Arithmetic is a skill that is in short supply among economists in policymaking positions. The Obama administration is about to come out with its plans for replacing Fannie and Freddie. The word in the media is that the administration will propose a range of options, with one option maintaining a Fannie/Freddie type structure and one option going to a completely private system for the main sector of the housing market. (Presumably the Federal Housing Authority would remain in place even in the private system to provide credit to moderate income households.)

The third option, that apparently many Washington policy wonks are smiling upon, is a hybrid system with private institutions buying mortgages with a government guarantee standing behind them. (Depending on the construction, the government may either guarantee the institution or the mortgage backed security -- more likely it will be the latter.) According to a new paper by Moody's, this sort of hybrid system will reduce the cost of a 30-year mortgage by 90 basis points (9/10ths of a percentage point) compared to a purely privatized system. The Moody's analysis also calculates that it will raise house prices by 8 percent compared to a privatized system.

There are some reasons for skepticism about the Moody's estimates of the cost advantages of the hybrid system, most notably that the spread between jumbo mortgages, which are not bought by Fannie and Freddie, and conformable mortgages that go into the Fannie and Freddie pools has generally been just 25 basis points. Even in the current environment, it is just 75 basis points, so a spread between mortgage rates in a purely private system and hybrid of 90 basis points seems somewhat high. But let's just take the Moody's estimates at face value and have some fun with numbers. 

The median house price is currently around $170,000. Prices are still falling, but let's assume for the moment that we freeze them at their current level. Let's see what the picture looks like.


                                          Private System                                Hybrid

House price                       $156,400                                    $170,000

Mortgage Rate                    7.1%                                            6.2%

Monthly payment                 $841                                          $833


I got the mortgage rates by assuming that the typical 30-year mortgage rate under the current system has been around 6.0 percent. The Moody's paper assumes that it will rise by about 20 basis points under their hybrid system. This gives us a 6.2 percent rate. If we add another 90 basis points for the purely private system, we get the 7.1 percent rate shown above.

So taking the estimates from the Moody's analysis exactly as written, we find that the hybrid system will save the buyer of the median home about $8 a month on their mortgage. The basic story is that the benefit of the lower interest rate is largely offset by the fact that buyers will have to pay more money for their house. So, is it important to set up a whole new system of finance, with all the regulatory problems with which we are now quite familiar, in order to save homebuyers $8 a month on their mortgage?

But wait, there's more. One big obstacle to homeownership is the downpayment. In both cases we have assumed a 20 percent downpayment, the standard for a conformable mortgage. In the case of the private system this requirement means that homebuyers would need $31,280 in cash. In the case of the hybrid model, following Moody's estimates, they would need to come up with $34,000 in cash. That might not be easy for many first-time buyers.

But wait, there is still more. In most parts of the country people pay property taxes on their homes. Let's assume that the tax rate is 1.0 percent, which is somewhere near the average. Let's see what happens to those monthly payments now.

                                                    Private System             Hybrid

Monthly Tax payment                  $130.00                       $142.00

Monthly payment including tax    $971                            $975


Hmmm, now it looks like our homeowner comes out somewhat worse under the hybrid system. It seems that their savings on mortgage payments is more than offset by higher property taxes. This one is not looking really good.

But, in the spirit of old-fashioned late night TV commercials, there is still more. The current value of residential real estate is around $16 trillion. if we take the Moody's numbers at face value then it will fall by roughly $1.3 trillion to $14.7 trillion under the private system. The housing wealth effect is around 6 percent, meaning that an additional dollar of housing wealth leads to 6 cents in additional consumption each year. This means that this should lead to a decrease in annual consumption and an increase in annual saving of around $78 billion, a bit more than 0.5 percent of GDP.

This would be a large increase in saving. While higher savings (and less consumption) would not be helpful at the moment, with the unemployment rate near 9.0 percent, when the economy is near full employment, higher savings means more investment and more growth, at least in standard economic models. And increasing savings by a half percentage point of GDP is a big deal.

So, what have we learned about the relative merits of the private system and the hybrid model? Well the hybrid model will mean slightly lower monthly mortgage payments, but this benefit is likely to be offset by higher property taxes. The higher house prices in the hybrid model will mean that it will be more difficult for first-time buyers to come up with a downpayment. And, the wealth effect associated with the higher house prices in the hybrid model will mean lower savings and less growth.

We could also point out that financial intermediaries (e.g. Goldman Sachs and J.P. Morgan) would stand to make more money on housing in a hybrid model, but there is no reason to get into such details.