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## The association between urban sprawl and obesity: is it a two-way street?

I. Research Question

Plantinga and Burnell’s 2005 paper draft proposes a model that addresses how obesity and urban sprawl are related. This question arose due to the recent rise in obesity in the United States. There is ample research in the public health and urban planning realms on this topic. However, Plantinga and Bernell challenge the existing literature’s conventional assumption that sprawl causes obesity.

Urban economics is perhaps a surprising avenue by which to analyze the problem of obesity. However, the analytical model put forth in this paper finds meaningful results that could have profound public health and policy implications. Urban planning specialists have drawn links between urban sprawl patterns and demographic and lifestyle characteristics.

Specifically, urban sprawl and obesity are related in three main ways. First, poor street networks and low density lead to longer travel distances. Longer travel distances mean people are forced to travel by car rather than bike or foot. Second, low density means that public transportation systems are less effective and less likely to exist. Therefore, people are traveling by car and have longer commute times and thus less time for physical activity. Lastly, sprawling areas often have poor or unsafe public parks, which discourages exercise.

The existing research holds that poor infrastructure and land use, as outline above, ultimately cause weight issues. As a result, many cities are investing in projects to encourage healthy living. For example, the Atlanta Regional Commission recently invested \$1.1 billion in bike and pedestrian infrastructure. Plantinga and Bernell’s model questions whether this will be effective. They assert that overweight people self-select for sprawling residential environments, and thus improving land use in these areas is futile.

Previous research has treated urban form as an exogenous variable. In other words, researchers have assumed that one’s Body Mass Index (BMI) has no influence on residential location choice. This study, however, poses that BMI indicates lifestyle choices that influence residential location choice. This distinguishes whether sprawl causes BMI to rise or whether high BMI individuals choose to live in sprawling locations. Treating BMI and location preference both as endogenous variables answers this question.

II. Theoretical Background

Plantinga and Bernell use the National Longitudinal Survey of Youth from 1979 (NLSY79) together with the sprawl index produced by McCann and Ewing (2003). The resulting dataset includes variables such as BMI, income, education, county of residence, and degree of sprawl. This paper builds on the conventional model for regressing BMI on locational attributes and a composite good.

The conventional function holds that utility is maximized by considering weight, attributes of the residential location (such as walkability), and a composite good. Weight (W) is given by:

Where W0 is initial weight of a person, N is a vector of locational attributes, and C is a composite good. Utility is maximized using the follow equation:

Given that p is a vector of prices for locational attributes and I is income. Using  standard constrained optimization techniques, the following equations give the locational attributes (N*I ) and weight (W*I) that result on the greatest utility for an individual.

However, this paper argues that there would be codependence between the weight and locational attribute variables. Also, the researchers hold that a complete model would distinguish between people who recently moved versus have been in the same county for four years or more. This is because if land use does have an impact on weight, it would take some years to manifest. Therefore, the researchers propose a simultaneous equation model that would treat BMI and locational attributes as endogenous. They also create two different models that look at movers and non-movers separately.

III. Empirical Model

The BMI model used in this paper is as follows:

given that i (i=1,…,N) indicates specific individuals, B0 is the intercept term, Bj (j=1,…,14) are the variable coefficients, and ɛi is the error term. The explanation of variables is given in Table 1.

Due to the fact that migration is a separate decision and difficult to factor into the model, the researchers decided to define the decision to move to a county as whether it is high or low density, income, education, marital status, and more. Therefore, their model for adjusted BMI on all the other variables as a follows:

Where y*I is the latent variable describing choice of a low or high density county, that i (i=1,…,N) indicates specific individuals, y1 and y2 are parameters on ADJBMIi and SPRAWLi, X1i and X2i are vectors of the exogenous variables, B1 and B2 are conformable parameter vectors (like race, sex, smoking, age, education, and regional dummies), and ɛ1i and ɛ2i are the error terms.

Using least squares and a probit maximum likelihood model, they created a set of covariant matrices of expected values for the endogenous variables. These estimates were made using data from the year 2000 in the NLSY79 and the sprawl index. To separate out movers from non-movers, the model was run twice, each time with only individuals who had lived in their counties for 4 years or more versus less.

IV. Results and Conclusions

The results of the simultaneous equation model suggest that BMI does, in fact, have a negative effect on whether an individual moves into a dense county. This holds true for both movers (coefficient -.789) and non-movers (coefficient -1.182). The researchers also accounted for the fact that their arguably arbitrary cutoff for density or their year cutoff for being a mover versus non-mover may have skewed the results. However, even with more conservative and liberal estimations of these cutoffs, their results generally held true. The implications of these results are that current policies about land use and public health may be misguided. Increasing infrastructure that encourages an active lifestyle in sprawling areas could just result on obese-prone people moving elsewhere.

V. Extensions

The fact that Plantinga and Bernell challenged the assumption that sprawl causes obesity could have profound policy implications. With this discovery, money will be saved on fruitless or inefficient policies. Also, researchers are one step closer to discovering the root of obesity problems. Their research helps society edge closer to the true causes and possible solutions for obesity. This investigative research model could also be applied to other public issues related to urban sprawl. For example, one could research whether violent people move to sprawling or dense areas. Does density versus sprawl cause the violence or is it a result of the type of person who chooses to live there?

Cited Source:

Andrew Plantinga and Stephanie Bernell, 2005, “The association between urban sprawl and obesity: is it a two-way street?”. Draft. americandreamcoalition.org *

Andrew Plantinga and Stephanie Bernell, 2007, “The association between urban sprawl and obesity: is it a two-way street?” Journal of Regional Science 47(5): 857-879.

*I used the 2005 draft because it explained which equations were used, while the 2007 version did not. The remainder of the article and analysis was largely the same.

## The Holdout Problem, Urban Sprawl, and Eminent Domain

By Spencer Rasmussen  The Holdout Problem, Urban Sprawl and Eminent Domain

1.  Introduction

Purpose: To acknowledge the holdout problem, which is a type of land market failure, that contributes to urban sprawl by creating a bias towards the fringes of cities for large land developments

The Holdout Problem: “is a form of monopoly power that potentially arises in the course of land assembly.  Once assembly begins, individual owners, knowing their land is essential to the completion of the project, can hold out for prices in excess of their opportunity costs” or “individual owners, realizing that they can impose substantial costs on the developer, seek prices well in excess of their true reservation prices.”

A holdout problem must require assembly, which is the need for at least two distinct properties for a development.

Result: Large-scale projects that require assembly, like housing developments, parks and open spaces, stadiums or shopping malls, will have high bargaining costs.  This will create incentives for developers to look for land where ownership is less dispersed, which will minimize assembly.  This will lead to these large building projects taking place on the fringes of cities leading to unnecessary urban sprawl

2. The Economic Literature on Urban Spraw

Definitions of Urban Sprawl:

• Galaster: “Sprawl is a pattern of land use in [an urban area] that exhibits low levels of some combination of eight distinct dimensions: density, continuity, concentration, clustering, centrality, nuclearity, mixed uses, and proximity.”
•  Nechyba and Walsh: “the tendency toward lower city densities as city footprints expand”
• Brueckner: “the excessive spatial growth of cities…implying inefficient outward growth”

Sources of market failure that can lead to excessive growth

• When the price of agricultural land does not fully represent its social value that it produces as open space, which causes its conversion to urban areas
• When commuters do not properly evaluate the costs of congestion when making commuting decisions, which results in excessively long commute times
• When real estate developers fail to acknowledge the full social cost of the required infrastructure, which artificially lowers the cost of development
• Miceli and Sirmans develop a fourth potential market failure, the holdout problem

3. Land Assembly and the Holdout Problem

There is a possible relationship between the holdout problem and urban sprawl suggested by the fragmentation of ownership in urban areas spatial variation in the fragmentation of ownership in urban areas…this is because lot sizes are generally smaller towards the center of cities and become larger as you move away from the heart of the city center.  As a result assembly in the middle of the cities generally requires more participation for a given area then at the fringes of a city.

3.1. A Simple Model of the Holdout Problem

A developer needing to acquire two adjacent, individually owned lots.  We assume that bargaining between the two parties, the developer and land owners takes place in one of two periods: now (t=1) or later (t=2).  The developer can only proceed with development if he (a) acquires both parcels of land in t=1 (b) acquires one parcel of land in t=1 and the other in t=2 or (c) acquires both parcels in t=2.  If the developer is unable to acquire all (two) pieces of land then he is forced to scrap the project.  In this model the lot owners have the option to wither “bargain,” selling their property to the developer, or “hold out,” not selling their property to the developer in t=1, 2.

i.     If the developer is able to acquire both pieces of land in t=1 V > 2v

1. V = the profit that the developer expects to earn if he is able to acquire both areas of land in t=1
2. 2v = the combined values of the two properties of land to the individual owners.  So v is the value of one property to one owner.
3. We know that V must be greater than 2v because the land developer would never assemble the two parcels of land if he could not obtain a profit from the proposed development

ii.     If the developer is able to acquire one piece of land in t=1 and one in t=2 or if the developer is able to acquire both pieces of land in t=2 V – ε > 2v

1. ε is the cost of the delay that the developer will incur.  We still assume that the development is profitable at this date because otherwise the project would not progress

iii.     Potential Outcomes

If both sellers bargained in t=1

Both sellers will get P~ = V / 2

If one seller bargained in t=1, and received P1, and the other held out in t=1…

• And then the seller who originally held out in t=1 sells in t=2 for P2

Net return for the project is V – ε – P1 – P2.  P1 = v because as shown below P2 = V – ε – v.  And assuming the developer is able to acquire the second parcel of land the V – ε – P1 – P2 = V – ε – P1 – (V- ε – v).  Here the development is able to take place because the developer obtained both parcels of land, but he does incur a loss because of the delay caused by own of the sellers holding out until t=2

• And then the seller who originally held out in t=1 holds out in t=2

Net return from the single parcel is v – P1 because the development was scrapped because the developer was not able to acquire both plots of land.

So the net gain from acquiring the second parcel of land in t=2 is V – ε – P1 – P2 – (v – P1) which when set equal to zero yields P2  = V – ε – v.  Obtaining the second parcel of land allows the developer to proceed with his land development and attempt to obtain the profit he expected.

If both sellers held out in t=1

And then sell in t=2 the price per parcel is P* = (V – ε) / 2. This is true because the two sellers will split the payment equally.  In this case the developer is once again able to start his development because he was able to assemble both parcels of land, but he once again has to incur the loss due to the delay of assembly

Conclusions:

1. Sellers would prefer to sell jointly in period one as opposed to period two, because the later involves a delay, ε.  This delay causes the overall profit of the development to be decreased.

2. It is better for a seller to be the lone holdout in period two, as opposed to the case where both sellers holdout and sell in period two, as seen by P2 > P*.  This is the same as the classical prisoner’s dilemma problem where both owners are better off selling out promptly, but each individually has the incentive to delay selling.

P2  = V – ε – v and P* = (V – ε) / 2

3. It is unknown if being the lone holdout or selling jointly in period one is better, because while the holdout has superior bargaining power, the available surplus in period two is smaller due to the cost of delay.  The ambiguity comes from the relationship between ε and (V-2v)/2.

4. The worst possible outcome for a seller is to be the lone seller in period one because the price the seller obtains is only v. P1 = v

5. The overriding takeaway form this model is that costly delays can arise in projects involving land assembly.  We can assume that the more parcels of land necessary for a certain development will make assembly even more difficult, and thus lead to more costly delays.  So developers will prefer locations where ownership is less dispersed, all else equal.

1. Equilibrium strategies (depend upon the relationship between P~, the price the sellers would get if they both bargained in t=1 and P2, the price that the lone holdout in period one would receive if he then sold in period 2)

i.     Suppose P~ > P2  which is true whenever ε > (V-2v)/2

1. The two Nash equilibriums are (bargain, bargain) and (holdout, holdout) holdout assumes that the seller will then bargain in period two

ii.     Suppose P~ < P2  which is true whenever ε < (V-2v)/2

1. There is only one Nash equilibrium (holdout, holdout)

3.2. The Spatial Configuration of Lot Sizes and Urban Sprawl

Lot sizes decrease towards the city centers for two reasons: 1) increasing land prices toward the city center cause housing producers to substitute land for capital and 2) increasing housing prices toward the city center also cause the demand for housing to decrease.  Due to these two reasons there is greater population density nearer to the city center.  Which we can reasonably extrapolate from and say that ownership of a piece of land of a given size is more dispersed the closer it is to the city center, meaning that more people own a given area of land the closer the closer this area of land is to the center of the city.

Remedies

In order to combat urban sprawl…

i.     Developers can maintain their secrecy about projects by utilizing dummy buyers to help acquire assemblies.  This would be useful because sellers would not know that a single buyer is attempting all of the land in a certain area.  This is more difficult for government-backed projects because they often require openness.

ii.     Governments can create incentives or subsidies for building in city centers or disincentives for building in the suburbs.  The justification for this can come from redevelopment of central areas.

iii.     The use of eminent domain, but this often raises issues about whether or not a private organization should be able to benefit from the use of eminent domain.

4. Conclusion

The holdout problem “represents a situation where landowners whose property is essential to the completion of some large development project to seek to block completion of the project in an effort to extract monopoly rents”

This biases development away from areas where ownership is the most dispersed, city centers, and towards areas where ownership is more concentrated, the fringes or suburbs of cities

References:

All quotes are from the following citation

Miceli, Thomas J., and C. F. Sirmans. “The Holdout Problem, Urban Sprawl, and Eminent Domain.” Journal of Housing Economics November 16.3-4 (2007): 309-19. Web. 1 Mar. 2014.

## Innovation in cities: Science-based diversity, specialization, and localized competition

By Olivia Nicolaus

Introduction

This paper by Feldman and Audretsch attempts to address the question of “whether diversity or specialization of economic activity better promotes technological change and subsequent economic growth” (409).  It finds considerable support for diversity as a catalyst for innovation and little support for specialization (409)

Context

A number of scholars including Krugman, Romer, and Lucas support the importance of concentration of people and firms as the most important factor for economic activity (410).  Concentration creates knowledge spillovers, which are the transmission of knowledge “through face-to-face interaction and through frequent contact” (411).  Scholars disagree over the significance of knowledge spillovers within and across disciplines, but it is widely accepted that physical proximity is key for the transmission of “sticky knowledge,” or that which is highly contextual (411).  Knowledge spillovers create increasing returns to scale within a geographically bounded space, primarily the relatively compact area of cities (410).

An important question to ask in relation to agglomeration economies is “does the specific type of economic activity undertaken within any particular geographic region matter?” (410). This opens the debate to two options: a geographic region that specializes in a particular industry, or a geographic region with diverse firms and economic agents.  In order to answer this question, Feldman and Audretsch attempt in this paper to classify the extent of diversity or specialization in geographic regions and then measure “how this composition influence innovation output” (410).

Connecting Innovation and Cities

In this paper Feldman and Audretsch use data from the United States Small Business Administration Data Base as a direct measure of innovative output.  This database is composed of product innovations, each with a four-digit standard industrial code (SIC).  Limitations to this data include the emphasis of product innovations over process innovations, variation in the quality of innovations, and the necessity to treat all innovations as homogenous (414).

By attributing each SIC to a Consolidated Metropolitan Statistical Area or Metropolitan Statistical Area, the researchers are able to rank cities in terms of gross quantity of innovation.  The results are exhibited in Table 1, which shows that the most innovative city in the United States in 1982 was New York.  It is also important to note the overwhelming source of innovation is urban areas, with less than 4% of all observed innovations occurring outside of metropolitan areas (415).  For reference, 70% of the population at this time lived outside of metropolitan areas (415).  The table also uses population statistics to provide a more accurate calculation of innovation, finding San Francisco with the highest innovation rate per capita (415).

Connecting industry clusters, academic departments, and geographical areas

Feldman and Audretsch then attempt to link “products on their closeness in technological space” (415).  To do so they utilize the relevance ranking scale in the Yale Survey of R&D managers to establish groupings between industries that share a common scientific base.  The results are shown in Table 2.

The researchers find that industries that rely on a “common science base” exhibit a tendency to cluster together geographically with regard to the location of employment and innovation (418).  This is the initial information that the researchers use to create a model for determining the effect of a variety of factors on the quantity of innovations in different locations.

Modeling Framework

Feldman and Audretsch establish the dependent variable of their analysis as the number of innovations attributed to a specific SIC industry in a particular city.  They isolate three explanatory variables: a measure of industry specialization, a measure for the presence of science-based related industries, and an index for localized competition (419).  The equation, mean, and standard deviation for these three variables are exhibited in Table 3.

Results

Feldman and Audretsch’s results are shown in Table 4, titled Poisson estimation results for the Poisson regression estimation method.  This method was selected because to model count variable because “the dependent variable is a limited dependent variable with a highly skewed distribution” (420).  This means that the events represented by the data are somewhat rare.  This type of distribution can be used for cancer, cases, number of accidents, or number of bird sightings, but in this case is used for counts of product innovation (Schwartz 1466).

The first column (Model 1) provides results for the three independent variable measures (specialization, science-based related industries, localized competition).  For industry specialization, the negative and statistically significant coefficient suggests that cities that specialize in economic activity in a certain industry have a lower rate of innovative activity.  For science-based related industries, the positive and statistically significant coefficient means that innovative activity is correlated with a strong presence of complementary industries sharing a common science base.  Finally, the negative coefficient on the third variable, localized competition, suggests that innovative activity of an industry is actually associated with less localized competition.  To translate these correlations: the results provide support for diversity in spurring innovation as opposed to specialization spurring innovation (421).

Potential Concerns

There are a few potential drawbacks to using this model.  The first is of city size; that large cities might be expected to have more innovation purely as a result of advantages in total manpower and resources.  There may be a greater degree of economic activity and localized competition.  In the second column of Table 3 (Model 2), total employment is normalized and the results for the third variable change.  This new positive coefficient means that localized competition is, in fact, conducive to innovative activity.  The other two coefficients remain unchanged. Another concern with Model one is the variation in innovation across industries.  In the third and fourth columns (Models 3 and 4), the number of innovations recorded for the specific industry is controlled.  The basic results remain the same.

Policy Implications and Importance

The answer to the debate of specialization versus diversity prompts two different policy implications.  If innovation is fostered more effectively in specialized economies, policymakers should “focus on developing a narrow set of economic activities within a geographic region” (410).  However, since the opposite is true and diversity prompts innovation, policymakers should attempt to “identify commonalities and foster diversity” within the geographic region (410).

The specialization versus diversity question draws parallels to two types of modern development: university research parks versus the traditional urban form.  According to this study, the diversity of work types that occurs in a traditional urban setting is more innovative and therefore more economically productive than a more focused research park.  If policymakers are purely hoping to pump out a vast quantity of innovation in the form of new products, they should focus primarily on developing a diversity of businesses and corporations in cities, and also figuring out ways to encourage face-to-face contact that is valuable to knowledge spillovers.

However, this research does not measure the quality of innovations, and thus should not be taken at face value.  Further research could incorporate the quality of innovations in the spatial analysis.  In addition, further research could measure how the degree of specialization within research parks affects the amount of innovation created.

Appendix

Table 1: Counts of innovation normalized by population

Table 2: The Common science bases of industrial clusters

Table 3

Table 4: Poisson estimation results

References:

Feldman, Maryann P., and David B. Audretsch. “Innovation in Cities:.” European Economic Review 43.2 (1999): 409-29. Print.

Schwartz, Carl J. “Poisson Regression.” Poisson Regression. Simon Frazer University, 7 June 2013. Web. 28 Mar. 2014. <http://people.stat.sfu.ca/~cschwarz/Stat-650/Notes/PDFbigbook-JMP/JMP-part025.pdf>.

## A Game-Theoretic Analysis of Skyscrapers

By David Lillington  A Game-Theoretic Analysis of Skyscrapers

Skyscrapers have received little attention from urban economists in the past according to Helsley and Strange (2008). What has been discussed relates to their place in the standard urban model, otherwise known as the monocentric city model. In this model, skyscrapers are attributed to the phenomenon of increasing land prices as one approaches the city center. Due to these higher prices, buildings are built up in order to save land costs. In their study, Helsley and Strange (2008) argue that higher land prices are not the only reason for the stratospheric height of these manmade marvels. To builders, the height (and relative height) of their building carries importance for issues of publicity and pride.

In order to capture this importance of building the highest building in any market, the study uses game theory to simulate a skyscraper building contest and then continues on to explain an equation that models overbuilding. Building profits are still a determinant in the builder’s payoff function (as they are in the monocentric city model); however in this particular case whether or not the builder has succeeded in constructing the tallest building becomes part of the function as well. They describe their model as an “all-pay auction” (Helsley and Strange, 2008). That is, builders spend their resources and he or she who bids the highest takes the prize. This prize does come at a cost; its value is partially diminished through the bad economics of skyscrapers. The article proposes two situations: simultaneous and sequential construction. In the simultaneous game theoretic model, no contestant gains any value from competing in the game except for the builder who constructs the highest skyscraper. He or she will enjoy the value of this prize; however dissipation occurs for reasons that will be discussed. In the sequential model, the cost comes before construction “where the leader builds a tall-enough building to deter competitors” (Helsley and Strange, 2008). They use the story of the Empire State Building as evidence for this model.

Introduction of Variables

The model first introduces a situation in which two risk-neutral builders exist, i = 1, 2. Both builders own land on which to build, however we assume that builder 1 possesses a better location.
This causes $h_{1}^{*}>h_{2}^{*}$, where $h_{i}^{*}$ is defined as profit maximizing building height. Because value is given to height in this situation, the model adds some exogenous variable $\nu$ >0,to include building height. This is multiplied by the indicator variable, $\delta$, which is given a value of 1 if the builder succeeds in building the tallest building in his or her market or 0 if he or she does not succeed. This gives the equation:
$\delta&space;\nu+\pi&space;_i(h_i)$
where, $\pi&space;_i$ is builder i’s profit and $h_i$ is building height. Building height can be expressed as equation:
$\nu+\pi_i(h_{i}^{P})=\pi_i(h_{i}^{*})$
The variable $h_{i}^{P}$ represents what Helsley and Strange (2008) call a “pre-emption”; that is, “if a rival builder j chose height $h_j>h_{i}^{P}$, builder i would concede the contest because it would never be in the builder’s interest to choose a height that would win”. In other words, when $b_i>h_{i}^{P},\nu+\pi_i(h_{i}^{P})<\pi_i(h_{i}^{*})$.  This expression also explains the prize dissipation experienced in a skyscraper contest. The contest payout will be less than the profit-maximized payout as shown above. In the following two games, $h_{1}^{*}$ is assumed to be less than $h_{2}^{P}$. This is because there would be no competition in the market otherwise.

The Sequential Game Theoretic Model

In the sequential model, $h_i$ is chosen sequentially. The model proposes that builder 1 goes first with the strategy to choose a height such that $h_1\geq&space;h_{2}^{P}$ so that builder 2 will surrender to building at his profit maximization height $h_2=&space;h_{2}^{*}$. His or her pre-emption will not surpass builder 1’s actual building height. If builder 1 chooses a height such that $h_1\leq&space;h_{2}^{*}\leq&space;h_{2}^{P}$, the equation $b_2&space;=h_{2}^{*}$ still holds because builder 2 will continue to build at his or her profit-maximizing height since this will win the competition and be economically rational. If $h_{2}^{*}\leq&space;h_1\leq&space;h_{2}^{P}$ then builder 2 will just top builder 1’s height in order to win the competition. Therefore, Helsley and Strange (2008) propose it is better for builder 1 to win the contest by surpassing $h_{2}^{P}$ to achieve $\nu+\pi_1(h_{2}^{P})$. In the sequential game theoretic model, a significant cost is the choice to build high enough that no other competitor will choose to build higher. This can lead to overbuilding, which will be discussed later.

The Simultaneous Game Theoretic Model and Overbuilding
The simultaneous model considers a game in which two builders choose building height simultaneously. Helsley and Strange (2008) propose that in this case, a positive probability weight $(\phi&space;)$ on is placed on building height $h_i$. This represents the probability that builder i will build at a height less than or equal to h. The payoff for this situation can be expressed as $\pi(h^{*})$, the profit maximizing situation. The model proposes that builder i’s payoff is equal to $\phi&space;(h_i)\nu+\pi(h_i)$. This expression is claimed to represent the probability that a builder wins choosing a height multiplied by the value of the prize in addition to the value of the building. This gives the general equation $\phi&space;_j(h_i)\nu+\pi(h_i)=\pi(h^{*})$
for which j=1,2 and h_i is an element of h* and $h^{P}$. This can be rearranged to be rearranged to be
$\phi_j(h_i)=[\pi(h^{*})-\pi(h_i)]/\nu$
Helsley and Strange (2008) then differentiate with respect to h_i , resulting in $\phi_j(h_i)=-\pi^{'}(h_i)/\nu$.
The expected building height can be calculated by integrating by parts the derivation of this equation. The equation is set up as $E[h]=\int_{h^{*}}^{h^{P}}-(\pi^{'}(h)/\nu)hdh$.
Helsley and Strange (2008) claim that integration by parts yields
$E[h]=h^{*}+\frac{1}{\nu}[\int_{h^{*}}^{h^{P}}\pi(h)dh-\pi(h^P)(h^{P}-h^{*})]>h^{*}$, knowing $\nu+\pi_i(h_{i}^{P})=\pi(h_{i}^{*})$. Through this equation, it is easy to see that overbuilding occurs. Expected building height, E[h], is greater than profit maximizing building height h* (the expression in brackets remains positive as π(h) is decreasing on the interval [h*, h_P ] according to Helsley and Strange (2008)).

Implications

Helsley and Strange (2008) present new work in the study of these urban marvels. They come to the conclusion that skyscrapers are not economical when they are built in a contest to reach the highest altitude. Their research includes plenty of historical data, citing stories of the construction of many of the world’s tallest skyscrapers. Some of them, such as the Burj Dubai, fulfill the proposed overbuilding prophecy. It has been hard for them to find enough tenants for their space. The game theoretic model alerts builders of the poor economics of building for height. The authors stress that this can impact the real estate market and its cycles, contributing to “increases in vacancies and declines in rents, leading to subsequent slowdowns” (2008). In fact, they cite that, when built, the Empire State Building, the Manhattan Company Building, and the Chrysler Building brought a whopping 4,000,000 extra square feet of commercial space to New York City (20% of the city’s stock) (2008). Perhaps further research might be done to measure the impact of the construction of a skyscraper on a city’s real estate market. How does it change prices? Also how does pricing within a skyscraper itself change?

Bibliography:

Robert Helsley and William Strange, 2008, “A game-theoretic analysis of skyscrapers,” Journal of Urban Economics 64: 49-64.

## Crime in Europe and in the US: Dissecting the “Reversal of Misfortunes”

By Peter Struckmeyer   Crime in Europe and in the US

When evaluating urban development, one area of interest to many policy-makers is the rate of crime. While much research has been conducted regarding crime rates in the United States, a smaller number of studies have tried to tackle these issues outside of the United States. In their 2011 investigation, Paolo Buonanno, Francesco Drago, Roberto Galbiati, and Giulio Zanella seek to correct this information gap by comparing crime rates in the United States and seven European countries from 1970 to 2008. The authors use demographic information, immigration information, abortion rates, unemployment statistics, and incarceration figures as their five explanatory variables for determining levels of crime. The results show that, although crime was higher in the United States than it was in Europe in the 1970’s, since then European crime rates have exceeded crime rates in the United States, a phenomenon referred to as the ‘reversal of misfortunes’ (Buonanno et al. 2011). This paper will analyze the model constructed in their paper, and it will explore potential implications and extensions of their assumptions and equations.

Upon surveying the economic literature regarding determinants of crime, Buonanno et al. highlight five factors as being relevant toward the study of crime rates: demographic changes, incarceration rates, abortion rates, unemployment rates, and immigration figures. Within a demographic structure, for instance, Buonanno et al. argue that young males are more likely to commit a crime than women or seniors. For incarceration, they identify two effects – one effect is that the threat of incarceration deters individuals from committing crimes, and additionally, those who are incarcerated cannot commit more crimes while they are in prison. The authors posit that abortions may have removed from society individuals who would have been more likely to commit a crime due to potential socioeconomic conditions in their families. For individuals who are unemployed, the lack of resources available to them lowers the opportunity cost of committing a crime. Due to age structure and low socioeconomic factors, immigrants are also statistically more likely to commit a crime. Based on these assumptions, the model constructed by Buonanno et al. includes the five aforementioned factors in order to investigate their relevance as measures of poverty in the United States and Europe (Buonanno et al. 2011).

In order to implement these factors into a model, Buonanno et al. establish several assumptions regarding the variables. Crime is measured in three categories: total crime, property crime, and violent crime. To categorize Europe as a whole, the study groups Austria, France, Germany, Italy, the Netherlands, Spain, and the United Kingdom together, since these seven nations account for more than eighty percent of the pre-2004 population (Buonanno et al. 2011). When constructing the equation for the model, one challenge the authors confront is the endogeneity of the variables. If the demographic structure of a population and the legalization of abortion, for instance, are exogenous with respect to crime, incarceration, unemployment, and immigration all have the potential to be endogenous. To account for this, the model utilizes several instrumental variables (IVs) to measure these factors. Amnesties and collective pardons serve as instruments to explain the relationship between incarceration and crime rates, the interaction between oil price and the share of manufacturing in GDP is an instrument for unemployment, and exogenous supply-push components are instruments immigration trends. Lastly, the model includes a measure of country fixed effects and common year dummy variables in order to ensure that the results are country and time specific. To calculate the results, the authors use OLS estimation, as well as 2SLS estimation for the IV analysis (Buonanno et al. 2011).

The resulting mathematical equation that the study estimates for its model is:

$ln(crime_{it})=\alpha&space;_{i}+\beta&space;ln(x_{it})+td_i+\lambda&space;_t+\varepsilon&space;_{it}$

where $crime_{it}$ represents the level of crime (total, property, or violent), $\alpha&space;_i$ is a country-fixed effect, $x_{it}$ contains explanatory variables for country i at time t (a constant, the share of males between 15 and 34 years old in the population, the immigration rate, the share of potential adults aborted, the unemployment rate, and the incarceration rate), t is a polynomial in time,$d_i$ is a dummy variable for country, and $\lambda&space;_t$ is a dummy variable for common year (Buonanno et al. 2011). For the explanatory variables, the values for each variable is inserted individually in order to evaluate their respective coefficients. Because the natural logs of these variables are used, the resulting coefficients can be interpreted as elasticities with respect to the corresponding rates. In order to evaluate country- specific time trends, the model relies on a quartic trend to explain the independent variables, since quartic trends have been used in other empirical literature as the most effective method for explaining life cycles similar to those evaluated in the variables (Buonanno et al. 2011).
Buonanno et al. break down the resulting coefficients of the model into two categories: OLS estimates and IV estimates. The authors warn that one cannot regard the OLS estimates as causal effects due to the endogeneity of incarceration, immigrant, and unemployment with respect to crime. For demographic structure, the effect of age structure on crime is positive and statistically significant with most coefficients exceeding 1.5, whereas the coefficient on abortion is close to zero (Buonanno et al. 2011). When speculating about potential sources of bias surrounding these coefficients, the authors identify the endogeneity of the other three variables as the primary potential source. When looking at the IV estimates, the authors first check the strength of the IVs used in order to evaluate whether or not they are appropriate instruments for the model. Amnesties are very strong as an instrument, with an F statistic that exceeds 10. In fact, during the first stage of the regressions, the estimates show that an amnesty on average reduces the incarceration rate by 13% (Buonanno et al. 2011). Conversely, the instruments constructed for unemployment and immigration are very weak; the authors are never able to reject the null hypothesis of weak instruments for these two variables. The IV estimates continue to uphold the assertion that demographic structure is a significant determinant for crime rates, while abortion rates are found as insignificant for explaining crime as found in the OLS estimates (Buonanno et al. 2011).
Upon evaluating the findings in the model created by Buonanno et al., several limitations stand out. With the use of instrumental variables throughout the model, narrowing down how the factors studied affect crime rates becomes difficult. The model highlights variables that are and are not relevant, but it does not provide deeper insight into the specific manner in which the relevant variables make a contribution to the crime rate beyond intuitive conjecture. Additionally, some of the instrumental variables are constructed using inconsistent methods of data evaluation. With immigration, for instance, because there is only data available starting from 1980, a large portion of data are lost for the years from 1970 to 1979 that cannot be found in this component of the model. Furthermore, a central limitation of the model is the choice of variables. While the five factors the authors choose to study are intuitively reasonable to include, they are by no means the only explanatory factors driving the current trends in crime. The authors are aware of the limitations of their model and acknowledge them openly before presenting their findings. They make it a point to “emphasize that we regard our empirical exercise as a starting point for further research rather than a conclusive word on an admittedly complicated question” (Buonanno et al. 2011). So while their model may not come to the in-depth, causal conclusions needed to prove a direct relationship, it never seeks to do this. Rather, it accomplishes its function of shedding light on further areas for explanation when evaluating the ‘reversal of misfortunes.’
Since the model serves as the beginning of further study regarding crime trends, it is important to consider what extensions are possible for future analyses. Despite finding mixed results for the variables included, Buonanno et al. affirm that, of the variables included, demographic structure and incarceration rates are both significant toward evaluating crime rates. Breaking down the segment of young men from ages 15 to 34 into smaller segments may narrow down analysis of crime rates even further to a more specific age group. For incarceration rates, amnesties serve as one explanatory instrument, but it is certainly not the only potential instrument to evaluate incarceration. Examining the proportion of prisons at maximum capacity rates of incarceration is a possible alternative angle from which to analyze the effect of incarceration on crime. Additionally, there are additional variables to consider beyond the five primary factors identified by Buonanno et al. Levels of education, for instance, would be a highly relevant factor to explore in future studies, since individuals who do not complete certain levels of education may have a higher potential to commit a crime. Additionally, policy incentives to deter individuals from committing a crime – for example, higher levels of probation, or the prevalence of the death penalty – seem appropriate to cite in further investigations.
In their concluding remarks regarding their model, Buonanno et al. posit several policy implications of their work. An important consideration to note is what can and cannot be heavily altered by a change in policy. Demographic structure, for instance, cannot easily be manipulated by new policies, with the exception of family planning laws similar to China’s one-child policy to control the number of individuals in each age segment, which would be improbable legislation for the countries being studied. Factors including in the model such as immigration, incarceration, and abortion, however, are all easily influenced by policy. With the model concluding that abortion was not highly relevant to the reversal of misfortunes, as well as finding instruments for immigration to be weak, focus shifts toward analyzing incarceration. One theory that the authors explore is the notion that incarceration rates may not be set an efficient level, since incarceration is proven to be highly relevant toward reducing crime. Upon further investigation, however, the authors discard this hypothesis, finding that the marginal benefits exceed the marginal costs of incarceration, suggesting that imprisonment is fixed at an approximately efficient level (Buonanno et al. 2011). For variables to consider in the future, such as education or incentives to deter crime, if these variables were found to be highly relevant for predicting crime rates, the findings would highlight devoting resources toward increasing education and creating incentives against crime as strong solutions to lower crime rates.
In their study of crime rates between the United States and Europe, Buonanno et al. seek to identify the principal factors influencing the ‘reversal of misfortunes’ that has caused crime rates in Europe to exceed similar rates in the United States. The authors focus on demographic structures, immigration rates, unemployment figures, abortion rates, and levels of incarceration as the five main factors to analyze in both the United States and Europe. Using OLS and IV estimations, the results show that demographic figures and incarceration rates are relevant variables for predicting crime levels, while abortion is an insignificant factor in their model. Based on the instrumental variables constructed, there is insufficient evidence to make conclusions regarding the relevance of immigration and unemployment as variables in the model. Though the findings presented in the model do not properly establish in-depth, causal effects regarding its variables and its outcomes, the study serves as a starting point for further postulation regarding appropriate policies that would mitigate the most prevalent determinants of crime.

References:
Buonanno, Paolo, Francesco Drago, Roberto Galbiatim, and Guilio Zanalla, 2011, “Crime in Europe and in the US: dissecting the “reversal of misfortunes,” unpublished ms.

## The Role of Speculation in Real Estate Cycles

By Cecilia, Ju The Role of Speculation in Real Estate Cycles

Technical Presentation: The Role of Speculation in Real Estate Cycles

Part I: Overview:

• Outrage over Real Estate Cycles: Across countries, it is a commonly held view that real estate cycles are the product of speculation – when speculation drives up demand, prices skyrocket and vice versa. However, it is in the nature of real estate prices to fluctuate on a cyclical basis. In reality, housing prices also depend not just on speculative demand, but also heavily on supply and interest rates. The model put forth by Malpezzi and Wachter examines the impact of speculation and housing supply on price and volatility.
• The Fundamentals of Asset Pricing: If we view housing at an asset, value is then based on the flow of services yielded over time. Thus, the value of a home is equivalent to the expectation of profit from rent over time (controlling for interest rates).
• Market value of a unit = present value of net rents = (rental price per unit of housing services) * (the quantity of housing services produced by a unit)

$V=\sum_{t=0}^T\frac{E[R_t-C_t]}{(1+i)^t}$

• V = market value of a unit
• E = expectations operator
• R = rent
• C = maintenance costs
• i = interest rates
o In cases where net rents are constant over a long time horizon:

$V\cong&space;\frac{E[R]}{i}$
o If we account for a property that has increasing value:
$V\cong&space;\frac{E[R]}{i-g}=\frac{E[R]}{c}$
• c: cap rate: the rate of return on a real estate investment property based on the expected income the property will generate.
$c=\frac{yearly&space;income}{total&space;value}$

• g: rate at which the net rent for the property is growing
• i: interest rate

So what is Speculation? The clever cheeky definition given by Malpezzi and Wachter is two-pronged: (1) If I purchase a home, it is investment but (2) If someone else buys, its speculation.

So if not a synonym for investment, then what is speculation?

o It depends on the time-horizon: rather than buying and holding, a speculation is a case of short-term ownership. Short-term ownership is defined as an ownership period in which the owner does not develop or make use of the property. Instead, the owner holds the property vacant in anticipation of a price increase and profitable sale.
• The key is to obtain optimal timing.

o Was their arbitrage involved? Arbitrage is easier to achieve in thick/liquid markets. A thick/liquid market is characterized by transparent pricing, many market participants (home buyers and sellers), as well as lots of information on prices and the market in general. On the other hand, thin/illiquid markets are characterized by price volatility and costly information. Thus, a higher amount of participants yields greater market stabilization. This is somewhat intuitive: when there are less participants in the market the official “market price” becomes less established and house prices depend more on each individual’s pricing range.
• However, it is important to note that an influx of ill-informed market participants actually contributes to destabilizing the market; these new entrants are generally more willing to overpay because they are engaging in short term investment.

o Expectations must be inaccurate: inaccurate expectations also lead to overpaying/underpaying or overpricing/underpricing for homes.

• Expectations are important because they affect:
o Real estate price
o Rent growth expectations
o Investors often speculate on a continuation of the past high rates of price appreciation. A housing bubble occurs when formulation of subjective probabilities based on the low likelihood of market collapse creates disaster myopia, in which the probability of low frequency shocks is not factored into the decision-making of market participants.

• Generators of Housing Bubbles: Backward facing/adaptive expectations driven speculative pricing behavior affects investment decisions → increases prices → increases supply (relative to demand) → unsustainable prices → bursting of the housing market → optimistic investors are wiped out as they lose capital and have no agency to continue participating in the housing market → credit crunch

o The “rational” bubble: serial correlation in price changes
$V_t=V^{*}_t+b_t$
where $b_t$ = overvaluation amount
$E_t[b_t+1]=(1+i)b_t$
Rational investors will be willing to invest and purchase a home overvalued by quantity b_t as long as b_t is expected to grow at a greater rate than that of interest rates. Serial correlation of price increase is necessary for the formation of housing bubbles.

The Impact of Environmental Regulation:

Excessive regulations → decrease the elasticity of supply → increase prices → increase defaults → can lead to credit crunches and higher volatility:

• e.g. South Korea

Part II: A Simple Dynamic Model of the Housing Market:

Based on the stock adjustment model by Malpezzi and Maclennan:
$Q_D=\delta&space;(K^{*}-K_{-1})$, where $Q_D$ = Quantity demanded, K* = Desired stock, $K_{-1}$ = Housing stock in the preceding period and$\delta&space;(K^{*}-K_{-1})$ = Change in stock

$K^{*}&space;=&space;\bar{a}+\alpha_1P+\alpha_2Y+\alpha&space;_3N$, where P = price, Y = income, N = population
$Q_s&space;=&space;\bar{\beta&space;}+\beta&space;_1P$: Quantity supplied as a function of price

-> Q_d = Q_d

• Simplification for the sake of simulation: lumps population and income as one variable (demand) and price as another

$K^{*}&space;=&space;D&space;+&space;\alpha&space;_1P_1,&space;\alpha&space;_1<0$

• D: the amount of stock demand conditional on realized income and population
• Extension: introduction of time as a main variable to measure temporal lags in supply
• New supply function: measures quantity supplied in housing based on price and time

$Q_{st}=\beta&space;_0P_t+\beta&space;_1P_{t-1}+B_2P_{t-2}+...+B_nP_{t-n}$

• For notational purposes, assume an order of two supply function, contemporaneous and one period lag:

$Q_{st}=\beta&space;_0P_t+\beta&space;_1P_{t-1}$

• Then, substitute
$K^{*}$ for $Q_d$
Setting Q_d = Q_s
Solve for $P_t$
$P_t=\frac{\beta&space;_1}{\beta&space;_0-\delta&space;\alpha&space;_0}P_{t-1}+\frac{\delta}{\beta&space;_0-\delta&space;\alpha&space;_0}D-\frac{\delta}{\beta&space;_0-\delta&space;\alpha&space;_0}K_{-1}$

However, speculation is generally a demand-side phenomenon, and speculators generally have adaptive expectations. Let’s assume that this is true. Here is an alternative model measuring demand:
$K^{*}=D+\alpha&space;_1P+\alpha&space;_4dP,&space;\alpha&space;_1<0,&space;\alpha&space;_4>0$

• D is exogenous; is either one-time isolated shock, or rows over time as populations, income or capital stock grows
• The Simulation Model: Malpezzi and Wachter then developed a simulation model to understand the whether real estate speculation is a factor or a result of the boom and bust cycle. In this model, speculation is linked to housing supply elasticity and to land price volatility. Note that the housing supply elasticity accounts for the effects of land development regulations. This model is important because patterns of financial crises are linked with business cycle downturns. The economies that are most affected quickly undergo an economic downturn/collapse that is usually preceded by a collapse in property prices which then leads into that of banking systems, exchange rate, business cycle bust etc. as seen in Asia: Japan, Indonesia, Thailand
• Focuses on parameters:
• Price elasticities of supply:$\beta_i$
• Elasticity of demand with respect to price changes:$\alpha_4$

o Other parameters:
$\alpha_1$ = price elasticity of demand for housing
$\delta$ = stock adjustment parameter

$K_{t}^{*}=D_t+\alpha&space;_1P_{t}+\alpha&space;_4(P_t-P_{t-1})$

$P_t=\frac{\beta&space;_1}{\beta&space;_0-\delta&space;\alpha&space;_0}P_{t-1}+\frac{\delta}{\beta&space;_0-\delta&space;\alpha&space;_0}K_{t}^{*}-\frac{\delta}{\beta&space;_0-\delta&space;\alpha&space;_0}K_{t-1}$

$Q_s=\beta&space;_0P_t+\beta&space;_1P_{t-1}$

$K_t=K_{t-1}+Q_s$

• Findings:
• The simulation model generates cycles with two sources:
• Since prices are a function of housing stock, new supply and stock is related to current and past prices
•  as a speculative parameter
• Inelasticity of supply increases market volatility:
• Under an inelastic supply case: housing supply does not expand to match changes in demand, and thus prices will rise, especially when investors form adaptive expectation
• Under an elastic supply case: housing supply expands rapidly to accommodate increases in demand, therefore prices stay relatively constant.
• Basic conclusions:
• Even a simple model of lagged supply response to price changes and speculation is sufficient to generate real estate cycles
• Volatility of prices is strongly linked to housing supply
• Effect of speculation depends on supply conditions
• Markets with more responsive regulatory environments (or less issue due to physical geography) experience less speculation
• Policy implications:
• Effects of speculation dominated by price elasticity of supply à large effects when inelastic supply à policy to increase supply efficiency where elastic supply can be achieved
• Demand conditions and speculation à factors in boom and bust cycles (bubbles)
• Possible extensions
• Finding alternative lag structures for the supply response
• Finding better estimates of parameters
• Finding alternatives to initial adaptive expectations mechanism for formation of housing market expectations

References:

Malpezzi, Stephen, and Susan M. Wachter. “The role of speculation in real estate cycles.” Journal of Real Estate Literature 13.2 (2005): 141-164.