Ph. Brion Insee The contribution of different ways of dealing with non-responses in french business surveys

Page 2 Introduction  The lecture will focus on annual enterprise surveys  For a general presentation of these surveys, see Rivière (Courrier des statistiques, 1997), particularly for the data editing method  Main subject of the lecture : the question of the timeliness (business surveys are mail surveys) and of the follow-up of non-respondents

Page 3 The treatment of non-responses  Sampling plan of the annual enterprise surveys : sampled strata (small and medium enterprises), exhaustive strata (big enterprises)  Non-responses : first, remind letters / visits of enumerators, depending on the size of the units  In the end, the treatment of « final » non-responses is also different according to the size of the enterprises  Small and medium enterprises : use of conventional statistical technics  Big enterprises : use of fiscal data (less complete than survey data)

Page 4 Two kinds of questions  1. Is it possible to define priorities for the follow-up of the non-respondents ? Is it possible to decide to publish some results, with given rates of responses ?  2. Generally, the estimation of the error is made, for the exhaustive part, as it was zero : is this approximation acceptable in this case ?  Use of a « framework » to quantify the amount of error due to each of the two categories of enterprises

Page 5 Formalizing the problem (1) : estimator used for small and medium entreprises

Page 6 Formalizing the problem (2) : estimator used for small and medium enterprises  Estimator of the total of a variable as the turnover of a given domain (economic sector), due to the stratum k :

Page 7 Formalizing the problem (3) : estimator used for big enterprises

Page 8 Formalizing the problem (4) : estimator used for big enterprises  For the big enterprises non-respondents, we get the value of the turnover in the fiscal source, and use the value of the APE (principal activity) code of the business register (approximation) : the estimator of the total of turnover due to the stratum h (for a given domain) is :

Page 9 Formalizing the problem (5) : estimator of the total (calculated on the two categories: small and medium, and big enterprises)  Sum on all strata (h and k)  Wrong classifying of some big enterprises introduces a bias  The two categories (small and medium, and big enterprises) give variance

Page 10 Formalizing the problem (6) : total mean square error  With :  And : is the « corrected » variance of

Page 11 Use of these indicators  During the execution of the survey : use of the values of A h, B h, S k calculated the previous year to decide to publish results for a given domain, by comparing the value of the mean square error to an expected level  « Remind strategy » : introducing cost elements : C1 = remind for a small or medium enterprise C2 = visit for a big enterprise  Minimize mean square error with a budget constraint

Page 12 First quantified results for the wholesale trade sector, variable = turnover ClassPrecision (coefficient of variation) Non-responses rate for big enterprises « Stability » rate for big enterprises Fee or contract basis 0.9%13%96.6% Agricultural raw materials, live animals 11%8%99.3% Food, beverages, tobacco 1.2%11%98.5% Household goods 2.4%14%97.2% Intermediate products 1.4%12%97.5% Machinery, equip., supplies 1.8%10%97.9% Other wholesale 7.8%16%98.3%

Page 13 First quantified results for the wholesale trade sector, variable = turnover ClassShare of the first term (square of bias) Share of 2nd term (variance big enterprises) Variance small medium enterprises Fee or contract basis 3%2.7%94.3% Agricultural raw materials, live animals --100% Food, beverages, tobacco 1.2%4.3%94.5% Household goods 1.4%1.3%97.3% Intermediate products 6%0.5%93.5% Machinery, equip., supplies -0.1%99.9% Other wholesale 0.6%7.1%92.3%

Page 14 Conclusion, further developments  Back to hypotheses  Further developments for other variables  Within the population of big enterprises, there are differences …  For small and medium enterprises, refine the treatment of non-respondents with the use of fiscal infra-annual data