Friday, March 6, 2015

The long run in the UK, redux

I was asked by an anonymous commenter how the model does over the long run in the UK using the three hundred year-long data set from the Bank of England. I had actually addressed this before, but it was at a time when I hadn't quite figured out the relationships between interest rates and various measures of the money supply.

Below are the model fits for the price level (actually, it's the GDP deflator, not CPI) and the long term interest rate. One problem is that I don't know British monetary history well enough to know where to put the monetary regime changes. I chose 1790, 1850 and 1950 because they worked the best; they roughly correspond to the "Restriction Period", the collapse of the railway bubble and Bretton Woods. I plan on doing a more scientific version later (using local fits and looking for the 'phase transitions'). There are some large deviations in the interest rate model that need explanations as well -- I'll discuss those after the graphs  ...

In the last graph, there are two significant deviations -- the 1850s to the 1900s and the 1960s to the 1990s. The former roughly corresponds to the period of the so-called Long Depression, which could be the reason interest rates fall below the ideal information transfer model result. The latter deviation could be the result of the Bretton Woods system where the pound was effectively pegged to the dollar, hence effectively importing US interest rates or it could be because the Bank of England held a lot of US dollar denominated debt, importing US rates per this mechanism. Your ideas are welcome, too.

The information transfer model doesn't explain everything! Economies aren't always in equilibrium. However it is a good place to start as you don't know what deviations from equilibrium are until you know what equilibrium is.


  1. These sorts of international comparisons looking at many countries' interest rate and growth histories are likely to be informative going forward as to what causes economic information dis-equilibrium. Thus, it would be useful to know what sort of policy interventions information equilibrium models would support to improve growth rate, decrease unemployment, keep inflation in a reasonable range, etc., and knowing what sort of historical events changed things from the model's predictions would be an important clue.

    1. I would agree -- getting a handle on what paths represent equilibrium should lead to a better understanding of the fluctuations ... or at least give us a baseline.

  2. I live in the UK so I am interested in this chart. I don’t have any answers as to why the two major periods of deviation occur. However, the chart (and mention of Bretton Woods) raised a couple of related questions in my mind.

    You often compare the economy to the behaviour of a gas. I am ok with the idea that the macro-economy might behave like a physics experiment. However, I have often wondered why you think of the economy like a gas rather than a solid or set of solids as it seems to me that economies have rigid structures.

    Natural and human systems often allow pressure to build up due to rigidities in the system. The pressure is then released as a major event. For example, earthquakes and volcanoes in nature, or revolutions in human societies. When we engineer systems, we build in mechanisms like escape valves to allow such pressure build-ups to release slowly and safely. Maybe democratic elections are like escape valves and that is why revolutions tend to occur in non-democratic societies where there is no equivalent escape valve.

    Following that line of thinking, in macro-economics the most significant rigidities are fixed exchange rates. There are at least three types: a currency is fixed against gold; a currency is fixed against another currency; a currency is shared across multiple countries without the escape value of government transfers between rich areas and poor areas.

    The reason I mention this here is that most of the key macro-economic events in the UK in the last fifty years have related to exchange rates. For example, the pound was devalued against the dollar in 1967. In 1976, there was another currency crisis when the UK had to ask for assistance from the IMF due to expectations of another run on the pound. In the early 1990s, the UK joined the ERM (predecessor of Euro) which fixed the rate of the pound against the DM. The pound was then forcibly ejected from the ERM in 1992 by the markets. This last event is probably the main reason why the UK did not join the Euro.

    The situation today in Euro countries like Greece and Spain is a further example of a crisis brought about by rigidities in currencies. Yet more countries feel macro-economic pressure when they borrow in a foreign currency and their local currency then depreciates in value against that currency. You might also argue that major increases in commodity prices can result in similar pressure build-ups e.g. the oil crisis in the early 1970s was one of the causes of the UK 1976 crisis.

    That leads to my questions. First, even allowing for using the analogy between the physical world and the economy, why do you focus on an analogy with gases rather than solids? Second, you talk about price signals. Surely exchange rates represent a major price signal. Have you thought about including exchange rates in your model?

    1. Hi Jamie,

      I'll answer this in parts -- the first part is why do I use an ideal gas? The simplest answer is that the ideal gas model has a 1-to-1 relationship with the supply and demand version model and many people see the ideal gas model in high school chemistry.

      In the Fielitz and Borchart paper, they reference a couple of other examples including percolation of atoms in solids and a falling object in a gravitational field:

      So it's not limited to a gas. I've used osmotic pressure in a liquid before as well.

      I will try to develop a good analogous model using some sort of solid system that isn't too esoteric.

    2. Continuing:

      Yes, I have looked at exchange rates:

      Regarding your other comments on exchange rates, it is true that they can be indicators of significant shifts in the economy ... it occurred to me while reading your comment that pegging currencies to gold and other currencies is like setting up an information equilibrium model between e.g. your currency and gold. Because information equilibrium is an equivalence relation, that means if G is gold, M is currency and N in output using the model on this blog, you have:

      G ~ M and

      M ~ N

      so G ~ N. It would be interesting to set up a model where this governs how the currency is treated in the economy.

      For example, if the pound was effectively pegged to the US dollar (as during the Bretton Woods period), we'd actually use the dollar to determine the price level and interest rates during that period instead of the pound.

      It has given me something to think about.

    3. Thanks for the reply. A point of clarification on my original comment. When I asked about comparing the economy with physical solids rather than gases, I was thinking about the INTERACTION between different solid components in a complex system rather than the behaviour of a single solid. For example, the interaction between two tectonic plates in nature. It’s the interaction between components which builds up the pressure in systems – not the individual components themselves.

      A recent macro-economic example would be the behaviour of the Swiss Central Bank. It fixed the exchange rate between the Euro and the SFr causing a pressure build up due to the inability of the SFr to appreciate in value. The ECB then came along with a policy which seemed like it intended to depreciate the Euro against other currencies including the SFr. The Swiss bank then changed its policy releasing the pressure build up and causing a one-off jump in the value of the SFr (of about 20% I recall). However, imagine that it had not done this. You would then have had two central banks implementing the exact opposite policies like two tectonic plates moving in different directions with a potentially explosive consequence.

    4. That is an interesting model -- the Franc and Euro exchange rate as a "fault line" between two tectonic plates. I hadn't thought of something like that.

      For the most part, I treat national economies as weakly interacting, but that surely could fail to be an accurate model.


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