1. 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

2. Goals of the system – Consistent with NA. – (As far as possible) free of assumptions.

3. 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)

4. Input / output model 1 Capital K Labour L Goods Energy E Unit Materials M Services Services S Input:Gross Output: Cost Revenue

5. Input / output model 2 Capital K Labour L Revenue Unit E,M,S Cost Input:Output: Cost Value added

6. Productivity measures K and LK,L,E,M,STotal factor - Combination of K,L,E,M,S Multi factor K or L K or L or E or M or S Single factor Value addedGross output Output Input

7. 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

8. 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.

9. 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.

10. 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.

11. User cost over year t (ex post) For unit of asset of age j (at midyear) that is available at start of period t : u t j = r t+,t- P t- j-0.5 + (P t- j-0.5 – P t+ j+0.5 ) (j=1,…,J). For unit of asset of age j (at midyear) that is invested at midyear : v t j = r t+,t P t j + (P t j – P t+ j+0.5 ) (j=0,…,J).

12. User cost (2) where r denotes nominal interest rate and P’s are prices (valuations). Total user cost of this asset type is U t = ∑ u t j K t j + ∑ v t j I t j, where K and I are quantities of assets (available at start of year and invested resp.).

13. User cost (3) Basic time-series depreciation model is P t+ j+0.5 / P t- j-0.5 = (P t+ 0 / P t- 0 )(1 – δ j ) where δ j is annual cross-section depreciation rate (from an age-price profile). Start / end of period prices are approximated by midyear prices.

14. User cost (4) New asset price ratios P t+ 0 / P t- 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.

15. Capital stock and investment – No quantities K j t but estimates of values (from PIM system). – All revaluations by PPIs. – No quantities I j t but values (from investment survey). – Depreciation calculated by δ j → CFC

16. 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).

17. 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.

18. 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 P t+ 0 / P t- 0 are estimated by CPI (for all goods) (Tables 6 and 7). – User cost: New asset price ratios P t+ 0 / P t- 0 are estimated by PPIs (for all goods) (Tables 8 and 9).

19. 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 P t+ 0 / P t- 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).