Definitely. Lower interest rate means that future dividends are worth more so same stream of dividends results in higher prices. True for stocks, bonds & houses. Also one reason that wealth inequality can rise with lower interest rates even when income inequality stays the same.
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What I'm particularly curious about is whether there are connections besides the obvious one that lower interest rates increase house prices. Could increasing house prices drive interest rates down? Could there be a third force driving both house prices and interest rates?
I worry that low interest rates on government bonds and rising house prices might be evidence of some more general "metabolic syndrome" in the economy.
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Yes, in the sense that people are afraid to raise interest rates for fear of a housing led recession. There's an old paper https://www.nber.org/papers/w13428
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There were two types of cities in the US, pre-crisis. One type has extremely tight controls on new housing supply, causing rents and prices to skyrocket, regardless of interest rates. Neither high rents nor low interest rates can trigger supply there. 1/
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Add low/declining fertility rates to the list of symptoms.
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