## Monday, May 27, 2013

### GST And Inflation Part III: The Economists’ Lament

The title, in case you missed it, is in plural. It’s a common complaint in the profession, and something the comments to my posts on GST make very clear – many people simply don’t understand inflation.

It’s actually a pretty easy concept to understand. Why then does virtually every non-economist get it wrong?

The textbook definition is that inflation is a general rise in the price level over a period of time, which is pretty straightforward – for economists anyway. But laymen generalise that to mean that any rise in the price level is inflation. And that’s false.

But it’s probably best to show this in an example, just to make the difference clear. I’ll try to make this as non-technical as I can.

Let’s start with a measure of consumer prices that starts with a value of 100 in period 1. I assume a constant rate of inflation of 5% per annum, and I’m examining the change in consumer prices over 30 periods. The graph will look something like this:

Like any time series that is subject to a constant rate of increase, this one actually describes an exponential curve over time. If we were to calculate the rate of change at any given point in time ({xt/xt-1}-1), we would get 0.05, or 5% in percentage terms.

But exponentials are hard to grasp intuitively, so the recommended procedure is to apply a natural log transformation, which yields this unambiguous straight line:

Here, it’s just a subtraction operation to get the rate of change ([Ln(xt) – Ln(xt-1)]) which yields 0.49, which while not quite the same, is close enough for jazz (especially since it’s a trivial exercise to convert it back to the original series). It’s also a lot easier to see the impact of changes in the price level.

The important thing to note here is that whether you use the original curve or the log-transformed curve, it’s the slope of the curve that defines inflation, not the particular value the curve has at any point in time.

Now, let’s assume the imposition of a 7% tax at time t=16. We further assume that this rate applies to all consumer goods, and we further assume in our perfect little world that there are no changes to supply or demand. This is what happens to the original CPI:

To make what happens clearer still, this is the log transformed series:

What’s going on here is that the price level simply shifts up – there is no change in the slope of the CPI line after the imposition of the tax. The tax, given our assumptions, is therefore not inflationary.

For any given shock or impetus to give rise to inflation, tax or otherwise, it must change not just the level but also steepen the slope of the CPI. If it doesn’t, it’s not inflationary. I’ll go further and say that an event or shock that steepens the slope but not the level is inflationary, even if there is no initial increase in the price level.

Just to buttress this argument, monetary policy in Singapore is unique in that they use the SGD exchange rate as the primary monetary policy instrument (I really must get round to writing about that one day). That in itself is not unusual – what is unusual is that they do not target a particular level for the exchange rate, or a particular currency. No, what MAS does is target the slope of the appreciation of the SGD, to influence the slope of the increase in their CPI.

It’s the slope that counts, not the level.

To summarise: a change in prices is not in itself inflation. It’s only when the overall rate of change in prices is affected over time can we call something inflationary.

What happens if we relax our assumptions? Some commentators appear to think that with the increase in prices associated with GST, these will be passed on to consumers in the form of even higher prices, thus igniting real inflation rather than a one-time increase in the price level. Others think that because GST will take time to spread through supply and distribution networks, the pace of price increases will be spread across many periods, and thus result in inflation. Others still think that as GST slowly gets imposed on goods and services that had previously escaped taxation, the resulting price increases result in inflation.

The answer in all the above is the same – the imposition of GST will result in a one-time and one-time only increase in prices, all other things equal. This is not inflationary but just a change in the price level alone. It doesn’t matter if the tax is spread across different sectors, or spread across time – in each sector and at each point in time, it’s a one-time only deal.

Experience in other countries invariably point to increases in prices consistent with the imposition of new taxes, but no changes in long term inflation trends i.e. the slope does not change, it only shifts up (or down).

Now, the transition period immediately after the imposition of a GST will be marked by an increase in measured inflation, but this is merely an artefact of the method of calculation. Since there’s no real change in the slope, this is illusory.

There’s something else as well that has bothered me about this intertwining of GST and inflation, which I’ll cover in the next post.

1. Hisham. wouldnt an increase in the price level result in a country becoming economically less competitive and thus present a cause for concern from a competitive standpoint?

1. Jon,

A higher price level is a necessary condition for being a high income nation. You can't improve wages without increasing the prices people have to pay. Focusing on low prices for the sake of competitiveness risks being caught in a low-cost/low-wage equilibrium e.g. the proverbial middle income trap.

2. Noted about your point on increased prices with increased wages. But can't you have increased wages with no change in prices through higher productivity?

3. roger,

One problem is, will increased productivity result in higher wages? On the evidence of the last decade, the answer is no.

A second reason is that, specifically for services, higher productivity = higher prices anyway.

2. I try to understand this, correct me if I'm wrong.
Inflation = general rise in price level over a period of time.
'over a period of time' is generic term.

So, in your example, there is an inflation, if we limit the time frame, i.e from period 14 to period 16 right? But not if we broaden the time frame.

1. @sicfallacy

If price increases happen in only one period and not in others, that is not inflation. This doesn't change, whichever time frame you choose.

3. Hi Hishamh, wouldn't the 1 time spike in CPI, already changes the slope of increase in CPI (inflation)?

In your graph, if I connect two points of Ln CPI2 (before and after the 1 time spike) to draw a straight line, the slope of the line is greater than Ln CPI. Thus, the 1 time spike in CPI does contributed to an increase in the rate of inflation if seen over a period of time, correct?

1. Kenny,

Mathematically, you're right. During the period of the price increase from the tax, the slope of the line will change, before returning to "normal".

The key to thinking about this is the time period of the change. Most tax implementations of this sort have a D-Day approach - you switch between different tax regimes at a cutoff date. So the temporary change in slope will only occur in that one day only.

If you want to get technical about it, the change in slope only occurs during those hours (minutes? seconds?) before and after the tax change comes into effect.

For practical purposes, it's really an instantaneous shift in the "normal" CPI curve.

2. I think I share his view. Even if you don't just focus on the minute-th the spike happened: if you draw a line to connect point before the spike, point A, to a point after the spike but further away, point B, then you can clearly see the inflationary slope change. I think a dual interpretation is warranted here. A sharp jump from point A to new level, and constant growth after that (your case), is the same as reaching from point A to new point B via an inflationary route. So one can still argue it is inflationary. Intuitively, if price spiked 10 folds yesterday but growth remained constant until today, it's hard to still say things are not inflationary if you compare prices two days before and today.

3. @anon 11.57

Actually you can't argue its inflationary, by definition. If the tax does not affect the long term growth rate of prices before or after its implementation, it is not "inflationary", irrespective of whether there is a change in prices or not.

Again, this is confusing the price level with inflation.

4. Hmm.... I don't think we're confused between price level and inflation, it's put forward quite clearly. We just moved one-step beyond that to say that this definition can be self-defeating. A sharp change in price level can be equated to a change in long term growth rate of prices, if you interpret it the right way. Imagine constant upward sloping line from time 1 through 20. If there is no spike, the slope of line connecting point 1 through 20 is constant 5%. When the spike happens at time 10, connecting a line from point 1 to 20 now show a slope of 8%. So in a way, by the definition of slope change, this is inflationary. Long term growth of prices have been changed depending on how you look at it.

5. @anon 11.06

What you are looking at is no more than the mechanical calculation of inflation, and the "increase" in the rate of inflation is a mathematical illusion. A sharp change in the price level cannot be equated to a change in the long term growth rate.

To illustrate, most expressions of inflation use both the monthly and annual growth rate of the CPI. With a monthly growth calculation, the spike in prices caused by a tax only raises the calculated growth rate in the month the tax is implemented.

With the annual growth calculation, the rate of inflation is only increased in the year following the implementation of the tax.

Once the denominator in the growth calculation moves past the tax implementation date, the calculated inflation rate reverts to its long term trend i.e. there is no change in long term inflation.

6. Well, what you claim in my case -a change in long term slope -a Mathematical illusion, your case of reverting to long term growth with annual calculation -is to me an unfortunate Economic illusion. Mathematically, the long term growth has been tempered with; this is not an illusion, it's a numbered, algebraically provable fact. For example, if you perform the spike for 10 times in a month, the long term trend line will be bent in the most recent period even if assumed constant growth after each spike. And I think this is more reflective of what is happening at the ground.

7. @anon 10.19

But we are not talking about 10 spikes in a month, we are talking about the effect of the imposition of a tax on the overall price level, which is just once.

4. Hi, how do u define one time in only one period? How long is your period? 12 months, 5 years, 20 years or forever? If Government set 4 percent gst, then after one year, change to 7 percent. And so on. So, based on your define, this is not inflation, but is a rise of price? Thank you.

1. @anon 8.06

I define it as the point in time that the tax takes effect. There's plenty of economic research in this field across many countries that show that the impact of such taxes result in only a one-time increase in prices, and not an acceleration in the rate of increase of prices.

2. So, u should draw a point at that time, not extrapolate it as a line. However, investopedia define it in addition the purchasing power will be falling, do u include it. Or is the fallacy of investopedia? Or u convince it is same no reduction in purchasing power? Thank you.

3. @anon 11.07

Purchasing power is just the flip side of rising prices, another perspective if you will - it does not change the fundamental analysis.

If you want to define inflation as the loss of purchasing power, it would properly speaking be the continuous loss of purchasing power, not a one-time loss as would occur with the imposition of a consumption tax.

5. One more thing, does CPI reflect our market price or just based on kedai 1 malaysia? So if CPI for certain goods decrease, does it mean maerketing price also decrease. For me, CPI only for paper view only, it doesn't make any sense.

1. @anon 8.12

No, it is not just from KR1M.

The overall collection methodology is described here.

Quote:

"The Department of Statistics, Malaysia carries out monthly consumer price collection for the whole country. It covers a total of 135 collection centres, that is, 98 price collection centres in Peninsular Malaysia, 19 price collection centres in Sabah and 18 in Sarawak. Field officers collect prices of about 512 items from these selected outlets. The main objective of the price collection is to obtain data on prices paid by the consumers for fixed items of goods and services in the Consumer Price Index basket. These data will be used to compute the Consumer Price Index where in general, the index will be used as an indicator for price changes and as a 'proxy' of the inflation rate for the country."

The composition of goods in the CPI basket is not arbitrary, but based on the Household Expenditure survey conducted every 2-3 years i.e. based on what Malaysians actually spend their money on.

This is no different than the way consumer prices are collected and aggregated into indexes in other countries around the world.