# Prejudice and Discrimination in Housing - PowerPoint PPT Presentation

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Prejudice and Discrimination in Housing. © Allen C. Goodman 2000. Yinger. Wants to work with housing price gradient that we used before. Discusses prejudice as disutility of W or B from living with or near members of the other race. U w = U w [ Z w , X w , r(u) ],

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## Prejudice and Discrimination in Housing

### Yinger

• Wants to work with housing price gradient that we used before.

• Discusses prejudice as disutility of W or B from living with or near members of the other race

Uw = Uw [ Zw, Xw, r(u) ],

Where Z is everything else, X is housing and r is race at u.

### Prejudice

ONE FORM OF r(u) IS:

Hw = Xw Dw [r(u)],

WHERE Dw(0) = 1, D' < 0.

1

DW

DB

D*B

D*w

REDEFINES TERMS AS:

Hw = Hw [Xw, r(u)].

R = fraction B

### Using a Cobb-Douglas Ftn.

USING A COBB-DOUGLAS UTILITY FUNCTION:

U = Zc1Hc2, OR

Ln U = c1 Ln Z + c2 Ln X + c2 Ln D [r(u)]

SUBSTITUTION, AGAIN, AS IN THE MILLS MODEL, YIELDS PRICE AND RENT-DISTANCE FUNCTIONS:

21> Pw (u) = Kw (Y - tu) 1/k Dw [ r(u)]; Kw is a constant of int.

_ __

22> Rw (u) = R [(Y - tu)/(Y - tu)] 1/ak {Dw [r(u)]/ Dw [r(u)]}1/a

k = constant, a = land coefficient in housing prod.

### For W, for B

___

22> Rw (u) = R [(Y - tu)/(Y - tu)] 1/ak {Dw [r(u)]/ Dw [r(u)]}1/a

For prejudiced W, function must be lower at locations with higher concentration of B.

Can come up with similar for B.

Hb = Xb Db [r(u)],

WHERE Db(1) = 1, D' > 0.

___

24> Rb (u) = R [(Y - tu)/(Y - tu)] 1/ak {Db [r(u)]/ Db [r(u)]}1/a

### Integrated eq’m

_ _ _

22> Rw (u) = R [(Y - tu)/(Y - tu)] 1/ak {Dw [r(u)]/ Dw [r(u)]}1/a

_ _ _

24> Rb (u) = R [(Y - tu)/(Y - tu)] 1/ak {Db [r(u)]/ Db [r(u)]}1/a

Must both hold if there will be an integrated eq’m.

If so:

_ _

Dw [r(u)]/ Dw [r(u)]} = Db [r(u)]/ Db [r(u)]}

For this to hold, r must be the same everywhere  total integration.

### Segregated eq’m

_ _ _

22> Rw (u) = R [(Y - tu)/(Y - tu)] 1/ak {Dw [r(u)]/ Dw [r(u)]}1/a

_ _ _

24> Rb (u) = R [(Y - tu)/(Y - tu)] 1/ak {Db [r(u)]/ Db [r(u)]}1/a

If B move in, neighborhood becomes more (less) attractive to B, less attractive to W. Leads to total segregation.

### Final conclusions

• If there is complete segregation, or integration, racial composition will not affect the rent-distance function.

• Complete segregation is stable eq’m ONLY in the case of prejudice on the part of all B and all W.

• Complete integration is unstable if everyone is prejudiced, or if SOME housholds prefer to live in a mixed area.

• To see this see next slide:

### Suppose full segregation

u*

r(u) = 1; u < u* all B

r(u) = 0; u > u* all W

RB*(u*) = RW(u*)

Since preference for mixing implies Db(0) > Db(1), some blacks will outbid some whites for white land  segregation cannot be stable.

Same for integration.

W

W

B

### Courant – Search Model

There seem to be lots of situations (such as racial steering) which require different models.

Suppose we have 2 groups, B and W. Several assumptions:

• Housing is heterogeneous

• Housing  hedonic price functions

• Usual utility functions

• Buyers know the distribution of housing available, and their utility functions. They evaluate each house:

Where VL is lowest utility, and VH is highest.

### Searching

• Enough houses on market at any one time.

• Constant cost of looking at a house is c.

At any stage, the utility of looking for one more house leads to utility such that:

Vo

V = max {

-c + (1 - F (Vo)) (E(V|VVo) + Vo F (Vo)

Vo is utility associated with best house found so far. Next line is expected utility after one more search.

### Searching

Rational buyer stops searching when first line of expression is equal to or greater than second.

This gives you the optimal V = V*.

### Example

Lowest value is 20,000  annual = 2,000

Highest value is 30,000 annual = 3,000

c = 30.

The larger the value of

c, the bigger the difference

between V and VO.

### Seller’s aversion

CONSIDER n NEIGHBORHOODS IN THE CITY, 1, ..., n. FOR EACH NEIGHBORHOOD, THERE IS A NONZERO PROBABILITY j THAT WHITES WON'T SELL. ASSUME THAT j FOR BLACKS = 0. PROB. THAT BLACK WILL FIND AVERSE SELLER = j * (PCT WHITE) = j.

Assume that j varies across neighborhoods.

Then, order neighborhoods:

1  2  3  4  5 …  n

### Seller’s aversion

Then, order neighborhoods:

1  2  3  4  5 …  n

When we optimize, we compare:

Vo

V = max {

-c + (1 - F (Vo)) (E(V|VVo) + Vo F (Vo)

Vo

V = max {

-c1 + (1-1)[(1 - F (Vo)) (E(V|VVo)+ Vo F (Vo)] + 1 V0.

cost + Return w/o averse seller + Return w/ averse seller

### Seller’s aversion

Vo

V = max {

-c1 + (1-1)[(1 - F (Vo)) (E(V|VVo)+ Vo F (Vo)] + 1 V0.

cost + Return w/o averse seller + Return w/ averse seller

-c2, etc.

If there isn’t an averse seller, then  = 0, and we’re back where we were before.

Otherwise we get:

### Seller’s aversion

Must look at 1/(1-j) houses for everyone s/he has option to purchase.

If housing prices are identical in neighborhoods, B will only search for housing in those neighborhoods where  is lowest.

This implies:

### Implications

• Sellers’ aversion is consistent with a price differential in which housing is purchased by B in B neighborhoods at higher prices than those obtaining in W and integrated neighborhoods.

• Maximum price differential is an increasing function of the fraction of W sellers in a neighborhood who are averse to dealing with B.

• If there is a small price differential, B will never search, so nothing will eliminate market segmentation.