In the case of the housing boom, we can't even answer the basic question of how much approval rates or loan-to-value ratios changed over time for a person with fixed characteristics.
The loan approval rate that Glaeser discusses is a meaningless number. Loan applications are determined by real estate agents and mortgage brokers. If a loan application is rejected, then this wastes the time of the mortgage broker and the real estate agent (it is a particular problem for the latter). The loan approval rate should only change with the willingness of mortgage brokers and real estate agents to waste their time. I don't know what drives that variable, but it need to be related to house prices.
It seems to me that if you look at the ratio of median house prices to median incomes, you learn something. That ratio rose significantly, particularly in California.
The house price equals the down payment plus the mortgage. Unless higher down payments were driving house prices (which is almost surely not the case), the increase in median house prices relative to incomes meant an increase in median mortgage amounts relative to incomes. QED.
Glaeser also cites data suggesting that down payments did not fall so much over the past ten years. That data is suspect. For one thing, does it include refi's as well as loans for purchase? When house prices are rising, refi's will tend to cause the loan-to-value ratio to fall over time. Your house was worth $200,000 when you bought it with a $180,000 mortgage, it is now worth $300,000 when you refinance with a $240,000 mortgage, and so your loan-to-value ratio drops from 90 percent to 80 percent.
Also, in 2006 and 2007, for many refinances the "value" in the loan-to-value ratio was a made-up number.