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).