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Since the single topic of the press conference that President Obama staged with his party's media collaborators on Tuesday, 8 October 2013 revolved around the topic of what could happen if the U.S. government chooses to default on its debt obligations, or as will more likely be the case, doesn't default on those obligations and instead doesn't spend as much as U.S. politicians would like it to spend, we thought we would go straight to the bottom line and find out how much the U.S. economy would be affected.

But first, we'll need some numbers, which CNBC tracked down for us:

Treasury Secretary Jack Lew is about to face the very same choices confronted by any financially struggling American household: Which bills to pay and when to pay them.

If Congress fails to raise the debt ceiling by around Oct. 17, Lew, who has been in the job less than a year, will have to sit at his desk and figure out how to make due on roughly one-third less in the way of government funds for the bills he has to pay. Because he can no longer borrow, according to the Bipartisan Policy Center, government spending will fall by about 32 percent, or $108 billion in the first month.

On a side note, to put that situation in context, this is no different from what could very well happen just 20 years from now when Social Security's trust fund has been fully depleted, as expected. At that time, the federal government will reduce all payments to Social Security beneficiaries by roughly 26%, unless it significantly increases the amount it borrows. And that's if everything goes as U.S. politicians have promised without any spending reform - this is one reason why the political fight over the debt ceiling and government spending levels is taking place now, because waiting will needed reforms so much more painful. Not to mention, more necessary.

Back now to the question at hand: how much would a government spending cut of that magnitude affect GDP?

The good news is that we can answer that question with just back-of-the-envelope math! And we can do it on a "daily" basis.

That $108 billion reduction in federal government spending works out to be $3.6 billion per day. We know that the GDP multiplier for all government spending in the U.S. is 0.6, which we know from research published by the U.S. Federal Reserve applies when the nation's official unemployment rate is over 7.5%. Which is the case at present, thanks to the furloughing of federal government employees! If it were under 7.5%, we would need to use a GDP multiplier of 0.5 to account for the shock of a sudden change in government spending, as government spending is considered to deliver even less of an impact to GDP when the economy is in a healthier state.

Taking our potential government spending reduction of $3.6 billion per day, and multiplying it by our GDP multiplier for government spending of 0.6, we find that the U.S. economy will lose out the equivalent of $2.16 billion worth of GDP per each day that Uncle Sam doesn't have his credit limit reset to a higher level.

Now, to measure the impact upon GDP, just multiply that number by the number of days the U.S. federal government operates in that situation!

If played out through the remaining 78 days of 2013, assuming we stick with President Obama's planned schedule for putting the U.S. federal government into default, that would reduce the nation's GDP for the fourth quarter of 2013 by $168.48 billion.

To put that number into perspective, the fiscal drag produced by the $56.3 billion by which U.S. federal taxes will be higher in the fourth quarter of 2013 than they were in the fourth quarter of 2012 thanks to President Obama's tax hikes that took effect back in January 2013, GDP in the U.S. will be nearly $168.92 billion smaller in 2013-Q4 than it would otherwise have been given the GDP multiplier for taxes.

Why, that's almost exactly the same amount! Perhaps that explains why President Obama has been so intent on doubling down on his "no negotiation with the duly elected representatives of American citizens" strategy - he'll produce twice the negative fiscal drag on the U.S. economy in 2013-Q4 if only he and his supporters can stick with it!

And yes, numbers like those mean a recession, as the Federal Reserve's quantitative easing programs won't produce enough juice for the economy to offset that kind of fiscal drag, offsetting only somewhere between $250 billion and $290 billion of the hit if the debt ceiling isn't increased by 31 December 2013.

Of course, if the debt ceiling situation is resolved sooner than than, it is very much possible that the U.S. will have positive economic growth in 2013-Q4 - only seeing slower growth than it would have had instead. Which is pretty much the story for every quarter during President Obama's entire tenure in office.

Source: How Much Would A Federal Default Affect The U.S. Economy?