Thursday, August 20, 2015

Don't forget the VAT

Update: Mark Sadowski (in comments below) correctly points out that there was no VAT change between 2008-2009. I have corrected my error in the figures and results. There is a tiny change in the conclusion (where the "VAT increase" is instead referred to as a "spike in inflation" in the second to last paragraph of the + 2 hour update)
Scott Sumner is linking to Mark Sadowski again and showing us that inflation as measured by the GDP deflator has risen in Japan since 'Abenomics' went into effect. However, the graph shown fails to take into account three two VAT increases -- which Scott Sumner explicitly pointed out might fool people -- that show up visibly in the GDP deflator data. Here's Sumner:
Japan will be hit by an adverse supply shock next year (higher sales tax rates) which will boost inflation–making it look like they will hit their 2% target. Don’t be fooled.
And here's the data and a version with the VAT increases filtered out ...


If you remove these VAT increases, the change is less dramatic and the change appears to start before the monetary policy changes were announced.


I make a pretty good case here that the change in direction of the price level (core CPI) is mostly due to the fiscal policy component. The information equilibrium model seems to get the data about right without any monetary policy effects.

...

Update + 2 hours:

If you reduce the size of the averaging window from 10 quarters to 4 (i.e. 1 year), you can see that the effect of the VAT doesn't stick around in 2015 ... much like the effect of the VAT increase in 2008 and 1997:


Also using a single year averaging means that the start of the increase in inflation is pushed all the way back to 2010 (that year is no longer impacted by the VAT increase spike in 2008). Heck, here's using only a single quarter 'average':


The trend towards increased inflation appears to start after the financial crisis; Abe appears in the middle of it.

29 comments:

  1. So both increasing interest rates and raising taxes increases inflation. Holy cow!

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    1. Hi Bill,

      Raising rates is only inflationary if kappa < 1 in the IT model; in the case of Japan above, kappa ~ 1.

      Delete
    2. Hi, Jason,

      I guess I should have included a ;). Raising taxes is supposed to be deflationary, by removing money from the economy, and raising interest rates is supposed to be deflationary, by discouraging lending.

      Delete
  2. Is that the same as the consumption tax Mark mentions? What of his argument that a similar tax increase in the 90s didn't do anything to inflation?

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    1. Hi Tom,

      Yes that is the same tax. He said it didn't have a sustained impact on inflation -- which is true as you can see in the second figure above (where the blue line is above the yellow one). It goes away in 2000.

      The impact of the 1997 increase lasts exactly as long as the averaging window (10 quarters = 2.5 years). I am sure a sizable fraction of the current increase will vanish when the 2.5 years since April of 2014 has elapsed -- which would put us at October of 2016.

      What is happening is that the spike from the VAT increase remains in the averaging window for 10 quarters and then falls out. Averages are sensitive to outliers, so the impact is large.

      Basically, if you reduce the window to a single year, the impact falls out after a single year ...

      https://twitter.com/infotranecon/status/634485890732163072

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    2. I updated the post as well ...

      Delete
  3. I'm not sure your point about timing is relevant...some studies seem to show that the market reacts to news before it is announced...especially when the "secret" is being kept by government officials

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    1. I agree and I had a line in there about expectations originally, but decided to take it out because I didn't want to get too combative :)

      However in the update graphs the trend clearly shifts right after the financial crisis (before the 2012 election was even a twinkle in Abe's eye) and there is no obvious change in that trend from 2010 to the present.

      Delete
  4. You're assuming that the change in the consumption tax caused a 3% increase in the price level as measured by the GDP implicit price deflator.

    This is totally implausible.

    To put this into perspective, according to the Japan Statistical Yearbook:

    http://www.stat.go.jp/english/data/nenkan/index.htm

    Consumption tax revenue in FY 2013 (which ran from April 1, 2013 to March 31, 2014) was 10.65 trillion yen. NGDP was 482.7 trillion yen in FY 2013 according to the Japan Cabinet Office. Thus consumption tax revenue was 2.2% of GDP in FY 2013 when the consumption tax was 5%. Thus the increase in the consumption tax to 8% very likely raised consumption tax revenue to 3.5% of GDP or an increase of about 1.4% of GDP.

    Even if *100* of the increase in consumption tax revenue passes through to the price level as measured by the GDP implicit price deflator, that's only a 1.4% increase, not 3%.

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    Replies
    1. Correction: the increase in consumption tax revenue is likely closer to 1.3% of GDP.

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    2. If everything in the economy has the same price p and the VAT applies to everything, then an increase in the VAT from 5% to 8% should increase the prices (if they are measured after VAT) by

      p(1 + 0.08)/(p(1+0.05)) ~ 2.86 %

      It doesn't matter the amount of revenue generated by the tax increase as the GDP deflator is a measure of prices, not quantities.

      A price index is a weighted sum of prices:

      P = Σₐ pₐ wₐ

      If the VAT is included and applies to all goods equally, then:

      P = Σₐ (1+v) pₐ wₐ = (1 + v) Σₐ pₐ wₐ

      and the change in VAT shows up in the price index

      P₂/P₁ = (1 + v₂)/(1 + v₁)

      Now only about 60% of GDP is consumption spending in Japan, so it's not the full 2.9%. In the graph above, the effect is only about 2% in 2014. But again, the jump is fairly obvious and occurs exactly where the VAT increases happen (and only where the VAT increases happen) and has about the magnitude expected. Occam's razor says it's the VAT.

      What is causing prices to spike by a few percent at the same time as the VAT increases (and only when there are VAT increases) if it's not the VAT increases?

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    3. The average rate of change in the GDP deflator in the 10 quarters through 2012Q4 is (-1.4%). The average rate of change in the GDP deflator in the 10 quarters through 2015Q1 is +1.4%. The change in average inflation is thus 2.8 points of which the most that the consumption tax increase could have contributed over that 10 quarter period is about 0.52 points.

      In short, the consumption tax increase’s contribution to the increase in average GDP deflator inflation over the past 10 quarters represents less than one fifth of the total.

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    4. Jason:
      "If everything in the economy has the same price p and the VAT applies to everything,...'

      But as you acknowledge later the consumption tax does not apply to everything.

      Jason:
      "It doesn't matter the amount of revenue generated by the tax increase as the GDP deflator is a measure of prices, not quantities."

      The GDP deflator is a measure of the price level of GDP. By definition the effect of a consumption tax increase on the price level of GDP cannot exceed the rate at which the tax revenue increases per unit of GDP. (This isn't even economics, this is mathematics.)

      "Now only about 60% of GDP is consumption spending in Japan, so it's not the full 2.9%. In the graph above, the effect is only about 2% in 2014."

      Lots of things classified as "consumption" are exempt from the Japanese consumption tax, not the least of which is rental housing.

      Delete
    5. avg = (t₂ - t₁)⁻¹ ∫dt (d/dt) log D = (t₂ - t₁)⁻¹ (log D(t₂) - log D(t₁))

      The impact of a VAT increase only depends on the endpoints of the averaging window (fundamental theorem of calculus). So if t₂ > t_vat > t₁, then D(t₂) is going to have a VAT increase and D(t₁) won't. If inflation from t₁ to t₂ is i, then

      D(t₂) = (1 + i) D(t₁)

      so

      avg = (t₂ - t₁)⁻¹ (log(1+i) + log D(t₁) - log D(t₁))

      take i to be small so that log(1 + i) ~ i and WOLOG take t₂ - t₁ = 1

      avg = i

      Now add VAT increase that happens at some time between t₁ and t₂

      D(t₂) = (1 + i + v) D(t₁)

      then

      avg = (log(1 + i + v) + log D(t₁) - log D(t₁))

      for small v and i small log(1 + v) ~ v + i so

      avg = v + i

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    6. Jason,
      The GDP implicit price deflator rose 1.95% in 2014Q2, the quarter that the tax increase took place. Based on the likely size of the increase in consumption tax revenue as a percent of GDP (approximately 1.2% of GDP), that means that over 60% of the increase in the GDP implicit price deflator that quarter was due to the tax increase.

      Sure if you increase the size of the averaging window the relative importance of the tax increase decreases. But so what?

      The point is that prior to Abenomics the GDP price deflator *fell* at an average annual rate of 1.4% in the previous 10 quarters. In the past ten quarters it has *risen* 1.4%. The *change in the rate of change* in prices dwarfs the plausible effect of the consumption tax increase on the *level* of priices.

      Delete
    7. Mark, you said:

      "By definition the effect of a consumption tax increase on the price level of GDP cannot exceed the rate at which the tax revenue increases per unit of GDP."

      I don't think this is true ...

      Take a price level that is mostly goods that the VAT applies to. And take a GDP that is mostly goods VAT doesn't apply to. In that case the change in the price level is going to be dominated by the VAT, but the revenue generated by the VAT is going to be a tiny fraction of GDP.

      In the limiting case, take zero goods sold subject to VAT and the price level is entirely goods where the VAT applies. There, the price level goes up by the VAT increase, but the revenue generated by the VAT is zero as a fraction of GDP.

      Here's a specific example using a two-good market:

      https://twitter.com/infotranecon/status/634522730440859648

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    8. "In the limiting case, take zero goods sold subject to VAT and the price level is entirely goods where the VAT applies."

      But the price level consists of both goods and services subject to the consumption tax *and* goods and services that are not subject to the consumption tax.

      In order for what you say to be true things like rental housing and government employee wages and salaries (both of which are *not* subject to the consumption tax) would have to be excluded from the GDP implicit price deflator, and that is clearly not the case.

      P.S. I mention government employee wages and salaries because they are by far the largest part of the government consumption component of GDP.

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    9. That's why I did the example at the link. There are goods excluded from VAT included in the price level and.

      In the particular case, the price level is 90% VAT goods and 10% not VAT goods, but GDP is 1 part VAT goods and 10 parts not VAT goods. In that case the change in price level for a VAT going from 5% to 8% is about 2.6%, but the change in revenue from the VAT as a fraction of GDP is about 0.27% ... thus the change in price level is larger than the change in revenue from the VAT as a fraction of GDP.

      https://twitter.com/infotranecon/status/634522730440859648

      This is not entirely a strange estimate. The GDP deflator doesn't show effects that are that different from core CPI, and much of that is made from consumption goods. However, rental housing, government spending and financial services, etc make up a big fraction of GDP and aren't subject to VAT.

      Delete
    10. The weight of goods in GDP is *the same* as the weight of goods in the GDP price level. In this particular case, if the GDP price level is 90% VAT goods then GDP is also 90% VAT goods.That is the *definition*.

      At the 5% level the revenue from the tax is equal to

      ((1.05-1)/1.05)*0.9x100=4.2857% of GDP

      assuming 90% of GDP is subject to the tax.

      At the 8% level the revenue from the tax rises to

      (((1.08-1)/1.05)*0.9)/(1+((1.08-1)-(1.05-1))/1.05*0.9)*100=6.685237% of GDP.

      Assuming the quantities sold in each case do not change.

      (The denominator reflects the fact that total GDP has gone up due to the 2.571% increase in the price level.)

      The change in tax revenue is thus 2.399537% of GDP.

      Yes there is a difference between 2.4% and 2.6% but it is trivial.

      Revenue is roughly the same as the change in the price level.

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    11. If the GDP is weighted the same as the prices, I still get the change in revenue as a fraction of GDP is 3/5 the change in the price level in my example:

      https://twitter.com/infotranecon/status/634550218571190272

      Your example neglects the quantity of sales at the price that gives you GDP ...

      GDP = Σₐ pₐ wₐ qₐ

      where q is the quantity sold of widget a.

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    12. "Your example neglects the quantity of sales at the price that gives you GDP ."

      The actual quantities are totally irrelevant. 90% of GDP consists of goods that are taxed and 10% of GDP consists of goods that are not taxed. Assume the initial price level is equal to one. And remember, both GDP and the price level include the tax.

      (This is actually a fairly simple concept. If you throw in too many bells and whistles you won't be able to see the forest for the trees.)

      Delete
  5. Even more important than any of this is the fact that NGDP rose at an average annual rate of 2.27% in the last ten quarters.

    https://thefaintofheart.files.wordpress.com/2015/08/m-sadowski_japan_31.png

    The last time NGDP rose that fast over a 10 quarter period was 1993Q3, nearly 22 years ago.

    That’s clearly not due to the consumption tax increase (that is, unless your model predicts that tax increases will be expansionary).

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    1. I have no particular issue with NGDP going up. It appears to have gone up by roughly the amount expected by the change in government spending ...

      http://informationtransfereconomics.blogspot.com/2015/03/the-keynesian-part-of-abenomics-is-part.html

      :)

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    2. Jason,
      NGDP has gone up from 472.2 trillion yen at an annual rate in 2012Q4, to 499.8 trillion yen in 2015Q2 or an increase of 27.6 trillion yen.

      General government consumption, investment and inventories went up from 117.8 trillion yen in 2012Q4 to 127.2 trillion yen in 2015Q2 or an increase of 9.4 trillion yen.

      In other words government investment and consumption has increased from 24.9% of GDP to 25.5% of GDP. (Gasp!)

      In order for this increase to explain the entire increase in NGDP the spending multiplier would have to be equal to 3 or more, and given the fact that net tax revenue has risen by an even larger amount, the tax multiplier would have to be zero or less.

      Not very plausible.

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    3. Never get involved in a land war in Asia
      Never go in against a Sicilian when death is on the line
      Never trust a monetarist estimating a Keynesian multiplier ...

      :)

      Net borrowing has gone from 5% to 10% of NGDP. It works out to a multiplier between 1 and 2 ...

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    4. The simplest way to check this is to consult Krugman’s favorite reference on these matters, which is the Cylically Adjusted Primary Balance (CAPB) found in the IMF Fiscal Monitor.

      http://www.imf.org/external/pubs/ft/fm/2015/01/pdf/fm1501.pdf

      According to Table A4 on page 79 Japan’s general government CAPB decreased from (-6.9%) of potential GDP in calender year 2012 to (-7.5%) of GDP in 2013. This decrease in the CAPB of 0.6% of GDP reflects the fiscal stimulus and was before the increase in the consumption tax in April 2014.

      But the CAPB rose to (-6.6%) of GDP in 2014 and is projected to rise to (-5.4%) of GDP in 2015. The CAPB is projected to increase by 1.5% of GDP between 2012 and 2015. So evidently the discretionary increase in taxes has exceeded the discretionary increase in spending.

      So no, by Krugman's favorite measure, Abenomics has on average been fiscally contractionary.

      P.S. My dissertation was on fiscal policy.

      Delete
  6. Also, there was no change in the consumption tax between April 1997 and April 2014.

    http://www.nippon.com/en/features/h00013/

    The change in the consumption tax you claim took place in 2008 simply is not true.

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    Replies
    1. You are absolutely right. I will correct the errors.

      Delete

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