The percentage change (a relative measure) is easy to interpret. It indicates the size of a change when the starting level is 100. Percentages therefore provide a consistent yardstick for interpreting changes.
Calculating percentages
This is a matter of simple arithmetic. Basic rules for calculating percentage changes are given below. The various operations in the examples are similar. They are designed to minimise the number of key strokes required when using a calculator. Multiplying or dividing by 100 and adding or subtracting 1 can be done by eye.
1 To find one number as a percentage of another
2 To find the percentage change between two amounts
3 To find a given percentage of an amount
4 To find an amount after a given percentage increase or decrease
Basis points
Financiers deal in very small changes in interest or exchange rates. For convenience one unit, say 1% (that is, 1 percentage point), is often divided into 100 basis points.
1 basis point = 0.01 percentage point
10 basis points = 0.10 percentage point
25 basis points = 0.25 percentage point
100 basis points = 1.00 percentage point
Common traps
Units and changes
Do not confuse percentage points with percentage changes. If an interest rate or inflation rate increases from 10% to 13%, it has risen by three units, or 3 percentage points, but the percentage increase is 30% (3 ÷10 × 100).
Up and back
A percentage increase followed by the same percentage decrease results in a figure below the starting level. For example, a 50% rise followed by a 50% cut leaves you 25% worse off.
$1,000 increased by 50% is $1,500.
50% of $1,500 is $750.
Starting levels
A 10% pay rise for chief executives earning $500,000 a year puts an extra $50,000 in their annual pay packets. The same percentage increase for cleaners on $10,000 a year gives them a mere $1,000 extra.
The importance of the base from which changes are calculated is also illustrated in Tables 2.4 and 2.5.
Table 2.4 When did inflation fall?
Table 2.5 Choosing the period for comparison
Using Table 2.4, it could be claimed that in February 2006 the 12-month rate of inflation fell from 10% to 0%. In fact all that happened is that the increase a year earlier fell out of the 12-month comparison. In this example, shop prices changed just once during the period January 2004–February 2006, perhaps owing to an increase in the rate of sales tax or VAT.
Table 2.5 shows that orders in the third quarter of 2006 were down from the previous quarter. However, the figure for the previous quarter was unusually high, and the third-quarter figures were better than the first quarter’s and any quarter of 2005. When comparing data over several years it is easy to overlook the distortion that can arise from using an unusually high or low starting or ending value.
Growth rates
If consumer spending rises by 1% a month, by how much will it increase over a full year? Not 12%, but 12.7%. Each month expenditure is 1% greater than the month before and each percentage increase is calculated (compounded) from a higher base. Thus 12.7% a year is the same as 1% a month annualised. It is important to distinguish between the following terminology (numerical examples from Table 2.5).
12-month or 4-quarter change. This compares one month or quarter with the same one in the previous year. For example, orders rose 2.6% between the third quarters of 2008 and 2009.
Change this year. This compares the latest figure with the very end of the previous year. For example, when third-quarter figures for 2009 were published, commentators might have said that orders had risen by 4.8% over the three quarters to the third quarter of 2009.
Annualised change. This is the change which would occur if the movement observed in any period were to continue for exactly 12 months. For example, orders rose 6.4% annualised during the first three quarters of 2009.
Annual change. This compares the total or average for one calendar or fiscal year with the previous one. For example, orders in 2009 were 2.7% higher than in 2008.
Change to end-year. This compares end-year with end-year: for example, orders fell by 2.1% over the four quarters to end-2009.
How to use Table 2.6.
Locate in column 1 any observed rate, say a 1% monthly increase in consumer prices. If this rate continues, prices will double after almost 70 months (column 2) and increase by 12.7% in a year (final column). If the 1% change took place over one quarter (three months), the doubling time is 70 quarters (column 2) and the annual rate of increase is 4.1% (column 3).
Table 2.6 Annualised and doubling rates
Table 2.6 shows annualised rates for a selection of simple rates. US commentators tend to focus on annualised rates. This makes it easy to compare monthly or quarterly changes with annual rates, but it can be misleading. Many economic figures bump around from month to month, and annualised rates exaggerate erratic fluctuations. A mere 0.1% change in a month adds 1.2% to the annualised figure. Columns C and D of Table 2.7 (see page 26) compare simple and annualised changes and show how annualising can emphasise erratic fluctuations.
Table 2.7 Analysing seasonal and erratic influences
Each week The Economist shows changes in indicators such as industrial production and consumer prices as the percentage change over 12 months.
The arithmetic for dealing with growth rates
1 To find the growth rate over several periods when the rate over one period is known.
Note on step 3
Raising a number to the power of n is a shorthand way of saying multiply it by itself n times. For example, 23 = 2 × 2 × 2 = 8. Use the calculator key marked xy (the letters might be slightly different) to perform this operation. If there is no xy key use logarithms (the LOG and 10x or LN and ex keys). Replace step 3 with the following.
The formula for these calculations is [(1 + r/100)n − 1] × 100 or, for PC spreadsheet users, = ((1 + r/100)^(n) −1)*100.
2 To find the growth rate over one period when the rate over several periods is known
Note on step 3
If your calculator does not have an x1/y key, use logarithms (the LOG and 10x or LN and ex keys). Replace step 3 with the following.
The formula for these calculations is [(1 + r/100)1/n − 1] × 100 or, for PC spreadsheet users, = ((1 + r/100)^(1/n) −1)*100.
Moving averages
One way to smooth out erratic fluctuations is to look at an average. When reviewing, say, total high street sales in June, you might take an average of figures for May, June and July. A sequence of such averages is called a moving average. Column E of Table 2.7 (page 26) and the footnote show the calculation of a three-month moving average for a short run of data.
The moving average can average any number of periods. A five-year moving average helps to smooth out the economic cycle described on pages 55–59, although a lot of data would be needed to calculate it. Moreover, the more periods covered by a moving average, the slower it will be to show changes in trend.
Seasonality
Most economic figures show a seasonal pattern that repeats itself every year. For example, prices of seasonal foods rise in the winter, sales of beachwear increase with the onset of summer, and industrial production falls in the months when factories close for annual holidays.
Seasonal adjustment
There is a simple numerical process called seasonal adjustment which adjusts raw data for the observed seasonal pattern. Briefly, if sales or output in February are typically 85% of the monthly average, the seasonal adjustment process divides all observations for February by 85%.
Many published figures are seasonally adjusted to aid interpretation, but it is important to remember that seasonal adjustment is not infallible. For example, in a particularly cold month energy use increases by more than the amount expected by seasonal adjustment, while more building workers than usual are temporarily laid
off. The adjusted figures might be erroneously taken to suggest that energy use or unemployment was rising when the underlying situation was very different. Climatic and other influences might be overlooked when viewing the economy from the comfort of seasonally adjusted data.
Coping with seasonality and blips
Table 2.7 indicates some problems of interpreting data which are subject to erratic or seasonal influences.
The figures in column A are an index of retail sales. At first glance it appears that sales in January 2010 were very poor, since there was a 4% decline from the previous month (column B). It seems that this interpretation is confirmed because the 4% fall is worse than the 0.2% decline in the same month a year earlier.
The percentage changes over 12 months (column D) give some encouragement. They indicate that the trend in sales is upward, though growth over the 12 months to January 2010 (6.2%) was slacker than in the previous few months (around 10%).
Column F smooths out short-term erratic influences by comparing sales in the latest three months with sales in the same three months a year earlier. This suggests that the fall in January was not as severe as it appeared at first glance, with the 12-month growth rate remaining at close to 10%.
This final interpretation is the correct one. Indeed, a full run of figures would show that sales fell in January only because this was a correction to an exceptionally steep rise in the earlier few months.
Commentators are inclined to interpret blips as changes in trend. In general you should examine a run of data, form a view about the trend, and stick to it until there is clear evidence that the trend has changed.
Chapter 3
Measuring economic activity
GDP should really stand for grossly distorted picture.
The Economist
Total economic activity may be measured in three different but equivalent ways.
Perhaps the most obvious approach is to add up the value of all goods and services produced in a given period of time, such as one year. Money values may be imputed for services such as health care which do not change hands for cash. Since the output of one business (for example, steel) can be the input of another (for example, automobiles), double counting is avoided by combining only “value added”, which for any one activity is the total value of production less the cost of inputs such as raw materials and components valued elsewhere.
A second approach is to add up the expenditure which takes place when the output is sold. Since all spending is received as incomes, a third option is to value producers’ incomes.
Thus output = expenditure = incomes.
The precise definition of economic activity varies. The three main concepts are gross domestic product, gross national product and net national product.
Gross domestic product
GDP is the total of all economic activity in one country, regardless of who owns the productive assets. For example, Britain’s GDP includes the profits of a foreign firm located in Britain even if they are remitted to the firm’s parent company in another country.
Gross national income or gross national product
GNI, a term which has replaced GNP in national accounts, is the total of incomes earned by residents of a country, regardless of where the assets are located. For example, Britain’s GNI includes profits from British-owned businesses located in other countries.
Net national income
The “gross” in GDP and GNI indicates that there is no allowance for depreciation (capital consumption), the amount of capital resources used up in the production process due to wear and tear, accidental damage, obsolescence or retirement of capital assets. Net national income is GNI less depreciation.
The relationship between the three measures is straightforward:
Capital consumption
Capital consumption is not identifiable from a set of transactions; it can only be imputed by a system of conventions. For example, when investment spending of $1m on a new machine is included in GDP figures, national accounts statisticians pencil in depreciation of, say, $100,000 a year for each of the next ten years. This gives a stinted view of productive capacity. After five years the machine might still be producing at full capacity, but the national accounts would show it as capable of producing only half the volume that it could when new.
Choosing between GDP, GNI and NNI
Net national income (NNI) is the most comprehensive measure of economic activity, but it is of little practical value due to the problems of accounting for depreciation. Gross concepts are more useful.
All the major industrial countries now use GDP as their main measure of national economic activity. America, Germany and Japan, which had until the early 1990s focused on GNP, now use GDP. The difference between GDP and GNI or GNP is usually relatively small, perhaps 1% of GDP, but there are a few exceptions; for example, in 2007 Ireland’s GDP was 19% bigger than its GNI, owing to the profits earned by foreign investors in the country. In the short term a large change in total net property income has only a minor effect on GDP. When reviewing longer-term trends, it is advisable to check net property income to see if it is making GNI grow faster than GDP.
Net material product
Some countries in the past, mainly centrally planned economies, used net material product (NMP) to measure overall economic activity. NMP was less comprehensive than GDP because it excluded “non-productive services”, such as banking, government administration, health and education, and was quoted net of capital consumption (depreciation). As a rule of thumb, NMP was roughly 80–90% of GDP.
Omissions
Deliberate omissions
There are many things which are not in GDP, including the following.
Transfer payments. For example, social security and pensions.
Gifts. For example, $10 from Aunt Agatha on your birthday.
Unpaid and domestic activities. If you cut your grass or paint your house the value of this productive activity is not recorded in GDP, but it is if you pay someone to do it for you.
Barter transactions. For example, the exchange of a sack of wheat for a can of petrol.
Second-hand transactions. For example, the sale of a used car (where the production was recorded in an earlier year).
Intermediate transactions. For example, a lump of metal may be sold several times, perhaps as ore, pig iron, part of a component and, finally, part of a washing machine (the metal is included in GDP once at the net total of the value added between the initial production of the ore and its final sale as a finished item).
Leisure. An improved production process which creates the same output but gives more recreational time is recorded in the national accounts at exactly the same value as the old process.
Depletion of resources. For example, oil production is recorded at sale price minus production costs and no allowance is made for the fact that an irreplaceable part of the nation’s capital stock of resources has been consumed.
Environmental costs. GDP figures do not distinguish between green and polluting industries.
Allowance for non-profit-making and inefficient activities. The civil service and police force are valued according to expenditure on salaries, equipment, and so on (the appropriate price for these services might be judged to be very different if they were provided by private companies).
Allowance for changes in quality. You can buy very different electronic goods for the same inflation-adjusted outlay than you could a few years ago, but GDP data do not take account of such technological improvements.
Some of the exclusions can be identified elsewhere. For example, environmental costs are seen in statistics on pollution and most countries report known oil or coal reserves (although these estimates may be over-optimistic or clouded by genuine ignorance about the size of underground reserves).
One other point to note is that the more advanced government statistical agencies include in GDP an allowance for the imputed rent paid by home owner-occupiers. This avoids an apparent change in nati
onal output because of any switch between owner-occupation and renting.
Surveys and sampling
Many of the figures which go into GDP are collected by surveys. For example, governments ask selected manufacturing or retailing companies for details of their output or sales each month. This information is used to make inferences about all manufacturers or all retailers. Such estimates may not be correct, especially as the most dynamic parts of the economy are small firms constantly coming into and going out of existence, which may never be surveyed.
Sample evidence is supplemented by other information, including documentation required initially for bureaucratic purposes such as customs clearance or tax assessment. Such data take a long time to collect and analyse, which is why economic figures are frequently revised even when they are several years old.
Unrecorded transactions
GDP may under-record economic activity, not least because of the difficulties of keeping track of new small businesses and because of tax avoidance or evasion.
Deliberately concealed transactions form the black, grey, hidden or shadow economy. This is largest at times when, and in countries where, taxes are high and bureaucracy is smothering. Estimates of the size of the shadow economy vary enormously. For example, differing studies put America’s at 4–33%, Germany’s at 3–28% and Britain’s at 2–15%. What is agreed, though, is that among the industrial countries the shadow economy is largest in Greece, at perhaps 30% of GDP, followed by Italy, Portugal and Spain, while the smallest black economies are in Japan, Switzerland and America at around 10% of GDP.
Guide to Economic Indicators Page 3