Comparing Estimation Methods in Product Surveys

Comparing Estimation Methods in Product Surveys • Ismo Teikari • ICES III • Montreal June 18-21.2007

What is PRODCOM ? • PRODCOM is the nomenclature for the EU production statistics • for mining and quarrying, manufacturing, and electricity, gas and • water supply. • It involves compilation of EU sales and production data from • information provided by Member States mainly on annual basis, • for some 5700 selected PRODCOM codes It is updated annually.

Background for the study • Due to the 5700 PRODCOM codes, especially in small countries as in Finland there happen to be many headings which have only one producer. This makes it difficult to have a control over all PRODCOM codes using the random sampling. • In the past in Finland the survey was yearly, including all establishments having more than 10-20 employees. • To reduce the size of the survey the establishment unit is now replaced by the enterprise unit. • Further the small enterprises having 10 to 20 employees will be rotated so that all small enterprises will be surveyed every second year. • The new enterprises will be forced to be included in the sample.

Problem We want to see if the selected method gives better results than the traditional survey methods. For this we have prepared a test frame including some randomly chosen enterprises which produce products having one producer, products having two producers, products having three producers etc. In this frame we will compare so called rotation method with the traditional sampling methods. Also we will study how many producers will be required to have sufficiently accurate estimates. The problem is the one of domain estimation, where the domains are the PRODCOM classes.

Initial Frame • Small firms (10-20 employees) are selected from PRODCOM statistics in years 2002 and 2003. • Some PRODCOM codes were eliminated because of changes in the code between 2002 and 2003. • Changes in business structures are taken into account in this paper • In 2003 the number of PRODCOM -codes was 1159 out of which 580 are single producer headings • For these 1159 products there are 3751 producers.

Final frame ( two steps) • First step • 1. Number of producers for each PRODCOM code is calculated2. The frame was arranged so that 10 such PRODCOM codes were selected which has 1 or 2 or 3 producers • 5 such PRODCOM codes were selected which has 4 or 5 or … 10 producers • All such PRODCOM codes were chosen which has more than 10 producers

Second step • All producers and needed information for the above chosen PRODCOM codes is read from the initial frame. • The final frame included 650 producers for 199 PRODCOM codes

Estimation Methods 1. HT-estimator 2. Ratio estimator 3. Rotation estimator

Rotation estimator can be seen as a ratio estimator for a particular choice of the auxiliary variable Used auxiliary variable Ratio estimator takes the form So the Method of estimation gets the formula

Simulation 1000 samples was drawn for each estimator and the following MC-estimates was calculated for each estimator.

Means of MC-estimators

Table for and for

Table for

Comparing Estimation Methods in Product Surveys