b'Estad\xc3\xadstica Espa\xc3\xb1ola \xef\x82\xb7 Volumen 59, n\xc3\xbamero 192 / 2017, pp. 45-57\n\nWeight adjustments after sub-sampling crosssectional data\nSurendra Prasad Sinha\nInstituto de Estad\xc3\xadstica Aplicada y Computaci\xc3\xb3n, Facultad de Ciencias Econ\xc3\xb3micas y\nSociales, Universidad de Los Andes, Venezuela\n\nJosefa Ramoni Perazzi\nUniversidad de Santander, Bucaramanga, Colombia\n\nGiampaolo Orlandoni Merli\nUniversidad de Santander, Bucaramanga, Colombia\n\nElizabeth Torres Rivas\nFundaci\xc3\xb3n Universitaria Colombo Internacional, Colombia\nAbstract\n\nTo avoid biased results, sample units must be included in the sample in the correct\nproportion. Sample weights are intended to correct potential disproportions\nobserved in survey sample data. While their use is widely accepted to estimate\npopulation descriptive statistics, their role to estimate causal effects is not clear.\nThis paper analyzes when and how to use weights, considering wages in Colombia\nas an example, providing a procedure for selecting the final weight components\nbased on empirical evidence. Results indicate that weights are required for\ndescriptive statistics to resemble the population ones. However, several coefficients\nobtained from weighted and unweighted wage equations show no significant\ndifferences.\nKeywords: sample weights, post-stratification weights, non-response weights.\nAMS Classification: 62D05, 62D99, 62D99.\nCorrecci\xc3\xb3n de los pesos en submuestras de datos de corte transversal\nResumen\n\nA fin de evitar resultados sesgados, las unidades muestrales deben ser incluidas en\nla muestra en la proporci\xc3\xb3n correcta. Los pesos muestrales se utilizan para corregir\nposibles desproporciones, frecuentes en datos muestrales. Mientras su uso es\nampliamente aceptado para estimar estad\xc3\xadsticas descriptivas de la poblaci\xc3\xb3n, su\npapel en la estimaci\xc3\xb3n de efectos causales no es claro. Este trabajo analiza cu\xc3\xa1ndo\n\n\x0c46\n\nSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\ny c\xc3\xb3mo utilizar dichos pesos, considerando salarios en Colombia como ejemplo,\nproporcionando un procedimiento para seleccionar los componentes del peso final\nbasado en la evidencia emp\xc3\xadrica. Los resultados indican que los pesos muestrales\nson necesarios para que las estad\xc3\xadsticas descriptivas de la muestra se asemejen a las\nde la poblaci\xc3\xb3n. Sin embargo, varios coeficientes obtenidos a partir de ecuaciones\nde salarios ponderados y no ponderados no muestran diferencias significativas.\nPalabras Claves: Pesos muestrales, pesos de post-estratificaci\xc3\xb3n, pesos de no\nrespuesta.\nClasificaci\xc3\xb3n AMS: 62D05, 62D99, 62D99.\n\n1. Introduction\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nIn social sciences many studies rely on survey data usually obtained from probability\nsampling methods intended to provide a given level of precision of the estimates and\nreduce costs, such as having biased results. Sample weights are estimated to correct\ndisproportions of the sample data with respect to the target population controlling, among\nothers, for differences in the probabilities of being part of the sample or non-response\nsituations.\nThere are not doubts about the importance of the appropriate estimation of sample\nweights. Their use, or the lack of it, may affect the results of any study, probably making\nthe difference between a correct diagnose of a situation and the subsequent course of\naction, and a wrong one. However, the when and how to used them is yet an unsolved\nproblem.\nFor official survey data, sample weights are regularly provided to resemble the original\npopulation. Researchers adapt these data sets to fit the purposes of their study, trimming\nout individuals that do not satisfy some required conditions. For the resulting subsample,\nsample weights may not satisfy the original properties so that some adjustments must be\nintroduced for the subsample to be representative. A representative sample is an unbiased\nrepresentation of the population, showing the same characteristics and holding their\nproportional distribution among units.\nThe concept of subsampling has been used in the statistical literature in many different\ncontexts and so, in order to avoid any confusion, we would like to indicate the technical\nsense in which it is used in this article. The idea of using subsampling is historically\nattributed to Mahalonobis who, in 1946, proposed it under the name of \xe2\x80\x9cinterpenetrating\nnetwork of subsamples\xe2\x80\x9d in order to evaluate non sampling errors and estimate standard\nerror in the study of crop yields. Later, the bootstrap research brought a revived interest\nin the subsampling, which is now used in a wide variety of situations. A combination of\ninterpenetration and repetition was used in a study of response errors in the 1961\nCanadian Census of Population. Also, the interpenetration method was used by the U.S.\nCensus Bureau in 1968 to estimate the correlated components of the total response\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n47\n\nvariances. Cochran (1977) gives a detailed account of many other research workers who\nused the interpenetration method to estimate the correlated response variance.\nEven though the interpenetration method is not possible when a complex sampling design\nis used without being available the details about its construction, necessary to plan the\nsampling design at priori, we suggest that a post interpenetration method is possible to\ndesign based on the distribution of demographic variables, which can be constructed in\nthe same manner as post-stratification is used in order to gain useful information about\ndifferent types of response errors and estimate its variance in a sampling survey.\nWe will use subsampling in the sense defined by Kotz, et al. (2006) as a non-parametric\ntechnique which can be used to estimate the sampling distribution of a statistic. For this\npurpose, a subsample of m(n) is taken from the original sample given by (X1, X2, \xe2\x80\xa6 , Xn)\nsuch that m < n. The procedure to be used in this type of subsampling is very similar to\nthe m out of n bootstrap method.\n\nParticularly, to analyze the wage distribution of workers, we limit our sample to employed\nindividuals aged between 15 and 80 years. The generated subsample just includes 27,407\nobservations whose combined weights go down to 18,719,563. We show that, once\noriginal weights are rescaled and post-stratification and non-response weights are\ncomputed, the main statistics for the original sample and the weighted subsample show\nno significant difference. We also examine the effect of sample weights on the estimated\nparameters of wage equation models. Our findings show that the impact of some variables\non wages may be overestimated when using the wrong weights, but are inconclusive when\ncompared to the unweighted coefficients.\n2. Post-stratification and non-response adjustments\n\nWeights allow making inference about the population from a sample, by adjusting for\neither unequal probabilities of selection, non-response, or both. When taken into account,\nthese weights are generally used in descriptive statistics. However, many studies neglect\nthe fact that changes in the original sample may affect the properties of the sample\nweights, jeopardizing the randomness or the representativeness of the resulting data set.\nBrewer and Mellor (1973) suggest that the decision about whether to use sample weights\nin a regression analysis depends on the structure of the model used. A similar conclusion\nis reached by DuMouchel and Duncan (1983) comparing different models. A general\nrecommendation is to recalculate the weights so that its sum in a sample or within groups\nis equal to the population size. Wooldridge (1999) develops the properties of the estimator\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nThis study uses information from the Colombia\xe2\x80\x99s Integrated Household Sample Survey\n(IHSS) corresponding to August 2014 to show the need for and the methodology used to\nrestore the sample weight properties for representativeness purposes, once some units are\nexcluded. The sample weights of the 60,337 individuals included in the original data set\nadd up to 35,626,316, pretty close to the population size of 35,626,302 individuals\nreported by the Colombia\xe2\x80\x99s Administrative Department of National Statistic (DANE) for\nyear 2014.\n\n\x0c48\n\nSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\nin the presence of weights, and describes how these properties can be affected in either\ndirection, depending on whether the sampling probabilities vary exogenously or\nendogenously.\nPfefferman (1993) compares the use of sampling weights for either ex -post corrections\nor as part of a regression model, in an attempt to determine if their use is justified and\ndraws some guidelines about their use. His remarks about different approaches leading to\nsimilar estimators speak by themselves. Solon et al. (2013) highlight the lack of clarity\non the sampling weights issue, through a collection of cases in which the use of sample\nweights helps or not to correct problems. Based on that, they conclude that knowledge\nabout the reasons for weighting spreads light on the need of using sampling weights.\nIn order to reduce survey costs, most of the household surveys use complex sampling\ndesigns which involve stratification, multi-stage sampling and unequal sampling rates. A\ncomplete sampling frame listing all possible sampling units is not always available or\nknown. Consequently, different techniques such as post-stratification and non-response\nadjustments are required to be used in order to increase the efficiency of the estimates.\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nSince it is impossible to collect all the expected information from all the surveyed units,\nnon-response adjustments have attracted a great deal of attention. Gelman and Carlin\n(2000) lay out the main assumptions required when using sample weights to correct for\nnon-response. Similarly, Yansaneh (2003) summarizes the stages to construct sample\nweights to be used in the analysis of survey data, emphasizing the need for adjustments\nto compensate for non-coverage and non-response.\nSchouten et al. (2009) suggest that controlling for high non-response rates do not\nnecessarily reduces the non-response bias, which we will show is not the case in the\nexample included ahead. According to them, the propensity to non-response should be\nconsidered. Vives et al. (2009) use both, field substitution and response propensity\nweights to adjust for non-response, concluding that both techniques show similar results.\n2.1\n\nPost-stratification\n\nResponses on sampling units in a survey will vary according to the different variables\nincluded in the sample. For example, in the case of a sample on persons, often data on\ndemographic variables such as age, race, education level, sex, etc. are collected. For some\nof these variables, it can be constructed the sample distribution frequency and compared\nit to the population frequency distribution obtained in a recent census; if a recent census\ndata is not available, data on a major national survey with variables similar as in the\nresearch being conducted may be used as an approximation. If a discrepancy exists\nbetween the distribution frequencies of the survey data under investigation and the census\ndata, the representativeness of the sample obtained in the survey sample is not assured\nand correctional measures should be taken using post-stratification methods to restore the\nrepresentativeness of such a sample.\nThe post-stratification is very similar to stratification but it cannot be applied before\nobtaining the sample in the survey. However the post-stratification is considered\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n49\n\npotentially more efficient than stratification itself, since it is possible to select factors in\nsuch a way as to maximize the gain in precision of the estimates.\nWe consider a population denoted by \xd0\x9f which is partitioned in strata for which we denote\nsuch that \xe2\x88\x91\n= N. We also consider a sample of size n for\nits strata size equal to\nwhich\nis the value of an observed variable for the i-th observation obtained that\nbelongs to the h-th stratum such that h=1 \xe2\x80\xa6, H; i = 1, \xe2\x80\xa6,\nand \xe2\x88\x91\n. The values\nof\nare known only after the sample is obtained. We can calculate the population strata\nmeans and variances and the whole population means and variances based on\n\xe2\x88\x91\n=\xe2\x88\x91\n\n\xe2\x88\x91\n\n/\n\n\xe2\x88\x91\n\n[1]\n/\n\n1\n\n[2]\n\nSimilar formulas may be used for estimators which are given below. The h-th\nstratum sample mean is\n\xe2\x88\x91\xe2\x88\x8a\n\n[3]\n\n\xe2\x88\x91\xe2\x88\x8a\n2.2\n\n/(\n\n1\n\n[4]\n\nNon-response adjustments\n\nNon sampling error is any type of error which is different than a sampling error. Biemer\nand Lyberg (2003) decompose the non-sampling errors into their components. The nonsampling error is the cumulative effect of the errors that have been made during data\ncollection, data processing and estimation of parameters of interest in the study. Some of\nthe errors which may frequently occur in a study are due to different sources given below:\na. Respondents may not wish to reveal information, for example their true incomes or\nparts of their incomes coming from different sources.\nb. The interviewer may make mistakes in entering data.\nc. The respondent may refuse to participate in the interview.\nd. There may be errors in data entry from the survey questionnaire that will be used to\nobtain the estimation of parameters.\nA non-sampling error is inevitable in a large survey and may not be controlled easily,\nwhereas a sampling error can be controlled just by using an optimum sample size.\nA non-response error is a type of non-sampling error that can be caused by the lack of\ncooperation to respond questionnaire by not revealing the true information required by\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nwhere \xe2\x88\x8a indicates the set of i in the sample such that the units belong to the hth stratum. The variance of the h-th stratum is then given by\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n50\n\nthe interviewer. Such an error can be of different types whether it is due to providing\ninformation which affects the whole sampling unit, or within unit or item. Non-response\nerrors can introduce bias in the survey results especially in situations in which the nonresponding units are not representative of those who responded the questionnaire. Nonresponse increases non-sampling errors as well as the sampling error, by decreasing the\nsample size.\nDifferent methods exist that can help reduce the non-response bias in a survey:\na. Non-response adjustments using the sample weights.\nb. Obtaining a large sample containing replacements that can be used in the case of non\nresponse.\nc. Using a substitution to replace a non-responding unit in the sample by another unit\nnot included in the sample but very similar to the sampled unit which did not respond.\nHowever non-response adjustment of the sample weight appears to be the method\npreferred by most of the research workers and will be explained in the next section, along\nwith the procedure for calculating sample weights.\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\n3. A procedure for selecting components for final weight\n\nOnce a subsample is generated, the next step is to re-estimate sample weights. In addition\nof rescaling the original ones (base), we compute the post-stratification weights based on\nsome characteristic variables, considering the proportion of observations in the subsample\nwith respect to those in the original sample. We also estimate the non-response weight\nbased on the number of units who did not report their wage. These weights are the\ncomponents of the final ones.\nThe number of components that will be used in calculating the final weights should be\ndecided based on a test of significance for the difference \xc9\x85\n, where is some\nparameter of interest. For example, if we are considering the household income, then\ncan be taken as the population mean and the test of significance of the difference\n\xcc\x82 between the household weighted income mean ( \xcc\x82\nand unweighted\n\xc9\x85\n\xcc\x82\nmean \xcc\x82 should be used to make the decision. Since the final weights are composed by\n3 types of weights, namely base, post-stratification and non-response, we decide which\none works better based the results of different significant tests, following the steps\noutlined below.\nTable 1\n\nSteps and tests of significance for the selection of components of the final weight\nStep\n1\n\nDifference to test\n\n2\n\n\xc9\x85\n\n\xce\x9b\n\nComparison\nBase weighted vs. unweighted\nBase and poststratification weighted vs.\nbase weighted\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n3\n\n51\n\nBase, poststratification and non-response\nweighted vs. base and poststratification\nweighted\n\n\xc9\x85\n\nSource: created by the authors\n\nThe selection of the final weight and its components should be done only after the results\nof all 3 steps are obtained. For example if the difference in step 1 is not significant,\nimplying that there is no apparent advantage in using base weight, it does not indicate\nthat such a base weight is not required as a component in the final one, since the results\nobtained in this step do not take into account further information, only available after\nperforming steps 2 and 3.\n4. An example\n\nThis study relies on data from the Colombia\xe2\x80\x99s IHSS corresponding to August 2014, for\nwhich the sum of sample weights equals the country\xe2\x80\x99s 2014 population size of\n35,626,3161 citizens. For the purpose of the study, only employed individuals between 15\nand 80 years of age are considered, so that the original sample size of 60,337 goes down\nto 27,407 observations, while the original sample weights add up only 18,719,563.\n\nNext, the non-response weight (w3) is calculated to correct for individuals who did not\nreport their wages. To do that, for each strata of the original sample weight we estimated\nthe number of non-response (kj) and the number of observations (nj), so that the nonresponse weight was obtained as given by w3j= nj/( nj -kj).\nFinally, all weights (including the original sampling weight, w1) are rescaled using the ratio\nbetween the population size and the sum of the corresponding weights, and multiplied\nbetween them to obtain w12=w1*w2 as well as w123=w1*w2*w3. All the computations\nwere done using Stata/SE 14.0 and Excel. Table 2 provides the main statistics for wages\nfrom the original sample as well as for the weighted and unweighted subsample.\nTable 2\n\nDescriptive statistics (August 2014)\nWages\n\nMean\n\nIHSS weighted original sample (y0)\nUnweighted subsample (y)\nw1 weighted subsample (y1)\n\n962,900.80\n909,336.90\n1,008,358.90\n\n1\n\nMedian\n\nSkewedness\nStandard\ndeviation\n640,000\n1,424,324\n9.02\n616,027\n1,714,030\n8.80\n680,000\n1,512,753\n9.06\n\nThis number differs from the DANE\xe2\x80\x99s estimates by only 14 individuals.\nEducation includes four levels: Basic (1); high school (2); technology (3) and university (4). In the original data\nset there are six age groups: less than 15 (1); 15-25 years (2); 26-45 (3); 46-60 (4); 61-80 (5) and above 80 (6).\n2\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nThe post-stratification weight (w2) is estimated nesting each level of education within\neach age group by gender2. For each group, we calculated the proportion of weighted\nunits in the original sample (bj) and the proportion of observations in the sample (dj), so\nthat w2j= bj/dj as shown in table A1 in appendix.\n\n\x0c52\n\nSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\nw12 weighted subsample (y12)\nw123 weighted subsample (y123)\n\n1,003,075.80\n950,609.30\n\n680,000\n680,000\n\n1,508,209\n1,082,838\n\n9.31\n6.43\n\nSource: estimated by the authors with data from IHSS 2014\n\nAs observed in this case, once a subsample is extracted from the original sample, the\naverage wage may be underestimated if the sample weights are ignored, or overestimated\nif the researcher insists in using the original base weights provided along with the data set.\nPost-stratification weights do seem to correct the problem at the light of the similarities\nbetween the y1 and y12 main statistics. These differences however, appeared to be solved\nonce all wages are corrected by their corresponding total combined weights. The\nsignificance of such differences is shown in table 3. Following table 1, all possible\ncombinations are considered, so that the equality between the original average wage (y0)\nand the weighted and unweighted wages are tested, assuming unequal variances. As\nexpected only the difference between \xef\x81\xady0 and \xef\x81\xady123 proved not to be statistically significant,\nmeaning that the weight adjustments restored the representativeness of the subsample3.\nTable 3\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nMean-comparison tests\nHypothesis\nmy0 = my\nmy0 = my1\nmy0 = my12\nmy0 = my123\nmy = my1\nmy = my12\nmy = my123\n\nZ \xe2\x80\x93 value p-value\nConfidence interval (95%)\n4.30\n0.00002\n(2.94E4 ; 7.86E4)\n-3.97\n0.00007\n(-6.78E4 ; -2.3E4)\n75.4\n0.00000\n(8.38E5 ; 8.82E5)\n1.32\n0.18800\n(-5.85E3 ; 2.99E4)\n-6.78 1.17E-11\n(-1.3E5 ; -7.18E4)\n-6.33 2.44E-10\n(-1.23E5 ; -6.5E4)\n-5.78 7.78E-09\n(-5.53E4 ; -2.73E4)\n\nSource: estimated by the authors with data from IHSS 2014\n\nThese findings point out not only that non-response for the variable of interest must be\nconsidered, but also that the researcher should analyze the reasons for the high incidence\nof such non-response situations. In the case considered here, several reasons can be\nblamed for it. Colombia\xe2\x80\x99s 32 Departments are divided into five natural geographical\nregions, based on their location and physical and climatic characteristics, although some\nDepartments may be part of more than one region. The Andean region is the most densely\npopulated, showing a very low non-response incidence, exception made by Norte de\nSantander. The Departments belonging to the Caribbean region tend to show very large\nnon-response rates, although the largest rate (68%) is observed in Choc\xc3\xb3 in the Pacific\nregion. The sparsely populated Llanos is barely represented in the IHSS by just one of its\nfour Departments. Finally, the Amazon region is larger and less populated than the\nprevious one, which may explain the fact that only Caquet\xc3\xa1 is considered in the sample.\nA look at a Colombia\xe2\x80\x99s map indicates two facts: first, the IHSS excludes the less\npopulated Departments, most of them located in the western regions and second, central\n3\nThese tests assume that ly follows a normal distribution, based on the results of the Shapiro-France test\n(Z=0.147, pvalue=0.44138). The Kolmogorov-Smirnov test corroborates the results shown in the table.\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n53\n\nDepartments show the lowest non-response rates. As for the other factors, there exists a\nrelatively higher level on non-response among women and people with low level of\neducation. However, it seems that the non-response is mostly attributable to regional\nlocation (see table 4).\nTable 4\n\nVariable\nGeographic area\n\nGender\nEducation\n\nRegion / Departments\nAndean: Antioquia\nBogot\xc3\xa1\nBoyac\xc3\xa1\nCaldas\nHuila\nN. de Santander\nQuind\xc3\xado\nRisaralda\nSantander\nTolima\nCaribbean: Atl\xc3\xa1ntico\nBol\xc3\xadvar\nCesar\nC\xc3\xb3rdoba\nLa Guajira\nMagdalena\nSucre\nPacific:\nCauca\nChoc\xc3\xb3\nNari\xc3\xb1o\nValle del Cauca\nAmazon: Caquet\xc3\xa1\nLlanos:\nMeta\nMale\nFemale\nElementary\nHigh School\nSuperior\n\nResponse\nNon-response\n90.35\n9.65\n90.41\n9.54\n90.69\n9.31\n93.88\n6.12\n88.33\n11.67\n76.32\n23.68\n88.50\n11.50\n92.97\n7.03\n92.60\n7.40\n89.87\n10.13\n58.76\n41.24\n44.60\n55.40\n72.21\n27.79\n90.48\n9.52\n83.68\n16.32\n81.48\n18.52\n86.75\n13.25\n71.09\n28.91\n32.28\n67.72\n79.44\n20.56\n86.34\n13.66\n90.91\n9.09\n86.59\n13.41\n84.19\n15.81\n79.07\n20.93\n79.63\n20.37\n82.82\n17.18\n83.43\n16.57\n\nSource: estimated by the authors with data from IHSS 2014\n\nFor descriptive analysis, sample weights are widely accepted as a way to restore the\nproportions observed in the target population. However, their role and need when trying\nto estimate parameters when modeling survey data is yet a matter of controversy. In order\nto determine whether our findings apply only to main statistics, we estimate traditional\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nNon-response possible sources\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n54\n\nwage equations always correcting for potential selection bias, so that our model may be\nrepresented as given by\nLy = f(gender, age, education, informal, sector, tenure, union, \xef\x81\xac) + \xef\x81\xa5\n\n[5]\n\nwhere Ly stays for the logarithm of wages and \xef\x81\xac accounts for the probability of being\nemployed. The results, assuming different scenarios regarding sample weights, are\nsummarized in table 5. As shown, the estimates exhibit similar patterns as those observed\nin table 2; that is, compared to the estimates obtained when considering the total combined\nweight (w123), the parameters tend to be underestimated when sample weights are\nignored, and overestimated when non-response weights are not considered (w1 and w12).\nTable 5\n\nWage equations estimates\nCovariate\n\nNone\n\nw1\n\nw12\n\nw123\n\nWeight\nGender (Male)\nAge\nAge2\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nEducation (High School)\nEducation (Superior)\nInformal (Yes)\nSector (Public)\nTenure (No)\nUnion (Yes)\nLambda\nConstant\nR2\n\n-0.0701**\n-0.0343\n0.0027\n-0.0076\n-0.0001\n-0.0001\n0.0501***\n-0.0299\n0.5173*\n-0.0404\n-0.1797*\n-0.0125\n0.2337*\n-0.401\n-0.0450*\n-0.0119\n0.0861**\n-0.0439\n3.6600*\n-0.8343\n10.3198\n0.3601\n\n-0.2305*\n-0.2188*\n-0.0613\n-0.0648\n-0.0443*\n0.0353*\n-0.0119\n-0.0119\n0.0003* 0.0002***\n-0.0001\n-0.0001\n0.1685*\n0.1407*\n-0.0339\n-0.014\n0.6463*\n0.6161*\n-0.0388\n-0.017\n-0.1981*\n-0.1944*\n-0.0393\n-0.0398\n0.3461*\n0.3222*\n-0.0527\n-0.0187\n-0.1075*\n-0.1076*\n-0.0223\n-0.0224\n0.1497* 0.13305***\n-0.0239\n-0.0718\n10.8085*\n10.8578*\n-1.4115\n-1.4702\n4.7726\n4.5125\n0.3596\n0.357\n\n0.2161*\n-0.063\n0.0300**\n-0.0153\n-0.0002\n-0.0001\n0.0529***\n-0.0299\n0.5177*\n-0.0405\n-0.1857*\n-0.0526\n0.2395*\n-0.0406\n-0.045\n-0.0307\n0.0898**\n-0.0446\n-5.883\n-6.2914\n18.8321\n0.3147\n\nSource: estimated by the authors with data from IHSS 2014\n\nFor example, the bargaining power of unions may go down from near 15% to less than\n9% once non-response weights are \xe2\x80\x9calso\xe2\x80\x9d considered. Similarly, the returns to human\ncapital may not be as large as 0.6 for highly educated workers, nor averaging 0.15 for\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n55\n\nunskilled workers, while tenure seems to be non-significant after all. Another important\nresult is that, once sample weights are included, there are not sample selection problems,\nas indicated by the fact that \xef\x81\xac becomes non-significant too. However, as some modelers\nargue, sample weights may be irrelevant especially if we consider the similarities between\nthe estimated parameters shown in the first and last columns of table 5 for variables such\nas education, union, tenure and sector of employment.\n5\n\nConclusions\n\nThis paper studies the convenience of using sample weights when analyzing survey\nsample data considering, as an example, a subsample of employed individuals aged 1580 years obtained from the Integrated Household Sample Survey in Colombia in August\n2014. For this data set, sample weights were obtained both rescaling the original weights\nand computing post-stratification and non-response weights based on wages. The product\nof these three forms the combined final sample weights.\n\nIn line with other studies, our first conclusion is that no generalization is possible when\ntrying to decide about whether or not to consider sample weights, since it is not possible\nto identify a pattern of behavior at this regard. The decision, therefore, relies on the\nempirical evidence and the researcher\xe2\x80\x99s experience. However, since computing sample\nweights may be cumbersome, a few words can be said about the conditions under which\nthe researcher should consider to undertake this task.\nAs said before, representativeness is required in order to avoid bias results. If the\nresearcher has information about the lack of representativeness of the sample or has\ndoubts about it, sample weights are likely to be required. On the other hand, a large and\nunequal incidence of non-response in the target variable across regions or groups is\nanother reason for sample weights to be computed and included in the analysis, a problem\nthat is very common is our region due to geographical or cultural factors.\nFinally, just rescaling the original sample weights once a subsample is tailored to the\npurposes of the study is not enough and the results, even basic statistics, are likely to be\nbiased.\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nThe results indicate that basic descriptive statistics obtained using the final sample\nweights resemble the population values, but can be wrongfully estimated if sample\nweights are ignored, especially non-response weights. However, there is no clear\nindication about the convenience of using sample weights when estimating the\nrelationship between variables as in wage equations models corrected by sample selection\nbias. In fact, some results obtained with weighted data are similar to those obtained\nignoring the weights.\n\n\x0c56\n\nSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\nAppendix\nTable A1\n\nPost-stratification weights\nVariables\nGender\nAge\nEduc\ngroup\nMale\n0\n1\n\n2\n\n3\n\n4\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\n5\n\nFemale\n\n0\n1\n\n2\n\n3\n\n4\n\n5\n\nTOTAL\n\n1\n2\n1\n2\n3\n4\n1\n2\n3\n4\n1\n2\n3\n4\n1\n2\n3\n4\n1\n2\n3\n4\n1\n2\n1\n2\n3\n4\n1\n2\n3\n4\n1\n2\n3\n4\n1\n2\n3\n4\n1\n2\n3\n4\n\nOriginal sample\nSub Sample\nB/D\nA\nB\nC\nD\nW2\nObs\nWeight\nProportion Obs\nProportion\n7,555 4,635,051\n0.130102\n0\n0.000000\n1\n96\n0.000003\n0\n0.000000\n2,556 1,613,441\n0.045288\n2,533\n0.056956\n0.79514\n2,739 1,462,708\n0.041057\n2,730\n0.061386\n0.66884\n466\n327,214\n0.009185\n464\n0.010433\n0.88032\n136\n53,027\n0.001488\n136\n0.003058\n0.48672\n3,307 2,278,335\n0.063951\n3,294\n0.074067\n0.86341\n3,406 2,040,401\n0.057272\n3,400\n0.076451\n0.74914\n1,128\n705,845\n0.019812\n1,125\n0.025296\n0.78322\n1,297\n825,976\n0.023184\n1,295\n0.029119\n0.79620\n2,931 1,786,148\n0.050136\n2,923\n0.065725\n0.76281\n885\n522,859\n0.014676\n883\n0.019855\n0.73918\n239\n138,742\n0.003894\n239\n0.005374\n0.72466\n666\n375,925\n0.010552\n666\n0.014975\n0.70462\n311\n186,857\n0.005245\n310\n0.006971\n0.75244\n34\n27,622\n0.000775\n34\n0.000765\n1.01416\n5\n7,688\n0.000216\n5\n0.000112\n1.91937\n16\n13,085\n0.000367\n16\n0.000360\n1.02092\n297\n174,959\n0.004911\n0\n0.000000\n24\n8,780\n0.000246\n0\n0.000000\n3\n3,235\n0.000091\n0\n0.000000\n18\n8,679\n0.000244\n0\n0.000000\n7,322 4,362,959\n0.122464\n0\n0.000000\n1\n107\n0.000003\n0\n0.000000\n2,415 1,357,939\n0.038116\n2,398\n0.053920\n0.70690\n3,108 1,562,278\n0.043852\n3,098\n0.069660\n0.62951\n771\n457,783\n0.01285\n768\n0.017269\n0.74409\n258\n127,403\n0.003576\n258\n0.005801\n0.61643\n3,785 2,244,693\n0.063007\n3,780\n0.084995\n0.74129\n3,875 2,305,183\n0.064704\n3,871\n0.087042\n0.74337\n1,831 1,021,049\n0.028660\n1,830\n0.041149\n0.6965\n1,881 1,014,323\n0.028471\n1,881\n0.042295\n0.67315\n4,064 2,329,171\n0.065378\n4,061\n0.091314\n0.71597\n1,019\n519,313\n0.014577\n1,019\n0.022913\n0.63618\n333\n203,729\n0.005719\n333\n0.007488\n0.76372\n644\n367,670\n0.010320\n644\n0.014481\n0.71268\n428\n255,117\n0.007161\n427\n0.009601\n0.74582\n38\n18,057\n0.000507\n38\n0.000854\n0.59320\n4\n768\n0.000022\n4\n0.000090\n0.23967\n10\n4,868\n0.000137\n10\n0.000225\n0.60765\n488\n250,020\n0.007018\n0\n0.000000\n30\n20,132\n0.000565\n0\n0.000000\n7\n2,501\n0.000070\n0\n0.000000\n5\n4,583\n0.000129\n0\n0.000000\n60,337 35,626,316\n1.000000\n44,473\n1.000000 24.22728\n\n\x0cSurendra Prasad Sinha et \xc3\xa1lli \xef\x82\xb7 Weight adjustments after sub-sampling\xe2\x80\xa6\n\n57\n\nReferences\n\nBIEMER, P. AND LYBERG, L. E. (2003), \xc2\xabIntroduction to survey quality\xc2\xbb, New Jersey,\nWiley & sons, Inc.\nBREWER, K. R. AND MELLOR, R. (1973), \xc2\xabThe effect of sample structure on analytical\nsurveys\xc2\xbb, Australian Journal of Statistics, 15, 145\xe2\x80\x93152.\nCOCHRAN, W. (1977), \xc2\xabSampling techniques\xc2\xbb, New York, John Wiley, 3rd ed.\nDUMOUCHEL, M. AND DUNCAN, G. (1983), \xc2\xabUsing sample survey weights in multiple\nregression analysis of stratified samples\xc2\xbb, American Statistical Association, 78, 535\xe2\x80\x93\n543.\nGELMAN, A. AND CARLIN, J. B. (2001), \xc2\xabPost stratification and weigting adjustments\xc2\xbb. In\nSurvey Nonresponse, Wiley Series in Probability and Statistics.\nKOTZ, S., BALAKRISHNAN, N., READ, C., AND VIDACOVIC, B. (2006), \xc2\xabEncyclopedia of\nstatistical sciences\xc2\xbb. New York, John Wiley.\nPFEFFERMAN, D. (1993), \xc2\xabThe role of sampling weights when modeling survey data\xc2\xbb,\nInternational Statistical Review, 61(2), 317\xe2\x80\x93337.\n\nSolon, G., Haider, S. J., and Wooldridge, J. M. (2013), \xc2\xabWhat Are We Weighting For?\xc2\xbb,\nJournal of Human Resources, 50(2), 301\xe2\x80\x93316. http://doi.org/10.3368/jhr.50.2.301\nVIVES, A.; FERRECCIO, C. AND MARSHALL, G. (2009), \xc2\xabComparaci\xc3\xb3n de dos m\xc3\xa9todos\npara corregir el sesgo de no respuesta a una encuesta: sustituci\xc3\xb3n muestral y ajuste\nseg\xc3\xban propensi\xc3\xb3n a responder\xc2\xbb, Gaceta Sanitaria, 23(4), 266\xe2\x80\x93271.\nWOOLDRIDGE, J. (1999), \xc2\xabAsymptotic properties of weighted M-estimators for variable\nprobability samples\xc2\xbb, Econometrica, 67(6), 1385\xe2\x80\x931406.\nYANSANEH, I. S. (2003), \xc2\xabConstruction and use of sample weights\xc2\xbb, in S. D. United\nNations Secretariat (Ed.), Draft handbook on designing household samples surveys\n(pp. 1\xe2\x80\x9314). United Nations.\n\nVol. 59 N\xc3\xbam. 192 / 2017\n\nSCHOUTEN, B., COBBEN, F. AND BETHLEHEM, J. (2009), \xc2\xabIndicators for the\nrepresentativeness of survey response\xc2\xbb, Survey Methodology, 35(1), 101\xe2\x80\x93113.\n\n\x0c'