1. Many cities in California have passed Inclusionary Zoning (IZ) policies (also known

as below-market housing mandates) as an attempt to make housing more a§ordable.

These policies require developers to sell a proportion of their houses to low-income

people at prices that are below the market price. The data set means.csv contains (the

natural logarithm of) housing prices (lnprice) in 311 cities in 1990 and in 2000 (these

are identiÖed using the indicator d01 = 0 for 1990 and d01 = 1 for 2000), as well as

another indicator called izlaw, where izlaw = 0 for those cities which donít have the

policy and izlaw = 1 for cities that have the policy.

(a) (4 marks) Use data for 1990 and regression to estimate and compare the mean

lnprice for those cities that had IZ laws and those cities that did not. Test the null

hypothesis (at the 5% level of signiÖcance) that IZ had no e§ect vs the alternative

that IZ achieved its desired intention.​
(b) (4 marks) Use data for 2000 and regression to estimate and compare the mean
lnprice for those cities that had IZ laws and those cities that did not. Find a 95%
conÖdence interval for mean lnprice for cities that had IZ laws in place.
(c) (5 marks) Use your regression results for (a) and (b) to draw a carefully labled
diagram that illustrates the e§ect of implementing IZ laws. If we assume a com-
mon trend, what mean lnprice change would we have observed between 1990 and
2000 without IZ, and what is the implied e§ect of the policy over this time?
(d) (4 marks) Use lnprice as the dependent variable in a di§erence-in-di§erences
regression to determine the IZ treatment e§ect and the standard error of this
treatment e§ect.
(e) (8 marks) Add the following control variables into your di§erence-in-di§erences
regression: lmedhhinc; 100(educattain); 100(proppoverty); and lpop; which re-
spectively measure the (natural) logarithm of median household income, the per-
centage of houseowners with a university degree, the percentage of houseowners
below the poverty line, and the natural logarithm of the population of each city.
Interpret the estimates of these new variables, including their signs and individual
signiÖcance, and test whether they are jointly signiÖcant. How do these additional
variables a§ect the estimates of the treatment e§ect?
(f) (5 marks) Consider the di§erences-in-di§erences regression for lnprice given by
ln priceit = 1 + 2
izlawi + 3D01t + 4
izlawi -
D01t + 5CIT Yi + eit:
In this model cityi represents some unobservable characteristic of each city that
stays constant over time. Write 1990 from
the expression for 2000. The dependent variable is
d ln pricei = [ln pricei;2000
(g) (5 marks) Regress d ln pricei against a constant and izlawi and compare the result
to the ln pricei regression in part d. What do you notice?
2. Consider the following equations which respectively describe the links between the
economic growth in a country and the development of its Önancial institutions:
Yt = a0 + a1Ft + vt (1)
Ft = b0 + b1Yt + b2Lt + b3It + "t (2)
where
Yt
is the annual growth in GDP in year t
Ft
is the annual growth in credit issued by private banks in year t
Lt
is an indicator of the quality of the legal system in year t
It
is a measure of how long the country has had independence at time t
(a) (4 marks) Brieáy discuss the problems that might arise if we use OLS to estimate
equations (1) and (2).
(b) (6 marks) Find expressions for the reduced form equations for this model. What prop-
erties will the OLS estimates of the reduced form parameters have?
(c) (7 marks) Discuss the identiÖcation status of each of equations (1) and (2). Does the
system of equations imply unique consistent estimates of the parameters in (1), and/or
unique consistent estimates of the parameters in (2)?
(d) (5 marks) Suppose that a t-test of the signiÖcance of the coe¢ cient for Lt
in the Örst
stage regression with dependent variable Ft
; delivers an observed t-value of 2.5. Brieáy
comment on whether you think that Lt will be an appropriate instrument for Ft
in
equation (1).
(e) (8 marks) Suppose that you use OLS to obtain Fbt from your reduced form in part (b).
Comment on the similarities and/or di§erences between estimates for a1 (and their
standard errors) if you used
(i) Fbt and a constant as instruments in a two stage regression
(ii) a constant and Lt as instruments in a two stage regression
(iii) a constant, Lt and It as instruments in a two stage regression
(iv) used Fbt
instead of Ft
in equation (1) and simply ran an OLS regression.