Productivity Measurement at Statistics Netherlands Dirk van den

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 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+, t. Ptj + (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).