1 – Statistical sources

5The sample surveys offering migration information in Spain are the LFS and the ENI-2007. The LFS is a well-known quarterly sample survey designed to estimate the labour market characteristics of the population aged 16 and over residing in principal family dwellings. Although it was never intended to measure mobility, the questionnaire now incorporates questions which can be used to estimate the stock of foreign immigrants and of domestic and international flows. The survey includes the variable of nationality and country of birth, so the stock of the non-national population or the population born abroad may be estimated. With regard to flows, the survey asks all foreigners to give their year of arrival in Spain and asks all respondents to indicate the country of residence one year before the survey.

6The ENI-2007 (Appendix 1) supplies information on the demographic and social characteristics of the foreign-born population aged 16 and over residing in family dwellings in Spain on 1 January 2007. The ENI-2007 is characterized by its wide geographical and population scope and its extensive subject matter, making it possible to study the dimensions of immigration across different groups throughout the whole of Spain.

7The registers that provide migration information in Spain are the Municipal Population Registers (MPR) and the residence variation statistics (EVR) derived from them. While the MPRs are the administrative registers of inhabitants in the municipality (usual domicile) and their data constitute proof of residence therein, the EVR is compiled from registrations and de-registrations due to changes in the place of residence (municipality) of people included in the MPRs. It is compulsory to register changes of residence in Spain, but there is no guarantee of a complete coverage of flows since compliance depends on the incentives/deterrents for registering movements. To register, the only documents required are proof of identity (identity card, driving licence, passport, etc.) and some kind of proof of residence at the address (title deeds, rental agreement, utility bills, or a letter from the first adult already registered at the address). A local residency certificate is required to access basic services such as public education or health care, to vote in elections, to renew identity cards, to obtain grants, public employment, parking permits or home purchasing grants.

8All of the above-mentioned sources are generated by the INE and, with the exception of the ENI-2007, are periodic or are continually updated. They all include the entire immigrant population, irrespective of their legal situation in Spain, and individuals can be selected by their place of birth. The demographic characteristics of the immigrants included in the surveys can thus be compared with those of the registers (Appendix 2). With the date of ENI-2007 serving as a reference point, the equivalent period is the fourth quarter of 2006 (4Q-2006) for the LFS, 1 January 2007 for the MPR and, for annual immigration flows, the net registrations recorded each year by the EVR.

2 – Do the surveys give the same results as the registers?

9While the differences between the ENI-2007, the LFS and the MPR are acceptable in terms of the basic demographic characteristics of the stock of immigrants, [3] when the time dimension is incorporated and the migration flows are compared, serious discrepancies appear. Figure 1 shows the number of immigrant arrivals provided by the ENI-2007, the LFS 4Q-2006 and the EVR between 1988 and 2010. Although their levels are different, the series reveal similar trends until 2001. After that year, while the ENI-2007 and the LFS show a decreasing trend, the EVR basically continues to rise until 2007. This disparity in trends is surprising, particularly in the last few years when the sources should become more similar. In fact, the differences actually increase between 2004 and 2006.

Figure 1

Figure 1

Year of arrival in Spain according to ENI-2007, LFS 4Q-2006 and EVR (1988-2010)

10A perfunctory analysis might conclude that the two surveys better reflect reality as their time profiles are highly similar. But it is unlikely that the entries, as estimated by the ENI and the LFS, slowed down after 2001 at a time when the Spanish economy was expanding, unemployment was decreasing and there were no substantial economic improvements in countries of origin. The EVR, on the other hand, shows a trend that is in line with the economic cycle, increasing until 2007 and falling sharply after 2008, coinciding with the change in the economic situation.

11With regard to this divergence, it is true that the surveys interviewed the “surviving” immigrants at a specific moment in time, while the EVR records the moment of registration. Only in the case where a significant share of the immigrants who arrived between 2002 and 2006 were no longer residing in Spain at the end of 2006 would it have been possible for them to be included in the registers but excluded from the ENI-2007 or LFS surveys because no longer present in the country. But once again, mass exits of this kind would have been unlikely in a period when the Spanish economy was experiencing an economic boom.

12In addition, statistical sources based on registers have some drawbacks associated with their administrative nature, as residential variations do not always correspond to a real change of municipality, but may be due to the individual advantages derived from residing in a particular place. However, Ródenas and Martí (2009) show that these types of registration are rare, and are likely to be much lower among recently arrived immigrants because they are unaware of these advantages. Another drawback of register-based data is the possibility of a delay between an immigrant’s arrival and his/her registration. However, it should be short for recently arrived immigrants as registration in the MPRs provides access to basic public services.

13The above factors should not significantly affect the general trend of the EVR, but this source could have been distorted by the exceptional immigrant regularization programmes in Spain in recent years and by changes in the legal register coverage. It is thus likely that the rise in 2000-2001 and 2004-2005 can be explained by the fact that registration in the MPR has become proof of residence in Spain accepted by the successive immigrant regularization procedures. This must certainly have represented a new and strong incentive for registration.

14Despite these shortcomings, we consider that the EVR records arrivals more accurately than the surveys. This is also confirmed by its consistency with additional external sources: firstly, with the official population estimates published by the INE, and secondly, with the residence visas issued annually by the Spanish Diplomatic Missions or Consular Offices. The INE (2009a) has been carrying out a Population Now-Cast (ePOBa) since 2002. These official estimates are based on the MPR, although the INE has implemented some procedures to estimate the number of unnotified departures of foreigners. This increases the international emigration flows registered in the EVR. By selecting only the population aged 16 and over residing in Spain from these estimates, it can be confirmed (Figure 2) that between 2002 and 2007 the population grew by 600,000 each year on average; that this growth was sustained and certainly did not decrease, reaching a maximum precisely in 2007. The time profile of growth of the ePOBa only begins to fall after 2008.

Figure 2

Figure 2

Year of arrival in Spain (ENI-2007, LFS 4Q-2006, EVR and ePOBa) and residence visas issued annually (2002-2010)

15While the ePOBa series shows the inter-annual increases of the population aged 16 and over on a national level, the rises can only be attributed to the net flows of immigration from abroad, never to births via the incorporation of newborns. For the purpose of the comparison, we do not know whether these immigrants are Spanish or foreign, or whether they were born in Spain or not, as these characteristics are not estimated in the ePOBa. However the ePOBa series reveals an annual inflow almost identical to the number of immigrants born abroad recorded in the EVR.

16Analysis of the residence visas series leads to a similar observation (Figure 2). While surveys suggest that the entry of immigrants has slowed since 2001, the number of visas issued continued rising until 2008. This implies an increase in intentions to reside in Spain until that year. We think that the rise in the number of visas of non-nationals is consistent with the increase in immigration flows indicated by the EVR until the onset of the economic crisis.

17In summary, the stock of immigrants estimated by the different statistical sources does not reveal major disparities in terms of distribution by sex, age, place of residence and place of birth. However, when compared with the arrival flows into Spain, some major discrepancies come to light. The discussion of these differences and their analysis in the light of additional information from external sources, such as the visas issued and the ePOBa, suggests that the problem could reside in the surveys. Their design may be ill-adapted for correct estimation of recently arrived immigrants, in which case not only are the values of the variable “year of arrival” estimated incorrectly, but the problem is actually much more serious. The bias may extend to all variables that are liable to change with the length of time spent at destination. There is no doubt that recently arrived immigrants will be less integrated in society and that their employment situation will be more precarious than those who have been residing in the country for longer. And to the extent that they are not adequately represented in the sample, if this is not duly corrected in the post-survey adjustments, the analysis of the degree of social integration, the legal situation, the family regrouping processes, the transfer of funds, the employment situation or living conditions could reflect a more optimistic vision than is actually the case.

18However, this problem barely affects the basic demographic characteristics. Not only because they do not change over time, but also because – as opposed to the variable “year of arrival” – these variables were taken into account in the sample design and in the adjustments made after both surveys. In fact, when a more significant difference in distributions is observed between the LFS and the MPR, such as for the country of birth, we find that, in the LFS, only two categories are considered for the nationality variable (holding Spanish nationality or not) and there is no breakdown by nationality of the persons residing in Spain, as is the case in the ENI-2007.

1 – Non-sampling errors

21Social desirability bias is included among the non-sampling errors. For the case in hand, given that the immigrant’s legal situation is usually correlated to the year of arrival, it is possible that some of the immigrants in the ENI or the LFS samples who have recently arrived in Spain declare a year of arrival that is far removed from the truth, to avoid arousing suspicions that their situation is illegal. This is difficult to prove, but when we analyse the “documentation situation” variable in the ENI, we can show that the number of illegal immigrants rises as the interval between their arrival and the interview becomes shorter. We suspect that this bias is not very large, however.

Non-response bias

25Non-response is the source of bias that most concerns researchers as it is difficult to control. Basically, non-response exists for three reasons: difficulties in locating the dwelling or human group; negative response or refusal to collaborate with the survey or to respond to certain questions, and lastly, an incapacity to answer (no knowledge of the language, inability to remember particular events in the past, etc.). The non-response of surveyed households generates bias when the value of the statistic estimated for the sample that is effectively surveyed (households with individuals who respond) differs from that based on the complete sample.

26In practice, in surveys carried out with individuals it is almost impossible to obtain a response from 100% of the sample and for 100% of the items in the questionnaire. Frequently, some of the people selected are unable to collaborate, are reluctant or even refuse to be interviewed or only partially collaborate and do not answer some items. As we can see in Table 1, the non-response rate in the LFS is approximately 18.5%, while in the ENI-2007 it reaches almost 28% of total eligible households.

Table 1

Response rate and non-response rate for ENI-2007 and LFS (first wave). Percentages of final sample^(*)

Response rate Non-response rate Total Total Refusals Non-contacts LFS (annual averages) 2006 80.40 19.60* 7.97 11.63 2007 81.15 18.85* 7.68 11.17 2008 82.99 17.01* 6.87 10.14 ENI-2007 72.10 27.90* na na

Response rate and non-response rate for ENI-2007 and LFS (first wave). Percentages of final sample^(*)

(*) Includes non-contacts, refusals and inability to respond.
na: not available.

27A higher non-response rate in the ENI-2007 than in the LFS is to be expected, as procedures are more complex and communication between interviewers and target population in the former are more difficult. Language problems are particularly prevalent and it is known that household surveys in which any member may act as the informer (LFS) usually obtain higher response rates than in those which randomly select one member (ENI-2007) (Groves et al., 2009). Fortunately, addressing non-response by substituting one household with another prevents the sample from shrinking to an unacceptably small size, which would increase the variability of the estimates. However, if this substitution is carried out with a tendency to incorporate households where the respondent arrived longer ago rather than more recently, a bias will be generated in terms of the year of arrival.

28With the information available it is not possible to estimate the covariance between the probability of being surveyed and the year of arrival. However, there is a reasonable probability that this covariance will be high, to the extent that recently arrived immigrants will be immersed in the first phases of the migration process (seeking employment, applying for papers or working long hours), making it more difficult to contact them as they do not have established and predictable timetables and routines. Furthermore it is more than likely that many of them will decide not to respond to surveys out of mistrust – especially those who are not legally residing in the country – or because they do not know the language. Later, as they adapt to their new environment, establish a routine and begin to master the language, immigrants’ mistrust towards the interviewer will diminish and they will be more inclined to respond, but they will have arrived longer ago. Taking this reasoning into account, and in view of the non-response levels, the risk of this type of bias is high in the LFS, but particularly so in ENI-2007.

2 – Sampling bias

29If an inappropriate sampling design is used, such that the selection probability of certain units of the frame does not correspond to their weight in the target population, this could represent another source of bias if the value of the characteristic being researched among these units differs from the value for the rest of the population. In the surveys that we are analysing, the sampling designs are quite complex in order to obtain quality information about highly sensitive variables at the lowest possible cost. In the case of the ENI-2007, the sampling design (Appendix 1) does not give reason to believe that recently arrived individuals are less likely to be included in the sample than the others.

30However, we reach a different conclusion when we analyse the design of the Spanish LFS. In this case, the INE uses a two-stage sample with stratification of the first stage units. In the same way as the ENI, the primary sample units are census sections and the secondary (and last) sample units are dwellings. All people living in the same dwelling are interviewed. The sample is selected such that all dwellings within each stratum have the same probability of being selected. In addition, in order to avoid over-burdening the families, the sample is divided into six sub-samples called waves. Every quarter, one-sixth of the selected dwellings in each section are renewed. Each dwelling thus forms part of the sample for six consecutive quarters after which it is replaced by another dwelling from the same section. In every quarterly interview, the non-national immigrants are asked to provide their year of arrival in Spain, irrespective of the interview number.

31This pattern of sample updating may reduce the probability of finding recently arrived immigrants in the sample because such individuals can only be found in dwellings newly incorporated into the sample. For example, assuming that the interview is carried out in the fourth quarter of year N, all the individuals of the sample may declare that they entered Spain during the year N – i (i = 1, 2, 3…). However, when we try to estimate how many arrived in year N, only two-thirds of the sample can declare that they did so: those surveyed for the first, second, third and fourth time. The rest of the sample cannot do this as the rotation scheme means that those who take part in the fifth and sixth interview – two-sixths of the sample – cannot have arrived in Spain during year N because to be interviewed five or six times by the LFS they must already have been living in the country for more than a year.

32Bias is therefore inevitable in the estimate of arrivals in year N, as the probability of obtaining N as the year of entry depends on the wave in which the surveyed individuals are placed. However, a higher estimate of the entry flow will be obtained for year N in the LFS in the 4th quarter of year N + 1. While this is contrary to the demographic prediction of “losing” immigrants over time as the number of “surviving” immigrants decreases, it is brought about by the rotation scheme: as time passes, the share of the sample able to give the date of arrival as year N progressively increases. This part of the bias related to LFS sampling design has not been adequately taken into account in the calculation of the expansion factors intended to adjust for differences in the probability of the year of arrival arising from the rotation scheme.

33With regard to the different sampling design in each national LFS, the greater or lesser weight of the bias in the EU-LFS will depend on the percentage of the sample that is replaced each year. Of all the countries that provide information to Eurostat, the only ones that are free from this bias are Belgium and Luxembourg (Appendix 4), as they renew the whole sample each year, while the most affected are Switzerland and Germany which renew 20% and 25% of their samples each year, respectively. [6]

34This effect in the Spanish LFS – together with the coverage and non-response biases – causes the estimate of those who arrived in a particular year to increase in successive surveys. Figure 3 shows how the volume of immigrants who arrive in a certain year increases as the year of reference of the LFS progresses, at least until the four or five subsequent years and, sometimes, more. For example, there were an estimated 244,672 entries in 2001 according to the LFS 4Q-2001, and seven years later this figure had doubled to 522,703 according to the LFS 4Q-2008. Moreover, despite the economic recession that should have intensified exits, the number of immigrants captured in the LFS 4Q-2010 who arrived during 2009 doubled with respect to the LFS 4Q-2009. Finally, and more importantly, the entries estimated by the LFS in 2006 increased from 260,723 according to the 4Q-2006 to 430,374 according to the 4Q-2010, a figure that is a lot closer to the 569,541 net entries registered in the EVR for that year.

Figure 3

Figure 3

Immigrants by year of arrival estimated from LFS on consecutive quarters (2000-2010)

35We have seen that, on average, between 2000 and 2010, the final estimate of those who arrived in a particular year may be as much as double that of the first annual estimation. However, this growth cannot be entirely attributed to the sample rotation effect, as part of it will be generated by coverage and non-response biases. In an attempt to differentiate the effect of each of these sources of bias in the LFS, we will assume an ideal situation in which there is no coverage or non-response bias. Theoretically, the sample bias may be identified in the following way.

36Surveying the sample in the fourth quarter of year N, 4Q-N, (assuming that the surveys are conducted on the last day of each quarter) the rotation system only captures arrivals during certain quarters of year N for specific subsamples (w_i). These are shaded in grey in the upper part of Figure 4, and we can observe that mobility during the first two quarters of year N is captured better than in the last two. A year later, in 4Q-N+1, when the new LFS sample is surveyed with respect to mobility in year N, we find that (except for the subsample w₂ which can only have arrived in the first three quarters of N), they could have arrived in any quarter of year N (lower part of Figure 4). The difference between the mobility estimate of year N based on 4Q-N and based on 4Q-N+1, is due primarily to differences in the estimation of mobility in the third and fourth quarters.

Figure 4

Figure 4

Estimate of immigrant arrivals in year N based on the samples of LFS 4Q-N and LFS 4Q-N+1

37Assuming that the annual arrivals are distributed uniformly over the quarters, we observe in the diagram that the estimate for 4Q-N+1 will be more than twice that for 4Q-N. However, if we assume, for example, that arrivals are more highly concentrated in the last two quarters of the year, there is reason to believe that the estimate for both 4Q-N+1 and for 4Q-N+2, may be much higher. The sample rotation effect disappears completely after N + 2. Any further rise in the estimate of arrivals in year N after this time is due to the progressive reduction in coverage and non-response biases.

38In practical terms, one way of differentiating the sample bias from the coverage and non-response bias in the LFS is to calculate the inter-annual growth rate of the subsequent estimates of the group of immigrants arriving in a given year N. In reality, the estimate of the year following arrival, N + 1, reveals coverage, non-response and sample bias. But we know that, in theory, the increase due to sample bias will begin to lessen in the second year, N + 2, and will disappear in N + 3. We can therefore consider that the difference between the growth in the number of immigrants in the first year and those in subsequent years is fundamentally due to the bias inherent in the rotation scheme.

39We calculated these rates using the LFS 4Q between 2005 and 2011. In Figure 5 we observe that the sample bias is very strong: a year after arrival, the LFS captures a volume of immigrants which has grown by 70.3% on average with respect to the initial year. The growth in the number of immigrants captured in other years is lower: 9.2% in N + 2, 3.3% in N + 3, 1.9% in N + 4, 0.6% in N + 5 and finally –3% in N + 6. These percentages could be largely due to the coverage and non-response biases. However, the effect of these biases would perhaps be greater if we were not immersed in an economic crisis which is causing immigrants to leave the country.

40This exercise to differentiate the effects of sample bias from those of coverage and non-response biases cannot be applied to the ENI; because, as indicated at the beginning of section III, the ENI does not exhibit sample bias. Therefore, the underestimation of recently-arrived immigrants in this survey is due to the other two biases: coverage and non-response. In fact, as we have already seen, there is a high non-response in the ENI (28% of the individuals surveyed, ten points above that of the LFS). And, also the concept of collective households is broader than in the LFS (Appendix 2), so coverage bias will also be higher.

Figure 5

Figure 5

Annual growth rate (%) of the number of immigrants by year of arrival computed in successive LFS-4Q (2005-2011)

3 – Reducing bias through post-stratification

41Coverage and non-response errors are generally corrected using techniques for re-weighting or calibrating the expansion factors which require external information referring to the target population. Based on this information, these adjustments seek to raise the weight of under-represented sample groups and to reduce the weight of those which are over-represented. In the case of the ENI, the variables used in the re-weighting procedure are the population projections by groups of nationalities and sex, while in the LFS the variables in the post-stratification are sex, age, region of residence and nationality (Spanish/non-Spanish). Using this information as a base, this technique has been applied to correct the non-response, with similar estimates being obtained from these variables in both surveys (Appendix 3). However, this technique is based on the assumption that within each category the surveyed individuals are a representative sample of the population of this sub-group. If, as we suspect, within each category the recently arrived immigrants are under-represented, this correction might not be successful in obtaining accurate entry flow estimates. This can be illustrated with a simple example.

42Let us assume that we draw a sample whose size is equal to n. To simplify, we also assume that there are only two variables, for example, the year of arrival and the nationality, and that both variables have only two categories. If during the data collection there were no problems (no coverage error or non-response error), the distribution of the sample could be like that shown in Table 2. This sample could be considered as a representative sample of the population (P). The weight of each category in the frame will thus be equal to n_ij/n.

Table 2

A hypothetical representative sample of the population

Immigrants arrived… Within last 5 years More than 5 years ago Total British immigrants n11 n12 n1 Moroccan immigrants n21 n22 n2

A hypothetical representative sample of the population

43Now, let us imagine that there is a poor response rate among the Moroccan immigrants who arrived during the last five-year period. In particular, F individuals do not collaborate with the survey, so only n₂₁ – F individuals answer the survey in this category. As a reasonable sample size is needed, it is decided to replace these elements with others (f_ij). As we are assuming that recently arrived immigrants are more difficult to survey, this usually means that they will be systematically replaced by Moroccan immigrants who arrived at earlier dates (f₂₂) or by British immigrants (f₁₁ and f₁₂), so the final distribution of the units in the sample (Table 3) will be quite different to that of the frame.

Table 3

Hypothetical distribution of immigrants in the sample with non-response in one category

Immigrants arrived… Within last 5 years More than 5 years ago Total British immigrants n11 + f11 n12 + f12 n1 Moroccan immigrants n21 – F n22 + f22 n2

Hypothetical distribution of immigrants in the sample with non-response in one category

44If we multiply the number of surveyed individuals by their corresponding expansion factor [7] (P/n), we will obtain the distribution of the estimated population by nationality and period of arrival whose totals will not coincide with those of the frame. Obviously, there will be a clear bias resulting in an over-estimation of those with British nationality and those who arrived more than five years earlier from any other country.

45To avoid this, let us assume that we have external information regarding the distribution of the population in the frame by nationality. To correct for this non-response, we apply the re-weighting procedure using a correction factor based only on nationality and not on year of arrival. In this case, the correction factor is the ratio between the weight of a particular nationality in the frame and the weight of the same group in the final sample. This post-stratification makes the flow estimates less accurate if the number of recent immigrants multiplied by the expansion factor is larger than the number of recent immigrants multiplied by the expansion factor and the correction factor, as we can see in (1).

46

47Simplifying (1) we obtain the inequality (2), stating the condition in which the re-weighting procedure worsens the estimations:

48

49After brief mathematical processing [8] our results revealed that in the Spanish case, the probability of generating worse estimates with post-stratification is very high. This result is related first to the distribution of the ENI sample into large groups by nationality (1 = rich countries; 2 = poor countries) and by period of arrival (1 = between 2002-2006; 2 = before 2002), and second, to the fact that when the ENI interviewers use the replacement households during the data collection, the probability that non-response is covered by immigrants of the same origin is very high since nationalities tend to concentrate spatially, especially in the case of poor countries. If this is the case, a non-response of just 5.77% among recently-arrived immigrants from poor countries covered with oversampling of immigrants of the same nationality but who have been residents for longer will be enough to underestimate the recent immigrants when using the post-stratification.