First random thought: a person who was very ignorant about future house prices would nevertheless be almost certain that real (inflation-adjusted) house prices will be lower than today at some time in the future.
If we want a null hypothesis about house prices, I think the best null hypothesis would be that the log of real house prices follows a martingale. That means they are equally likely to rise (say) 10% next year as they are to fall 10% next year. And equally likely to rise 20% next year as fall 20% next year. Etc. For any year, regardless of anything. I think that is what someone who admitted total ignorance would assume.
The martingale null hypothesis would give something like the following graph (I think, could someone please check my maths/stats?):
There is a 50% probability that real house prices will be lower tomorrow than today, but a probability that approaches 100%, as T goes to infinity, that real house prices will be lower than today some time between today and T years from today.
So if you buy a house today, you can be almost certain that at some time in the future, you (or your kids or grandkids) will say "It's worth less now than when we bought it!"
But that does not mean you made a mistake in buying it. It would only have been a mistake if you could have rented a house for less than the foregone interest and other costs of buying the house.
(Saying that house prices follow a martingale is not the same as asserting the Efficient Markets Hypothesis. For example, suppose it were public knowledge that rents were higher in even-numbered years than in odd-numbered years. Then the EMH would say that house prices would he higher in January of even-numbered years than in January of odd-numbered years.)
Second random thought: If we accept the martingale hypothesis as the null hypothesis, that someone who admitted complete ignorance would accept, what would be the minimum we would demand from someone who claimed to know something about house prices and said that (real) house prices are "too high today and will be lower than today in the future"?
Clearly we need a date, but we also need a probability. And the later the date, the higher the probability would need to be. The forecaster would need to pick a date/probability combination that is above the red curve I have drawn above. (Presumably, a forecaster who picked a date/probability combination below my red curve would actually be saying that house prices are too low?). Can anyone reading this do the math and actually solve for that red curve? What does the exact shape of the red curve depend on?
Third random thought: the standard narrative is that US house prices were too high in 2006, and that's why they fell (though they might have fallen too low in the recession). Canadian house prices fell a little in 2008, but had recovered all they lost by 2010, and have kept on rising since. (Here's the Teranet-National Bank graph, which is like a Canadian version of Case-Shiller.) The standard narrative fears that Canadian house prices are too high, and have been too high since 2010, and that's why they will fall, to match what happened in the US. The US came back down to reality sooner, but Canada will eventually follow. An alternative narrative is that US house prices were not too high in 2006, but were too low in the recession, and that Canadian house prices are not too high. Canada came back up to reality sooner, but the US will eventually follow. Here's the question: what evidence would it take to make the alternative narrative as plausible as the standard narrative?