Should housing be considered a form of capital for the purpose of capital gains taxation? Economists across the political spectrum almost unanimously oppose the home mortgage interest tax deduction. While I'm sure there are a few whom I've missed, I could only find a single professional economist who supports it. Greg Landsburg believes that capital income should be untaxed, based on the Chamley-Judd model and its subsequent refinements. He argues that the home mortgage interest tax deduction effectively cancels the distortionary tax on home mortgage interest capital income, and so represents a step in the right direction, although he would prefer a complete elimination of all capital income taxation.

But does housing really counts as "capital" in the Chamley-Judd sense? A textbook example of capital gains is a lender lending money to a borrower who uses it to buy sewing machines, tractors, etc. and start up a new company, which then turns a profit and allows the borrower to repay the loan with interest. In this example, everybody wins (the borrow, the lender, and the new company's customers), and the Chamley-Judd result that these kind of loans should not be taxed is very reasonable and intuitive.

But as Greg Mankiw's Intro to Economics textbook points out, housing is somewhat of an edge case between capital and consumption, and the fact that "capital" is traditionally defined to include housing is a bit of a historical accident. Morever, there is debate among economists about whether or not housing should be properly classified as capital. (Mankiw also wrote a New York Times column on this issue.)

I'm not familiar with the precise assumptions of the Chamley-Judd model, but does the main result that capital income should be untaxed include income from housing appreciation? People typically buy first homes (the only kind to which the mortgage interest deduction applies) for their own personal use, not primarily as investment opportunities. It's not obvious to me why housing purchases would lead to the creation of new economic wealth as more traditional capital investments do. In contrast to Landsburg, Uwe Reinhardt claims that


  If pressed, the proponents of the capital-gains preference might concede that a tax preference for gains on transactions in residential real estate is hard to defend.


Under the assumptions of the Chamley-Judd model (or looser, less formal economic reasoning), is housing naturally classified as capital whose appreciation should not be taxed?
I think there are a few different ways one can go about examining the topic and general question you bring up. For that reason, I'd like to highlight that this isn't my primary field, and so my answer might not align with a more expert view from that field. However, to get the ball rolling...

First, we should probably take a short digression and consider the intuition behind what their results suggest; why exactly is taxation on capital income so problematic? Generally, it's because it creates a comparatively large distortion in future consumption. As Banks and Diamond (2010) shows starting on page 31, capital taxation leads to increasingly large wedges in consumption as the number of periods increases. Unlike labor taxation, which creates large, but contemporary, distortions in consumption, capital taxation creates intertemporal distortions.

From that point, I think there's a growing literature questioning whether the traditional Chamley-Judd result is actually as substantial in application (as opposed to theory) as some consider it to be. For example, there are several, different papers which get non-zero optimal taxation rates on capital if there's endogeneity in wages, or if wages from different types of labor cannot be taxed at their individually optimal rates. In fact, one of these potentially problematic areas is entrepreneurship: as Reis' dissertation (2007) points out in the third chapter, "when entrepreneurial labor income cannot be observed separately from capital income, then it is optimal to have positive capital taxation in the long run." A pretty comprehensive analysis by Straub and Werning (2015) does a wonderful job of thoroughly analyzing both models presented by Chamley (1986) and Judd (1985) and highlighting which assumptions end up leading to their landmark result. Perhaps a useful workthrough of the math can be seen in Moll's lecture notes, where it's relatively straightforward to get a positive optimal taxation rate, depending on the intertempoiral elasticity of substitution considered in utility.

Second, I'd point out that there are reasons to be skeptical, even inside either Chamley or Judd's frameworks, that housing interest payments should be considered as capital. Most prominently, both models (I believe) assume no financial constraints (they only require no-Ponzi scheme conditions). Therefore, any agent would be able to purchase a house "out of pocket" (or through costless single-period bonds where the only interest payment is the one imposed by discounting). This in and of itself suggests that mortgages (as we observe them in real life) shouldn't ever be used, since you never ought to pay for liquidity beyond the natural rate of interest. Since mortgages are effectively assumed away in the model, I'd be cautious of applying the model to the optimal taxation of mortgage interest in the first place.

This, I hope, is a bit instructive for the third point- I agree with your skepticism that housing should be viewed as a capital good in this context. Not only because it isn't clear in the general debate of whether housing is capital or not, but also because it doesn't seem to create the same distortionary effects that lead to the zero-capital taxation result even if we accept the Chamley-Judd result. Given that the interest payments aren't an infinite horizon stream of payments (you'd hope), the wedge wouldn't necessarily lead to the same "intertemporal snowballing" that we observe in both models (and that serves as the basis of their zero-capital tax rate finding to begin with).

If I think of any more, I'll be sure to come back and update this answer. And I hope that this just gets the ball rolling for others (which more specialized knowledge in either public economics or optimal taxation theory) to provide more insightful comments. And let me know if this answer was just totally non-responsive to the question you were really interested in to begin with- it's pretty early in the morning here, so I can't guarantee my mind is working at capacity yet!