Istat - Structural Business Statistics Purpose: to measure the impact of frame errors on SBS sampled-based estimation Contents Sample-based estimates - quality Frame errors The SME survey and the Business register - quality aspects The SME survey sampling and estimation method Simulation study Measures of errors Results and future plans 19th Roundtable Meeting

Istat - Structural Business Statistics Quality: accuracy It denotes the closeness of estimates to the true value Errors: sampling errors non sampling errors coverage (frame) much very much non response much very much processing model measurement variability bias much not much Overall error: MSE = [bias]2 + Variance 19th Roundtable Meeting

Istat - Structural Business Statistics Frame errors (1) under-coverage: BR does not reflect units in scope for the survey omission (lags and leakage) falsely not active units mistakes in stratification variables impact on estimations increasing bias 19th Roundtable Meeting

Istat - Structural Business Statistics Frame errors (2) over-coverage: BR considers in scope businesses that are out duplications falsely active units mistakes in stratification variables impact on estimations increasing bias and sampling error 19th Roundtable Meeting

Istat - Structural Business Statistics Frame errors (3) Incorrect information: units correctly recorded hold incorrect variables stratification v. identification v. (location) For postal survey errors in location cause a non response impact on bias and sampling variance (reduction of the sample size). Frame errors and non-responses are correlated 19th Roundtable Meeting

Istat - Structural Business Statistics SME survey and BR (1) yearly sample survey BR is the frame for sampling and grossing up produces estimates of aggregated economic variables (turnover, value added at factor cost, total purchases of goods and services, personnel costs,..) In the estimation process frame errors and non-responses are treated similarly sampling errors are calculated (CVs) Errors in the BR Errors in estimations 19th Roundtable Meeting

Istat - Structural Business Statistics SME survey and BR (2) Tool: Statistical information system To manage links between each surveys (SBS and STS) and the BR (by the unique ID code) to monitor surveyed information for samples coordination ( to reduce statistical burden) to record response (non response) 19th Roundtable Meeting

Istat - Structural Business Statistics SME survey and BR (3) Quality information: a system of DATE reference date of the survey date questionnaires have been sent response date a system of CODES 1) Respondents 2) Total non response 3) not useful data 4) Rejected, unknown, moved 5) Units are ceased, not active, in bankruptcy 19th Roundtable Meeting

Istat - Structural Business Statistics Quality information- Dates 19th Roundtable Meeting

Istat - Structural Business Statistics SME survey and BR (4) CODES Type 4 (rejected, unknown, moved ) and type 5 (units ceased, not active, in bankruptcy) FRAME ERRORS type 4 counts for errors in location variables (i.e. ADDRESS) type 5 depends on delay in BR updating (i.e. state of activity) 19th Roundtable Meeting

Istat - Structural Business Statistics 19th Roundtable Meeting

Istat - Structural Business Statistics The SME survey sampling and estimation method target population: enterprises <100 persons employed Stratified simple random sample 26,000 strata (NACE Rev.1.1, Size, Region) sample size:120,000 Survey technique: postal questionnaire; 2 call-backs Calibration estimators methodology (Deville and Särndal,1992): - estimates are constrained to two auxiliary variables, known totals in the population (n.of enterprises and persons employed) 19th Roundtable Meeting

Istat - Structural Business Statistics Simulation study (1) Variable of interest: Business Turnover (SME estimate) (BT) Variable used in the estimation process: Business fiscal turnover (BFT) High correlation between BT and BFT BFT (Fiscal register) Advantage Availability for the whole BR population Disadvantage Lack of quality (missing and outliers) 19th Roundtable Meeting

Istat - Structural Business Statistics Simulation study (2) Data set 1 =respondent units to SME Data set 2 =respondent units to SME+ non respondent units to SME for frame errors Estimate 1 ( ) and Estimate 2 ( ) are calculated at NACE 3-digits. Measures of errors: Bias Sampling error (CVs) MSE 19th Roundtable Meeting

Istat - Structural Business Statistics Effect on estimates’ bias (1) 19th Roundtable Meeting

Istat - Structural Business Statistics Effect on estimates’ bias (2) 19th Roundtable Meeting

Istat - Structural Business Statistics Effect on estimates’ sampling error 19th Roundtable Meeting

Istat - Structural Business Statistics Effect on estimates’ sampling error 19th Roundtable Meeting

Istat - Structural Business Statistics Effect on estimates’ sampling error 19th Roundtable Meeting

Istat - Structural Business Statistics MSE=(bias)2 + sampling variance 19th Roundtable Meeting

Istat - Structural Business Statistics 19th Roundtable Meeting

Istat - Structural Business Statistics Results Overestimate of the BFT in the population (both estimate 1 and estimate 2) The inclusion of Frame errors : reduces the bias (estimate 2 is lower that estimate 1) reduce the sampling variance (sample size increase) improvement of MSE 19th Roundtable Meeting

Istat - Structural Business Statistics Interpreting results and future plan the estimation method the peculiarity of the variable of interest (very high figures) the structural difference between the respondents and the frame errors units Next step: to add a further constrain to the estimates procedure of economic variables that is the BFT in order to reduce bias 19th Roundtable Meeting