Understanding Economic Indicators

1. Understanding Economic Indicators Scottish GDP as a case study in Indexation and Time Series Methods

2. What is GDP • “Size” of economic output • Overall Value (Annual) • Blue book, IO tables • Short Term Trend Indicators • More frequent (quarterly) • (ONS do three estimates that successively incorporate three types of data.)

3. GVA concept • Turning grapes into wine generates GVA • Opening the bottle for you in a nice environment generates GVA • Burning coal and transmitting power along lines generates GVA • It’s a measure of “economic activity” • GDP is the sum of all the GVA in the economy

4. Main Techniques 1 • Sample Surveys • Mainly collected in cash values at current prices • Aggregated using standard techniques • Ratio estimation • Deflation • To convert current price to volume (constant price)

5. Main Techniques 2 • Index numbers • To generate series that are comparable between different industries – there are no “units” • To weight together disparate measures to provide a whole economy picture • Time Series methods • To allow publication of comparable quarterly figures for industries that are not comparable quarter by quarter

7. Simple Volume Indexation • Imagine the price of your favourite commodity.

8. Year Price Formula Index 100.00 2000 £2.41 =100x(£2.41/£2.41) 2001 £2.48 =100x(£2.48/£2.41) 102.9 2002 £2.55 =100x(£2.55/£2.41) 105.8 2003 £2.62 =100x(£2.62/£2.41) 108.7 2004 £2.70 =100x(£2.70/£2.41) 112.0 2005 £2.79 =100x(£2.79/£2.41) 115.8 2006 £2.88 =100x(£2.88/£2.41) 119.5 2007 £3.00 =100x(£3.00/£2.41) 124.5 2008 £3.13 =100x(£3.13/£2.41) 129.9 134.4 2009 £3.24 =100x(£3.24/£2.41)

9. Man cannot live on beer alone

10. Obvious Strategy • Is to track the rate of change of a weighted sum of the quantities of interest. • E.g. price of an evenings entertainment: 2 x + 1 x + 2/77 x But what about appropriate weights?

11. General price indices use a “basket” of goods “Currently, around 120,000 separate price quotations are used every month in compiling the indices, covering some 650 representative consumer goods and services” ONS CPI Note http://www.statistics.gov.uk/articles/nojournal/CPI-Basket-of-Goods-2009.pdf

13. Price vs Volume • A volume index: • Aims to track change in quantities • Market price is an often used weight • A price index: • Aims to track price • i.e. inflation • Typically based on a basket of “output”

14. Base Weighted Volume Index Index of weighted volume Weights come from base year Also known as Laspeyres

15. Current Weighted Volume Index Index of volume Weights come from current year Also known as Paasche

16. Examples of Volume Index Calculations Exercise: Calculate Base and Current Weighted Volume Indices for these data.

17. Comparison

18. Economics • People buy more things that get cheaper • And less things that get more expensive • Known as the “Substitution effect” • Laysperes index ignores this • Artificially high weight to fast growing/falling price commodities • Paasche over weights its influence • Artificially low weight to fast growing/falling priced commodities

19. More Economics • Laysperes generally considered an upper bound for growth • Paasche generally considered a lower bound for growth • “True Growth” is somewhere in between

20.  Geometric Mean =

21. Fisher “ideal” index

22. Comparison

23. Chainlinking • Fisher is indeed an “ideal” measure • But to compute it, you need price and volume data with the same resolution you want to publish • In practice we use “chainlinking” on Laspeyres type indices

24. Chainlinking isBeyond the scope of this seminar

25. But it looks a bit like this.

26. Price Index Calculations • Handout.

27. Answers Beer 2000 – 2004: 12.0% Cheese Toasty 2000-2004: -7.4% Beer 2004-2009: Cheese Toasty 04-09: Average Rate: Well, i.e. 3.9%

28. Time Series Analysis

29. 700 500 300 100 - 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 1 2 3 4 5 6 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 2000 2001 2002 2003 2004 2005 2006 2007 2008 Typical input series

30. Smoothing and Moving Averages • Some data sources are highly volatile and/or seasonal; • We may not be interested in these short-term fluctuations; • Smoothing reduces these fluctuations and makes it easier to identify long-term trends;

31. A Store Retail Series 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 - 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4

32. A Store Retail Series 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 - 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 Raw Data 4-Point Moving Average MAt = average(xt-0.5,xt-1.5,xt+0.5,xt+1.5)

33. A Store Retail Series 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 - 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 Raw Data 4-Point Moving Average 2 by 4 Moving Average MAt= (xt-2 + 2*(xt-1 + xt + xt+1) + xt+2)/8

34. A Store Retail Series 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 - 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 Raw Data 2 by 4 Moving Average MAt= (2*xt + 2*xt-1 + xt-2)/5

35. A Store Retail Series 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 - 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 2005Q1 2005Q2 2005Q3 2005Q4 Raw Data 2 by 4 Moving Average

36. Retail - Predominantly Non-food Store 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 - 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 2005Q1 2005Q2 2005Q3 2005Q4 Raw Data Previous 2 by 4 MA Revised 2 by 4 MA Revisions

37. Exponential Smoothing • Applies exponentially decreasing weights to observations as they get older; • Alpha is essentially the proportion of the most recent data point that is allowed through; • Fresh data doesn’t cause revisions; • Movements are lagged compared with moving averages.

38. Comparison of MA with Exponential Smoothing for Volatile Soure Data 300 250 200 150 100 50 0 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Source Data 2*4 MA Exponentially Smoothed

39. Choice of Alpha • Alpha can be between 0 and 1; • Generally this is a judgement call; • but if it looks like we need a small alpha (below 0.7) then… • Optimal value is one that minimises the Mean Squared Error: • i.e. the sum of

40. Summary • Moving Average • Approximates the trend line; • Can remove seasonality; • Has difficulty at end points; • Prone to revisions. • Exponential Smoothing • Lags movements in the data; • No Revisions.

41. Decomposing a time series • A time series can be decomposed into: • The trend cycle component (medium and long term growth and cycles in the series) • The seasonal component (effects that are largely stable in timing, size and direction from year to year) • The irregular component (made up of anything remaining e.g. short term fluctuations, sampling and non-sampling errors, unpredictable effects due to one-off events such as strikes or disasters

42. Additive and Multiplicative series • Additive series – seasonal effects are constant • Multiplicative series – seasonal effects grow as series grows (and vice versa) 400 450 400 350 350 300 300 250 250 200 200 150 150 100 100 50 50 0 0 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2000 2001 2002 2003 2004 2005 2006 2007 2008 2000 2001 2002 2003 2004 2005 2006 2007 2008

43. Time Series Models • The additive model is: Time Series = Trend Cycle + Seasonal Component + Irregular Component Y = C + S + I • The multiplicative model is: Time Series = Trend Cycle x Seasonal Component x Irregular Component Y = C x S x I

44. X-12-ARIMA • Developed by the US Census Bureau. • Estimating and removing regular seasonal patterns from time series data. • This leaves the long term trend and short term irregular movements • Worked example – Mains Gas supply (a component series of GDP) which is an additive series.

45. Question • What was the quarterly change in Mains Gas Supply in the second quarter of 2009? • In 2009Q1 the index was 121 and in 2009Q2 it was 79 giving a 35 per cent decrease. • Is this a sensible answer?

46. Outlier Outlier Original Series = Trend-cycle + Seasonal Component + Irregular Component

47. Automatically identified as an ‘unusual’ value and effect scaled

48. Prior Adjusted Series – Initial Estimate of trend = Seasonal + Irregular Component

49. Decomposing Seasonal-Irregular Components into individual quarters…