Trade deficits, multiplier effects and where Keynesian maths breaks down

So, from the Wall Street Journal:

The U.S. trade deficit narrowed sharply in December despite a record foreign oil price, shrinking to a gap smaller than expected as overseas sales rose and imports receded.

The U.S. deficit in international trade of goods and services decreased by 6.9% to $58.76 billion from November’s unrevised $63.12 billion, the Commerce Department said Thursday.

The December deficit was smaller than expected by Wall Street. Economists surveyed by Dow Jones Newswires estimated a $61.70 billion shortfall.

For all of 2007, the U.S. ran a trade deficit of $711.6 billion, $46.9 billion less than the 2006 deficit of $758.5 billion.

Remember our handy equation for the macroeconomy:

Aggregate Demand = Consumption + Investment + Government Expenditure + Net Exports

So the trade deficit is still, well, big: NX, or Net Exports, is still heavily negative in the US equation:

balance of payments

That is month-by-month: every month another big negative bar. However NX is not important: the change in NX is what is important. A decrease in NX of USD47bn(ish) means USD50b47bn back in the US economy.

The Multiplier Effect determines the scale of the contribution this will make to US equilibrium GDP. It is defined as 1/MPS, the Marginal Propensity to Save (Marginal Propensity to Save + Marginal Propensity to Consume = 1).

Now, what is the US’ MPC? According to my Eco 1 textbook (somewhere), it’s 97%. According to Kyle Mudry it’s about 97.87%:

MPC

Personal savings as a percentage of disposable income is described in column 5. U.S. personal savings rates have experienced a sharp decline over the period. From the 70’s through the mid-eighties, U.S. citizens saved steadily around 9%-11% of their disposable income. From the mid-eighties to the present there has been a drastic decline, with the sharpest decrease coming during the mid-nineties on, dropping below 5% and almost coming to a complete stop at 1% in 2000.

You will note a discrepancy between Consumption, proportional, and Consumption, Marginal Propensity of – think of it is expenditure on financial services (for example), interest on debt, etc. It’s money not saved, at any rate.

So what does this mean for our USD47bn decline in the trade deficit? Well, according to the Multiplier Effect, it means a 47bn/.02 = USD2.35tr increase in equilibrium GDP!

Ah. This would be where our Multiplier runs into problems. Like many things in statistics and economics, the laws of our physics rather break down, near the corners. In this case, as MPC becomes very close to 1, the Multiplier gets somewhat non-realistic.

Extrapolation! As of last December, total Consumer Credit Outstanding was USD2.52tr, having risen 5.5% over the year. Total household debt is USD12.8tr.

The US population is a little over 301 million people – that’s people, not consumers. With an average household size of 2.6 people, Consumer Credit Outstanding becomes something like USD21,000 per household (total debt USD110,000 or so, but that is mostly secured – i.e. a mortgage).

The punchline? In the United State, the Marginal Propensity to Consume is basically greater than 1. So – give us a USD600 cheque, and we’ll spend some USD800. For example.

Now – what happens to the Multiplier Effect when MPC > 1? It would appear that the increase in GDP is infinite (the limit of the Multiplier as MPS approaches zero). In fact equilibrium GDP decreases. Counter-intuitive? Not so much. The Multiplier Effect works on the long-run equilibrium GDP, and in the long run, we have to repay our debt. More income only invites more expenditure and more borrowing, meaning more money lost to interest payments.

So – just think about that, when you get your recession-fixing cheque, or you read about the trade deficit. As long as we’re not saving for our rainy days, we’re really only getting that little bit more rope with which we’re hanging ourselves.

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