Various observers have continued to ascribe a central role to real RMB appreciation to effect global rebalancing. I think it's useful to remember that, given a Chinese trade balance in excess of 260 billion USD, appreciation can only have a certain impact. From Cheung, Chinn and Fujii (forthcoming):

...using a single equation error correction model, allowing for coefficient shifts with Chinese accession to WTO, leads to a statistically insignificant estimate of the price elasticity. In the 2000-06 period, the implied price elasticity is zero. Using this point estimate, then a 10% appreciation would actually lead to a shrinkage of the trade balance from 400.9 billion to 355.2 billion. This estimate of 45.7 billion (2000$) is somewhat less than the $88.6 billion current dollars reported in Marquez and Schindler (forthcoming) [working paper version].

The export equations take the form:

Δ exp _t = θ ₀ + ρ exp _t-1 + θ ₁ y^* _t-1 + θ ₂ r _t-1 + θ ₃ k _t-1 + σ ₁ Δ exp _t-1 + 2 lags of first differenced right hand side variables + quarterly dummies + WTO dummy + v _t

Where exp is log exports, y^* is log RoW GDP, r is the real exchange rate, and k is the Chinese capital stock. The import equations take the form:

Δ imp _t = β ₀ + φ imp _t-1 + β ₁ y _t-1 + β ₂ r _t-1 + γ₁ Δ imp _t-1 + 1 lag of first differenced right hand side variables + quarterly dummies + WTO dummy + u _t

Where imp is log imports, y is log GDP.

Separate regressions are run for ordinary and processing trade, over the 1993Q4-07Q1 period. The adjusted R²'s range from 0.77 to 0.92.

If we take the Goldstein-Lardy misalignment estimates of 20% to heart, then a 20% appreciation would lead to an approximately 91.4 billion (2000$) reduction in the Chinese trade balance. As best as I can tell, the export prices from China, and to China (as proxied by unit value indices for Hong Kong) have probably stayed constant relative to 2000; hence the nominal impact is around 90 billion USD (with considerable uncertainty surrounding this point estimate).

This leaves a large Chinese trade surplus in place, around 170 billion even before the rebound in the Chinese surplus anticipated as the world aggregate demand recovers. Now, to the extent that Chinese reserve accumulation is due to a current account surplus and capital inflows, one could hope that a revaluation would have an additional knock-on effect by deterring capital inflows (the argument would be revaluation would eliminate expectations of appreciation that would provide capital gains on holding RMB). That is, recall the balance of payments identity:

CA + KA + ORT ≡ 0

Where CA is the current account, KA is private capital account, and ORT is official reserves transactions.

Figure 2, drawn from Prasad and Sorkin (2009) shows that net inflows were not a major factor, at least in 2008.

This suggests to me that rebalancing requires as much or more Chinese fiscal stimulus and a concerted effort to encourage private consumption via enhancing the social safety net, in addition to RMB revaluation. (This can be seen in a Mundell Fleming framework, as applied to China [3]). And it also requires determined action from the US side as well (see here). If only we'd conducted a sane fiscal policy in 2001-08 [4], our range of action would now be wider in this respect.

...The increase in September was more than accounted for by a large positive contribution from nonfarm inventories (slower inventory paring in September than August). The level of monthly GDP in September was 0.9% above the third-quarter average at an annual rate. Average monthly increases of 0.3% per month during the fourth quarter support our latest tracking forecast of 3.3% growth in the fourth quarter.

The series are plotted below.

With regard to 2009Q3, the Macroeconomic Advisers estimate suggests the 2009Q3 second release will contain a downward revision from 13014.2 billion Ch.2005$ (SAAR) to 12984.6 billion. The e-forecasting estimate suggests roughly no change, at 13014 billion.

The receiver operating characteristics curve plots the false positive rate on the horizontal axis and the true positive rate on the vertical axis, moving along the curve by specifying alternative possible values for c. For example, here's Berge and Jorda's estimate of the ROC for Y_t corresponding to the Chicago Fed National Activity Index. The greater the area under the ROC, the more useful that indicator Y_t would be for identifying recessions.

ROC curve for Chicago Fed National Activity Index. Source: Berge and Jorda (2009).

Berge and Jorda evaluate a number of possible indicator series Y_t that one might use for this purpose, and find that the Chicago Fed index is one of the best. If you put equal weight on the two kinds of errors you can make with this measure (declaring a false positive versus missing a true positive), Berge and Jorda calculate you'd use an optimal threshold of c = -0.82, that is, declare the economy to be in a recession whenever the Chicago Fed index falls below -0.82. The figure below plots the values for the Chicago Fed index, with shaded regions corresponding to recessions as dated by the NBER. On the basis of this indicator, Berge and Jorda would say that the U.S. recovery began in September, for which the index came in at -0.69, its first reading above -0.82.

Three-month average value for Chicago Fed National Activity Index with -0.82 threshold. Shaded regions correspond to NBER recession dates.

Another indicator that comes out well on the basis of the area under the ROC is the ISM Manufacturing PMI Composite Index, for which Berge and Jorda propose a threshold of c = 44.7. Note that this is below the Y_t = 50 reading at which as many managers are reporting improvement as report deterioration-- things need to be getting significantly worse before it would be characterized as a recession. By this indicator, the recovery began in July.

ISM manufacturing PMI with 44.7 threshold. Shaded regions correspond to NBER recession dates.

(1) y_t = α_t + β x _t + ε _t

(2) y_t = γ + δ x _t + Γ z _t + u _t

How would one analyze the impact of a public policy, such as an increase in government procurement of widgets to place in public places, on the total number of widgets consumed?

First, solve the system for the endogenous variables. Suppose I want to know the reduced form expression for the quantity of widgets purchased. The invert the second equation, solving for x, and substituting into the first (supply) equation. This leads, after solving:

(3) y_t = [α _t(δ-γ)/(δ-β)] + [(βΓ)/(δ-β)] z_t + (δ/(δ-β))(ε_t - (β/δ) u _t)

Suppose I wanted to forecast widget consumption next year, taking into a government policy involving z. How would one best undertake this exercise? For myself, I would take the time differential of the above expression (3). Let the Δ(.) operator indicate the time difference, hence Δ y ≡ y_t+1-y_t.

(4) Δ y = [Δ α (δ-γ)/(δ-β)] + [(βΓ)/(δ-β)] Δ z + (δ/(δ-β))(Δ ε - (β/δ) Δ u )

Suppose additionally capital services demand (i.e., the derived factor demand) is given by:

(5) k_t = Θ y _t + e_t

Where e is another random error term. Since the error terms are random, and serially uncorrelated, then my best guess of the change in widget consumption (and widget industry capital usage) in the absence of a change in government procurement is:

(6) Δ y = Δ α [(δ-γ)/(δ-β)]

(6a) Δ k = Θ × Δ α [(δ-γ)/(δ-β)]

And my best guess of widget consumption with the government policy change is:

(7) Δ y = Δ α[ (δ-γ)/(δ-β) ] + (βΓ)/(δ-β) Δ z

(7a) Δ k = Θ × {Δ α[ (δ-γ)/(δ-β) ] + (βΓ)/(δ-β) Δ z}

Where I would use estimates of δ , β , γ , Γ , and Θ from the literature on widget supply and demand, presumably obtained by way of econometric studies. Δ α would be a variable based upon forecasts, presumably based upon observations on real time data.

Of course, what we observe in reality is:

(8) Δ y = Δ α [(δ-γ)/(δ-β)] + [(βΓ)/(δ-β)] Δ z + (δ/(δ-β))(Δ ε - (β/δ) Δ u)

(8a) Δ k = Θ × {Δ α [(δ-γ)/(δ-β)] + (βΓ)/(δ-β) Δ z + (δ/(δ-β))(Δ ε - (β/δ) Δ u )} + Δ e

Wherein (8) differs from (7) by virtue of the unpredictable errors, (δ/(δ-β)(Δ ε - (β/δ) Δ u )). Employment differs by Θ [(δ/(δ-β)(Δ ε - (β/δ) Δ u)] + Δ e

Thus far, I don't think many economists would have trouble with this methodological approach, although they could clearly argue against this particular set of exogenous variables in, say, the demand equation; or they could reasonably argue that expectations of future widget demand (as well as future government procurement policies with respect to widgets) should matter. But the key is thinking structurally, and about shocks to the three structural equations. In this analysis, I don't think one would want to compare (8) against (6), nor (8a) against (6a), since one is conflating shocks with policy effects.

Now, inexplicably, in current discourse, the troubles begin...

Now, let's think about what happens if (1) is short run aggregate supply of real GDP, and (2) is aggregate demand, where x is the price level, and z is government spending. Equation (3) now defines the output-labor relationship, of the nature examined in this post. The critics of the Administration's approach to estimating the number of jobs created are doing one of two things: (i) they are comparing (8a) against (6a) when the errors have been large, so the composite error (δ/(δ-β)) × (Δ ε - (β/δ) Δ u) is large and negative; or (ii) they are arguing for different estimates of the relevant coefficients. By far, (i) is more popular discourse (such as discussed in this post). Regarding (i), I'll note that there was a substantial deterioration in everybody's expectations regarding the course of the economy in January and February [1]. The more relevant comparison would be (8) against (6) (and (8a) against (6a)) where the shocks (that have now been realized) are added in. That is, compare (8) against (6'), and (8a) against (6a'):

(6') Δ y = Δ α [(δ-γ)/(δ-β)] + (δ/(δ-β))(Δ ε - (β/δ) Δ u)

(6a') Δ k = Θ × {Δ α [(δ-γ)/(δ-β)] + (δ/(δ-β))(Δ ε - (β/δ) Δ u )} + Δ e

More reasonable critiques rely upon (ii), although I have not seen detailed quantitative analyses which break down the sources of mis-prediction. (There is a third route, which involves arguing as an article of faith that there is going to be no, or negative, effect of the government widget procurement policy on widget consumption).

From Temperature Anomaly FAQs:

The term "temperature anomaly" means a departure from a reference value or long-term average. A positive anomaly indicates that the observed temperature was warmer than the reference value, while a negative anomaly indicates that the observed temperature was cooler than the reference value.

The reference value used to create this graph was the average over the 1901-2000 period.

The table at the right summarizes the percent change between January 6 and November 11 in the cash prices of 19 commodities reported in the Wall Street Journal (downloaded via Webstract). The average commodity in this list has appreciated 37% since the start of the year.

A recent paper by Ke Tang and Wei Xiong documents an increasing tendency for commodity prices to move together over the last few years. A decade ago, what happened to oil prices was largely unrelated to movements in most other commodity prices. The graphs below show how the correlations between oil prices and the prices of four representative commodities have increased significantly over time.

Correlation (using a rolling sample beginning one year before indicated date) between returns on oil and specified commodity. Source: Tang and Xiong (2009).

One explanation I often see in the popular press is that movements in commodity prices are driven by changes in the value of the dollar relative to other currencies. However, the magnitude of movements in commodity prices greatly exceeds the size of changes in the exchange rate. For example, the table above shows that since the start of this year oil prices have increased five times as much as the dollar price of a euro; see also Steve Gordon's graphs. While the depreciation of the dollar is part of the story, most of the explanation must be found elsewhere.

Another important factor is resurging real economic growth outside the United States, which produces pressures for both the dollar to depreciate and the real price of commodities to appreciate. According to this theory, the increasing correlations between commodity prices results from the fact that countries like China are so much more important for the world economy today than they were a decade ago.

A third explanation is that investors are making increasing use of commodities as an investment class. Although Treasury Inflation Protected Securities offer a hedge against an increase in the U.S. consumer price index, they don't offer protection for foreign investors against depreciation of the dollar. Insofar as increases in the prices of commodities like oil may depress real economic activity, holding commodities as an investment also offers useful diversification against risks to equities. Particularly when interest rates are low, there is an incentive to hoard physical commodities as an investment vehicle.

The paper by Tang and Xiong proposes that the increased use of commodities as a financial investment accounts for the increasing correlation among commodity price changes over time. In support of that claim, they note the growing popularity of investment strategies based on the Goldman Sachs Commodity Index or the Dow Jones Commodity Index. Tang and Xiong document that correlations among commodities included in the indexes have increased faster than those not included. For example, one of the regressions they estimate relates the return on commodity i to equity returns, bond yields, the value of the dollar, and oil prices, where the coefficients are allowed to grow with time at different rates before and after 2004, and with different trends on these coefficients estimated for commodities included in indexes as for those excluded. The figure below shows their estimated time path for the coefficient on oil prices comparing the indexed and non-indexed groups.

Coefficient relating return on average commodity to return on oil as a function of time for commodities included in the GS or DJ indexes (top curve) and those excluded (bottom curve). Source: Tang and Xiong (2009).

For any of the explanations in this third class, one of the important challenges is to reconcile the story of commodity speculation with supply and demand for the underlying physical commodity. If we propose that speculators have driven the price of the commodity up, the physical quantity demanded should decline as a result. In order to be sustained, a coherent speculation-based theory of commodity price appreciation requires increased physical storage of the commodity.

The solid black curve in the figure below plots the typical U.S. crude oil stocks (excluding those held in the Strategic Petroleum Reserve) for each week of the year, based on the average over 1990-2007. The red line gives the actual values for 2008, which were significantly below the historical average, particularly in the spring of 2008 when oil prices were rising so dramatically. Those below-normal inventories were one reason I focused on what was going on to the fundamentals of supply and demand in trying to understand the behavior of oil markets in the first half of 2008.

Weekly U.S. crude oil ending stocks, excluding SPR, in thousands of barrels, from EIA. Black line: average over 1990-2007. Red: 2008. Green: 2009.

On the other hand, inventories of crude oil this year, shown in green above, have been substantially above normal, meaning that in the absence of that oil going into storage, we would have expected to see lower oil prices than we currently have.

Moreover, much of the current stockpiling may be taking place outside the United States. For example, Yves Smith noted this story from Bloomberg last August:

Copper, nickel and other base metals stockpiled by speculative Chinese investors including pig farmers may be sold when "market sentiment turns," said Scotia Capital Inc.

A price surge and easy bank credit this year encouraged pig farmers, stock brokers and businessmen to buy copper and nickel for speculation, Liu Na, an analyst with Scotia Capital, wrote in a note dated Aug. 17, citing reports from the state-owned China Central Television....

"These stockpiles are in 'weak hands' as speculators have no real use for base metals," Liu wrote. "When the market sentiment turns, they are very likely to turn into quick sellers, especially when the bank's money is involved."

I also found this November 3 story from the Financial Times of interest:

Gold prices continued to rise on Wednesday extending the all-time highs which followed India's central bank bought 200 tonnes of the precious metal, swapping dollars for bullion as the country's finance minister warned the economies of the US and Europe had "collapsed".

India's decision to exchange $6.7bn for gold equivalent to 8 per cent of world annual mine production sent the strongest signal yet that Asian countries were moving away from the US currency.

Policy-makers in the Federal Reserve have traditionally thought of inflation as a broad movement in all wages and prices, which to some extent is under their control, and viewed changes in relative commodity prices as outside their control. I believe that this is not the correct understanding of the current situation. Concerns about inflation, particularly on the part of foreign dollar-holders, are likely to show up first in the relative prices of internationally traded commodities. Insofar as these relative price changes can be destabilizing in themselves, it cannot be wise for U.S. policy-makers to ignore them.

From "'Created or saved' doesn't add up", by Joseph Lawler:

...[t]he "created or saved" numbers are meaningless. The administration purposefully devised the metric to be nebulous. Without a counterfactual, showing the trend of unemployment in the absence of the stimulus, it is impossible to know how many jobs the stimulus saved.

As the President has discussed, analysis done within the Administration has shown how his tax cuts have substantially offset the series of adverse shocks that have been buffeting the economy. Simulations of a conventional macroeconomic model show that, without the tax cuts, the level of real GDP would have been about 2 percent lower in the middle of 2003. About 1.5 million fewer people would have jobs today. The job market is not what we would like it to be right now, but it would have been worse without the Administration's actions.

One can view the short-run effects of these tax cuts from a classic Keynesian perspective. The tax cuts let people keep more of the money they earned. This supported consumption and thus helped maintain the aggregate demand for goods and services. There is nothing novel about this. It is very conventional short-run stabilization policy: You can find it in all of the leading textbooks.

The writer is Greg Mankiw, discussing in 2007 a particular fiscal measure, namely the 2003 tax cuts (h/t, Brad Delong).

So let us return to how the Congressional Budget Office (CBO) conducted analysis. In their February analysis, they presented this set of results, based on a range of multipliers in the literature.

So GDP is estimated to be between 1.4 to 3.8 percentage points (ppts) higher than baseline in 2009Q4, due to the stimulus bill. The midpoint of this range is 2.6 ppts. Relatedly, the range of employment gain relative to baseline is 0.8 to 2.3 million; the midpoint of this range is 1.55 million.

Interestingly, taking the CEA's model based approach (Table 2, Joint Economic Committee testimony of 22 October), and assuming the same incremental growth rate in 09Q4 as in 09Q3, the implied deviation from baseline is 2.56 ppts, or right in the midpoint of the CBO's range.

Now using the error correction model that I estimated in last Tuesday's post (where the cointegrating relationship between log GDP and log nonfarm payroll employment is 0.37), I find the range of increased employment relative to baseline is between 0.68 and 1.84 million, slightly lower than the CBO range of 0.8 and 2.3 million. The estimated employment impact is 1.26 million, using the midpoint of the CBO range for impact on GDP.

I know counterfactuals and math are hard to fit on a bumper sticker. But one would hope that in an 800-plus word essay on economics (even if in Politico), some economic content could be included.

By the way, Jeff Frankel debunks a similar misapprehension in National Journal.

Solid line: 100 times the natural log of real GDP. Dotted line: dynamic forecast (1- to 9-quarters ahead) based on coefficients of univariate AR(4) estimated 1949:Q2 to 2001:Q3 and applied to GDP data through 2007:Q3. Dashed line: dynamic conditional forecast (1- to 9-quarters ahead) based on coefficients reported in equation (3.8) in Hamilton (2003) (which was estimated over 1949:Q2 to 2001:Q3) applied to GDP data through 2007:Q3 and conditioning on the ex-post realizations of the net oil price increase measure.

In the figure above I extend the earlier-reported forecast an additional four quarters and compare the projection with what actually happened to GDP through 2009:Q3. The dotted green line is a forecast formed in October 2007 of what would happen to U.S. GDP if you used nothing more than the values of GDP observed through 2007:Q3. Basically that forecast simply extrapolates the recent prior trend. The dashed red line is the forecast that uses GDP values only through 2007:Q3 but also uses knowledge of what was going to happen to oil prices between 2007:Q4 and 2009:Q3. If you treated oil prices as the only thing that matters for the economy, you would have predicted the bottom would be reached in 2009:Q1, flat growth between 2009:Q1 and 2009:Q2, and normal growth resuming in 2009:Q3. That's exactly the trajectory that GDP has taken so far, although the bottom in 2009:Q2 was 2-1/2 percent lower than would be predicted on the basis of oil prices alone.

I have no doubt that the problems with financial markets were a bigger factor than oil prices in the striking collapse in output in 2008:Q4 and 2009:Q1. The other approaches to measuring the contribution of oil to the downturn surveyed in my Brookings paper would estimate a smaller contribution of oil to the downturn than suggested by the figure above. On the other hand, all of the approaches surveyed in that paper suggest that oil made a material contribution to the initial downturn, and it seems hard to deny that that the severity of the financial crisis was exacerbated by the fact that the U.S. had spent three quarters in recession prior to the failure of Lehman in September 2008.

What do these estimates imply looking forward, with oil prices now back up to $80 a barrel? The relation used to produce the figure above assumes that there is a threshold effect before the next oil price shock would begin to do its damage. According to that relation, oil has to get back above $130 before it would matter again for GDP growth. On the other hand, the original research on which that relation is based acknowledged that there's really not a very compelling basis in the data for choosing among various plausible nonlinear possibilities. The other approaches surveyed in my Brookings study assume a simple linear relation, according to which the recent resurgence in oil prices would already begin to exert a drag on spending.

Another magnitude that I think is important to watch is the share of the budget of an average U.S. consumer that is devoted to energy purchases. This had fallen considerably in the 1990s, making it easier for many consumers to largely ignore modest energy price fluctuations. When this share rises above 6%, it seems to become a more significant factor. The consumer energy expenditure share peaked last summer at 6.8%, but collapsing energy prices subsequently brought it back down to 4.7%. The resurgence in oil prices this summer had pushed that share back up to 5.4% in September.

Energy expenditures as a fraction of consumer spending. Calculated as 100 times nominal monthly consumption expenditures on energy goods and services divided by total personal consumption expenditures. Data source: BEA Table 2.3.5U, "Personal Consumption Expenditures by Major Type of Product and Expenditure," obtained from Econstats. Dashed line is drawn at 6.0%.

And the price of oil is up another 15% since September.

So a year later, in September 2009, after living through a year of "disaster," how did real consumption expenditure (one economists' favorite measures of living standards) compare to what it was in September 2008?

Since we're concerned with living standards, as opposed to economic activity, I thought it of interest to look at per capita consumption. Since population is available only on quarterly basis, I compare consumption per capita in 2009Q3 to that in 2008Q3.

Per capita consumption is 0.3 0.9 percent (in log terms) below the level in 2008Q3. Moreover, per capita consumption is 6.5 6.1 percent below the 1967Q1-09Q3 trend (which grows at 2.9 2.2 percent per annum). [Corrections made 1pm Pacific]

Is that a disaster? Maybe not. But one wonders how much lower per capita consumption would have been in the absence of the actions undertaken by fiscal and monetary authorities around the world.

Update, 1pm Pacific

Thanks to confused for pointing out the monthly population series. Here is a plot of log montly personal consumption expenditures, and analogous trend:

Note that relative to September 2008, consumption is 0.65 percent lower (in log terms), and is 6.4 percent lower than the time trend.

Today, we're fortunate to have Joe Gagnon, senior fellow at the Peterson Institute for International Economics, as a guest contributor.

Is there any evidence on the effect of central bank purchases of longer-term or riskier assets?

In recent months, central banks have purchased large quantities of longer-term assets. These purchases appear to have been effective at pushing down longer-term interest rates, which should stimulate economic activity. For example, the Federal Reserve (Fed) has purchased large quantities of longer-term agency-backed securities and Treasury bonds. The following table shows that Fed communications about such purchases had substantial effects on a range of long-term interest rates, including on assets that were not included in the purchase program, such as interest rate swaps and corporate bonds.

Since March 19, the Fed has not made any substantive changes to its planned purchases of longer-term assets. Over this period, the 10-year Treasury yield has risen about 75 basis points and the corporate yield has fallen about 200 basis points, reflecting a relaxation of the extreme financial strains and flight-to-quality that characterized the first few months of this year. Conventional fixed mortgage rates, a key target of the Fed's policy easing, have changed little on balance since late March.

Paul Krugman has argued that potential gains and losses when long-term interest rates move make a policy of purchasing such bonds especially risky, and that fiscal stimulus is a safer bet. However, central banks, including the Fed, have always held risky assets, including long-term bonds, foreign exchange reserves, loans to private banks, and even equities. In many cases, such assets comprise the bulk of the central bank's portfolio.

A good definition of expansionary monetary policy is the printing of money to purchase financial assets. Expansionary fiscal policy is the selling of financial assets to purchase goods and services, to cut taxes, or to increase transfers. On these definitions, both monetary and fiscal policy can be effective when short-term interest rates are zero.

This post written by Joe Gagnon

Source: Sterling (2009)

Here's Sterling's graph of the behavior of the Bloomberg index, in which the remarkable character of events following September 12 is pretty striking.

Source: Sterling (2009)

Even if the Lehman failure is agreed to as a definitive event, it is not clear to me that this establishes that all would have been fine if the Fed had only bailed out Lehman as they had Bear Stearns and AIG before. That question is inherently and unavoidably counterfactual. We can't know-- and decision-makers at the time couldn't know-- which domino might have been next to fall had this one been propped up.

But I think it is fair to conclude that the middle of September of 2008 marked a clear turning point in the unfortunate sequence of events through which we have recently come.

The above series is the Hodrick-Prescott filtered net exports to GDP series for the United States. (I've discussed the HP filter in the context of output gaps before [1].) If one believes that the HP filter properly identifies the cyclical versus trend components, then the plot shows the cyclical component of net exports; hence in this context cyclical net exports were in rough balance in 2007.

Of course, this series is much different than the one we are accustomed to. I plot the filtered and actual series in Figure 2.

While it would appear that the HP filtered series does capture essential features of business cycle fluctuations in net exports (consider how the cycles correlate with NBER-defined recessions), filtering does impart some substantively different properties to the series. For instance, the unfiltered series is highly persistent, with the autoregressive coefficient in an AR(1) specification equal to 0.98, standard error 0.013. On the other hand, the filtered series exhibits much lower persistence, with an AR coefficient of 0.79.

In many studies, the variable of interest is the ratio of real exports to real imports. Here are the unflitered and filtered series:

The degree of persistence is once again lower with the HP-filtered data, as is the variability, especially during the latter portion of the sample. The HP-filtered series also indicates almost no business cycle related fluctuation in the exports/imports ratio over the entire 1997-2007 period. Perhaps that's the right interpretation. It certainly does give one pause for thought.

What's the bottom line? For me, it's not that HP-filtering is necessarily a bad idea. It's just that one has to be real careful, and think about what is being extracted, and what remains, when applying any detrending technique.

For more formal discussion of the use of various filters, see Cogley and Nason [link updated 4pm Pacific].

Data source: Wardsauto.com

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U.S. light vehicle sales last month were up slightly from September and about the same as October 2008. Given how dismal those comparison months were, that's not saying much. Last month's sales were 3.5% below the average level of April through June, which, because sales usually decline a bit more than that in the fall, counts as a modest seasonally-adjusted improvement. We seem to be past the bottom for autos, but climbing back painfully slowly at this point.

Source: Calculated Risk

The same might be said of new home sales, which despite a slight setback in the most recently reported month (September), have definitely been gaining from the lows reached in March. But there's still a long way to go before new home sales would reach the average levels seen in the 1980s.

Source: Calculated Risk

Existing home sales, which don't contribute directly to GDP but which do help absorb some of the overhang of distressed properties for sale, have been growing more solidly, and NAR's pending home sales index is up 12.5% over the last two months.

Source: Calculated Risk

Other new indicators have also been mixed. The Manufacturing ISM PMI, an index summarizing the responses of managers answering their survey, registered its third consecutive month above 50, indicating more respondents said that conditions were improving than said things were getting worse.

Source: FRED

On the other hand, real personal consumption expenditures and real disposable personal income both dipped back down in September.

Source: FRED

Source: FRED

I remain convinced that the key indicator for a normal recovery will be a resumption of growth in U.S. employment. Unfortunately, ADP is estimating that the U.S. lost 203,000 private-sector jobs in October on a seasonally adjusted basis.

Bill McBride says we are a long way from normal. And I say, don't bet against Bill McBride.

I estimate the following error correction specification, which includes 4 lags of first differences, using OLS:

Δ nfp_t = 0.54 - 0.069 nfp_t-1 + 0.026 y _t-1 + 0.60 Δ nfp_t-1 + 0.173 Δ y _t-1 + ... + 0.00046 time - 0.0000017 time ²

Adj. R² = 0.85 SER = 0.0018, n = 95, DW = 2.02. Breusch-Godfrey LM test, 2 lags, F = 1.84 (p-val = 0.16). HAC robust standard errors. (Nonsignificant coefficients suppressed.)

The long run elasticity of employment with respect to GDP is 0.37, while the short run elasticity is 0.17.

I conduct dynamic simulations (using the regression estimated over the entire sample) for the five years after each recession: 1991Q2-1996Q1, 2002Q1-2006Q4. I also conduct a dynamic forecast for 2009Q3-2010Q4, using the WSJ October mean forecast for GDP growth over that period (discussed in this post) as the right hand side variable.

The results are shown in Figure 2:

The dynamic simulations initially underpredict nonfarm payroll employment, before overshooting (in the 1990's) and essentially being on target (in the 2000's). What does the model imply for the trajectory of employment going forward? The dynamic simulation for the 2009Q3 through 2010Q4 period is shown in Figure 3 (with employment expressed in levels, instead of logs).

(Note: for sticklers out there -- e.g., juan in comments to this post -- what I am conducting here for the 2009Q3-10Q4 period is a conditional forecast, since I am taking the GDP path forecasted by the WSJ survey as given).

I calculate the WSJ forecast for employment by adding the October mean prediction of seventeen thousand per month net job creation to the 2009Q3 figure (literally, this forecast is for October 2010, and should be 17,000 × 12 added to the October employment figure).

Hence, if historical correlations persist, then nonfarm payroll employment will continue to decline through 2010Q2. However, given the imprecision of the estimates, nonfarm payroll employment could begin rising as early as 2010Q2 (the upper gray line).

Of course, not only is there sampling uncertainty; there's also uncertainty regarding the true model. I've imposed cointegration in the estimation procedure (and according to the Johansen maximum likelihood procedure, one can reject the null hypothesis of no cointegration at the 20% level, allowing for deterministic trends in the data). But one could drop that assumption, and assume a relationship in first differences. I estimate:

Δ nfp _t = -0.001 + + 0.687 Δ nfp _t-1 + 0.210 Δ y _t + 0.113 Δ y _t-1

Adj. R² = 0.89 SER = 0.0015, n = 95, DW = 2.05.

The adjusted R² statistic is slightly higher in this ARMAX specification, but of course R² shouldn't be the key determinant of whether one specification is to be preferred over another. In fact, one might wish to impose the long run cointegrating relationship especially if longer horizon prediction is of central import. Hence, I compare the two (conditional) forecasts in Figure 4.

In this case, job losses taper off, and net job creation occurs in 2009Q3. Or, it could be that the error correction model is correct (cointegration between GDP and employment holds), but the recovery will be more akin to that of the 1970's and early 1980's, because of the depth of the downturn. That specification (which would not fit well for the past two recoveries) yields the salmon colored line in Figure 4, and predicts strong job creation in 2009Q2.

James Hamilton says recent output indicators (as of 10/18) are not consistent with a jobless recovery. Paul Ashworth says manufacturing employment has may have [correction added 11/4, 8:45am] already "stabilized", while Robert Gordon predicts a resumption of employment growth in 2010Q1. David Altig at Macroblog and Mary Daly, Bart Hobijn, Joyce Kwok at SF Fed enumerate the reasons for a slow start in employment growth.

Revisions

We're all tempted to make predictions on the basis of the last data point. And even more difficult to resist is the temptation to make definitive statements on the basis of data that are sure to be revised. For instance, we see this question from Casey Mulligan, "Where's the GDP Disaster?".

Last October, when we were told that spending and incomes were about to collapse, I predicted that "real GDP will not drop below $11 trillion (chained 2000 $)."

I think this is an excellent time to recapitulate the hazards of making definitive assessments on the basis of data that are sure to be revised [0] [1]. To illustrate this point, I go back to the last recession, which according to the NBER extended from 2001Q1-01Q4.

I plot the vintages of GDP in Ch.1996$ available as of April 2002 (the advance release for the first quarter after the recession ended), and October 2003 (advance release for 2003Q3).

Note that GDP in the latter vintage was 1.6% lower (in log terms) in 2001Q2 than it was in the corresponding period according to the earlier vintage. This amounted to a 5 148.6 [corrected 11/1, 10:35am] billion Ch.1996$ difference.

Now, I replicate Professor Mulligan's graph. I draw Professor Mulligan's floor, along with real GDP, and an alternate for 09Q1-09Q2 that would obtain if GDP turned out to be 1.6% lower in a later vintage.

I calculate GDP in Ch.2000$ by dividing the 2005-base chained price index by the average value of the index in 2000, which is 88.648, and then dividing nominal GDP by this base-year-2000 index.

The graph indicates that in 09Q2, GDP was only 2.3% above Mulligan's floor.

And Conditional Forecasts

In some sense, the critical aspect of Professor Mulligan's argument that the events of 2008-09 were never going to be disasterous is that he made his projection conditional on none of the extraordinary measures undertaken by the Fed, nor on the the fiscal stimulus by the Federal government being implemented. It's useful to recap his statement from October:

NO DEPRESSION; NO SEVERE RECESSION

The medium term fundamentals point toward more real GDP, more employment, and (to a lesser degree) more consumption. Some employment and real GDP declines may occur in the short run, but they will be small by historical standards. Professor Cooley recently explained "The losses to date represent less than .5% of the work force. In the relatively mild recession of 2001 to 2002, job losses equaled about 1% of the work force. In the much more severe recession of 1981 to 1982, job losses totaled nearly 3% of the labor force--six times today's figure. And in the (truly) Great Depression--invoked, now, with an alarmist frequency--job losses between 1929 and the trough in 1933 were 21% of the labor force." Note that 21% over 3 1/2 years is an average decline of 2% every quarter for 14 consecutive quarters! If employment declines 2% in even one quarter, or 5% over a full year, I will admit well before 2010 that a severe recession is happening and that my 2010 forecasts are unlikely to be attained.

According to the BLS, national nonfarm employment was 136,783,000 (SA) at the end of 2006, as the housing price crash was getting underway. Real GDP was $11.4 trillion (chained 2000 $). Barring a nuclear war or other violent national disaster, employment will not drop below 134,000,000 and real GDP will not drop below $11 trillion. The many economists who predict a severe recession clearly disagree with me, because 134 million is only 2.4% below September's employment and only 2.0% below employment during the housing crash. Time will tell.

Now, I assume that Mulligan feels free to compare a forecast conditioned on no fiscal policy against one with fiscal policy to the extent he believes multipliers are near zero or even negative. And perhaps he believes money is neutral in the short run. If so, then of course it's fine to make the comparisons he does. But for those of us who believe that monetary and fiscal policy have textbook effects, then making that comparison is problematic. In the absence of these stimulus measures, I believe we may very well have breached that 11 trillion floor.

To see this, consider CBO's assessment that by 2009Q4, the stimulus package would have an impact of between 1.4 to 3.8 ppts of baseline GDP. The midpoint is 2.6 ppts. That's well within the range of the Mulligan floor.

So, to conclude, in my view, a "GDP disaster" would have occurred in the absence of aggressive actions by the Federal Reserve, the US Government, as well as fiscal and monetary authorities abroad.