Michael D. Eriksen 1 Department of Finance and Real Estate Lindner College of Business University of Cincinnati. June 29, 2016

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1 DIFFICULT DEVELOPMENT AREAS AND THE SUPPLY OF LOW-INCOME HOUSING TAX CREDIT UNITS Michael D. Eriksen 1 Department of Finance and Real Estate Lindner College of Business University of Cincinnati June 29, 2016 ABSTRACT The designation of a metropolitan area as a Difficult Development Area (DDA) by the U.S. Government increases the per-unit generosity of the subsidy that private developers receive for supplying housing units under the Low-Income Housing Tax Credit (LIHTC) program. The top 20% of metropolitan areas ranked by the ratio of rent divided by household income receive the designation and a resulting 30% increase in subsidy for developers. Regression discontinuity (RD) methods are used to compare how DDA designation affects the quantity, composition, and location of LIHTC units based on the 20% threshold. Increasing the generosity of the subsidy on a per-unit basis through DDA designation results in a 40% decrease in LIHTC units constructed in the metropolitan area. DDA designation is also found to increase competition among developers to receive the subsidy and results in LIHTC projects being less likely to be located in low-income neighborhoods. Keywords: Housing Policy; Tax Credits; Housing Supply; Regression Discontinuity JEL Classification: H23, H42, R31, R38 1 Contact Information: Lindner College of Business; University of Cincinnati; Cincinnati, OH Phone: mike.eriksen@uc.edu. Acknowledgements: I would like to thank Jeff Zabel, Yannis Ioannides, David Brasington, and Bree Lang for helpful comments on earlier drafts of the research. I would especially like to thank Mike Hollar for helpful comments and providing the administrative data on DDA designations used in the analysis. Any remaining errors are my own.

2 I. INTRODUCTION A survey conducted in 2016 by the MacArthur Foundation found that 81% of Americans felt housing affordability was a problem with 57% saying it was a problem in their local area. 2 Within this context, the United States government spends over $50 billion per year subsidizing the rent of low-income households (US OMB, 2015). These expenditures represent a combination of subsidies targeted to individual households (i.e., tenant-based) and suppliers of housing (i.e., placebased). Earlier research has shown that tenant-based subsidies are more cost-effective in providing housing services to low-income households (Olsen, 2003; Olsen and Zabel; 2015). Recent research has provided evidence that tenant-based subsidies may increase the rent of unsubsidized households, especially in inelastically supplied housing markets (Susin, 2002; Eriksen and Ross, 2015). Place-based housing subsidies may therefore be beneficial in some housing markets. This paper explains how the nation s largest place-based housing subsidy, the Low-Income Housing Tax Credit (LIHTC), affects the incentives of private developers in where to locate subsidized housing. The LIHTC is the nation s largest place-based subsidized rental housing program, and has subsidized the construction of at least 40,502 housing projects and 2.6 million units since the program s inception in 1987 (HUD, 2015). The program is governed by Section 42 of the United States Tax Code and permits state agencies to allocate federal income tax credits to private developers who construct or rehabilitate rental housing units with maximum tenant incomes and rents for at least 30 years. The U.S. Joint Committee on Taxation (2014) estimated the program resulted in $7.6 billion in lost tax revenue in 2015, and that this amount will increase to $8.6 billion by Private developers can receive a subsidy of up to 91% of non-land development costs 2 See

3 through the LIHTC program and often bundle additional federal and state subsidies to finance projects (Eriksen, 2009). In recent years additional subsidies used by developers to finance LIHTC projects have been reduced, making some policymakers concerned if the LIHTC subsidy alone is sufficiently generous to produce affordable housing units (Lawrence, 2011). Others have argued the LIHTC subsidy is too generous and are concerned about potential rent-seeking behavior by developers associated with the allocation process (Case, 1991; Stegman, 1991; Olsen, 2003). Earlier research on the LIHTC program has analyzed how the program affects neighborhoods (Baum-Snow and Marion, 2009; Freedman and Owens, 2011; Lang, 2012) and crowds-out unsubsidized rental housing (Eriksen and Rosenthal, 2010). A key feature of the LIHTC program not addressed in the earlier literature is that private developers must apply for and then be allocated a subsidy by their respective state agency where the property is located. Better understanding how the program alters incentives of developers in where to locate subsidized units is important because the affordability of housing differs widely between metropolitan areas in the U.S.. Eriksen and Rosenthal (2010) also showed a high degree of crowd out of unsubsidized rental housing occurs due to LIHTC construction, which may be exacerbated in some markets. To the extent LIHTC developers are encouraged to increase the supply of subsidized units in neighborhoods with positive externalities on tenants is a further potential justification of place-based subsidies in some markets. It is shown the current LIHTC program is poorly targeted based on the above geographic goals and that the opportunity to improve targeting exists. The first contribution of the research is to document the subsidy structure and existing locational incentives. In particular, the program does not subsidize the cost of land and developers have an incentive to locate properties in the lowestincome areas where land values are often the cheapest within metro areas. This incentive is 2

4 reinforced by the practice of increasing the generosity of the subsidy by 30% for developers that locate properties in census tract where a sufficient number of existing residents are defined as lowincome (so called Qualified Census Tracts (QCTs)). Earlier research has shown the majority of LIHTC development occurs in these low-income areas, and opportunities to expand the locations of where housing affordable to lower-income households is available are missed. The second, and main empirical contribution of the research is to illustrate the economic cost of increasing the generosity of the subsidy for LIHTC developers locating properties in high-rentto-income metro areas (so called Difficult Development Areas (DDAs)). Developers locating subsidized properties in the top 20% of metro areas based on an annual ranking of rent divided by income receive a 30% increase in the generosity of their subsidy, but this does not increase the aggregate amount of tax credits available allocated to those developers. Despite these areas having the greatest potential affordability needs, the use of administrative data and regression discontinuity estimation techniques show that up to a 40% reduction in the annual number of completed LIHTC subsidized units occurs due to the increase in generosity at the margin. Novel data from LIHTC applications and allocations in California are also used to show the increase in generosity associated with DDAs lead to developers submitting more failed applications, a previously unrecognized cost of the program. In summary, place-based housing subsidies may be justified in some housing markets. The LIHTC program, however, is currently structured to discourage developers to increase the supply of subsidized units in locations between and within metro areas where the justifications are strongest. The manuscript conclude with policy implications of the research, including a discussion of the US Department of Housing and Urban Development s (HUD) proposal to redefine DDAs starting in

5 II. BACKGROUND AND PRIOR RESEARCH The U.S. federal government first subsidized rental housing in 1935 by directly constructing and operating units that income means-tested households would occupy and pay a fixed proportion of their income as rent. These projects came to be known as public housing and have since constructed 1.3 million units, although virtually no new projects have been constructed since the early 1980 s and large-scale demolitions of remaining units started in the 1990 s (Quigley, 2000). One of the reasons public housing was phased out was the recognition that tenant-based subsidies (e.g., housing vouchers) were more cost effective to provide an equivalent subsidy than constructing new units strictly for that purpose (Olsen, 2003). Another reason was that public housing was predominantly located in the lowest-income neighborhoods, and the hope was that voucher recipients would voluntarily move to better areas (Quigley, 2000). In 2015, the federal government spent $19.3 billion on housing vouchers as compared to $6.6 billion to maintain and operate the remaining public housing units (US OMB, 2015). An original concern of the shift to tenant-based subsidies was the uncertain supply response of private market landlords. These landlords would supply units to voucher recipients who would pay a fixed proportion of their income towards the landlord, with the government paying the difference between that contribution and a market standard rent. The primary concern was that without a sufficient supply response, the increased demand of voucher recipients would increase housing rents for unsubsidized households. It was also unclear whether landlords in higher-income areas would be willing to accept voucher recipients. This concern was initially assuaged based on evidence that rents did not increase in 4 cities when vouchers were first allocated in the 1970 s, although Susin (2002) provides evidence rents 4

6 were higher in cities with more vouchers in the early 1990 s. Eriksen and Ross (2015) provide evidence that a large increase in housing vouchers starting in 2000 did not result in an overall increase in rents, but did result in at least a temporary increase in rents in metropolitan areas shown in earlier research to be more supply inelastic. Devine et al (2013) showed voucher-eligible units were often available in higher-income areas, but voucher recipients were still predominantly located in lower-income neighborhoods. Evidence from the Moving to Opportunity field experiment showed a relatively high percentage of households (52%) awarded a voucher and required to find a voucher eligible unit in a low-poverty area failed to find a suitable unit within 90 days and forfeited the subsidy (Katz, Kling, and Liebman, 2001). In summary, research generally supports the shift to tenant-based housing subsidies in most housing markets. Place-based housing subsidies, however, may be important in housing markets that are inelastically supplied. There may also be a role for place-based subsidies if there is a policy desire to increase the number of units with specific characteristics (e.g., located in a low poverty neighborhood) able to be rented by low-income households with or without a subsidy. The Low-Income Housing Tax Credit The LIHTC was created by the Tax Reform Act of 1986 and administered by the U.S. Internal Revenue Service under Section 42 of the tax code. The basic premise of the program is to award tax credits to developers who construct or rehabilitate rental housing with maximum income and rent limits for at least 30 years. 3 The maximum household-size adjusted tenant income of an 3 The Omnibus Reconciliation Act of 1990 statutorily changed the minimum number of years of rental restrictions to 30 years for LIHTC projects, although in practice this has remained 15 years unless state agencies meet certain guidelines (Wallace, 1995). 5

7 LIHTC subsidized unit is 60% of the area median income as determined by HUD, and the maximum rent is 18% of the area median income. 4 The tax credits are allocated to developers by state housing finance agencies, and there are two variants of the program to which developers can apply. The first program variant awards a 10- year stream of tax credits equal in present value to 70% of a project s non-land development costs of either newly supplied units, or the substantial rehabilitation of existing units (Keightley and Stupak, 2013). 5 State allocating agencies are constrained by their population in the total dollar amount of tax credits they can allocate to developers under the competitive variant of the LIHTC program. 6 The competition by developers to receive these tax credits is high in most states, with some estimates as high as $3 requested for every $1 available to be allocated (Olsen, 2003). State agencies are required to create a Qualified Allocation Plan for how they determine which developers receive a tax credit allocation, and often results in developers making several concessions to appear more attractive in the allocation process (Gustafson and Walker, 2002; Ellen et al, 2015). For example, developers can increase the probability of being awarded an allocation of tax credits by their state agency by voluntarily lowering maximum rents, incomes, or where the project is located (Ellen et al, 2015). 4 LIHTC developers are eligible to charge rents up to 18% of AMI if at least 40% of their units are subsidized through the LIHTC program, but only 15% of AMI if between 20 and 39% of their units are subsidized under the program. In practice, virtually all LIHTC developers elect to receive a subsidy for 95% or more of their units, so the higher 18% cap is most common (Eriksen, 2009). 5 The 70% variant of the LIHTC program is also know at the 9% credit, since the present value calculation based on prevailing discount rates used by the IRS at the program s inception resulted in developers receiving a 10-year stream of annual credits equal to approximately 9% of the project s eligible basis. Likewise, the 30% variant of the program resulted in developers receiving a 10-year stream of tax credits equal to 4%. 6 The maximum amount of federal income tax credits state agencies can allocate to LIHTC developers is determined annually by their population. As of 2014, each state agency was able to allocate $2.30 per state resident to LIHTC developers applying for the competitive version of the program awarding a base subsidy equal to 70% of the present-value of non-land development costs. 6

8 Developers also have the option to apply for a non-competitive variant of the LIHTC program that awards tax credits equal in present value to 30% of non-land development costs. Despite the lower base subsidy level, this variant of the program is available to developers conducting less substantial rehabilitations, and also enables them to utilize additional subsidy sources, including the use of federal income tax exempt bonds to finance the project. The aggregate number of tax credits allocated to LIHTC developers under the 30% variant are also not capped, and therefore does not require developers to make voluntary concessions in order to receive an allocation from the state agency. In summary, LIHTC developers have the option to either apply for a non-competitive subsidy equal to 30% of non-land development, or apply for a competitive higher level of subsidy equal to 70%. 7 Developers may also receive an additional 30% increase in subsidy, so a total subsidy equal in present value to either 91% or 39% of construction costs, depending on where the project is located. First, they may receive the subsidy increase if they locate their project in a Qualified Census Tract (QCT). Neighborhoods are designated a QCT by HUD, and determined by whether an individual census tract, which is approximately 1,600 households, is within the lowest 20% of incomes within the metro area. 8 The effect of QCT designations on neighborhood-specific outcomes was first studied by Baum-Snow and Marion (2009). They found QCT designation at the margin resulted in an increased number of LIHTC units, increased homeowner turnover, and raised property values in declining areas. Freedman and Owens (2012) also used the QCT 7 The variants of the LIHTC program where developers receive a base subsidy equal to 70% and 30% of their nonland developments costs will be referred to as the competitive and non-competitive variants, respectively. 8 See Freedman and Owens (2011) for a history of QCT designations. Prior to 2002, QCT status was solely determined by if 50% of census tract population had an estimated income less than the LIHTC maximum of 60% of the area median gross income, with no more than 20% of the metro area s population in a tract deemed as such. Starting in 2002, this was expanded to include census tracts where at least 25% of its respective population lived in poverty, subject to the same 20% constraint. 7

9 discontinuity to find LIHTC units were associated with a reduction in violent, but not property, crime. Developers may also receive a 30% increase for locating their LIHTC project in a metro area designated as a Difficult Development Area (DDA). A metro area is designated by HUD as a DDA based on the ratio of metro area s rent divided by income, subject to a 20% population constraint nationally. For annual ranking purposes, HUD defines a metro area s rent as equal to its estimated 40 th percentile of rent for a 2 bedroom unit, and income as 18% of the area median income for a 4-person family. 9 It is important to note that LIHTC developers can only receive one 30% increase in subsidy from locating their project in either a DDA or QCT. There are a number of potential reasons to increase the subsidy for LIHTC developers in relatively high rent-to-income metro areas. First, such metro areas are where rental housing is arguably least affordable as a percentage of income, and suggestive of possible supply constraints. Second, housing developers in cities with the highest rents may also have the greatest opportunity cost in producing rent-restricted units. The gap between a metro area s market rent and maximum LIHTC rent represents the developer s lost rent for participating in the program and agreeing to the restrictions. If the gap between the market and LIHTC maximum rent is sufficiently large, profit-driven developers may choose not to apply to receive a subsidy under the program without the additional 30% increase in subsidy. 10 A third potential justification for the increase in the generosity of the subsidy is to compensate developers for higher non-subsidized costs in higher-rent metro areas. In particular, land costs are 9 HUD is required to publish annually in the Federal Register the criteria to how DDAs are designated. For example, see Federal Register (2015). 10 The LIHTC program only caps a tenant s contribution towards rent, not the total rent inclusive of additional government subsidies. For example, a LIHTC project would receive the tenant s 30% contribution towards rent plus gap between contribution and FMR if they were a housing choice voucher recipient. In other words, there is a strong incentive for LIHTC developers to attract voucher recipients in these relatively higher rent-to-income areas. 8

10 not subsidized through the program and earlier research has shown LIHTC developers are more likely to construct more capitally intensive housing units holding land constant (Lang, 2015). The cost of land to construct units could therefore be higher in DDA designated metropolitan areas, and the additional subsidy may offset the differences in these unsubsidized expenses. III. CONCEPTUAL MODEL Private housing developers have several decisions to make when deciding to apply to their state housing authority to receive an LIHTC subsidy. First, a developer needs to decide where to locate housing units. Next, they need to decide how market rents compare to LIHTC rent-restricted units for a given quality of housing services provided, and whether to apply for either the competitive or non-competitive versions of the LIHTC program. Developers deciding to apply for the higher subsidy-level associated with the competitive version of the LIHTC program, must also then decide which concessions to make in their application to win an allocation from their state agency. The exact sequence of these decisions, and how DDA-designation affects each of them, is unclear. A simple conceptual model is constructed below to better understand the effects of the LIHTC program on developer behavior. First, consider a potential developer of a known parcel of land (l) with fixed acquisition cost of LC and non-land development costs DC, which is a function of quality of capital (k) installed on the land. This hypothetical developer is deciding between the supply of a single housing unit, but is unsure of quality of housing to supply and whether to apply to receive a competitive subsidy from the LIHTC program. Without the LIHTC program and land costs as given, the developer will maximize their profit function (π) by charging net market rents (R), or max π = Rt ( l, k) DC( k) LC( l). (1) t= 0 9

11 A potential motivation for the LIHTC program is due to increasing returns to quality k for developers at the region perceived affordable for some socially-important (e.g., low-income) households. The intent of the LIHTC program is to instead offer the alternative for developers to charge restricted rent R in exchange for a subsidy equal to Subsidy = γθdc( k), (2) where θ represents the subsidy level (e.g., 70%) and γ represents the probability of being awarded a subsidy. If it is assumed that developers install the same level of quality k regardless of applying for the program, developers will apply for the program if 30 * t t, (3) t= 0 γθ DC( k) ( R (, l k) R ) * when the program s rental restrictions last 30 years and the developer selects rental restrictions R t in order to maximize γ. Three things are interesting to note with regards to the LIHTC program. First, the rental restriction R is not a function of land and capital of the development as it is a fixed percentage of the metro-wide area median income. Second, the decision of how much capital to install enters the participation decision in a strictly positive fashion by increasing the subsidy an amount θ. This result is consistent with Eriksen (2009) who illustrated that LIHTC construction costs in California are 22% higher than average-quality unsubsidized construction, but arguably inconsistent with motivating the program through a need to reduce quality of housing provided by private developers. Last, developers must be compensated with additional subsidy if uncertainty exists in their * ability to select the package of concessions ( R t ) due to the state allocation process, resulting in γ < 1. It is costly for developers to submit an application as they are usually required to submit design plans, market studies, and purchase land options to apply. Since in some states 2 out of 10

12 every 3 competitive LIHTC applications are rejected, it is common practice to employ consultants aware of the individual state allocation process to increase the probability an application is selected. Although what happens to developments associated with failed LIHTC application is an open area of research, it is thought developers either construct market rate units, submit an application for the non-competitive LIHTC variant, or wait to submit a revised LIHTC application. To the extent that uncertainty surrounding the LIHTC application process delays otherwise viable market-rate construction is a previously unrecognized, and perhaps important, cost of the program. Effect of DDA Designation The effect of a metro area designated as a DDA compounds these decisions by developers. At the margin, an increase in the generosity of the subsidy θ by 30% would lead to increased competition by developers to receive the fixed supply of tax credits. How this ultimately affects the supply and composition of LIHTC units is less clear. This may increase the number of LIHTC units in the metro area designated a DDA if previously the tax credit constraint was not binding at either the state or metro area. 11 The overall number of competitive LIHTC units will increase if the allocation constraint was not previously binding at either level. If the constraint was binding at the state level, the number of competitive tax credit units in the metro area designated as a DDA may increase, but result in an offset elsewhere in the state. Increased competition by developers 11 This assumption is consistent with Eriksen and Rosenthal (2010), which showed metropolitan areas with a higher voting share for the sitting governor in 1988 was correlated with additional LIHTC units constructed throughout the 1990s. Eriksen (2009) also indicated the state allocating agency in California divides the state into 12 geographic regions with explicit set asides for each area. The allocating process of other states are less clear and the estimates in the paper would be attenuated if DDA-designation of one metro area results in fewer tax credits allocated outside of that metro area. 11

13 for the more generous subsidy should lead them to bid lower rents in order to increase their probability of receiving an allocation if binding at either level. The effect of DDA designation on the supply of LIHTC units under the non-competitive LIHTC variant is even less clear. State allocating agencies are not constrained in the aggregate dollar amount of tax credits they can allocate under this program, and being designated a DDA would increase the per-unit subsidy received by LIHTC developers from 30 to 39%. There is an unclear effect on the supply of units depending on the degree of competition to receive a competitive LIHTC allocation of 91%. If the competition is sufficiently high to drive down equilibrium rents bid by winning developers, the number of non-competitive LIHTC units may increase. Conversely, the increased generosity of the subsidy may induce some developers who would have applied for the 30% subsidy to forgo the 39% subsidy, and instead apply for the 91% subsidy associated with competitive LIHTC applications. The effect of DDA designation on where LIHTC units are located within metro areas is more clear. As mentioned above, the land cost of development is unsubsidized through the LIHTC program and restricted rents are indexed as a percentage of the metro area s median income, and therefore independent of the underlying land. LIHTC developers therefore have a strong incentive to supply subsidized units through the program on the lowest quality of land. This incentive is further reinforced if the land is located in a low-income neighborhood designated a QCT, as developers would receive the 30% increase in subsidy if the metro area was not already designated a DDA. The designation of the metro area as a DDA would remove this additional financial incentive, and therefore fewer subsidized units are anticipated to be constructed in low-income neighborhoods as a result. 12

14 Numerical Example of DDA Designation For initial simplicity, assume state allocating agencies set aside a fixed percentage (e.g., 20%) of their total annual allocating authority for each metropolitan area, resulting in $70 million available for competitive allocations for a hypothetical geographical area. Further assume land costs a fixed $1 million per development to install 100 LIHTC units each with a per-unit cost of $100,000. In equilibrium, 10 developers would apply to receive the subsidy, each would receive $7 million, and 1,000 units would be constructed. Now consider if the above hypothetical metropolitan area was designated as a DDA. The above developers would instead receive $91,000 in subsidy per each supplied unit, although the total allocation authority set aside by the state agency for that geographical area would still be capped at $70 million. Holding all other development parameters constant, DDA designation would therefore result in 769 units alternatively being supplied, a 23% reduction from when the area was not designated as a DDA. Based on that reference point, a lower estimate of displacement may suggest developers substituting to the non-competitive LIHTC variant. A higher estimate suggests the increase subsidy generosity results in either developers substituting away from the non-competitive LIHTC variant, or increasing their development costs. IV. Where is Housing Unaffordable? Before disentangling how the LIHTC program affects the incentives of developers in where to locate subsidized housing, it is important to better understand where housing is unaffordable based on LIHTC definitions. The LIHTC program defines a household as low-income and eligible to live in subsidized units is if it earns less than 60% of their metropolitan area s median income (AMI), adjusted for household size. The maximum statutory rent under the program for 13

15 tenants is also set to 18% of the AMI, unless developers make voluntary concessions to the state agency during the allocation process. As suggested by Green (2011), one way to compare housing affordability between regions is to measure the dollar gap between the 40 th percentile of rent as estimated by HUD and 18% of the AMI. 12 This dollar amount also represents the effective subsidy for tenants living in LIHTC housing if they would have been charged the 40 th percentile of market rents in absence of the subsidy. Figure 1 illustrates this affordability gap for the 100 largest metropolitan areas in The x- axis in the figure is 60% of the area median income for a 3-person household. The y-axis is the gap for that household to contribute 30% of their income and rent a 2-bedroom unit at the 40 th percentile. The figure displays a wide gap in affordability across the U.S.. The largest positive gap exists in New York, NY with an estimated $6,030 needed per 3-person family to contribute 30% of their income. Approximately 50% of the population living in the top 100 metro areas would require them to contribute more than 30% of their income to rent a 40 th percentile unit. The population weighted average would be $105 per year. It is interesting to note that in almost half of the metropolitan areas 18% of the AMI exceeds the 40 th percentile of rent. For example, in Cincinnati, OH the median income for a family of 3 is $61,050 and the 40 th percentile of rent for a 2-bedroom unit was $738. The affordability gap for such households would be -$3,474. The most negative gap was -$4,086 in Des Moines, IA. Other notable metro areas with a negative affordability gap were Washington, DC (-$1,536), Minneapolis, MN (-$3,570), Seattle, WA (-$2,400), and Denver, CO (-$2,286). These negative affordability gaps imply the 18% LIHTC maximum rent threshold is potentially non-binding, unless developers voluntarily charge lower rents as a result of the allocation process. 12 This dollar amount is also meaningful as it represents the amount HUD would compensate landlords of housing voucher recipients to reside in LIHTC subsidized units. 14

16 Although the exact determinants of why housing is unaffordable in some locations is beyond the scope of this paper, one explanation is natural and artificial supply constraints. Examples of natural supply constraints is the share of developable land due to elevation changes or water, and an example of artificial supply constraints are land-use regulations. Figure 2 illustrates the affordability gap for the 100 largest metropolitan areas as a function of local supply elasticity as estimated by Saiz (2011). The correlation between the two variables is and r-squared of a naïve regression of the two variables is This figure illustrates the affordability gap is the largest in the most supply inelastic metropolitan areas. V. DATA The main data used in the analysis were obtained from HUD s Database on the LIHTC. The database was originally assembled by Abt Associates for HUD and is available at the project-level for 40,502 projects containing 2.6 million housing units constructed, or placed-into-service, between 1987 and The sample is restricted to projects located in a metropolitan area and constructed between 1993 and 2013 as HUD administrative records for DDA designations prior to 1993 were not available. The annual number of LIHTC units constructed in metro areas during this time period is illustrated in Table 1. There were 1.5 million units constructed in 274 metropolitan areas, of which 21.5% of units were first located in a DDA at the time of 15

17 completion. 13 The annual share of units constructed in a DDA ranges from a low of 11.5% in 1996, to a high of 42.9% in These data are merged with several sources of administrative data provided by HUD. By law, DDAs are designated by HUD based on the ranking of the ratio of local rents to income, given the constraint that no more than 20% of metropolitan areas by population receive the designation. The precise rent of the ratio is defined as the 40 th percentile of rents. Table 2 displays summary statistics of the constructed sample. The average annual rent used as the numerator was $9,725 in 2013 equivalent dollars. The denominator of the ratio to rank metro areas by HUD is equal to the maximum allowable rent paid by LIHTC tenants. In principal, the maximum allowable LIHTC rent is defined as a 4- person household earning 60% of the metro area s median income (AMI), contributing 30% of their income towards rent, or 18% of the AMI. However, HUD does not actually use published AMI to rank metro areas, but instead uses their published 4-person very low-income limit (VLIL) for the metro area, which is approximately equal to 50% of the AMI minus a couple of statutory adjustments. 14 The income used to rank metro areas for purposes of DDA designation is therefore equal to 30% of 120% of the VLIL (Federal Register, 2015). The annual average maximum LIHTC rent in the sample was $11,921. The average ratio of 40 th percentile of rent divided by the LIHTC maximum rent was 81.5%. This means the LIHTC maximum rents exceeded at least the 40 th percentile of rent in the majority of metro areas unless developers voluntarily lowered tenant maximum rent and income in an effort 13 DDA designations are made at the metropolitan area level, but geographic boundaries defining each metropolitan area may periodically change. Geographically consistent metropolitan areas based on 2004 HUD definitions are used throughout the analysis. 14 See HUD (2015) for a list of exact adjustments to AMI by area, which potentially change annually and outlined in their mandatory reporting of adjustments in the Federal Register. Examples of these manual adjustments are for relatively high housing cost-to-income areas and national maximums. 16

18 to gain favor of allocating agencies. Figure 3 illustrates the 40 th percentile of rent by LIHTC maximum rent for the 561 metro areas designated a DDA between 1993 and The figure displays DDA designations are not exclusively high rent metro areas. 76 different metro areas at some point have been designated a DDA. For example, relatively low rent metropolitan areas such as Laredo (TX), McAllen (TX), Brownsville (TX), El Paso (TX), and Ocala (FL) have received the DDA designation with monthly rents at or below $700 per month (in constant 2015 dollars). Despite relatively wide variation in LIHTC maximum rents relative to market rents at the metropolitan level, the dollar amount of tax credits available to be allocated to developers through the competitive process are determined solely by the number of residents in each state. There is, however, discretion granted to the state allocating agencies in how they redistribute tax credits within their state to metropolitan areas (Eriksen and Rosenthal, 2009). There is also virtually no cap on the number of tax credits state agencies can allocate to developers seeking the noncompetitive LIHTC subsidy with the lower base generosity. Figure 4 illustrates the number of LIHTC subsidized units per 1,000 residents constructed between 1993 and 2013 for the 100 largest metropolitan areas, where the x-axis is now defined as the affordability gap discussed. The figure illustrates there is virtually no correlation between the affordability gap and per capita number of LIHTC subsidized units. The raw correlation of the two variables is and the r-squared of their naïve regression is less than In summary, despite wide variation in affordability between metropolitan areas based on LIHTC definitions of need, the supply of LIHTC units is uncorrelated. VI. METHODS Identification of the causal effect of DDA designation on developer behavior is confounded by the status being determined as a non-linear function of the local area rent and income, which may itself 17

19 directly affect developer behavior and incentives. To the extent that incentives overlap, the counter-factual in absence of the designation is unobserved. I am interested in estimating the causal effect β associated with an indicator variable of DDA designation. In regression form, the variable Y is the aggregate number of LIHTC units constructed during year t in metropolitan areas i, or ( ) Y = α + β DDA + θx + u (4) it i it it where u is an idiosyncratic error term and α is an intercept that may vary across metropolitan areas. There are several concerns about interpreting β as the actual causal effect. First, DDA designation could be correlated with some unknown omitted variable also correlated with the idiosyncratic error term u. This could be partially remedied by controlling directly for observable attributes X used by HUD in making their designation, although would still be reliant on relatively strong assumptions about no further omitted variables and possible trends, especially given the nonlinearity of ratio used in the designation. For example, developers will locate units based not only on current and observable market attributes, but also unobserved conditions anticipated in the future. Fortunately for identification purposes there is seemingly an arbitrary cutoff; only the top 20% of metropolitan areas based on the ranking of rent divided by income can receive the DDA designation annually. Regression discontinuity (RD) empirical methods were first popularized by Hahn, Todd, and van der Klaaw (2001), although applications of RD within Urban Economics have been relatively limited (Baum-Snow and Ferreira, 2015). There are 2 main requirements for an RD empirical approach to be valid (Baum-Snow and Ferreira, 2015). First, the researcher needs to know the selection into treatment based on a continuous function Z, and a discontinuity (zo) needs to exist within that assignment. The selection into treatment is the annual designation by HUD of DDA 18

20 status, where the 20% threshold provides the discontinuity needed. The second requirement is that areas are not allowed to self-select, or sort across the boundary threshold. This is not possible because HUD independently makes the annual designation, and the exact value of the ratio required for DDA designation is unknown beforehand. Given the above conditions hold, the coefficient β can be interpreted as the weighted causal effect of DDA designation around the discontinuity. However, there are several practical decisions to be made when using a regression discontinuity estimator. Hahn, Todd, and van der Klaauw (2001) showed local linear regressions provide a nonparametric way of consistently estimating the treatment effect when adopting a regression discontinuity identification strategy. An additional challenge with such non-parametric methods is the seemingly arbitrary decision of kernel and bandwidth. Triangular kernels place more weight on closer observations and have been shown to have been superior conditions at the boundary, which are essential in regression discontinuity designs (Lee and Lemieux, 2010). As suggested by Imbens and Kalyanaraman (2011), the bandwidth is selected to minimize the squared bias plus variance, or mean-squared error. Since estimates are potentially sensitive to kernel and bandwidth selection, alternative estimates using a rectangular kernel, and then 50% and 200% of the selected bandwidth are also reported. I also initially omit the conditioning of the regression discontinuity estimates on the observable covariates of metropolitan area income, rent, and population. While such control variables are essential in a more traditional regression analysis to account for potential omitted variable and selection biases, such concerns do not exist within a regression discontinuity framework if the 2 main identification conditions are valid. In fact, the conditioning on such control variables may themselves bias regression discontinuity estimates if they either are themselves endogenous, or have a non-linear impact of the mean treatment (Imbens and Lemieux, 2008). 19

21 Last, a number of steps are taken to accommodate the panel structure of the data. First, the number of LIHTC units are normalized by the population in each metropolitan area to adjust for possible non-linear differences based on the metropolitan area size. Second, the average number of LIHTC units completed in each metropolitan area between 1993 and 2013 are subtracted from annual completions in order to remove any possible time-invariant determinants in supply of LIHTC units specific to the metro area. Last, to the extent serial correlation in errors may persist even after the above steps, standard errors are clustered at the metropolitan area level. VII. MAIN RESULTS. The first evidence of a difference in number of units constructed based on DDA designation is from comparing the average number of units completed in Table 2. Of the 274 metropolitan areas in the sample between 1993 and 2013, there were 561 instances of a metro area being designated a DDA, for an average of 28.5 designations each year. There were LIHTC units constructed annually in DDAs as compared to in non-ddas, but on average the population of DDAs was more than double that of non-ddas. 15 On a population-adjusted annual basis, there were LIHTC units constructed in non-ddas as compared to in DDAs over this time period, which results in fewer LIHTC units constructed per 1,000 residents in DDAs. A t-test indicates this difference is not statistically distinguishable at the 10% level using standard errors clustered at the metro level. Table 3 presents main regression discontinuity estimates as discussed in Section IV. The outcome variable in Column 1 is the number of LIHTC units per 1,000 metro residents. The 15 In practice, not all housing units in a LIHTC subsidized project need to be subsidized, although in practice most developers choose to receive a subsidy for all units (Eriksen, 2009). Only the number income-restricted, and thus subsidized, units within projects is used in the analysis, although similar estimates were obtained if the total number of units within LIHTC-subsidized were alternatively used. 20

22 outcome variable in Column 2 is defined as the number of LIHTC completed units per 1,000 metro residents subtracted by the metro average in construction from 1993 until 2013, which is equivalent to a metro fixed effect. The first row of Table 3 reports the estimated discontinuity based on a triangular kernel, no covariates, and a bandwidth selected to minimize MSE as suggested by Imbens and Kalyanaraman (2009). Depending on the subtraction of the metro average, DDA designation resulted in between a to decrease in the number of LIHTC units per 1,000 metro residents. Clustered standard errors below each estimate in parentheses imply the estimates are different from 0 at the 5% and 1% level, respectively. Given on average units per 1,000 residents were constructed on average in each metro area, the estimates imply the designation decreased LIHTC construction by approximately 40%. Estimates of the discontinuity using the optimally selected bandwidth of is presented in Panel A of Figure 5. The robustness of the RD results are illustrated in multiple ways. First, alternative estimates using 50% and 200% of the optimal bandwidth are presented in row 2 and row 3 of Table 3. A smaller bandwidth will produce an estimate with lower bias, but at the cost of higher variance (Nichols, 2007). Those estimates range from to and are illustrated in Panel B and C of Figure 5. Figure 6 illustrates the estimated discontinuity as a function of 25% to 300% of the optimal bandwidth. The dashed lines in Figure 6 represent 90% confidence intervals and indicate the estimates were not sensitive to bandwidth selection. Significant differences of observable covariates at the discontinuity may imply an improper RD design (Imbens and Lemieux, 2008). Accordingly, it was confirmed that no significant discontinuity in the metropolitan area income, rent and population was estimated to exist at Z0. The same observable covariates were then directly included in the specification as their inclusion may result in improved efficiency in reduction of residual variance, but threaten consistency if 21

23 incorrectly specified (Nichols, 2007). The estimates inclusive of covariates are listed in column 1 of Table 4. Reassuringly, the estimates are similar with such controls, with a point estimate of As a last robustness check, a rectangular, as opposed to a triangular, kernel was specified in the in the nonparametric local linear regressions. Estimates using 50%, 100%, and 200% of the optimal bandwidth with and without covariates are listed in Columns 2 and 3 of Table 4. The results are similar to those obtained using a triangular kernel, remain statistically meaningful, and range from to Competitive v. Non-Competitive Allocation A metro area being designated as a DDA may also affect the location and composition of LIHTC units within metro areas. As explained in Section II, the LIHTC is actually 2 separate programs where developers have the option to apply to receive either a competitive or non-competitive allocation equal to either 70%, or 30% of non-land development costs, respectively. While the competitive subsidy is more generous on a per-unit basis for developers, developers may have to make significant concessions to state agencies allocating the tax credits in order to receive the subsidy. It is therefore unclear how increasing the generosity of the subsidy by 30% for all LIHTC developers in the metropolitan area by designation of a DDA affects the composition of units. Three sets of estimates are presented in Table 5. First, in columns 1 and 2 it is shown how DDA designation affects the per capita number of LIHTC units placed into service by developers of the 30% and 70% variants of the program, respectively. As before, these estimates were obtained using a triangular kernel and a bandwidth selected to minimize mean-squared error. DDA designation resulted in fewer LIHTC units receiving the 30% subsidy, and fewer LIHTC units receiving the 70% subsidy scaled each per 1,000 metropolitan residents. With 22

24 clustered standard errors of and 0.034, only the reduction in units receiving the 30% subsidy is statistically different from 0 at conventional levels using the optimal bandwidth. In the third column of Table 5, it also is shown DDA designation affects the percentage share of LIHTC constructed under the 30% variant of the program. 16 DDA designation was found to result in a 10.1% relative decrease in LIHTC units receiving the 30% as compared to 70% subsidy level. Qualified Census Tracts QCTs are designations, similar to DDAs, made by HUD based on the share of the population earning less than 60% of the area median income. LIHTC developers would receive an additional 30% increase subsidy for locating a project in a QCT if the metro area was not already designated as a DDA. In other words, these are relatively low-income areas that LIHTC developers would have received a financial incentive to locate projects without the DDA designation. Presented in Table 6 are estimates that parallel Table 5, but instead stratified by number and share of LIHTC units located in a QCT. The estimates show DDA designation resulted in fewer LIHTC units constructed in QCT, which is statistically different than 0 at the 5% level of significance. DDA designation also resulted in fewer units per 1,000 residents in non-qcts as well, a difference statistically different from 0 at the 10% level. In the third column, it is also shown DDA designation resulted in 4.8% fewer share of LIHTC units in QCTs, but that difference is not statistically different from 0 at conventional levels. In Table 7, the analysis is concluded by comparing how DDA designation simultaneously affects the type of credit developers applies to receive and if the project is located in a QCT. The 16 An important caveat of these estimates of the percentage share is that metropolitan areas without any LIHTC construction during the year were omitted. There were 5,605 unique year-metro observations where LIHTC could have been constructed, of which 3,165 (56.5%) had at least 1 unit constructed. 23

25 estimates were obtained from 4 separate RD regressions where the dependent variable is the share of each category of subsidy. In the top left quadrant, DDA designation is estimated to result in a 4.6% decrease in the share of LIHTC units where developers receive the 30% credit and located in a QCT. This estimated effect is different from 0 at the 10% level. The estimate in the bottom left quadrant implies DDA designation has virtually no statistical or economic effect on the share of LIHTC units receiving higher competitive subsidy and located in a QCT. In the upper right, DDA designation is estimated to result in a 6.4% decrease in share of 30% projects not in a QCT, but is not statistically different from 0. In the bottom right quadrant, the largest effect (i.e., an 11.0% increase) of DDA designation is shown to be on the share of LIHTC units receiving the competitive type of credit and not locating in a QCT. IV. EVIDENCE FROM APPLICATIONS The above results were obtained using a national database of LIHTC projects receiving an allocation. To gain further insights of how DDA designation affects developer behavior data on developers applications to receive a competitive LIHTC allocation in California were collected. Application data are beneficial because they indicate how DDA status affects demand between developers to receive a fixed supply of tax credits. Application data in California are specifically interesting because it has the largest authority in allocating tax credits as the most populous state and a high share number of its metro areas have been designated a DDA. The data were obtained from the California Tax Credit Allocation Committee, which oversees the LIHTC allocation process in the state. Information on submitted applications between 1997 and 2013 were obtained, including aggregate dollar amount of requested tax credits. The number of requested units to be subsidized under the program were obtained from 2003 until There 24