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The Importance of the Long Form Census to Canada 385 7KH,PSRUWDQFHRIWKH/RQJ)RUP&HQVXVWR&DQDGD 'DYLG$*UHHQ.HYLQ0LOOLJDQ Canadian Public Policy, Volume 36, Number 3, Septembre/septembre 2010, pp. 383-388 (Article) 3XEOLVKHGE\8QLYHUVLW\RI7RURQWR3UHVV DOI: 10.1353/cpp.2010.0001 For additional information about this article http://muse.jhu.edu/journals/cpp/summary/v036/36.3.green.html Access provided by Western Ontario, Univ of (2 Jan 2015 19:12 GMT) The ImportanceThe Importanceof the of the Long Long Form Census to Canada 383 Form Census to Canada david a. green and kevin milligan Department of Economics University of British Columbia, Vancouver n June the federal government published plans population. The key issue is the conditions under which Ito replace the mandatory long form census with a a given sample will provide an accurate, or unbiased, new National Household Survey (NHS) for the 2011 estimate of the population mean. Census cycle. The new NHS is to be circulated to more households but will be voluntary rather than manda- To continue with our example, suppose we select- tory. The announcement generated a response unique ed two adults at random from the whole population. both for its breadth across civil society and its near By basic laws of statistics, the average of their uniformity. The breadth reflects the plethora of uses for incomes would be an unbiased estimate of the true census data, stretching into so many important deci- population mean. But for any specific sample, we sions made by businesses, municipal and provincial would not expect the sample mean to be the same governments, and non-profits. The near uniformity as the population mean. The difference between the reflects the certainty of science on the statistical nature sample and population mean, however, would not be of voluntary versus mandatory sampling techniques. systematically too high or too low. If we drew many We begin by showing the statistical importance of the such samples and then took the average of the mean distinction between voluntary and mandatory sampling incomes for each of the two-person samples, that techniques, and then explain how the ubiquity of the average would equal the mean income for the entire census in Canada’s national statistics is even greater adult population.1 This, in fact, is the definition of an than many appreciate due to the census’s role as the unbiased sample: one that delivers estimates that are ultimate benchmark for other surveys. not systematically off in one direction or the other. Of course, in most surveys we sample many more Why voluntary samPling fails than two people. The larger we make the sample size, the closer we expect the sample mean in any specific To understand the issues in choosing between the sample to be to the population mean. This is called mandatory long form census and the NHS, it is the Law of Large Numbers, and it is what underlies useful to consider an example. Suppose that we are the size of the long form census. With a sample of interested in knowing the value of a parameter for the 20 percent of the Canadian population chosen at whole adult population of Canada—mean income, for random, we can expect that the sample mean income example. The most accurate way to proceed would be will be very close to the true population mean. to get the incomes for every adult and then average them. Mandatory censuses, which have been used in What happens with a voluntary survey? As we Canada and around the world, aim to get responses for discuss below, a sizeable proportion of people do everyone in the country. But if it is too costly to survey not answer such surveys. If people refuse to answer everyone in the country, then we can get an estimate at random, then non-response would not cause a of adult mean income by surveying a sample of the problem; we just would not get as large a sample. Canadian PubliC PoliCy – analyse de Politiques, vol. xxxvi, no. 3 2010 CPPVolume36No3.indb 383 02/09/10 12:29 PM 384 David A. Green and Kevin Milligan We would expect more variation in the mean incomes Minister Tony Clement’s claim that the accuracy of we calculate, but they would not be systematically a voluntary survey is preserved by sampling more different from the population mean. But if there is households is wrong. It is an incorrect application of something systematic in non-response (if, say, poor the Law of Large Numbers. Former Chief Statistician people respond less than rich people), then there will Munir Sheikh made this point famously in his resigna- be biases—the sample produced from the survey will tion letter with his definitive statement that a voluntary not be representative of the Canadian population. It survey cannot substitute for a mandatory census. is as if we are sampling from a different population; rather than sampling from the population of all adults How pervasive is non-response in voluntary in Canada, we are sampling from the population of surveys? Response rates in voluntary surveys con- adults who chose to respond to a survey. Increas- ducted by Statistics Canada are in the range of 60 ing the sample size will not fix the fact that we are to 70 percent. To take one example, the Survey of sampling from a systematically different population. Household Spending, which is used as part of the construction of the Consumer Price Index, had a If there is systematic bias in the response rates response rate of 63.4 percent in 2008. As shown across groups in Canadian society, then Industry in Figure 1, this response rate has fallen since the Figure 1 Survey of Household Spending Response Rates, 1997–2008 78 76 74 72 70 68 Response Rate (%) 66 64 62 60 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Year Source: Authors’ compilation from Income Statistics Division, Statistics Canada, “User Guide for the Public-use Microdata File Survey of Household Spending.” Canadian PubliC PoliCy – analyse de Politiques, vol. xxxvi, no. 3 2010 CPPVolume36No3.indb 384 02/09/10 12:29 PM The Importance of the Long Form Census to Canada 385 1990s, and the trend shows no sign of abating. This example is representative of the broad patterns in re- Table 1 sponse rate levels and trends in Canada and abroad. Ratios of Mean Income by Vingtile from Various Data Sources, 1995 Crucially, there is strong evidence that survey Vingtile SCF/Census Tax Data/Census non-response is non-random. That is, certain groups systematically are less likely to respond. There are Bottom 2.33 0.87 many examples of this fact, but we focus here on 2nd 1.26 0.94 one example coming out of our own research. In 3rd 1.13 0.89 three studies (Frenette, Green, and Picot 2004; 2006; 4th 1.08 0.87 Frenette, Green, and Milligan 2007), we examined 8th 1.01 0.90 trends in family income inequality over the last three 10th 1.00 0.91 decades in Canada. In the 2006 study we compared measures of the income distribution based on three 12th 1.00 0.93 different sources. The first was a combination of 17th 0.98 0.97 the Survey of Consumer Finances (SCF), which ran 18th 0.98 0.97 annually up to 1997, and the Survey of Labour and 19th 0.97 0.98 Income Dynamics (SLID), which took over as the Top 0.93 1.02 flagship income and labour survey after 1997. These surveys were both special voluntary surveys sent Source: Table 3.5, Frenette, Green, and Picot (2006). to a subset of those surveyed for the Labour Force Survey. Their response rates changed over time but were near 80 percent for both. We also examined in the SCF is about 7 percent lower than that found incomes using census data and tax data. We found in the census. We tried to investigate the sources very substantial differences between the SCF/SLID of these discrepancies and came to the conclusion and the other two data sources, with a tendency for that “a likely explanation for the discrepancy be- the SCF/SLID to overstate incomes at the bottom tween the SCF and the other data sources is relative of the distribution and to some extent to understate under-coverage at the very bottom of the income incomes at the top. Table 1 recreates part of Table distribution in SCF (and SLID)” (Frenette, Green, 3.5 from that study, showing the ratio of either the and Picot 2006, 89). mean income from the SCF/SLID or from tax data to the mean income from census data for a variety of vingtiles for 1995 (a year in which we have data the hidden ubiquity of the Census from all three sources).2 The public debate on the census has made clear the The column showing the relative means obtained multitude of direct uses for data coming from the from census and tax data shows a relatively close census long form. For example, housing informa- agreement across the income distribution.3 In tion is used by the Canadian Mortgage and Housing contrast, for the poorest 5 percent of families, the Corporation to fulfill its legislative mandate, and mean income reported in the SCF is over double also by local governments and private sector ac- that in the census and the tax data. This problem tors to learn about trends in housing. Information decreases at higher incomes. The SCF and census on languages is used to determine local linguistic data provide nearly identical mean incomes for service levels—again both by governments and those in the middle of the distribution.
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