Disentangling the channels of the 2007-09 recession.

Stock, James H. ; Watson, Mark W.

IV. The Slow Recovery

On its face, the unusually slow recovery following the 2009Q2 trough seems inconsistent with the conclusion of the previous sections that the macroeconomic dynamics of this recession are consistent with those of prior recessions, simply with larger shocks. Indeed, during the 8 quarters following that trough, GDP grew by only 5.0 percent, compared with an average of 9.2 percent after 8 quarters for the recessions from 1960 through 2001, and employment increased by only 0.6 percent, compared with a 1960-2001 average of 4.0 percent. (20) The contrast between the current slow recovery and the robust recoveries of 1960-82 is even more striking: those recessions averaged 8-quarter GDP growth of 11.0 percent and 8-quarter employment growth of 5.9 percent following the trough. In this section we therefore take a closer look at the extent to which the current slow recovery is or is not consistent with historical experience.

Why has the recovery in employment since 2009Q2 been so much slower than the 1960-82 recoveries? In the context of the DFM, employment growth after a trough is the sum of four terms: trend employment growth, the predicted cyclical common component (deviations from trend) given the state of the economy at the trough, the prediction errors in the cyclical common component, and the series-specific idiosyncratic errors. Accordingly, the weakness of the recovery since 2009Q2 relative to, say, that after 1982Q4 could arise from differences in underlying trends (such as in demographics), differences in recovery paths after different types of recessions (such as one induced by monetary policy versus one following a financial crisis), differences in macroeconomic luck once the recovery commenced, or peculiarities of employment unrelated to the rest of the economy. Although the latter two terms might be of historical interest, the former two shed more light on structural differences between the two recoveries. In this section we therefore focus on the first two of these terms--the trend and the predicted cyclical common component--comparing their values in the post-2009Q2 recovery with their values in previous recoveries.

As in section III, the calculations here require a VAR for the factors, which we estimate using four lags and the "old" factors over the 19592007Q3 period. With this model held constant, differences in the predicted cyclical component across recoveries reflect differences in recovery paths implied by the shocks that produced the recessions. This permits a decomposition of the slow pace of the recovery after 2009Q2, relative to previous recoveries, into changes in the trend plus changes in the predicted cyclical component.

IV.A. Different Shocks Imply Different Recovery Paths

Different structural shocks induce different macroeconomic responses. For example, Bloom (2009) predicts a fast recovery after an uncertainty shock (investment and consumption pick up as soon as the uncertainty is resolved), whereas Carmen Reinhart and Kenneth Rogoff (2009) describe recoveries from financial crises as typically slow. In terms of the factor model, the state of the economy at the trough is summarized by the current and past values of the factors as of the trough. Because the values of the shocks (and thus of the factors) vary across recessions both in composition and in magnitude, the recovery paths predicted by the DFM also vary across recessions.

Figure 4 plots actual quarterly employment growth, its common component, and its predicted common component following each of the eight post-1960 troughs. All series are expressed as deviations from trend, so that a value of zero denotes employment growth at trend. The predicted common component is computed using the values of the factors through the trough date; that is, the predicted common component is the forecast of the common component one would make standing at the trough, given the historical values of the factors through the trough date and the model parameters (because the DFM was estimated through 2007Q3, the predicted components in figure 4 are in-sample for the first seven recessions and pseudo-out-of-sample forecasts for 2009Q2). The difference between actual employment growth and its common component is the idiosyncratic disturbance ([e.sub.t] in equation 1). The difference between the common component and the predicted common component arises from the factor innovations ([eta], in equation 2) that occurred after the trough.

Three features of figure 4 are noteworthy. First, there is considerable heterogeneity across recessions in both the shape and the magnitude of predicted recoveries of employment. By construction, the sole source of this heterogeneity is differences in the state of the economy, as measured by the factors, at the trough. Strong positive employment growth is predicted following the 1982Q4 trough--employment growth returns to trend only 3 quarters after the trough--whereas slow employment growth is predicted following 1980Q3, 1991Q1, and 2009Q2.

Second, in most recessions the predicted values track the actual common component. The main exception is the 1980Q3 recovery, which was interrupted early on by the next recession.

Third, given the values of the factors in 2009Q2, the DFM predicts 6 quarters of subtrend employment growth following the 2009Q2 trough. In fact, the DFM predicts a slower employment recovery from the 2009Q2 trough than actually occurred; that is, the current recovery in employment is actually stronger than predicted. (21)

[FIGURE 4 OMITTED]

IV.B. Decomposition of the post-2009Q2 Recovery into Trend and Cyclical Components

We now turn to the decomposition of the post-1959 recoveries into their trend and predicted cyclical components, where the latter are computed as described in the previous subsection using the factors at the trough. Table 9 summarizes the results for 8-quarter cumulative post-trough growth of GDP, employment, and productivity.

Consistent with the trends plotted in figure 1, table 9 shows that the trend component of predicted growth in GDP and employment falls over time. Consistent with the cyclical components plotted in figure 4, there is considerable variation in the predicted cyclical components, which arises from variation in the composition and magnitude of the factors at the trough. The predicted cyclical contributions to 8-quarter employment growth range from +1.1 percentage points following the 1982Q4 trough to -3.1 percentage points following the 2009Q2 trough.

The final rows of table 9 report the decomposition into trend and cycle of the difference between the predicted 8-quarter growth following 2009Q2 and the corresponding averages for pre-1984 recoveries. Predicted GDP growth emerging from 2009Q2 is 3.0 percentage points less than the pre-1984 average; four-fifths of this gap (2.4 percentage points) is due to differences in trend. Predicted employment growth is 6.0 percentage points less than the pre-1984 average; of this gap, 2.7 percentage points is attributed to differences in the cyclical components, whereas most, 3.3 percentage points, is attributed to differences in trend employment growth. The predicted cyclical component of productivity growth in the post-2009Q2 recovery is unusually large, 6.3 percentage points, although this predicted value is perhaps comparable to its values in the recoveries after 1975Q1 and 1982Q4. The difference between the trend components of productivity growth in the recovery after 2009Q2 and in the average for the pre-1984 recoveries is 0.5 percentage point; that is, trend productivity growth in the post-2009Q2 episode is slightly higher than its 1960-82 average. Most of the difference in productivity growth between the post-2009Q2 recovery and the 1960-82 recoveries is attributed to differences in the cyclical component. (22)

IV.C. The Slowdown in Trend Labor Force Growth and Slow Recoveries

A striking result of the previous section is that the decline in the trend component accounts for nearly all of the slowdown in GDP growth, and for over half the slowdown in employment growth, in the current recovery relative to the pre-1984 averages. Table 10 decomposes the change in trend GDP growth from 1965 to 2005 into GDP per employee, the employment-population ratio, the labor force participation rate, and the growth of the labor force. As seen in the first panel of table 10, the decline in the trend growth rate of GDP of 1.2 percentage points from 1965 to 2005 is, in this accounting sense, almost entirely due to declines in trend employment, which in turn is approximately equally due to declines in growth of the employment-population ratio and in population growth. In this accounting sense, the third panel of the table shows that declines in the growth of the employment-population ratio are in turn due to declines in the growth of the labor force participation rate, which in turn are largely due to declines in the growth rate of the female labor force participation rate. Figure 5 presents the estimated trends for the terms in the first panel in table 10 for the full 1959-2011 period.

Because the trend value of the unemployment rate is approximately the same in the 1960s as in the early 2000s (after peaking in the early 1980s), understanding the decline in mean employment growth amounts to understanding the decline in the growth of the labor force. (23) A significant literature examines long-term labor force trends and links them to two major demographic shifts (figure 6). (24) The first is the historic increase in the female labor force participation rate from the 1960s through the 1990s and its subsequent plateau; see Claudia Goldin (2006) for an extensive discussion. The second is the (smaller) decline in the male labor force participation rate. Stephanie Aaronson and others (2006) and Bruce Fallick and Jonathan Pingle (2008) attribute this decline to a combination of changes in the age distribution of workers and changing cohort labor force participation rates associated with the aging of the baby-boom generation (also see Fallick, Fleischman, and Pingle 2010). The main conclusion from this demographic work is that, barring a new surge in female labor force participation or a significant increase in the growth rate of the population, these demographic factors point toward a further decline in trend growth of employment and hours in the coming decades. Applying this demographic view to recessions and recoveries suggests that future recessions with historically typical cyclical behavior will have steeper declines and slower recoveries in output and employment.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

V. Conclusions and Discussion

Three main substantive conclusions emerge from this work. First, the recession of 2007-09 was the result of shocks that were larger versions of shocks previously experienced, to which the economy responded in a historically predictable way. Second, these shocks emanated primarily, but not exclusively, from financial upheaval and heightened uncertainty. Third, although the slow nature of the subsequent recovery is partly due to the nature and magnitude of the shocks that caused the recession, most of the slow recovery in employment, and nearly all of that in output, is due to a secular slowdown in trend labor force growth. This slowdown provides a simple explanation for the jobless recoveries of the 2001 and 2007-09 recessions. To the extent that it derives (as the literature suggests) from persistent demographic changes, recoveries from future recessions can be expected to be "jobless" as well. To these substantive conclusions we would add a fourth, methodological conclusion: that ignoring these changing trends will impart low-frequency movements to the errors, which seems likely to introduce subtle problems into structural VAR analysis.

The above three substantive conclusions are subject to a number of caveats. First, although the evidence for the stability of the factor loadings is relatively strong, it is difficult to draw inferences about the stability of the factor VAR parameters with only 15 quarters of post-2007Q3 data, particularly in the presence of evident heteroskedasticity in the factor innovations. The tact that the current recovery in employment has been stronger than predicted by the DFM given the state of the economy at the trough could reflect the effectiveness of the extraordinary monetary and fiscal policy measures taken during the recession, or it could be an indication of parameter instability; we are unable to distinguish between these two possibilities with the current limited data.

Second, the structural DFM analysis using the method of external instruments estimates shocks that are correlated with each other. The ability to estimate this correlation, rather than needing to impose it as an identifying restriction, is a strength of this methodology. Finding sometimes-large correlations across different types of shocks suggests that different identification strategies are estimating similar features of the data, but interpreting them differently. This raises broader challenges for the structural DFM and VAR literatures, which lie beyond the scope of this analysis. Sorting out credible instrumental variables methods for separately identifying liquidity shocks, market risk shocks, exogenous wealth shocks, and uncertainty shocks constitutes a large research agenda.

ACKNOWLEDGMENTS We thank John Driscoll, Lutz Kilian, Valerie Ramey, Eric Swanson, Egon Zakrajsek, and Tao Zha for providing or helping us construct their shock series and for comments. We also thank Alan Blinder, Nick Bloom, Markus Brunnermeier, Marty Eichenbaum, Jon Faust, Florencio Lopez-de-Silanes, Karel Mertens, Salil Mehta, Neil Shephard, Chris Sims, Mike Woodford, Tom Zimmerman, and the editors for helpful comments and discussions.

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Comments and discussion

COMMENT BY ALAN S. BLINDER James Stock and Mark Watson, as skilled a pair of time-series econometricians as the profession boasts, ask in this paper how the 2007-09 recession differed from other U.S. postwar recessions. Their answer is provocative: not much, actually, it was just bigger. They conclude that "the 2007-09 recession was the result of one or more large shocks, that these shocks were simply larger versions of ones that had been seen before, and that the response of macroeconomic variables to these shocks was almost entirely in line with historical experience."

Provocative? Yes. I must admit to being provoked. For starters, virtually every previous postwar recession was caused by either tight monetary policy, an oil shock, or both. (1) This one was not. Instead, it appears to have been caused by the bursting of a gigantic home-price bubble and an even more gigantic fixed-income bubble, which together led to the near-collapse of a jerry-built financial system, causing massive wealth destruction and severe impairment of the economy's credit-granting mechanisms. It looks more like a Reinhart-Rogoff recession, the first in U.S. postwar history, or better yet, a Minsky recession. (2) Furthermore, the Federal Reserve quickly (in December 2008) encountered the zero lower bound (ZLB) on nominal interest rates, forcing it to rely on a wide variety of "unconventional" monetary policies. Finally, long-term unemployment soared to levels not seen since the 1930s. In short, the years following 2007Q4 did not look like your father's recession--more like your grandfather's (or your great-grandfather's, if you are very young).

Let me start by reviewing why the conventional wisdom sees the 200709 recession and its aftermath as something different. Then I will take up Stock and Watson's challenge to this wisdom.

THE CONVENTIONAL WISDOM The U.S. economy entered 2007 with incredibly high leverage, virtually everywhere. Leverage is not something new. But as recently as the last mega-recession, in 1982-83, total debt in the United States was only about 150 percent of GDP. By the end of 2007, it was about 350 percent of GDP. High leverage, of course, spells high vulnerability to shocks. That vulnerability, in turn, was exacerbated by a variety of complicated (and mostly unregulated) financial linkages--through complex derivatives, a variegated shadow banking system, and more--that created a house of cards in the years leading up to the crisis. These novel financial developments sound like "slope things" to me--aspects of the economy that would likely change impulse response functions--as opposed to "intercept things" that only change levels of variables. This financial house of cards, by the way, was poorly understood, which makes the standard assumption of rational expectations something between dubious and ludicrous.

Yet more "slope things" relate to monetary policy. When the Federal Reserve hit the ZLB in December 2008, that presumably reduced the power of monetary policy. Certainly it ended the ability to use the federal funds rate as a policy instrument, even though linear equations in standard models call for the funds rate to go negative. Stuck at the ZLB, the Federal Reserve turned to new, untested weapons like emergency lending facilities, large-scale asset purchases, and forward guidance--policies whose "multipliers" are mostly unknown.

Finally, as mentioned, the share of long-term unemployment (spells over 26 weeks) in total unemployment rose to over 45 percent, having never before topped 26 percent in postwar history. Might all those long-term unemployed people affect the responses of measured employment and unemployment to stimulative policies?

For all these reasons and more, there is a strong a priori case that empirical models based on historical data might be expected to perform poorly after 2007. Before we jump to that conclusion, however, let us note several other factors pointing in the opposite direction, which tend to support Stock and Watson's claim that this recession wasn't different, just bigger.

Bubbles have burst before, although this one was the whopper. We have also regularly witnessed deterioration in underwriting standards and other signs of irrational exuberance in lending during past booms. The financial zaniness of 2004-07 was not the first "Minsky moment" in postwar U.S. history--though it looked more like a Minsky quinquennium. Nor was what followed the Lehman Brothers bankruptcy the first banking crisis. The sheer size of the 2007-09 recession was unprecedented: real GDP declined by nearly 5 percent; even nominal GDP fell. The decline in employment (and the rise in unemployment) also appeared to be unusually large, even given the miserable GDP performance, and the bounceback of employment after the trough seems unusually slow. But maybe these are all just exaggerated versions of what we have experienced in past recessions: normal reactions to shocks that, although abnormally large, are not qualitatively different.

This last thought leads to a philosophical question that is, in some sense, at the heart of Stock and Watson's analysis: When does a quantitative change become so large that it becomes a qualitative change? For example, the earth's tectonic plates are always moving, but somehow, earthquakes are different. Years ago, Thomas Sargent (1982) called our attention to the unusual behavior around "The Ends of Four Big Inflations" in Central Europe in the 1920s. There is certainly no apparent Phillips curve trade-off, and no "stickiness," when the inflation rate drops by hundreds or thousands of percentage points within a few months, as it did then. And Robert Shiller (2008) has pointed out that the U.S. housing boom and bust of the 2000s was unlike anything seen in the nation's history dating back to 1890. So was the recent bubble sui generis, or just "normal but bigger?" Stock and Watson implicitly argue for the latter. I wonder.

And while we are thinking this way, is the bursting of a bubble a "shock," as we conventionally use the term? After all, we all knew with near certainty that the housing bubble was going to burst; the only question was when. If so, did the e in the home-price equation still have a mean of zero after, say, 2005? Indeed, were Christopher Sims, who does not allow such words, not the other discussant of this paper, I might be tempted to ask whether bubbles are exogenous or endogenous variables.

THE STOCK-WATSON VIEW The essence of Stock and Watson's econometric methodology is as follows. Back in ancient times, economists used to estimate giant "structural" macroeconomic models that could be used to derive reduced forms like

(1) Y = X[beta] + [epsilon],

where Y is a vector of "endogenous" variables explained by the model, X is a vector of "exogenous" variables not explained by the model, and [epsilon] is a vector of error terms, or "shocks." One problem was that Y and X might be very long vectors, making [beta] a truly gigantic matrix, with more parameters than one can reliably estimate. The factor analysis approach is an attempt to economize on parameters, starting from the observation that one can always find a much smaller set of variables, Z, such that

(2) X[beta] = Z[GAMMA] + u,

where u is another error vector. How well equation 2 fits the data is an empirical question whose answer will depend, among other things, on the number of Z variables--the "factors." Using equation 2, one can rewrite equation 1 as

(3) Y=Z[GAMMA]+[epsilon]*.

Whereas X (and thus [beta]) may be huge, Z (and thus [GAMMA]) will be of manageable size. In Stock and Watson's particular application, Z is only six-dimensional. The operational question is how much information is lost in going from equation 1 to equation 3; that is, how good an approximation equation 2 is.

This formalism is mathematically valid, of course, but let me point to three weaknesses. The first is what I call the reification fallacy: One tends to treat the [epsilon]s in either equation 1 or equation 3 as actual things--"shocks"--when they are really deviations from conditional expectations ("error terms"). To be sure, there are such things as genuine unexpected shocks, like surprise movements in oil prices or in monetary policy. But what economists typically call a "consumption shock," for example, is just the error term in the consumption equation; it expresses, among other things, our inadequate understanding of consumer spending. This distinction is highly relevant to the "was it just bigger?" question. For example, when several 5- or 6-standard-deviation shocks are observed, are those just unusually large error terms, or do they signify that something virtually unprecedented happened? (3) I lean toward the latter.

Second, although moving from equation 1 to equation 3 is legitimate, both algebraically and statistically, the Zs and [GAMMA]s cry out for interpretation. Often that interpretation is hard to give, or simply not given. In the old days, the Xs in equation 1 had clearly understandable names like "exports" or "government purchases." So, for example, [TEXT NOT REPRODUCIBLE IN ASCII] might be interpreted as the multiplier effect of higher exports on real GDP. In describing their factor analysis methodology, by contrast, Stock and Watson write, "arbitrary normalization means that the individual factors do not have a direct economic interpretation." I am, no doubt, an old fuddy-duddy, but this strikes me as a drawback. If, in the old methodology, our computations found that [partial derivative]GDP/[partial derivative]exports was 10 or -1, we would know immediately that something was wrong. We have no such intuition about [partial derivative]GDP/[partial derivative][F.sub.1].

The third problem is obvious, but it is also important in the context of deciding whether some phenomenon is "new" or just "bigger." If something has not been experienced before, it obviously will not be in a statistical model based on real data. For example, oil shocks were nowhere to be found in pre-1973 macroeconomic models, although James Hamilton (1983) later taught us that they should have been there all along. How, then, can a purely statistical model--as opposed to observation, common sense, or an economic model--tell us whether some unusual development is "new" or just an unusually large deviation from historic norms?

With all that said, Stock and Watson's factor analysis model performs surprisingly well. For most of the major macroeconomic variables, such as GDP, employment, and their main components, their factor analysis model estimated on pre-2007Q4 data captures the post-2007Q4 data amazingly well. (See many of the panels in their figure 2.) I was impressed. (4)

But who ever expressed the view that, say, consumption behaved abnormally relative to its major determinants (disposable income, wealth, and so forth) during this period? The Stock-Watson factor analysis model misses badly more or less where events lead you to think any model would. Home prices, bank lending, the federal funds rate, the monetary base, and long-term unemployment are some examples (again from their figure 2). I do not say this to criticize the authors; those variables are awfully hard to "get right" during the recession and its aftermath. But it does lead me back to the thought that the 2007-09 recession and subsequent recovery really were different, not just bigger.

Perhaps the gentlemen protest too much.

REFERENCES FOR THE BLINDER COMMENT

Bernanke, Ben S., Mark Gertler, and Mark Watson. 1997. "Systematic Monetary Policy and the Effects of Oil Price Shocks." BPEA, no. 1: 91-142.

Hamilton, James. 1983. "Oil and the Macroeconomy since World War II." Journal of Political Economy (April): 228-48.

Minsky, Hyman P. 1992. "The Financial Instability Hypothesis." Working Paper no. 74. Jerome Levy Economics Institute of Bard College.

Reinhart, Carmen M., and Kenneth S. Rogoff. 2009. This Time Is Different: Eight Centuries of Financial Folly. Princeton University Press.

Sargent, Thomas J. 1982. "The Ends of Four Big Inflations." In Inflation: Causes and Effects, edited by Robert E. Hall. University of Chicago Press for the National Bureau of Economic Research.

Shiller, Robert J. 2008. The Subprime Solution. Princeton University Press.

(1.) Among the many papers that could be cited, see Bernanke, Gertler, and Watson (1997).

(2.) By a Reinhart-Rogoff recession I mean a recession caused or prolonged by the harmful balance-sheet effects of a financial crisis (Reinhart and Rogoff 2009); by a Minsky recession I mean a recession caused by the (inevitable) bursting of an asset bubble after excessive speculation (see, for example, Minsky 1992).

(3.) Stock and Watson's table 5 contains six shocks larger than 5 standard deviations; three of them are larger than 8 standard deviations.

(4.) Maybe more than I should have been. Some Panel members suggested during the general discussion of the paper that one of the six factors must have closely resembled real GDP.

COMMENT BY CHRISTOPHER A. SIMS This paper by James Stock and Mark Watson is an exercise in descriptive statistics, attempting to provide insight into what was surprising about the Great Recession compared with historical statistical patterns. Economists are attempting to revise their theories and empirical models to account for what happened in 2007-11, so this paper's systematic examination of what happened, using a wide range of economic time series, is valuable.

The paper has two themes: some things about the Great Recession were very different from historical patterns, and some were not. The story it tells, with some qualifications, is that the Great Recession was characterized by big "shocks" (forecast errors in a linear model), but that those shocks fed through the dynamics of a linear model much as one would have expected from historical patterns. The paper identifies the recent phenomenon of "jobless" recoveries as differing from historical patterns, but in a smoothly trending way that was visible well before the Great Recession.

That there were big shocks is clear, and it is interesting to see when they occurred and in which variables. The downward bend in trend employment growth that the authors find looks statistically convincing, and the paper informally suggests plausible reasons for it. The case for the linear dynamics having been stable is less convincing to me, however, and there are aspects of the data's behavior that have been unusual and that are not captured in pre-2008 economic models or in the models that this paper fits to the data.

The biggest statistical surprise in the recession was the size of the forecast errors in the linear model, both during the 2008Q4 crash and to some extent preceding it. The paper does not actually display any such forecast errors, but table 5 shows estimated surprise components of 11 variables, constructed from the authors' dynamic factor model. It would be easier to interpret the results if these were actual forecast errors in the variables listed at the top of the table, but as the paper's figure 2 shows, the variables are fairly close to the same thing as their "common components," so the table comes fairly close to showing us forecast errors in these variables. The errors are scaled by the standard deviation of forecast errors over 1960-2007Q3, so those larger than 4 in absolute value--in productivity, housing starts, oil prices, the VIX, and the TED spread--are extremely unusual by historical standards. If the disturbances were normally distributed, even those larger than 3 would be unlikely to have occurred in the historical sample, but the data are not normal. Three-sigma errors occurred fairly often in the sample, but four-sigma and larger errors did not. In fact, all the series with over-four-sigma errors had no disturbances of that magnitude in the sample period. (These conclusions are all based on data related to table 5, extending it to earlier periods, that the authors made available to me.)

That there were large unforeseen changes in economic time series in this period is, of course, not news. It is good to have the size of the surprise quantified, however, and to observe where the surprises concentrate: Except for the 2008Q4 productivity shock (about which more below), each of these extremely large surprises was in a variable related to housing or financial markets. That these variables showed large unexpected changes is again not news, but their size relative to historical norms is worth noting.

Perhaps more unexpected is that for GDR consumption, and investment there were large disturbances, but they were not larger than had been seen during the 1960s and 1970s. This raises an interesting question that the paper does not explore: did the large shocks in financial variables feed through into large predicted changes in the nonfinancial variables, and did those effects lead to more accurate forecasts?

My curiosity aroused, I used monthly data from the authors' database on the 3-month Treasury bill rate, the 3-month London Eurodollar deposit rate, and logs of industrial production, employment, oil prices, and the personal consumption expenditures deflator to estimate a vector autoregression (VAR) on data from 1971 through September 2007. (I used 13 lags and an improper prior shrinking toward persistent behavior of the data.) If, as seems likely to me, the paper's six factors can be well approximated by linear combinations of current and lagged values of these six variables, one can use the VAR to gain insight into how the paper's model works.

The VAR confirms that the Eurodollar rate (which, combined with the Treasury bill rate, can reproduce a version of the TED spread) has substantial power in explaining industrial production over medium to long horizons. When the Eurodollar rate is excluded from the VAR, forecasts conditioned on data through September 2008 (although still with coefficients estimated through September 2007) are considerably worse. The Eurodollar rate variable allows the VAR to underestimate the decline in output and employment through mid-2009 by substantially less.

As can be seen from my figures 1 and 2, however, the VAR residuals contrast with the findings reported in the paper's table 5 in some respects. One is that the very large forecast errors are spread evenly across variables in the VAR, not concentrated as in the authors' model in its one financial-stress variable LIBOR. This could happen because the VAR does not include as rich a set of financial variables, but in my view it is more likely a reflection of the difference in time units. What happened to output, employment, and the PCE deflator in September 2008 was extremely large and sudden by historical standards. The suddenness is partly smoothed away by the use of quarterly rather than monthly data. The large positive shock to productivity shown in the paper's table 5 probably reflects the complicated and rapid changes in output and labor markets during this period. No positive shock to productivity shows up in the VAR residuals, and the authors in a personal communication to me showed that the positive shock occurs only in the projection of productivity on the factors, not in the productivity series itself. Most of the surprises in table 5 correspond well with sharp movements in the series labeling the columns, but not this one.

Many of the monthly series show VAR residuals that are both large and oscillating in sign during the final 3 months of 2008 and the first half of 2009. During this period the large shocks were not simply feeding through the usual dynamics. The usual dynamics were producing large error after large error. After this period, however, the residuals return to a size commensurate with historical norms. My conclusion is that the notion that the crisis consisted merely of large shocks feeding through the usual dynamics is somewhat misleading. The usual dynamics did not explain what was going on for several months around the peak of the crisis. During that period existing linear models may have been unhelpful. But after that period, starting from a new, depressed economic state but with the financial markets stabilized, models fitted to history began tracking reasonably well again.

My figure 1 brings out another point that is implicit in the paper's methods but could be further emphasized. The historical data before the end of 2007 already showed clear evidence that large outliers and sustained periods of unusually high or low volatility are recurring phenomena. All the statistical tests that the paper applies carefully avoid assuming normality of residuals or even constant variances, sacrificing power because the stronger assumptions would be clearly counterfactual. If one is looking for what the standard macroeconomic models have been missing, this is a good place to start. We should be modeling the evolution of volatility and its potential interaction with mean dynamics, not treating these phenomena as "nuisance parameters" to be worked around. Our statistical descriptive models should go beyond linear models, in other words, and our theoretical models should be required to provide interpretations for the results. The interaction of financial market malfunction with the macroeconomy may be a good part of what generates the outliers and time-varying volatility that we observe.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The authors were among the first to point out the value of interest rate spread variables in forecasting. In their seminal 2002 paper they included a number of spread variables, but not the TED spread or a Eurodollar rate. In this recent crisis the Eurodollar rate has done particularly well in after-the-fact forecasting models, as it measures distress in interbank lending, which was central in this crisis. It was useful before the crisis as well, as otherwise models estimated through late 2007 would not have detected its effects. But the fact that it plays a prominent role in the paper's model does reflect what economists have already learned about the deficiencies in precrisis models. Measures of financial distress are important, and we have been sifting through candidates for measuring them better. Financial institutions and regulations are continually changing, however, so that the markets where we need to look for measures of stress will probably continue to shift. This suggests a reason for caution in interpreting this paper's results as showing big shocks feeding through stable dynamics.

My conclusions about the substance of the paper's results are that it is correct to point to the continuing usefulness of models fitted to historical data in the wake of the crisis, but that to suggest that this means the crisis was "just large shocks" is misleading. Linear model dynamics did not work well during the peak of the crisis, and linear models turn a blind eye to what should be one of our most important scientific tasks, that of understanding recurrent instances of high volatility in macroeconomic and financial time series.

I turn now to some comments on the paper's methods. The paper uses the principal-component dynamic factor model setup that the authors developed and have used before. The approach requires stationary data, and economic data are not stationary. Accordingly, the authors prefilter all series to make each one plausibly stationary, first-differencing real variables and second-differencing prices. My view of the econometric literature on cointegration is that its complicated prescriptions for frequentist inference--which would be totally impractical for the model of this paper--are misguided. But the literature begins from an important observation: when cointegration may be present, simply getting rid of nonstationarity by differencing individual series so that they are all stationary throws away vast amounts of information and may distort inference. That is why the VAR that I used above to interpret the paper's results was estimated in levels, allowing the model dynamics to account for any nonstationarity.

In addition to this differencing, the paper removes "trend" through another layer of filtering, then applies factor analysis to the residuals from these two layers of preprocessing. Any inference that is carried out ignores uncertainty about the prefiltering and about the factors themselves. As mentioned above, all the statistical tests are in a form that, in a large enough sample, would be robust to nonnormality. Because of these layers of data processing and of the authors' reluctance to present an explicit model of nonnormality and time-varying volatility, it would not be reasonable to ask them for error bands around the statistics they develop. Perhaps most important, their plots of out-of-sample forecast and actual values of employment growth (figure 4 in the paper) are presented only as point forecasts. One can see that the model, in most but not all recessions, gets the overall growth rate of employment about right, but there are errors, and no standard exists by which to judge whether these errors are big or small. This is one main reason that I prefer to work with an explicit probability model of the data, which becomes testable because it attaches uncertainty measures to its forecasts.

The preprocessing also raises some doubts about the result that jobless recoveries are explained by a downward bend in the trend rate of growth of employment. Because the trend is estimated with a two-sided filter that uses data for several years ahead of the current date, the precrisis trend could actually be affected by crisis-period data.

The complexity of the dynamic factor model structure could in principle be providing better forecasts and more accurate modeling of the macroeconomy. This paper does not provide any direct evidence on whether this approach is an advancement over one that would directly model the time-series behavior of, say, a dozen major standard aggregate series, explaining the remaining 150 or so as functions of these central aggregates. My reading of the previous literature on these methods is that it does not provide evidence on this point either. This matters, because the task of explicit probability modeling is much harder if it requires extraction of unobservable factors from hundreds of series.

I have not commented on the paper's attempts to give behavioral interpretations to its factors by correlating them with external variables. I find

this exercise completely unconvincing. The external variables have themselves in most instances been constructed by modeling macroeconomic aggregates, many of which are included in the factor model or have close analogues in it. The intuitive interpretation of this procedure is similar to that underlying the projections of individual variables on factors that generated the results in table 5. Some variable or group of variables to which one can give a name is regressed on the factors, and the resulting linear combination of factors is given a name. That may help in interpreting the six nameless factors, but it is in no sense "structural" estimation. The authors do not even provide a structural model of the data within which these estimates would be valid estimates of something structural.

The paper represents hard work and has produced much food for thought. Like most good empirical work, it required making decisions about how to analyze and present data (that is, "assumptions") that provide plenty of targets for critics. But despite my having taken aim at some of these targets, I hope the paper will stimulate more work along this line.

REFERENCE FOR THE SIMS COMMENT

Stock, James H., and Mark W. Watson. 2002. "Macroeconomic Forecasting Using Diffusion Indexes." Journal of Business and Economic Statistics 20, no. 2: 147-62.

GENERAL DISCUSSION William Brainard noted that the authors' conclusions depended heavily on how they distinguished between changes in structure and shocks. That distinction, in turn, depended on how they detrend and how they weight the roughly 200 time-series variables. Their estimate of a variable's trend was approximately the same as its average rate of change over a centered window of plus or minus 30 quarters. If a shock is large and persistent, as arguably some were in the 2007-09 recession, this procedure may improperly allocate a significant fraction of a shock to the trend. Brainard cited as an example the case of housing starts, which were relatively steady at a high level until the bubble burst, declined rapidly starting in 2005, and have remained low ever since. When the authors' detrending procedure is used, much of the large drop in housing starts is likely to appear as a decrease in trend. The dramatic drop in starts does not average out; the shocks in the window covering 2007-09 go in one direction. The same danger of confounding trend and cycle, Brainard continued, arises in the case of employment growth, where the authors attribute most of the recent slow recovery to a slowdown in trend employment growth.

Brainard also reasoned that the results could be sensitive to the authors' use of unweighted percentage changes for the real variables. As a consequence, their results could reflect large percentage changes in variables that are relatively unimportant to aggregate output, while underweighting variables that are more important but have smaller percentage changes. Principal component analysis, which the authors use to compute the factors, is not scale independent, Brainard noted. He wondered what the results would have been if the authors had weighted changes by their importance to the overall economy or had conducted their analysis in levels.

Finally, the authors' finding that the structural dynamics of the pre-2007 recessions matched those of the most recent one puzzled Brainard, since the most recent recession was so deep and the current levels of variables like housing starts and unemployment are so different from what was observed during previous recoveries. In the case of housing starts, the authors' scatter-plot makes clear that the errors using the dynamic factor model are autocorrelated, which is inconsistent with the model's assumptions. Brainard suggested that such autocorrelation of errors might explain similar discrepancies between the observed levels of other variables and the predicted levels implied by the authors' model.

Refet Gurkaynak observed that after every big macroeconomic event, economists feel pressure from the public and policymakers to look at that event as something entirely new and unique and to forget all lessons from previous experience and research. He saw this paper as an important counter to that kind of thinking, because it showed that economists have accumulated some wisdom over the years that remains relevant from event to event and could be used to give policy advice even in the face of new challenges.

Gurkaynak was troubled, however, by the fact that a large financial shock was driving the results of the authors' model for the recent recession. He interpreted financial asset prices as forward-looking information aggregators, which measure whatever is missing in the rest of the economic model. The fact that the model required a large financial shock to explain the Great Recession data meant that there are probably important variables that were observable over the period leading up to and during the recession but are omitted from the model and instead show up indirectly as the large financial shock.

Olivier Blanchard argued that it is in the nature of dynamic factor models to explain aggregate variables fairly well, because many of the series are closely related to each other and therefore highly correlated. For example, some of the authors' series might be different components of industrial production, which the industrial production index, an aggregate of these, will explain quite well.

Blanchard did not take the fit of the linear model as evidence that structural relationships in the economy were truly linear. On the contrary, he thought Stock and Watson did not provide a way to test empirically for nonlinear relationships, but he felt confident that such relationships exist. The effect of the interest rate on debt dynamics, for example, depends on whether the national debt is 50 percent of GDP or 100 percent, as the recent European experience shows. The effect of a 1-percentage-point drop in the rate of GDP growth on loan performance, as another example, depends on whether the GDP growth rate starts out at 4 percent or at 1 percent. Blanchard suspected that coming up with appropriate ways to measure these relationships would be hard but could be done.

Martin Baily said that given the unusual nature and size of the shocks that had provoked the Great Recession, he was surprised by the extent to which Stock and Watson found the shape of the recession and subsequent recovery to match that of previous recessions and recoveries. The recent recession had featured a strong inventory cycle, as had previous ones, for example. And a financial accelerator effect appeared to have depressed investment, again as in previous recessions.

What Baily found most puzzling was the performance of the labor market, which he thought had suffered more initially and recovered more slowly than in previous recessions even after accounting for demographic changes. He was therefore surprised that the dynamic factor model was able to match employment data in the recession and recovery as well as it did. Baily thought that cross-country data might shed some light on the poor U.S. labor market performance. He noted that patterns in GDP growth and employment growth varied widely across countries during and after the Great Recession. Germany and the United Kingdom both suffered larger drops in GDP but experienced smaller declines in employment than the United States. Spain, on the other hand, experienced a similar drop in GDP as the United States but an even larger employment decline. The other aspect of the Spanish economy that paralleled the U.S. experience was its large housing boom and subsequent collapse of residential construction. That parallel led Baily to wonder whether the exceptional labor market decline in both countries could be traced to the collapse in housing construction. The theory might explain why Stock and Watson's model could explain the collapse in employment, since their analysis includes housing market data.

Frederic Mishkin, like Blanchard, thought that modeling nonlinear features of the business cycle was very hard but worth further study. The literature has long noted the existence of financial disruptions and financial accelerators as important factors in recessions, he said, but these phenomena had not been incorporated in the dynamic stochastic general equilibrium models used for policy analysis. He wished especially that models could better incorporate the extreme nonlinearities that are constantly present in the financial sector and worsen during recessions. Some of these nonlinearities could even independently help trigger recessions, as he thought was true of Enron's crash in late 2001 and the recession that soon followed. For the most recent recession, he saw the crash of Lehman Brothers as an important source of nonlinearity.

Robert Hall described a related exercise he had recently carried out to examine the causes of the recession. Using a dynamic, nonlinear macroeconomic model, he computed the paths that two driving forces--financial friction and deleveraging--must have taken to explain the pattern of unemployment and investment observed during the downturn. He found that financial friction was a large and persistent factor in explaining unemployment and investment, whereas deleveraging was an important factor early on but diminished in importance quickly. The same exercise would have been easy to carry out for earlier business cycles using the same model, the only difference being that the movements of the variables would have been smaller. That the same model and driving forces could explain patterns of unemployment and investment across different recessions was unsurprising, since they did so by design.

Because Hall saw Stock and Watson's exercise as similar to his own, he found their results mostly unsurprising, with the possible exception that they could explain a large number of time series well using a much smaller number of factors. However, he understood it to be a well-known feature of dynamic factor models that only a few factors could explain the movement of many variables.

Linda Tesar wondered how well the authors' model could explain imports and exports, since both dropped significantly during the recession even though the exchange rate changed little. She also suggested that another test of the model might be to test how well it fits the data in other countries.

Justin Wolfers thought the authors had neglected to highlight one of the most striking findings of the paper, namely, that numerous variables that had previously been identified by macroeconomists as exogenous instruments were in fact highly correlated with each other. In one of their tables, for example, the fiscal shock identified by Christina Romer and David Romer in 2010 exhibited a -0.8 correlation with the monetary policy shock identified by the same authors in 2004. Wolfers noted that if labor economists somehow discovered that the typical instruments for educational attainment--quarter of birth, Vietnam draft lottery number, and distance to college, for example--were in fact highly correlated, they would regard the finding as enormously destructive to most of what modern labor microeconomics had achieved. He wondered, then, what this correlation of supposedly instrumental variables meant for macroeconomics. Wolfers also found it puzzling that the authors' factors seemed to explain GDP and some other macro time series too well given the margin of error with which those series are measured.

John Driscoll offered a possible insight into why one of the series, commercial and industrial loan volume, fit less well than some others. Early in a recession, business loans often rise before eventually falling, because firms are using previously unused parts of credit lines that had been approved before the recession started. The recent recession featured a particularly large run-up and a subsequent crash in commercial and industrial loans. One could observe this effect more directly by examining measures of unused loan commitments from banks' call reports, which fell at the start of the recession as businesses used up their available credit.

Valerie Ramey suggested a caveat to the authors' finding that an oil shock was an important contributor to the start of the recession. Previous research had found that the effects of oil price shocks on the U.S. economy had declined since the mid-1980s. However, in a 2010 paper, she and Daniel Vine had found that the appearance of a structural shift in the effect of oil shocks could be traced to the removal of price controls on oil after the 1970s, which had caused severe misallocation. With price controls absent, an increase in the price of oil in 2008 ought to have had a smaller effect on the economy than a comparable shock in the 1970s.

Ramey also commented on the difficulty of separating shocks from long-run trends, noting that the latter may actually help drive what we think of as the business cycle. In unpublished work, using a standard real business cycle model, she had modeled the effects of an anticipated change in the growth rate of the labor force and found that decreases in that rate in the 1930s had led to decreased productivity and investment. Similarly, John Maynard Keynes and Alvin Hansen had suggested that the cutoff of immigration in the 1920s, which slowed labor force growth, was a factor in the Great Depression. Ramey had also found that, in the 1940s, an increase in the labor force growth rate led to increased productivity and investment even without a World War II shock in the model.

Christopher Carroll thought the paper was helpful for focusing economists' attention on the shocks that had led to the recession. However, he thought the most credible method of calculating the recession-causing shocks might be to use a model that was published just before the recession. David Wilcox reported that several of his colleagues, Hess Chung, Jean-Phillipe Laforte, David Reifschneider, and John Williams, had completed an exercise similar to the one Carroll had suggested; their paper was forthcoming in the Journal of Money, Credit, and Banking. Before the Great Recession, using the 2007 version of the Federal Reserve's main macroeconometric model, the FRB/US model, Reifschneider and Williams had found that the likelihood of a multiyear zero-lower-bound event was so low as to be practically a statistical impossibility. The forthcoming paper uses a range of other models and considers a wider spectrum of sources of uncertainty. With those adjustments, recent events are seen as less remotely improbable, but still relatively unlikely. On this basis, Wilcox was surprised that Stock and Watson's paper seemed to suggest that their model could account for basic features of the recession.

To Ricardo Reis, the fit of the model to the post-2007Q4 data was useful for demonstrating that over the course of the recent recession and recovery, the six-factor model was not missing a major seventh factor. Reis highlighted a footnote in the paper in which the authors specify the algebraic manipulations they used to estimate the post-2007Q4 factors and to compute the common component of the macroeconomic time series in the post-2007Q4 period. There they explain that they use principal component analysis to find the six linear combinations of the series that best account for the data over the 1959-2007Q3 period. These linear combinations are described by the factor loadings matrix, [??] (59-07). The six factors are then estimated for the post-2007Q4 period by applying the transpose of the factor loadings matrix to post-2007Q4 data for the macroeconomic series. Finally, the factor loadings matrix is applied to the six estimated factors to predict the same series in the post-2007Q4 period. The key point for Reis was that, with this methodology, the post-2007Q4 factors are "old" in the sense that they are based on the pre-2007Q4 linear combinations of the series. As the footnote explained, if there were a new factor, the space spanned by the factors would change, so the new factor would not be spanned by the post-2007Q4 estimated factors.

Reis likened this process to a much simpler exercise: Imagine being given data on durable goods output and nondurable goods output for a number of years. These two series sum to total goods output. Then suppose one is given total goods output for the next few years and asked to predict durable goods output and nondurable goods output during that period. The strength of the prediction will depend on how well one is able to capture the relationship among durable goods, nondurable goods, and total output over the period for which data on all three series are available, and whether this relationship continues to hold in the period over which the prediction is made.

Reis drew from the authors' analysis a much weaker claim than some other panelists had suggested. The exercise did not, he argued, imply that the world did not change in 2007. The six factors may have undergone larger innovations than in past decades, or become more stochastically volatile, but such changes would still be consistent with the authors' finding, so long as no new type of shock had emerged.

Reis saw the authors' "no new shock" finding as consistent with theorizing by other economists trying to explain the sources of the financial crisis. That work often focuses on just one or two types of structural shocks--such as preference shocks, technology shocks, or monetary policy shocks--and abstracts away other aspects of the economy. Thanks to Stock and Watson's work, Reis thought, these researchers could rest assured that they are not ignoring some unidentified "animal spirit" or other type of shock that could undermine their models.

Finally, following on Wolfers' point, Reis thought that the correlations between variables that had previously been identified as instrumental show that economists have limited understanding of what structural shocks are driving the factor innovations in Stock and Watson's model.

Wendy Edelberg noted that, at the trough of the recession, if policy-makers had been able to predict the path of GDP growth over the next few years, they presumably would have enacted different policies. She wondered, then, whether the authors' analysis shed any light on what policy-makers should have done during the recession.

Christopher Sims highlighted the fact that Stock and Watson's results were driven, in part, by large deviations from historical norms in the interest rate and in monetary aggregates. He thought it was misleading to acknowledge these large historical deviations but ignore the fact that, in their absence, other macroeconomic variables would have behaved very differently. He saw Stock and Watson's inability to predict what would have happened in the absence of significant policy intervention as a limitation of their analysis.

Sims analogized the issue to tracking the temperature in one's kitchen from day to day. On a typical day, the temperature rises while dinner is cooking and then falls. Suppose one day a fire started while dinner was being prepared and a fire extinguisher was used to put the fire out. The time path of temperature in the kitchen would look relatively normal, but it would be incorrect to say nothing unusual had happened, because had the fire extinguisher not been used, the temperature in the kitchen would have developed very differently that evening.

Michael Kiley characterized the authors' work as a tracking exercise rather than a prediction exercise. He did not find it surprising that their factors were able to track macroeconomic aggregates well. He saw their principal component analysis as identifying an "economic activity" factor, which, much like the Federal Reserve Bank of Chicago's National Activity Index, could track GDP well using a linear combination of other macroeconomic time series. Applying Okun's Law, one could also use the same factor to track the unemployment rate fairly well.

Kiley thought the authors were correct to identify the financial shock as an important driver of the recession, and correct to say that, conditional on the large shock to financial prices, the macrodynamics that followed were not so surprising. However, their model did not incorporate a rich enough picture of the financial system to determine whether the forces that created or amplified the large financial shock were surprising or unusual or nonlinear. The panic related to mortgage-backed securities and the collapse of three investment funds held by the French bank BNP Paribas, for example, were unusual events that seemed to have induced large movements in financial markets but were not captured by Stock and Watson's model.

Responding to the discussion, James Stock agreed with Brainard that his and Watson's detrending method may not always distinguish well between shocks and trends, especially near the end of certain data series. He and Watson had run sensitivity checks that gave them confidence in their results, but they thought that more work needed to be done in identifying trends in macroeconomic series and that researchers would do well to study trend identification more closely.

Replying to Wolfers, Stock felt that macroeconomists' work on finding exogenous instruments was very constructive and well worth continuing. He did not view the correlations between instruments as a setback but rather as a source of new questions to pursue.

Stock also thought that Reis's interpretation of his and Watson's findings was essentially correct. To further clarify, he explained that, in the post-2007Q4 period, there did not appear to be any new factor driving correlation across the idiosyncratic errors in their model. And in linear algebraic terms, the space spanned by the factors also spanned the innovations in time series over the course of the recession. This seemed reasonable to Stock since the shocks driving the crisis, such as financial and uncertainty shocks, had occurred before on smaller scales.

Replying to Sims, Stock conceded that the results reflected only the net effect of financial shocks and countervailing policy interventions, measured on a quarterly basis. He and Watson had hoped to be able to examine these shocks at a finer level, but data limitations had prevented this.

Finally, Stock acknowledged that linear models like theirs were subject to substantial limitations and that nonlinearities could well be driving some patterns in the data. However, not all nonlinearities present problems; some should and do translate into shocks in their model. The zero lower bound, for example, is a nonlinear constraint that prevents the interest rate from falling below zero. In their framework this constraint translates into a contractionary monetary policy shock during the latter part of the Great Recession. However, nonlinearities that cannot be captured by shocks are not handled well by their model.

JAMES H. STOCK

Harvard University

MARK W. WATSON

princeton University

(1.) The view that financial recessions and recoveries are different from "normal" recessions has been articulated most notably by Reinhart and Rogoff (2009); see also Reinhart and Reinhart (2010), Hall (2010), Mishkin (2010), Bank of Canada (2011), and Jorda, Schularick, and Taylor (2011).

(2.) Various reasons have been proposed for why this recovery is exceptional, including the deleveraging that followed the financial crisis (for example, Mian and Sufi 2011), regional or industry job mismatch (for example, Sahin and others 2011), changes in labor management practices (for example, Berger 2011), and monetary policy rendered ineffective because of the zero lower bound.

(3.) Online appendixes and replication files for the papers in this volume may be accessed on the Brookings Papers website, www.brookings.edu/about/projects/bpea, under "Past Editions." They are also accessible at Mark Watson's personal website at Princeton University, www.princeton.edu/~mwatson/.

(4.) Equations 1 and 2 are the static form of the DFM, so called because the factors F, enter with no leads or lags in equation 1. For a discussion of the relationship between the dynamic and the static forms of the DFM, see Stock and Watson (2011).

(5.) Endpoints are handled by truncating the kernel and renormalizing the truncated weights to add to 1. This approach has the desirable feature that it makes no assumption about reversion to the local mean, in contrast to the mean reversion imposed by the standard approach of using a stationary time-series model to pad the series with forecasts and backcasts. We alternatively computed the local means using a Baxter-King (1999) highpass filter with a pass band of periods with [less than or equal to] 200 quarters, and using the trend implied by a "local level" model (the sum of independent random walk and white noise with a ratio of disturbance standard deviations of 0.025), and obtained similar results. The weights for these different filters are given in the online appendix.

(6.) Our procedure produces a smooth but not necessarily monotonic trend. Kim and Eo (2012) model the trend decline in the growth rate of GDP as a single Markov switching break and estimate a decline of 0.7 percentage point over this period, less than our estimate of 1.2 percentage points. If the trend is in fact smoothly declining, one would expect their step-function approximation to estimate a smaller average decline than our local mean.

(7.) Specifically, let [[??].sub.t] denote the vector of 132 disaggregated time series used to estimate the factors, and let [??] denote their corresponding factor loadings. These factor loadings are estimated by principal components using data on [[??].sub.t] over 1959Q1-2007Q3 (modified for some series having missing observations; see the online appendix). Denote the resulting estimates of [??] by [[??].sup.59-07], normalized so that [[??].sup.59-07], [[??].sup.59-07]=I. The estimated "old" factors are computed using [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], ..., 2011Q2. The values of [[??].sub.t] post-2007Q4 are those of the "old" factors in the sense that they are based on the pre-2007Q4 linear combinations of [[??].sub.t]. The factor loadings for the remaining 68 series (the high-level aggregates) are obtained by regressing each series on [[??].sup.59-07.sub.t] using data through 2007Q3; these estimates, combined with [[??].sup.59-07] yield the estimated "old" factor loadings, [[??].sup.59-07]. The vector of common components of the full vector of time series associated with these "old" factors and "old" factor loadings is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(8.) The assumption that the factors and DFMs can be estimated with no breaks over the 1959Q1-2007Q3 period is only partially consistent with the empirical evidence. On the side of stability, in Stock and Watson (2009) we use a similar data set and find that the space spanned by the full-sample (no-break) factors spans the space of the factors estimated using pre- and post-1984 subsamples; against this, there we also find breaks in some factor loadings in 1984Q1. These apparently contradictory findings can be reconciled by the property of DFMs that the space spanned by the factors can be estimated consistently even if there is instability in A (Stock and Watson 2002, 2009, Bates and others 2012). These findings suggest that, in the present analysis, we can ignore the 1984Q1 break when estimating the factors; however, tests of coefficient stability might be sensitive to whether the comparison sample includes pre-1984Q1 data. We therefore consider a DFM with a break in 1984Q1 as a sensitivity check. Additional sensitivity checks, with breaks in 1984Q1, are reported in the online appendix.

(9.) The Bai-Ng (2002) [IC.sub.P1] and [IC.sub.P2] criteria select either three or four factors, depending on the sample period, whereas their [IC.sub.P3] criterion selected 12 factors. The scree plot (the plot of the ordered eigenvalues of the sample covariance matrix of [X.sub.t] drops sharply to four or five factors and then declines slowly.

(10.) Using the notation of footnote 7, let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the prediction error using the "old" model and factors. The subsample [R.sup.2] for series i is computed as [R.sup.2] = 1-([[summation].sub.t] [[??].sup.2.sub.it])/([[summation].sub.t] [X.sup.2.sub.it]) where the sums are computed over the column subsample.

(11.) Giannone, Lenza. and Reichlin (2012) examine the stability of the relationship between various types of loans and macroeconomic indicators in the euro zone during and after the crisis, relative to a precrisis benchmark: they find no surprising behavior of loans to nonfinancial corporations, conditional on aggregate activity, although there are departures from historical patterns for household loans.

(12.) The negative quarterly [R.sup.2]s for output per hour reflect a timing mismatch, and 4-quarter growth in productivity is well predicted. The predicted values for average hourly earnings growth change from procyclical to countercyclical in the mid-1980s, and the negative [R.sup.2] reflects this apparent instability in the factor loadings in 1984, not something special to the 2007-09 recession.

(13.) The Andrews (2003) test is based on an analogue of the usual (homoskedasticity-only) Chow break-test statistic, with a p value that is computed by subsampling.

(14.) Rewrite the factor VAR (equation 1) as [F.sub.t] = [??](L)[F.sub.t-1] + [[eta].sub.t], so, from equation 2, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the contribution of the past factors and [LAMBDA][[eta].sub.t], is the innovation in the common component. The innovations in table 5 are the residuals from a four-lag VAR estimated using the "old" factors over 1959-2011Q2.

(15.) The approach to structural VAR identification laid out here, including the estimator in the just-identified case, was originally presented in Stock and Watson (2008). This approach was also developed independently in Mertens and Ravn (2012), of which we became aware after presenting the conference draft of this paper. The idea of using constructed exogenous shocks (what we call external instruments) as instruments in structural VARs dates at least to Hamilton (2003); also see Kilian (2008a, 2008b).

(16.) Other candidate instruments include the market announcement movements of Cochrane and Piazzesi (2002) and Faust, Swanson, and Wright (2004).

(17.) Lee, Rabanal, and Sandri (2010) take the uncertainty shock to be the innovation to the VIX.

(18.) In the notation of equations 3 and 5, the factor component due to the jth structural shock is A[PHI][(L).sup.-1][H.sub.j][[epsilon].sub.jt]. The [R.sup.2] of the jth variable with respect to the jth shock is thus computed as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [[??]'.sub.i] is the ith row of [??].

(19.) Again, to be clear, these statements concern correlations among the shock series estimated using the instruments, not correlations among the underlying instruments themselves. For example, whereas the correlation between the shock estimated using the Fisher-Peters (2010) spending instrument and the shock estimated using the Romer-Romer (2010) tax instrument is -0.93, the correlation between the Fisher-Peters and the Romer-Romer instruments themselves is only -0.06.

(20.) These averages exclude the recovery that began in 1980Q3 because the next recession started within the 8-quarter window of these calculations.

(21.) Allowing for a break in [PHI](L) in 1984Q1 produces somewhat faster predicted recoveries before 1984 and somewhat slower ones after 1984; for details see the online appendix.

(22.) The online appendix reports results for five- and seven-factor models. The only notable departure from the results reported in this paper for the six-factor model is that the five- and seven-factor models predict a stronger post-2009Q2 recovery, so they attribute even more of the gap between that recovery and the 1960-82 recoveries to the slowdown in trend growth.

(23.) Two pieces of evidence suggest that the observed decline in employment growth is not an artifact of long-term mismeasurement. First, trend growth in employment measured by the household survey exhibits the same pattern as that in the establishment survey, with a decline from 2.1 percent annually in 1970 to 1.0 percent annually in 2000; this 1.l-percentage-point decline is close to the 1.4-percentage-point decline in the establishment survey (see the online appendix). Second, the small net trend in GDP per worker (from the establishment survey) matches the small net trend in output per hour (nonfarm business), which would not be the case if nonfarm business hours (a narrower measure) are correctly measured but employment is increasingly underestimated.

(24.) Focusing solely on demographic shifts ignores other potential factors affecting labor force participation. One such factor is an endogenous response to the stagnation of median real wages; however, although the magnitude of the labor supply elasticity is debated, micro studies generally suggest that it is small (see Saez, Slemrod, and Giertz 2012, Chetty 2011, and Chetty and others forthcoming for discussions). Another such factor is a possible trend increase in the mismatch between worker skills and available jobs. For example, Goldin and Katz (2008) point to a plateau in the supply of educated Americans around 1980. Jaimovich and Siu (2012) present evidence that the trend adjustments in employment occur mainly through permanent losses of mid-skill jobs during and following recessions; this view of step-like adjustments differs from our smooth trend. It goes beyond the scope of this paper to examine these factors in any detail.

Table 1. Subsample R's of Regressions of Common Components on
Actual Data for Selected Macroeconomic Variables (a)

                                              1959-    1984-
Series                                        2007Q3   2007Q3

GDP                                            0.73     0.62
Consumption (total)                            0.63     0.45
Consumption (services)                         0.35     0.22
Nonresidential fixed investment                0.63     0.57
Industrial production (total)                  0.87     0.79
Industrial production (automobiles)            0.58     0.29
Nonfarm employment                             0.92     0.91
Unemployment rate                              0.84     0.75
Short-term unemployment rate                   0.82     0.70
Long-term unemployment rate                    0.61     0.58
Housing starts                                 0.59     0.39
OFHEO house price index                        0.49     0.44
PCE inflation                                  0.51     0.54
PCE gas and energy inflation                   0.37     0.48
Federal funds rate                             0.44     0.34
Real monetary base                             0.16     0.09
Real commercial and industrial loans           0.44     0.54
TED spread                                     0.54     0.02
Gilchrist-Zakrajsek spread                     0.48     0.48
S&P 500 index                                  0.72     0.69
VIX                                            0.47     0.50
SLOOS lending standards                        0.60     0.18
Household net worth-disposable income ratio    0.16     0.14
Household liabilities                          0.57     0.48

                                                 Computed over 15
                                                 quarters starting
                                                   at indicated
                                                   cyclical peak

Series                                        1960Q2   1969Q4   1973Q4

GDP                                            0.81     0.79     0.83
Consumption (total)                            0.59     0.77     0.66
Consumption (services)                         0.28     0.46    -0.06
Nonresidential fixed investment                0.64     0.77     0.90
Industrial production (total)                  0.90     0.86     0.94
Industrial production (automobiles)            0.59     0.61     0.70
Nonfarm employment                             0.93     0.94     0.93
Unemployment rate                              0.77     0.88     0.95
Short-term unemployment rate                   0.81     0.87     0.90
Long-term unemployment rate                    0.55     0.62     0.68
Housing starts                                 0.27     0.59     0.83
OFHEO house price index                        n.a      n.a      n.a
PCE inflation                                  0.25     0.70     0.66
PCE gas and energy inflation                  -0.42    -1.69    -0.63
Federal funds rate                            -0.01     0.47     0.57
Real monetary base                             0.18     0.39     0.22
Real commercial and industrial loans           0.48     0.47     0.55
TED spread                                     n.a      n.a      0.78
Gilchrist-Zakrajsek spread                     n.a      n.a      0.89
S&P 500 index                                  0.75     0.68     0.89
VIX                                            n.a      0.38     0.74
SLOOS lending standards                        n.a      n.a      0.65
Household net worth-disposable income ratio   -0.18     0.67     0.48
Household liabilities                         -0.19     0.73     0.90

                                                 Computed over 15
                                                 quarters starting
                                                   at indicated
                                                   cyclical peak

Series                                        1980Q1   1981Q3   1990Q3

GDP                                            0.79     0.85     0.73
Consumption (total)                            0.82     0.72     0.74
Consumption (services)                         0.62     0.47     0.47
Nonresidential fixed investment                0.58     0.57     0.50
Industrial production (total)                  0.93     0.94     0.89
Industrial production (automobiles)            0.64     0.39     0.66
Nonfarm employment                             0.95     0.98     0.93
Unemployment rate                              0.91     0.88     0.76
Short-term unemployment rate                   0.88     0.84     0.81
Long-term unemployment rate                    0.74     0.71     0.44
Housing starts                                 0.79     0.76     0.62
OFHEO house price index                        0.59    -0.01     0.60
PCE inflation                                  0.44     0.40     0.57
PCE gas and energy inflation                   0.25     0.23     0.55
Federal funds rate                             0.48     0.41     0.72
Real monetary base                             0.65     0.59    -0.18
Real commercial and industrial loans          -1.42    -1.07     0.70
TED spread                                     0.74     0.70    -0.05
Gilchrist-Zakrajsek spread                     0.11     0.49     0.12
S&P 500 index                                  0.62     0.65     0.37
VIX                                           -0.78    -0.69     0.40
SLOOS lending standards                        0.79     0.67     0.55
Household net worth-disposable income ratio    0.78     0.06     0.28
Household liabilities                          0.76     0.70     0.79

                                               Computed over
                                                15 quarters
                                                starting at
                                                 indicated
                                               cyclical peak

Series                                        2001Q1   2007Q4

GDP                                            0.64     0.64
Consumption (total)                            0.02     0.57
Consumption (services)                        -0.25     0.84
Nonresidential fixed investment                0.69     0.86
Industrial production (total)                  0.76     0.95
Industrial production (automobiles)            0.13     0.57
Nonfarm employment                             0.91     0.96
Unemployment rate                              0.79     0.89
Short-term unemployment rate                   0.75     0.78
Long-term unemployment rate                    0.51     0.64
Housing starts                                 0.29     0.53
OFHEO house price index                        0.42     0.57
PCE inflation                                  0.56     0.82
PCE gas and energy inflation                   0.48     0.71
Federal funds rate                             0.14    -1.51
Real monetary base                            -0.35    -0.03
Real commercial and industrial loans           0.62     0.46
TED spread                                    -0.04     0.76
Gilchrist-Zakrajsek spread                     0.65     n.a
S&P 500 index                                  0.81     0.89
VIX                                            0.75     0.89
SLOOS lending standards                       -1.49     0.47
Household net worth-disposable income ratio   -0.46     0.51
Household liabilities                          0.18     0.77

Source: Authors' calculations; see the notes to figure 1 and the
online appendix for further details.

(a.) Common components are calculated using the six static factors
from the DFM estimated using quarterly data over 1959Q1-2007Q3;
predicted values are the "old model/old factors" values computed
as described in footnote 7 in the text. All entries are 1 minus
the ratio of the sum of squared prediction errors to the sum of
squares of the observed variable (see footnote 10). "n.a."
indicates that the regression was not performed because data for
that series were not available for the indicated period. All
series are transformed and detrended as described in sections
1.13 and LC and in the online appendix

Table 2. Subsample [R.sup.2] of the Common Component Regressions by
Category (a)

                                        [R.sup.2]

                                      1959-    1984-
Series category                  N    2007Q3   2007Q3

National income and product      21   0.56     0.43
  accounts
Industrial production            13   0.72     0.60
Employment and unemployment      46   0.62     0.50
Housing starts                    8   0.37     0.21
Inventories, orders, and sales    8   0.54     0.35
Prices                           39   0.15     0.05
Earnings and productivity        13   0.37     0.29
Interest rates                   18   0.40     0.30
Money and credit                 12   0.44     0.26
Stock prices and wealth          11   0.47     0.52
Housing prices                    3   0.67     0.67
Exchange rates                    6   0.56     0.66
Other                             2   0.42     0.42

                                              [R.sup.2]

                                 Computed over 15 quarters starting
                                      at indicated cyclical peak

Series category                  1960Q2   1969Q4   1973Q4   1980Q1

National income and product       0.56    0.46     0.62     0.66
  accounts
Industrial production             0.78    0.77     0.86     0.86
Employment and unemployment       0.64    0.68     0.76     0.76
Housing starts                    0.09    0.26     0.54     0.46
Inventories, orders, and sales    0.39    0.69     0.72     0.73
Prices                            0.00    0.15     0.37     0.18
Earnings and productivity         0.52    0.38     0.35     0.30
Interest rates                   -0.07    0.39     0.30     0.50
Money and credit                  0.22    0.47     0.55     0.65
Stock prices and wealth           0.00    0.67     0.74     0.62
Housing prices                    n.a     n.a      n.a      0.59
Exchange rates                   -2.64    0.47     0.64     0.48
Other                            -0.40    0.15     0.87     0.89

                                             [R.sup.2]

                                 Computed over 15 quarters starting
                                     at indicated cyclical peak

Series category                  1981Q3   1990Q3   2001Q1   2007Q4

National income and product       0.59    0.64      0.49     0.65
  accounts
Industrial production             0.80    0.66      0.61     0.80
Employment and unemployment       0.81    0.61      0.63     0.78
Housing starts                    0.54    0.44     -0.16     0.27
Inventories, orders, and sales    0.68    0.66      0.43     0.64
Prices                            0.08    0.03      0.14     0.13
Earnings and productivity        -0.03    0.32      0.36    -0.11
Interest rates                    0.44    0.29      0.07    -0.50
Money and credit                  0.63    0.40      0.06    -0.37
Stock prices and wealth           0.50    0.37      0.31     0.77
Housing prices                   -0.01    0.60      0.72     0.57
Exchange rates                    0.66    0.75      0.72     0.60
Other                             0.89    0.48     -0.60     0.31

Source: Authors' calculations.

(a.) Based on the six-factor DFM estimated over 1959Q1-2007Q3.
Entries are the median of the R's of the common component,
computed for the series in the row category over the indicated
period, where the R' is computed as described in the notes to
table 1. "n.a." indicates that the regression was not performed
because data for that series were not available for the indicated
period.

Table 3. Tests of Absence of a Break in Factor Loadings

                                         Percent of series in the
                                         category for which the
                                        hypothesis of a break at
                                        2007Q4 is rejected at the
                                            5 percent level (a)

Series category                   N    1959-2007Q3   1984Q1-2007Q3

National income and product      21        0              0
  accounts
Industrial production            13        0              0
Employment and unemployment      46       15             15
Housing starts                    8       25             13
Inventories, orders, and sales    8       13             13
Prices                           39       26             23
Earnings and productivity        13       15              8
Interest rates                   18        0             11
Money and credit                 12       42             17
Stock prices and wealth          11       18              0
Housing prices                    3       33             33
Exchange rates                    6        0              0
Other                             2        0              0

Source: Authors' calculations.

(a.) The Andrews (2003) end-of-sample stability test is used to
test the hypothesis of stability of the factor loadings. The
statistic tests the null hypothesis of constant factor loadings
against the alternative of a break in the final 15 quarters
(2007Q4-2011Q2) relative to the value of the factor loading
estimated over the indicated period.

Table 4. Standard Deviations of Four-Quarter Growth Rates of
Major Activity Variables (a)

                                    Standard deviation of  series

Series                            1959-83   1984-2004   2005-11 (b)

GDP                                 2.6        1.6          2.8
Consumption                         2.1        1.3          2.3
Investment                         11.4        8.5         15.3
Industrial production (total)       5.2        3.1          6.4
Nonfarm employment                  2.0        1.4          2.3
Change in unemployment rate (c)     1.1        0.8          1.5

                                     Standard deviation of factor
                                              component

Series                            1959-83   1984-2004   2005-11 (b)

GDP                                 2.6        1.4          2.8
Consumption                         2.1        1.2          2.4
Investment                         10.5        6.8         11.4
Industrial production (total)       4.9        3.2          5.9
Nonfarm employment                  1.9        1.3          2.5
Change in unemployment rate (c)     1.1        0.7          1.4

(a.) Entries are standard deviations of 4-quarter detrended
growth rates, except where noted otherwise, over the indicated
period. The first three columns report standard deviations of the
row series. and the second three columns report standard
deviations of the factor component of the row series.

(b.) Calculations go through the final quarter in the data set,
201 IQ2.

(c.) Entries refer to the 4-quarter detrended change in the
unemployment rate.

Table 5. Innovations to Factor Components of Selected Series,
2007Q1-2011Q2

Standard deviation units

                    Total
Quarter   GDP    consumption   Investment   Employment   Productivity

2007Q1    -0.9      -1.3          -0.4         -0.7          -1.2
2007Q2     0.3      -0.2           0.5         -0.1           0.2
2007Q3    -0.3      -0.8           0.0         -0.7           0.0
2007Q4    -0.3      -1.3           0.1          0.3          -0.7
2008Q1    -0.3      -0.7           0.1          0.2          -0.4
2008Q2    -1.4      -2.1          -0.4         -1.1          -2.1
2008Q3    -1.7      -1.7          -1.0         -0.7          -1.4
2008Q4     1.0       2.1          -0.1         -0.4           4.6#
2009Q1     0.3      -2.7           2.3          0.9          -0.3
2009Q2     2.9       1.8           3.3#         3.8#          0.7
2009Q3     1.6       0.4           1.9          2.3          -0.6
2009Q4    -1.2      -0.9          -2.0         -2.1          -0.2
2010Q1     0.3      -0.1           0.6          0.5           0.0
2010Q2     0.7       0.3           0.7          0.3           1.3
2010Q3     0.8      -0.3           1.1          0.4           0.9
2010Q4     0.3      -0.6           0.6          0.0           0.0
2011Q1     0.4      -0.6           1.1          0.5          -0.6
2011Q2    -0.9      -0.8          -1.1         -1.3          -0.6

Standard deviation units

          Housing    Oil      Federal      TED             Household
Quarter   starts    price    funds rate   spread    VIX     wealth

2007Q1      0.2       1.7        0.3        0.0    -0.6       0.0
2007Q2      0.8       1.1        0.5       -0.9    -1.4       0.8
2007Q3     -0.7       0.3       -0.6        0.7     1.2      -1.0
2007Q4     -1.3       1.3        0.4        0.4     0.5      -0.9
2008Q1     -1.3       0.2       -0.1        1.4     2.2      -2.0
2008Q2      1.0       3.4#       0.5        0.1    -0.4      -0.8
2008Q3     -3.5#     -0.6        0.2        3.9#    2.9      -2.6
2008Q4     -8.3#    -10.3#      -2.5        7.7#    8.3#     -4.1#
2009Q1     -4.7#      2.5        3.5#       4.0#    1.4      -3.3#
2009Q2      2.9       2.8        3.8#      -3.0#   -3.4#      1.2
2009Q3      4.8#      5.0#       1.5       -5.2#   -3.5#      1.5
2009Q4      0.1      -0.4       -2.1       -1.7    -2.1       2.7
2010Q1     -0.5       0.3        1.2        0.9     0.0      -0.6
2010Q2     -2.4      -1.8        0.3        2.1     1.6      -1.2
2010Q3     -1.7       0.0        0.9        1.0     0.3      -0.7
2010Q4      0.6       1.7        0.8       -1.0    -1.8       0.8
2011Q1      1.5       2.8        1.2       -0.9    -0.8      -0.5
2011Q2      0.5       0.4       -1.5       -0.7     0.1       0.3

Sources: Authors' calculations.

(a.) Entries are the standardized innovations in the factor
component of each series, computed relative to the six factors;
series are standardized by dividing by the standard deviation of
the 1959-2007Q3 factor component innovations for that series.
Standardized innovations equal to or exceeding 3 in absolute
value are italicized.

Note: Standardized innovations equal to or exceeding 3 in absolute
value are indicated with #.

Table 6. Subsample R's of Regressions Evaluating the Factor
Component of GDP Growth Associated with Individual Identified
Shocks (a)

                                          F          1959-    1984-
Structural shock and instrument      statistic (b)   2007Q3   2007Q3

Oil shock

Hamilton                                  2.9         0.18     0.01
Kilian                                    1.1         0.08    -0.03
Ramey-Vine                                1.8         0.14    -0.04

Monetan, policy shock

Romer-Romer                               4.5         0.23    -0.16
Smets-Wouters                             9.0         0.18    -0.01
Sims-Zha                                  6.5         0.19    -0.30
Gurkaynak-Sack-Swanson                    0.6         0.12    -0.07

Productivity shock

Fernald TFP                              14.5         0.29     0.14
Gali long-run output per hour              NA         0.07     0.02
Smets-Wouters                             7.0         0.20    -0.04

Uncertainty shock

Bloom financial uncertainty (VIX)        43.2         0.08     0.03
Baker-Bloom-Davis policy                 12.5         0.11     0.02
  uncertainty

Liquidity-financial risk shock

Gilchrist-Zakrajsek spread                4.5         0.12    -0.09
TED spread                               12.3         0.18    -0.08
Bassett and others bank loan              4.4         0.11     0.04
  supply

Fiscal policy shock

Ramey spending                            0.5         0.21    -0.06
Fisher-Peters spending                    1.3         0.23     0.04
Romer-Romer tax                           0.5         0.16    -0.20

Principal components of
uncertainty and credit spread
shocks

First principal component                 NA          0.14    -0.03
Second principal component                NA          0.19     0.07

                                    Computed over 15 quarters starting
                                        at indicated cyclical peak

Structural shock and instrument     1969Q4   1973Q4   1980Q1   1981Q3

Oil shock

Hamilton                             0.26     0.49     0.10     0.11
Kilian                               0.15     0.10     0.20     0.24
Ramey-Vine                           0.27     0.24     0.38     0.49

Monetan, policy shock

Romer-Romer                          0.35     0.31     0.57     0.57
Smets-Wouters                        0.24     0.25     0.32     0.23
Sims-Zha                             0.29     0.44     0.54     0.51
Gurkaynak-Sack-Swanson               0.07     0.39     0.26     0.26

Productivity shock

Fernald TFP                          0.39     0.08     0.31     0.28
Gali long-run output per hour        0.12     0.06     0.10     0.05
Smets-Wouters                        0.35     0.39     0.18     0.17

Uncertainty shock

Bloom financial uncertainty (VIX)    0.12     0.16     0.18     0.31
Baker-Bloom-Davis policy             0.15     0.40     0.15     0.14
  uncertainty

Liquidity-financial risk shock

Gilchrist-Zakrajsek spread           0.17     0.21     0.25     0.38
TED spread                           0.28     0.45     0.31     0.21
Bassett and others bank loan         0.20     0.25     0.13     0.31
  supply

Fiscal policy shock

Ramey spending                       0.36     0.35     0.50     0.55
Fisher-Peters spending               0.27     0.02     0.32     0.36
Romer-Romer tax                      0.21     0.25     0.36     0.31

Principal components of
uncertainty and credit spread
shocks

First principal component            0.21     0.36     0.25     0.26
Second principal component           0.17     0.49     0.31     0.40

                                    Computed over 15 quarters
                                      starting at indicated
                                         cyclical peak

Structural shock and instrument     1990Q3   2001Q1   2007Q4

Oil shock

Hamilton                             0.23    -0.55    -0.14
Kilian                              -0.03    -0.26     0.37
Ramey-Vine                           0.20     0.40     0.23

Monetan, policy shock

Romer-Romer                          0.16     0.08     0.26
Smets-Wouters                        0.37     0.16     0.46
Sims-Zha                            -0.01     0.03     0.03
Gurkaynak-Sack-Swanson               0.00    -0.05     0.34

Productivity shock

Fernald TFP                          0.33    -0.42    -0.14
Gali long-run output per hour        0.00    -0.11    -0.04
Smets-Wouters                       -0.05    -0.36    -0.17

Uncertainty shock

Bloom financial uncertainty (VIX)    0.22     0.23     0.34
Baker-Bloom-Davis policy             0.48     0.15     0.62
  uncertainty

Liquidity-financial risk shock

Gilchrist-Zakrajsek spread           0.07     0.30     0.57
TED spread                           0.21     0.30     0.38
Bassett and others bank loan         0.27     0.45     0.41
  supply

Fiscal policy shock

Ramey spending                       0.06     0.01     0.19
Fisher-Peters spending               0.41    -0.06     0.09
Romer-Romer tax                      0.08    -0.38    -0.02

Principal components of
uncertainty and credit spread
shocks

First principal component            0.30     0.23     0.48
Second principal component           0.38     0.32     0.54

Source: Authors' calculations.

(a.) Structural shocks are computed using the full-sample
six-factor DFM and the indicated instrument, as described in sections
III.A and III.B of the text. [R.sup.2]s are for the contribution
of the indicated shock to the variation in GDP growth, computed
over the indicated subsample, as described in footnote 19. NA =
not applicable.

(b.) Non-HAC F statistic from the regression of the indicated
instrument on the six factor innovations.

Table 7. Correlations among Estimated Structural Shocks

                 [O.sub.H]   [O.sub.K]   [O.sub.RV]

[O.sub.H]           1.00#
[O.sub.K]           0.42#       1.00#
[O.sub.RV]          0.15#       0.60#       1.00#
[M.sub.RR]          0.37        0.65 *      0.77 *
[O.sub.SW]          0.09        0.11        0.39
[O.sub.MZ]          0.33        0.35        0.68
[O.sub.GSS]         0.44       -0.12       -0.08
[P.sub.F]          -0.64 *      0.30        0.24
[P.sub.G]          -0.40        0.34        0.01
[P.sub.SW]         -0.91 *     -0.03        0.00
[U.sub.B]          -0.37       -0.37       -0.58
[U.sub.BBD]         0.10        0.11       -0.37
[L.sub.GZ]         -0.20       -0.42       -0.51
[L.sub.TED]        -0.09        0.01       -0.05
[L.sub.BCDZ]        0.04        0.22        0.79 *
[F.sub.R]          -0.17       -0.64 *     -0.77*
[F.sub.FP]          0.04       -0.21       -0.35
[F.sub.RR]          0.20        0.15        0.30

                 [M.sub.RR]   [M.sub.SW]   [M.sub.SZ]   M.sub.GSS]

[O.sub.H]
[O.sub.K]
[O.sub.RV]
[M.sub.RR]          1.00#
[O.sub.SW]          0.09#        1.00#
[O.sub.MZ]          0.93#        0.16#        1.00#
[O.sub.GSS]         0.24#        0.43#        0.39#        1.00#
[P.sub.F]           0.20        -0.09         0.06        -0.57
[P.sub.G]          -0.30         0.36        -0.S3        -0.37
[P.sub.SW]         -0.24        -0.07        -0.36        -0.S9
[U.sub.B]          -0.39         0.30        -0.29         0.37
[U.sub.BBD]        -0.17         0.45        -0.22         0.S7
[L.sub.GZ]         -0.41         0.44        -0.24         0.34
[L.sub.TED]         0.03         0.73 *       0.10         0.48
[L.sub.BCDZ]        0.56         0.13         0.55         0.04
[F.sub.R]          -0.84 *      -0.32        -0.72 *      -0.34
[F.sub.FP]         -0.72 *       0.20        -0.78 *      -0.03
[F.sub.RR]          0.77 *      -0.10         0.88         0.37

                 [P.sub.F]   [P.sub.G]   [P.sub.SW]

[O.sub.H]
[O.sub.K]
[O.sub.RV]
[M.sub.RR]
[O.sub.SW]
[O.sub.MZ]
[O.sub.GSS]
[P.sub.F]           1.00#
[P.sub.G]           0.52#       1.00#
[P.sub.SW]          0.82#       0.68#       1.00#
[U.sub.B]           0.19        0.34        0.27
[U.sub.BBD]        -0.06        0.4S       -0.01
[L.sub.GZ]          0.07        0.24        0.08
[L.sub.TED]         0.21        0.37        0.09
[L.sub.BCDZ]       -0.09       -0.28       -0.06
[F.sub.R]          -0.17       -0.01        0.01
[F.sub.FP]         -0.49        0.40       -0.02
[F.sub.RR]          0.18       -0.59       -0.28

                 [U.sub.B]   [U.sub.BBD]

[O.sub.H]
[O.sub.K]
[O.sub.RV]
[M.sub.RR]
[O.sub.SW]
[O.sub.MZ]
[O.sub.GSS]
[P.sub.F]
[P.sub.G]
[P.sub.SW]
[U.sub.B]           1.00#
[U.sub.BBD]         0.78 *       1.00
[L.sub.GZ]          0.92 *       0.66 *
[L.sub.TED]         0.80         0.76 *
[L.sub.BCDZ]       -0.69 *      -0.54
[F.sub.R]           0.26        -0.08
[F.sub.FP]          0.03         0.25
[F.sub.RR]          0.01        -0.10

                 [L.sub.GZ]   [L.sub.TED]   [L.sub.BCDZ]

[O.sub.H]
[O.sub.K]
[O.sub.RV]
[M.sub.RR]
[O.sub.SW]
[O.sub.MZ]
[O.sub.GSS]
[P.sub.F]
[P.sub.G]
[P.sub.SW]
[U.sub.B]
[U.sub.BBD]
[L.sub.GZ]          1.00#
[L.sub.TED]         0.84#         1.00#
[L.sub.BCDZ]       -0.73#        -0.40          1.00#
[F.sub.R]            0.4         -0.13         -0.13
[F.sub.FP]          0.03         -0.12         -0.12
[F.sub.RR]          0.02          0.19          0.19

                 [F.sub.R]   [F.sub.FP]   [F.sub.RR]

[O.sub.H]
[O.sub.K]
[O.sub.RV]
[M.sub.RR]
[O.sub.SW]
[O.sub.MZ]
[O.sub.GSS]
[P.sub.F]
[P.sub.G]
[P.sub.SW]
[U.sub.B]
[U.sub.BBD]
[L.sub.GZ]
[L.sub.TED]
[L.sub.BCDZ]
[F.sub.R]           1.00#
[F.sub.FP]          0.38#       1.00#
[F.sub.RR]         -0.45       -0.93#        1.00

Source: Authors' calculations.

(a.) Entries are correlations between individually identified
shocks, computed over the full 1959-2011 Q2 sample. Shading
denotes correlations within categories of shocks; italicized
correlations are cross-category correlations exceeding 0.60 in
absolute value. Shocks are those listed in table 6, abbreviated
as follows:

Oil: [O.sub.H], Hamilton (1996,2003); [O.sub.RV], Kilian (2008a);
ORV, Ramey-Vine (2010)

Monetary policy: [M.sub.RR], Romer and Romer (2004); [M.sub.SW],
Smets and Wouters (2007); [M.sub.GSS], Sims and Zha (2006);
[M.sub.SZ], Giirkaynak, Sack, and Swanson (2005)

Productivity: [P.sub.P], Fernald (2009) TFP; [P.sub.G], Gali
(1999); [P.sub.SW] Smets and Wouters (2007)

Uncertainty: [U.sub.VIX], Bloom (2009) financial uncertainty;
[U.sub.BBD] Baker, Bloom, and Davis (2012) policy uncertainty

Liquidity and financial risk: [L.sub.GX], Gilchrist and
Zakraj"sek (forthcoming) spread; [L.sub.TED], spread;
[L.sub.BCDZ], Bassett and others (2011) bank loan supply

Fiscal policy: [F.sub.R], Ramey (201la) spending; [F.sub.FP],
Fisher-Peters (2010) spending; [F.sub.RR], Romer-Romer (2010)
tax.

Note: Shading denotes correlations within categories of shocks is
indicated with #.

Note: Correlations indicated with * are cross-category correlations
exceeding 0.60 in absolute value.

Table 8. Contributions of Identified Shocks to Cumulative
Post-2007Q4 Growth of GDP and Employment

                                      Cumulative percentage change
                                           in detrended GDP (a)

                                      2007Q4-   2007Q4-   2007Q4-
Shock and instrument                   2008Q3    2009Q2   2011Q2

Actual outcome                         -2.8      -8.7      -8.2
Factor component                       -4.0      -9.2      -6.0

Oil shock

Hamilton                               -1.0      -0.8      -0.8
Kilian                                 -1.0      -2.1      -0.6
Ramey-Vine                             -l.4      -1.6       0.7

Monetary policy shock

Romer-Romer                            -1.1      -1.6       0.1
Smets-Wouters                          -0.4      -3.7      -5.0
Sims-Zha                               -0.3      -0.1      -0.1
GSS                                    -0.8      -3.2      -4.3

Productivity shock

Fernald                                -0.7       0.0       1.4
Gali                                    0.4       0.3       1.1
Smets-Wouters                          -0.5      -0.1       0.6

Uncertainty shock

Financial uncertainty (VIX)            -1.0      -4.1       0.2
Political uncertainty (BBD)            -2.3      -5.8      -4.8

Liquidity/financial risk shock

Gilchrist-Zakrajsek spread             -1.5      -6.3      -1.2
TED spread                             -1.2      -5.6      -4.9
Bassett and others bank loan           -2.0      -3.2       0.1

Fiscal policy shock

Ramey spending                         -1.6      -1.6      -1.0
Fisher-Peters spending                 -0.3      -0.3       0.3
Romer-Romer tax                         0.2       0.3      -0.2

Principal components of uncertainty
and credit spread shocks

First principal component              -1.5      -6.2      -3.4
Second principal component             -2.3      -7.6      -5.4

                                         Cumulative percentage
                                         change in detrended
                                        payroll employment (a)

                                      2007Q4-   2007Q4-   2007Q4-
Shock and instrument                  2008Q3    2009Q2    2011Q2

Actual outcome                         -1.4      -6.2      -7.4
Factor component                       -2.1      -7.3      -8.9

Oil shock

Hamilton                               -0.4      -1.1      -1.0
Kilian                                 -0.5      -1.7      -1.2
Ramey-Vine                             -1.1      -2.1       0.2

Monetary policy shock

Romer-Romer                            -0.7      -2.l       0.4
Smets-Wouters                          -0.5      -2.5      -6.2
Sims-Zha                               -0.5      -1.0       0.3
GSS                                     0.0      -1.0      -3.8

Productivity shock

Fernald                                -0.1       0.1       0.9
Gali                                    0.0      -0.6      -0.9
Smets-Wouters                           0.2      -0.1       0.4

Uncertainty shock

Financial uncertainty (VIX)            -0.9      -3.7      -2.2
Political uncertainty (BBD)            -1.6      -4.6      -6.8

Liquidity/financial risk shock

Gilchrist-Zakrajsek spread             -0.8      -4.6      -3.5
TED spread                             -0.8      -3.7      -6.8
Bassett and others bank loan           -1.5      -3.5      -1.1

Fiscal policy shock

Ramey spending                         -0.9      -1.6      -0.5
Fisher-Peters spending                 -0.2      -0.7       0.3
Romer-Romer tax                         0.2       0.0       0.3

Principal components of uncertainty
and credit spread shocks

First principal component              -1.0      -4.5      -5.8
Second principal component             -1.5      -5.8      -8.4

                                       2009Q2 forecast
                                       growth in factor
                                          component,
                                      2009Q2-2011Q2 (b)

Shock and instrument                  GDP    Employment

Actual outcome
Factor component

Oil shock

Hamilton                               1.8       1.0
Kilian                                 1.3       0.3
Ramey-Vine                             1.5       1.2

Monetary policy shock

Romer-Romer                            1.4       1.2
Smets-Wouters                         -0.6      -3.3
Sims-Zha                               0.4       0.8
GSS                                   -1.3      -2.7

Productivity shock

Fernald                                0.2       0.2
Gali                                   1.0       0.5
Smets-Wouters                          0.9       0.7

Uncertainty shock

Financial uncertainty (VIX)            3.5       0.6
Political uncertainty (BBD)            1.4      -2.0

Liquidity/financial risk shock

Gilchrist-Zakrajsek spread             3.6      -0.4
TED spread                             0.8      -3.2
Bassett and others bank loan           2.7       1.3

Fiscal policy shock

Ramey spending                         0.3       0.1
Fisher-Peters spending                 0.4       0.5
Romer-Romer tax                       -0.1       0.3

Principal components of uncertainty
and credit spread shocks

First principal component              2.4      -1.8
Second principal component             2.7      -2.5

Source: Authors' calculations.

(a.) Each entry after the top panel is the contribution of the
indicated shock to cumulative growth in GDP or employment over
the indicated period, computed as described in footnote 19 in the
text.

(b.) Implied forecasts of GDP or employment growth from 2009Q2 to
2011Q2, constructed in 2009Q2 associated with the indicated
shock.

Table 9. Predicted and Actual Cumulative Growth of Output, Employment,
and Productivity Following a Cyclical Trough (a)

Percent

                                 Cumulative growth of common component
                                 (or actual) over 8 quarters following
                                                trough

                                        Non farm     Output per hour
Trough             Source       GDP    employment   (nonfarm business)

1961Q1             Cyclical      1.1      -1.0              2.0
                   Trend         7.5       4.9              4.8
                   Total         8.7       4.0              6.8

1970Q4             Cyclical      2.4       0.0              2.6
                   Trend         6.9       4.7              4.0
                   Total         9.3       4.6              6.6

1975Q1             Cyclical      3.3      -1.8              5.4
                   Trend         6.6       4.5              3.7
                   Total         9.9       2.7              9.1

1980Q3             Cyclical      1.1      -1.5              2.9
                   Trend         6.3       4.2              3.5
                   Total         7.5       2.7              6.4

1982Q4             Cyclical      5.0       1.1              4.3
                   Trend         6.2       4.1              3.5
                   Total        11.2       5.2              7.8

1991Q1             Cyclical      0.8      -1.6              2.5
                   Trend         5.9       3.3              3.8
                   Total         6.7       1.6              6.3

2001Q4             Cyclical      2.9       0.5              2.6
                   Trend         5.1       2.1              4.3
                   Total         8.0       2.6              6.9

2009Q2             Cyclical      2.4      -3.1              6.3
                   Trend         4.4       1.2              4.5
                   Total         6.8      -1.9             10.8

Averages

1960-82            Cyclical      3.0      -0.4              3.6
                   Trend         6.8       4.5              4.0
                   Total         9.8       4.1              7.6
                   Actual (a)   11.0       5.9              7.3

1960-2001          Cyclical      2.6      -0.5              3.2
                   Trend         6.4       3.9              4.0
                   Total         9.0       3.5              7.3
                   Actual (a)    9.2       4.0              7.2

Differences

2009Q2 minus       Cyclical     -0.6      -2.7              2.7
average, 1960-82   Trend        -2.4      -3.3              0.5
                   Total        -3.0      -6.0              3.2

Source: Authors' calculations.

(a.) Entries are cumulative predicted growth rates of the common
component (or the actual value) of the indicated series, computed
using the factors at the trough and the DFM estimated through
2007Q3. Predicted paths are decomposed into the detrended
cyclical component (the contribution of the factors at the
trough) and the trend growth rate.

(b.) Excludes the post-1980Q3 recovery because the next recession
commenced within the 8-quarter window used in this table.

Table 10. Contributions of Trend Productivity, Labor Force, and
Population to Trend GDP Growth Rate (a)

                                       Trend growth rate (a)
                                        (percent per year)

Series and component                   1965   1985   2005

GDP                                     3.7    3.1    2.5
  GDP-employment ratio                  1.6    1.3    1.5
  Employment-population ratio           0.3    0.4   -0.2
  Population                            1.7    1.4    1.1
GDP-employment ratio                    1.6    1.3    1.5
  Ratio of GDP to NFB output           -0.2   -0.3   -0.2
  Ratio of NFB output to NFB hours      2.3    1.8    2.2
  Ratio of NFB hours to NFB            -0.4   -0.3   -0.2
    employment
  Ratio of NFB employment to total      0.0    0.1   -0.3
    nonfarm employment
Employment-population ratio             0.3    0.4   -0.2
  Employment as share of labor force    0.0    0.1    0.0
  Labor force as share of population    0.3    0.4   -0.1
Labor force share of population         0.3    0.4   -0.1
  Female                                0.5    0.4    0.0
  Male                                 -0.2   -0.1   -0.2
Labor force                             2.0    1.7    0.9
  Female (prime-age)                    0.7    0.8    0.3
  Male (prime-age)                      0.4    0.6    0.2
  Female (non-prime-age)                0.5    0.2    0.2
  Male (non-prime-age)                  0.4    0.1    0.2

                                         Difference 2005
                                         minus 1965 (c)
Series and component                   (percentage points)

GDP                                           -1.2
  GDP-employment ratio                        -0.1
  Employment-population ratio                 -0.5
  Population                                  -0.6
GDP-employment ratio                          -0.1
  Ratio of GDP to NFB output                   0.0
  Ratio of NFB output to NFB hours            -0.1
  Ratio of NFB hours to NFB                    0.2
    employment
  Ratio of NFB employment to total            -0.3
    nonfarm employment
Employment-population ratio                   -0.5
  Employment as share of labor force           0.0
  Labor force as share of population          -0.5
Labor force share of population               -0.5
  Female                                      -0.5
  Male                                         0.1
Labor force                                   -1.1
  Female (prime-age)                          -0.4
  Male (prime-age)                            -0.2
  Female (non-prime-age)                      -0.3
  Male (non-prime-age)                        -0.2

Source: Authors' calculations.

(a.) Growth rates and differences for components may not sum to
those for totals because of rounding. Standard errors for the
estimated trends range from 0.1 for the labor force variables to
0.5 for GDP; for details see the online appendix. NFB = nonfarm
business.

(b.) Each entry is the growth in the trend component of the
indicated series in the indicated year, computed as described in
section I.C.

(c.) Difference between 2005 and 1965 trend values.