk, local politicians chose to hold constant and even increase taxes rather than cut back on the levels of service provision. Philadelphia's taxes are now the highest in the region. Figure 1 gives a breakdown of the tax burden faced by the median household in different parts of the Philadelphia metropolitan area.


Figure 1: Median Household Tax Burden in the Philadelphia Region




This comparison of the tax burden faced by median households in the region illustrates how much greater the tax burden currently is for Philadelphia residents. Figure 1 also illustrates that the tax burden for workers commuting into Philadelphia is greater than for people living an working outside of Philadelphia. This adversely affects both employees and employers. Businesses located in the city that wish to remain competitive, must pay their employees more to compensate for the tax burden they face as commuters.

In its January 2001 A Philadelphia Report Card, the Federal Reserve Bank of Philadelphia found that, "the city is near its peak of revenue-generating capacity - that is, raising taxes shrinks the city's economy and tax base so much that revenues will not rise significantly."[1] This leaves elected city officials in a difficult position; they cannot raise taxes and they cannot easily reduce service levels, which would upset the municipal unions and would likely cause more residents to flee to the suburbs in order to find better schools and safer streets. Some experts, such as those at the Federal Reserve Bank of Philadelphia, suggest that though it may at first seem counterintuitive, the solution lies in cutting taxes. "While lowering taxes will reduce the city's tax revenues it will increase economic activity in the city. Thus, in the long run, the annual revenues loss will be less than the initial loss in taxes."[2] The City Controller takes a different approach and suggests that by readjusting rather than reducing the tax burden, it will be possible to stimulate the economy without causing a loss of revenue and therefore a loss in services.


2.1 The City Controller's Tax Structure Analysis Report


Recognizing that a change in Philadelphia's economic climate is necessary, the City Controller's Office created a comprehensive Tax Structure Analysis Report. This report describes many of the economic problems facing Philadelphia. It explains how recent tax cuts have produced favorable results and proposes a series of key changes. The City Controller's goal was to stimulate the economy through tax reform without reducing aggregate revenues. By significantly reducing business taxes and by shifting the tax burden to reduce the Residential Wage Tax to encourage development, the Controller's Office argues that it will be possible to stimulate the economy without changing the city budget. Part of the Controller's plan involves transforming the Real Estate Tax into a split-rate land value tax and then shifting the tax burden from the Wage Tax onto the newly modified Real Estate Tax. See Appendix A to read excerpts from the Tax Structure Analysis Report related to land and wage tax reform.

The Controller's Office proposes taxing land at 3.44 times the rate of structures so that half of the Real Estate Tax revenues come from land and half from buildings. Currently, land only generates 22.5% of the Real Estate Tax revenues even though it is taxed at the same rate as structures. Initially the shift towards land value taxation would be revenue neutral, meaning that, in the first year, revenues generated by the higher tax on land and the lower tax on structures would be sufficient to meet the current revenue projections for the Real Estate Tax. Using property assessment data from the Board of Revision of Taxes (BRT), the Controller's Office estimates that approximately 78% of residential taxpayers would see their Real Estate Taxes reduced with this shift, while approximately two thirds of those whose taxes might increase would see increases of less that $100 per year.[3]

The Controller's Office also proposes reducing the City Wage Tax to 4% and increasing the city's Real Estate Tax to create a budget neutral first year shift. In this context, the term budget neutral refers to the fact that aggregate revenues generated by the Wage Tax and the Real Estate Tax would remain constant. After the proposed shift, there would be sufficient revenues to meet the current combined revenue projections for those taxes. In this scenario, the Controller's Office predicts that, "only individuals whose homes have a resale value of more than three times their annual household income might see an increase in taxes."[4] This proposed shift builds on the fact that land taxes distort people's economic incentives less than other types of taxation. People can leave the city but they cannot take their land with them. See Appendix B for a brief discussion about Philadelphia's Wage Tax. This appendix contains information about why, out of all the different typed of distortionary taxes, the Controller's Office focuses on reducing the Wage Tax.


3. What is the Land Value Taxation?


The concept of land value taxation can be traced all the way back to Adam Smith and the birth of modern economics. In the 19th century, classical economist David Ricardo advanced land tax theory by studying the existence and importance of land rents.[5] Ricardo noticed that all of the earnings from poor quality land must be used to cover labor and capital cost; yet, because it is more economically productive, high quality land produces more than enough to cover these basic labor and capital costs. Ricardo considers these extra earnings to be economic rent. Ricardo's law of economic land rent is as follows: the rent of land is determined by the excess of its product over that which the same application can secure from the least productive land in use.[6] Ricardo goes on to theorize that, as the population grows, more poor land must be cultivated in order to meet the growing demand. Thus the rent "earned" by good land increases. This phenomenon (coupled with the fact that poor land necessitates increased labor input to maintain minimal output) results in falling profit levels for everyone except for the few lucky land owners who prosper without themselves contributing to the productive process. Ricardo claimed that since rents gobble up profits, and profits lead to investment, which leads to growth, rising rent costs indirectly hinder societal economic progress.

The late 19th century social philosopher Henry George built upon Ricardo's theory, that land rents would absorb all of the fruits of progress. Convinced that, "the association of poverty with progress is the great enigma of our times," George sought to unravel this riddle in his groundbreaking book, Progress and Poverty. In this book, George eloquently expresses his belief that poverty exists in America's rapidly growing cities (in the midst of unprecedented prosperity and unparalleled rates of growth) because owners of land and other "natural opportunities," appropriate the benefits derived from other people's capital and labor. To bring about greater economic justice without stifling economic progress, George proposed that the government adopt a "single tax" on land. George's argument for land value taxation has two primary components, one ethical and one relating to economic efficiency.

George believed that, because increases in land values are caused by society rather than by land owners, land rents should be taxed away for the good of society. To support his theory, George points out that land or "site" value is not created by the actions of an individual owner but by the community, acting in three capacities. First, society provides the legal institutions of land ownership from which the concept of land value springs. Land would be of little value without the legal framework which assures land owners that their investments won't be taken away from them without due compensation. Second, the larger community is the provider of infrastructure and amenities such as good schools, roads, and police protection, which give land much of its value. Third, it is the community, in the shape of the market, which causes local economies to grow and develop directly affecting land values. At first it may appear as if the value of land is only linked to the soil's fertility but without legal protection, a network of roads upon which crops can be transported, or markets in which to sell these crops, agricultural land becomes infinitely less valuable. Thus, as scholar Dick Netzer claims, "the ethical conclusion is than that the community, not the individual site owners, should recoup the fruits of these economic activities."[7]

In addition to the ethical argument, George claims that there are convincing economic reasons for implementing the single land tax; namely that a tax on land rent it is the most efficient type of taxation possible. Unlike other forms of taxation, a tax on land rents does not stifle economic growth. In order to understand this claim it is first important to understand that typically, under perfect competition, economic rents only exist when a change in supply is not possible. Because the supply of land is fixed, land rents can accrue.[8] Although theoretically, any type of economic rents could be taxed without distorting production decisions, in the long run it is nearly impossible to tax excess wages or interest earned by capital. When the market is working perfectly, the supply and price of capital and labor continuously adjust until equilibrium is reached and no excess economic wages or profits from interest rates remain. Thus, in a perfectly functioning market, it is impossible to tax the rent on capital and labor. Any tax on elastic goods (such as labor and capital) will simply reduce the amount people are willing to consume or produce. This stifles economic growth and leads to economic inefficiencies.[9] In contrast, because the supply of land is fixed, it is possible for land rents to accrue, allowing the land to be taxed without distorting production decisions and leading to economic inefficiency.[10]

Throughout the rest of our discussion it is important to note the difference between property and land. Although these two terms are commonly viewed as interchangeable, in this paper the term property will be used to describe the combination of land and all structures on the land. Hence, property rent is the combined return on land and capital improvements. The term land value refers to the value of land without improvements, the residual value after the values of other assets that exist on the land are removed. Unlike land taxes, the implementation of property taxes results in economic distortions because people no longer have as good of an incentive to improve their property and use it efficiently.


3.1 What do Critics Say About the Land Value Tax?


Leo Tolstoy once claimed that, "people do not argue with the teachings of George, they simply do not know it…and it's impossible to do otherwise with his teachings, for he who becomes acquainted with it cannot but agree."[11] Most critics of the land tax often question how practical it would be to implement such a policy.

Some scholars, such as Dick Netzer, point out that the sudden implementation of a new land value tax would unjustly victimize recent buyers of land.[12] Netzer claims that (until the market had time to adjust) a pure land tax could be confiscatory in its nature.[13] A similar criticism is that voters and elected officials would likely be sympathetic to any individuals who found themselves bankrupt as the result of the new tax. These may be valid concerns, but as Steven B. Cord argues, a gradual shift towards land value would give both markets and people time to adjust and to begin putting land to its best use.[14] Land owners who are not currently maximizing their land's productive potential would have time to adjust and would be able to prepare for a large tax increase. Though gradual implementation delays potential benefits, land tax proponents such as Walter Rybeck suggest that a full tax reform would arouse too much political opposition to gain acceptance, thus a land tax should be gradually adopted.[15] This can easily be achieved by gradually increasing the land tax to structure tax ratio.

George and the original single tax supporters advocated replacing all local, state, and federal taxes with a single tax on land rents. Several prominent land tax critics claim that though a single tax may have been possible at the turn of the century, when George first wrote Progress and Poverty, such a tax is no longer feasible. Since 1933, persistent and reoccurring unemployment has produced pressure for increased federal spending. This has caused government spending to skyrocket. According to economist Arthur P. Becker, "government intervention has grown to the point where the public sector now comprises 35 percent of Gross National Product and 49 percent of national income."[16] Thus, because the magnitude and focus of U.S. government expenditures has greatly increased in the past 100 years, it is no longer possible to generate sufficient revenue from a land tax to run the federal government. Other land tax critics argue that because the trend of increasing government spending permeates all levels of government, it is not even feasible to finance local government expenditures with a single land tax. While this may be a valid argument against single taxation, this criticism does not hold when a two-rate land tax is implemented alongside other types of taxes. Despite the fact that property taxes are currently a major source of revenues for local jurisdictions,[17] many ardent advocates of land value taxation seem to agree that, "with the commitments of modern governments, land value taxation would, by itself, be hard pressed to raise sufficient revenue to cover all spending demands."[18] Rather than advocating for a single tax, most modern followers of George envision a scenario in which land value taxation accounts for a significant share of all local public sector revenue (10-20%).[19]

Perhaps the most frequent criticism of land value taxation is that an accurate assessment of land values is impossible, or too costly, to obtain. In theory, a tax that is levied on the value of land alone does not cause any economic distortions, but in order to levy such a tax, assessors must have the ability to estimate the value of land separately from improvements. Jerome German, Dennis Robinson, and Joan Youngman suggest that George's single tax argument is based on the assumption that appraisers would always be well supplied with plenty of nearby unimproved land, so that the improved land sites could be valued easily by comparison.[20] Although this assumption made sense in George's day, the American landscape has dramatically changed since then. Now, data on the value of unimproved land can be difficult to obtain because in urban areas most parcels of land have already been improved.[21]

Virtually everyone on both sides of the land tax debate agrees that "the single greatest challenge to any type of land value taxation system is accurate valuation of land on a large scale."[22] Skepticism about the feasibility of urban land valuation has historically proven to be a major stumbling block to serious consideration of two-rate property taxes. However, recent advances in computerized property assessment tools have important implications for this debate. Assessors now have access to a vast array of sophisticated techniques that would enable them to accurately determine the value of urban land. For a detailed description of the most common land assessment techniques see Appendix C. More then twenty years ago, Oliver Oldman of Harvard Law School wrote, "the key to developing an accurate land value assessment role is the process of land value mapping."[23] New computerized methods of spatial data analysis make this type of mapping possible and make it difficult to reject land value taxation on the grounds that accurate land valuation is not possible.


3.2 What do Proponents of Land Value Taxation Claim?


Most scholars agree that the majority of the benefits associated with land value taxation accrue because land is fixed both in supply and location. Arlo Woolery, points out that one of the strongest arguments for a land-based tax is its relative stability. Woolery claims that since land, unlike other forms of wealth, is fixed in its location, it makes an ideal tax base.[24] Similarly, Andrew Reschovsky suggests that revenues from land value taxation would be more stable over the course of the business cycle than either a tax on income or consumption (although he conditions his statement by claiming that there is a need for more research on the topic).[25] Often government deficits arise because while government spending is relatively fixed in the short term, tax revenues fluctuate with the business cycle. Any method of taxation that promises a relatively constant revenue stream would have obvious benefits.

Advocates of the land value tax argue that land value taxation results in increased societal economic prosperity by encouraging landowners to maximize the productive potential of their land. Working from the assumption that people own productive sites and capital assets because of the return they yield, Georgian theorists claimed that the most efficient economic climate occurs when land owners seek the use of their assets that yields the greatest return available. Thus, when every parcel of land is already being put to its highest and best use, within the legal limits imposed by zoning regulation, the land tax is neutral and does not affect production decisions. However, if speculators are holding large amounts of land fallow and off of the market, scholars argue that a land tax would increase productivity by encouraging speculators to use their land more productively. Because, as Becker claims, "high speculative land values lower profitable investment opportunities and lead to unemployment," thus any system that discourages speculation would increase economic productivity.[26]

Economists and policy makers have long assumed that, even if land value taxation is not allocatively neutral, because of existing inefficiencies in land use, it is more efficient than other existing forms of taxation. In the past twenty years, several scholars have demonstrated that a tax on land value is non-neutral,[27] but Duck-Ho Lim suggests that because the land tax is still more efficient than other forms of taxation, any such findings are of little practical significance.[28] Using a two period model, Lim proves that while a land value tax may be distortionary, its economic impact is significantly less than the impact caused by a wage tax of equivalent yield. Lim's findings reinforce what other scholars have long argued: namely that, in order to alleviate poverty and stimulate progress, the introduction of a land value tax must be commensurate with sharply reduced taxes on earnings and other economic endeavors.[29] Analyzing the tradeoff between a tax on land rents and a tax on capital income, Thomas J. Nechyba, demonstrated that land taxes are significantly more efficient than capital taxes.[30] Similarly, in a purely theoretical paper, Mitch Kunce proves that when local jurisdictions are allowed to tax land as well as two distinct types of capital, the most efficient choice will always be a pure land tax.[31]

Not only do proponents of the land tax claim that it is an economically efficient form of taxation, they argue that it is an incredibly powerful urban planning tool. George predicted that, "if land were taxed to anything near its rental value, no one could afford to hold land that he was not using."[32] By penalizing random, unplanned withholding of land from more extensive development, land value taxation could theoretically reduce land speculation and promote increased urban density. Because a pure land tax would result in lower taxes in decaying areas and higher taxes in rapidly growing areas, land taxes could help cover the cost of new development and could channel development back into the largely abandoned urban core. Jeff Wuensch, Frank Kelly, and Thomas Hamilton claim that, "if true land values have fallen to very low levels, as they do in 'urban decay settings,' a moderate stimulus to redevelopment should emerge, given that the costs of demolition are not too high and potential profits can become sufficiently large."[33] Thus, when properly implemented, a land value tax would promote urban renewal in the city core.


4. Empirical Research on Land Value Taxation in Pennsylvania


In the Unites States, most municipalities collect some form of property tax, yet a few of these municipalities have a pure, gradated, or two-rate land tax. This makes empirical analysis of land value taxation difficult. As a result, the bulk of all empirical research has focused on a handful of cities in Pennsylvania. Because it is the only state that allows all of its first, second, and third class cities to tax land and structures at different rates, the overwhelming majority of land tax municipalities are in Pennsylvania. A host of research has been done on these municipalities to determine whether land value taxation significantly impacts the economy. In all of the Pennsylvania studies, researchers use the value of new construction as a proxy for economic growth.

Three separate empirical studies found little direct connection between land taxation and economic growth in Pennsylvania. In the late 1970's, when only three cities had adopted two-rate taxes, Mathis and Zech undertook a cross-sectional analyses of 27 Pennsylvania cities; they were unable to detect a statistically significant correlation between construction activity and the structure to land tax ratio.[35] In a more comprehensive study using fourteen years worth of data from 53 different Pennsylvania cities Tideman and Johnson found no statistically significant correlation between new construction and structure to land tax ratios.[36] However, these authors speculated that limitations in both the data and the econometric techniques used in this analysis could have an obfuscating effect. Performing separate time series analysis for three Pennsylvania cites that had previously adopted two-rate taxes, Bourassa was equally unable to show any connection between land tax rate and new construction.[37]

In all three aforementioned studies, estimated coefficients capturing the effect of a change in the tax regime had strikingly large standard errors. The resulting lack of statistical significance can be attributed to insufficient data, poor choice of proxy measurements, and data that is already biased against finding a tax effect. Because two-rate taxes were primarily adopted by small municipalities in severe economic distress, and because in these municipalities school real estate taxes were not reformed, tax relief might not have created a sufficiently incentive to overcome economic depression. Furthermore, because the existing capital stock in many of Pennsylvania's older towns exceed the residents' needs, it is unlikely that researchers using the value of new construction as a proxy for economic growth would be able to fully capture the effect of any tax reform. Additionally, according to Plassmann and Tideman, inconsistencies in the data make the traditional econometric methods of analysis used in previous studies unreliable.[38] In any given year many of these municipalities did not experience any new construction, which skewed the calculation of the mean and median number and monetary value of new construction permits. In their mathematically sophisticated model, Plassmann and Tideman estimate key parameters with a Markov chain Monte Carlo method, the Gibbs sampler, to correct for the this irregularity in the data. After comparing 15 land tax municipalities with 204 similar Pennsylvania municipalities, over a period of 22 years, their research shows that two-rate and land tax cities do indeed experienced significantly higher levels of construction.

In addition to the comparative research done in Pennsylvania municipalities, a large body of research focuses specifically on two-rate taxation Pittsburgh.[39] In 1914, Pittsburgh became the first large city in the Unites States to implement any sort of land value tax. Initially Pittsburgh taxed land at twice the rate as buildings. The 2:1 ratio was adopted for political rather than theoretical reasons. At the time, because the majority of local government revenues were generated by property taxes, this was considered to be a significant tax reform policy. In 1979, as part of a wide sweeping urban revival project, Pittsburgh restructured its property tax system by raising the rate on land to more than five times the rate on structures. During the 1980's, Pittsburgh bucked the trend of steady decline set by similar rust-belt cities and experienced a dramatic boom in new building construction. An empirical analysis, conducted by Oates and Schwab, found that an increased reliance on land taxation was not a direct cause of Pittsburgh's dramatic economic revival. In their regression analysis, Oates and Schwab found that the coefficient for the dummy variable representing the change in tax regime was not statistically significant. They claim that this is inline with economic theory, which holds that a tax on land rents should be neutral and will not impact people's decisions. However, the researchers argue that just because this tax is "neutral" does not mean that the tax played no part in Pittsburgh's revival. Oates and Schwab argue that land value taxation, "played an important supporting role by enabling the city to avoid rate increases in other taxes which would have impeded development."[40] A land tax allowed the city to provide more public services, which attracts people to the city, without imposing a tax which dampens economic growth. These authors also suggest that, because the role of land value taxation is best understood in terms of the revenue alternatives, "the interesting and the relevant issue here is the response of the Pittsburgh economy to such an alternative tax."[41]

The results from these empirical studies are somewhat inconclusive. Three early studies executed with various degrees of complexity failed to find any link between economic activity, measured as a change in the total number and value of new construction permits. However recent research indicated that there might indeed be a connection. It is simply difficult to find without sophisticated econometric techniques. Oats and Schwab offer an eloquent explanation as to why the connection between new construction and land taxation should be difficult (or even impossible) to identify. They suggest that to truly understand the impact land taxation can have on an economy, it is necessary to study land taxation in terms of its revenue alternatives.


5. General Equilibrium Modeling and Land Taxation


A general equilibrium model examines how changes in one market affect all other markets. Increasingly sophisticated and complex modeling techniques have allowed researchers to thoroughly analyze the economic effects of different fiscal policy proposals. This makes it possible to understand how different types of taxes impact different aspects of the economy. Although a rich literature exists on this type of modeling, few researchers have used these methods to directly study land value taxation; Tideman, Nechyba, and Andrew Haughwout have all recently presented or published papers that use equilibrium modeling techniques to understand the impact of a shift to land taxation.


5.1. Open and Closed Case for Property Tax Reform (Tideman)[42]


Although Tideman is interested in the economic impact of replacing local property taxes with a land tax, his dynamic general equilibrium model is calibrated using national data. Tideman rationalizes this by pointing out that economic behavior depends on all taxes which a person is subject to and that the best data is available only for the national economy. As such, he argues that even though the model uses national data it should, "be considered an expansion of a model of a city, by a scale factor that does not affect the question of interest."[43]

Tideman's fairly straightforward model involves three factors of production (land, labor, and capital) as well as a parameter capturing technological advances over time. Unlike most general equilibrium models, which assume that the amount of land available in the economy never changes, Tideman's model attempts to capture the effect of land speculation. The percentage of economically available land is given by T = e?(1-n) where n is the percentage of land rent that is collected by the property tax and ? is chosen to yield an estimate of land efficiency under the existing tax regime. The model analyzes the labor and investment decisions of one infinitely lived representative household that, following a linear approximation of U.S. population growth, expands over time. Although a constant portion of the household is employed, the model contains a parameter capturing labor-leisure decisions. Household utility is a symmetric CSE function based upon: private goods per worker, public goods per worker, and leisure per worker.

What makes Tideman's research particularly interesting is the fact that he conducts separate model simulations for both closed and open economies. In the closed model, the quantity of capital that is used in any year is the amount that the household has accumulated in maximizing its intertemporal utility function. In the open model, the quantity of capital that is used in any year is the amount that earns an after tax return equal to what the after tax return on capital would have been that year without tax reform. Tax reform would mirror that of a closed economy, if taxes were simultaneously reformed all over the country (or at least throughout out one large region). However, if tax reform only occurred in a single locality, an open economy model would be more suitable.

According to the model, eliminating the structural component of the property tax and increasing the tax on land, in a revenue neutral manner, would significantly enhance real per capita income. In a closed economy, tax reform causes per capita income to grow between $650 and $2,000 per year. In an open economy, real income grows by approximately $500 per worker per year. Significantly larger wages do not lead to an increase in real per capita income; in the short term wages rise by 1% to 2% and in the long they rise by 2.75%. Real income grows because, in a closed economy, property tax reform leads to significantly larger returns to capital (5% per year for the first 20 years), and because, in both open and closed economies, people have an increased incentive to invest. Increased investment causes capital stock in a closed economy to grow by 100% and capital stock in an open economy to grow by 130%.


5.2 Prospects for Land Rent Taxes in State and Local Tax Reforms (Nechyba)[44]


Nechyba, building on Jan Brueckner's property tax analysis,[45] created a general equilibrium model of an economy that produces output using capital, land and labor as inputs. He uses this model to predict how the economy would respond if different types of distortionary taxes were replaced (in a revenue neutral manner at the state level) with a tax on land. Nechyba conducted this analysis for all 50 states and one "typical" state. When developing state specific tax rates for the individual factors of production (capital, land, and labor) Nechyba was forced to make a series of simplifying assumptions. Specifically, he assumed that the property tax is a tax on land as well as all forms of capital; the corporate income tax is a tax solely on capital; and the personal income tax, the sales tax, and all "other" taxes are born by all forms of income. After developing a series of state specific models, Nechyba preformed policy simulations to identify which types of tax reforms are likely to be economically and politically successful. Under plausible yet conservative assumptions about the elasticity of substitution between capital and land as well as the supply elasticities for capital and labor, Nechyba found that large tax reforms replacing entire classes of distortionary taxes with land taxes are feasible in virtually all states.[46] One of the Nechyba's more intriguing findings is that a tax on land could actually increases the value of that land. Typically, experts in local finance agree that property taxes, consisting of a tax on land and a tax on capital, are quickly and completely capitalized into the price of the land.[47] Nechyba concedes that because it reduces the discounted present value of land rents, when considered in isolation, a tax on land should reduce land prices. However, in his model, Nechyba considers land taxation to be part of a revenue-natural tax reform in which land taxes replace other classes of taxes. Because these other classes of taxes are distortionary, eliminating them stimulates the economy and indirectly increases land values. Furthermore, a land tax that replaces capital taxes increases the intensity of capital usage, which in turn raises land prices (because the land is now more desirable). Thus, when capital/building taxes are lowered, construction of an office building becomes more profitable and investors are willing to pay a higher price for the land upon which the office building is being constructed.


5.3. General Equilibrium Analysis of Land Taxation in NYC (Haughwout)[48]


By modifying the computable general equilibrium model of a small open economy originally presented by Haughwout and Inman in 2001, Haughwout is able to examine the impact land tax reform in New York City.[49] Readers interested in a detailed overview of the original Haughwout and Inman model are referred to section 7 of this paper. For Haughwout, conducting research on land value taxation in New York City required several different steps. First, it was necessary to calibrate the original model using fiscal, economic, and demographic data from New York City. This made it possible for Haughwout to conduct two different model simulations calculating the economic impact created by replacing part or all of New York City's current tax system with a land tax. Haughwout also modified the original model by stipulating that the all purpose public good "G" might not be a pure public good. By definition, pure public goods are "non-rivalrous" in consumption; there is no congestion and the marginal cost of providing the good to an additional person is zero. This may be true for some traditional public goods, such as street lights, but at the local level many publicly funded programs are subject to a degree of congestibility. For example, after a threshold level has been surpassed, the addition of another child to a classroom becomes noticeable as the quality of education provided to all students is diminished.

Haughwout's first simulation looked at what might happen if the land portion of the property tax remained unchanged while all sales, capital, and income tax rates were eliminated. Although the removal of these distortionary taxes would make New York City a more attractive place to live and work, Haughwout found that a reduction in the tax rates reduced government revenues and public good provision. This reduction in public good provision decreased the relative attractiveness of living and working in the city, effectively negating some of the benefits caused by the removal of distortionary taxes. Haughwout's second simulation increased the land portion of the property tax so that if all sales, capital, and income tax were eliminated, the aggregate tax revenue would remain at its pre-tax reform equilibrium level. Originally land was taxed at a rate of 2.83%, but in order to conduct the prescribed tax reform in a revenue neutral manner, the rate on land would increase to 21.7%.

One interesting feature of Haughwout's second simulation is that, when the size of the public sector is constrained, this type of land tax reform would cause land values to fall. The model predicts that, under these specific conditions, the removal of distortionary taxes would actually make the city less attractive as a place to live and do business.[50] A possible explanation as to why land prices fell in the second model simulation has to do with the fact that the tax shift dramatically increased the number of city residents and workers. At this new city size it may not be efficient to provide services to everyone in the city. This problem would be even worse if the large public sector was financed with distortionary taxes.[51] This explanation is partially supported by the fact that when Haughwout conducted further test simulations, the net effect of a reduction of the land tax rate (and public service provision) actually increased land values.


6. The Need for New Research Analyzing Policy Proposals in Philadelphia


The existing body of empirical and general equilibrium research done on land value taxation provides a good base from which to broadly speculate about the impact that a land value tax would have in Philadelphia. However, this research does not lend itself well to analyzing the effect that the City Controller's land tax proposal would have on Philadelphia's economy.

All of the empirical research done on land taxation in Pennsylvania municipalities relies on time series data. Because land tax reform has not yet been implemented in Philadelphia there is no time series data on which to draw. This makes a isolated, forward-looking Philadelphia analysis quite complicated. Furthermore, because Pittsburgh is the only large city to have implemented a land tax, it is not clear that conclusions drawn from the majority of these studies should be directly extended to a city as large as Philadelphia. These studies can generally indicate how Philadelphia might be impacted, but they cannot provide a detailed understanding of how such a tax reform would effect the city's economy.

Although the three general equilibrium models provide a better framework from which to analyze the effect of a proposed land tax reform in Philadelphia, to some extent their findings are inconclusive and inapplicable. Part of the discrepancy among these three researchers' results has to do with the fact that they all modeled different types of economies: Tideman examined the effect of revenue neutral property tax reform on both open and closed economies, Nechyba looked at how revenue neutral replacement of different classes of distortionary taxes would impact large non-open economies, and Haughwout studied the effect that replacing all distortionary taxes with a land tax (both in a revenue neutral and non-neutral manner) would have on a small open economy.[52] Although it might seem as if Tideman's work on open and closed economies could be used to easily link the work done by Nechyba and Haughwout, this is not entirely true. Tideman's study nicely complements existing general equilibrium research, but his model is quite different from the other two models described in this paper. Although Tideman looks at factors largely ignored by Nechyba and Haughwout (such as labor-leisure decisions and the incidence of land speculation), Tideman's model does not provide a mechanism for measuring how tax reform would effect property values. This is a crucial component of the other two models. Furthermore, while the Nechyba and Haughwout's models are static, Tideman's model is dynamic and looks at the yearly equilibrium effect of tax reform.[53]

Another source of discrepancy between these models stems from the fact that they all look at different types of land tax reform: Tideman transformed traditional property taxes into land value taxes by removing the tax on structures and improvements, Nechyba replaced entire classes of distortionary taxes with land taxes, and Haughwout eliminated all taxes except for the tax on land. Despite the fact that they look at different types of land tax reform, in each of the models at least one entire type of tax is eliminated and replaced with a tax on land. All three models could have been set up to examine the effect of a more modest tax reform. However, these researchers all chose to publish the results of dramatic tax reforms. This not only allowed them to remain fairly true to George's original vision of a single tax on land rents, it also allowed them to illustrate what would happen in the best (or worst, depending on your personal view of land taxation) case scenario.[54] However, by focusing on the impact of dramatic tax reforms, these researchers worked outside of the realm of political reality. It is true that Nechyba and Haughwout discuss the political feasibility of their proposed tax reform (by examining the likely impact on land values and thus on land owners), but they never take account of the fact that public policy proposals always reflect a political compromise. Proposed tax reforms, such as the ones studied by these researchers, would likely face staunch political opposition.

Not only are these extreme tax reform packages politically unrealistic, but from an econometrician's perspective, the results from such model simulations are only marginally reliable. All three of the discussed general equilibrium models are very sensitive to elasticity estimates and to assumptions made about the relative importance of land capital consumption.[55] Elasticity estimates play a central role in determining the equilibrium effect of policy proposals, yet relatively little is known about them. Typically, aggregate elasticity estimates are formulated by looking at large amounts of historical data. If the economic climate of a city were to be suddenly altered by the introduction of a new and dramatic type of tax reform, it would be difficult to predict how the elasticities of supply and demand might change. Similarly, if such a drastic tax policy were introduced, existing ratios relating to personal consumption and firm production might no longer be accurate. This is not to discredit the structure of these models, but simply to say that the less policy proposals differ from the status quo, the more reliable equilibrium estimates will be.

After identifying why none of the existing empirical or equilibrium research should be used to evaluate the impact of the Philadelphia City Controller's land tax proposal, it is necessary to identify what type of research would be the most appropriate. Because the Controller's policy proposal would only be implemented within city limits, it makes sense to use small open economy model. Ideally, this model should be calibrated to Philadelphia's fiscal, economic, and demographic conditions. In order to replicate the Controller's proposal, land tax reform would have to be limited in its scope and all simulations would have to be conducted in a revenue neutral manner.


7. Modeling Philadelphia's Economy (Haughwout and Inman)[56]


In this paper, rather than creating an entirely new general equilibrium model, a modified version of Haughwout and Inman's open city model is used to analyze the effect that land value taxation would have on Philadelphia's economy. The following section contains an overview of the model's structure and important features.


The Model:


The model is of a small open economy with mobile firms, resident workers, and commuters (who work in the city while consuming housing and other goods outside of the city).[57] In the model, there is a fixed supply of land and an exogenously determined number of non-working, non-mobile, dependent residents. All factors of production (except land) must meet certain criteria in order to remain located in the city: capital must earn its competitive rate of return, firms must be able to sell the goods they produce in the city at competitive world prices, labor working within the city, but living in the suburbs, must earn a competitive after-tax wage, and residents living and working in the city must maintain an overall level of utility comparable to that outside of the city. Equilibrium is achieved in this open city model when no mobile firm, resident, or commuter has an incentive to change its location, residence, or job. For each combination of different fiscal polices, a unique equilibrium is reached. When evaluating tax reform policies it is necessary to find and contrast the initial equilibrium outcome with the equilibrium outcome created after implementing the tax reform. The model consists of 15 exogenous parameters and 18 endogenous variables. See Appendix D for a complete list of these parameters and variables.


Commuting Workers:


In addition to hiring resident workers, firms employ commuting workers. In this model commuters have been classified as "managers" which mirrors the existing pattern of labor location in the United States. However, the model is sufficiently general to allow managers to live within the city and workers to commute from the suburbs, as they do in other parts of the world. Commuters consume private goods, housing, and land outside of the city; it is assumed that they purchase these goods at competitive and constant world prices. Although commuters work in the city, they have the option of working in a suburban location. Thus, in order to retain and attract commuters, not only must city firms pay a wage equal to the commuter's suburban wage, but these firms must also compensate commuters for all disamenities of working within the city (such as an additional tax the city might levy on a commuter's labor income). It is assumed that there is an infinite supply suburban residents who would become commuters if they were adequately compensated.

In Philadelphia many skilled workers (such as professors, physicians, and technical staff) live in the suburbs and commute into the city because, for them, no regional suburban employment alternatives exist. Although the argument could be made that the model is flawed because these workers do not get compensated for working in the city, it is important to remember that the model assumes perfect mobility of labor. Thus, even though there may not be another school like the University of Pennsylvania in greater Philadelphia region, if a Penn professor felt that he was not adequately being compensated for having to work in the city he would be free to leave the region and seek employment at another ivy league institution.


Solving the Model:


All of the model's 18 exogenous characteristics, along with the parameterized household preference and firm production technologies, are used to derive the 15 endogenous variables and find an equilibrium solution. By adjusting these exogenous variables it is possible to calibrate the model so that it mirrors the economic, fiscal, and demographic composition of any city in the United States. See Appendix E for a complete list of exogenous variables and parameters. The model is solved iteratively using a starting value of G (=G(0)). This yields a set of private market outcomes which in tern yields a new equilibrium level of public services. This process is repeated until the model converges and G(t-1) = G(t) = G. Equilibrium exists within the model when no mobile firm, resident household, or commuter has an incentive to change their location, residence, or job.


8. Model Modifications and Simulations


Modifying the original Haughwout and Inman model and running simulations to answer the research questions set forth at the beginning of this paper involved three distinct steps. First, it was necessary to modify the structure of the original model and to calibrate the reformed model to Philadelphia's economic, fiscal, and demographic environment. Next, a series of simulations were conducted to evaluated two distinct policy proposals. Although these policy proposals closely resemble the ones made by the Philadelphia Controller's Office, due to the constraints of the model, some adjustments were necessary.

Both of the policy proposals examined in this paper involve adjusting tax rates in a revenue neutral manner. By revenue neutral the Philadelphia Controller's Office means that the revenues generated by a select group of taxes will be sufficient to meet the current budgeted revenue projection for those same taxes.[68] General equilibrium modeling makes it possible to more comprehensively define revenue neutrality. The model makes it possible to predict how changing the rate for any one type of tax would alter the tax base (and thus the revenues collected) for each type of tax. Therefore, in these simulations, the term revenue neutrality is applied to all taxes (net government revenues are equal before and after tax reform).

By linking revenue neutrality to current budget projections, the Controller's Office implicitly assumes that total government expenditures will remain constant. In this situation household utility derived from government spending would remain constant if: (1) changing the city's tax structure did not alter city demographics, (2) and/or if the all-purpose government produced public good were a pure public good. However, the modified version of the model assumes full congestion of public service provision. Thus, household utility derived from constrained government expenditures would only remain constant if the city's population remained constant. Because total city population is endogenously defined, in the model, tax reform could lead to changes in the city's total population. Therefore, in order to isolate the true economic impact caused by a tax reform policy, revenue neutrality must be defined as constant household government spending (average household tax revenue collection). If household government spending was not held constant in the face of a changing city population, it would be impossible to determine if the city's relative economic "attractiveness" changed because the tax structure changed or because the level of public service provision per household changed.

Once the model was properly calibrated a simulation was run in order to determine the equilibrium baseline residential wage (W), rental rate of land (R), total city population (N+ D), total number of jobs (N+M), the value of capital used by firms (K), and the value of the city's housing stock (H).

8.3 The Second Policy Proposal


The second part of the Controller's proposed land tax reform involves shifting the tax burden from the Residential Wage Tax onto the Land Tax. See Appendix B for more information about Philadelphia's Wage Tax. Rather than running one simulation to examine the effect of the Controller's proposed 11.86% resident wage tax reduction, five different simulations were run to identify what would happen if Philadelphia's Residential and Non-residential Wages Taxes are reduced by 10%, 20%, 50%, 90%, and 100%.[69] The decision not to strictly model the Controller's proposal was made because compelling research indicates that, like the Resident Wage Tax, the Non-Resident Wage Tax adversely affects job creation and economic growth in Philadelphia.[70]

9. Results


When general equilibrium modeling is used to analyze a specific policy proposal, the equilibrium results should be viewed as a crude indication of the nature and magnitude of any economic change resulting from the policy's implementation. To reinforce the fact that the results generated by equilibrium models are not precise numerical projections, all results in this paper are presented as proportion changes from an established baseline.

These results indicate that the city's current property tax depresses land values and stifles economic growth. Reforming the property tax by decreasing the tax on structures and increasing the tax on land would stimulate Philadelphia's economy. This stimulation would increase total city employment, increase the city's population, increase the amount of capital (both housing and productive) investment in the city, and increase property values. All economic indicators, except for residential wage, would be dramatically increased if this tax policy were implemented. Given that the decrease in residential wage is relatively negligible (-0.7%), and that total city employment significantly and simultaneously increases (78%), land tax reform would cause wage tax revenues to increase.

Initially, the Controller's Office predicted that, in order to generate half of the current Real Estate Tax revenues from land and half from buildings, land would have to be taxed at 3.44 times the rate of structures. The modified general equilibrium model found that such a split in revenues would occur when land is taxed at 4.36 times the rate of structures. To understand why the results presented in this paper differ from the Controller's predictions, it is necessary to look more closely at the equilibrium results and at the definition of revenue neutrality. The model found that this type of tax reform would have significant positive effects on the amount of jobs, residents, productive capital, housing stock, and land rents in the city. Even if the Controller's Office took into consideration relative increase in city land rents, housing stock, and capital stock, their definition of revenue neutrality would preclude them from looking at how this type of tax reform would effect revenue collection from other types of taxes. Although there was a slight decrease in residential wages, the magnitude of this decrease is insignificant when compared to the large increase in city employment.

Discrepancy between results put forth in this paper and predictions made by Controller's Office arises because revenue neutrality is defined in different ways. In the first policy simulation, government spending per household is held constant. However, the Controller's Office holds aggregate government spending constant. If the city population never changed, or if city services were pure public goods, aggregate revenues would be an acceptable proxy for per household government spending. However, empirical research indicates that the city's population is sensitive to changes in the city's fiscal structure, and that, at the margins, city services are congestible. If tax reform caused the city's population to increase, and if aggregate revenues were held constant, it would be impossible to separate the impact of the tax reform from the impact caused by a drop in service provision.


The Second Policy Proposal:

When analyzing the second policy proposal, the general equilibrium resulting from the first policy proposal are used as a baseline. Five different simulations were run in order to identify what would happen when per household tax revenues, lost as a result of wage tax reduction, are replaced by increasing the land tax. In each simulation, wage taxes were proportionally reduced by 10%, 20%, 50%, 90%, or 100%. The magnitude of the resulting economic change varied depending on the size of the wage tax reductions, yet in all simulation there was a slight reduction in residential wages, a more significant reduction in land rents, and a large positive increase in city employment, city population, the value of the housing stock, and the value of the productive capital. See Table 2 [not provided here] for the complete simulation results.

These results generally indicate that shifting the wage tax burden onto a land value tax would stimulate the economy. In fact, these simulations suggest that, if policy makers were interested in maximizing the total number of city jobs, or the total city population, or the total capital stock (both of housing and productive capital), they would eliminate the wage tax completely and make up lost revenues by taxing land more heavily.

When interpreting these results, it is important to remember that the percentage change of each variable is calculated against the values generated in the first policy proposal. If one were to compare the equilibrium levels from the second policy proposal to the existing economic conditions in Philadelphia, the change in city employment, city population, housing stock, and productive capital stock would be much larger. Although the change in residential wage would be smaller, when compared to the magnitude of change experienced by other variables this finding remains fairly insignificant. Because the first policy proposal increased land rents by 24%, not until the wage tax rates are cut in half do land rents drop below their current values.

Because there are sound theoretical reasons for believing that land taxation is more efficient than wage taxation, it was somewhat surprising to discover that land rents decrease when the tax burden is shifted from the taxation of residential and non-residential wages to a land value tax. In theory, firms and households should be attracted to the city when a more efficient tax structure is implemented. Thus, given the significant increase in other economic indicators, decreasing land rents were unexpected. More than anything else, this unexpected finding emphasizes the fact that local taxation is inextricably linked to the size of the local public sector. Thus, theories which seek to identify an optimal system must also be concerned with identifying the optimal size of both the city and the local public sector.


10. A Word of Caution


Before moving on to the paper's conclusion, it is important to issue a word of caution about the limits of economic modeling techniques. Modeling inherently involves simplifying, consolidating, and even ignoring many different variables in hopes of capturing the essence of the forces that drive the economy. For example, although research indicates that a whole host of city provided services (well kept infrastructure, good schools, adequate police protection, etc.) factor heavily into location decision, in this model these variables have been condensed into one all purpose public good "G". This type of consolidation allows researchers to easily take a variety of different, yet related, variables into account. It would be an error to assume that these factors are incorporated into the model simply because the model sheds no light on their individual or relative importance (e.g. how important are good schools when compared to low crime rates or low taxes). This being said, even the most sophisticated models omit a great number of factors that could potentially affect the outcome. If these omitted factors are not random, the estimated impact of tax reform on the economy would be biased.

Another limitation of this paper's general equilibrium model is related to the fact that the model implicitly assumes that the structure of the relationship between factors remains constant over time. If these relationships are not stable, then the inferences derived from the model simulations may not be warranted. Thus, if the economic climate of a city were suddenly altered by the introduction of a new and dramatic type of tax reform, the relationship between factors might change. This word of caution is not to discredit economic modeling, but simply to suggest the less policy proposals differ from the status quo, the more reliable equilibrium estimates will be. Similarly, the model assumes that there will be no outside events or influences introduced to change the relationship between factors. For example, if World War III erupted tomorrow it is likely that the relationship between tax base and tax rate might change in an unpredictable way.

When looking at the results of this or any economic model, it is important to exercise a good deal of caution. Model simulations allow researchers and policy makers to understand the nature and the magnitude of the economic change that would result from certain types of tax reform. As such, the numbers generated by this model should simply be viewed as general indicator of trends that might happen.


11. Conclusion


The goal of this research was to determine the nature of Philadelphia's economic response to land tax reform. Analyzing the effect of a policy proposal which has not yet been implemented can be difficult, however this was accomplished by studying the theoretical arguments offered in support of land value taxation, reviewing the existing body of economic land tax research, and conducting policy simulations using a general equilibrium model. Economists generally agree that land value taxation is an economically efficient method of generating government revenue. Yet, empirical studies of land tax municipalities provide little insight into how land tax reform would effect Philadelphia's economy. To truly understand the impact land taxation could have on Philadelphia's economy, it is necessary to study this tax in terms of its revenue alternatives. This type of investigation can be done by running policy simulations on a general equilibrium model. Although several different economists have used general equilibrium modeling to examination land value taxation, all of this research focuses on the elimination of entire classes of distortionary taxes. Though this type of tax reform can be conducted in a revenue neutral manner, passage of such radical tax reform would require strong political support. Throughout this paper, a comprehensive policy proposal, developed by the Philadelphia Controller's Office, was set forth as an example of a politically feasible, modest land tax reform. Using a general equilibrium model, two policy proposals, similar to the ones designed by the Controller's Office, were analyzed in terms of their revenue alternatives. A series of model simulations found that, if these policies were implemented, Philadelphia would experience significant job creation and population growth. Assuming that these are considered to be socially desirable outcomes, city residents and elected officials should embrace the concept of land value taxation and work towards shifting some of Philadelphia's tax burden onto land values.


LIST OF APPENDIXES IN THE ORIGINAL PAPER

Appendix A: The Controller's Tax Structure Analysis Report

Appendix B: Arguments for Wage Tax Reduction in Philadelphia

Appendix C: Assessing Land Value

Appendix D: Model Variables

Appendix E: Model Assumptions and Parameterization