Eurostat

Macro integration

Presented by

Piet Verbiest

Statistics Netherlands

Macro integration

Reconciliation of inconsistent statistical data on a high level of aggregation

Balancing is reconciling inconsistent statistical information from independent sources brought together in an ‘accounting’ framework consisting of well-defined variables, accounting identities on combinations of variables and other less strict relations between the sets of variables.

Macro integration

National accounts an example

National accounts• Comprehensive overview of all economic transactions in

a country• Quarterly and annual report of a country

Key indicators Gross domestic product (GDP): economic growth; Gross national income Consumption of households, investment, foreign trade Government debt Employment

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Labour accounts

National accounts in the Netherlands

Supply and use tables

Sector accounts

Supply and use tables

Variables and basic identities identities(1) P + M = IC + C + I + E(2) Y = P - IC(3) Y = C + I + E - M(4) Y = W + OS/MI

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What we want:

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GDP production method 930 - 460 = 470GDP expenditure method 350 + 90 + 300 - 270 = 470

P M IC C I EThe Netherlands ltd 930 + 270 = 460 + 350 + 90 + 300

What we get:

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P M IC C I EThe Netherlands ltd 930 + 245 ≠ 450 + 350 + 90 + 275

GDP production method 930 - 450 = 480GDP expenditure method 350 + 90 + 275 - 245 = 470

P M IC C I EThe Netherlands ltd 930 + 245 ≠ 450 + 350 + 90 + 275

Whisky 5Other 930 + 240 ≠ 450 + 350 + 90 + 275

Macro integration / balancing

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GDP production method 930 - 450 = 480GDP expenditure method 350 + 90 + 275 - 245 = 470

5355

475355

Macro integration / balancing

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P M IC C I EThe Netherlands ltd 930 + 245 ≠ 450 + 355 + 90 + 275

Whisky 5 5Crude oil 40 20

Other 930 + 200 430 + 350 + 90 + 275

GDP production method 930 - 450 = 480GDP expenditure method 355 + 90 + 275 - 245 = 475

Industry dataRefineries

Production Fuel 30

Intermediate consumptionCrude oil 20other 5

Value added 5

20

225

495225

Macro integration / balancing

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GDP production method 930 - 450 = 480GDP expenditure method 355 + 90 + 275 - 225 = 495

P M IC C I EThe Netherlands ltd 930 + 225 ≠ 450 + 355 + 90 + 275

Whisky 5 5Crude oil 20 20Tablets 60 30 10

Components 50Other 870 + 200 ≠ 380 + 320 + 80 + 275

Industry dataComputer industry

ProductionTablets 60

Intermediate consumptionComponents 50other 5

Value added 5

20

295 275

295

50

465

275

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SUPPLY USEOutput of

industries Impo

rt

Tota

l

Input ofindustries

Cons

Expo

rt

Inve

st.

Tota

l

Com

mod

ities

YTotal P M IC+Y C E I

Value added

=P IC+ Y = GDP

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SUPPLY USE

Output of

industries Impo

rt

Tota

l

Input ofindustries

Cons

.

Expo

rt

Inve

st.

tota

l

Com

mod

ities

Y

Total P M IC+Y E C I

P - IC = Y = GDP P–IC = Y =C+I+E-M

P M IC C IE+ + ++=

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Commodities: 500 Industries: 150 Final expenditure: 20 Simultaneous: cup and cop

Domestic production Imports Total Final Totalsupply expenditure use

basic prices cif

Valuation

Taxes/

margins

subsidieson products

Value addedTotal output

Intermediate consumption

purchasers prices excl. VAT

Use tableSupply table

Total output

Non deductable VAT

trade andtransport

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Eurostat

Macro integration

Presented by• Jacco Daalmans

• j.daalmans@cbs.nl

Mathematical models

2+9=10

5=7

15/2=722=17

1=0

3+7=106=6

22=17+5

Mathematical Models

12+3+10=25

Mathematical models• Can be automated

• Reproducible results

• Flexible

• Large scale applications

BUT: Small discrepancies, without known cause

Example 1: WhiskyImports = Consumption

Given:

Imports = 5, Consumption=0

Model outcome could be: Imports= 2.5 Consumption = 2.5

NOT DESIRABLE!

Example 2: Remaining discrepancies

Production (P) = 930 Imports (M) = 275 Interm. Cons. (IC)= 450 Cons. Invest. Export (CIE)= 740

P+ M = IC + CIE 1205 ≠ 1190 P – IC = CIE – M 480 ≠ 465

Example 2: Remaining discrepancies

Production (P) = 930 928Imports (M) = 275 272Interm. Cons. (IC)= 450 455Cons. Invest. Export (CIE)= 740 745

P+ M = IC + CIE 1205 ≠ 1190 1200=1200P – IC = CIE – M 480 ≠ 465 473=473

Different models• RAS/IPF/RAKING

- easy, numerical technique - for a specific problem• STONE - broad scope of applicability

- mathematical optimization• DENTON (benchmarking)

- Time component (quarterly and annual data)

STONE’s Method• Broad applicability

• Achieves consistency by solving a minimum adjustment problem

STONE’s MethodSearches for a result with minimum deviation from the input.

Mathematical:Translation to a least squares optimization problem

Consistency rules translate to constraints of the model.

STONE’s MethodLinear constraints, like:

• Total is the sum of components: Manufacturing = Food + Textiles + Clothing;• Commodity balances; Total use = Total supply;• Definitions: Value added = Output – Intermediate consumption

ExtensionsInequality constraints:

Total Use ≥ 0Soft constraints:

Stocks of perishables goods ≈ 0Ratio constraints:

Value added Tax / Supply = 0.21

Refineries: use of crude oil / output ≈ 0.7

A man with a watch

knows what time it is

A man with two watches

is never sure

(Segal’s Law)

Reliability weightsImportant instrument to steer the results.

Example 2: Remaining discrepancies

Production (P) = 930 928 Imports (M) = 275 272 Interm. Cons. (IC)= 450 455 Cons. Invest. Export (CIE)= 740 745

P+ M = IC + CIE 1200=1200 P – IC = CIE – M 473=473

Example 2: Remaining discrepancies

Production (P) = 930 928 930Imports (M) = 275 272 270 Interm. Cons. (IC)= 450 455 450Cons. Invest. Export (CIE)= 740 745 750

P+ M = IC + CIE 1200=1200 1200=1200P – IC = CIE – M 473=473 480= 480

green = p and IC more reliable

Conclusions

Mathematical methods powerful instrument

Elaborate modelling constructions possible

But should be used properly!