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# A PuzzleRobert Skidelsky Wednesday, October 06, 2010

The other day I was giving a lecture on economic policy at a well-known British independent school. I argued that an easy way of increasing total spending was for the government to issue every household with a time-limited voucher, e.g. £100 to be spent within a month. A bright student from Hong Kong then asked the following question, “If the receiver of the voucher was rational, she would realise that her taxes would have to go up by £100 in order to finance the voucher, so she would spend the voucher but increase her saving by £100. Wouldn’t this mean that no extra spending would be generated by the issue of the vouchers?”

After the lecture I gave the question to two economics graduates:

(I) Question: why would people spend their £100 time-limited, government-granted voucher knowing that there might be a tax increase to finance the vouchers later?

In a superrational world the recipient of the voucher knows that he is holding £100 voucher that cost £100.01 to produce. Calculating that there are 60m Brits, he realises that the government has incurred that an expense of £600,000 even if no one uses the vouchers and he therefore saves 1p to guard against the perfectly off-setting tax that will be levied with 100% certainty within to balance the budget at the end of every financial year. And there we have it: government expenditure is waste.

But let's play with this. What is needed for the effect of the £100 voucher to be more than nil (either because they spend it all and save the same amount (Ricardian equivalence) or because they don't spend it at all)? The answer is: not much.

1) The superrational recipient may use all available information to gather that a tax increase is far from certain. There is only one year until the next election and tax increases are unlikely. Of course the next government may feel the need to balance the budget after the excesses of its predecessor but the voucher recipient is not entirely sure. Or, maybe more likely, the government commits to covering the expense of the 60m x £100 one-off expense by selling off some asset. Of course there is also the option of resoring to issuing government debt but that complicates things a bit. In any case, all of this to say that there is uncertainty about the raising of taxes. The superrational voucher recipient will spend proportion of the voucher that corresponds to the probability of no tax increase. So, say that it is 95% certain that there will be a tax increase, then £5 will be spent and £95 saved.

2) And then there is time. Even if the superrational voucher receipient knows with 100% certainty that a tax increase will follow but does not know for sure if (or how much) he will be taxable (maybe he is in heaven, or at any rate in a tax haven) then the same logic applies as under point 1): he discounts how much he has to save. If a tax is believed only to be levied in 50 years and the recipient is 80 years old he will probably calculate that he will not be hit. And if he thinks about his children, then he might reason that "who knows what will happen in 50 years?" Uncertainty makes superrationality rather blunt. And even if everything is for certain, a time discount factor may apply with the same result: you simply treat your present self better than your future self. You spend those £100 on something nice today and leave your future self to deal with it.

3) And of course, even with 100% certainy about a tax and no discount factor the superrational recipient might believe in the positive multiplier. In that case, he knows that spending at least some of the voucher results in an increased national income and because he is a representative agent he will receive a representative share of this. In fact, a positive multiplier implies that - in absolute terms - the more he spends, the more his income increases. So he has every reason to spend all of the £100 voucher because he know that his marginal utility of those £100 today is larger than the marginal disutility of losing those £100 in raised taxes later since £100 is larger share of his income today than of his income in the future.

For all these reasons, and for the obvious reason that people are not actually superrational representative agents but creatures of habit and vice, the £100 voucher spent will not be offset one-for-one by increased savings.

(II) Question: If I receive an £100 time-limited voucher from the government, will I increase my spending or offset it with saving elsewhere? Don’t I know that it will have to be paid for by future taxation?

Firstly, what kind of person would I have to be to “know” my tax bill will increase in the future? The level of knowledge I need to have is unrealistically high, and doesn't straightforwardly follow from "rationality". Actors who know there will be future taxation seem to need to already subscribe to specific economic theories about government spending. In the current climate, we are talking about spending financed by government borrowing – but deficit spending done right doesn’t need to mean future tax rises. At a low cost of borrowing, the multiplier effect of spending can outweigh the interest paid on it.

Rational expectations theory already assumes that certain tenets of neo-classical economics are right, and that people know they're right. But even if we take a weaker form of this argument, and say that people have adapted their expectations through a process of learning and experience, when and how did they do so? The complexity and the time-delayed nature of government tax and spend decisions make this pretty implausible.

Secondly, this just doesn't happen in real life. The best recent example is probably the VAT cut last Christmas, where spending did increase despite the explicitly time-limited nature of the cut. It’s much more reasonable to predict that people will spend the voucher, and save only some proportion of its value, a net increase in spending which stimulates the economy. The question is whether a handout to consumers, rather than government investment in infrastructure, is the best way to do it.

One last thing to think about: if rational expectations hold, everyone already understands how the economy works and can predict its future state with only random errors – so what's the point of economists?

(III) What do you think?

By A.Mason (England) on Wed 20 Oct 2010 - 5:50

Depends on how hungry the recipient is: consequently a calculation of utility value now as opposed to discounted utility value at some future date when the tax is repayable.  Which latter hinges on the extent of the individual’s liability to taxation.  Another aspect - depends on the level of aggregate demand. At less than full employment the multiplier effect may increase Income to the extent of of at least paying for the level of debt incurred by the government in issuing the vouchers.  If the economy is working at or near full capacity then the stimulus engendered by the vouchers may lead to inflation in which case the cost of the vouchers will be met by the increased prices of goods and services.

If one were a cynic one would look very carefully at a gift of £100 from the present government!

By phil armstrong (york england) on Sun 10 Oct 2010 - 12:53

When I was a student in the late 1970s I remember reading NME. The writers were very clever and let us know that in a very ‘showy’ way, with complex vocabulary and ‘in’ jokes. You had to work hard to find out what they really thought of the album. When you did understand it was often a great disappointment. ‘Cleverness’ in expressing an opinion is never a substitute for clearness of thinking. If your starting point is wrong then intellect is dangerous indeed. The above commentator (Mr Buckley) could have learned his trade at NME. Keynesian corruption? He starts from a presumption, I guess, of a ‘natural economy’ which can be spoilt by nasty Keynesian interference in the order of things. This is not so; economists have a critical role in guiding policy, especially Keynes and his true successors, the Post Keynesians.

By adrian buckley (Harrogate) on Thu 07 Oct 2010 - 13:31

Strangely I was giving an economics lecture to sixth formers at a small Northern Independent school last night. At that lecture I explained that due to the nature of a debt based monetary system and the symbiotic relationship between commercial banks and Government , exponentially increasing debt would ultimately cause the collapse of the fiat currency . Issuing time limited spending vouchers would only accelerate that collapse. I further posited that due to the fact that we are enjoying the confluence of Kondratiev’s winter , at the peak of the greatest credit bubble in global history , during a period of exclusively fiat currency across the industrialised world , we must expect asset prices , inflated by excessive credit to deflate. Ergo avoid property purchases until they cost the equivalent of the bricks and mortar required to build them. I also explained to these poor souls that the Government would have to extend its Q.E. program shortly due to the solvency problems faced by both States and Banks that are integrated with the British economy. I warned them that in the event that such monetization did not circumvent banks , and was not used to purchase personal debt and forgive that debt there would likely be a revolution. They queued up at the end of the lecture to purchase the stock of pitchforks that I had carefully placed at the side of the hall and promised that they would all get involved in the revolution unless this Keynesian corruption of our economy didn’t stop soon.

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