Creating Affordable Housing Using a Vacancy Tax

Caleb Brobst, Archan Das, Liam Doherty

Overview of the Problem

• Need 17,241 new affordable units for 50% of MHI
• 17,491 true vacancies in the City of Pittsburgh¹
• Journal of Affordable Housing - most are left intentionally vacant to hold out for higher rent
• Vacancy Rate has increased by 15% from 2000 to 2014 despite a 5.2% decrease in overall housing units²

Solution

• Vacancy Tax
• Tax landlords or owners of units that keep them vacant
• Acts like a Pigouvian Subsidy but is a tax to keep the policy revenue neutral or positive
• Would Tax those properties determined vacant using the same definition as the Allegheny Housing Report
• Tax Revenue can go to other affordable housing programs in the city that need funding
• No Renovation Exemptions
• Journal of Affordable Housing - Failure of past vacancy taxes is exemptions for renovations that favor wealthy property owners that can move to a second property during the renovation period³

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Why It Works?

• Shifts supply curve to the right as suppliers are now willing to supply more to avoid paying tax
• Forces landlords to realize opportunity cost⁴
• Not everyone is an economist
• Without tax they they don’t have negative accounting profit
• With tax, now there's a negative accounting profit which makes them realize negative economic profit
• Is a Pigovian Tax that acts like a subsidy
• Sets baseline that suppliers owe the government money, which they government then gives back to them when someone occupies their unit
• Subsidy where the government is paying suppliers with their own money

Background

• Different implementations and aspects of vacancy taxes have been studied
• France⁵, Taiwan⁶, and Vancouver⁷
• France: Vacancy tax caused vacancy rates to fall by 13%
• Taiwan: 1% vacancy tax decreased the market price of housing between 2.6% and 8.8%
• France and Vancouver: Did not decrease new home construction

Model

ε_S = elasticity of supply

Around 2.2 in Pittsburgh housing market⁸

Determines slope of supply curve (in blue)

Model

P₁= current median unit annual cost

Q₁= current housing supply

P₁ and Q₁ determine current market equilibrium

All prices converted to annualized cost based on average rent/mortgage numbers, using price-rent ratio of 9.34

P₁=$9528

Q₁=513585

Model

Δ_P= necessary change in price to make 17,491 additional homes affordable⁹

Based on fair market value assessments

11% decrease in housing costs pushes enough homes below affordability threshold (30% of 50% of MHI)

P₁=$9528

Q₁=513585

Model

P₂= New equilibrium medium price = P₁ - Δ_P

Q₂= Housing supply after vacancies enter market

From here, we can draw a new supply curve with our new equilibrium (in orange)

P₁=$9528

Q₁=513585

P₂=$8545

Q₂=531076

Model

P₀= price at Q₂ under old supply curve

V = P₀ - P₂ = Vacancy tax

Because all of the prices have been converted to annual housing costs, V is an annual tax

P₁=$9528

Q₁=513585

P₂=$8545

Q₂=531076

P₀=$9676

V=$1131

Model

Because we know exactly which homes would become affordable after the price decrease, we can map out which neighborhoods add affordable housing.

The Vacancy Tax

• V =1130 but to allow the tax to adjust year on year the tax will be expressed as a percentage of the median home value
• R_v = 1130/89,000 = 1.27 % of median fairmarket unit value as determined by the Allegheny Property Assessment
• Flat rate, same amount is charged to every vacant unit
• Disproportionally incentivizes low-value, i.e. more affordable, units to be occupied as the supplier has to pay a greater percentage of the property value in vacancy taxes
• Worst case scenario and no vacant units become occupied, $19,764,830 increase in government revenue to put toward affordable housing policies

Assumptions

1. Pittsburgh Housing Market is perfectly competitive
2. All buyers and sellers are rational and act to maximize their utility
3. Supply Curve is linear with a constant Ɛ_s that doesn’t change when tax is added
4. Market is in equilibrium to begin with
5. Demand is constant
6. The distribution of vacant units is the same as the the entire housing market

Advantages of a Vacancy Tax

1. Revenue Neutral or Positive
1. Can fund other affordable housing programs in Pittsburgh
2. Cheaper and Faster than Building
• Technical Notes point out that its $5.1 billion to build and subsidize new housing
3. Spreads Out Distribution of Affordable Housing
• New affordable units are in areas where there aren’t a lot of affordable units for those making 50% of MHI

Newly affordable units vs. currently affordable units

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Appendix A - Model Variables

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• Inputs
• Ɛ_S = Elasticity of Supply, found by the Bank of England Study
• P₁ = Rent Adjusted Median Unit Price, calculated from all unit data set and price-rent ratio
• Q₁ = Number of Units are initial market equilibrium, calculated from all unit data set
• Q_v = Number of True Vacant Units, found in Allegheny Housing Report
• Outputs
• P₂ = Rent Adjusted Median Unit Price needed to make 17,491 home affordable
• Q₂ = Number of Units with Vacant Units occupied, Q₁ + Q_v
• P₀ = Price of Q₂ Units without Vacancy Tax
• V = Vacancy Tax, P₀ - P₂
• R_v = Tax as Percentage of Median Unit Price, V/Median Unit Price

Appendix B - Vacancy Unit Calculations

• Natural Vacancies include seasonal and rented or sold, not occupied⁶
• Always going to be frictions in the market, excluding natural vacancies accounts for that
• True Vacancies = Other vacant + for sale vacant + for rent vacant
• 12,683 + 1,278 + 3,530 = 17,491
• Q_v = 17,491

Appendix C - P₂ and Price to Rent Ratio Calculations

Price to rent ratio was calculated as the average rent divided by median

Appendix D - Model Code

https://colab.research.google.com/drive/1u9fBr73B-dwgU_QQMFPqOJLv7uqrZEcd?usp=sharing

Google Colab notebook with all the code used for analysis and visualization. To run the code and see the charts, click Runtime > Run all.

Appendix E - Citations

Bibliography

Aastveit, Knut, Bruno Albuquerque, and Andre Kallak Anundsen. “Changing Supply Elasticities and Regional Housing Booms.” Bank of England Working Paper No. 844, January 2020. https://doi.org/10.2139/ssrn.3520650.

Chen, Yen-Jong. “Modeling the Impacts of Vacancy Taxes on the Taiwan Housing Market.” Proceedings of the National Science Council, ROC Part C: Humanities and Social Science 11, no. 2 (2001).

“Comprehensive Housing Market Analysis Pittsburgh, Pennsylvania.” Office Of Policy Development And Research. Department of Housing and Urban Development, January 1, 2020. https://www.huduser.gov/portal/publications/pdf/PittsburgPA-CHMA-20.pdf.

Gallmeyer, Charles. “Vancouver Empty Home Tax: An Analysis of Taxation as a Solution to a Housing Crunch.” Pittsburgh Tax Review 18, no. 1 (2020). https://doi.org/10.5195/taxreview.2020.124.

Gilgoff, Julie. "Pandemic-Related Vacant Property Initiatives," Journal of Affordable Housing and Community Development Law 29, no. 2 (November 2020): 203-228

Hu, Jingting. “The Effects of British Columbia’s Vacancy Tax and Foreign-Buyer Tax Act on the Supply of New Residential Housing in Vancouver,” 2018.

“Pittsburgh_Housing_Needs_Assessment.” Pittsburgh: The City of Pittsburgh Affordable Housing Task Force, May 2016.

“property_assessments_post.” Pittsburgh, n.d.

Segú, Mariona. “The Impact of Taxing Vacancy on Housing Markets: Evidence from France.” Journal of Public Economics 185 (May 2020). https://doi.org/10.1016/j.jpubeco.2019.104079.

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Appendix F - Endnotes

1. Gilgoff, Julie. "Pandemic-Related Vacant Property Initiatives," Journal of Affordable Housing and Community Development Law 29, no. 2 (November 2020): 203-228
2. “Pittsburgh_Housing_Needs_Assessment.” Pittsburgh: The City of Pittsburgh Affordable Housing Task Force, May 2016.
3. Gilgoff, Julie. "Pandemic-Related Vacant Property Initiatives," Journal of Affordable Housing and Community Development Law 29, no. 2 (November 2020): 203-228
4. Segú, Mariona. “The Impact of Taxing Vacancy on Housing Markets: Evidence from France.” Journal of Public Economics 185 (May 2020). https://doi.org/10.1016/j.jpubeco.2019.104079.
5. Segú, Mariona. “The Impact of Taxing Vacancy on Housing Markets: Evidence from France.” Journal of Public Economics 185 (May 2020). https://doi.org/10.1016/j.jpubeco.2019.104079.
6. Chen, Yen-Jong. “Modeling the Impacts of Vacancy Taxes on the Taiwan Housing Market.” Proceedings of the National Science Council, ROC Part C: Humanities and Social Science 11, no. 2 (2001).
7. Hu, Jingting. “The Effects of British Columbia’s Vacancy Tax and Foreign-Buyer Tax Act on the Supply of New Residential Housing in Vancouver,” 2018.
8. Aastveit, Knut, Bruno Albuquerque, and Andre Kallak Anundsen. “Changing Supply Elasticities and Regional Housing Booms.” Bank of England Working Paper No. 844, January 2020. https://doi.org/10.2139/ssrn.3520650.
9. “property_assessments_post.” Pittsburgh, n.d.
10. ​