Here is a table of intrinsic home values, based on the present value of 50 years of rent payments. All homes are based on $12,000 in net implied rent per year. (edit - By net rent, I mean rent minus costs of ownership, like taxes & maintenance.) I am assuming that rent inflation equals the expected inflation portion of the discount rate, so the intrinsic value is completely dependent on the real portion of the discount rate. (edit - expected rent inflation should differ from location to location. In locations with higher expected rent inflation, we should see higher home prices, relative to net rents.)
The total nominal rates in these tables is a combination of the real and the inflation rates, so the nominal discount rate where inflation is 3% and the real rate is 5% is the same as the discount rate where inflation is 5% and the real rate is 3% (approx. 8% in both scenarios).
Here are the monthly mortgage payments for the same home. (I have assumed, for simplicity, that the mortgage interest rate is equal to the discount rate applied to future rent payments.)
The intrinsic value of the home is only a product of the real rate, but the mortgage payment is a product of the total nominal rate. Since the mortgage payments happen sooner, on average, than the rent payments that create the home's intrinsic value, real rates affect the value of the home more intensively than they affect the size of the mortgage payments. This has the odd effect of causing real rates and inflation premiums to have the comparatively opposite effect on mortgage payments. Higher inflation causes higher mortgage payments, but higher real rates cause lower payments.
So, the most expensive home, in terms of mortgage payments, is the home that has a 10% mortgage rate that is entirely an inflation premium. But, the home with the lowest mortgage payment is also a home with a 10% mortgage rate - the home with no inflation and 10% real rates.
This is why viewing the housing market through the lens of nominal rates is incoherent. It seemed coherent when inflation rates were high and volatile in the 1970's & 1980's, and inflation was the most influential element. Then, other factors like cyclical and demographic demand factors would have been noticeable, and since inflation was very high in the 1970's when real rates were very low, the mitigating effect of those high mortgage payments on demand masked the valuation effects of real rates.
But, the taming of inflation has exposed the effect of real rates. Over the past 20 years or so, we have gone from 8% rates (4% real + 4% inflation) to 4% rates (2% real + 2% inflation). This would lead to an intrinsic value moving from $258,000 to $377,000, with mortgage payments staying roughly the same.
Here's an example of the kinds of problems that crop up when we set public policies based on imperfect models (and they are all imperfect). If the Fed managed to push inflation expectations up to 3%, which would probably be beneficial in the current low rate context, the positive effect this would have on markets in general and home markets specifically would probably move home prices up. (I believe they are below intrinsic value now, due to the damaged credit market.) In addition, the higher inflation premium would cause the average mortgage payment to go up another 12%. If that happened, the standard "home affordability" indexes that compare mortgage payments to household incomes would trigger red flags, everyone would start yelling "bubble" and "housing inflation", and the Fed will be obliged to sucker punch us again.
Since low real rates are probably going to be around for another cycle or two, we will continue to have this phantom housing "inflation", along with high nominal levels of capital, high nominal levels of household debt, and low nominal rates. All of these artifacts of low real rates are false signals of loose monetary policy and over-expansion, and are important reasons why I expect the Fed to continue to be erroneously hawkish. Fed members even refer to their recent policy stance as loose or accommodative.