Week 9 Household Tenure Decisions

Question 1

What does a household tenure decision refer to?

Answer 1

An individuals decision to rent or buy a house.

Question 2

Give 3 reasons why housing is important

Answer 2

• Housing provides shelter
• Housing wealth is a major component of asset holding in the UK and other countries- this can be a capital gains investment.
• Housing is seen as a measure of success and achievement.

Question 3

How do we calculate value of the rent for a rent?

Answer 3

𝑝𝑞 (rent) = 𝛼𝑝^𝛽+1𝑦^𝜃

Question 4

What do the symbols in the equation 𝛼𝑝^𝛽+1𝑦^𝜃 mean?

Answer 4

• p is the price per unit of housing
• y is income
• parameters 𝛽 𝑎𝑛𝑑 𝜃 are price (negative) and income (positive) elasticities

Question 5

For a homeowner, what is the purchase price per unit of housing, and the is the value of the house?

Answer 5

• 𝑝𝑞 = 𝛼𝑝^𝛽+1𝑦^𝜃
• 𝑝 is the purchase price per unit of housing
• 𝑝𝑞 is the is the value of the house

Question 6

How can we explore our elasticities of demand?

Answer 6

• Substitute E for pq, then take logs
• E = 𝛼𝑝^𝛽+1𝑦^𝜃
• ln(E) = ln(𝛼) + (𝛽+1) ln(𝑝) + 𝜃ln(y)

Question 7

• What does this equation do and what doesn’t it require?

* ln(E) = ln(𝛼) + (𝛽+1) ln(𝑝) + 𝜃ln(y)

Answer 7

• This gives housing expenditure as a function of price and income
• It does not require a physical measure of housing consumption (q)

Question 8

Give one empirical fact each about housing demand and housing expenditure.

Answer 8

• Housing demand is price inelastic, indicating low price
responsiveness
• Housing expenditure comprises a smaller and smaller share of income as income rises

Question 9

• What is an alternative way to calculate housing demand called?
• What is this?

Answer 9

• The Hedonic approach
• This recognises that a dwelling is a bunch of attributes, where the value is the function of a constant and a list of attributes, eg number of bedrooms/bathrooms/square footage etc
• The houses value is then a regression of the form:
𝐻𝑜𝑢𝑠𝑒 𝑣𝑎𝑙𝑢𝑒 = 20 + 600 ∗ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑡ℎ𝑟𝑜𝑜𝑚𝑠 + 150 ∗ 𝑔𝑎𝑟𝑎𝑔𝑒 …
Here a second bathroom is worth £600, a garage is worth £150…

Question 10

Who were one of the first people to estimate a house price regression?

Answer 10

Grether and Mieszkowski (1974)

Question 11

What do traditional models claim tenure choice is based on, and who introduced this model?

Answer 11

• Traditional models the decisions are based on relative user costs based on either renting or owning. This can include the households level of income and Life-cycle traits which reflect preferences for homeownership.
• This model was introduced by Rosen (1979)

Question 12

What is utility from home ownership given by?

Answer 12

• The following indirect utility function:
𝑈𝑜 = 𝑓(𝑝𝑜, 𝑝𝑥, 𝑦)
• 𝑝𝑜 is the user cost of housing services associated with homeownership,
• 𝑝𝑥 is the price of all other goods
• 𝑦 is the permanent income

Question 13

Utility from renting is given by what following indirect utility function?

Answer 13

• 𝑈𝑟 = 𝑓(𝑝𝑟, 𝑝𝑥, 𝑦)
• 𝑈𝑟, is the indirect utility achieved conditionally on renting
• 𝑝𝑟 is the user cost/or unit price of services associated with renting

Question 14

When does a household choose to own a house instead of renting?

Answer 14

• A household choses to own if the indirect utility of owning is greater than utility associated with renting:
• 𝑈𝑜 > 𝑈r

Question 15

What is the binary choice model of a household choosing to buy instead of renting?

Answer 15

𝑈∗ = 𝑈o − 𝑈𝑟 = 𝑈(𝑝𝑜/𝑝𝑟,𝑦,𝑧)

Question 16

Why is the cost per unit more complicated when a consumer owns a home rather than rents?

Answer 16

As costs include:
◦ Mortgage payments
◦ Property taxes
◦ Depreciation
◦ Capital gains
◦ Maintenance costs…

Question 17

What is the annual cost faced by the homeowner denoted by?

Answer 17

(𝑖 + ℎ + 𝑑 − 𝑔) V
V →the value of the house bought using 100 percent mortgage (no deposit).
iV→the annual interest cost, where i is the interest rate and V is the full mortgage value which is the price of the house
dV → the depreciation
hV → the property tax payment
gV → the capital gains (as a result of rising overall demand in the economy)
◦ Note: g could be negative

Question 18

What is house value (V) given by?

Answer 18

• Punit*q
• 𝑝𝑢𝑛𝑖𝑡 is the price per unit of housing
• 𝑞 is the amount of housing consumption e.g. size of the house (square metres of floor space)

Question 19

What is the owner occupied cost?

Answer 19

• (𝑖 + ℎ + 𝑑 − 𝑔) P𝑢𝑛𝑖𝑡q

Question 20

Therefore what is the cost per unit of consumption?

Answer 20

• (𝑖 + ℎ + 𝑑 − 𝑔) P𝑢𝑛𝑖𝑡

Question 21

What do households compare when deciding to be an owner or a renter?

Answer 21

Households compare the cost per unit of owning to the cost per unit of a renter, 𝑝r

Question 22

What can of costs can be tax deductible?

Answer 22

• Mortgage payments
• Property taxes
• Depreciation (landlords only)

Question 23

What does 𝜏 denote?

Answer 23

𝜏 denotes the owner occupiers income tax rate.

Question 24

So, including tax deductions, what is the cost per unit of housing?

Answer 24

(1 − 𝜏 (𝑖 + ℎ) + 𝑑 − 𝑔)𝑉 and (1 − 𝜏 (𝑖 + ℎ) + 𝑑 − 𝑔) 𝑝𝑢𝑛𝑖𝑡 = User cost of owning

Question 25

What will happen to the quantity of housing demand if the purchase price per unit of housing 𝑝𝑢𝑛𝑖𝑡, mortgage interest rate (i) or the property tax rate (h) rise?

Answer 25

Q will fall

Question 26

What will increased depreciation do to housing demand?

Answer 26

Increased depreciation will raise the user cost, thus reducing housing demand.

Question 27

What will be the effect on housing demand of an increase in capital gains (g)?

Answer 27

Increases in capital gains (g) will reduce user costs and as a result should increase demand

Question 28

What does μ denote?

Answer 28

μ is the landlord’s income-tax rate

Question 29

What is the landlord’s after-tax cost per unit of housing purchased?

Answer 29

(1– 𝜇)(𝑖 + ℎ + 𝑑)P𝑢𝑛it

Question 30

What happens to a landlords capital gains?

Answer 30

The landlord also earns capital gains of value g, but is only able to keep, (1– 𝜇)𝑔P𝑢𝑛𝑖𝑡 of these since they are taxed.

Question 31

What is the revenue a landlord gains from renting?

Answer 31

(1– 𝜇)Pr

Question 32

As we assume perfect competition, what does this mean for the housing market?

Answer 32

That profits in the housing market = 0

Question 33

What is the profit per unit of housing?

Answer 33

• the after tax income minus costs

* (1– 𝜇) (𝑝𝑟−(𝑖 + ℎ + 𝑑 − 𝑔) 𝑝𝑢𝑛𝑖𝑡)

Question 34

What is therefore the user cost of rental housing, and how does this differ to the price of owning?

Answer 34

• 𝑝𝑟 = (𝑖 + ℎ + 𝑑 − 𝑔)𝑝𝑢𝑛𝑖𝑡 = 𝑢𝑠𝑒𝑟 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑟𝑒𝑛𝑡𝑎𝑙 ℎ𝑜𝑢𝑠𝑖𝑛g

* The price of renting doesn’t include income tax term

Question 35

Which tenure mode will individuals choose?

Answer 35

The cheaper one

Question 36

Why will owning always be preferred?

Answer 36

• As due to the inclusion of the household’s income tax rate, the unit cost of owning < the unit cost of renting
• ((1 − 𝜏)(𝑖 + ℎ) + 𝑑 − 𝑔) 𝑝𝑢𝑛𝑖𝑡 < (𝑖 + ℎ + 𝑑 − 𝑔) 𝑝𝑢𝑛𝑖t

Question 37

Does a renter’s user cost depend on the household’s income tax rate?

Answer 37

No

Question 38

In the US, what are landlords allowed to deduct?

Answer 38

• Accelerated depreciation

* For the landlord this is d+e

Question 39

So when accounting for accelerated depreciation, what is the new user cost of renting?

Answer 39

(𝑖 + ℎ + 𝑑 − 𝑔) 𝑝𝑢𝑛𝑖𝑡 − 𝜇𝑒𝑝𝑢𝑛𝑖𝑡/(1–𝜇) = 𝑝𝑟 = new user cost of renting

Question 40

What is the slope of the demand curve for owning a home?

What about for renting?

Answer 40

• For owning a home, since, user costs fall as 𝜏 increase, this will give a downward sloping curve
• Since rent does not depend on the income tax rate, this is horizontal

Question 41

What is therefore the general conclusion on tenure choice?

Answer 41

• Owning is cheaper for those with higher tax rate 𝜏 and renting is cheaper for those who have lower tax rates.
• Low income household will be renters, higher income households will be owners.

Question 42

What does 𝜏* represent?

Answer 42

The threshold 𝜏* is the tax rate that divides renters and owners.

Question 43

What will happen if there is a decrease in landlord’s income tax?

Answer 43

A decrease in the landlords income tax, increases the user cost associated with housing and increases the share of home owners.

Question 44

What is the biggest emission from the standard tenure model?

Answer 44

Deposits- a consumer lacking the funds for a down payment will not be able to own a home, so renting is the only option.

Question 45

What conclusions can we take from the amendment of a deposit requirement to the model?

Answer 45

• Consumers with income-tax rates below the cut off level 𝜏* will still rent
• Consumers with income-tax rates above the 𝜏* threshold will have to be patient enough to accumulate the deposit. Impatient consumers will rent instead.

Question 46

What is the constraint to home ownership?

Answer 46

Current liquid wealth

Question 47

How can the difference in utility between owning and renting be written?

Answer 47

• 𝑉∗= 𝑣(𝑊, 𝑝ℎ, 𝑧)
• 𝑊 → the net wealth of the household,
• 𝑝ℎ → the price of housing
• z → captures demographics that reflect how permanently formed and/or mobile the household is

Question 48

Empirically, which constraint dominates in terms of their practical impact on home ownership decisions- the wealth constraint or the income constraint?

Answer 48

Empirically we find wealth constraints dominate income constraints in terms of their practical impact on
home ownership decisions

Question 49

What did Jones (1989) find?

Answer 49

• Jones (1989) found that wealth opposed to income has a important impact of ownership decisions
• The adverse impact of being highly wealth constrained exceeds that of being highly income constrained

Question 50

What did Linneman & Wachter (1989) suggest?

Answer 50

Linneman & Wachter (1989) suggested that if a

family cannot make the required down-payment on its desired home, its most viable alternative is to rent.

Question 51

How does the presence of borrowing constraints

adversely affects homeownership propensities?

Answer 51

If people cannot afford a deposit, they do not have access to credit- aka they cannot obtain a mortgage

Question 52

• What happened to home ownership rates in the US in the 1990s?
• Why was this?
• What does this imply?

Answer 52

• Home ownership rates rose significantly in the 1990s
• As many mortgages had loan-to-value ratios of >95%
• This implies that wealth and not income is the key constraint in determining home ownership

Question 53

What did Jones (1995) find?

Answer 53

The higher the net wealth, the greater the liklehood of being a homeowner.

Question 54

What is the effect on home ownership rates for those with income uncertainty?

Answer 54

• Greater income uncertainty reduces the probability of home ownership
• Borrowers facing greater income uncertainty may face restrictions in accessing the mortgage market

Question 55

What did Robst et al. (1999) find?

Answer 55

Their findings suggested greater uncertainty

is associated with a lower likelihood of home ownership

Question 56

What other factors effect tenure decisions?

Answer 56

• Expected mobility, for example if you are moiving frequently, undergoing transaction costs (eg solicitors fees) may not be worth it
• Pride of ownership- any derived utility from owning a home could lower the cost of homeowning
• Risk- for example if an individual’s income is correlated with house prices, it may be more risky for them to purchase a house.