This is a follow up to my last blog on causal valuation. I played around with draw.io this morning with the intentions of specifying a causal model of residential housing valuation. This is all very preliminary and is based on very little research on the indicators of real estate valuation. I stumbled upon a few related to housing demand and stuck them in the hacked up model below. The point is not to argue for the truth of this model, just that it is not rocket science to create a causal model of real estate valuation. Whether it is true or useful is a different question.

In social sciences research they are used to dealing with big factors like net migration, economic growth, and wage levels so one could consult some of this literature to try to verify if the model might be correct in regards to the macro determinants of housing demand. We might find in our research that the net migration factor needs to be imploded into more nodes and edges to better represent the impact of this factor upon housing valuation.

Similarly, the "Intrinsic Features" node would need to be unpacked into things like square footage, age and other important "intrinsic" determinants of the price of the house. At the bottom we have the causal factor of how the price of the house compares to the price of similar houses.

In this model, residential house prices are determined by more that one valuation approach. We are not just using relative pricing (e.g., prices of similar homes) to value the home, we are also using intrinsic pricing (e.g., square footage, age and other intrinsic determinants of house prices). The causal part comes in when we start to embed the pricing model into the larger picture of housing demand.

The take home from this blog is that causal modelling can probably be worked into residential housing valuation and that housing valuation probably involves using more than one valuation approach. The options pricing approach (see video in last blog) is not included as a causal factor but can be an important factor in hot real estate markets.

What differentiates a causal graph from a nice diagram is that there is alot of math you can potentially throw at determining if your causal graph is statistically valid and corresponds with observations. Each node in the graph implies a certain relationship between variables that can be tested for in the data (e.g., d-sep tests) to determine if the causal pathways correspond to what you would expect in the data.

The geneticist Sewall Wright pioneered the use of path analysis in a 1921 paper called Correlation and Causation (PDF link). Path analysis has been incorporated into the broader field of causal graph theory with many advances in the field since then. This paper is still worth browsing through to see how Sewall approached doing path analysis. It should be noted that this paper had no immediate effect on research practice for a long time as people didn't know what he was up to and were also suspicious of the term "cause" as a holdover from some medieval metaphysics. The "modern view" of causation in 1911 was with the leading statistician Karl Person who suggested that a cause was nothing more than a limiting form of correlation and not really that relevant to the concerns of a statistician:

The newer, and I think truer, view of the universe that all all existences are associated with a corresponding variation among the existences in a second class. Science has to measure the degree of stringency, or looseness, of these concomitant variations. Absolute independence is the conceptual limit at one end to the looseness of the link, absolute dependence is the conceptual limit at the other end of the stringency of the link. The old view of cause and effect tried to subsume the universe under these two conceptual limits of experience - and it could only fail; things are not in our experience either independent or causative. All classes of phenomena are linked together and the problem in each case is how close is the degree of association. ~ Karl Pearson A Grammar of Science, 3rd Edition (1911) , p. 166.

I'm doing some research on real estate valuation and came across Aswath Damodaran, professor at NYU Stern School of Business. He is a prolific author of books and youtube videos on valuation. Today I checked out his entertaining and informative "Introduction to Valuation":

He mentions that there are three, and only three, approaches to valuation: Intrinsic, Relative, and Options Pricing valuation.

The idea that I am toying with is that there might be another one called Causal Valuation.

Causal valuation is an approach that tries to take advantage of some recent mathematical and conceptual work on causal graphs by Judea Pearl. See his Engines of Evidence conversation for a taste. That research is starting to emerge into the mainstream but it is not trivial to master the tools or the ideas associated with causal graph theory.

To give you a flavor of what causal valuation might look like I'll show you what a simple causal graph looks like for a non-controversial case. Below is a causal graph depicting the relationship between smoking cigarettes, lung cancer, and yellow fingers.

We might contrast this causal graph with an associative graph between the Cigarette Smoking and Yellow Finger factors and the Lung Cancer outcome.

Note that there probably is an association between yellow fingers and lung cancer but it is not a causal one, it is an associative relationship.

Most of our statistical models are associative, not causal. They might tell you to clean your fingers more often if you want to avoid lung cancer. A causal model, on the other hand, explicitly tells you there is no causal relationship between yellow fingers and lung cancer because there is no connecting line between them. Causal models also provide more guidance on where you need to intervene in order to affect an outcome.

Real estate valuation often uses the "Relative" method of valuation, or what similar homes are selling for in the neighborhood. There may, however, be factors such as net migration, wage levels, and business growth or decline in the area that are actually driving real estate valuation levels. Instead of using associative metrics to arrive at a valuation, perhaps a causal approach would lead to better valuations. That is the big idea that I have started to explore.

If you want to play around with making causal graphs, a tool I would recommend is the free and powerful online drawing tool draw.io. I used it to make the graphs above.

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