Price Discrimination and Mortgage Choice 

Jamie Coen1 Anil Kashyap2 May Rostom3 

1Imperial College London 

2Chicago Booth and NBER 

3Bank of England 

FDIC Consumer Research Symposium - March 2024 

Views are solely those of the authors and so cannot be taken to represent those of 

the Bank of England or any of its committees. 

1 
What we fnd 

1 Most people face a daunting number of mortgages to choose 

from. 

2 On average, people don’t pick particularly well, but cost 

implications small. 

3 A small percentage (7%) leave a lot of money on the table. 

• High LTV & LTI customers ! Young, frst-time-buyers. 

• Bad menus ! Expensive choices. 

4 Evidence consistent with price discrimination to proft from 

poor decisions or lack of alternatives. We rule out cost and 

risk. 

Literature Summary Stats 

2 
UK market structure 

• Most mortgages: fxed rate period of 2, 3, or 5 years. 

• Long period of foating rate. 

• People roll over their mortgage multiple times. 

• 5 components: initial period, initial rate, upfront fee, reset 

rate, maximum LTV. 

• Customers face multi-product menus at multiple banks. 

Choice Set Data 

3 
Evaluating choices 

1 Find all mortgages on o ̇er at given LTV for given loan 

amount and initial payment period. 

• Both within the chosen bank, and across all 6 banks. 

2 Compute NPV of payment over frst 7 years. 

3 Rank NPVs. 

4 Defne baseline mortgage: 15th percentile of choice set. 

NPV calculations Example Within vs. Across Banks 

4 
Alternative Ranking 

Results hold for two other ranking methods: 

1 Immediate refnancing: Assume refnancing at the end of 

the promotion period 

• Eliminates relevance of the reset rate 

2 Dominance: Find mortgages that dominate in at least one 

dimension 

• Rules out private information 

Ranking Pros and Cons 

5 
How well do people pick? 

Choice set size Pctile chosen

25 46 27 th pctile

Median 73 47

75th pctile 101 70

66%

0.00

0.25

0.50

0.75

1.00

−4 −3 −2 −1 0 1

Cost saving vs reference (% income)

Cumulative distribution

Expensive choice: costs  2.5% of monthly net income. 

Within bank Choice proliferation 

6 
Time Series of Expensive choices 

0

10

20

30

2009 2010 2011 2012 2013 2014 2015

Probability expensive choice (%)

Across Within

7 
Where do expensive choices come from? 

Two aspects to an expensive choice: 

1 Quality of your choice: given your menu, did you pick well? 

• choice = percentile rank of choice you made.

2 Quality of choice set: how many bad choices were on o ̇er? 

• bad tail = % of expensive mortgages on o ̇er.

8 
Menu variation 

0

20

40

60

80

2009 2010 2011 2012 2013 2014 2015

Bad tail (%)

75th pctile 90th pctile Median

Menu prevents the median person from picking expensive option, 

but sometimes the menu is flled with bad choices. Within bank

9 
Menu Quality and Expensive Choices 

• Plot probability of making expensive choice in a given month

against average size of bad tails in menu o ̇erings.

• Menu quality is the key driver in making expensive choices.

Within bank 

10 
Is it more important to get the right bank or to pick well? 

MFX 

Dependent variable:

Expensive choice across 

MFX MFX MFX MFX 

Cost di ̇erence within bank 

Cost di ̇erence vs. best bank 

Bad tail 0.304

(0.001) 

0.016

(0.0002) 

0.279

(0.001) 

0.023

(0.0002) 

0.224

(0.001) 

0.023

(0.0002) 

0.029

(0.0002) 

0.150

(0.001) 

Bank dummies 

Product dummies 

Pseudo R-squared 

Mean dependent variable 

Observations 

No

Yes 

0.09 

0.067

883,459 

No

Yes 

0.56 

0.067 

883,459 

No

Yes 

0.63 

0.067

883,459 

No

Yes 

0.59 

0.067

883,459 

No

Yes 

0.71 

0.067 

883,459 

Note: p<0.1; p<0.05; p<0.01 

• Role for where you shopped and what you picked, but menu 

quality biggest driver of expensive choices. 

11 
Low LTI High LTI Low LTI High LTI

Low LTV Low LTV High LTV High LTV

(53%) (27%) (15%) (5%)

0

5

10

15

20

25

Bad tail (%)

Who gets a bad menu? 

Note: High LTV=LTV> 85%. High LTI=LTI> 4 

Banks o ̇er worse menus to high LTV & LTI customers. Within Banks 

12 
Low LTI Low LTI High LTI High LTI

Low LTV High LTV Low LTV High LTV

(53%) (26%) (15%) (5%)

0

5

10

15

20

Bad tail (%)

Outside Within

Choice sets within and outside banks 

Note: High LTV=LTV> 85%. High LTI=LTI> 4 

13 
What does LTV and LTI load on? 

High LTV MFX 

Dependent variable:

High LTI High LTV & LTI 

MFX MFX 

Young 

Old 

First-time buyer 

Poor 

Rich 

0.071

(0.001) 

−0.095

(0.002) 

0.234

(0.001) 

−0.076

(0.001) 

0.032

(0.001) 

0.023

(0.001) 

−0.079

(0.001) 

0.037

(0.001) 

0.065

(0.001) 

−0.067

(0.001) 

0.016

(0.001) 

−0.035

(0.001) 

0.042

(0.001) 

−0.003

(0.001) 

−0.014

(0.001) 

Bank dummies 

Product dummies 

Pseudo R-squared 

Mean dependent variable 

Observations 

Yes 

Yes 

0.12 

0.32

894,901 

Yes 

Yes 

0.05 

0.2

894,901 

Yes 

Yes 

0.05 

0.05

894,901 

Note: p<0.1; p<0.05; p<0.01 

Young people & frst-time buyers choose high LTV and high 

LTI mortgages. 

14 
Who chooses poorly? 

Dependent variable:

Expensive choice across MFX MFX

Young 0.018

(0.001) 0.005(0.0004)

Old −0.031

(0.001) −0.006(0.001)

First-time buyer 0.005

(0.001) −0.005(0.0004)

Poor 0.003

(0.001) 0.001(0.0004)

Rich −0.006

(0.001) −0.006(0.0004)

Bad tail 0.303

(0.001)

Bank dummies Product dummies Pseudo R-squared Mean dependent variable ObservationsNo

Yes

0.09

0.067

883,459

No

Yes

0.56

0.067

883,459

Note: p<0.1; p<0.05; p<0.01

• Young people and FTB are more likely to pick expensively. 

• ! These e ̇ects are driven by quality of the menu. 

Within bank Dominated 

15 
Potential explanations 

Risk? 

16 
Potential explanations 

Risk? 

1 Default extremely rare. 

2 Default patterns do not follow menu pattern. 

3 Risk may cause average price to vary by leverage, but not 

price dispersion. 

16 
Potential explanations 

Risk? 

1 Default extremely rare. 

2 Default patterns do not follow menu pattern. 

3 Risk may cause average price to vary by leverage, but not 

price dispersion. 

Approval standards? 

16 
Potential explanations 

Risk? 

1 Default extremely rare. 

2 Default patterns do not follow menu pattern. 

3 Risk may cause average price to vary by leverage, but not 

price dispersion. 

Approval standards? 

Cannot rule this out for across-banks, but within lenders (and 

conditional on loan size and house values) approvals don’t vary 

across products. 

16 
Potential explanations 

Risk? 

1 Default extremely rare. 

2 Default patterns do not follow menu pattern. 

3 Risk may cause average price to vary by leverage, but not 

price dispersion. 

Approval standards? 

Cannot rule this out for across-banks, but within lenders (and 

conditional on loan size and house values) approvals don’t vary 

across products. 

Refnancing? 

16 
Potential explanations 

Risk? 

1 Default extremely rare. 

2 Default patterns do not follow menu pattern. 

3 Risk may cause average price to vary by leverage, but not 

price dispersion. 

Approval standards? 

Cannot rule this out for across-banks, but within lenders (and 

conditional on loan size and house values) approvals don’t vary 

across products. 

Refnancing? 

Results same if we assume customers refnance once initial period 

ends. 

16 
Menu-based Price Discrimination 

Suppose there are two types of customers: 

1 Sophisticated customers: go to all banks and pick the 

cheapest product available. 

2 Randomizers: walk into a random bank and pick a random 

option on the menu. 

Menu design trade-o ̇: 

1 Cheap options to entice sophisticated customers. 

2 Expensive o ̇ers to proft from the randomizers. 

O ̇er menu with price dispersion that is increasing in the 

fraction of randomizers. 

Menzio and Trachter (2018) set out a model in this spirit. 

17 
Menu-based Price Discrimination 

Young, and frst-time-buyers: 

• Constrained - can’t a ̇ord a bigger mortgage; may not 

qualify at other lenders. 

• Less likely to pick well (Lusardi & Mitchell, 2011; Agarwal 

et al, 2009). 

As a consequence, these customers are prone to picking expensive 

mortgages. 

18 
Conclusions 

1 People face a large number of choices. 

2 Most don’t pick well, but cost implications low. 

3 Competition: Disciplines the banks and protects customers. 

4 Small group face menu with huge price dispersion - young, 

frst-time-buyers. 

5 Evidence consistent with banks using menu to price 

discriminate. 

19 
Literature 

Product choice and shopping 

Bhutta et al. (2021); Woodward & Hall (2012); Foà et al. (2019); 

Célérier & Vallée (2017); Agarwal et al (2016); Andersen et al 

(2020); Fisher et al. (2021); Keys et al. (2016); Allen et al. 

(2019); Allen & Li (2021). 

UK mortgage market 

Liu (2019); Iscenko (2020); Benetton (2020); Benetton, Gavazza & 

Surico (2022); Robles-Garcia (2020); Mysliwski & Rostom (2022). 

Price dispersion 

Huge literature, recently Menzio & Trachter (2018); Kaplan & 

Menzio (2015); Kaplan et al (2017). 

Our contribution 

Novel mechanism: dial up price dispersion to price discriminate. 

Back 

20 
Summary Statistics 

Mean Std. dev. 25th pctile Median 75th pctile

Demographics

Young (%) 36 48 0 0 100

Old (%) 11 31 0 0 0

First-time buyer (%) 40 49 0 0 100

Net income (£000s) 42 26 28 37 50

Loan characteristics

Loan value (£000s) 157 90 100 136 190

House price (£000s) 201 119 125 172 242

Loan-to-value (%) 79 8 74 80 85

Loan-to-income ratio 3.2 0.9 2.6 3.2 3.8

Prices

Fee (£000s) 0.66 0.57 0.10 0.76 1.00

Initial rate (%) 4.0 1.0 3.2 3.9 4.7

Reset rate (%) 4.1 0.4 4.0 4.0 4.2

Back 

21 
The choice set 

Mortgages on o ̇er via Moneyfacts for a given LTV 

Back 

22 
Data 

Product Sales Database 

• Data on universe of mortgages for 6 top UK banks 

• 2009 - 2014 

• Limited borrower characteristics; loan contract details 

Moneyfacts 

• Mortgage comparison site/booklet 

• Shows all mortgages on o ̇er each month 

• Compare what they picked with what they could have picked 

! Allows us to compare the chosen mortgage with 

alternatives. Back 

23 
Choice set example 

• Customer borrows £150k; Deposit of £35k ! LTV = 77%. 

• Choice set is all mortgage products where: 

1 Max loan-to-value is 80%. 

2 Max loan size is greater than £150k. 

+ the customer’s chosen mortgage if not in this set. 

• In principle, customers qualify for all mortgages with higher 

max LTV, but these would represent expensive choices and 

relatively few customers (8%) do this. 

• We restrict the choice set to focus on the menus banks target 

at particular customer groups, and run a number of 

robustness checks. 

Back 

24 
NPV calculation details 

X

TF 84 IP X RP NPV = fee+ + (1 +i)t (1+i)t

t=1 t=TF +1 

where 

• TF is the fxation period; 

• IP is the monthly payment in the initial period; 

• RP is the monthly payment after the initial period; and 

• the monthly discount rate i is computed using the 7yr LIBOR. 

where TF is the fxation period, IP is the monthly payment in the initial 

period, RP is the monthly payment after the initial period, and the 

monthly discount rate i is computed using the 7yr LIBOR. Back 

25 
Which comparison set: within or across? 

They address di ̇erent questions, and have di ̇erent pros and cons. 

Within 

• Pros: Covers choices that were defnitely available, and is 

informative about how banks price discriminate. 

• Cons: Many people use brokers and/or comparison shop, so 

actual choice set is likely bigger. 

Across 

• Pros: Likely closer to the options people had and past work 

suggests even modest shopping leads to savings. 

• Cons: Not sure if any particular person shopped or, if they 

did, what they saw. Indirectly related to price discrimination. 

Back 

26 
Ranking Pros and Cons 

• Baseline: Supposes people care about the average total 

monthly payment, not the components – assumes 

intermediate (7year) horizon. 

• Immediate refnancing: Assumes unrealistic aggressive 

refnancing but eliminate reset rate relevance. 

• Strong dominance: Assumes people care about cost 

components and eliminates any private information, but can 

ignore very costly choices. 

Back 

27 
How well do people pick? 

Within Across

Choice set size Pctile chosen Choice set size Pctile chosen

25th pctile

Median

11

16

33

53

46

73

27

47

75th pctile 23 75 101 70

85%

0.00

0.25

0.50

0.75

1.00

−4 −3 −2 −1 0 1

Cost saving vs reference (% income)

Cumulative distribution

66%

0.00

0.25

0.50

0.75

1.00

−4 −3 −2 −1 0 1

Cost saving vs reference (% income)

Cumulative distribution

Back 

Cost savings within bank Cost savings across banks 

28 
Choice Proliferation 

Banks usually o ̇er: 

• Multiple max loan amounts (e.g. £250,000; £500,000;

£1,000,000)

• Several initial fees (e.g. None; £99; £199; £499; £999;

£1499)

• Several initial rates (lower rates for lower fees)

• Typically one reset rate

Back 

29 
Menu variation 

0

5

10

15

20

2009 2010 2011 2012 2013 2014 2015

Bad tail (%)

75th pctile 90th pctile Median

0

20

40

60

80

2009 2010 2011 2012 2013 2014 2015

Bad tail (%)

75th pctile 90th pctile Median

Bad tail within Bad tail across 

Menu prevents the median person from picking expensive option, 

but sometimes the menu is flled with bad choices. Back

30 
Menu Quality and Expensive Choices 

Within bank Across banks 

• Plot probability of making expensive choice in a given month

against mean size of bad tails in menu o ̇erings.

Back 

31 
Who gets bad menus? 

Low LTI Low LTI High LTI High LTI

Low LTV High LTV Low LTV High LTV

(53%) (26%) (15%) (5%)

0

2

4

6

Bad tail (%)

Within banks 

Note: High LTV=LTV> 85%. High LTI=LTI> 4 

• Banks o ̇er worse menus to high LTVs & LTI customers. 

• Young & FTBs (highly leveraged mortgages) face worse menus 

Back 

32 
Who chooses poorly? 

Dependent variable:

Expensive choice within 

MFX MFX 

Expensive choice across 

MFX MFX 

Young 0.005

(0.0004) 

0.001

(0.0002) 

0.018

(0.001) 

0.005

(0.0004) 

Old −0.008

(0.0004) −0.0003 (0.0003) −0.031(0.001) −0.006(0.001) 

First-time buyer 0.006

(0.0004) −0.0003 (0.0002) 

0.005

(0.001) −0.005(0.0004) 

Poor 0.0005 

(0.0004) 

0.001

(0.0002) 

0.003

(0.001) 

0.001

(0.0004) 

Rich −0.0001 

(0.0003) −0.001

(0.0002) −0.006(0.001) −0.006(0.0004) 

Bad tail 0.117

(0.001) 

0.303

(0.001) 

Bank dummies 

Product dummies 

Pseudo R-squared 

Mean dependent variable 

Observations 

Yes 

Yes 

0.3 

0.023

894,901 

Yes 

Yes 

0.69 

0.023

894,901 

No

Yes 

0.09 

0.067

883,459 

No

Yes 

0.56 

0.067

883,459 

Back 

33 
Dominated choices 

• Compare mortgage to one that dominates in 1 dimension 

• If savings 2.5% ! Strongly dominated 

Dependent variable:

Strongly dominated across MFX MFX

Young 0.043

(0.001) 0.015(0.0001)

Old −0.075

(0.001) −0.036(0.001)

First-time buyer 0.003

(0.001) −0.030(0.001)

Poor 0.034

(0.001) 0.010(0.001)

Rich −0.043

(0.001) −0.029(0.001)

Strongly dominated tail 0.870

(0.001)

Bank dummies Product dummies Pseudo R-squared Mean dependent variable ObservationsNo

Yes

0.04

0.277

883,459

No

Yes

0.16

0.277

883,459

Note: p<0.1; p<0.05; p<0.01

34 

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