Property Tax Capitalization ECN741, Urban Economics Professor John Yinger, The Maxwell School, Syracuse University, 2018

Property Tax Capitalization Class Outline What Is Property Tax Capitalization? How Does Property Tax Capitalization Arise? Estimating Property Tax Capitalization Evidence on Property Tax Capitalization The Implications of Property Tax Capitalization for Public Policy

Property Tax Capitalization Class Outline What Is Property Tax Capitalization? How Does Property Tax Capitalization Arise? Estimating Property Tax Capitalization Evidence on Property Tax Capitalization The Implications of Property Tax Capitalization for Public Policy

Property Tax Capitalization Bidding and Capitalization As shown in a previous class, the basic bidding model implies that the price of housing services will be higher in jurisdictions with lower property taxes. This is called property tax capitalization. Although he was not the first to estimate property tax capitalization, Wallace Oates brought new attention to the topic with his famous JPE paper (Nov./Dec. 1969). Oates used data for suburbs in NJ and found evidence of tax and service capitalization.

Property Tax Capitalization What Is Property Tax Capitalization? It is just the impact of expected annual property tax payments on the value of a property. It can be derived from an asset pricing model or from the household maximization problem in bidding models. It provides a test of the consensus bidding model and raises important policy issues. For more see Property Taxes and House Values (PTHV, 1988) by Yinger et al.

Property Tax Capitalization Asset Formulation The value of an asset equals the present value of the net benefits from owning it. Without property taxes, the amount someone is willing to pay for a house is the present value of the rental benefits, or where is the pre-tax price of housing services, H is housing services, r is the real discount rate, and L is the expected lifetime of a house.

Property Tax Capitalization The Magic of Algebra!

Property Tax Capitalization Key Simplification If the real value of rental services is constant over time and L is large, this equation reduces to: The value of a house equals its annual rental value divided by a discount rate. Because housing lasts a long time, this is a reasonable—and obviously helpful— simplification.

Property Tax Capitalization Formulating Tax Payments A property tax payment, T, is the product of a nominal tax rate, m, and an assessed value, A. It is also the product of an effective tax rate, t, and a market value, V In symbols Annual property taxes represent an expense for a homeowner.

Property Tax Capitalization The Asset Price with Property Taxes Adding property taxes as an expense, the house value equation becomes: Note that property taxes are added as a flow because they must be paid every year—a flow that is “capitalized.”

Property Tax Capitalization The Degree of Capitalization This equation assumes that property taxes are fully capitalized. As we will see, this might not be the case, so a more general form is: where β is the “degree of property tax capitalization;” i.e., the impact of a $1 decrease in the present value of property taxes on the value of a house.

Property Tax Capitalization Interpreting β A value of β equal to 1.0 corresponds to full capitalization. A value of β equal to 0.0 corresponds to no capitalization. If β equals 0.5 a $1 increase in the present value of property taxes leads to a $0.50 decrease in the value of a house. The value of β need not be the same under all circumstances.

Property Tax Capitalization The Capitalization Equation Solving the above for V yields the capitalization equation: Thus, houses with higher effective property tax rates (t) will have lower values (V). The strength of this relationship depends on β. This is, of course, just the bidding result—with β added.

Property Tax Capitalization Class Outline What Is Property Tax Capitalization? How Does Property Tax Capitalization Arise? Estimating Property Tax Capitalization Evidence on Property Tax Capitalization The Implications of Property Tax Capitalization for Public Policy

Property Tax Capitalization How Does Tax Capitalization Arise? House buyers are usually aware of property tax payments. Even though they may not be sophisticated about present values and asset pricing, they may alter their bids on different otherwise- comparable houses based on their knowledge of property tax payments.

Property Tax Capitalization How Does Tax Capitalization Arise?, 2 Real estate brokers indicate anticipated property tax payments so buyers can make comparisons across houses. Lenders require mortgage plus tax payments to equal a fixed percentage of an applicant’s income. An increase in T must be offset by a drop in the mortgage, and hence a drop in how much the applicant can pay for the house, V.

Property Tax Capitalization Class Outline What Is Property Tax Capitalization? How Does Property Tax Capitalization Arise? Estimating Property Tax Capitalization Evidence on Property Tax Capitalization The Implications of Property Tax Capitalization for Public Policy

Property Tax Capitalization Expectations about Taxes Another issue is that the expected lifetime of current tax rates might be N ≠ L. In this case, we need to use r', not r . This leads to: where β' is the “degree of property tax capitalization” after accounting for differences in expectations.

Property Tax Capitalization Incorporating Expectations Now when we solve for V we get:

Property Tax Capitalization Interpreting Estimates of β The coefficient to be estimated, β, is the expression in front of t, so it includes both β' and the impact of different expectations about the lifetime of a house and of property taxes. This explains why we need both β and β'; the first is what we estimate but the second is the underlying degree of capitalization. It is still not obvious why we need to consider expectations—hold on.

Property Tax Capitalization Intra and Inter These equations apply within a community. Recall that Poor assessments result in higher assessment-sales ratios, and hence higher effective tax rates, for some houses than for others. These equations also apply across communities, which may have very different effective tax rates.

Property Tax Capitalization Change Formulation One can also derive a change form of the equation: Note that this equation contains the 2nd sale tax rate

Property Tax Capitalization Adding a Housing Price Index In PTHV, this equation is applied to intra- jurisdictional capitalization, i.e., the capitalization of differences in t within a community. To remove the impact of inter-jurisdictional tax changes and other factors that vary over time, V is deflated using a housing price index. This removes from V the impact of any change in the average effective tax rate (among other things) and leaves just the impact of the change in the deviation from the average tax rate.

Property Tax Capitalization Formulation with Price Index Now express the effective tax rate as and put an “*” on V to indicate deflation. Deflating implies that Accurate revaluation implies that

Property Tax Capitalization Final Specification Now define so that where and Thus, with data on , an estimate of b, and an assumption about r, one can obtain an estimate of β.

Property Tax Capitalization Error in PTHV Please note that these equations correct an error in PTHV. The algebra in that book mistakenly ignores the term in the denominator of the last equation. As we will see below, this mistake implies that the book understates the value of β by about 30 percent.

Property Tax Capitalization Research Issues in Estimating β First, this estimation involves a non-linear relationship between t and V, even after taking logarithms, so it cannot be directly estimated with linear regression methods. After taking logs, the basic equation is:

Property Tax Capitalization Research Issue 1, Continued One can use the ln{1+a} ≈ a approximation, but it may not be very good in this case, as (β/r)t may not be close to zero. A nonlinear form may work better. It can be estimated with NL2SLS. In the case of reassessment, the linear form derived earlier can be used under the assumption that assessments are accurate, i.e. that

Property Tax Capitalization Research Issue 1, Continued Note that it is impossible to separate β and r in the estimation. One can only estimate their ratio. This leads to the next issue….

Property Tax Capitalization Research Issue 2 The value of the discount rate, r, is not observed, and it is impossible to estimate r and β separately. Most studies follow Oates by estimating a value of β/r, assuming a value for r, and then calculating the implied value of β. The trouble with this approach is that the value of β depends on an untested assumption that varies across studies. In fact, the most extreme estimates in the literature, in either direction, are driven largely by extreme assumptions about r.

Property Tax Capitalization Research Issue 2, continued Moreover, scholars are amazingly careless about r, often using a nominal interest rate, when the theory clearly shows that a real rate, say 3 to 5 percent, is needed. A real rate equals the nominal or market rate minus anticipated inflation. PTHV takes a long-run, low-risk nominal rate (as for an investment in housing) and subtracts anticipated inflation based on a study of the factors that determine inflation expectations. This leads to a 3 percent rate.

Property Tax Capitalization Research Issue 3 The asset-pricing logic behind tax capitalization requires assumptions about house buyers’ expectations. This logic predicts that a $1 increase in the present value of future property taxes will lead to a $1 decline in house value (i.e. β' = 1), but it does not say that current tax differences will be fully capitalized (i.e. β = 1) if they are not expected to persist.

Property Tax Capitalization Research Issue 3, Continued Virtually all the literature estimates the capitalization of current property tax differences. Under the assumption that current tax differences will persist indefinitely, the assumption that β = 1 makes sense. In fact, however, current differences may not be expected to persist. In this case, we can use the result derived earlier, namely,   where N is the length of time current tax differences are expected to persist. The theory indicates that β = 1, but the estimated β clearly need not equal 1, and indeed need not equal the same value under all circumstances.

Property Tax Capitalization Research Issue 3, Examples If current property tax differences across (or within) communities are expected to disappear in 10 years and r = .03, then this equation implies that the estimated β will be only 26 percent even if β = 1. If revaluation is scheduled every 6 years, as in North Carolina, then the estimated β should decline as one moves closer to the year of revaluation.

Property Tax Capitalization Research Issue 4 Because t = T/V, one must treat t as endogenous.  This endogeneity is definitional (t is a function of the dependent variable) and behavioral (factors unobserved by the researcher but observed by the assessor may  influence both T and V).   PTHV uses a model of assessor behavior to identify some instruments and then uses either NL2SLS or 2SLS.

Property Tax Capitalization Research Issue 4, Continued The PTHV instruments build on two features of assessor behavior. First, the 2nd sale effective tax rate depends on time since revaluation, and the nominal tax rate and the price index in the year of 2nd sale can be used as instruments. Second, the A/V ratio is supposed to be constant, but actually varies systematically with housing traits, X. Post-revaluation double sales can be used to identify X’s that predict A/V—and that can serve as instruments.

Property Tax Capitalization Research Issue 5 One must be careful about possible omitted variable bias. Good data on housing traits are needed.  This is not quite such a big problem with double-sales data, which difference out time-invariant traits. Even with double-sales data, it helps to control for renovations.   Deflating V eliminates the possibility that the estimated impact of a change in t is biased by the omission of other changes at the jurisdiction level.

Property Tax Capitalization Research Issue 5, Continued Because property tax rates are correlated with many other variables that affect house values, one may not even be able to estimate property tax capitalization in many cases. PTHV takes advantage of court-encouraged revaluations in Massachusetts, which resulted in large changes in t. This study also makes use of double-sales data to remove time-invariant unobservable factors.

Property Tax Capitalization Research Issue 6 One must consider itemization on federal income taxes. If a taxpayer itemizes on federal income taxes, she can deduct property taxes.  So a $1 increase in the PV of property taxes does not cost this taxpayer $1.  Estimates of β may reflect this effect. However, mortgage interest payments are also deductible, so an income tax correction applies to the numerator and denominator of β/r.  If s is the marginal income tax rate, this ratio with full deduction of interest is [β(1-s)]/[r(1-s)]= β/r. For household that do not itemize, of course, no correction is needed.

Property Tax Capitalization Research Issue 6, Continued Other approaches to itemization are possible. E.g., if r is interpreted not the mortgage interest rate, but instead as the opportunity cost of investing in housing (the return on other low-risk, long-term investments), it is not deductible. For more on these issues, see Elliott Eisenberg’s 1996 Maxwell PA dissertation. de Bartolomé and Rosenthal. “Property Tax Capitalization in a Model with Tax Deferred Assets and Standard Deductions,” ReStat, February 1999.

Property Tax Capitalization Class Outline What Is Property Tax Capitalization? How Does Property Tax Capitalization Arise? Estimating Property Tax Capitalization Evidence on Property Tax Capitalization The Implications of Property Tax Capitalization for Public Policy

Property Tax Capitalization Evidence on Property Tax Capitalization Every reasonable study of property tax capitalization finds a statistically significant negative impact of property taxes on house values. Estimates of β vary from 15 to 100 percent, but the range is smaller with the same r. These estimates are usually mis-interpreted as β (the tax capitalization rate) instead of β (which is β adjusted for expectations).

Property Tax Capitalization Expectations Recall that β = β if current tax differences across houses are expected to persist indefinitely. But if tax differences are not expected to persist, the estimated coefficient, β has two components, β and r/r. A difference observed today that will disappear upon sale has no impact on V (because r = ∞ and r/r = 0). A difference observed today that is expected to last one year will have only a tiny impact on sales price (because r/r = r/(1+r) < r).

Property Tax Capitalization Two Capitalization Rates One can define 2 capitalization rates: The capitalization of the expected present value of property taxes. The capitalization of the flow of current taxes assuming it persists forever. The first is the theoretically interesting concept. It indicates whether people are willing to pay $1 less for a house if the present value of expected taxes goes up $1. The second mixes the value of taxes with expectations about tax persistence. Many people misinterpret it!

Property Tax Capitalization Expectations in Massachusetts In Massachusetts, revaluations were required by the state supreme court, but enforcement was weak. Communities knew they could avoid revaluation for many years. Existing tax differences were expected to persist, but not forever. PTHV finds that current tax differences were capitalized at a rate of 32 percent. This is consistent with the expectation that current tax differences would disappear in 13 years.

Property Tax Capitalization Corrected Estimates of Capitalization in Waltham for Property Taxes and House Values   Nonlinear Version (equation (8)) Linear Version (equation (9)) Estimate of b 7.4233 7.0433 Value of 0.0420 Value of 1-b 0.6882 0.7042 Original β 0.2227 0.2113 Corrected β 0.3236 0.3000 Understatment (%) 31.2 29.6 Implied N (years) 13.2 12.1

Property Tax Capitalization Eisenberg In Syracuse in the early 1990s, revaluation had not occurred for decades and did not appear likely to happen any time soon. But the city council unexpectedly decided to revalue. A dissertation on capitalization in Syracuse by a PA Ph.D. student (Eisenberg) found capitalization rates near 100 percent—exactly what the theory predicts when tax differences are expected to persist. This applies to people borrowing to the limit and not itemizing.

Property Tax Capitalization Class Outline What Is Property Tax Capitalization? How Does Property Tax Capitalization Arise? Estimating Property Tax Capitalization Evidence on Property Tax Capitalization The Implications of Property Tax Capitalization for Public Policy

Property Tax Capitalization Stay or Go? If property taxes are fully capitalized, then any tax changes show up in house values immediately and there is no way to escape them. An owner with a tax increase must either stay and pay the higher tax or leave and suffer a capital loss. An owner with a tax cut gets a capital gain. Moreover, the loss is the full present value of the future increases in taxes.      

Property Tax Capitalization Property Tax Capitalization and Public Policy Because of these gains and losses, tax capitalization has bizarre implications for public policy. Consider revaluation, which is a systematic revision of all assessed values. Revaluation leads to capital gains for homeowners who were over-assessed and to capital losses for homeowners who were under-assessed.

Property Tax Capitalization Fairness of Revaluation For long-term residents, these changes are fair. A resident who has been under-assessed for a long time has been given, in effect, a loan from the city and revaluation just claims back this “loan.” But for new residents, these changes are not fair. If someone bought an under-assessed house one day and the change is announced the next, this person has a capital loss even though she did not benefit from the poor assessment system.

Property Tax Capitalization Minimizing Unfairness Two ways to minimize this fairness problem: First, introduce a long lag between announcement and implementation. This lag allows owners at the time of announcement to escape some of the burden of the tax changes. Second, make sure houses are revalued upon re-sale, which they were not in Massachusetts or Syracuse.

Property Tax Capitalization Costs of Poor Evaluation Revaluation imposes unfair gains and losses but restores fairness in the near term and boosts faith in local government. This trade only makes sense if assessments are updated regularly. Otherwise, gains and losses are handed out each year as assessment errors mount. Poor assessments also lead to court cases, which the city usually loses. People who buy over-assessed property pay low prices—and then can sue the city for a rebate because of unfairly high taxes. This happened in Boston, to the tune of tens of millions of dollars. The only way to avoid this crazy situation is to keep assessments up to date!

Property Tax Capitalization California Proposition 13 in California represents another unusual case. The proposition fixes assessment growth at 2%, so the assessment/ sales ratio, and hence t, declines over time for long-term owners. This cannot be turned into a capital gain because houses are revalued upon sale. The result is that some homeowners have tax rates that are 100 or more times greater than the tax rate of their neighbors.

Property Tax Capitalization California, 2 These provisions represent a gift to long-term owners and discourage mobility. The U.S. Supreme Court said this was legal. Voters in California and a few other states like this reward to long-term residents. But different tax treatment for different citizens leads to resentment and undermines faith in local government.