Ask a generic economist about the importance of a significant down payment for the housing market and they will reply with something about homeowners needing skin in the game so they don't bail at the first sign of trouble, and/or as a protection for the lender. This ought to have gone up in smoke during the financial crisis as many of the defaults and write downs came from homes with large down payments and well documented incomes. The primary tool of the large down payment is as a selection mechanism, and the slashing away at that mechanism was a major factor in the run up in prices.
The basic principle is simple, if you can save a significant sum of money then you are a much better risk for a loan than someone who doesn't. Home ownership via a mortgage comes with a double whammy, first you have structured regular payments for the mortgage, insurance and property taxes, then you have lump sum costs for repairs. A new roof, leaky pipes, broken windows, some large some small but persistent and sometimes lumpy. In short once you buy the house and commit to the recurring costs and dump your savings into the down payment you need to start saving again to handle these costs. This is where habit comes in, who is more likely to be able to maintain the house (ie the collateral), the one who saved 20% of the purchase price or the one who didn't? The answer is obvious.
Rising home prices didn't break the truism, but it did muddy the waters a lot. Having a 20% down payment could still have been due to a high savings rate, but it also could have been due to luck. If you bought a $100,000 house with 20% down early in the 2000s and home prices pushed its 'value' up 50% over the next few years then you could sell your house and have ~$70,000 available for your next down payment which would qualify you for a $350,000 loan (obviously your income might not) on the next one. Or you might have borrowed against that 50k in new equity and purchased a second house as a rental/vacation home/speculative asset. This is a very different situation than a person who bought a house, and then over several years saved up another down payment worth of cash. In both cases there is an incentive to keep the 2nd house with the down payment, but in one case you have a buyer who clearly was living below their means for several years and another case where it is unclear if they were or weren't.
During the financial crisis one of the largest segments for defaults was second homes purchased with normal down payments, which I believe was largely caused by the rise in home prices distorting the signal that a down payment usually brings.
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