Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Thursday, November 10, 2011

Fiscal multipliers: another caveat

James Hamilton reminds us of what all Econ 101 students learn (or are supposed to learn) about the peculiarities of national income and product accounting and the caveats that need to be kept in mind when equating the measured GDP to true economic activity. The lesson is hammered home by Yoshiyasu Ono in this paper The Keynesian Multiplier Effect Reconsidered published earlier this year. Here is Hamilton's nice summary of the paper:
According to traditional Keynesian models, even for the case of a completely useless government project, if we were to raise private-sector taxes by just the amount needed to pay the salaries of the hole-diggers, GDP would increase, with a balanced-budget multiplier of one. Yet, Professor Ono asks, how could paying the crew a salary to dig a useless hole possibly lead to an improvement in welfare relative to simply handing them a direct transfer and allowing them to spend more time safely and comfortably at home with the family? And, to make things very simple, if the source of funds for paying the workers was in fact a tax levied on those same individuals, how could we possibly conclude that the enterprise has increased total national income?  
The answer is, we include government spending, even on useless projects, in the definition of GDP, and assume that the value of what is produced is the dollar sum that the government paid for it. The reason even useless government spending has a balanced-budget multiplier of one is that we now have a filled-in hole that we didn't have before. So we have more goods and services (in the form of a newly filled-in hole) than we used to, and impute the value of this new extra stuff as added income for the nation as a whole.
To understand what underlies this phenomenon, we have to revisit the definition of GDP. The Gross Domestic Product is defined as the market-value of all final goods and services produced by domestic factors of production over some specified time period.

It is also useful to keep the following in mind. All production is, by definition, sold (inventory accumulation is treated as a capital expenditure). Therefore, total output equals total expenditure. Moreover, as any expenditure on one side of a transaction constitutes income on the other side, it follows that total expenditure equals total income. To summarize:
 Output (GDP) is equivalent to Expenditure is equivalent to Income
Just to be clear, this is not a theory. It is an accounting identity (something that is true by definition). Now let me work through a series of examples.

First, suppose that a firm pays a worker $1 to produce an object that has a market value of $2. What is the contribution to GDP? The answer is $2. There are two ways to see this. First, the market-value of what has been produced/sold is $2. Second, total income has increased by $2. (Labor income has increased by $1 and profit income has increased by $1).

Now, suppose that a firm pays a worker $1 to produce an object that has a market value of $0. What is the contribution to GDP? The answer is zero. Again, there are two ways to see this. First, the market-value of what has been produced is zero. Second, while it is true that the income of the worker has increased by $1, this income gain is offset exactly by a $1 income loss for the firm. All that has happened in this example is a transfer of purchasing power from the firm to the worker. This is redistribution, not production.

Next, suppose that the government pays a worker $1 to produce an object that has a market value of $0. What is the contribution to GDP? The true contribution is zero. But that's not how the contribution will be measured in the NIPA. The NIPA assumes that the market value of the object produced by (or on behalf of) the government is $1. All that has happened in this example is a transfer of purchasing power from the taxpayer to the worker. This is redistribution, not production. But it will nevertheless be measured as production.

Why does this happen? Is someone trying to pull the wool over our eyes? No. As it turns out, many of the government services produced by government workers are provided for "free" and are hard to value at market prices (national defense is a classic example). When this is the case, it does not seem unreasonable to impute the market-value of a non-priced service by the cost of production.

Having said this, the lesson here is that one should nevertheless use caution in interpreting the estimated multiplier effects of fiscal stimulus programs using historical data as indicators of the likely impact of contemporaneous spending measures on true (as opposed to measured) GDP. The estimates are surely biased upward, although by how much likely depends on the exact nature of the expenditure.

What I have just described is a caveat for those who are inclined to perform cost-benefit exercises using "Keynesian" multiplier analysis. This type of analysis emerged out of a static model (the Keynesian Cross), where the benefit of a $1 expenditure by the government had to exist contemporaneously (there is no explicit future in a static model), which explains why the existence of multipliers greater than unity are so important in this way of thinking about things.

There is a better way of evaluating the net benefit of a government stimulus program. This involves estimating the expected net present value of the program (easier said than done, of course). With the real return on U.S. Treasuries so low (see my previous post), with U.S. infrastructure reportedly in a sorry state, and with so many unemployed construction workers, I would be surprised to learn that there are few positive NPV infrastructure projects currently available.

Unfortunately, political shenanigans (from all sides) sometimes make a mockery out the attempt to estimate NPV in a systematic and unbiased manner. We appear to be living in such times.


  1. "sometimes make a mockery out the attempt to estimate NPV in a systematic and unbiased manner."

    is this actually done, even at the federal level?

  2. Anonymous: Take a look at this,

  3. Hi David,

    Under current measurement, if I burn down my house and rebuild it, does that raise GDP? How does GPD deal with replacement and repair costs?

  4. Edward,

    Let's say you burn down your house and rebuild it within the time period under consideration (say, one year).

    When you rebuild your house, this will be measured as a contribution to GDP (in the form of residential investment, which is a newly produced capital good).

    That is gross investment, however (which is why it is counted as part of the gross domestic product).

    There is another concept called the net domestic product, which subtracts capital depreciation from the GDP. If the value of the house you build equals the value of what you burned down, then there has been zero net investment, and hence, zero change to the net domestic product.

  5. Thank you, I wasn't aware of that. All I can conclude is that they aren't doing a very good job.

  6. "Anonymous: Take a look at this,"

    so how does the government conduct a cost/benefit analysis for, say, afpak (cost: 4 trillion and counting)? or homeland security (cost: 1 trillion and counting)?

    the phrase "pretense of knowledge" immediately springs to min.

  7. Very didactic.
    It is for this reason that I prefer to look at business sector activity. NIPA is very clear on this, quite much clear that any other National Account, because it is always possible to separate private and public sectors data.

  8. Anonymous @ 0:01AM,
    So, if the project under consideration is only (say) $10,000, then no "pretense of knowledge" exists, right? Please tell us the precise cut off line here. You seem to know.

  9. Sorry for nitpicking, but it's Yoshiyasu Ono, not Yoshiasu Ono.

  10. Totally off topic but, i was wondering what are you're thoughts about the walkout that occurred during Mankiws lecture, and whether or not students taking intro classes should read papers written on current events?

  11. "Please tell us the precise cut off line here. You seem to know."

    you're missing the point. there is no "cut off line" - having the government allocate resources is ridiculous irrespective of whether they use cost/benefit analysis or a magic 8 ball to evaluate the decisions, and irrespective of whether the sum involved is "only (say) $10,000" or "4 trillion and counting".

  12. Anonymous: Fair enough. I do not think that most people share your extreme view, however. Many, if not most, might agree that there is too much government spending. I don't think that most people would argue that the optimal amount is zero, though. In any case, it is you have that have missed my point: "pretense of knowledge" has nothing to do with your argument (surely it is not too difficult to calculate the cost-benefit of a small government project, for example).

  13. my first comment (901) was supposed to highlight how silly it is to think that anyone can conduct a meaningful cost/benefit analysis when it is impossible to quantify either the costs or the benefits (irrespective of the sums involved), hence the "pretense of knowledge" comment.

    that said, one can argue against government spending based on incentives, with no recourse to "pretense of knowledge" arguments.

    as to calculating the cost/benefit of a "small" project - what is "small"? and is it really the case that it's any easier to quantify the costs and benefits involved simply because the sums are smaller? i don't think one can simply assume that away.

  14. Anonymous, you are being silly now. How does anyone conduct a meaningful cost/benefit analysis? We all do it every day.

  15. Hi, very interesting post.
    I have a paper in which I needed to calibrate the elasticity of public capital (infrastructure) to output for the US and it turn out to be at most 10%! As you correctly say the value of this parameter crucially depends upon the assumed rate of return of investment projects carried out by the government.