It depends on the source of the inflation. Real assets (i.e. Real Estate, Commodities, and ILBs) generally exhibit positive correlations to inflation (as measure by CPI), however is very important to distinguish between Headline CPI (which includes food and energy, Read: Commodities) from Core CPI which does not.
For the past several years we have witnessed a divergence between headline CPI and Core CPI, with the former running ~2% head of the latter on average. This is uncharacteristic of the relationship between the two measures. Typically, the high volatility in the headline components average out over time, thus the Fed (Bernanke) uses Core as the preferred inflation measure.
The wage-price spiral (
http://en.wikipedia.org/wiki/Price/wage_spiral) is the dreaded scnenario where labor is able to accrue inflation into incomes. Since affordability (therfore pricing) of housing is based in large part on income, rising wages should have a direct positive impact on housing prices. Recently we have not seen the increase in wages expected during inflationary times. There are several reasons why we would expect wages to lag inflation over the medium term including (cheap global labor, slowing GDP growth, decreases in corporate earnings, tighter lending conditions, etc.) The point real estate thought positively correlated to inflation, is not positively correlated to headline inflation (which is kind we are experiencing now).
So what does this mean for housing? Nothing good. Increasing costs across the consumption basket of the U.S. consumer in fodd and energy is leaving less money on the table to housing purchases (not to mention dampening consumer sentiment, an indicator long held to portend large expenditures on capital assets. Coupled with rising mortgage interest rates due to increased inflationary expectations, the simple conclusion is that there is more pain to come for housing.
