Abstract
There are cities in the world which have experienced substantial numbers of foreign buyers in the local housing markets, thereby pushing up the real estate prices to the levels beyond the affordability of local residents. To suppress foreign influences in the forming of housing bubbles, governments have resorted to short-term measures of stamp duty or raising the duty rate for non-local buyers, increasing down payments and restricting or even forbidding non-local purchases. These new measures may help contain the demand for housing, but short of being the first-best optimal housing policy for an open economy with significant non-local and foreign buyers. We argue that the first-best policy is to tax non-local and foreign buyers and then use the tax revenue generated to subsidize domestic low- and middle-income buyers. The optimal tax rate under this compensated scheme is smaller than the tax rate under the lump-sum transfer of tax revenue to all residents.
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Notes
Hong Kong is even more densely populated than Singapore that has a population of more than 3 million with a land area of 648 sq km. In Singapore, more than 80 % of the people stay in public housing.
This important new factor of foreign purchase on housing demand was non-existent a decade ago. See the early studies on the Hong Kong property prices, e.g., Chou and Shih (1995).
Tourism is another notable example in transforming non-traded goods into tradable.
On the top of the current stamp duty, a special stamp duty (SSD) of 5–15 % was imposed after November 20, 2010 for the residential property sold within 24 months of purchases.
By normalizing housing expenditure of each foreign buyer to unity, their total demand for housing is C ∗2 (p,α) = α/p.
The stability analysis is provided in the Appendix.
Note that Δ τ = S τ − (1 + τ ∗)(m/p)[C ∗2 + τ ∗ p(∂C ∗2 /∂(1 + τ ∗)p)] > 0 is required for stability, in which S τ = R 22 − E 22 − (1 + τ ∗)(∂C *2 /∂(1 + τ ∗)p) > 0.
The formula for computing the optimal tax rate resembles that for optimum tariff (cf., Caves, et al., 1996, p. S-43).
In the literature, this is referred to as the cash-in-advance constraint. See Stockman (1981).
Hong Kong has adopted the linked exchange rate system to the U.S. dollar since 1983, resulting in her interest rate to follow closely with the U.S. interest rate. Thus, Hong Kong has no monetary policy.
Note that Δ ϕ = (1 − tm)S ϕ − (m/p){(1 + s ∗)[C ∗2 + s ∗ p(∂C ∗2 /∂(1 + s ∗)p)] + s(1 + s)pE 22} > 0 and S ϕ = R 22 − (1 + s)E 22 − (1 + s ∗)(∂C ∗2 /∂(1 + s ∗)p) > 0.
During 2010, the ratios of domestic households in Hong Kong live in public rental housing, subsidized sale flats and private housing are respectively 31.6 %, 16.7 % and 50.9 %.
The public housing units in Hong Kong have been fully occupied.
We need to have that Δ s = (n/q)(p − q)S s + (n/q − m/p)[H 2–t ∗ C ∗2 − t ∗(1 + t ∗)p(∂C ∗2 /∂(1 + t ∗)p)] − (m/p)(n/q)(p − q)(H 2 + C ∗2 ) > 0 for stability, where S s = R 22 − E 22 − (1 + t ∗)(∂C ∗2 /∂(1 + t ∗)p) > 0.
It is noted that t * o = 1/[(1 + B)ε * − 1] < τ * o = 1/(ε * − 1), where B = (n/q)C ∗2 /(n/q − m/q)H 2 > 0.
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Appendix
Appendix
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1.
Stability
Following Dei (1985), the adjustment for the housing price is:
$$ \overset{\cdot }{p}=\rho Z(p), $$where the dot denotes a time derivative, ρ is the speed of adjustments and Z is the excess demand for housing, i.e., Z = E 2(1,p,u) + C ∗2 (p,α) − R 2(1,p,V). From (1) and (2), u is a function of p and so is Z for given α and V. A necessary and sufficient condition for stability is: dZ/dp < 0. Solving (1) and (2), we obtain: dp/dZ = − 1/Δ, where Δ = R 22 − E 22 − ∂C ∗2 /∂p − (m/p)C ∗2 . By the stability condition, it requires that Δ < 0.
Letting η[ = (∂R 2/∂p)(p/R 2)] denote the price elasticity of the housing supply and also letting ε [= − (∂C 2/∂p)(p/C 2)] and ε ∗[= − (∂C ∗2 /∂p)(p/C ∗2 )] be respectively the price elasticities of housing demand by domestic and foreign buyers, we can rewrite Δ as Δ = − (R 2/p)(m + ε − ε *)[ρ * − (η + e)/(m + ε − ε *)], where ρ ∗( = C ∗2 /R 2) is the ratio of housing bought by foreigners in the economy. Hence, stability requires that ε * < m + ε and ρ * < (η + ε)/(m + ε − ε *).
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2.
Derivation of (7)
Totally differentiating (5) and (6), we have:
$$ \begin{array}{l}{E}_u du+\left\{{E}_2-{R}_2-{\tau}^{\ast }{C}_2^{\ast }-{\tau}^{\ast}\left(1+{\tau}^{\ast}\right)p\left[\partial {C}_2^{\ast }/\partial \left(1+{\tau}^{\ast}\right)p\right]\right\} dp=p\left\{{C}_2^{\ast }+{\tau}^{\ast }p\left[\partial {C}_2^{\ast }/\partial \left(1+{\tau}^{\ast}\right)p\right]\right\}d{\tau}^{\ast },\hfill \\ {}\hfill {E}_{2u} du+\left\{{E}_{22}-{R}_{22}+\left(1+{\tau}^{\ast}\right)\left[\partial {C}_2^{\ast }/\partial \left(1+{\tau}^{\ast}\right)p\right]\right\} dp=-p\left[\partial {C}_2^{\ast }/\partial \left(1+{\tau}^{\ast}\right)p\right]d{\tau}^{\ast }.\hfill \end{array} $$Solving these two equations by using Cramer’s rule and then combining the terms, we obtain du/dτ * given in (7).
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3.
Derivation of (9)
Totally differentiating (1) and (2), we have:
$$ \begin{array}{l}\hfill {E}_u du-{C}_2^{\ast } dp={R}_V dV,\hfill \\ {}\hfill {E}_{2u} du+\left({E}_{22}-{R}_{22}+\partial {C}_2^{\ast }/\partial \mathrm{p}\right)\mathrm{dp}={R}_{2V}\mathrm{d}V.\hfill \end{array} $$Solving these equations yields the expression of dp/dV in (9).
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4.
Derivation of (13)
Totally differentiating (10) and (11), we have:
$$ \begin{array}{l}\left({E}_u- sp{E}_{2u}\right) du+\left\{\left(1+{s}^{\ast}\right){C}_2^{\ast }+s\left(1+s\right)p{E}_{22}+s\left(1+{s}^{\ast}\right)p\left[\partial {C}_2^{\ast }/\partial \left(1+{s}^{\ast}\right)p\right]\right\} dp=\hfill \\ {}\begin{array}{cc}\hfill \hfill & \hfill \hfill \end{array}p\left\{{C}_2^{\ast }+s{p}^{\ast}\left[\partial {C}_2^{\ast }/\partial \left(1+{s}^{\ast}\right)p\right]\right\}d{s}^{\ast },\hfill \\ {}{E}_{2u} du+\left\{{E}_{22}\left(1+s\right)-{R}_{22}+\left(1+{s}^{\ast}\right)\left[\partial {C}_2^{\ast }/\partial \left(1+{s}^{\ast}\right)p\right]\right\} dp=-p\left[\partial {C}_2^{\ast }/\partial \left(1+{s}^{\ast}\right)\mathrm{p}\right]d{s}^{\ast },\hfill \end{array} $$By using Cramer’s rule to solve these two equations, we obtain du/ds * in (13).
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5.
Totally differentiating (14) yields:
$$ {E}_u du+{H}_v dv-\left({R}_2-{E}_2\right) dp=-\left({R}_V-{G}_V\right) Vd\beta, $$and then using (15), we obtain (17) as:
$$ {E}_u du+{H}_v dv-{C}_2^{\ast } dp=-\left({R}_V-{G}_V\right) Vd\beta . $$Totally differentiating (15) and (16), we have:
$$ \begin{array}{l}{E}_{2u} du+\left\{\left.{E}_{22}-{R}_{22}+\partial {C}_2^{\ast }/\partial p\right]\right\} dp=-{R}_{2V} Vd\beta, \hfill \\ {}\hfill {H}_{2v} dv={G}_{2V} Vd\beta .\hfill \end{array} $$Solving the above three equations, we obtain dp/dβ given in (18).
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6.
Totally differentiating (20) and then using (19), we obtain (22) as:
$$ {E}_u du+{H}_v dv=\left({C}_2^{\ast }+{H}_2\right) dp={C}_2^{\ast } dp+{t}^{\ast}\left[p/\left(p-q\right)\right]{C}_2^{\ast } dp. $$Totally differentiating (19), (20) and (21), we have:
$$ \begin{array}{l}\left(p-q\right){H}_{2v} dv+\left\{{H}_2-{t}^{\ast }{C}_2^{\ast }-{t}^{\ast}\left(1+{t}^{\ast}\right)p\left[\partial {C}_2^{\ast }/\partial \left(1+{t}^{\ast}\right)p\right]\right\} dp=p\left\{{C}_2^{\ast }+{t}^{\ast }{p}^{\ast}\left[\partial {C}_2^{\ast }/\partial \left(1+{t}^{\ast}\right)p\right]\right\}d{t}^{\ast },\hfill \\ {}{E}_u du+{H}_v dv-\left({H}_2+{C}_2^{\ast}\right) dp=0,\hfill \\ {}{E}_{2u} du+{H}_{2v} dv+\left\{{E}_{22}-{R}_{22}+\left(1+{t}^{\ast}\right)\left[\partial {C}_2^{*}/\partial \left(1+{t}^{\ast}\right)p\right]\right\} dp=\left.-p\left[\partial {C}_2^{\ast }/\partial \left(1+{t}^{\ast}\right)p\right]\right\}d{t}^{\ast },\hfill \end{array} $$Solving these three equations, we obtain dp/dt * expressed in (23).
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7.
Derivation of (24)
According to (22), the change in social welfare is
$$ {E}_u\left( du/d{t}^{\ast}\right)+{H}_v\left( dv/d{t}^{\ast}\right)=\left({H}_2+{C}_2^{\ast}\right)\left( dp/d{t}^{\ast}\right). $$Substituting dp/dt * in (23) into this equation, we have:
$$ \begin{array}{l}{E}_u\left( du/d{t}^{\ast}\right)+{H}_v\left( dv/d{t}^{\ast}\right)\hfill \\ {}=-p{C}_2^{\ast}\left({C}_2^{\ast }+{H}_2\right)\left(n/q-m/p\right)\left[\left(1+B\right){\varepsilon}^{\ast }-1\right]\left[{t}^{\ast }-1/\left[\left(1+B\right){\varepsilon}^{\ast }-1\right.\right]/\left(1+{t}^{\ast}\right){\varDelta}_{\mathrm{s}}\hfill \\ {}=-p{C}_2^{\ast}\left({C}_2^{\ast }+{H}_2\right)\left(n/q-m/p\right)\left[\left(1+B\right){\varepsilon}^{\ast }-1\right]\left({t}^{\ast }-{t}^{\ast_{\mathrm{o}}}\right)/\left(1+{t}^{\ast}\right){\varDelta}_{\mathrm{s}},\hfill \end{array} $$
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Chao, CC., Yu, E.S.H. Housing Markets with Foreign Buyers. J Real Estate Finan Econ 50, 207–218 (2015). https://doi.org/10.1007/s11146-014-9454-3
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DOI: https://doi.org/10.1007/s11146-014-9454-3