With just over a week left to the QE2 announcement, discussion over the amount, implications and effectiveness of QE2 are almost as prevalent (and moot) as those over the imminent collapse of the MBS system. Although whereas the latter is exclusively the provenance of legal interpretation of various contractual terms, and as such most who opine either way will soon be proven wrong to quite wrong, as in America contracts no longer are enforced (did nobody learn anything from the GM/Chrysler fiasco for pete’s sake), when it comes to printing money the ultimate outcome will certainly have an impact. And the more the printing, the better. One of the amusing debates on the topic has been how much debt will the Fed print. Those who continue to refuse to acknowledge that the economy is in a near-comatose state, of course, hold on to the hope that the amount will be negligible: something like $500 billion (there was a time when half a trillion was a lot of money). A month ago we stated that the full amount will be much larger, and that the Fed will be a marginal buyer of up to $3 trillion. Turns out, even we were optimistic. A brand new analysis by Jan Hatzius, which performs a top down look at how much monetary stimulus is needed to fill the estimated 300 bps hole between the -7% Taylor Implied Funds Rate (of which, Hatzius believes, various other Federal interventions have already filled roughly 400 bps of differential) and the existing 0.2% FF rate. Using some back of the envelope math, the Goldman strategist concludes that every $1 trillion in new LSAP (large scale asset purchases) is the equivalent of a 75 bps rate cut (much less than comparable estimates by Dudley, 100-150bps, and Rudebusch, 130bps). In other words: the Fed will need to print $4 trillion in new money to close the Taylor gap. And here we were thinking the economy is in shambles. Incidentally, $4 trillion in crisp new dollar bills (stored in bank excess reserve vaults) will create just a tad of buying interest in commodities such as gold and oil…

Here is the math.

First, Goldman calculates that the gap to close to a Taylor implied funds rate is 7%.

Our starting point is Chairman Bernanke’s speech on October 15, which defined the dual mandate as an inflation rate of “two percent or a bit below” and unemployment equal to the committee’s estimate of the long-term sustainable rate. The Fed’s job is then to provide just enough stimulus or restraint to put the forecast for inflation and unemployment on a “glide path” to the dual mandate over some reasonable period of time. Indeed, Fed officials have implicitly pursued just such a policy since at least the late 1980s.

To quantify the Fed’s approach, we have estimated a forward-looking Taylor-style rule that relates the target federal funds rate to the FOMC’s forecasts for core PCE inflation and the unemployment gap (difference between actual and structural unemployment). At present, this rule points to a desired federal funds rate of -6.8%, as shown in Exhibit 1.3 Since the actual federal funds rate is +0.2%, our rule implies on its face that the existence of the zero lower bound on nominal interest rates has kept the federal funds rate 700 basis points (bp) too high.

It is important to be clear about the meaning of this “policy gap.” It does not mean,as is sometimes alleged, that policy is tight in an absolute sense, much less that it will necessarily push the economy back into recession. In fact, policy as measured by  the real federal funds rate of -1% is very easy. However, our policy rule implies that under current circumstances, with the Fed missing to the downside on both the inflation and employment part of the dual mandate (and by a large margin in the  latter case), a very easy policy is not good enough. Instead, policy should be massively easy to facilitate growth and job creation, fill in the output gap, and ultimately raise inflation to a mandate-consistent level.

Next, Goldman calculates how much existing monetary, and fiscal policy levers have narrowed the Taylor gap by:

The 700bp policy gap clearly overstates the extent of the policy miss because it ignores (1) the expansionary stance of fiscal policy, (2) the LSAPs that have already occurred and (3) the FOMC’s “extended period” commitment to a low funds rate. We attempt to incorporate the implications of these for the policy gap in two steps.

First, we obtain an estimate of how much the existing unconventional Fed policies have eased financial conditions. In previous work we showed that the first round of easing pushed down short- and long-term interest rates, boosted equity prices and led to depreciation of the dollar. Although our estimates are subject to a considerable margin of error, they suggest that “QE1″ has boosted financial conditions, as measured by our GSFCI, by around 80bp per $1 trillion (trn) of purchases. Moreover, our estimates suggest that the “extended period” language has provided an additional 30bp boost to financial conditions. A number of studies undertaken at the Fed similarly point to sizable effects on financial conditions. A New York Fed study, for example, finds that QE1 has pushed down long-term yields by 38-82bp. A paper by the St. Louis Fed also finds a sizable boost to financial conditions more generally, including equity prices and the exchange rate.

Second, we translate this boost to financial conditions, as well as the expansionary fiscal stance, into funds rate units. To do so, we attempt to quantify the relative impact of changes in the federal funds rate, fiscal policy and the GSFCI on real GDP. As such estimates are subject to considerable uncertainty we take the average effect across a number of existing studies (see Exhibit 2). With regard to monetary policy, the studies we consider suggest that a 100bp easing in the funds rate, on  average, boosts the level of real GDP by 1.6% after two years. A fiscal expansion worth 1% of GDP, on average, raises the level of GDP by 1.1% two years later. Using existing studies to gauge the effects of an easing in our GSFCI on output is more difficult as other researchers construct their financial conditions indices in different ways. Taking the average across studies that report effects for the components of their indices, thus allowing us to re-weight the effects for our GSFCI, and our own estimate suggests that a 100bp easing in financial conditions increases the level of GDP by around 1.5% after two years.

What does this mean for the real impact on the implied fund rate from every incremental dollar of purchases?

Combining these two steps suggests that $1trn of asset purchases is equivalent to a 75bp cut in the funds rate (calculated as the effect of LSAPs on financial conditions (80bp), multiplied by the effect of financial conditions on GDP (1.5%), divided by the effect of the funds rate on GDP (1.6%)). This estimate reinforces the view that QE1 helped to substitute for conventional policy. Our estimate, however, is less optimistic than the 100-150bp range cited by New York Fed President Dudley, or the 130bp implied by Glenn Rudebusch of the San Francisco Fed.

In terms of the other policy levers, our analysis implies that the “extended period” language is worth around 30bp cut in the funds rate and a fiscal stimulus of 1% of GDP is equivalent to around 70bp of fed funds rate easing.

So how much more work should the FOMC do? Exhibit 3 shows that consideration of policy levers other than the funds rate cuts the estimated policy gap by more than half, from 700bp to 300bp. Of this 400bp reduction, the easy stance of fiscal policy is worth 240bp; QE1 is worth 130bp; and the existing commitment language is worth another 30bp.

And the kicker, which shows just how naive we were:

We can then express the remaining policy gap in terms of the required additional LSAPs. Using our estimate that $1trn in LSAPs is worth an estimated 75bp cut in the federal funds rate and assuming that all other policy levers stay where they are at present, Fed officials would need to buy an additional $4trn to close the remaining policy gap of 300bp.

Now, for the amusing part: what does $4 trillion in purchases means for inflation. Or, a better question, when will $4 trillion be priced in…

In reality, the FOMC is unlikely to authorize additional LSAPs of as much as $4trn, unless the economy performs much worse than we are forecasting. The committee perceives LSAPs as considerably more costly than an equivalent amount of conventional monetary stimulus, and is therefore not likely to use the two interchangeably. Many Fed officials believe that there are significant “tail risks” associated with LSAPs and the associated increase in the Fed’s aggregate balance sheet. These  risks include the possibility of substantial mark-to-market losses on the Fed’s investment, which might prove embarrassing in the Fed?s dealings with Congress and could, in theory, undermine its independence. They also include the possibility that the  associated sharp increase in the monetary base will lead households and firms to expect much higher inflation at some point in the future.

Unfortunately, it is extremely difficult to put a number on the perceived or actual cost of an extra $1trn in LSAPs in terms of these tail risks. However, we have some information on how the FOMC has behaved to date that might reveal Fed officials’ perception of these costs.

Oddly, nobody ever talks about the impact of “unconventional” printing of trillions on commodities such as oil and gold. They will soon.

Our analysis is therefore consistent with additional asset purchases of around $2trn if the FOMC’s forecasts converge to our own. It is unlikely, however, that the FOMC will announce asset purchases of this size in the very near term. Rather, our analysis suggests that the timing of the announcements should depend on whether, and how quickly, the FOMC’s forecasts converge to ours.

Hatzius pretty much says it all- suddenly the market will be “forced” to price in up to 4 times as much in additional monetary loosening from the “conventional wisdom accepted” $1 trillion. We have just one thing do add. If Goldman has underestimated the impact of existing fiscal and monetary intervention, and instead of closing 4% of the Taylor gap, the actual impact has been far less negligible (and if Ferguson is right in assuming that all this excess money has in fact gone to chasing emerging market and commodity bubbles), it means that, assuming 75bps of impact per trillion, the Fed will not stop until it prints nearly ten trillion in incremental money beginning on November 3. That’s almost more than M1 and M2 combined.

Is the case for $10,000 gold becoming clearer?