### Kahn and Rich: Tracking Productivity in Real-Time

Mark Thoma watches Jim Kahn and Bob Rich try to track changes in trend productivity growth in "real time":

Economist's View: NY Fed: Tracking Productivity in Real-Time: The good news is that, according to these estimates, "the underlying trend remains strong despite recent weak productivity data":

Because volatile short-term movements in productivity growth obscure the underlying trend, shifts in this trend may go unrecognized for years--a lag that can lead to policy mistakes and hence economic instability. This study develops a model for tracking productivity that brings in additional variables to help reveal the trend. The model's success is evident in its ability to detect changes in trend productivity within a year or two of their occurrence....

The difficulty in assessing the trend in productivity growth stems primarily from the extreme volatility of quarterly growth rates. In any one quarter, annualized growth rates in excess of 5 percent or below zero are common (Chart 1).[3] Moreover, the volatility is not confined to short-term movements in this series; productivity growth also fluctuates with the business cycle, typically declining during a recession and rising sharply at the onset of a recovery. Thus, economists cannot easily distinguish changes in trend productivity from quarterly or cyclical swings, and years may pass before a trend shift can be ascertained.

Not surprisingly, the misidentification of trend changes can have significant consequences for the economy. It is widely believed, for example, that the inability to recognize the slowdown in trend productivity growth in the early 1970s led policymakers to overestimate potential GDP growth and set interest rates too low--actions that contributed to double-digit inflation over the next several years....

[W]e construct a statistical model that includes, in addition to productivity, two variables that economic theory predicts will move together with productivity over the long term: real (inflation-adjusted) consumption expenditure and real labor compensation. By looking at all three of these economic series at once, the model can more easily uncover the trend that underlies them all. In this respect, our approach resembles the way policymakers gauge the current state of the economy by extracting a signal, with the help of an analytical framework, from a wide array of noisy indicators....

Trend Shifts in the Postwar Period:With the advantage of hindsight, economists have been able to chart the trend in productivity growth in the postwar period. Close to 3 percent from 1948 to 1973, the average growth rate of nonfarm output per hour fell to 1.5 percent between 1973 and 1995, then returned to approximately 3 percent from 1996 to the present. At the time these shifts in trend occurred, however, they were difficult to detect. The trend shift in 1973 went unrecognized for many years.[6] During the late 1990s, the notion that the trend growth rate had picked up found favor with those who believed in the advent of a "new economy," but many economists continued to dispute the notion that the productivity gains of the post-1996 period represented a return to permanently higher growth....The regime-switching model, introduced in Hamilton's (1988) study of nominal interest rates, has been applied to a number of economic and financial time series.... We consider four time series over the period from first-quarter 1947 to third-quarter 2005: (1) output per hour of work, (2) real labor compensation per hour of work, (3) real consumption expenditure divided by hours of work, and (4) hours of work. The standard one- sector neoclassical growth model of economic theory implies that the first three variables should have a common trend related to technical progress, while any trend in the fourth variable, hours of work, is unrelated to technical progress....

We find that the model would have picked up the change in trend within two years of when it is now known to have occurred....

What does our regime-switching model suggest about the possibility of a trend shift in the current environment? Interestingly, for a period of roughly a year beginning in mid-2005, an apparent slowdown in real compensation growth caused the model to give warning signs of a return to lower trend productivity growth. Subsequent data releases from the Bureau of Labor Statistics, however, revised compensation growth upward, with the result that the model is again indicating strong productivity growth going forward. The shifts in our model estimates are evident in Chart 6, which depicts the probability of being in the low-growth regime (trend growth of 1.3 percent as opposed to 2.9 percent in the high-growth regime), tracked over recent data vintages, including quarterly updates since the third quarter of 2005. We see noticeable increases in this probability beginning in third-quarter 2005, reflecting the sluggish growth in real labor compensation. The latest estimate plotted in the chart, however, assigns a probability of less than 0.05 to productivity's being in the low-growth state. Thus, the model once again places high probability on a trend path that is roughly 2.9 percent, close to the trend over the past ten years and to that in the interval between World War II and 1973....

One variable conspicuous by its absence in our analysis is the stock market. One might think that stock market values would act as a natural leading indicator of a change in trend productivity, since asset prices in general can respond much faster than measures of real activity. We find, however, that the stock market is simply too volatile to be of practical use in detecting a change in trend productivity....

In fact, it may be more useful to consider the interplay between the stock market and trend productivity in the reverse direction. In other words, tracking the trend in productivity growth may illuminate trends in asset values. Chart 8 shows how long-term fluctuations in stock market values (as measured by the S&P 500, adjusted for inflation, and normalized by hours of work) appear to move in line with the level of trend productivity estimated from our original four-variable model. As we have seen, the model identifies changes in the growth regimes of productivity relatively quickly and therefore could be informative about future movements in stock prices...

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