Housing Density and the Low-Income Housing Tax Credit

Housing Density and the Low-Income Housing Tax Credit Bree J. Lang Xavier University Department of Economics Abstract Using data on construction in Los Angeles County between 1991 and 2007, this paper estimates how the Low-Income Housing Tax Credit subsidy a ects the density of newly constructed apartment buildings. I measure the e ect on housing density by comparing the number of housing units in subsidized and unsubsidized buildings, holding land area constant. Theoretically, a subsidy should increase the pro t-maximizing number of units. The e ect should be less pronounced if the housing units are required to rent for less than the market rate. I nd that subsidized buildings in low-rent locations include 26 percent more housing units than unsubsidized buildings built in the same zip code during the same year. In high rent locations, there is no sign cant di erence in density. This e ect has several implications for the e ectiveness and e ciency of the Low-Income Housing Tax Credit program. Keywords: housing, subsidies, density JEL Classi cation: R, H2 1

1 Introduction The Low-Income Housing Tax Credit (LIHTC) was created in 1986 to improve the e ciency of project-based subsidized housing programs in the United States. While funding for LIHTC has grown substantially since 1986, research identi es many of the program s shortcomings. Among other critiques, studies nd that LIHTC is expensive to produce (Eriksen 2009, Cummings and DiPasquale 1999) and does not signi cantly increase the housing supply (Eriksen and Rosenthal 2010, Baum-Snow and Marion 2009, Sinai and Waldfogel 2005, Malpezzi and Vandell 2002). In this study, I examine a new, but related, question: how does the LIHTC subsidy a ect housing density? Through LIHTC, private developers of a housing project apply for federal and state tax credits with values proportional to non-land construction costs. If the housing project is selected for subsidization, developers must agree to rent apartment units for no more than a program-designated rent ceiling for at least 30 years. 1 Theoretically, the trade-o between cost and future revenue directly a ects the density of the building that is constructed. Subsidization should increase the number of units, but any required rent reduction decreases the e ect. To estimate the e ect on density, I use parcel data from the Los Angeles County Assessor to compare newly constructed subsidized apartment buildings to unsubsidized buildings that are built in the same zip code and time period. Controlling for land area, I use the number of housing units to measure housing density. For multi-family housing constructed between 1991 and 2007, LIHTC buildings have 26 percent more housing units than comparable unsubsidized buildings in the bottom half of the rent distribution. In the top half of the distribution, there is no signi cant di erence in the number of units. This suggests that more restrictive rent requirements eliminate the majority 1 In California, the source of data for this study, the compliance period was increased to 55 years in 1996 (CTCAC Compliance Manual 2013). 2

of the positive e ect that the subsidy has on housing density. These results provide insights to some of the topics found in past LIHTC research. First, increased housing density may have implications for how LIHTC construction a ects housing supply. Previous research nds evidence that the majority of LIHTC units simply replace private construction. Depending on the geographic scale used, crowd out is estimated to be between 50 to 100 percent. Where previous studies measure crowd out at larger geographies, the current study examines it at the building level. Assuming that a residential building would have been constructed without a subsidy, this suggests that additional units are provided on the intensive margin, but primarily in low-rent locations. This does not suggest, however, that potential downward pressure on rents does not disincentivize future construction in the local market (Eriksen and Rosenthal 2010). In addition to crowd out implications, this study compares the production cost of LIHTC housing to unsubsidized construction. Eriksen (2009) uses a sample in California to estimate that construction costs per square foot are 21 percent higher than unsubsidized apartment buildings of average quality. My estimates suggest that total construction cost is 50 percent higher and per unit construction cost is 23 percent higher for LIHTC in low-rent locations in Los Angeles County. 2 There is no signi cant di erence in high-rent locations. The results are consistent with Eriksen s explanation that LIHTC developers substitute subsidized capital inputs for land, but suggest that the e ect is strongest in low-rent locations. It also indicates that higher per unit costs may be the result of increased scale, not necessarily increased quality. Finally, these results suggest that LIHTC developers who construct buildings in low-rent locations may be receiving excess pro t from the subsidy. Developers will increase building size per 2 I use the Los Angeles County Assessor Building Improvement Value to proxy for construction cost. 3

unit of land in response to expected increases in marginal revenue or decreases in marginal cost. As a result, higher density buildings are constructed in locations where developers expect higher pro t (DiPasquale and Wheaton 1995). If LIHTC buildings are signi cantly larger per unit of land in low-rent locations, it is possible that developers in these locations are capturing more bene t than is necessary to motivate participation in the program. Research by Burge (2011) suggests that only 13 percent of the cost of the LIHTC subsidy in Tallahassee, Florida is passed on to low-income tenants in the form of lower rents. If higher density is indicative of excess pro t, there may be opportunities to transfer more of the subsidy to low-income tenants. This paper proceeds with the details of the Low-Income Housing Tax Credit Program. Then I characterize a model that predicts how the subsidy will a ect building size. Section four outlines the data used in the empirical model and presents results. The nal sections conclude with a more detailed discussion of the implications of the analysis. 2 The Low-Income Housing Tax Credit Before 1986, public housing was the primary source of project-based subsidized housing in the United States. With growing sentiments that public housing was related to negative tenant outcomes (Katz et al. 2001, Currie and Yelowitz 2000, Wilson 1987), the government created the Low-Income Housing Tax Credit (LIHTC). The purpose was to stimulate private investment in low-income housing construction. By providing subsidies to developers in exchange for the construction of rentrestricted housing, the LIHTC program funded the production of nearly 1.6 million housing units between 1986 and 2006 (Eriksen 2009). While the LIHTC program is federally funded, private developers apply to receive the subsidy 4

through state housing nance agencies each year. Because demand for tax credits is high, many agencies create a systematic process to determine which proposals will provide the highest bene t to the community (Gustafson and Walker 2002). If a proposal is selected for funding, the developer is awarded a ten-year stream of tax credits to reduce tax liability. If the proposal is new construction and has limited nancial support from other sources, the subsidy is valued at approximately nine percent of the non-land construction costs for each of the ten years. 3 Because the tax credits are not awarded until after the building is complete, the future stream of tax credits is usually sold to investors to raise the necessary capital for construction. This process is called syndication and there is a substantial literature dedicated to assessing its e ciency (Eriksen 2009, Case 1991, Stegman 1991). In California, the source of data for this study, the California Tax Credit Allocation Committee (CTCAC) has developed a point system that determines which proposals receive the subsidy. Points are awarded to projects for attributes like developer experience, providing additional rent reductions, or demonstrating that the project is part of a neighborhood revitalization plan. In 2012, California received 236 applications for new construction subsidies. Because of limited funds, only 102 projects were funded. Over the last decade, the average demand has outmatched supply by a factor of three to one (CTCAC Annual Report 2012). Further evidence of excess demand is that out of the 236 applications in 2012, only 17 projects did not receive the maximum possible points in the allocation process. In these cases, a tie-breaker system based on the ability to acquire external funds is used to allocate the subsidy (CTCAC Regulations 2013; CTCAC Applicant List 2013). 4 3 Projects with less than $3,000 of development cost per unit or projects that receive certain federal subsidies are awarded approximately four percent of the construction costs each year. The IRS publishes the actual rate of subsidy each month. A more detailed explanation of the credit calculation is found in Schwartz (2006). 4 Addtionally, California has "set-asides" for projects that meet certain requirements like being partnered 5

One of the CTCAC point system categories is dependent on the rent level charged in LIHTCfunded buildings. Unlike tenant-based programs like Section 8 vouchers, LIHTC rents are not determined by an individual tenant s income. Instead, the developer chooses which income level to target, relative to the Area Median Income (AMI) for a particular unit. If the targeted tenant is a household that makes 50 percent of AMI, then the LIHTC rent level is determined by multiplying 50 percent of AMI by 0.3. A household living in a LIHTC unit could actually make much less than 50 percent of AMI, but the rent level will not be adjusted to their income. Developers receive points in this category by using di erent combinations of the fraction of units and the a ordability of those units. For example, a developer could receive the maximum possible points by making 50 percent of units a ordable to tenants who earn 50 percent of AMI and dedicating the other 50 percent to tenants who earn 45 percent of AMI. A di erent developer can receive the same number of points by dedicating 30 percent of units to tenants who earn 30 percent of the AMI, 50 percent of units to tenants who earn 50 percent of AMI and having no rent restriction on 20 percent of units. The CTCAC reports the points awarded to projects between 2003 and 2008 and these documents demonstrate that the majority of proposals receive the maximum points in this category. 5 The AMI used by the LIHTC program is constant across Metropolitan Statistical Areas (MSAs) and is updated annually. Consequently, the same general rent ceiling is used for buildings within the same MSA. This program detail is an important part of the theoretical and empirical analysis that follows. with a non-pro t or being located in a rural area. Because of this, a project may receive the subsidy even if its point total is lower than another proposal. 5 The monetary size of the subsidy is reduced proportionally as developers build units that are not subject to a rent ceiling. Consequently, most buildings dedicate nearly all of the units to low-income use. 6

3 Model Speci cation A developer will bene t from the subsidy if the decrease in construction costs is larger than the required decrease in the discounted revenue stream. As such, developers will not subsidize construction in locations with the highest market rent (Lang 2012). There is some set of developers that can bene t from the subsidy and apply to receive tax credits. Because the supply of tax credits is limited, or because information about the subsidy is not the same for all developers, only a fraction of the applying developers receive the subsidy. This theoretical model characterizes how building density should change in response to receiving that subsidy. Consider a developer with a cost function of producing apartment units, c(q; L), where Q is the number units constructed and L is square footage of land. 6 To allow the cost to be a function of the number of units, the model assumes that production methods and factor costs are the same for all developers and locations. Although this may not be true, the general theoretical predictions are similar if the model allows factor costs to di er. Assuming a diminishing marginal product of housing production, the rst derivative of the cost function is increasing in Q. Because this is a cost function for non-land production, additional land inputs decrease the total cost at a given value of Q (DiPasquale and Wheaton 1995). On a particular piece of land, a developer can determine the value of construction by maximizing a pro t function of apartment construction. Allowing for the possibility of subsidization, the pro t function for a developer is = r (1 l(r)) Q (1 s) c(q; L): 6 It may be more appropriate to use square footage of building space, but I use housing units because accurate square footage is not available in the data. Di erences may exist in the size of units, which I examine in the empirical model. 7

where r is the discounted expected rental revenue stream per unit over the lifetime of the building. The function l(r);where 0 l(r) 1; indicates the required rent reduction if the building is subsidized. The rent reduction is a function of rent because the general rent ceiling is the same across all locations in an MSA. If the building is constructed in a location with high market rent, the required rent reduction is larger than in locations with low rent. The variable s, where 0 s 1, is the fraction of non-land construction costs that is funded by the subsidy. I assume s is constant across locations. 7 Both variables l(r) and s equal zero if the building is not subsidized. The term l(r) can equal zero when s is greater than zero if the market rent is low enough that no rent reduction is necessary. For ease of exposition, consider a generalized cost function of non-land production, c(q; L) = A Q L, where A,, and are positive constants. To ensure that the marginal cost of production is increasing in Q, assume that > 1. Replacing this cost function in the equation above and maximizing pro t with respect to Q yields (1 Q = l(r)) r L (1 s) A 1 1 : Taking the natural log of both sides of the equation and rearranging yields ln Q = 1 1 ln( A) + 1 1 ln r 1 1 ln(1 s) + ln(1 l(r)) + ln L: (1) 1 1 1 Using this expression, we can characterize some predictions of how optimal building size will respond to di erences in external environment. First, holding land area constant, an increase in the market 7 Some projects receive a 30 percent subsidy increase for their location in a high-poverty locations called Quali ed Census Tracts (QCTs) or MSAs designated at di cult to develop. Because Los Angeles is designated as a di cult to develop area, locating in a QCT does not determine the receipt of this additional subsidy. I control for this subsidy increase in the empirical model but omit it from the theoretical model for simplicity. 8

rent, r, increases the number of units built, which leads to higher density. 8 Similarly, increases in the subsidization rate should lead to higher density. If a building is subsidized, the required rent reduction is expected to decrease density. Finally, as additional land area is available, production becomes cheaper, which increases the optimal number of units to construct. Using this framework, it is possible to simulate an empirical experiment that compares two buildings, one subsidized and one unsubsidized, constructed on the same piece of land. Because all LIHTC buildings are subsidized at a similar rate, s is measured as a binary variable. Similarly, the variable l(r) is not directly observed but it is a function of rent and only positive when a building is subsidized. That term is rewritten as an interaction between receiving the LIHTC subsidy and the market rent. Using building observations i, I rewrite (1) as: ln Q i = 0 + 1 ln r i + 2 LIHT C i + 3 ln r i LIHT C i + 4 ln L i + " i ; (2) where Q i is the square footage of building i. The variable r i is the median market rent of the census tract the building is located in, LIHT C i is a binary variable equal to one if the building is subsidized and L i is the land area of the parcel on which the building is constructed, in square feet. The coe cient 1 is expected to be positive, measuring how units increase in response to an increase in market rent. The coe cient 2 is also expected to be positive, measuring how receiving the subsidy a ects density. The sign of 3 should be negative, reducing the positive e ect of the subsidy as rent increases. Under the assumed form of the cost function, the magnitude of 1 and 3 should be equal with opposite signs. In equation (2), a snapshot of market rent in a given year does not perfectly measure the expected 8 This assumes that additional units would be the same size as the units that would constructed in a smaller building. The units would likely be smaller, which would a ect the rent of those units. This secondary e ect exists but it not modeled for simplicity. 9

revenue stream for a new apartment building. To improve the measurement of the expected rental stream, I include xed e ects variables for the year a building is constructed, zoning regulations and the zip code. 9 The nal baseline speci cation for the empirical analysis is ln Q itzc = 0 + 1 ln r ic + 2 LIHT C itzc + 3 ln r ic LIHT C itzc + 4 ln L itzc + t + z + c + " i ; (3) where t, z, and c represent the year of construction, zoning and zip code of construction xed e ects, respectively. The year and zip code xed e ects capture the market conditions of a general location during the time of construction and the zoning xed e ect captures any building constraints due to regulation. The empirical analysis uses speci cations (2) and (3) to estimate the e ect of the LIHTC subsidy on the number of units constructed in a housing project. Based on the theoretical predictions, the subsidy should increase housing density. This e ect is estimated in the coe cient 2. The e ect of the subsidy should become less pronounced in locations where market rent is high, because the more restrictive rent ceiling reduces the pro tability of development. The coe cient 3 measures this e ect in the analysis that follows. 4 Data and Results Assessment data from the Los Angeles County Tax Assessor for the 2008 tax year identi es each apartment building in Los Angeles County that includes at least ve housing units. The data also report the number of housing units, improvement value, the year the building was constructed, the size of the parcel in square feet and the county zoning classi cation. 9 I also control for increases in the subsidy due to location in a quali ed census tract and di erent types of LIHTC housing. 10

The Department of Housing and Urban Development (HUD) publishes a LIHTC database that describes every LIHTC project placed in operation since the beginning of the program. Using this data, each LIHTC new construction project is linked to a parcel within the tax assessor data. Data for rehabilitation projects are not used because the number of units may be restricted by the size of the existing building. In the data, I identify every multi-family residential building, subsidized and unsubsidized, constructed between 1991 and 2007. 10 To ensure property valuation is representative of the value at the time of construction, buildings are excluded from the analysis if they were sold after the year of construction. Growth of property value is xed in California, except for when a property is sold, which is when the property is reassessed for tax purposes. 11 I also collect the median rent by census tract for Los Angeles County, as reported by the 2010 American Community Survey, 5-year estimates. While the rent in 2010 does not represent the rent at the year of construction, it captures the relative rental rates of census tracts within a zip code. As long as relative rent values among census tracts in a zip code do not substantially change over time, this variable should capture the variation needed to identify the e ect from rent di erences. The nal data set includes 1,179 buildings, of which 273 are subsidized by the tax credit. These buildings house 50,301 apartment units, of which 17,497 units are subsidized. Figure 1 is a map of Los Angeles County that shows the locations of the buildings, identi ed as subsidized or unsubsidized. The underlying map represents census tract boundaries. [F igure1here] 10 Before 1991, data for some of the projects is missing, so I omit these observations. Including the information that is available does not meaningfully alter the results. 11 Proposition 13 was enacted in 1978. Under this proposition, property taxes cannot exceed more than one percent of property value. Property value will be assessed at the time of sale and then grow by two percent every year. The property is not reassessed until it is resold. 11

Table 1 reports the descriptive statistics, dividing observations into subsidized and unsubsidized buildings. The statistics in Table 1 demonstrate that compared to an unsubsidized building, the average LIHTC building has twice the number of housing units. The improvement value, however, is not statistically di erent between the samples. I utilize improvement value as a proxy for cost of construction, where improvement value is the market value that the assessor assigns to the building structure when it is constructed. Because the value is only reassessed when the building is sold in California, this variable captures the relative perceived building value at the time of construction. In the last comparison of Table 1, subsidized buildings are constructed on larger parcels, which may contribute to lower construction cost per unit. Among LIHTC buildings, about half receive additional subsidies, called a "basis increase" because of their location. The quali ed census tract (QCT) incentive is a policy within LIHTC where developers have access to a 30 percent increase in the subsidy if the project is located in a designated, high-poverty census tract. The same subsidy boost is available to projects built in areas designated as di cult to develop. Because Los Angeles is designated as di cult to develop, location in a QCT does not necessarily determine access to the additional subsidy. Consequently, instead of controlling for a building being located in a QCT, I include whether or not the LIHTC project received the basis increase, which is reported in the HUD data. The LIHTC database also reports the population that the LIHTC building is built to serve. The majority of buildings are created for families. Other types include senior, special needs, and single room housing. I include all observations in the analysis and control for the targeted population. Because unsubsidized buildings are less likely to be targeted, I focus the interpretation of results on subsidized construction that is targeted to families. 12

Table 1 Descriptive Statistics Variable Unsubsidized LIHTC Signi cant Di erence Number of Units 36 64 * Improvement Value 5,021,675 4,971,640 Improvement Value Per Unit 110,702 86,335 * Parcel Square Footage 35,045 55,025 * Mean Year Built 2001 2000 * Census Tract Median Rent 1,160 883 * Basis Increase Indicator 0.45 Senior Housing Type 0.24 Other Housing Type 0.15 Building Observations 906 273 Final column reports a star (*) if the mean is di erent at the 1% level between the two samples. "Basis Increase Indicator" equals one if LIHTC building received a 30 percent subsidy increase because of its location in a QCT of a di cult to develop area. "Other Housing Type" includes special needs and single room housing. Family Housing is omitted category. Ideally, one could compare an unsubsidized building and a subsidized building both constructed on the same parcel. Because it is impossible to observe two di erent buildings on the same parcel, I compare parcels that are similar but house the two di erent construction types. To do this, it is necessary to accurately control for the market conditions at the time of construction. To improve the measurement of local market conditions, I include a zip code xed e ect. The observations are located in 200 unique zip codes. Of those zip codes, 110 zip codes include both subsidized and non-subsidized buildings. Of the 273 LIHTC buildings 246 are in a zip code with at least one unsubsidized apartment building. The distribution of units across the geography allows for a more accurate comparison of developments using zip code xed e ects. A yearly xed e ect is included to control for market conditions at the time of construction. Table 2 reports the observations by year of construction, demonstrating that LIHTC construction is evenly distributed over the time period. 13

Table 2 Building Construction by Year Variable Unsubsidized Buildings LIHTC Subsidized Buildings Total 1993 65 16 81 1994 29 23 52 1995 36 24 60 1996 32 21 53 1997 27 15 42 1998 34 16 50 1999 63 18 81 2000 39 21 60 2001 73 19 92 2002 84 16 100 2003 99 18 117 2004 101 21 122 2005 89 20 109 2006 81 15 96 2007 54 10 64 The nal control variable in the analysis is the zoning classi cation, as de ned by the Los Angeles County assessor. The zoning classi cation includes 255 unique zoning classi cations. Even with this detailed classi cation system, there exists an unsubsidized building for comparison for 214 of the LIHTC buildings in the sample. 12 Even with these control variables, there are other issues that may confound the estimation of the e ects on housing density. The most obvious relates to the developers that receive the subsidy. It is possible that developers who receive the subsidy use less expensive production methods and materials. If this is the case, the empirical analysis may assign the positive e ect on density to the subsidy when it actually other developer characteristics driving the result. To address this possibility, I also examine if construction costs per unit are signi cantly di erent between subsidized and unsubsidized buildings. 12 Thirty percent of building observations are coded as LAR3, which indicates a "limited multiple residence". 14

I begin the analysis by estimating regression speci cations (2) and (3) with the natural log of housing units as the dependent variable. The results of those regressions are reported in rst two columns of Table 3. In column (1), the coe cients all have the expected sign, although the coe cient for market rent is not statistically signi cant. There is strong evidence that buildings that receive the subsidy are more dense than unsubsidized buildings. That e ect is smaller in locations with high rent. The second column of Table 3 reports the estimates from speci cation (3), which includes additional controls. Including control variables does not meaningfully change the results. The LIHTC subsidy still has a statistically signi cant and positive e ect on number of units constructed. The coe cient on rent indicates that a 10 percent increase in market rent increases housing units by 34 percent. If a building is subsidized, increases in rent have no statistically signi cant e ect on units because the e ect of 3 cancels out 1. The coe cients in column (2) can be used to predict that in a census tract with the 2010 county median rent of $1017, a LIHTC building has 19 percent more units than an unsubsidized building 13 The basis increase does not signi cantly a ect density, even though it represents a substantial increase in the subsidy. It is possible that because the additional subsidy is not awarded before the developer proposes the building, developers do not respond to the incentive. It is also possible that because all projects in Los Angeles are eligible for the basis increase, developers cannot determine if they will receive the additional funds before they propose the building characteristics. Additional research using a more diverse geography may be able to address this question more fully. The rst two columns of Table 3 suggests that LIHTC a ects the number of units constructed 13 If the dependent variable is the ratio of housing units to land area, regressions yield nearly identical results. 15

in residential buildings. In addition to the e ects on building size, I also estimate the e ect on the natural log of total cost of construction, using improvement value as a proxy. Column (3) reports the e ect of LIHTC on construction costs, which is similar to the e ects on number of units. The subsidy increases construction costs, with the e ect diminishing as market rent increases. At the median rent level, total construction costs for LIHTC buildings are predicted to be 25 percent higher than unsubsidized buildings. Table 3 Linear LIHTC Subsidy E ects Ln(Units) Ln(Cost) Ln(Cost/Unit) Dependent Variables (1) (2) (3) (4) 1 : ln(census Tract Median Rent) 0.22 0.34* 0.55** 0.21 (0.19) (0.18) (0.22) (0.20) 2 : LIHTC Indicator 6.18*** 2.89* 4.96** 2.08 (1.66) (1.48) (1.99) (1.72) 3 : ln(census Tract Median Rent)LIHTC -0.84*** -0.39* -0.68** -0.28 (0.24) (0.22) (0.29) (0.25) 4 : ln(parcel Square Footage) 0.77*** 0.86*** 1.00*** 0.14*** (0.036) (0.047) (0.056) (0.041) QCT Increase Indicator 0.071-0.055-0.13 (0.13) (0.19) (0.14) LIHTC Senior Housing 0.30** -0.036-0.33* (0.15) (0.23) (0.17) LIHTC Other Housing 0.11-0.0052-0.12 (0.16) (0.14) (0.17) Constant -6.21*** -8.21*** -0.16 8.06*** (1.44) (1.48) (1.63) (1.53) Zoning, Year & Zip Code Fixed E ects No Yes Yes Yes R 2 0.66 0.89 0.83 0.67 *** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses, clustered on zip code. Omitted LIHTC housing category is housing for families. All regressions include 1,179 building observations. Cost is proxied with assessor determined improvement value from 2008. The regression reported in the nal column of Table 3 uses the natural log of total cost divided by number of units as the dependent variable, to proxy for quality of the units constructed. These results indicate that LIHTC has no strong e ect on this measure of quality. If this is an accurate 16

measure of quality, the results suggest additional units that are constructed as a result of the subsidy are not at the expense of quality. The estimates in Table 3 indicate that the LIHTC subsidy will alter construction decisions, but the speci cations assume that rent will have a linear e ect on the number of units constructed. To explore an alternate possibility, I estimate a non-linear relationship between the subsidy, rent and building density. To do this, I split the sample into two groups, based on whether the median rent of the census tract falls above or below the median rent for Los Angeles County in 2010. There are 578 buildings in census tracts with median rent less than the county median of $1017, 221 of which are subsidized. There are 601 buildings in census tracts with rent above $1017 and 52 of those buildings are subsidized. Speci cation (3) is altered to allow for a non-linear relationship between building size and rent, ln Q itzc = 0 + 1 HIGH ic + 2 LIHT C itzc + 3 HIGH ic LIHT C itzc + 5 ln L itzc + t + z + c + " i ; where HIGH ic is an binary indicator that equals one if the market rent in the census tract of building i is above the median. Each column of Table 4 reports a regression that uses a di erent dependent variable. In the rst column, the dependent variable is the natural log of number of units. The estimates in the rst column of Table 4 indicate that the number of units in high-rent locations is 22 percent higher than buildings in low-rent locations. Within low-rent locations, subsidized buildings have 26 percent more units than unsubsidized buildings. In high-rent locations, however, there is no signi cant di erence in the number of units between subsidized and unsubsidized units. The e ect of the subsidy is o set by the requirement to reduce rent. 14 14 The negative coe cient on the interaction term becomes smaller as the threshold between high-rent and 17

Regressions that estimate the non-linear e ect on construction costs produce similar results. Subsidized buildings in low-rent locations cost 50 percent more than unsubsidized buildings. In high-rent locations, there is no signi cant di erence in total cost. Table 4 Non-linear LIHTC Subsidy E ects (1) (2) (3) Dependent Variables ln(units) ln(cost) ln(cost/unit) High Rent Indicator 0.22** 0.32** 0.10 (0.10) (0.14) (0.091) LIHTC Indicator 0.26*** 0.50*** 0.23* (0.084) (0.13) (0.13) High Rent LIHTC Indicator -0.22-0.57** -0.35** (0.15) (0.23) (0.16) ln(parcel Square Footage) 0.87*** 1.01*** 0.14*** (0.047) (0.057) (0.042) Basis Indicator 0.071-0.066-0.14 (0.12) (0.19) (0.14) LIHTC Senior Housing 0.30** -0.049-0.35** (0.15) (0.22) (0.17) LIHTC Other Housing 0.13 0.036-0.095 (0.16) (0.13) (0.17) Constant -5.91*** 3.54*** 9.45*** (0.64) (0.56) (0.54) R 2 0.889 0.833 0.671 *** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses, clustered on zip code. Omitted LIHTC housing category is housing for families. All regressions include 1,179 building observations, yearly, zoning and zip code xed e ects. High rent indicator equals one if tract rent > $1017. The nal column of Table 4 indicates that subsidized buildings in low-rent areas have 23 percent higher cost per unit than unsubsidized buildings, although the e ect is only signi cant at the 10 percent level. This estimate is consistent with ndings in Eriksen (2009) and may suggest that low-rent locations is decreased. The di erence in the number of units between subsidized and unsubsidized buildings in high-rent locations is statistically signi cant if the threshold is set to $950. At this threshold, the coe cient on the High Rent Indicator is 0.08 and not statistically signi cant. 18

LIHTC units are higher quality in low-rent locations. Without additional information, it is di cult to determine if increased quality or larger buildings causes this di erence. The result only suggests that as density of LIHTC buildings increases, the quality of units is not necessarily decreasing. The empirical analysis supports the theoretical prediction that there is a positive relationship between building density and receiving LIHTC, with the largest e ect in locations where the market rent is low. This nding has implications for the e ciency of the LIHTC subsidy. The following sections discuss these implications in more detail. 5 Discussion This paper provides evidence that a LIHTC building in a low-rent location is more dense than the unsubsidized building that may have been built in its place. In high rent locations, LIHTC buildings exhibit similar density as their unsubsidized counterparts. This outcome provides some insights into topics of past research. While previous research nds that LIHTC crowds out private construction at very high rates, the e ect on density suggests that LIHTC may be more e ective at increasing housing supply in locations where the market rent is low. This conclusion is consistent with Murray (1999), who nds that subsidized housing exhibits less crowd out when it serves the lowest income populations. In locations with moderate rent, more crowd out may occur with only small reductions in the rent paid by LIHTC tenants. Eriksen and Rosenthal (2010) make this point when they argue that crowd out in LIHTC may be high because it primarily serves moderate income tenants. In high-rent locations, LIHTC units appear to o er relatively fewer housing units, but those units are more likely provide a ordable options for low-income tenants where they were not previously available. 19

Higher density buildings allow more households to live in a particular neighborhood. Recently, many research articles have examined whether living in a community with LIHTC is bene cial. The majority suggests that LIHTC improves neighborhoods by reducing poverty concentration (McClure 2006, Ellen et al. 2009, Horn and O Regan 2011, Freedman and McGavock 2013), improving or providing access to better schools (Horn, Ellen and Schwartz 2014, Di and Murdoch 2013) and decreasing local crime rates (Freedman and Owens 2011). If LIHTC buildings with more units increase access to better environments, this e ect may be considered a positive by-product of a developer s reaction to pro t incentives. Despite the positive outcomes associated with LIHTC, higher density does not necessarily indicate increased access to amenities, even if those amenities exist. If the increase in LIHTC units disincentivizes future private construction, then the total number of units in a local market may remain unchanged. Even if LIHTC increases housing supply, that alone does not guarantee better access to a ordable housing. McClure (2010) argues that the majority of LIHTC units are constructed in neighborhoods that have an excess supply of housing at rents comparable to the LI- HTC rent ceiling. Examining a survey of LIHTC tenants, O Regan and Horn (2013) nd that many households cannot a ord LIHTC rents without supplementary nancial assistance. Additional units may be available, but whether or not households receive any nancial bene t from living in them remains uncertain. 6 Conclusion As research on LIHTC progresses, attention to what causes the outcomes observed in previous research will determine how to improve the program. This paper provides evidence that a developer 20

responds to the subsidy by altering the density of the building he constructs. In low-rent locations, subsidized buildings are denser than unsubsidized buildings. There is no signi cant e ect in highrent areas. This e ect on density may signal a potential ine ciency in the LIHTC program. Theory indicates higher housing density results from increased pro t expectations from developers (DiPasquale and Wheaton 1995). Could the discrepancy in density point to additional pro t gains by LIHTC developers in low-rent locations? If developers are subsidized to build in low-rent locations, but the rent ceiling is not restrictive, developers may receive the bulk of the subsidy in the form of pro t. Burge (2011) provides convincing evidence of this possibility. Subsidized developers in low-rent locations may need to be compensated more than the LIHTC developers in high-rent locations to participate in the program, which would lead to higher density in low-rent locations. Evidence against that argument is that the majority of LIHTC construction is found in low- to moderate-rent locations and the demand for subsidies greatly outweighs supply. In either case, the LIHTC program allocates billions of dollars to fund the construction of low-income housing (Eriksen and Rosenthal 2010). A program that uses funding at such a large scale should be critically examined for ine ciencies. Subsidized buildings that are signi cantly more dense than the surrounding unsubsidized buildings may be an indication that the LIHTC program is paying developers too much or that low-income tenants are receiving too little of the subsidy. References [1] Baum-Snow, N., Marion, J., 2009. The E ects of Low Income Housing Tax Credit Developments on Neighborhoods. Journal of Public Economics, 93(5-6), 654-666. [2] Burge, G. S. 2011. Do Tenants Capture the Bene ts from the Low-Income Housing Tax Credit Program?. Real Estate Economics. 39: 71 96. 21

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[19] Horn, K. E. and K. O Regan. 2011. The Low Income Housing Tax Credit and Racial Segregation. Housing Policy Debate 21 (3): 443-473. [20] Lang, B.J. 2012. Location incentives in the low-income housing tax credit: Are quali ed census tracts necessary? Journal of Housing Economics 21 (2): 142-150. [21] Katz, L. F., J. R. Kling and J. B. Liebman. 2001. Moving to Opportunity in Boston: Early Results of a Randomized Mobility Experiment. The Quarterly Journal of Economics 116 (2): 607-654 [22] Malpezzi, S. and K. Vandell. 2002. Does the Low-Income Housing Tax Credit Increase the Supply of Housing. Journal of Housing Economics 11: 360 380. [23] McClure, K. 2006. The Low-Income Housing Tax Credit Program Goes Mainstream and Moves to the Suburbs. Housing Policy Debate 17 (3): 419-446. [24] McClure, K. 2010. Are low-income housing tax credit developments locating where there is a shortage of a ordable units? Housing Policy Debate 20 (2): 153-171. [25] Murray, M., 1999. Subsidized and unsubsidized housing stocks 1935 to 1987: Crowding Out and Cointegration. Journal of Real Estate Finance and Economics 18: 107 124. [26] O Regan, K. M. and K. M. Horn. 2013. What can we learn about the Low-Income Housing Tax Credit Program by looking at the tenants? Housing Policy Debate 23 (3): 597-613. [27] Sinai, T., Waldfogel, J., 2005. Do low-income housing subsidies increase the occupied housing stock? Journal of Public Economics 89, 2137-2164. [28] Stegman, M. 1991. The Excessive Costs of Creative Finance: Growing Ine ciencies in the Production of Low-Income Housing. Housing Policy Debate. 2 (2): 357-373. [29] Schwartz, A. 2006. Housing Policy in the United States: An Introduction. Routledge: New York, NY. [30] Wilson, W. J. 1987. The truly disadvantaged : the inner city, the underclass, and public policy. Chicago: University of Chicago Press, 1987. 23