Dr Administrator

This blog post seeks to answer the question: what economic growth rate does the UK need to sustain in order to reduce the deficit to zero?

This seems like a relevant question at the moment, and I’ve not seen a straightforward calculation of the answer – so I thought I’d give it a go myself. The idea being that even if the end result is not particularly informative the thinking behind getting the end result is useful.

The key parameter of interest here is the gross domestic product (GDP): the amount of goods and services produced in a year in the UK; it’s a measure of how wealthy we are as a nation, how it increases with time is a measure of economic growth. Also important are the deficit (how much the government’s annual spending exceeds its income) and debt (how much the government is borrowing).

Inflation means that the GDP can appear to grow each year with no increase in real economic activity, therefore I decided to use “inflation adjusted” GDP figures. I also preferred to use annual GDP figures rather than quarterly ones.

To model this I took a starting point of a known GDP, debt, deficit and government spend which I then propagated forwards in time: I made the GDP grow by a fixed percentage each year, and assumed that government spending would be flat (I’m using GDP adjusted for inflation so I think this is reasonable). Assuming that the total tax take is a fixed proportion of GDP I can calculate the deficit and hence increasing debt in each year, I add the debt servicing cost to the government spending in each. Since I’m doing everything else in the absence of inflation I’ve used a debt servicing rate of 2% rather than the 5% implied by a £43bn debt interest cost in 2010 – this makes my numbers a bit inconsistent.

I’ve put the calculation in a spreadsheet here.

Given this model my estimate is that the UK would need to sustain GDP growth of 4.8% per year until 2020 in order to reduce the deficit to 0%. This 4.8% GDP growth brings in approximately an additional £30bn in taxes for each year for which the growth is 4.8%. During this time the debt would rise to nearly 80% of GDP and so the cost of servicing the debt will double. These numbers seem plausible and fit with other numbers I’ve heard knocking around.

To get a feel for how GDP has varied in the past, this is the data for inflation adjusted annual GDP growth in the UK since 1950:

The red line shows the “target” 4.8% GDP growth, and the blue bars the actual growth in the economic, adjusted for inflation. The data comes from here. What’s notable is that GDP growth has rarely hit our target and what’s worse, over the last 40 years there have been four recessions (where GDP growth is negative), so the likelihood must be that another recession before or around 2020 is to be expected.

In real-life we are actually using a combination of GDP, government spending cuts and tax increases to bring down the deficit. These calculations indicate 0.5% GDP growth is approximately £7bn per year which is equivalent to a couple of pence on basic rate (see here) or about 1% of government spending (see here).

Doing this calculation is revealing because it highlights why there is an emphasis on cuts in government spending as a means of reducing the deficit. This had been a bit of a mystery to me with the figure of 80:20 cuts to taxes ratio being widely quoted as some sort of optimum, although there is some indication of other countries working with a ratio closer to 50:50. The thing is that when you cut your spending, you are in control. You can set a target for reduction and have a fair degree of confidence you can hit that target and show you have hit that target relatively quickly and easily. On the contrary relying on growth in GDP, or taxes, is a rather more unpredictable exercise: taxes because the amount of tax raised depends on the GDP.

The Office for Budget Responsibility (OBR) published uncertainty bounds for it’s future predictions of GDP in their pre-budget report last year (see p10 and Annex A in this report), their central forecast is for growth of 2.5% but by 2014 (i.e. in only 4 years) they estimated only a 30% chance that it lay between 1.5% and 3.5% actually they only claim a 40% chance of being in that range for this year (2011).

At the risk of being nearly topical, GDP is reported to have shrunk by 0.5% in the last quarter of last year, 2010. This is largely irrelevant to this post, although forecasts for GDP were growth of ~0.5% which supports the idea that GDP is not readily predictable. It’s worth noting that the ONS will revise this figure at monthly intervals until they get all the data in – the current estimate is based on 40% of the data being available.

Given this abysmal ability to predict GDP I suspect that there is little governments can do to influence the growth in GDP. It would be interesting to estimate the influence government policy has relative to prevailing global economic conditions, and what timelags there might be between policy changes and growth.

I think these calculations are illustrative rather than definitive, and what I’d really like is for someone to point to some better calculations!

This blog post attempts to answer the economic question: What country is the United Kingdom like economically?

The question arises from discussions of deficit (how much the government’s annual spending exceeds its income) and debt (how much the government is borrowing). To use a digging analogy: debt is a hole, deficit is how fast you are deepening the hole. We can get a feel for how countries compare in this sense by plotting them as a function of their deficits and debts on a graph. I’ve done this for the countries of the OECD (data here). The horizontal axis tells you  the deficit, whilst the vertical axis is the debt. These values are plotted as a percentage of the gross domestic product (GDP) so we can compare big countries and small countries, rich countries and poor countries on an equal footing.

As we go to the top left area of this graph we find countries which are in the deepest hole, digging fastest. Out of the extreme left we find the UK – it is digging its hole fastest at the moment, but it is not in the biggest hole – that honour currently goes to Japan. On this graph our nearest neighbours are Ireland, the United States and Iceland, with Greece and Japan having higher debt but lower deficit. France and Spain have similar debts but rather lower deficits.

Norway is actually bringing in more money than it spends and building a surplus, they have large oil revenues and are saving against the day when it runs out. Korea is doing this too but to a far smaller extent.

Economically it is often said that the PIGS or PIIGS countries are in most trouble in Europe, these are Portugal, Ireland, (Italy), Greece and Spain.

But is it true to say we are like Ireland, the US and Iceland? Ireland and Greece have much higher levels of unemployment than us, whilst the US has slightly higher levels and Iceland’s levels are comparable. Iceland has very high inflation (12%) whilst most other countries have moderate inflation including the UK, with a few countries having moderate deflation including the US and Ireland. We have moderate levels of unemployment, with Ireland, Greece, the US having much higher levels. It’s also worth pointing out that the UK has a population of 60,000,000 whilst Ireland only has 4,000,000 and Iceland a mere 300,000.

So whilst in deficit/debt terms we may resemble other countries in other, economically relevant ways, we are quite different.

From a mathematical point of view there are methods for measuring the closeness of things based on large numbers of variables, called clustering algorithms. These algorithms amount to our eyeballing of the debt/deficit data – they are a measure of distance. However, in economic problems things aren’t so simple. The economy is described by many variables and I don’t know their relative importance in determining economic similarity. The problem that the numbers involved may vary tremendously in size is trivially solved. My suspicion is that economists have probably spent a great deal of time arguing about economic similarity and haven’t come to a definitive answer.

So in answer to the question: What country is the United Kingdom like economically? Although the UK may be most like Ireland, the US and Iceland in debt/deficit terms. In terms of many other economic factors such as inflation, unemployment and so forth it is quite different. I suspect the real answer to this question is that the UK is most like France, Germany and Italy economically: these countries are of similar size, have similar unemployment rates, have inflation of the same sign, usually run public sector/ private sector ratios of similar size furthermore given their common membership of the EU their economic behaviour is probably similar. Of this group of countries Italy has the largest debt and we have a largest deficit.