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    7. Actual application: estimation of population gross flows for the PME survey

    Andrés Gutiérrez, Leonardo Trujillo and Pedro Luis do Nascimento Silva

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    The Pesquisa Mensal de Emprego (PME - Brazilian Monthly Labour Survey) is a survey providing monthly indicators about the labour market in the main metropolitan areas in Brazil. Its main aim is to estimate the monthly work force and to evaluate the fluctuations and tendencies of the metropolitan labour market. It is also possible to get indicators regarding the effects of the economic conditions in the labour market and to satisfy important needs for policy planning and socio-economic development. This survey has been conducted since 1980, with some major methodological changes in 1982, 1988, 1993 and 2001 (IBGE 2007).

    This section illustrates the use of the proposed estimators and the final results for the PME are shown. We will consider the panel P6 from this survey from November, 2010 to February, 2011 and then from November, 2011 to February, 2012. This window of observation administered 21,374 interviews to different people. We have chosen the first two measurements of the panel (November and December, 2010) in order to implement the proposed estimation procedure for the corresponding gross flows. Following an algorithm using the library TeachingSampling (Gutiérrez 2009), we obtain the classification at panel P6, for the months of November and December, 2010 given in Table 7.1.

    Table 7.1
    Labour classification and response for the occupation level in the sample of panel P6 of the PME survey.
    Table summary
    This table displays the results of Labour classification and response for the occupation level in the sample of panel P6 of the PME survey.. The information is grouped by November 2010 (appearing as row headers), December 2010 (appearing as column headers).
    November 2010 December 2010
    Employed Unemployed Inactive Not in the labour force Row complement
    Employed 5,231 62 227 10 386
    Unemployed 51 183 113 0 28
    Inactive 235 93 4,200 12 281
    Not in the labour force 2 0 17 1,426 96
    Column complement 499 27 372 132 7,691

    However, since panel P6 corresponds to a probabilistic complex sample of the metropolitan areas in Brazil, every individual in the panel represents themselves and other additional people in the population. Then, using the proposed estimation procedure in this paper and using the corresponding expansion factors from the survey, we notice that the estimated population values for panel P6 correspond to those obtained in Table 7.2.

    Table 7.2
    Estimated contingency table for the population showing level of occupation and nonresponse at the two considered measurements for the panel P6 in the PME survey.
    Table summary
    This table displays the results of Estimated contingency table for the population showing level of occupation and nonresponse at the two considered measurements for the panel P6 in the PME survey.. The information is grouped by November 2010 (appearing as row headers), December 2010 (appearing as column headers).
    November 2010 December 2010
    Employed Unemployed Inactive Not in the labour force Row complement
    Employed 2,162,635 20,602 76,303 3,074 160,768
    Unemployed 16,233 80,169 37,786 0 11,504
    Inactive 70,551 31,822 1,707,675 6,018 122,412
    Not in the labour force 958 0 7,035 566,530 38,171
    Column complement 205,033 9,293 136,146 53,640 3,076,388

    Using the estimation procedure proposed in this paper, we computed the estimated population gross flows given in Table 7.3. The corresponding estimators are unbiased under the complex design of the PME survey. According to this, the number of employed people in both periods of measurement is estimated as 3,913,274, whereas the number of inactive people for both periods is estimated as 3,035,463.

    Table 7.3
    Population estimated gross flows for both periods at the PME survey. Estimated coefficients of variation in percentage are shown in brackets.
    Table summary
    This table displays the results of Population estimated gross flows for both periods at the PME survey. Estimated coefficients of variation in percentage are shown in brackets.. The information is grouped by November 2010 (appearing as row headers), December 2010 (appearing as column headers).
    November 2010 December 2010
    Employed Unemployed Inactive Not in the labour force
    Employed 3,913,274 (0.2) 36,570 (3.1) 136,102 (1.6) 5,573 (7.2)
    Unemployed 29,776 (3.5) 144,253 (1.7) 68,320 (2.1) 0 (-)
    Inactive 127,193 (1.6) 56,296 (2.3) 3,035,463 (0.3) 10,872 (6.5)
    Not in the labour force 1,727 (17.3) 0 (-) 12,496 (5.8) 1,022,836 (0.5)

    The estimates in the last table above are the result of the proposed estimation procedure in this paper. Next, we show the estimated parameters on the first stage of the model, defined as the transition probabilities from one category to another in both observation periods.

    Table 7.4
    Estimation of the probabilities p ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaaBa aaleaacaWGPbGaamOAaaqabaaaaa@38E5@ . Estimated coefficients of variation in percentage are shown in brackets.
    Table summary
    This table displays the results of Estimation of the probabilities p ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaaBa aaleaacaWGPbGaamOAaaqabaaaaa@38E5@ . Estimated coefficients of variation in percentage are shown in brackets. The information is grouped by November 2010 (appearing as row headers), December 2010 (appearing as column headers).
    November 2010 December 2010
    Employed Unemployed Inactive Not in the labour force
    Employed 0.9564 (0.1) 0.0089 (3.1) 0.0332 (1.6) 0.0013 (7.2)
    Unemployed 0.1228 (3.4) 0.5952 (1.1) 0.2819 (2.0) 0 (-)
    Inactive 0.0393 (1.5) 0.0174 (2.3) 0.9398 (0.1) 0.0033 (6.5)
    Not in the labour force 0.0016 (17.6) 0 (-) 0.0120 (5.8) 0.9862 (0.1)

    The initial probabilities of classification on the first period of interest are shown in Table 7.5. It can be noticed that, for this particular survey, the highest classification probabilities can be found for the categories of employed and inactive.

    Table 7.5
    Estimation of the probabilities η i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaadMgaaeqaaaaa@38AD@ . Estimated coefficients of variation in percentage are shown in brackets.
    Table summary
    This table displays the results of Estimation of the probabilities η i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaadMgaaeqaaaaa@38AD@ . Estimated coefficients of variation in percentage are shown in brackets.. The information is grouped by November 2010 (appearing as row headers), (appearing as column headers).
    November 2010
    η 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaaigdaaeqaaaaa@3A9D@ η 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaaikdaaeqaaaaa@3A9E@ η 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaaiodaaeqaaaaa@3A9F@ η 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaaisdaaeqaaaaa@3AA0@
    0.4757 (0.2) 0.0281 (1.2)  0.3755 (0.3) 0.1205 (0.5)

    Finally, the general response probability was estimated as ψ ^ mpv =0.595 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqiYdKNbaK aadaWgaaWcbaGaamyBaiaadchacaWG2baabeaakiabg2da9iaaicda caGGUaGaaGynaiaaiMdacaaI1aaaaa@3F90@ (with an estimated coefficient of variation of 0.1%). That means that the rate of response is around 60%. Also, the transition probability that a nonrespondent in the first period is still a nonrespondent the next time was estimated as ρ ^ MM,mpv =0.883 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyWdiNbaK aadaWgaaWcbaGaamytaiaad2eacaaISaGaamyBaiaadchacaWG2baa beaakiabg2da9iaaicdacaGGUaGaaGioaiaaiIdacaaIZaaaaa@41DC@ (with an estimated coefficient of variation of 0.1%). The transition probability that a respondent in the first period stays on as a respondent the next time was estimated as ρ ^ RR,mpv =0.934 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyWdiNbaK aadaWgaaWcbaGaamOuaiaadkfacaaISaGaamyBaiaadchacaWG2baa beaakiabg2da9iaaicdacaGGUaGaaGyoaiaaiodacaaI0aaaaa@41E3@ (with an estimated coefficient of variation of 0.1%). In general terms, it is possible to state that a status response of an individual in the first period is not changing significatively by the second.

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