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

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.)

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

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)

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

Simple Volume Indexation Imagine the price of your favourite commodity.

=100x(£2.41/£2.41)£ =100x(£3.24/£2.41)£ =100x(£3.13/£2.41)£ =100x(£3.00/£2.41)£ =100x(£2.88/£2.41)£ =100x(£2.79/£2.41)£ =100x(£2.70/£2.41)£ =100x(£2.62/£2.41)£ =100x(£2.55/£2.41)£ =100x(£2.48/£2.41)£ IndexFormulaPriceYear

Man cannot live on beer alone

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?

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

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”

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

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

Examples of Volume Index Calculations Year price (£) Number purchased per annum Amount spend on CDsMP3sCDsMP3sCDsMP3s Exercise: Calculate Base and Current Weighted Volume Indices for these data.

Comparison Number purchased per annum Laspeyres volume index Paasche volume index CDsMP3s

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

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

Geometric Mean = 

Fisher “ideal” index

Comparison Number purchased per annum Laspeyres Volume index Paasche Volume index Fisher Volume Index CDsMP3s

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

Chainlinking is Beyond the scope of this seminar

But it looks a bit like this.

Price Index Calculations Handout. YearBPICTPI

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

Time Series Analysis

Typical input series

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;

A Store Retail Series ,000 1,500 2,000 2,500 3,000 3,500 4, Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q4

MA t =average(x t-0.5,x t-1.5,x t+0.5,x t+1.5 ) A Store Retail Series ,000 1,500 2,000 2,500 3,000 3,500 4, Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q4 Raw Data4-Point Moving Average

MA t =(x t-2 + 2*(x t-1 + x t + x t+1 ) + x t+2 )/8

MA t =(2*x t + 2*x t-1 + x t-2 )/5 A Store Retail Series ,000 1,500 2,000 2,500 3,000 3,500 4, Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q4 Raw Data2 by 4 Moving Average

A Store Retail Series ,000 1,500 2,000 2,500 3,000 3,500 4, Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q42005Q12005Q22005Q32005Q4 Raw Data2 by 4 Moving Average

Revisions

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.

Comparison of MA with Exponential Smoothing for Volatile Soure Data Source Data2*4 MAExponentially Smoothed

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

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.

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

Additive and Multiplicative series Additive series – seasonal effects are constant Multiplicative series – seasonal effects grow as series grows (and vice versa)

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

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.

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?

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

Automatically identified as an ‘unusual’ value and effect scaled

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

Decomposing Seasonal-Irregular Components into individual quarters…

Combining Seasonal Components for the individual quarters…

‘Outliers’ put back in 8923-=

X-12-ARIMA actual process

Question What was the quarterly change in Energy Use in the second quarter of 2009? In 2009Q1 the index was 121 and in 2009Q2 it was 79 giving a 35 per cent decrease. In 2009Q1 the seasonally adjusted index was 89 and in 2009Q2 it was 95 giving a 7 per cent increase.

Level Shift A step change In GDP could be caused by companies opening/closing Seasonal Break A change in the seasonal pattern In GDP could be caused by administrative changes

Exercise Discuss the charts on the handouts indentifying outliers, level shifts and seasonal breaks. Index of sales of motor vehicles, motorcycles and parts Index of sales biscuits, preserved pastry & cakes

1. Index of sales of motor vehicles, motorcycles and parts Seasonal break 1999Q1 Additive Outlier 2001 Q4 Level Shift 2008 Q3?

2. Index of sales biscuits, preserved pastry & cakes Seasonal break 1998Q3 Seasonal break 2002Q3 Additive Outlier 1995Q2 Additive Outlier 2009Q1?

Revisions New data always gives you new information Which will tell you more about your modelling assumptions Revisions are good