## April 26, 2007

### Further implications of the productivity slowdown for the dollar

In a previous post, I noted that the slowdown in economic growth in the US relative to rest-of-OECD would have a number implications for the dollar's value in nominal and real terms.

To see this, suppose we use a simplified cash-in-advance model forwarded by Alan Stockman in the Richmond Fed Review back in 1987 [pdf]. The cash in advance constraint, when assumed to bind, makes the money demand appear to follow a simple quantity theory:

M d/px = a

Where M is home money, p is the nominal price, x denotes the good produced by the home country, and a is the real demand for home money, expressed in terms of home goods. This can be thought of as approximating domestic production, in an endowment economy. Assume the foreign money demand has analogous properties.

M *d/py = a*

Note the foreign country produces good y. Hence, this is a two good model, with no nontraded goods.

Further assume money supply equals money demand equals a given money stock. Finally, to make the model international, let the real exchange rate be given by Zy = Epy*/px, where E is the number of USD required to buy a single unit of foreign currency. Then:

E = [Msa*/M*sa]Zy

So E is the nominal exchange rate, Zy is the relative price in terms of how many units of home goods it takes to buy a single unit of foreign goods. Now, there is a real (pun intended) question here in which direction the causality runs. As written, the causality runs from the relative price Z to E. However, if prices are sticky, one can make the argument that it runs in the other direction. Since I'm interested in medium term effects, I'll assume (like Stockman did) that the causality runs from right hand side to left.

If one thinks of a and a* as being endowment shocks, one sees that an increase in home endowment (sort of like an increase in home GDP) will tend to decrease E (i.e. appreciate the home exchange rate) because it increases the demand for home currency. On the other hand Zy is generally not unchanged. Rather, Zy will tend to depreciate if the propensity to consume home goods is the same as the propensity to consume foreign. The extent of the effect will also depend on the price elasticity of demand for home goods. So in this interpretation the nominal and real exchange rate can go in different directions (this is one reason why one wouldn't always want to use this model for short run analysis).

What will make the relative price Zy fall (appreciate) in response to an increase in endowment (which can be interpreted as an increase in productivity of GDP)? If there is home bias in consumption (here bias toward consuming good x by home country residents), or ownership of firms producing good x is biased toward home country residents. Then an increase in home endowment a could lead to an appreciation of the relative price of the home good.

How does the model relate to the real world? It shows that increases in home GDP -- either through higher production or higher productivity -- will tend to appreciate the nominal exchange rate, but will have ambiguous effects on the real exchange rate. If one adds in nontradable goods, another layer of complication is introduced, such that it depends upon where the productivity increase occurs.

What is the evidence? I've written a number of papers on the subject ([1],[2],[3]), but I'll just present a picture and a regression for now. The real exchange rate and the productivity differential are plotted in a way such that comovement indicates higher productivity is associated with a stronger dollar.

Figure 1: Log real CPI deflated value of US dollar against Euro (-Z) and log US-Euro area productivity differential. Source: ECB, FREDII, author's calculations.

Obviously, there is not a close fit, especially in the 1980's. However, if one is interested in the productivity effect, one might want to focus on the period when there is a wide variation in productivity trends. I estimate a dynamic OLS regression [(DOLS(2,2), no trend] over the 1990q1-2006q2 period to obtain.

log(Z) = constant - 1.09[log(proddif)] + 0.21 [log(real oil price)] + first diff terms

The coefficients on both key variables are statistically significant using Newey-West standard errors. The coefficient on productivity indicates that higher productivity will appreciate the USD against the Euro.

Bottom line -- with the dollar already depreciated against the Euro, and the productivity trends just now moving against the US, my view is -- with respect to a broad basket of currencies -- watch out below.

Technorati Tags: , , productivity growth, exchange rates

Posted by Menzie Chinn at April 26, 2007 09:27 AM

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Professor Chinn, you say "and the productivity trends just now moving against the US", but on Bloomberg TV they put up a chart which showed that y/y productivity growth has *already* declined for 5 years.

What could be done to increase capital deepening here in America? (It seems that U.S. companies prefer to do business fixed investment abroad.)

Posted by: Charlie Stromeyer at April 26, 2007 11:11 AM

Charlie Stromeyer: In this model, it's relative trends that matter. The trend reversal in the red line in Figure 1 is partly due to acceleration in Euro area productivity.

In order to foster capital deepening, one could reduce the cost-of-capital by introducing an investment tax credit for investment, or by eliminating tax breaks for investment in residential investment (for second homes, e.g.). Decreased public consumption would also divert additional resources to domestic business fixed investment. To the extent that one thought that multi-factor productivity was important, one could devote more public resources to R&D spending (NSF, NIH, etc.).

Posted by: menzie chinn at April 26, 2007 03:04 PM

Professor Chinn, I saw the relative trend in the red line of Figure 1 but I should say more clearly what confused me. First, you mentioned that U.S. economic growth is slowing relative to other OECD countries (which of course includes non-European countries like Canada and Japan).

Then, for simplicity you model the USD vs. the Euro which I understand, however, you then say "with respect to a broad basket of currencies".

What I don't understand is why higher productivity in the Euro zone should cause the USD to decline with respect to the Yen or other currencies that are not the Euro.

Also, against a broad basket of currencies, didn't the USD peak in 2002 which is also when U.S. productivity growth peaked. Is this a coincidence? How would one go about figuring out if the 5 year decline in productivity is cyclical or structural or is it just too early to tell? Thanks.

Posted by: Charlie Stromeyer at April 26, 2007 03:32 PM

Charlie Stromeyer: I can see your confusion. I'm assuming that the slowdown in US productivity growth is also going to show up as a decline in the productivity differential vis a vis the rest-of-OECD. Sorry that I didn't make that explicit. If this conjecture proves accurate, then the dollar should depreciate against a broad basket of currencies, not just the Euro.

In my mind, the big question is whether the deceleration in US productivity growth is cyclical or of a more persistent nature. I don't have an answer on that count, although, as cited in my previous post, some people in the financial sector are betting that way.

Posted by: Menzie Chinn at April 26, 2007 03:50 PM

In retrospect, it seems obvious. Post cold war Europe has a deep pool of underused human capital available in the former communist countries.

Posted by: Robert at April 26, 2007 07:00 PM

The fact is, this is the greatest economic boom in world history that has no end in sight.

Granted from the American position, we are not directly causing this event like in the 90's expansion nor have we reached the capacity that we did by 2000, but it is getting there.

Simply a amazing world boom. Except it and enjoy the fruits.

Posted by: Sammy at April 27, 2007 01:42 AM

Thanks, Menzie. This model provides some helpful intuition. I'm concerned about the exogeneity of monetary policy. What if monetary policy is endogenous? I know this complicates the model substantially but I think there are a couple of likely implications. First, money supply would move with/accommodate the shock to GDP when it can. Consequently, such a model would would show an exchange rate impact only from unanticipated and/or unobserved GDP shocks (i.e. central bank can't accommodate them for some reason). Third, if we add reasonable lags to monetary policy, the effects of the shocks on the exchange rate would diminish as the shocks become observed and the monetary policy response kicks in over time. Thus, we are back to a situation where only short run differences in GDP growth (shocks) can influence exchange rates (setting aside Balassa-Samuelson issues). Long run differences from population growth or productivity growth across all sectors should be sterilized.

Posted by: jfund at April 27, 2007 06:21 AM

As the dollar keeps falling, inflation expectations keep rising and the fed is unable to stop it because they are unwilling to raise rates. This has caused a stagflationary scenario with 1.3% growth and 2.2% inflation in the 1st quarter. It's starting to look like the only way to stop this, support the dollar and get inflation under control is to raise rates and cause an artifical recession like the 1980s. After that, the dollar will rise, all the excess be leave the economy and the economy will be positioned again for another boom in a couple years. Any other opinions?

Posted by: Ryan at April 27, 2007 06:30 AM

Thank you, Dr. Chinn, for raising the issue of our decreasing rate of productivity increase, again. I'm not an economist but it would not be a surprise if the US economy was heading into a long, slow period of retrenching. Energy prices are foremost in my mind although the future availibility of skilled, educated workforce when a third of the population is retired is another nagging doubt.

Common sense says personal lifestyle in the US should begin to pick up more similarities with Europe and developed Asian countries it begins to make more financial sense to live closer to the workplace and needed services. Public transportation should have a better business case; especially if the fifty-five mile per hour speed limit returns. It is far easier to concerve water and energy in a high-rise apartment building.

Posted by: Anchoku at April 27, 2007 07:48 AM

jfund: If you add in Taylor fundamentals, you get the type of model estimated in a paper by Molodtsova and Papell [pdf] that I discussed in this post. See also this recent paper by Engel, Mark and West [pdf].

Ryan: I agree the Fed is in a tough spot, given the most recent 07q1 GDP figures and the upward trend in core inflation. However, it's not clear to me the Fed pays much attention to the dollar in the conduct of its monetary policy.

Posted by: Menzie Chinn at April 28, 2007 04:28 PM