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For example, if a homeowner originally made a 20 percent down payment (origination LTV ratio=80 percent), a 15 percent decline in property value following the date of purchase would push the post-origination LTV ratio to nearly 95 percent, typically the maximum allowable with conventional financing. Loan underwriters would likely be concerned that the recent downward trend in property values would continue and therefore would be reluctant to approve such a loan.
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In addition, an LTV ratio exceeding 80 percent would typically require some form of mortgage insurance, which would increase transaction costs and reduce the effective interest rate spread by as much as 25 to 50 basis points. If the original LTV ratio was greater than 80 percent, correspondingly smaller declines in property value would have similar effects. In contrast, increases in property value would likely raise the probability of refinancing. Greater equity simply makes it easier for homeowners to qualify for a loan since the lender is exposed to less risk.
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It may also increase the incentive to refinance for homeowners who wish to take equity out of their property (known as a cash-out refinancing). Furthermore, if price appreciation substantially lowers the post-origination LTV ratio, a borrower may be able to use refinancing to reduce or eliminate the cost of mortgage insurance, thereby increasing the effective interest rate spread.
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To capture the effect of changes in home equity on the probability of refinancing, we enter an estimate of the post-origination LTV ratio as an explanatory variable. The LTV ratio's numerator is the amortized balance of the original first mortgage on the property, calculated by using standard amortization formulas for fixed-rate mortgages and the interest rate assigned to that loan, as discussed above.(13)
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The denominator is the original purchase price indexed using the Case Shiller Weiss repeat sales home price index for the county in which the property is located. While repeat sales home price indexes are not completely free of bias, they are superior to other indicators in tracking the movements in home prices over time. This approach allows us to calculate a post-origination LTV ratio for each month from the date of purchase to either the date of refinance or the end of the sample period.
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For loans that were refinanced, the post-origination LTV ratio used is the estimate for the month in which the refinance loan closed. However, as in the case of interest rate R, a value of the post-origination LTV ratio must be assigned to those observations that did not refinance. We noted that, on average, homeowners who refinanced did so at the forty-fifth percentile of values of the LTV ratio observed from the date of purchase to the date of refinance. On the basis of this observation, the LTV ratio assigned to those who did not refinance is the average over the entire period from the date of purchase to the end of the sample period.
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We should note that virtually all of the movement in the LTV ratio is the result of changes in the value of the home. The amount of amortization of the original balance of a mortgage is relatively modest over the typical life of the mortgages in our sample. In contrast, over the time period represented by this sample, home price movements have been quite dramatic in some regions. For example, the Case Shiller Weiss repeat sales indexes suggest that home prices in the California counties included in our sample declined by roughly 30 percent from 1990 to 1995.
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