Tag Archives: economics

Tumbling oil prices and what it means for GDP

The collapse in oil prices has been truly remarkable and it get TH wondering how the oil price shock would affect a country’s income, so he cracked open his old textbooks and worked through what it should mean, at least in theory. The analysis here is for a country that imports oil. But the analysis goes in reverse for a country that exports oil (or another commodity, such as coal or iron ore, for that matter). This post is very technical and possibly boring, but TH thought it would be useful to write down and share what he figured out, just in case it is of use to anyone else.

Oil Price

Consider a simple small (island) open economy (call it Wallaby Island, or WI for short).  WI produces one good (bread) and imports oil. Some of the bread is consumed and the rest is exported. It can borrow from or lend to the rest of the world if exports don’t match up with imports. There is no investment. We’ll keep prices of the locally produced consumption good fixed at $1 each (apparently the central bank is really good at maintaining price stability), but let the price of oil, which we’ll write as “p”, be something that can change (in response to developments in the global oil market). This last assumption is what we need to investigate the oil price shock.

Since all of WI’s income is derived from spending on the wheat it produces, we just add up that spending to get its national (gross domestic) income. Total expenditure on wheat equals WI’s total consumption spending (on wheat and oil), minus their spending on imported oil, plus their exports. Mathematically, where Y is income and M is the quantity of oil imports and the rest are what you think they are (C, consumption and X, exports), this is how we calculate income:

Y=C+X-p.M                         (1)

Next, we need to write down what determines spending on consumption and imports. We make the same assumptions as any first year textbook, and assume that the islanders spend a fixed amount (A) to cover basic needs plus a fraction of their income on consumption. They do the same for imports. Foreign spending on WI’s goods (i.e. WI’s exports) is assumed to be fixed for now.

C=A+cY                                 (2)

M=B+mY                             (3)

Now we can start to figure out how income changes in response to a change in the oil price. Mathematically, when we want to write a change in a variable, we put a d in front of it, so, in the language of mathematics, we want to figure out dY due to dp.

When one thing in the economy changes, everything else changes too, so the total change in WI’s income, we need to add up all the changes in consumption and imports (you’ll see that we separate the change in spending on imports into the change in the quantity and the part due to a change in the price):

dY= dC + dX – dM – M.dp                             (4)

This is a good moment to highlight an important problem with how terms of trade changes are measured by statisticians in charge of the national accounts. GDP, which is the standard measure of national income reported in the news, is generally measured keeping prices constant (to avoid confusing inflation with economic growth). That means that the last term in the equation (the M.dp bit) gets left out of the GDP calculation.  The statisticians are smart people and are fully aware of the short coming of the GDP measure, so they have an alternative measure, known as GDI, that includes the impact of a change in the terms of trade (i.e. the change on the price of imports). You will note that the change in GDI that we are calculating equals the change in GDP plus the change in import spending only due to the change in p.  That is, dGDI=dGDP+M.dp .

Getting back to how everything changes, note that since A, B, and X are assumed to be fixed, the only changes in C and M that are triggered by the oil price are those that flow through changes in income.

dC=c.dY                                (5)

dM=m.dY                            (6)

We can now work out how a change in the oil price affects income by substituting (5) and (6) into (4) and collecting terms.

dY=c.dY-m.dY – M.dp                    (7)

dY =-M.dp /(1-c+m)                        (8)

dY = -(c-m)M.dp/(1-c+m)  – M.dp                             (9)

What equation 9 tells us is that the change in national income equals an induced fall in GDP plus the direct reduction in income due to the higher price of oil. Of the total fall in income only a fraction, (c-m) of the total fall in income is accounted for in GDP statistics. For example, if c=0.7 and m =0.05, then only about two thirds of the total effect is captured by GDP.

We can multiply both sides of 8 by p/Y to work out the percentage change in GDP due to a one percent increase in the oil price as –pM/[Y{1-c+m)] =- m’/(1-c+m), where m’ is the share of import spending in income.  Let’s throw in some hypothetical numbers. Let m’ bet 0.1, c = 0.7, and m be 0.05, then the percentage change in income from a percentage increase in the oil price is minus 0.25.  So for our small open heavily oil dependent economy a 10 percent increase in oil prices reduces income by 2.5 percent. A 50 percent increase in the price of oil reduces income by about 12.5 percent (of which 8 percent shows up in GDP).

To do a fall in oil prices, we just reverse the sign, so a 50 percent fall in the price of oil causes a 12.5 percent rise in income (8 percent rise in GDP) for the residents of Wallaby Island.  Most economies don’t import only oil and so the effect is not likely to be so large. On the other hand, the reverse of this analysis largely hold for exporters, and some economies like those in the Middle East or Venezuela depend heavily on oil exports.  For these economies, large numbers like these seem reasonable. Either way, it gives you an idea of how important the oil price is.

This same simple technique can be used to figure out the impact on the world economy rather than the isolated effect on a small island economy.  But that is left until a later post.


How to balance inflation on the end of your finger

Five years after the  beginning  of the financial crisis, there are still a lot of people trying to come to grips with monetary policy and inflation. Here is an analogy that TH thinks might (usefully) help make monetary policy setting seem less like rocket science and more like child’s play.

Imagine that you have a stick balancing on the end of your index finger.  It’s a nice straight stick, about a metre or so long – perhaps a pool cue made for a child.  The stick is unstable, it could fall any which way, but for the sake of this thought experiment, imagine that it can only fall forwards, away from you, or backwards towards you.

If you are standing still and are lucky, you have it perfectly balanced, but at any moment, some random event could cause the still to fall forwards or backwards. If you do nothing, the force of gravity will quickly cause the pace at which the stick falls forwards or backwards to increase.  If the stick starts falling forwards, your natural instinct will be to push your finger away from you so that the base of the stick gets out in front of the top of the stick and halts the stick from falling over. With some skill, you’ll soon have it well-balanced on the end of your finger again.

By now, you have a pretty well-developed model in your mind of that stick.  It is also a pretty good model of (the Wicksellian cumulative process of) inflation and monetary policy. Where the bottom of the stick is and what it is doing (remember it can’t go sideways, only backward or forward) tells you about the nominal rate of interest; closer to you is a lower rate of interest, further away from you  is a higher rate of interest.  The top of the stick tells you about inflation – if it is falling forwards, inflation is increasing, backwards and prices are falling.  Clearly there is going to be a relationship between interest rates and inflation – you can play with the model in your head – or get a stick and try it out for yourself. The model has some pretty good predictive power. Try pulling the (virtual) stick towards you (cut interest rates) and what see happens to inflation.  Anyway, before going further you need two simple equations that might help to better convert our balancing stick into a model of inflation:


which simply says that the real rate of interest on a financial investment (a loan) is the nominal rate of interest (i.e. the interest rate on loans, which we will assume to be the same as the policy rate set by the central bank) minus the inflation rate, p*.

The other equation is


In this equation, R is the natural rate of interest – it is the rate of return on physical investments – from building a house or a factory.  The equation says that inflation is a function of (which is what the f stands for) the gap between the natural rate of interest and the real interest rate expected to be earned on a financial asset.  If r is less than R, so that it is profitable to borrow money and buy a real investment (a house or a factory), then the increased demand for goods such as these will cause the inflation rate to rise.

Let’s return to our stick analogy. Suppose you have the stick perfectly balanced on your finger.  It’s not falling forward or backward.  The base of the stick is right under the top. You are standing still. Remember that top of the stick tells you about inflation.  Since the top of the stick is not moving, inflation is currently zero. The real rate of interest is therefore equal to the natural rate of interest (this comes from the information summarised by Equation 2).  If you expect things to stay this way, or at least that the chances of the stick falling forward in the future to be the same as it falling backwards, then the expected rate of inflation would be zero too. And since the expected rate of inflation is zero, it is also the case that the nominal rate of interest must just equal the real rate of interest, which, as we said, is equal to the natural rate of interest.   Got it?     p* =0 and  p=0, so from Equation 2, R=r and from Equation 1, r=i, so i=R too.

Now all the hard work is done, try doing the same thought experiment again.  Imagine that you pull your finger towards you just a bit so that you pull the base of stick from under the top. This shock causes the nominal rate of interest and consequently the real rate of interest to fall below the natural rate and stimulates people to borrow and invest. It drives up demand in the economy and prices start to rise – i.e. inflation goes up.  The top of the stick starts falling forward.  Quickly, people start to realise that, unless something is done soon, there is going to inflation in the future.  The higher expected inflation means that, given the nominal rate of interest, the real rate of interest (real cost of borrowing) is now even less than before, which further fuels an increase in investment and inflation.   The process feeds on itself in a vicious circle, creating a process of accelerating inflation and the stick is soon accelerating rapidly towards the floor.

The inflationary process can be stopped by pushing forward on the bottom of the stick – this is analogous to increasing the interest rate.  Just as you would have to push the bottom of the stick forward to get in front of the top to stop its fall, to make the real rate of interest equal to the natural rate of interest and set inflation back to zero, the increase in the interest rate will have to overshoot the rate of increase in prices. For example, if the shock has caused inflation to increase from 0 to 5%, then the increase in the nominal rate of interest – the policy rate – will have to be more than 5%.  This is because of the effect of inflation expectations.  Just like the stick has some momentum, so do expectations about future inflation, and the policy rate must increase by enough to offset not only the current rate of inflation but any expectations that are forming based on the current behaviour of the economy about future inflation.

So what does our simple model tell us about current monetary policy? TH reckons it tells us quite a lot. First, monetary policy, like balancing a stick on your finger, is more of an art than rocket science. You don’t need to know the laws of physics to balance the stick, you just need practice. There are also different styles too.  Some stick balancers (read inflation-targeting central bankers) could prefer slow graceful adjustments to the policy rate – that allows for longer periods of inflation away from the central bank’s target (Australia says inflation will be around 2 to 3 percent, on average, over the course of the cycle, which could be up to 10 years!). Others might prefer swifter, sharper policy adjustments and more stable prices.    Both could work. We could call the two types of policy reactions  as Type I and Type II. Australia would be a Type I inflation targeter.

Expectations about inflation

As you might have guessed, expectations about future inflation are also important in this model.  Suppose that the central bank has a zero inflation target, and people are firmly convinced that the central bank will keep inflation close to zero, then an inflationary shock won’t need such a swift or large interest rate response from the central bank because it won’t need to offset the stimulatory, self enforcing  effect of inflation expectations causing a reduction in the real interest rate and stimulating demand.  To make their life easier, central bankers will continuously remind you of their inflation objective to do what they can to keep you convinced that inflation expectations are “well-anchored.”

The zero lower bound on interest rates and forward guidance

You can do the inflation thought experiment for deflation too. Imagine that the stick starts falling towards you.  What do you do? The obvious thing is  to pull the base of the stick towards you and cut interest rates. With some manoeuvring, the deflation will be halted.  But what do you do if you can’t pull the still towards you.  If there was nothing else you could do, then there would be a deflationary spiral and you would have lost the stick. But of course there are other things you can do.  Suppose you were once a quick reacting (Type I) central bank that kept inflation close to target with swift and large if necessary interest rate responses.  Now you only have a little bit of lee-way, maybe to cut the interest rate to zero from say, 2%.  One trick is to switch type from a Type II central banker into a central banker that prefers slow and small adjustments (Type I).  If you don’t tell people that you have switched to Type II from Type I monetary policy, they may mis-read a small interest rate cut for policy ineffectiveness. Those deflationary expectations could start getting away from you, reinforcing the downward spiral.  So what do you do? You provide guidance to the markets that you are going to stay “low for long”, possibly until some condition outside of the control of the central bank like unemployment is met, and remind them of your inflation target to keep inflation expectations well anchored. This has become known as forward guidance. TH prefers Open Mouth Operations.

The zero lower bound on interest rates and quantitative easing

But interest rates are not the only game in town.    Everyone knows that printing money (aka quatitative easing) is inflationary right?  So another way to prevent deflation when you can’t pull back on the stick is to print money.  This will create the expectation that there will be some inflation, which will lower the real rate of interest for borrowers and stimulate demand.  Effectively, it’s finding a way to push on the top of the stick.  Again, by helping to anchor inflationary expectations (in this case offsetting expectations about deflation), quantitative easing can give help make the interest rate tool more effective at the lower bound.

Monetary policy to increase inflation with rational expectations

As noted above, inflation expectations are important in this model .  The momentum in the stick, which keeps it falling forward or backwards, even after some policy response, is a proxy for what economists call adaptive expectations. It simply means that people form expectations, at least partly, on the basis of what happened in the past.   What would happen if they were fully rational or forward looking? In that case, then things might be a bit topsy turvy. For example, suppose that the central bank announced a new inflation target of 10% (up from 0).  If the natural rate of interest was 3%, then, if everyone fully believed that the central bank would hit is target, starting a year from today (or tomorrow at annualised rates), all the central bank would have to do is INCREASE interest rates immediately to 3+10 = 13% to create inflation.  Using our stick analogy, the central bank would announce a new inflation strategy, which would stimulate demand and get the top of the stick moving forward, and then simultaneously start walking forward, pushing on the bottom of the stick.  The central bank would then just keep on walking forward at a constant pace that was analogous to constant increase in prices of 10% (perhaps ten steps a minute), with the top of the stick perfectly aligned with the bottom.

If you are quick, you might wonder whether the model with adaptive expectations could ever be consistent with the model with rational expectations.  After all, in the adaptive expectations case you cut interest rates to create inflation, in the rational case you raise them.  The answer is relatively simple, once you think of monetary policy as just balancing a stick on your finger.  After all, you know that you could, with practice initiate a process where you went from standing still while balancing the stick, to walking forward at a constant pace of 10 steps per minute. First you would cut interest rates, get inflation moving and soon adaptive expectations would learn that you were serious about targeting 10% inflation. Once you were advancing forwards at close to 10 steps per minute, you would tighten policy by pushing forward on the stick to alleviate the acceleration created by gravity and momentum. It might require a bit of back and forth, but eventually you’ll achieve  your goal.  You understand this, and so do market participants who seek to learn to come to rational conclusions through adaptive means.  All you need to know is that, in addition to cutting rates to increase inflation, you can raise them in the future to prevent accelerating inflation. So long as you know that, you will quite rationally understand that you can raise inflation by cutting interest rates.


QE3 and the Assignment Problem

The US Federal Reserve recently announced its third round of quantitative easing – i.e. loosening monetary policy by increasing the supply of money. It got Torrens Hume thinking about whether monetary policy was really the right tool and whether US monetary policy might be too loose. There are many ways of thinking about the problem, but TH was reminded of one of the most important classes he had in his undergrad international economics course on the assignment problem. We talked about it once before (here).

In its simplest form, the assignment problem says that if you have two policy objectives you need two policy instruments. Understanding this simple bit of Dutch inspiration was pretty important when the global economy was on a system of fixed exchange rates. This was because it meant that if you were trying to maintain external balance (i.e. balance in the balance of payments – basically net exports – to avoid a crisis that required a visit from the men in black at the IMF) and internal balance (full employment) then you needed two policy tools – monetary and fiscal policy. Monetary policy was best suited to fixing the exchange rate, leaving fiscal policy to maintain full employment.

All that came to an end about 30 (well actually 29) years ago when Nixon nixed the Bretton Woods system, and, in doing so, drove the world towards a system of mostly floating exchange rates. Countries like Australia, which finally adopted a floating exchange rate in the 1980s and Canada, which pretty much had one from day one, found that now the market automatically adjusted the exchange rate to maintain full employment, leaving policy makers free to choose whether to assign fiscal or monetary policy to the maintenance of internal balance.

Fast forward to today. Pretty much every advanced economy has decided to assign the job of maintaining full employment solely to monetary policy – thus leaving fiscal policy to achieve other objectives: mostly social objectives such as income redistribution, education, health and so on. And to ensure that they did their job free of political influence, governments went further made their central banks independent and gave them explicit targets (such as inflation targets) to pursue. With the exchange rate free to adjust monetary policy no longer had to be coordinated with fiscal policy, it just had to respond to it – if the government deemed it fit to spend more on schools, roads and so forth, the central bank could simply offset the expansionary effect with a tighter monetary policy. Likewise fiscal contraction could be offset with monetary expansion.

The trouble is that the US doesn’t have a fully flexible exchange rate. It has some hangers on, most notably China. This means that to a certain extent its exchange rate is effectively fixed. But the US behaves like it has a flexible exchange rate: its central bank is mandated to maintain full employment not external balance. As a consequence, it is setting a loose monetary policy. Because the exchange rate can’t respond vis-a vis the China’s of the world the adjustment tends to fall on other economies, the US dollar tends to depreciate against those that it can (e.g. the Aussie and Canadian or Brazilian) currencies, but not against the fixers (e.g. China). This means that the monetary policy tend to help US exports to the former group of countries, but encourage imports from the latter. Since monetary policy is targeted at internal balance the effect on external balances is not clear.
That leaves the US with a problem. It has a partially fixed exchange rate and the monetary policy tool is being assigned to internal balance. But no policy tool has been assigned to maintain external balance. It’s just flapping in the wind, determined partly by monetary policy, partly by the whims of policy makers in the rest of the word that tinker with capital controls, fix exchange rates and just generally intervene with the global economy, and partly by some troublesome market distortions too.

Perhaps the US needs to assign a policy tool to maintain external balance. US Fiscal policy is “stranded” at the moment – caught between the need to control the growth of the US government debt and do so without causing another recession. Arguably, the US could use fiscal policy tools to encourage a “fiscal devaluation” – changes in taxes and subsidies that raise the prices received by producers and paid by consumers of goods relative to services to bring about a structural transformation of the economy. This would tend to reduce the trade deficit and encourage investment in manufacturing, which could help boost growth. But this sounds a bit like central planning and it’s not obvious that it will work in practice.

And speaking of Europe …, OK we weren’t, but now that we are, the assignment problem is even more relevant for them. Nearly all the Europeans governments external and internal balance problems of some sort. The periphery have exceptionally high unemployment and are mired in recession as well as having current account deficit problems. But policy tools that they have at their disposal are limited. They all have high debt levels and many (especially in the periphery) can’t use fiscal policy. None of them have monetary policy instruments (because the ECB only sets a euro-wide monetary policy) nor a flexible exchange rate. So how will they achieve internal and external balance? What two instruments do they have at their disposal? TH reckons this problem explains why the regulators are going so easy on periphery banks, which are able to create credit and support the local economies. But then what policy instrument do you assign to financial stability? TH has a head ache now. He’s going to bed.