Will the British royal baby boy buoy the economy? Probably not

Catherine, Duchess of Cambridge carrying her newborn son on July 23, 2013.
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Catherine, Duchess of Cambridge carrying her newborn son on July 23, 2013.

Will the royal baby boy buoy the economy? This question was on almost no one's lips as the third in line to the throne was born on Monday. But on the day the Prince of Cambridge emerged into the world, some economists could not restrain themselves.

Howard Archer, chief European and UK economist at IHS Global Insight, published a note predicting the effect of the birth would be "overwhelmingly positive". His analysis was reported with more gusto outside the UK, but he was not alone in his economic soothsaying.

(Read more: Duchess of Cambridge gives birth to baby boy)

The Center for Retail Research, a Nottingham-based company that claims to provide "authoritative and expert research and analysis of the retail and service sectors in Britain, Europe and globally" made something of a splash with an even more specific forecast. The new prince will boost retail sales, it said, by the rather exact figure of £243 million in the very specific period of nine weeks between 1 July and 31 August.

The center boasts on its website that it has had coverage "all over the world" in at least 20 different media outlets for its estimate that festivities spending will rise £87 million, souvenirs by £80 million and books and DVDs by £76 million. According to its expert and authoritative analysts: "Three million bottles of champagne and sparkling wine will be opened to celebrate the new baby".

As far as questions related to royalty go, the macroeconomic effects of the new heir to the throne pale into insignificance, especially when compared with the Queen's pertinent 2008 question on the economic crisis, "Why did no one see it coming?"

But the life of many professional economists is to answer questions they think are intrinsically uninteresting, so here is a quick back of a cigarette packet guide to the effect of the new prince on growth and Britain's economic fortunes.

(Read More: Royal baby to give $400 million bump to British economy)

First, we should distinguish between "sign" and "scale", hoping that the former is easier to answer than the latter.

By "sign", economists attempt to distinguish between a positive or a negative economic impact. To this question, Mr Archer is categoric in asserting that the sign will be "overwhelmingly positive". He says that unlike the royal wedding in 2011 and diamond jubilee in 2012, which came with additional public holidays, detracting from output, the 2013 royal birth has "no obvious negative repercussions".

More from the Financial Times:

New prince born to Duchess of Cambridge
Royal birth heralds constitutional change
Time to get used to 'God Save the King' again

He then says the effect will be limited to an increase in retail sales, alcohol sales and bookies' takings, making a traditional economic assumption that all spending has the same intrinsic merit. To this he adds some spending effect from a "feel good factor" and some rise in tourism linked to the UK being in the global spotlight.

Hang on a second. With the exception of any tourism effect – pretty tenuous, unless you have also been encouraged to visit Belgium after its coronation last Sunday – the other spending increases are far from guaranteed to be net additions to UK gross domestic product. A growth in spending on baby-related products might simply offset a decline in other spending. And it matters if the goods are domestically produced. Spending on champagne helps the French and the souvenirs will mostly be imported.

(Read more: US bookmakers cash in on royal baby bets)

If a household changes its pattern of expenditure to favor foreign rather than UK-produced goods, the retail distribution sector is unaffected while imports have risen. That effect detracts from spending on British-produced goods and services.

Scale is rather easier. Assume for a second that the ludicrously precise estimates from the Center for Retail Research are accurate and £243 million is additional and spent over three months on retail goods. In the most recent three months, retail sales stood at £87 billion, so the birth might increase sales for the three-month period a little under 0.3 percent. As the distribution sector contributes 7 percent of national output, the increased business might boost GDP by 0.02 percent with an equal and negative effect in the following quarter.

(Read more: Don't panic! UK recovery is 'firmly entrenched')

If all the spending was additional and all was spent on British goods and services, GDP would rise at most by 0.06 percent in a quarter. However you look at it, even if the sign is positive, the scale is puny.

By all accounts, the new prince is a big and beautiful baby boy. But we shouldn't look to him for economic recovery.