Monday, June 2, 2014

Depreciation

From a post by Brad DeLong on Krusell and Smith's comment on Piketty's "Capital in the Twenty-First Century:"
As time passes, it seems to me that a larger and larger fraction of Piketty's critics are making arguments that really make no sense at all--that I really do not understand how people can believe them, or why anybody would think that anybody else would believe them. Today we have Per Krusell and Tony Smith assuming that the economy-wide capital depreciation rate δ is not 0.03 or 0.05 but 0.1--and it does make a huge difference...
From page 43 of Piketty's book:
This depreciation is substantial, today on the order of 10 percent of GDP in most countries...

32 comments:

  1. Very timely, esp. since Brad just issued this complaint, "I regret that I really have run out of DeLong Smackdowns--run out of people making what I think are good, or even arguable, criticisms of me that show that I do or perhaps might need to mark my beliefs to market."

    http://delong.typepad.com/sdj/2014/06/monday-smackdown-watch-naughty-naughty-salim-furth-how-can-we-have-a-dialogue-with-these-people-growth-and-debt-yet-agai.html#more

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  2. As was pointed out in the comments of this post by Alex, 10% of GDP is not the same as 10% of the capital stock which is what is being used by Krusell and Smith. That being said, I am not sure DeLong's argument really matters for Krusell's and Smith's point anyway.

    http://marginalrevolution.com/marginalrevolution/2014/06/piketty-v-solow.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+marginalrevolution%2Ffeed+%28Marginal+Revolution%29

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    Replies
    1. So this put's us back in DeLong's ballpark or lower given Piketty's number. I know Krusell and Smith to be serious empirical guys. They didn't pull that number out of thin air. What's appropriate here?

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    2. A 10% depreciation rate seems to be RBC practice. From Prescott's "Theory Ahead of Business Cycle Measurement"

      The artificial economy has but one type of capital,
      and it depreciates at rate delta. In fact, different types of
      capital depreciate at different rates, and the pattern of
      depreciation over the life of any physical asset is not
      constant. Kydland and I (1982, 1984) simply pick
      delta = 0.10. With this value and an annual real interest rate
      of 4 percent, the steady-state capital-annual output
      ratio is about 2.6. That matches the ratio for the U.S.
      economy and also implies a steady-state investment
      share of output near the historically observed average.

      But note that Piketty is using a number for the the capital/output ratio of 5 or 6, not Prescott's 2.6. Looks like they are counting different things as part of the capital stock. Maybe Prescott doesn't include housing?

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    3. I have heard that Piketty includes more in his measure of the capital stock. It looks like Krusell and Smith use 0.025 for depreciation (quarterly calibration) in a lot of their papers. I tried to backtrack to when they first used it to find a discussion or citation on it, but I haven't had any luck yet.

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    4. You can see where Prescott gets his number. He's using long-run observations and the steady state properties of the growth model to pin down the depreciation rate. Same for Krusell and Smith, I think.

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    5. Piketty appears to use 0.02 for delta at some points. See note 7 of his lecture notes:

      http://piketty.pse.ens.fr/fr/teaching/10/25

      Which is on the lower end.

      More on K/Y up to 5 and 6:

      http://www.voxeu.org/article/capital-back
      http://piketty.pse.ens.fr/files/PikettyZucman2013WP.pdf

      From page 10 of the PDF, the starting point for getting to a measure of K/Y, some of which raised my eyebrows:

      "Following SNA guidelines, assets include all the non-financial assets – land, buildings, machines, etc. – and financial assets – including life insurance and pensions funds – over which ownership rights can be enforced and that provide economic ben-efits to their owners. Pay-as-you-go social security pension wealth is excluded, just like all other claims on future government expenditures and transfers (like education expenses for one’s children and health benefits). Durable goods owned by households, such as cars and furniture, are excluded as well. 12
      As a general rule, all assets and liabilities are valued at their prevailing market prices. Corporations are included in private wealth through the market value of equities. Unquoted shares are typically valued on the basis of observed market prices for comparable, publicly traded companies.
      We similarly define public (or government) wealth Wgt as the net wealth of public adminis- trations and government agencies. In available balance sheets, public non-financial assets like administrative buildings, schools and hospitals are valued by cumulating past investment flows and upgrading them using observed real estate prices."

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    6. This is where you need a model. If you're using a standard growth model, then the capital measure has to be consistent with the output measure you're using. You're saying that the capital is a factor of production that is used with labor - or whatever other factors of production you want to include - to produce measured output. In that context you wouldn't include financial assets in the capital measure, for example, at least in conventional growth models.

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  3. K/Y equal to just under 6 is the estimate of McGrattan/Prescott, who include land, inventories, and intangibles.

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  4. You are comparing apples and oranges, δ in the Solow model measures depreciation as a fraction of capital and not as a measure of income.

    "So this put's us back in DeLong's ballpark or lower given Piketty's number. I know Krusell and Smith to be serious empirical guys. They didn't pull that number out of thin air. What's appropriate here?"
    Well, after having established that you are not a serious theoretical guy (gee, I learned the Solow model in my first year as student) we can establish that Krusell and Smith did pull the number out of thin air. Quickly glancing at the numbers shows that depreciation is around 15% of GDP and with capital income ratios around 5 δ is about 3%.

    So DeLong is right in this respect but wrong in another. Krusell and Smith correctly point out that (even with more realistic depreciation rates below) Piketty's assumption of positive net saving rates implies that the gross savings rate will increase sharply when the GDP growth rate declines. Piketty could have avoided such a basic mistake if he had worked with gross instead of net variables.

    In general I find it interesting that everybody gets basic stuff wrong: Piketty the net/gross distinction Krusell&Smith the depreciation rate and Williamson depreciation/Y vs. depreciation/K.

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    Replies
    1. "everybody gets basic stuff wrong:"

      Except you of course. Thank God your are alive! What would we do without you?

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    2. Except that, in the Solow model, depreciation has to do with reductions in the production value of capital, and therefore does not correspond to the Capital Consumption Allowance series constructed by NIPA. Talk about getting basic stuff wrong -- you don't even understand the national income accounts. Fortunately, you're unemployed and have lots of time to learn.

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    3. "Except that, in the Solow model, depreciation has to do with reductions in the production value of capital, and therefore does not correspond to the Capital Consumption Allowance series constructed by NIPA."

      No idea what your point is, the one is empirics, a statistic that measures depreciation, the other is theory, a model in which depreciation is a fraction of capital.

      Even for this blog these are fairly weak attempts at deflecting from Williamson's gross mistake (say what you want but the dude is really good at elementary mistakes, first he mistook an identity like the Fisher equation for a behavioural relationship and now he shows that he really should have taken those undergraduate courses that deal with the Solow model): not understanding that δ refers to K and not Y.

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    4. Wow, you're really dim. Capital in the model =/= the series used to construct the CCA. Ergo, the CCA is not informative about the depreciation rate. You must be Broad DeLarge, to be so incapable of logic.

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    5. Someone needs a refresher course on calibration. :)

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    6. "You must be Broad DeLarge, to be so incapable of logic."

      At least you right-wing hacks are funny.

      Delete
    7. "At least you right-wing hacks are funny."

      While you don't even have that going for you.

      Delete
  5. Steven, O/T: Where's the best place to find a chart of the price level (P) vs year which compares a theoretical model of P to empirical data? Here's two examples of what I mean for Canada and for Japan. Those both use the same model, by the way, and the author of the model also created a related pair of curves for the interest rates in those two countries (and others). He's trying to compare his model results with professional examples but he can't find any professional examples (he says when he does a Google image search for "price level model" he only finds his own plots (again he's looking for model results vs empirical data)!). Do you have any idea where he should he be looking?

    Thanks!

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    Replies
    1. Good God what is that garbage?

      Delete
    2. This comment has been removed by the author.

      Delete
    3. It's the results from a economic model based on the theory of information transfer. Here's how his three-parameter model compares directly with the Fed's P* model, which has somewhere between two and three times the number of parameters:

      http://informationtransfereconomics.blogspot.com/2014/07/notes-from-ben-bernanke-and-p-model.html

      Delete
    4. That website is complete nonsense.

      Delete

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  9. Late to the game here but in the FRB/US model database, the depreciation rate for structures (office buildings and mines) is 3.3 percent; for producers' durable equipment, is is 14 percent; and for intellectual property it is 24.4 percent, all measured at annual rates.

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