Economists struggle with simple things. Two examples.

**National Saving, Trade Deficits etc.**

In a blog article Has Anyone Heard of the Trade Deficit?, Dean Baker uses the sectoral balances identity to make a claim which is presented like a no-go theorem.

Baker says:

Fans of arithmetic (a tiny minority among DC policy types) like to point out that a large trade deficit implies negative national savings. In other words, if we have a trade deficit then by definition the United States as a whole has a negative saving rate.

This means that we either

musthave budget deficits (negative public savings) or negative private savings, or both. There is no way around this fact.

Baker confuses saving with saving net of investment – just like the Neochartalists. (Confuses S with S minus I)

Without proof, the sum of saving of a whole economy is given by

S = I + BP

where (here) S is the sum of the savings of all resident sectors of the economy – the “national saving”, I is the total investment expenditure of the resident sectors of the economy (i.e., both private and public) and BP is the current account balance of international payments.

So it is possible for an economy to have a trade deficit and hence a negative BP (although it’s not always the case that the trade deficit translates into a current account deficit) and still have I + BP positive if investment is sufficiently high. So an economy can have positive national saving with a trade deficit.

Of course it must be said that the persons he is attacking are wrong. The claim (of the persons he is criticizing)* is that the United States should save more (by a reduction in budget deficits brought about by a tightening of fiscal policy and/or higher propensity to save of the private sector achieved in some way). This is illegitimate as such a policy will induce a recession in the United States. Via the paradox of thrift, an increase in the private sector propensity to save can lead to lower saving of the private sector. Investment will fall because of lower sales expectations and the recession in the United States caused by the fiscal tightening will most likely lead to a recession in the rest of the world reducing its exports so that the only thing achieved is higher world unemployment.

**Debt/GDP Ratio**

In a series of posts aimed at showing something, Randall Wray claims the following:

… To simplify, if the interest rate is higher than the economy’s growth rate, then the debt ratio rises continuously…

Of course he also claims that if g>r, the debt ratio stabilizes.

Now, the debt sustainability conditions relating the interest rate and the growth rate of output are misleading. I showed this two posts back, where I showed that the claim that the condition that g>r *ensures* stabilization of the public debt/gdp ratio is incorrect. The above quote claims the opposite and is equally erroneous and misleading.

An economy can have the growth rate lower than the interest rate and still not have an exploding debt ratio.

A standard error in such analysis is to treat the budget deficit as *exogenous. *

Consider an economy without a strong **balance of payments constraint** and with inflation less of a trouble. A fiscal expansion brings about an increase in output and this has the effect of stabilizing the debt ratio in two ways: the higher output itself and an increase in tax revenues of the government due to higher output. The budget balance may go into primary surplus automatically even though the government may not be targeting this.

In other words, if r>g, the *sequence* d_{n }given by the relation

d_{t} – d_{t-1 }= λd_{t-1 }– pb_{t}

(where λ is equal to (r-g)/(1+g) and d_{t}_{ }is the debt/gdp ratio at the end of time period t and pb_{t} is the primary budget balance of the government in the period) would seem to explode because of the first time on the right hand side. But higher output will automatically lead to a dynamics for pb_{t }ensuring sustainability.

How this works was shown by Wynne Godley in an article *The Dynamics Of Public Sector Deficits And Debts* written in 1994 written by his co-author Bob Rowthorn in J. Michie and J. Grieve Smith (eds), *Unemployment in Europe* (London: Academic Press), 1994 pp. 199-206 and which was originally a paper to the UK Treasury around ’92-’93.

For a demand constrained economy:

… Note that the primary budget balance adjusts automatically so as the stabilise the debt to GDP ratio. This spontaneous adjustment occurs through induced variations in GDP.

The government cannot directly determine the primary balance.It can only control r, θ and G, and once the time path of these is fixed as above, the variable Y will evolve so as to stabilise the ratio B/Y. If this ratio is too large, Y will grow rapidly and generate sufficient tax revenue to bring this ratio down.There is a standard proposition that the government cannot permanently maintain a primary deficit if the interest rate is greater than the growth rate (r>g) … even if true, the statement can be misleading. In a demand-constrained economy, the level of Y relative to G will automatically adjust so as to produce a primary balance (deficit or surplus) to stabilise the ratio B/Y …

[Emphasis mine]

(θ is the tax *rate* in the model in above paper). Also see this post Wynne Godley And The Dynamics Of Deficits And Debts

It is counterproductive to go around making statements about the conditions on interest rate and the growth rate without qualifications and care and considering a situation/history and future scenarios.

There is one place where this condition is useful. Consider a balance of payments constrained economy. In studying the sustainability of the external debt of a country, one can conclude that if r>g (where r is the effective interest rate paid on foreign liabilities), then the debt dynamics will lead to an exploding debt even if the trade balance is held constant. Of course that doesn’t mean if r<g alone ensures sustainability.

*Updated 1650 GMT 17 Jan 2013 to make it clear.