Productivity Measurement at Statistics Netherlands

Dirk van den Bergen, Myriam van Rooijen-Horsten, Mark de Haan, Bert M. Balk

OECD Workshop, Bern, 16-18 October 2006

Goals of the system

– Consistent with NA.

– (As far as possible) free of assumptions.

Productivity measurement and growth accounting

IPROD ≡ Q(output) / Q(input)

Q(output) = IPROD × Q(input)

ln Q(output) = ln IPROD + ln Q(input)

%Δ (output) = residual + %Δ (input)

Input / output model 1

Capital K

Labour L Goods

Energy E Unit

Materials M Services

Services S

Input: Gross Output:

Cost Revenue

Input / output model 2

Capital K

Labour L Revenue

Unit

E,M,S Cost

Input: Output:

Cost Value added

Productivity measures

K and LK,L,E,M,STotal factor

-Combination of

K,L,E,M,SMulti factor

K or LK or L or E

or M or SSingle factor

Value addedGross output Output

Input

Relations between TFP indices

IPROD-GO ≡ Q(gross output) / Q(KLEMS)

IPROD-VA ≡ Q(value added) / Q(KL)

If profit = 0 then ln(IPROD-VA) =

Domarfactor × ln(IPROD-GO)

Domarfactor ≡ GO / VA ≥ 1

Choice of index formula

– Selection should be based on properties (axioms, tests).

– For the time being: Laspeyres quantity index for year t relative to year t-1, and

chaining for comparisons over longer time spans.

– Sensitivity analysis for alternatives pending.

Aggregation

– Aggregation means consolidation (= netting-out of intra-unit flows).

– No simple relation between IPROD-GO of aggregate and subaggregates.

– Simple relation between IPROD-VA of aggregate and subaggregates.

Capital

– 20 asset types, 60 industries, 18 institutional sectors.

– Age measured from midpoint of year. – Year t has beginning t- and end t+; thus

t = [t-,t+]; t also indicates midpoint.– Scrapping and sales of assets is supposed

to happen at end of year; that is, at t+.– Investment (new and used) happens at midpoint of year and is immediately operational.

User cost over year t (ex post)

For unit of asset of age j (at midyear) that is available at start of period t :

utj = rt+,t-Pt-

j-0.5 + (Pt-j-0.5 – Pt+

j+0.5) (j=1,…,J).

For unit of asset of age j (at midyear) that is invested at midyear :

vtj = rt+,tPt

j + (Ptj – Pt+

j+0.5) (j=0,…,J).

User cost (2)

where r denotes nominal interest rate and P’s are prices (valuations).

Total user cost of this asset type is

Ut = ∑ utj Kt

j + ∑ vtj It

j ,

where K and I are quantities of assets (available at start of year and invested resp.).

User cost (3)

Basic time-series depreciation model is

Pt+j+0.5 / Pt-

j-0.5 = (Pt+0 / Pt-

0)(1 – δj)

where δj is annual cross-section depreciation rate (from an age-price profile).

Start / end of period prices are approximated by midyear prices.

User cost (4)

New asset price ratios Pt+0 / Pt-

0 are estimated by PPIs (for ICT goods) and CPI (for all other; to ensure non-negativity of user cost).

Exogenous nominal interest rate r = α + %ΔCPI. Baseline: α = 0.04.

Taxes less subsidies are added at a higher level of aggregation.

Capital stock and investment

– No quantities Kjt but estimates of values

(from PIM system).

– All revaluations by PPIs.

– No quantities Ijt but values (from investment

survey).

– Depreciation calculated by δj → CFC

Labour

– Two types (employees and self-employed) and 49 industries.

– Unit of measurement: hour worked.

– Assumption: self-employed have same annual income as employees (with one exception).

Other inputs and outputs

– GO, VA and EMS obtained from detailed supply and use tables (120 industries and 275 commodity groups).– Consolidation: problem with trade and transport margins due to the way of recording.– Breakdown of EMS into E, M, and S not self-

evident for any industry.– Allocation of taxes-/-subsidies on production

(according to NA) problematic.

Results 1995-2004 and sensitivity analysis (1)

– Baseline results: Tables 1 (GO) and 2 (VA). – Alternative treatment of trade and transport

margins at consolidation (Table 3).– Different assumption on income of self-employed (Tables 4 and 5).– User cost: New asset price ratios Pt+

0 / Pt-0

are estimated by CPI (for all goods) (Tables 6 and 7).– User cost: New asset price ratios Pt+

0 / Pt-0

are estimated by PPIs (for all goods) (Tables 8 and 9).

Results 1995-2004 and sensitivity analysis (2)

– Exogenous nominal interest rate r = α + %ΔCPI. Alternatives: α = 0.03 and 0.05 (Tables 10-13).– Endogenous r with user cost new asset price

ratios Pt+0 / Pt-

0 estimated by PPIs (for all goods) and two assumptions on income of self-employed (Tables 14-19).

– Comparison of ln(IPROD-VA) / ln(IPROD-GO) and Domarfactor ≡ GO / VA ≥ 1(Tables 20-23).