In the case of supply limits, rents will rise because the implied rent of the unimproved lot will rise. In the case of lower long term interest rates, rent will remain the same, but the price of the entire property will rise.
In the case of supply limits and rising rents, households will purchase or rent relatively less lot and more home (the blue line) of a property with a lower real value.
In the case of lower real long term interest rates and higher price/rent, since the cost of the improvements will be relatively stable, the higher price must be attributed to the lot. This means that with lower rates, the lot comprises a larger portion of the total value of the property. This will have the same relative effect as rising rents. Households will purchase or rent properties with less lot and more home. Here, I don't think that total utility will change. The house will still have the same real and nominal rental value. It will just have a different mix of home and lot.
If the lot is already a sufficiently large portion of the total cost, it is possible that rising rents could lead households to buy homes with larger square footage, or at least higher value (on less valuable lots).
Next is a graph of the ratio of Home Square Footage to Lot Square Footage. In the chart, I also show home Price/Net Rent (this is the inverse of real long term interest rates) and the telative price level of Owner Equivalent Rent / Core CPI over time. We can see that all of these measures tend to move together. Regressing the square footage ratio against the other two, inflation has the strongest effect.
|Rent Inflation & Lot/Home ratios - left scale|
Rent/Price - right scale
It's important to keep clear the difference between all of these measures. My proxy here for a housing shortage is housing inflation. This has nothing to do with home prices. This is the relative change in the rent of a property over time. Housing consumption (which is different than home ownership) and home supply are both slow moving variables over time, having to do generally with the number of households and the stock of housing. Real housing consumption (measured as rent or imputed rent) has been declining for three decades, while nominal housing consumption has remained flat (both as a portion of personal consumption expenditures). This suggests a supply constraint. Housing is becoming more expensive (in terms of rent, not price) because this shortage has led to above normal rent inflation.
Counterintuitively, larger average square footage of single family homes does not contradict the housing shortage hypothesis or the home-as-real-long-term-security model. It confirms them. Believe it or not, I had not even looked at this data on lot sizes until after my exchange with baconbacon.
The suggestion from this data is that rent inflation has a larger influence on the changing size of homes and lots than long term real interest rates. I am beginning to convince myself that building constraints are a larger influence on housing costs (and consequently, real incomes) than either tax issues or low interest rates. I am beginning to think that by the time I am done with this, I will have an explanation for a large amount of the stagnation in low quintile household incomes.
This is a real shame, because, if we did not have these constraints on housing supply, the effect of this global context of low real interest rates should have been to entice investors into building, lowering rents instead of raising them. Between this factor, and the imposition of taxes on renters, I think these housing supply and tax issues could explain a decline in real incomes of 20% or more among the lowest income households. That's my guess now. I should be able to eventually come up with more detailed numbers, but this has become a larger project than I ever expected.