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You are interested in studying whethe

 You are interested in studying whether an increase in mortgage credit by banks causes an increase in house prices. The dataset credit.dta on the course website contains data for counties in the United States for the period from 1995 to 2005 on the log change in the house price index and on three measures of credit growth: the log change in the number of loans, the log change in the loan volume and the log change in the loan-to-income ratio (defined as the amount of the loan divided by the income of the borrower). 

 
 
𝑙𝑛𝑃𝑐,_𝑡−𝑃𝑐,_𝑡−1_=_𝛿(_𝑙𝑛𝐿𝑐,_𝑡−𝑙𝑛𝐿𝑐,_𝑡−1_)_+_𝛼𝑐+_𝛾𝑡+_𝜀𝑐,_𝑡 _
 
where 𝑐 _indexes counties and 𝑡 _indexes years. 𝑃𝑐,_𝑡 _is the county house price index, 𝐿𝑐,_𝑡 _is one of the three measures of credit growth (number of loans, loan volume or loan-to-income ratio), 𝛼𝑐 _are county fixed effects and 𝛾𝑡 _are year fixed effects. 
 
To overcome the identification challenges discussed in part a), Favara and Imbs (2015) adopt an instrumental variables (IV) strategy using regulatory changes to bank branching across states as an instrument for credit growth. In 1994, the US adopted legislation allowing banks to open branches across state borders without needing authorisation from state authorities. However, states still had some power to limit the entry of out-of-state branches. The dataset contains an index of restrictions to interstate branching (inter_bra). The index covers the period from 1994 to 2005 and takes values between 0 and 4, with high values referring to deregulated states. 
 
The dataset contains data on credit growth for two types of institutions: commercial banks (indexed by _b) and independent mortgage companies (IMCs, indexed by _pl). Commercial banks use branches to collect deposits and originate loans, while IMCs rely on wholesale funding and mortgage brokers. Only banks should respond to branching deregulation, as IMCs are unaffected by it. 
In the analysis that follows, and in line with Favara and Imbs (2015), you should estimate all regressions by weighted least squares, with the weights given by the inverse of the number of counties per state (variable w1 in the dataset). 
c) Run the first-stage regressions for the three measures of credit growth for commercial banks: 
 
𝑙𝑛𝐿𝑐,_𝑡−𝐿𝑐,_𝑡−1_=_𝛽𝐷𝑠,_𝑡−1_+_𝛼𝑐+_𝛾𝑡+_𝜀𝑐,_𝑡 _
where 𝐷𝑠,_𝑡−1_ _is the (lagged) deregulation index in state 𝑠 _and the other variables are as described in part a). Explain what type of standard errors you are using and why. Comment on the first-stage results. 
What do you conclude about the causal effect of branching deregulation on house prices? 
 
f) Estimate the IV regressions for the effect of the three measures of credit growth for commercial banks on house prices using deregulation as an instrument. What do you conclude about the causal effect of credit growth on house prices? 
 
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