Andrew Lilico of The Telegraph takes issue with the arguments presented using the sectoral balances identity. The website describes him as:

Andrew Lilico is an Economist with Europe Economics, and a member of the Shadow Monetary Policy Committee. He was formerly the Chief Economist of Policy Exchange.

After interpreting the accounting identities in his own way, Lilico goes on to say:

Here’s where the argument goes wrong.  When we talk about “private sector deleveraging” what do we mean?  We mean things like households paying off loans to the bank, or corporates paying off bonds or other loans.  The vast, vast majority of such loans are loans private sector agents make to each other.  So for every pound reduction in borrowing made by one household or company, there is one pound fall in savings by other households and companies.  The net change in the indebtedness of the private sector as a whole, relative to other sectors (i.e. relative to the government or to foreigners) is zero.  Within the private sector, households could pay off all of their debts to each other, and that would (in an accounting sense) make no difference whatever to the net lending of the private sector as a whole to the government.

Unfortunately for him, his argument is erroneous at the most elementary level.

What did the financial crisis lead to? Before the crisis, in many advanced economies, private expenditure was rising relative to income and the difference was increasing. A sudden U-turn in this behaviour led to a fall in output and simultaneously increased the public sector deficit because of lower taxes caused by the fall in output.

Lilico’s argument seems to think of the budget deficit as exogenous – i.e., under the control of the government but a careful study reveals that this ain’t so. His argument is another example where accounting identities are misinterpreted as behaviour.

There are various other errors: Lilico confuses the terms borrowing and saving – as if they are exact opposites. Various intuitions go wrong when one applies it without a proper understanding of national accounts and I showed this in my post from last year for this particular case: Saving And Borrowing.

The most fundamental error of Lilico of course is that he holds output constant in his entire argument. When discussing a scenario with sectoral balances, it is also important to keep in mind the behaviour of output. Most economists who come across the sectoral balances approach err on this. Part of the reason why he errs on this – knowingly or unknowingly – is the chimerical neoclassical production function view of the world where output is determined by supply side factors.

Update:

Seems Lilico has been arguing with people in Twitter. Here is a Tweet from him:

@dsquareddigest Why? Why doesn’t my mother invest or consume the £1000 I pay her?

— Andrew Lilico (@AndrewLilico) May 1, 2013

This is confusing the two usages of the phrase investment in macroeconomics – investment as fixed capital formation and investment as allocation in financial assets! If you give your mother £1000, she can consume or have investment expenditures or allocate the remaining in financial assets.