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19 April 2013 Last updated at 19:53 ET By Ruth Alexander BBC News

This week, economists have been astonished to find that a famous academic paper often used to make the case for austerity cuts contains major errors. Another surprise is that the mistakes, by two eminent Harvard professors, were spotted by a student.

It's 4 January 2010, the Marriott Hotel in Atlanta. At the annual meeting of the American Economic Association, Professor Carmen Reinhart and the former chief economist of the International Monetary Fund, Ken Rogoff, are presenting a research paper called Growth in a Time of Debt.

At a time of economic crisis, their finding resonates - economic growth slows dramatically when the size of a country's debt rises above 90% of Gross Domestic Product, the overall size of the economy.

Word about this paper spread. Policymakers wanted to know more.

And so did student Thomas Herndon. His professors at the University of Massachusetts Amherst had set his graduate class an assignment - pick an economics paper and see if you can replicate the results. It's a good exercise for aspiring researchers.

Thomas chose Growth in a Time of Debt. It was getting a lot of attention, but intuitively, he says, he was dubious about its findings.

Some key figures tackling the global recession found this paper a useful addition to the debate at the heart of which is this key question: is it best to let debt increase in the hope of stimulating economic growth to get out of the slump, or is it better to cut spending and raise taxes aggressively to get public debt under control?

EU commissioner Olli Rehn and influential US Republican politician Paul Ryan have both quoted a 90% debt-to-GDP limit to support their austerity strategies.

But while US politicians were arguing over whether to inject more stimulus into the economy, the euro was creaking under the strain of forced austerity, and a new coalition government in the UK was promising to raise taxes and cut spending to get the economy under control - Thomas Herndon's homework assignment wasn't going well.

No matter how he tried, he just couldn't replicate Reinhart and Rogoff's results.

"My heart sank," he says. "I thought I had likely made a gross error. Because I'm a student the odds were I'd made the mistake, not the well-known Harvard professors."

His professors were also sure he must be doing something wrong.

"I remember I had a meeting with my professor, Michael Ash, where he basically said, 'Come on, Tom, this isn't too hard - you just gotta go sort this out.'"

So Herndon checked his work, and checked again.

By the end of the semester, when he still hadn't cracked the puzzle, his supervisors realised something was up.

"We had this puzzle that we were unable to replicate the results that Reinhart-Rogoff published," Prof Ash, says. "And that really got under our skin. That was really a mystery for us."

So Ash and his colleague Prof Robert Pollin encouraged Herndon to continue the project and to write to the Harvard professors. After some correspondence, Reinhart and Rogoff provided Thomas with the actual working spreadsheet they'd used to obtain their results.

"Everyone says seeing is believing, but I almost didn't believe my eyes," he says.

Thomas called his girlfriend over to check his eyes weren't deceiving him.

But no, he was correct - he'd spotted a basic error in the spreadsheet. The Harvard professors had accidentally only included 15 of the 20 countries under analysis in their key calculation (of average GDP growth in countries with high public debt).

Australia, Austria, Belgium, Canada and Denmark were missing.

Oops.

Herndon and his professors found other issues with Growth in a Time of Debt, which had an even bigger impact on the famous result. The first was the fact that for some countries, some data was missing altogether.

Reinhart and Rogoff say that they were assembling the data series bit by bit, and at the time they presented the paper for the American Economic Association conference, good quality data on post-war Canada, Australia and New Zealand simply weren't available. Nevertheless, the omission made a substantial difference.

Thomas and his supervisors also didn't like the way that Reinhart and Rogoff averaged their data. They say one bad year for a small country like New Zealand, was blown out of proportion because it was given the same weight as, for example, the UK's nearly 20 years with high public debt.

"New Zealand's single year, 1951, at -8% growth is held up with the same weight as Britain's nearly 20 years in the high public debt category at 2.5% growth," Michael Ash says.

"I think that's a mistaken way to examine these data."

There's no black and white here, because there are also downsides to the obvious alternatives. But still, it's controversial and it, too, made a big difference.

All these results were published by Thomas Herndon and his professors on 15 April, as a draft working paper. They find that high levels of debt are still correlated with lower growth - but the most spectacular results from the Reinhart and Rogoff paper disappear. High debt is correlated with somewhat lower growth, but the relationship is much gentler and there are lots of exceptions to the rule.

Reinhart and Rogoff weren't available to be interviewed, but they did provide the BBC with a statement.

In it, they said: "We are grateful to Herndon et al. for the careful attention to our original Growth in a Time of Debt AER paper and for pointing out an important correction to Figure 2 of that paper. It is sobering that such an error slipped into one of our papers despite our best efforts to be consistently careful. We will redouble our efforts to avoid such errors in the future. We do not, however, believe this regrettable slip affects in any significant way the central message of the paper or that in our subsequent work."

Accidents do happen, and science progresses through the identification of previous mistakes. But was this a particularly expensive mistake?

"I don't think jobs were destroyed because of this but it provides an intellectual rationalisation for things that affect how people think about the world," says Daniel Hamermesh, professor of economics at Royal Holloway, University of London.

"And how people think about the world, especially politicians, eventually affects how the world works."

Discovering a spreadsheet error was never going to end the debate over austerity - and nor should it, according to Megan McArdle, special correspondent for Newsweek and The Daily Beast.

"There is other research showing that you can have these slowdowns when you get to high levels of debt," she says. "We have a very vivid [example] in Greece."

Thomas Herndon 's view is that austerity policies are counter-productive. But right now he's delighted that the first academic paper he's ever published has made such a splash.

"I feel really honoured to have made a contribution to the policy discussion," he says.

19 April 2013 Last updated at 11:11 ET By Helen Bushby BBC entertainment and arts reporter

Fourteen pilot shows - including Alpha House and Zombieland - are to be put to the public vote on Lovefilm and Amazon.com.

Viewers can submit feedback influencing which shows get made into full series.

The 14 shows are made by independent production companies and produced by Amazon Studios, the film and series production arm of Amazon.

"This is the first time Amazon Studios has done this," said Simon Morris, Lovefilm's chief marketing officer.

Eight adult comedies and six children's animation series will be put to the public vote.

The shows will be aired on Amazon's pay subscription services - Amazon Prime in the US, and Lovefilm in the UK - but Morris told the BBC they would be available to everyone and not just subscribers.

The adult pilot shows include Alpha House, about four senators who live together in a rented house in Washington DC and stars John Goodman, who was recently in Oscar-winning film Argo.

"Bill Murray has got a cameo in Alpha House, looking a bit older, a little bit more bedraggled, but definitely Bill Murray," Mr Morris added.

Onion News Empire is set behind the scenes of the Onion News Network, a satirical daily news service, and "shows just how far journalists will go to stay at the top of their game", according to Amazon Studios.

It stars Arrested Development's Jeffrey Tambor as the "egomaniacal lead anchor".

Musical comedy Browsers stars Cheers and Frasier actress Bebe Neuwirth as the "terrifying" boss of a news website in Manhattan.

Other pilot shows include Zombieland - based on the film of the same name - featuring four survivors attempting to outwit zombies, while animated comedy Dark Minions, written by Big Bang Theory's Kevin Sussman and John Ross Bowie, is about two "slackers" working on an intergalactic warship.

The children's shows include animations Sara Solves It, where Sara and Sam solve maths-based mysteries, and Creative Galaxy, an interactive art adventure series.

"This isn't X Factor for some new titles where you get to vote and they're fairly gimmicky," Mr Morris said. "It has a unique position in the world in that it has a platform that's a pay platform, it has an entertainment platform."

He said that the "world of digital has been growing, driven in large part by the BBC iPlayer, from about 2008" and that he saw this move as the next stage.

"Mass-market digital consumption and streaming have come of age in the last few years," he added.

'Promotional tool'

But Toby Syfret, TV analyst for Enders Analysis, was sceptical about the venture, describing it as a "gimmick" and said he did not think it would make much of a dent in the TV landscape.

"I think the success of this will have a huge amount to do with the publicity they can get for it."

Amazon and Lovefilm were able to put pilots to the public vote because "they are not TV channels with set budgets", he said, adding that "you cannot sustain a programming operation if you let viewers decide - you're losing control of the purse strings".

He also queried whether programme-makers would want the public vote to potentially leave them "committed to the most expensive thing which is least good".

"Programme makers may end up saying 'we'll go with it, but it's a bit expensive so we'll cut the budget' - and then you've done what the public's asked but it's been slashed by half," he added.

"Ultimately, this is a promotional tool - Amazon's thinking that Netflix has done it this way [by broadcasting Kevin Spacey's House of Cards drama series] so we'll come at it from another way."

Earlier this year, the streaming TV and movie service Netflix made and broadcast House of Cards, and revealed plans to make at least five new shows a year.

YouTube, owned by Google, also recently launched its original channels initiative with 20 new channels coming from the UK.

Mr Morris said that the key thing that marked his venture out was that "the platform is open".

"Not everyone has the opportunity to go and pitch an idea to HBO in New York, not everyone can get on a plane to Cannes and pitch a script," he said.

"But there is now a vehicle whereby people are in a place that independent writers - whether they've got a track record or not - can put content through and it can be evaluated and brought to market. And that's the exciting thing about this."

19 April 2013 Last updated at 20:17 ET

The pre-historic stones of Stonehenge are to be cared for by a general manager for the first time.

English Heritage says it needs "a dynamic and inspirational leader" to look after the site in Wiltshire.

Duties for the £65,000-a-year job include leading the Wiltshire monument's 180 staff and volunteers and liaising with druid leaders.

Other responsibilities include overseeing arrangements for summer and winter solstices.

'Brightest and best'

English Heritage's Tim Reeve said it was "important to ensure we keep the dignity of the stones".

"You could be up at the stones one minute, in outdoor garb trying to help visitors, then you can be back in a state-of-the-art visitors' centre," he added.

"The next time you could be in a suit, representing our site."

He said it was also important to make sure "solstice celebrations aren't in some way compromising the mystery and integrity of the stones".

English Heritage has called for only "the brightest and best" candidates to apply for the position.

The closing date for applications is 5 May.

Meanwhile, an excavation by volunteers on a shoestring budget has shown that the site of Stonehenge was a settlement 3,000 years before it was built.

19 April 2013 Last updated at 16:31 ET

US aircraft regulators have approved a revamped battery design for Boeing's 787 Dreamliner, paving the way for the fleet to return to the skies, after problems grounded it for months.

The Federal Aviation Administration (FAA) said airlines needed to replace the batteries to return to service.

It said it will publish a final directive next week.

Other international regulators are likely to follow but it will still be a couple of weeks before flights resume.

Boeing's chairman and chief executive Jim McNerney said: "FAA approval clears the way for us and the airlines to begin the process of returning the 787 to flight with continued confidence in the safety and reliability of this game-changing new airplane."

'High bar'

Transportation Secretary Ray LaHood said: "Safety of the travelling public is our number one priority. These changes to the 787 battery will ensure the safety of the aircraft and its passengers."

The FAA said it would "closely monitor" modifications of the aircraft and teams of inspectors would be sent.

Boeing said the regulator had set a "high bar for our team and our solution".

Planes now need to be fitted with a "containment and venting" system for both the lithium-ion batteries. That includes a stainless-steel enclosure to prevent heat, fumes or fire from spreading if a battery overheats in flight, said the FAA.

"This is a comprehensive and permanent solution with multiple layers of protection," said Boeing's head of commercial aircraft Ray Conner.

"The ultimate layer of protection is the new enclosure, which will ensure that even if a battery fails, there is no impact to the airplane and no possibility of fire.

"We have the right solution in hand, and we are ready to go," he added.

All of the 50 Boeing 787 planes in service were grounded in mid-January after their lithium-ion batteries emitted smoke on several separate occasions.

The problems sparked a battery fire on a parked Japan Airlines 787 at Boston's Logan International Airport and another incident in which battery smoke forced an emergency landing of an All Nippon Airways (ANA) 787 in Japan.

The 787 is said to be one of the most fuel-efficient in the industry, and Boeing delivered 46 Dreamliners to customers in 2012.

The plane is the first in the world to use the lithium-ion batteries, which are lighter, hold more power and recharge more quickly.

But the grounding has cost Boeing an estimated $600m (£393m). Japanese carrier ANA lost some 1.4bn yen ($15m; £9.5m) in revenue through January's disruption alone.

19 April 2013 Last updated at 19:23 ET

Rates for retirement incomes are unlikely to rise soon, a report says.

A typical retiree now will get £10,000 less in total retirement income than would have been the case with the same pension savings in 2011, the report for MGM Advantage and Prudential says.

Its authors say people should consider less conventional forms of annuity, which turn an individual's pension savings into annual retirement income.

But this came with a warning that they need to be aware of the risks involved.

Shopping around

Nearly 400,000 annuities were sold to retirees last year, bought for an average of £28,000 from their pension pot.

There has been criticism of the industry for not explaining to retirees that they can buy their annuity from any provider that they choose. This has led to the introduction of a new code of conduct ensuring that pension companies tell their clients that they can shop around.

But now, a report for MGM Advantage and Prudential has suggested that people should shop around for the type of annuity that suits them, not just the provider.

'Risks involved'

Authors Billy Burrows, an annuity expert, and academic Professor John Maule say that annuities linked to investments might be a better choice for people with a larger pension pot.

Typically, people buy a guaranteed pension income at the point of retirement, but in an investment-linked product this income might go up or down depending on the success of the investments during the individual's retirement years.

"Alternative options such as investment-linked annuities can produce better outcomes for many pensioners by combining the peace of mind of an income for life with the potential for future income growth and flexibility," the report said.

"However these policies are not without risk, and it is important that investors fully understand all the risks associated with these options."

Mr Burrows said that anyone considering an alternative product needed to be very engaged in the process and get sensible advice from the industry.

He described annuity rates as being at a "tipping point".

Recent figures from MGM Advantage showed a 3% increase in rates in the first three months of 2013. However, this was set against a backdrop of falling rates for some time.

In March, somebody with a typical £50,000 pension pot, aged 65, could secure an annual pension income of £2,875. Two years earlier, they could get £3,443, which equated to a difference of more than £10,000 over an average 18 years of retirement.

19 April 2013 Last updated at 20:10 ET

The UK government has launched a legal challenge against plans for a European financial transactions tax (FTT).

The FTT, which aims to raise public funds and discourage speculative trading, will be adopted by 11 EU states - but not by the UK.

Ministers fear it could be imposed on UK firms trading with businesses based in one of those states.

The Robin Hood Tax campaign group said the legal move was about "defending one rather rich square mile".

The 11 countries going ahead with the FTT are Germany, France, Italy, Spain, Belgium, Austria, Portugal, Greece, Slovenia, Slovakia and Estonia.

Under their plans, transactions of shares, currencies and bonds would be taxed.

The City of London could be hit by the tax if, for example, a British firm trades with branches of French or German banks based in the capital.

The British government would have to collect the tax but would not be allowed to keep it.

BBC business editor Robert Peston said that, by increasing the costs of these deals, there could be big falls in the value of business carried out in the City, running to many billions of pounds.

'Tax on pensioners'

UK Chancellor George Osborne said an application had been lodged at the European Court of Justice on Thursday.

"We think that the financial transaction tax which the European Commission has put forward is not right for Britain," he told the BBC.

"Britain doesn't want to take part but it also doesn't want to be caught in the effects of this tax being introduced by other countries. Let's be clear - financial transaction tax is not a tax on banks or bankers, it's a tax on pensioners and people with savings and investments.

"So we want to make sure that yes ok, fine, if some European countries want to introduce those kind of taxes they can do so but they should not do so in a way that impacts Britain."

A European Commission spokesman said: "We remain confident that the decision to approve enhanced co-operation on the FTT, which was voted by EU member states on January 22 is legally sound.

"It is fully in line with international law and the principles of the single market. Transactions will only be taxed if there is an established economic link to the FTT-zone, in a way that is fully compatible with the principles of cross-border taxation."

'Great displeasure'

Some European governments have blamed speculators and excessive trading for exaggerating the swings in financial markets during the 2008 crash and the recent eurozone crisis.

They believe the FTT will help to encourage more responsible trading by financial institutions.

The BBC's Robert Peston said the British government felt the 11 were interfering in an illegal way with the UK's sovereignty.

While it may have a point, there would be great displeasure at the UK's blocking tactics among the 11, especially in Paris, he added.

The perception would be reinforced of the UK moving further and further away from the EU's core, he said.

The Robin Hood Tax campaign group says that, if the UK signed up to a tax on the financial sector, "it could give a vital boost to the NHS, our schools, and the fight against child poverty in the UK".

Spokesman Owen Tudor said the legal challenge was "against the wishes of people in Britain and across Europe"

"Not content with letting our banks off scot-free, Osborne now wants to prevent European countries from making their financial sectors pay to repair the damage caused by the crisis.

"Resorting to lawyers is the last refuge of a chancellor who has lost the argument."

He said the move was "breathtakingly hypocritical - the UK's own £3bn stamp duty on shares is collected wherever UK shares are traded and regardless of who is trading them".