Productivity Measurement at
Statistics Netherlands
Dirk van den Bergen, Myriam van RooijenHorsten, 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
Labour
Energy
Materials
Services
K
L
E
M
S
Input:
Cost
Goods
Unit
Services
Gross Output:
Revenue
Input / output model 2
Capital
Labour
K
L
Revenue
Unit
E,M,S Cost
Input:
Cost
Output:
Value added
Productivity measures
Output
Gross output
Value added
Single factor
K or L or E
or M or S
K or L
Multi factor
Combination of
K,L,E,M,S
-
Total factor
K,L,E,M,S
K and L
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 (= nettingout 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+,tPtj + (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 Ktj + ∑ vtj Itj ,
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 selfevident 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 selfemployed (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(IPRODGO) and Domarfactor ≡ GO / VA ≥
1(Tables 20-23).