Incomplete metaphors

Over at WCI Nick Rowe has a post up about central banks and economic activity. There is a lesson there, but not the one Nick thinks.

If a house has a good thermostat, we should observe a strong negative correlation between the amount of oil burned in the furnace (M), and the outside temperature (V). But we should observe no correlation between the amount of oil burned in the furnace (M) and the inside temperature (P). And we should observe no correlation between the outside temperature (V) and the inside temperature (P).

Let us start with a quibble, a thermostat is fine but a proper building envelope is equally important. That said, my oil stove does not have a thermostat. In fact, I am the thermostat and I can adjust the heat only through a drip valve. In a mild winter I am far too hot (i.e., I am burning more oil than I need). In a cold winter I am capable of making an adjustment in the drip rate to compensate. In a super cold winter even with the drip valve at maximum I am cold. That means the colder it is, to a point, the more control I have over the temperature. But after that point I am too cold. Now throw in the quality of the building envelope.

Now transcribe this into macroeconomic terms. What are the implications?

4 thoughts on “Incomplete metaphors

  1. Here is one implication:

    In your house, taking all three types of winters together, there will be a weak negative correlation between amount of oil burned and the inside temperature of the house. (Mild winters, little oil, hot house; cold winters, medium oil, warm house; very cold winters, lots of oil, cold house.) An econometrician looking at the data, and seeing that negative correlation, might falsely conclude that you are turning the drip valve the wrong way, and advise you to turn down the drip valve if you want to warm up the house.

    I like your example, because it actually reinforces the point I was making in my post.

    BTW typo in title.

  2. Warm winter (3) low oil consumption (1) hot house (3); average winter (2) medium house (2) medium oil consumption (2); cold winter (1) cold house (1) high oil consumption (3). Depends what the poorly trained econometrician focuses on. If she looks for a correlation between outside and inside temperature it will be positively correlated. If she looks at the correlation between oil consumption and house temperature it will be negatively correlated. If she has any decent training at all she will take both inside and outside temperatures as parametric variables and conclude that oil consumption and house temperature are negatively correlated if and only if we ignore the outside temperature. If outside temperature is taken as the causal variable then oil consumption will be viewed as a dependent on the outside temperature but not a good indicator of inside temperature. This is why you need your thermostat b/c you need to hold the inside temperature constant. And that is where I think your metaphor fails.

    As an aside: are you saying that the first and second are industry standard and the third is an exotic practice? Please say it is not so.

    Me I have other problems. My envelope is compromised so when the temperature goes up so too does the amount of condensation. Thus in the attempt to ameliorate the house temperature I create the conditions in which it begins to rot. A much more interesting public policy metaphor with respect to CBs I think.

    PS thanks for the H/T on the typo. There is now far too much Latin and French dancing in my head to spell in any language.

  3. “As an aside: are you saying that the first and second are industry standard and the third is an exotic practice? Please say it is not so.”

    Well, the two posts I was commenting on (written by people who know much more econometrics than me), were looking at simple correlations between two variables!

    And, if you try to do it right, by including all three variables, you actually run into a problem of perfect multicolinearity in the thermostat case. So, the standard “correct” method doesn’t actually work in this peculiar case. The econometrician’s computer will tell her that it can’t detect any effect from either oil or outside temperature on internal temperature.

    I had misunderstood your metaphor. “Envelope” means vapour barrier? If so, I get it now.

  4. Hi Nick,

    Last first. Envelope is the trade term for the ensemble of materials that make up the “skin” of the building. So you could have a envelope that consisted of (working from the outside in) cedar siding, tar paper, insulation, vapour barrier. Also, normally the term envelope also encompasses the roofing system. In my case I have not fully solved the mystery of where my envelope is compromised. More investigation is required.

    I have a friend that went to U of T for his Ph.D. after finishing his masters at York and was doing his doctoral work specifically on the problem of multicollinearity. He says that multicollinearity is not a problem per se, and that any number of strategies can be deployed to limit the various problems that arise from multicollinearity but that most econometricians do not do so for one of two main reasons. First, they want more robust results than they can obtain taking all the relevant variables into account. Hence they drop a variable here and there so they can get what appears to be a robust result (knowing full well they have actually lost information by doing so and thus likely have less robust results which only appear robust). Second, they are simply too lazy or too poorly trained to take the series of counter measures necessary to limit the noise created by multicollinearity.

    In any case my friend did his Ph.D work at U of T so I doubt he was doing bleeding edge econometric work rather he was chewing on a rather small part of a well known problem. Totally respectable but not exotic. So I am little shocked to hear that dropping a variable is the standard practice in the industry. Must create a huge degree of insecurity because even poorly trained econometricians know what they are doing.

    My question is this. If we can talk this problem out to the point where we understand what the relationship is between outside temperature, inside temperature and oil consumption why do we need to do a multiple regression model in the first place? I thought multiple regressions were to be used more like a microscope; as in reveal that which was not apparent to the naked eye.

    If I want to know what my hand looks like my eyes give me the macro rendering required; if I want to know what the skin cells look like then a microscope is the relevant technology. But if I use a micro-scope to look at my whole hand it will never work because the intervening technology has obscured that which is perfectly clear to the naked eye.

    P.S., never pay full price at Canadian Tire.

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