Discussion of Kahn-Rich on Tracking the New Economy Robert J. Gordon Northwestern University and NBER Federal Reserve of San Francisco, November 7, 2003

Productivity Growth is the Hot Topic in Macroeconomics Look at the numbers, 6.8 in 2003:Q2, 8.1 in 2003:Q3 Look at the numbers, 6.8 in 2003:Q2, 8.1 in 2003:Q3 How much of this is an unusual cyclical event? How much of this is an acceleration of trend? How much of this is an unusual cyclical event? How much of this is an acceleration of trend? Advertisement: Read another paper, “Exploding Productivity Growth: Historical Context, Possible Causes, Future Implications” BPEA 2003:2, forthcoming Advertisement: Read another paper, “Exploding Productivity Growth: Historical Context, Possible Causes, Future Implications” BPEA 2003:2, forthcoming Brookings disallows NBER Yellow-covered Papers Brookings disallows NBER Yellow-covered Papers Will be on my web site by Monday morning. Search Google (not that Scottish University). Will be on my web site by Monday morning. Search Google (not that Scottish University). 97 double-spaced pages 97 double-spaced pages

Two New Ideas in Kahn-Rich Paper Idea #1. Productivity growth shifts between regimes. “High” and “Low” productivity growth. Idea #1. Productivity growth shifts between regimes. “High” and “Low” productivity growth. Idea #2. We can do better in estimating the trend of productivity growth by using outside information going beyond productivity growth itself Idea #2. We can do better in estimating the trend of productivity growth by using outside information going beyond productivity growth itself Info A: Real compensation per hour Info A: Real compensation per hour Info B: Real consumption per hour Info B: Real consumption per hour

Does their Approach Signal Increase in late 90’s Trend Earlier than Other Methods? Their claim: Their claim: “One could not decisively conclude that there was a return to a higher growth regime on the basis of productivity alone.” “One could not decisively conclude that there was a return to a higher growth regime on the basis of productivity alone.” “Only the corroborating evidence from other cointegrated series can swing the balance strongly in favor of a regime switch.” “Only the corroborating evidence from other cointegrated series can swing the balance strongly in favor of a regime switch.” Does Their Series Detect Post-1995 Acceleration Faster than Alternatives? Does Their Series Detect Post-1995 Acceleration Faster than Alternatives?

Motivations for the Kahn-Rich Reevaluation of Growth Trends One can be skeptical about both ideas One can be skeptical about both ideas “We treat that trend as a stochastic process whose mean growth rate has two `regimes’”. “We treat that trend as a stochastic process whose mean growth rate has two `regimes’”. Why two? Why two? Why not high medium low? Why not high medium low? Why not four regimes? Ten regimes? Why not four regimes? Ten regimes? Use two additional series to provide additional information Use two additional series to provide additional information Skeptic: Why do these two series provide independent information? Why do the authors not take us through the arithmetic of labor’s income share? Skeptic: Why do these two series provide independent information? Why do the authors not take us through the arithmetic of labor’s income share?

Additional justifications for their approach Criterion for use of two additional variables, consumption and real wage: Criterion for use of two additional variables, consumption and real wage: #1 “We show that aggregate productivity data alone do not provide as clear... a signal of changes in trend growth as does the joint signal from the series we examine.” #1 “We show that aggregate productivity data alone do not provide as clear... a signal of changes in trend growth as does the joint signal from the series we examine.” What aspect of time-series dynamics provide an additional contribution from those two series? What aspect of time-series dynamics provide an additional contribution from those two series? #2 We do not have to choose break dates #2 We do not have to choose break dates Nor do H-P filter nor Kalman time-varying coefficient Nor do H-P filter nor Kalman time-varying coefficient #3 How long regimes last (contingent on only two regimes?) #3 How long regimes last (contingent on only two regimes?)

Arithmetic of Labor’s Share Does their real compensation variable provide additional information? Does their real compensation variable provide additional information? S = (WH/PY) S = (WH/PY) Change in log labor’s income share Change in log labor’s income share Δs = Δw – Δp – (Δy – Δh) Δs = Δw – Δp – (Δy – Δh) Usual cyclical behavior, labor’s share rises in recessions, shrinks in recoveries (like now). Usual cyclical behavior, labor’s share rises in recessions, shrinks in recoveries (like now). In using compensation per hour as a proxy for the productivity trend, they are making a statement about the cyclical behavior of labor’s share. But they have no model. In using compensation per hour as a proxy for the productivity trend, they are making a statement about the cyclical behavior of labor’s share. But they have no model.

Consumption/Hour How is Consumption/Hour related to productivity? How is Consumption/Hour related to productivity? C/H = (C/Y) * (Y/H) C/H = (C/Y) * (Y/H) So now we need a model of the share of consumption in GDP. Lots of models – Keynesian, RBC, but not in this paper. So now we need a model of the share of consumption in GDP. Lots of models – Keynesian, RBC, but not in this paper.

Alternative Productivity Trends to Compare to Kahn-Rich #1 Hodrick-Prescott (H-P) filter #1 Hodrick-Prescott (H-P) filter Parameter value: meaning Parameter value: meaning Everyone uses This is the square of 5/(1/8) =40. When detrending GDP, a 5 percent GDP gap causes the trend to decelerate by 1/8 percent per quarter. Everyone uses This is the square of 5/(1/8) =40. When detrending GDP, a 5 percent GDP gap causes the trend to decelerate by 1/8 percent per quarter. Great Depression: 25 percent GDP gap, trend decelerates at 5/8 percent per quarter, 2.5 percent per year, 10 percent after four years. Great Depression: 25 percent GDP gap, trend decelerates at 5/8 percent per quarter, 2.5 percent per year, 10 percent after four years. Starting at 3 percent per year in 1929, trend by 1933 is growing at 3 – 25 percent or -22 percent per year. Starting at 3 percent per year in 1929, trend by 1933 is growing at 3 – 25 percent or -22 percent per year. H-P parameter 6400 is much better than 1600 H-P parameter 6400 is much better than 1600

#2 Kalman Filter with Time-Varying Coefficients The Kalman filter explains the change in productivity growth (Δpt) by a time-varying constant and any set of other explanatory variables (βXt): The Kalman filter explains the change in productivity growth (Δpt) by a time-varying constant and any set of other explanatory variables (βXt): (5) Δy - Δh(t) = α(t) + βX(t) + w(t) (5) Δy - Δh(t) = α(t) + βX(t) + w(t) The next step is to specify a time-series process for the time-varying productivity trend, and the most straightforward is a random walk: The next step is to specify a time-series process for the time-varying productivity trend, and the most straightforward is a random walk: (6) α(t) = α(t-1) + v(t) (6) α(t) = α(t-1) + v(t)

Implementation of Kalman Filter Productivity Trend with Time- Varying Coefficient Replace βX(t) by change in output deviation from trend (or change in unemployment rate). Replace βX(t) by change in output deviation from trend (or change in unemployment rate). Could also use supply-shock variables, e.g., change in oil prices, that cause temporary changes in productivity Could also use supply-shock variables, e.g., change in oil prices, that cause temporary changes in productivity Kalman filter can use more info than H-P Kalman filter can use more info than H-P Compare K-filter with H-P filter Compare K-filter with H-P filter Without output variable they are identical, same smoothness coefficient Without output variable they are identical, same smoothness coefficient

Kalman with Output vs. H-P

Kahn-Rich Compared

Summary: Problems with their Productivity Growth Trend Problem #1. Why is it so Jagged? Problem #1. Why is it so Jagged? Problem #2. Why must there be only two regimes? Problem #2. Why must there be only two regimes? Problem #3. Why does the behavior of the real wage tell us something about the productivity trend? Problem #3. Why does the behavior of the real wage tell us something about the productivity trend? What if super-normal productivity growth goes into profits? How long does it take for real wage growth to catch up? What if super-normal productivity growth goes into profits? How long does it take for real wage growth to catch up? Problem #4. Why does consumption tell us anything about the productivity trend. What is the theory of the behavior of the C/Y ratio? Problem #4. Why does consumption tell us anything about the productivity trend. What is the theory of the behavior of the C/Y ratio?

Thanks to the Authors For bringing the Productivity Growth Trend to the Attention of this Audience one day after the announcement of 8.1 For bringing the Productivity Growth Trend to the Attention of this Audience one day after the announcement of 8.1 For helping to focus attention on the strengths and weaknesses of Hodrick-Prescott and Kalman For helping to focus attention on the strengths and weaknesses of Hodrick-Prescott and Kalman And for reminding us that there is a lot of macroeconomics devoted to explaining the change in labor’s income share and the C/Y ratio And for reminding us that there is a lot of macroeconomics devoted to explaining the change in labor’s income share and the C/Y ratio