Canada's famously low levels of productivity and low rates of productivity growth have preoccupied Canadian economists for decades. But increased productivity - as it is usually measured - is not a sufficient condition for higher standards of living. It's not even necessary. For instance, the post-2001 fall in Canadian productivity is simply a mathematical artifact of an income-increasing sectoral reallocation of capital and labour.
Gérard Debreu was once asked why he titled his landmark monograph Theory of Value instead of something like the more usual Price Theory. His answer was "Because value equals price times quantity." And this is the point: increasing quantities increases the value of production only if prices hold steady, or at least don't fall too much. But if prices are falling, increasing productivity won't necessarily show up as higher income.
Yi = AiFi(Ki,Li)
where:
- Yi is output in industry i
- Ki is capital employed in industry i
- Li is labour employed in industry i
- Fi() is a function describing how capital and labour inputs are transformed into output
- Ai is a measure of the state of technology.
The model can be generalised to include more than two inputs, and Statistics Canada does so when calculating its estimates. Technical change is interpreted as changes in Ai. For a fixed level of inputs, an increase of 10% in Ai will increase output by 10%.
From the standard theory of the firm, wages are set equal to the marginal revenue product, which is the amount of extra revenue generated by an extra unit of labour:
wi = Pi Ai FLi(Ki,Li)
where FLi is he derivative of Fi with respect to the labour input Li. Wages will increase if
- Ai increases: Technical progress increases worker productivity and real wages.
- Ki increases: For a given level of technology, 'capital deepening' (usually) increases worker productivity and wages.
- Pi increases: Higher prices are passed on to workers. (Yes, really.)
In developing economies - such as China - you can produce significant gains in productivity and wages by just by accumulating capital. But at some point, diminishing returns set in, and growth stagnates without technical progress.
It's surprisingly easy to recover the growth rate of Ai, and Statistics Canada (see here for the gory details) publishes its estimates in Cansim tables 383-0021 and 383-0022. Here are a couple of graphs from those tables:
These measures are cyclical, falling during recessions: a reduction in capacity utilisation rates shows up as a fall in productivity. But even so, an increase in business sector MFP of just over 10% in the span of almost 50 years is still not particularly impressive. And business sector MFP has fallen over the past ten years.
Part of the explanation is the Baumol Effect: technical progress in the services sector is slower - or at least, harder to measure - than in the good sector, so the shift to services brought down average productivity growth. If we take the MFP estimates seriously, there has been no technical progress in the service sector since 1961.
But this is only part of the explanation. Here is a graph of the MFP for two important components of the goods sector:
Here is where one's faith in MFP starts to falter. Whatever MFP is measuring in the mining, oil and gas extraction sector, it cannot possibly be technical progress. No-one would seriously claim that output in this sector would be tripled if they returned to 1960s-era technology. It's much more easy to believe that technical change in this sector takes the form of making it possible to extract resources that were previously unreachable.
This MFP artifact appears to be driving the fall in goods sector MFP since 2001. If resources are shifted out of the manufacturing sector and towards the resource sector, aggregate MFP measures will fall. For a given level of labour and capital, a reallocation that reduced aggregate MPF will produce a lower level of GDP.
Everything else being equal, lower GDP means lower income. But everything else has not been equal. As we know from my old beer-and-pizza post, an increase in the terms of trade can increase incomes, even if output as measured by GDP stays constant. This recent StatsCan paper provides an overview of the distinction between GDP, Gross Domestic Income (GDI) and Gross National Income (GNI). (Fun fact: the old GNP measure is now called GNI. Am I the last to know this?)
This distinction is not as well-known as it might be, quite possibly because up until recently, it really didn't matter which measure you used. But the post-2001 increase in the prices of oil and other commodities have produced an unprecedented gap between GDP and GDI:
Here is a plot of the ratio of the industrial price index to the Bank of Canada's commodity price index:
Since 2001, the ratio of resource and manufacturing MFPs has fallen by one-third. But if relative prices of resources with respect to manufactured goods have doubled, then shifting away from manufacturing to resources will still increase incomes.
When we think about productivity, output is the implicit measure for economic welfare: more output means more income. But this only works if prices are held constant. Large increases in quantities multiplied by even larger reductions in prices reduces value. Making more of something people don't want to buy doesn't guarantee prosperity.
Steve, great message.
Posted by: Frances Woolley | July 31, 2011 at 08:35 PM
I think the focus on national productivity is again symptomatic of equating a country with a firm. With firms, increasing productivity is good. It lowers a firm's cost and increases profit. With a country, increasing productivity might be bad. It decreases the population's income, and stagnates the economy.
Posted by: rogue | August 01, 2011 at 12:09 AM
It's an intriguing argument and worthy of serious consideration. In an extreme case, not only a productivity loss, but negative value added at constant prices for an extractive industry can occur. At constant prices, gross output may be less than the value of intermediate inputs, even though the industry is earning a healthy surplus at current prices.
I'm not sure about the statement that gross national income (GNI) is the new name for gross national product (GNP). Certainly this is true at current prices. I don't think it is true in volume terms, or as Statistics Canada wishes to call it, in real terms. The old volume estimates of GNP were based on double deflation of exports and imports using export- and import-specific deflators. Interest income received from abroad was part of service exports and interest income paid abroad was part of service imports. The index of real GNI published by StatsCan is based on direct deflation of net exports using the same definitions by the deflator for gross domestic final expenditures (GDFE), which, abstracting from a questionable treatment of the statistical discrepancy, is esentially final domestic demand plus investment in inventories. Therefore the real GNI estimates will incorporate gains from terms of trade that Professor Gordon mentions in his blog which were never part of the real GNP estimates.
One can debate whether it is really useful to define real GNP and real GNI in such different ways when their nominal aggregates are the same. Arguably, real GNI should be defined as GNI at current prices deflated by the real GNP deflator. But that's not what is done now.
Posted by: Andy Baldwin | August 01, 2011 at 11:23 AM
How does productivity get calculated for industries whose focus is to increase reserves (mining or oil & gas)? I understand widgets per workhour, I can even understand design engineering hours per piece of new equipment, but if nothing is "produced" what is productivity?
I am no economist (nor did I stay at a Holiday Inn Express last night :-}) but the shape of our economy must surely affect the way its metrics are calculated.
Posted by: Stuart Elliot | August 01, 2011 at 10:06 PM
That makes sense to me, but I have had another idea for some time, which I am not sure is sensible.
Could the faster measured growth of "productivity" in the U.S. than in Canada be the product of free trade? Suppose that, when free trade came in, more production from Canada moved to the U.S. than the other way around, attracted by the larger market there. That would bid up wages in the U.S. relative to Canada, raise prices of things made in the U.S. relative to things made in Canada, and therefore the value of production per hour worked would go up more there.
I presume that there is some effort made to account for such changes in the terms of trade, but how good can that possibly be, when so many things made now were not even made 10 years ago. How can you compare today's prices in any meaningful way with prices even 10 years ago?
Even if the above idea is true, it would not, of course mean that free trade has necessarily been bad for us. Both Canada and the U.S. might have gained, only the U.S. gained more.
Posted by: Paul Friesen | August 02, 2011 at 03:05 PM
I'm not sure if you're drawing the right conclusions here.
For one thing, MFP is not equal to technological change - as I'm sure you're aware, it's "everything else" that's exogenous to the model. So, its decline is not an artifact - it's just telling you something other than the rate of technological change. In this case, there's an apparent connection with resource extraction. If you look at the price of oil over the last several decades (e.g., http://www.wtrg.com/oil_graphs/oilprice1947.gif), there seems to be a correlation with MFP in the resource sector. That makes sense, since resource extraction is very energy-intensive (not sure how your MFP calc deals with price controls on oil, so I'll ignore that). Long-term, if price of oil rises, at least a component of MFP should decrease in any industry that is reliant on oil (technological change could offset).
In addition, the recent rise in price is associated (at least in part) with decreasing supply of conventional and increasing production of unconventional oil. Unconventional = harder to extract = decreased MFP. So, any increase in the price of oil will increase income in some form among oil producers - but this is just a case of rent-seeking (i.e., not driving future economic growth). Then, as lower and lower quality resources are extracted (since best will be extracted first) in, e.g., the oil sands, you're pouring increasing amounts of capital into a sector with ever-decreasing productivity. Unless technological change outpaces the rate of resource quality decrease, but that doesn't seem to be occurring at this point.
So, I think my point is that the MFP decrease does matter in the long-term and that any increase in income at this point is mainly due to rent-seeking and not contributing significantly to future growth - in the sense that the income comes from sucking wealth from more productive sectors. This should motivate people to come up with alternatives, however such alternative paths have to compete with, e.g., oil sands for capital - which creates a problem for a country that is pouring capital into the oil sands at an increasing rate.
Posted by: Surdas | August 03, 2011 at 12:15 PM
Isn't the price change already taken out when estimating the productivity? All these Quantities (GDP numbers) are at constant prices.
Posted by: Abhay | August 03, 2011 at 07:42 PM
Nice post Stephen.
Surdan: I don't think I understand your post. Let me see if I can break it down.
1) Suppose relative prices change (e.g. oil prices rise.) If we're a net exporter of that stuff, we're unambiguously better off. We'll probably try to produce more of it, shifting resources from other sectors (e.g. Quebec) into the now-more-valuable sector (e.g. NFLD)
2) But the law of diminishing marginal returns says productivity in the shrinking sector should now rise(!) Wages and returns to capital in the oil sector should go up by less than the rise in oil prices because the new oil is harder to extract.
3) But our productivity calculations (I think) abstract from price changes. They just see that it take more person-years and corporate bonds to produce a barrel of oil. That means productivity goes down in the oil sector.
4) But we noted in (1) that we're better off with the higher price of oil, and moving more resources into oil production helps us even more. Sure, productivity looks like its gone down....but the price increase more than compensates us for this. Hence we're better off with the new, lower level of productivity(!)
Okay, I've abstracted from a few things (e.g oil reserves can run out; low capacity in the non-oil sector may hurt productivity there). But I think that I agree with Stephen's point; productivity measures ignore price changes, and those price changes can have large permanent influences on our standard of living.
Posted by: Simon van Norden | August 06, 2011 at 05:08 PM
Interesting.
I wonder how much of this is attributable to factors that confound the measuring of Ai. How are the effects of harder-to-get oil and more environmental protections captured? One might not believe that 1960s technology was superior, but given those reserves and regulations...
I would also be wary of relying on GNI to trend over GDP. Producers will respond by producing more, pushing down prices so that eventually GNI should return to GDP.
Posted by: TallDave | August 10, 2011 at 12:35 PM