1. The determinants of housing demand An analysis for French households
59th North American Meetings of the RSAI
9 November 2012
The determinants of housing demand
An analysis for French households  
Nicolas Coulombel, Clémence Morel
Université Paris – Est, LVMT
 :

2. presentation outline Introduction Methodology
Comparison of the LES and the QES: a simple model
Impact of household size on housing demand
Conclusion

3. context & motivation
Housing: increasing weight in French households’ budget
yet limited research on housing demand in France
Aim of this research
determinants of housing demand
influence of household size
Motivation
recover households’ preferences for LUTI modeling
design of housing policies

4. methodology Comparison of two demand systems Step 1: simple models
Linear Expenditure System
Quadratic Expenditure System
Step 1: simple models
estimation with expenditure and budget share
Step 2: introduction of HH size
use of « scaling »

5. the linear expenditure system (les)
Expenditure for good i
Derives from the Stone-Geary utility function
For two goods : housing h and composite z
income elasticity of housing :
price elasticity of housing :

6. the quadratic expenditure system (qes)
Expenditure for good i
Derives from the indirect utility function
For two goods :
income elasticity
price elasticity

7. properties of the les and the qes
Estimation
LES & QES: only 2 periods/regions required
QES: non linearity  log-likelihood maximization
Interpretation of coefficients in the LES
ai: marginal budget share
bi : subsistence quantity?
Elasticities
LES: ηy  with Y, ηy  1 and ηP  with Y, ηP  -1
QES: more flexible

8. data 2006 French Housing Survey Sample Housing price Income
private renters
excluded: students, outliers (income & net budget share)
5 907 observations
Housing price
observed mean regional rental price
Income
current income

9. housing expenditure Gross monthly rent Preliminary analysis
rental charges/utilities excluded
subsidies not taken into account ( control variable)
Preliminary analysis
marked heterogeneity
trend: increase with HH income
heteroscedasticity

10. housing (gross) budget share
Definition: Gross Housing Expenditure / HH Income
> net budget share
case of low-income HHs
Preliminary analysis
budget share decreases with income
volatility strongly decreases with income
same remarks for net budget share

11. estimated models Housing outlays
LES
QES
Budget shares: same model divided by Y
Heteroscedasticity
housing budgets : weight Y-1
budget shares : weight Y0.66

12. estimation results LES QES Exp Budget Share ah 0.099*** 0.101***
LES
QES
Exp
Budget Share ah
0.099***
0.101***
0.124*** aS
0.187***
0.213***
0.206***
0.228*** bz
***
***
-2028***
*** bh
12.43***
11.88***
6.11***
6.71*** ch
2.31***
2.12*** λ
-0.157* d
0.0109***
0.0108*** R²
0.326
0.624
0.337
0.626
B-P (p-value)
0.01
0.24
0.08
0.17

13. engel curves (budget share)

14. income elasticity

15. price elasticity

16. impact of household size
Same models as before (LES & QES)
estimated on budget shares
Use of scaling (Pollak and Wales, 1981)
parameters vary with HH composition
Representation of household size
4 dummies: partner/spouse, 1 child, 2 children, 3 children and more  test non-linear effects

17. estimation results
LES
QES ah
0.101***
0.158***
ah,spouse
-0.011**
-0.031***
ah,child1 **
-0.026***
ah,child2 **
-0.019***
ah,child3+ **
-0.022*** as
0.110*** bz
-1881***
***
bz,spouse
-766.6***
-908.7***
bz,child1
-797.9***
-298.4***
bz,child2
-918.7***
-702.2***
bz,child3+
-659.6***
-553.9*** bh
12.25***
1.67
bh,spouse
-4.55***
-4.60**
bh,child1
0.43***
7.13**
bh,child2
-0.90***
2.46**
bh,child3+
3.31***
6.89** ch
1.106***
ch,spouse
0.692***
ch,child1
0.782***
ch,child2
0.561**
ch,child3+
0.714** λ
*** d
0.0107***
0.0105***
Log-likelihood
6324
6373 R²
0,634
0,64
B-P (P-value)
0,19
0,23
QES : significant compared to LES (likelihood ratio test)
LES
children  housing expense increases by a constant
spouse: more complex effect
QES
impact harder to interpret
QES > LES: likelihood ratio-test

18. les – engel curves

19. qes – engel curves

20. les – income elasticity

21. qes – income elasticity

22. housing budget share and household size in expensive areas
Ile de France (Paris area)
average rental price = 14,4€/m²
≈ twice the national average
Specific feature: couples have a lower housing budget share than single persons
plausible interpretation: dual-earner couples might keep the previous home of one of the households’ members

23. conclusion Comparative analysis of the LES and the QES
similar explaining powers
LES easier to interpret
but elasticities provided by LES are likely biased
Household composition and size matters
partner/spouse and children do not have the same impact on housing demand
Future research
investigating the strong heterogeneity of housing budget shares for low-income HHs
analysis of the linear and quadratic AIDS