Numerical Impact of a Simple Random Subsample on Consumer 

Spending for Children 

Daniel K. Yang 

Office of Survey Methods Research 

U.S. Bureau of Labor Statistics 

Suite 1950, Postal Square Building, 2 Massachusetts Avenue, NE Washington, DC 20212 

Proceedings of the 2013 Federal Committee on Statistical Methodology (FCSM) Research Conference 

Abstract 

The Bureau of Labor Statistics is in the process of redesigning the Consumer Expenditure Survey (CE). The primary 

goal of this effort is to reduce measurement error while neither increasing data collection costs nor imposing a greater 

burden on respondents. One redesign option that was initially considered was a split questionnaire design. The 

implementation of the split questionnaire we considered was a simple random subsample (SRSS). To evaluate the 

impact of this approach, we simulated data following a SRSS approach and examined to what extent, if any, it might 

affect data users and their respective economic analyses. One particular use of CE data is to characterize spending on 

children by different types of households. To do this, we compared estimates of childrens expenditures derived from 

the full CE sample to those based on the simulated SRSS approach. Specifically, we examined results from descriptive 

statistics, logistic and linear regressions. We also explored the use of a Craggs two stage model for estimating the 

marginal propensity to consume and income elasticities of expenditures on children. We found that compared to the 

full sample, the SRSS produces different estimates of expenditure means and generally higher standard errors as well 

as different estimates for regression coefficients. Finally, based on our findings, we provide recommendations for 

general design changes to the data collection procedures and statistical analysis methods. 

1 
Contents 

1 Introduction 4 

2 Literature Reviews 5 

2.1 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 

2.2 Food . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 

2.3 Medical and Health Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

2.4 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

2.5 Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

2.6 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

3 Data set construction 7 

3.1 Discrepancies in variable definitions and limitations of the data source . . . . . . . . . . . . . . . . . 8 

3.1.1 Variable definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

3.1.2 Differences in data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

3.1.3 Other discrepancies and and limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

3.2 Description of expenditure variables comparing to Omori (2010): Table 2 . . . . . . . . . . . . . . . 8 

4 Basic analysis 8 

4.1 Basic demographic and expenditure estimates: Table 3 . . . . . . . . . . . . . . . . . . . . . . . . . 9 

4.1.1 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

4.1.2 Expenditures on children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

5 Medium analysis 10 

5.1 Model specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

5.2 Comparing the Standard deviations (SD), Skewness and Kurtosis: original and log scale . . . . . . . 10 

5.3 Comparing the logistic regression results for reporting nonzero expenditures on children . . . . . . . 11 

5.4 Comparing the linear regression results for nonzero expenditures on children . . . . . . . . . . . . . 11 

5.4.1 Under the SRSWORSS condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

5.4.2 Reduced SE under the SRSWORSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

5.4.3 Potential contributing factors for the discrepancies could be: . . . . . . . . . . . . . . . . . . 11 

6 Refined analysis 11 

6.1 Data set construction for Cragg’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

6.2 Model specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

6.3 Comparing the Cragg’s model results for children’s expenditures . . . . . . . . . . . . . . . . . . . . 12 

6.3.1 First stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

6.3.2 Second stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

6.3.3 Small groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

7 Advanced analysis 13 

7.1 Model specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

7.2 Comparing the HGLMM Cragg’s model results for children’s expenditures . . . . . . . . . . . . . . 14 

7.2.1 First stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

7.2.2 Second stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

7.2.3 Small groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

7.2.4 Impacts of accounting for the variation among geographical regions . . . . . . . . . . . . . . 14 

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8 Conclusion 15 

8.1 Summary of potential sensitivities from the above economic analyses under a simple random subsample condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

8.2 Preliminary recommendations for improvement of expenditure estimates precision . . . . . . . . . . 15 

8.2.1 Oversampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

8.2.2 Dynamic interview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

8.2.3 Pooling additional quarters/years of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

8.2.4 Implement Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

8.2.5 Hierarchical modeling with random components . . . . . . . . . . . . . . . . . . . . . . . . 16 

8.3 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

List of Tables 

1 Level of analyses, methods and variables for expenditure types . . . . . . . . . . . . . . . . . . . . . 22 

2 Expenditure variables description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

3 Household expenditures on children and demographic descriptive statistics for the Consumer Expenditure Interview Survey, CEQ 2011 Q1 and its SRSWORSS. (weighted) . . . . . . . . . . . . . . . . 24 

4 Selected original and logarithmic statistics for expenditures discussed in the text, CEQ 2011 Q1 and 

its SRSWORSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

5 Logistic regression results: likelihood of expenditures on items in selected categories, CEQ 2011 Q1 

and its SRSWORSS (weighted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 

6 Ordinary least squares regression results: estimates of (the natural logarithm of) quarterly expenditures 

on items in selected categories, CEQ 2011 Q1 and its SRSWORSS (weighted) . . . . . . . . . . . . . 27 

7 Number of observations and number of reporting expenditures by household types . . . . . . . . . . 28 

8 Cragg’s model probability of purchase, predicted expenditure (buyers only), marginal propensity to 

consume and elasticity, and so forth under “ceteris paribus” . . . . . . . . . . . . . . . . . . . . . . . 29 

9 Hierarchical Generalized Linear Mixed (HGLMM) Cragg’s model probability of purchase, predicted 

expenditure (buyers only), marginal propensity to consume and elasticity, and so forth under “ceteris 

paribus” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

List of Figures 

1 Household incomes before tax, poverty threshold among family size . . . . . . . . . . . . . . . . . . 20 

2 Box Plot of Expenditures on Children: Original Scale vs. Natural Log Scale . . . . . . . . . . . . . . 21 

3 
1 Introduction 

The Division of Consumer Expenditure Survey (DCES) has been conducting redesign research activities for the Consumer Expenditure (CE) Surveys under the Gemini Project since 2009. The primary goal of the Gemini Project is 

to redesign the CE Surveys to improve data quality, through a verifiable reduction in measurement error, while not 

inducing extra burden on survey respondents. A key input to the redesign was proposed by Gonzalez et al. (2009). 

They recommended adopting a multidimensional definition of data quality based on the Total Quality Management 

(Brackstone, 1999) and Total Survey Error (Groves et al., 2004) paradigms, denoted as TQM and TSE, respectively. 

These paradigms help to characterize the quality of CE data products1 while incorporating the needs of primary data 

users. Henderson et al. (2010) expanded on the multidimensional definition of data quality by summarizing the specific needs and issues of the CE data users’ community. 

There are diverse applications and uses of CE data products. Data users from other federal agencies, academic and 

research organizations, and congressional leaders conduct numerous and diverse economic analyses from CE data 

products. For instance, the Consumer Price Index (CPI) program is interested in obtaining detailed expenditure and 

demographic information for US consumer units, market basket of goods and services and their relative importance. 

The Department of Defense (DOD) uses CE quarterly expenditure estimates to adjust the cost of living for military 

personnel. Bureau of Economic Analysis (BEA) uses CE data for benchmarking, annual growth rates, and National 

Income and Product Accounts (NIPA). More broadly, other researchers use CE data to study consumer behavior. Regardless of the type of economic analysis, a variety of statistical models have been applied to CE data products to meet 

the needs of each individual data user. These include, but are not limited to, descriptive statistics, regression analysis, 

generalized logistic regression, two-stage analysis, and hierarchical modeling. 

Staff from the Office of Survey Methods Research has been conducting a numerical evaluation of the impact of a simple random subsample condition on these types of economic analyses. This process is a crucial step in understanding 

how data users and their respective economic analyses might be affected by a simple random subsample condition. 

Going through the exercise of conducting these economic analyses under that condition will allow us to learn about 

the process of assessing the impact of a simple random subsample condition on data users. Furthermore, the outputs 

of this process will inform the work of other DCES teams and provide beneficial inputs to the CE redesign. 

The Impact of Design Changes on Economic Analyses Project (EAP) will explore economic analyses of varying sophistication (basic, medium, refined and advanced models approved and/or chosen by stakeholders). The EAP will 

address the numerical impact of how those economic analyses will be affected under a simple random subsample condition. The simple random subsample condition is akin to implementing a split questionnaire design (see Raghunathan 

and Grizzle 1995 for a definition of split questionnaire designs). The primary research objective is: What are the specific sensitivities (e.g., are there particular parameters of the economic models that are compromised?) of utilizing a 

simple random subsample to conduct the various economic analyses? 

This paper provides the results of our investigation for the Impact of Design Changes on Economic Analyses Project. 

The purpose of this document is to summarize literature that used CE data to study different economic phenomena, 

to replicate and summarize the results of various economic analyses under a simple random subsample condition with 

a 0.5 probability of selection. In addition, we characterize potential sensitivities in the differences found in these 

analyses under simple random subsample condition. Based on these differences and sensitivities, we then provide 

preliminary recommendations for general changes to the design and statistical methods used to collect and analyze the 

CE data. 

The organization of the paper is the following: In Section Two, we will provide a literature review of publications that 

used CE data to study different economic phenomena. In Section Three, we will describe the data set obtained for the 

analyses.In Section Four, we will provide the basic analysis of simple univariate statistics estimation such as means, 

1We use the phrase “data product” to refer to any product produced by the DCES and disseminated to the public or other entity. These include, 

but are not limited to, the full microdata CDs and the published tables. 

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standard errors (SE). In Section Five, we will provide the medium analysis of logistic and linear regression model 

coefficients and their associated SE. In Section Six, we will provide the refined analysis of two-stage regression models 

to compute probabilities of purchase, predicted expenditures (buyers only), marginal propensities to consume (MPC) 

and elasticities. In Section Seven, we will provide the advanced analysis of two-stage hierarchical generalized linear 

mixed models (HGLMM) that account for the variation among geographical regions to compute purchase probabilities, 

predicted expenditures (buyers only), MPC and elasticities. In Section Eight, we will summarize the major findings 

from those economic analyses, and conclude with preliminary recommendations for general changes to the design and 

statistical methods used to collect and analyze the CE data. 

2 Literature Reviews 

CE data products have been examined in different contexts, such as spending patterns, life cycle analysis, poverty, 

demographic subsets, savings and assets, etc. For example, life cycle is generally referred to as a period reflecting 

different generations of consumers according to their ages. The life cycle hypothesis assumes that consumer unit 

(CU) or household expenditures change by their life cycle, and age is found to be an important factor in spending 

pattern of consumer expenditures. There are some types of expenditures that are considered essential for survival, 

e.g. housing, basic food and clothing; other types are considered optional, e.g. leisure and education. The DCES 

Branch of Information and Analysis (BIA) has been documenting research papers of economic analyses using CE 

data. In terms of total expenditure, household type has an impact on financial resources distribution (Lino 1998 pp. 

12 third paragraph, cited in Omori 2010 pp. 4 right column last paragraph). However, higher income level does not 

always result in higher expenditure levels (Paulin and Lee 2002 Table 3, pp. 23 left column first paragraph, cited in 

Omori 2010 pp. 4 left column fourth paragraph). This section reviews literature referenced by BIA, among different 

expenditure types in education, food, medical and health care, demographics, assets and energy. 

2.1 Education 

Omori (2010) reviewed education expenditures and found literature suggesting disadvantages of single-parent households, especially for single-mother households, they have lower likelihood of high school graduation, higher likelihood 

of unsatisfactory grades, lower economical support and more social behavioral problem as compared to two-parent 

households (McLanahan and Sandefur 1994, Powell et al. 2006). Other literature indicated that higher income parents 

allocate more resources to their children than lower income parents. Omori (2010) then studied education expenditures and found that single-mother CUs have higher probability of education expenditure than married-couple CUs; 

higher income CUs have higher probability of children’s education expenditure than lower income CUs; African and 

Hispanic CUs have lower probability of education expenditure than White CUs; the probability of education expenditure increases as number of children increase; single-parent CUs have higher probability of entertainment expenditure 

than married-couple CUs; higher income, educational attainment and occupation level are all associated with higher 

probability of entertainment expenditure. The major influences on children’s education expenditure are household 

income, educational attainment and occupation level, not marital status or household type. 

2.2 Food 

Fan et al (2007) applied cluster analysis on CE data to classify consumers into eight groups based on food expenditure patterns. They are: (1)balanced, (2) full-service-dominated, (3) fast-food-dominated, (4) meat-eater, (5) 

miscellaneous-food-dominated, (6) alcohol-dominated, (7) beverages-dominated, and, (8) food-at-work-dominated. 

The full-service, fast-food and food-at-work dominated groups are considered as the food away from home (FAFH) 

dominated group. They found that higher working hours and lower income-to-needs ratio are associated with higher 

probability of being in the FAFH group. Younger consumers have a higher probability of being in fast-food-dominated 

group as compared to older consumers; single-men consumers have a higher probability of being in the alcohol group 

than married consumers; Blacks and Hispanic consumers have a higher probability of being in the meat-eater group 

as compared to White consumers. Zan et al (2010) found that younger cohorts of consumers spend more on food 

away from home than older cohorts, and these cohort effects are likely due to dinning and food preferences shift 

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among generations. U.S. consumers are likely to continue spending more on their food away from home expenditures. 

Those analyses on consumer food expenditures would inform the decision making of certain nutritional education and 

prevention. 

2.3 Medical and Health Care 

Hong and Kim (2000) investigated medical expenditure and found that household health insurance coverage, liquidity, 

“life cycle stage, household size, self-employment status” and educational attainment all have influences on health care 

expenditures. More single person and single parent families are uninsured. Families with children have higher health 

care expenditure than couples with no children. Medicaid enrollment probably reflects smaller health care expenditure 

of single parent households than others. The older population has the highest financial burden compared to other 

groups across life cycle stages. Older people with needs of nursing homes tend to support federal subsidy programs. 

Families who have higher unearned incomes spend more on health care than lower level unearned income families. 

Self-employed people spend more on health care with high premiums and higher deductibles, and consequently, they 

become more likely not to purchase health insurance. 

Health care expenditures are an important part of the household budget. U.S. households have been increasing their 

health care expenditures and elderly households have been spending a larger share of overall budget on health care 

than other households (BLS 2011 2(12) and 2011 1(8)). Medical expenditures comprise a larger budget share for low 

income households. In 2001, Census proposed “medical out-of-pocket expenses subtracted from income (MSI) and 

medical out-of-pocket expenditures (added) in the threshold (MIT)” as alternative poverty measures. Short and Garner 

(2002) compared MSI and MIT to official U.S. poverty measures. They suggested that these alternative poverty 

measures can be used to assess the depth of impoverished subpopulation’s economic hardships and can be used to 

evaluate the effectiveness of government programs which provide tax incentives and transfers (“redistribution effect”) 

to those households. As for Medicare households, it has been observed that the prescription drugs expenditure and its 

share in the overall health care budget were lower after the implementation of Medicare Part D (BLS 2011 2(8)). 

2.4 Demographics 

It has been indicated that consumer expenditures are associated with CU characteristics, such as race, occupation, and 

age of the household head, and are also affected by their socioeconomic class, demographics and residential location 

(Omori, 2010). Paulin (2008) studied generational demographics. He found that comparing to 1984-1985 generation, 

the later generation of 2004-2005 of single young adults has higher educational attainment and proportion of home 

ownership, spends a smaller share on food away from home, and spends a larger share on food at home and on housing, 

which is a sign of living along (Paulin 2008 pp. 35 left column second paragraph, right column first paragraph). The 

economic situation of the later generation of single young adults may not improve, but it does not decline. Another 

publication has shown that sharing expenses by young married couples does not cut costs to one person level; they do 

spend less per person than singles. However, they have higher per-person expenditure on transportation, health care, 

personal insurance and pensions than singles (BLS 2011 2(4)). 

2.5 Assets 

Melzer (2010) studied the impact of mortgage and debt on household expenditures and found that a substantial portion of homeowners decrease expenses on their homes due to the prospect of default. Homeowners with negative 

equity (“underwater”) decreased their expenses on mortgage principal payments, home improvements and maintenance expenditures, by approximately 30%, regardless of their financial stress in terms of higher income, liquidity and 

borrowing capacity. In contrast, no change has been found on household expenditures for vehicles, furniture and appliances (non-home-related). Negative equity homeowners decreased more mortgage principal payments in non-recourse 

states than in recourse states where creditors were allowed to repossess homeowners’ other properties as the collateral could not cover the mortgage balance. The mortgage principal reduction policy seems to encourage underwater 

homeowners paying their mortgage principal and investing in their properties by recovering homes’ positive equity. 

6 
2.6 Energy 

The CE estimates of energy expenditures has been compared to the Residential Energy Consumption Survey (RECS), 

sponsored by the Energy Information Administration (EIA) of the U.S. Department of Energy (BLS 2010 1(12)). 

Abbot (2008) conducted a regional in-depth study and found that the Southern region of the U.S. spent a smaller proportion of total expenditures on energy in 2006 as compared to 1984, a similar pattern was observed at national level 

and other regions. However, the South spent the largest proportion of total expenditure on energy among other regions. 

The Southern region had increased its electricity consumption two times when comparing to the electricity prices increase in the South. He suggested that more expenses are expected to be transferred from non-energy transportation 

to energy-oriented transportation, e.g. consumers would spend more on gasoline and mass transit at the expense of 

shopping for cars, auto insurance and financing. 

Ethridge (2009) found that the steady increase in the proportion of gasoline expenditures over total expenditures has 

helped to curtail the vehicle purchase expenditures during 2003-2007. Nevertheless, overall transportation expenditures did not appear to affect the spending pattern of other expenditure categories. In 2010, Gicheva et al found that the 

gasoline prices shock had a significant impact on consumer price sensitivity (CPS) in retail grocery spending pattern. 

As a consequence, consumers adapted lower price products replacement to absorb the short term income shock caused 

by fuel costs spike, and their primary strategy was shopping on sale items. They suggested that the gasoline prices 

shock might further influence CPS in terms of broader supply, demand and product expenses. 

2.7 Summary 

In general, CE data products have been applied for a variety of economic analyses with diverse research interests. The 

variaty of expenditure variables had been studied but not limited to: food, medical, health care, utility and income 

before tax (for income-to-poverty-threshold ratio), education, entertainment, books, children’s apparel, etc. Those 

economic analyses also include socioeconomic and demographic characteristic variables: for member level, using 

reference person’s record of Age (years), Sex (Male, Female), Race, Education attainment, Employment status and 

Occupation level; for CU level, using Geographic region (Northeast, Midwest, South, and West), Household type 

(married couple, single mother, single father and Cohabiting, etc.) and Household tenure (homeowner, renter). Table 

1 provides the level of analyses, methods and variables for each of the different types of expenditure categories identified in the reviewed literature. 

Next, we will use the 2011 first quarter CE interview data to conduct the various economic analyses in the following 

sections. 

3 Data set construction 

The analyses we replicated reflects the focus of Omori (2010) – household spending patterns for children. Previous 

literature suggested that there is an association between allocating resources to children and household income level 

(Omori 2010). So it is an important topic to study because it may have many economic and policy implications. As a 

preliminary and ancillary analysis tool, we provide a boxplot of income before tax by number of members in the CU 

in Figure 1 below. For reference, we also provide the poverty threshold for each family size (represented by a closed 

circle). This graphic is useful for illustrating the overall CU incomes in CE data. 

Omori (2010) pooled 2007 and 2008 CEQ public-use micro data for her analysis. She excluded CUs with missing 

values for demographic and expenditure variables on children (apparel, education, books and entertainment), as well 

as CUs with children all above 18 years old. Expenditures on gifts or for non-CU children were also excluded. She 

pointed out a caveat in her analysis: the current CE is structured to collect certain expenditures at the CU-level (e.g. 

entertainment), so it is impossible to identify whether an expenditure incurred by the CU was for a child 18 years old, 

or under or for the parents, etc. 

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To replicate the analyses, we selected the first quarter of 2011 CEQ Phase III data (denoted as, CEQ 2011 Q1). This 

yielded an initial sample size of 6,869 CUs. Consistent with Omori (2010), we subset these 6,869 CUs by excluding 

those with missing values for demographic and expenditure variables, CUs with children all above 18 years old, and 

expenditures on gift or for non-CU children. The final sample used for our analysis contains 2,262 CUs. Under the 

simple random sampling without replacement (with a 0.5 probability of selection) subsample (SRSWORSS) condition, 

we obtain a total of 1,131 CUs. 

3.1 Discrepancies in variable definitions and limitations of the data source 

In Table 2 below, we describe the components of the expenditure variables used in our analysis and offer comparisons 

to the definitions of these expenditure categories used in Omori (2010). Specifically, we listed the expenditure variable 

names, definitions provided by Omori (2010), how we constructed each variable using CEQ 2011 Q1 (including codes 

from CEQ dictionary) and the corresponding data file names from which the variables are contained. 

In conducting the economic analyses, we acknowledge the following limitations on our data: 

3.1.1 Variable definitions 

We have tried as close as possible to construct the demographic variables and expenditures on children in a similar 

fashion to Omori (2010). However, there is some lack of documentation and ambiguity in her article on how those 

variables were defined and how the subsetting of data occurred. These issues might lead to discrepancies in the two 

data sources. Two examples are provided in the following: 

1. Educational attainment in Omori (2010) Table 1 could be defined as the highest level achieved of education for 

the CU’s reference person and as a consequence, the High School (HS) category may include persons with some 

college education, but no degree. 

2. Occupation level was not specified with details of categorical components in Omori (2010). From the CEQ dictionary for this data, we define the occupational category “Managerial/professional” as professional, administrator, manager, either self-employed or salaried (POCC REF = 101, 120, 201, 220) and define ”Administrative” 

as administrative support including clerical, either self-employed or salaried (POCC REF = 108, 208). 

3.1.2 Differences in data sources 

Differences in sample size, time periods, and duration between the two data sets might also contribute to the discrepancies in demographics and expenditure estimates (e.g. means, SE) on children. For example, spending patterns prior 

to the economic downturn experienced in late 2008 might result in differences in the spending patterns reflected in our 

data source because it was constructed using 2011 data. 

3.1.3 Other discrepancies and and limitations 

Total and ratio estimates were not provided in Omori (2010) Table 1. Even if they were, we expect similar differences 

and/or discrepancies due to (but not limited to) the factors described above (e.g. discrepancies in the time periods of 

the two data sources). 

3.2 Description of expenditure variables comparing to Omori (2010): Table 2 

4 Basic analysis 

The purpose of this section is two-fold. First, we sought to replicate a key “basic” analysis under a simple random 

subsample condition with a 0.5 probability of selection. For the purpose of this research, we define a basic analysis 

as the lowest level of statistical sophistication which includes the calculation of simple univariate statistics such as 

8 
means, standard errors (SE). In this analysis, we chose to replicate Omori (2010) Table 1: Descriptive statistics of 

households with children, Consumer Expenditure Interview Survey, 2007-08. 

The second purpose is to characterize potential sensitivities in the differences found in this analysis under simple random subsample condition. Based on these differences and sensitivities, we provide preliminary recommendations for 

changes to the design and statistical methods used to collect and analyze the CE data in Section Eight. 

Omori (2010) examined household expenditures on children using Consumer Expenditure Interview Survey (CEQ) 

2007-2008 data. She concluded that the major influences on children’s education expenditure were household’s income, educational attainment and occupation level, but not on marital status or household type. 

4.1 Basic demographic and expenditure estimates: Table 3 

The unweighted categorization of family type using the CEQ 2011 Q1 sample of 2,262 CUs with children 18 years 

old or under contains 1,574 married couple CUs, 336 single mother CUs, 59 single father CUs, and 293 cohabiting (or 

other family type) CUs. The unweighted family type categorization of the SRSWORSS of 1,131 CUs with children 18 

years old or under contains 786 married couple CUs, 175 single mother CUs, 24 single father CUs, and 146 cohabiting 

CUs. In Table 3, we offer comparisons of the expenditure estimates on children and demographic characteristics derived from the following: (1) CEQ 2011 Q1 sample; (2) the SRSWORSS condition. Our primary goal is to observe the 

numerical impact of SRSWORSS condition. We take into account the final weight (”FINLWT21” in CE dictionary) 

from CE production for all estimates including mean, percentage, SE and 95% confident interval (CI) in Table 3. In 

addition, for SRSWORSS, the final weight is also adjusted by the subsample selection probability. 

From Table 3, we identify certain differences (or “sensitivities”) and similarities under the SRSWORSS condition. We 

describe those findings in the following statements: 

4.1.1 Demographics 

Demographic descriptive statistics are not different (or “sensitive”) for most cases in terms of percentage and mean. 

The SRSWORSS demographic estimates remain similar to those in the full sample (CEQ 2011 Q1), with wider 95% 

CIs reflecting the larger SE. This is an expected finding since we have subsampled with 0.5 probability of selection. 

The exception to this trend is from the single father group. This is likely due to the small initial sample size of this 

group and the subsequent subsampling. 

4.1.2 Expenditures on children 

Expenditures on children are different in terms of means and SE. Specifically, Household children’s expenditure means 

under the SRSWORSS condition are different than the means computed from the full sample, with wider 95% CIs 

which indicate larger SE (e.g. children’s education expenditure of married couple and children’s apparel expenditure 

of single mother). However, there are a few exceptions, SE of married couple’s entertainment expenditures and 

single mother’s education expenditures on children decreased under SRSWORSS condition, SE of single mother’s 

books expenditures and cohabiting CUs education expenditures on children remained similar under SRSWORSS 

condition. Potential contributing factors could be: (1) temporal differences (or seasonal fluctuation) between the 

various data sources; (2) the weighting adjustment used in the analysis; (3) sample sizes of those groups and the 

subsequent subsampling. For the single father group, large SE associated with means of children’s education and 

apparel expenditures produce negative lower bounds for their respective 95% CIs. It is worth noting that there are a 

few situations in which the SE under the SRSWORSS condition decreased or remained unchanged when compared to 

the full sample. We conjecture that these may be outliers or simply anomalies from only drawing one subsample. One 

way to verify this conjecture would be to draw repeated subsamples and then calculate the empirical SE from multiple 

subsamples. 

9 
5 Medium analysis 

The purpose of this section is two-fold. First, we sought to replicate and summarize the results of a key “medium” analysis under a simple random subsample condition with a 0.5 probability of selection. For the purpose of this research, 

we define a medium analysis as the middle (above “basic” in Section Four) level of statistical sophistication such 

as analyzing logistic and linear regression model coefficient and their associated standard errors (SE). The medium 

analysis may also include variable transformations such as the natural logarithm (to insure model assumptions are met). 

In this analysis, we replicate the following tables from Omori (2010): 

1. Table 2: Logistic regression results: likelihood of expenditures on items in selected categories, Consumer Expenditure Interview Survey, 2007–08; 

2. Table 3: Ordinary least squares regression results: estimates of (the natural logarithm of) quarterly expenditures 

on items in selected categories, Consumer Expenditure Interview Survey, 2007–08; and 

3. Table A-1: Selected original and logarithmic statistics for expenditures discussed in the text. 

The second purpose is to characterize potential sensitivities in the differences found in this analysis under simple 

random subsample condition. Based on these differences and sensitivities, we provide preliminary recommendations 

for changes to the design and statistical methods used to collect and analyze the CE data in Section Eight. Omori 

(2010) examined household expenditures on children using Consumer Expenditure Interview Survey (CEQ) 2007– 

2008 data. We documented her research conclusions as references in Yang and Gonzalez (2012a). 

5.1 Model specifications 

Omori (2010) utilized weighted logistic regression models to estimate the odds ratio (OR) of households’ reporting 

nonzero expenditures on children. The weight used was the final weight (“FINLWT21” in CE dictionary) from production. She also applied the same weights to a series of weighted linear regression models to analyze the households’ 

log expenditures on children by only using households reporting nonzero expenditures on children. 

For each of the four expenditure categories (education, entertainment, books, and apparel), the outcome variable of 

the logistic regression model is whether a household reported a nonzero expenditure on children, and the outcome 

variable of the linear regression model is the category-specific nonzero expenditure on children. Both logistic and linear regression models use the same set of socioeconomic and demographic characteristic covariates: household type, 

income percentile, education attainment, occupation level, ethnicity, number of children in the household between age 

0 and 5, between age 6 and 12, between age 13 and 18, and geographic region. 

In this analysis, we offer comparisons of logistic and linear regression models between the CEQ 2011 Q1 sample and 

the SRSWORSS condition. We take into account the final weight (“FINLWT21”) for logistic regression estimates 

including odds ratios and 95% confident intervals (CIs), and for linear regression estimates including coefficients and 

their associated SE. 

5.2 Comparing the Standard deviations (SD), Skewness and Kurtosis: original and log scale 

Omori (2010) indicated that the sampling distributions of all four expenditure categories (education, entertainment, 

books and apparel) were skewed, so she adopted the logarithm transformation on nonzero expenditures for those categories. We provided Table 4 below to compare the SD, Skewness and Kurtosis between the original and log scales 

among different data sources. For reference, we also provide a boxplot of nonzero expenditures on children for four 

expenditure categories in Figure 2. 

Table 4 shows that the SD under the SRSWORSS condition on the original scale are generally larger than those of 

the full sample. However, for entertainment nonzero expenditures on children, the original SD from the SRSWORSS 

10 
condition is smaller than that of the full sample. This is probably due to the fact that the full sample contains six 

households which spent from above $10,000 to $40,000 on entertainment. For nonzero expenditures on children’s 

books, the original SD from the SRSWORSS condition decreased when compared to the full sample. These may be 

outliers or simply anomalies from the first quarter of 2011 CEQ data. These can be assessed via simulation techniques. 

5.3 Comparing the logistic regression results for reporting nonzero expenditures on children 

In Table 5 we compare the various logistic regression results for reporting nonzero expenditures on children. In this 

table, we use wt to denote weighted analyses using the final weight variable “FINLWT21.” From Table 5, we identify 

differences (or “sensitivities”) under the SRSWORSS condition in the following. The OR estimates of reporting 

nonzero expenditures on children’s education, entertainment, books, and apparel are different than those from the full 

sample. The 95% CIs associated with these OR estimates under the SRSWORSS condition are generally wider than 

those from the full sample. These 95% CIs do not overlap between the SRSWORSS condition and the full sample. 

This pattern is consistent across all four expenditure categories for this particular one subsample. Except for income 

percentile where the SRSWORSS produces similar estimates and 95% CI as the full sample. 

5.4 Comparing the linear regression results for nonzero expenditures on children 

In Table 6 we compare the linear regression results for nonzero expenditures on children. From Table 6, we identify 

certain differences (or “sensitivities”) and similarities under the SRSWORSS condition. We describe these findings as 

follows: 

5.4.1 Under the SRSWORSS condition 

In general, the regression coefficient estimates of nonzero log expenditures on children’s education, entertainment, 

books, and apparel are different than those from the full sample. The SE of these coefficient estimates under the 

SRSWORSS condition are wider than those from the full sample. 

5.4.2 Reduced SE under the SRSWORSS 

However, it is worth noting that for children’s education and books expenditure, the SE of income percentile under the 

SRSWORSS condition remains similar when compared to the full sample. 

5.4.3 Potential contributing factors for the discrepancies could be: 

1. temporal differences (or seasonal fluctuation) between the various data sources; 

2. the weighting adjustment used in the analysis; and 

3. sample sizes of those data sources and the subsequent subsampling. 

We conjecture that these may be outliers or simply anomalies from only drawing one subsample. One way to verify 

this conjecture would be to draw repeated subsamples and then calculate the empirical SE from multiple subsamples. 

6 Refined analysis 

The purpose of this section is two-fold. First, we sought to replicate and summarize the results of a key “refined” 

analysis under a simple random subsample condition with a 0.5 probability of selection. For the purpose of this 

research, we define a refined analysis as a statistical analysis that employs sophisticated theory and/or methods to 

explain various phenomena such as the advanced (above “medium” in Section Five) level of statistical sophistication. 

For example, implementing two-stage regression models, e.g. Cragg’s model to compute probability of purchase, 

11 
predicted expenditure (buyers only), marginal propensity to consume (MPC) and elasticity. The refined analysis may 

also include variable transformations such as the natural logarithm (to insure model assumptions are met). 

We had originally planned to extend Omori’s research (presented in Section Five) using a refined analysis, but her 

research did not apply a refined model, such as a two-stage regressions model, like Cragg’s model. Paulin and Duly 

(2002) evaluate the influence of retirement on spending in terms of marginal propensity to consume and elasticity. 

Here, marginal propensity to consume is defined as “the change in expenditure given a unit change in income”and 

income elasticity is defined as “the percent change in expenditure for a specific good given a 1-percent increase in 

income.” Thus in this analysis, we replicate the following tables from Paulin and Duly (2002 pp. 57 left column first 

paragraph, right column last paragraph): 

1. Table 5: Number of observations for ordinary least squares regressions; and 

2. Table 7: Elasticities, and so forth under “ceteris paribus”. 

The second purpose is to characterize potential sensitivities in the differences found in this analysis under simple 

random subsample condition. Based on these differences and sensitivities, we provide preliminary recommendations 

for changes to the design and statistical methods used to collect and analyze the CE data in Section Eight. 

6.1 Data set construction for Cragg’s model 

The data set we used for this analysis was constructed in a similar fashion as the data set we used for replicating 

Omori’s (2010) analysis which reflects the focus of household spending patterns for children (Yang and Gonzalez 

2012a, b). This was because we wanted the procedure of our analyses from basic to the highest level of sophistication 

to be as consistent as possible. Also, Paulin and Duly (2002) data could not be compiled for this analysis to be 

completed as planned. In this analysis, we selected the first quarter of 2011 CEQ Phase III data (denoted as, CEQ 

2011 Q1). This yielded an initial sample size of 6,869 CUs. Consistent with Omori (2010), we subset these 6,869 CUs 

by excluding those with missing values for demographic and expenditure variables, CUs with children all above 18 

years old, and expenditures on gift or for non-CU children. In addition, to meet the requirement of two-stage Cragg’s 

regressions model implemented in Paulin and Duly (2002), we further exclude CUs with non-positive annual income. 

The final sample used for our analysis contains 1,977 CUs. Under the simple random sampling without replacement 

(with a 0.5 probability of selection) subsample (SRSWORSS) condition, we obtained a total of 988 CUs (Table 1). For 

reference, we also described discrepancies in variable definitions and limitations of the data source in Section Three. 

6.2 Model specifications 

Similar to Paulin and Duly (2002), we compare the estimated averages of probability of purchase, predicted expenditure (buyers only), marginal propensity to consume and elasticity for each of the married couple, single mother, single 

father and cohabiting household type groups. In the first stage analysis, we implement unweighted logistic regression 

and ordinary least squares models to obtain probability of purchase and predicted expenditure (buyers only). For each 

of the four expenditure categories (education, entertainment, books, and apparel), the outcome variable of the logistic 

regression model is whether a household reported a nonzero expenditure on children, and the outcome variable of the 

linear regression model is the natural log of category-specific nonzero expenditure on children. Both logistic and linear 

regression models use the same set of socioeconomic and demographic characteristic covariates: household income 

natural logarithm, education attainment, occupation level, ethnicity, number of children in the household between age 

0 and 5, between age 6 and 12, between age 13 and 18, and geographic region. See Paulin and Duly (2002) Appendix 

B for computational details. 

6.3 Comparing the Cragg’s model results for children’s expenditures 

In Table 8 we compare the linear regression results for nonzero expenditures on children. From Table 8, we identify 

certain differences (or “sensitivities”) and similarities under the full sample and SRSWORSS condition. We describe 

these findings as follows: 

12 
6.3.1 First stage estimates 

The simple random subsample produces close results for probability of purchase and predicted expenditure (buyers 

only), as compared to the full sample. 

6.3.2 Second stage estimates 

Marginal propensity to consume and elasticity from the simple random subsample deviate from the full sample. We 

conjecture that these may simply be anomalies from only drawing one subsample. One way to verify this conjecture 

would be to draw repeated subsamples and then calculate the empirical averages from multiple subsamples. 

6.3.3 Small groups 

Due to the small samples in the single father and cohabiting group, the Cragg’s model estimates seem unreliable for 

both the full sample and simple random subsample. As evident from Paulin and Duly (2002) Appendix B. (pp. 57-58), 

the negative coefficient estimates from logistic regression and ordinary least squares regression may produce a negative 

estimate of marginal propensity to consume, and lead to a negative income elasticity of demand which is associated 

with an inferior good (whose demand reduces as consumer income increases). 

7 Advanced analysis 

The purpose of this section is two-fold. First, we sought to replicate and summarize the results of a key “advanced” 

analysis under a simple random subsample condition with a 0.5 probability of selection. Heeringa et al (2010) categorizes generalized linear mixed models (GLMM) as an advanced modeling topic (one of the highest levels of statistical 

sophistication presented in the textbook). For the purposes of this research, we define an advanced analysis as a statistical analysis that employs highly sophisticated theory and/or methods to explain various phenomena (above “refined” 

in Section Six). There is a desire from DCES to apply a more sophisticated model to analyze consumer’s marginal 

propensities to consume (MPC), and elasticities (Henderson 2012). One example of an advanced analysis is utilizing 

two-stage hierarchical generalized linear mixed models (HGLMM) that account for the variation among geographical 

regions to compute purchase probabilities, predicted expenditures (buyers only), marginal propensities to consume, 

and elasticities. This analysis may also include variable transformations such as the natural logarithm (to insure model 

assumptions are met). 

We had originally planned to extend Omori’s research (presented in Section Five) using an advanced analysis, but her 

research did not apply an advanced model, such as a two-stage Cragg’s model using generalized linear mixed regressions to account for geographical region variations. Therefore, we chose to extend the research of Paulin and Duly 

(2002) in which they evaluated the influence of retirement on spending in terms of marginal propensity to consume 

and elasticity by using logistic regression and ordinary least squares models. In their research, marginal propensity 

to consume is defined as “the change in expenditure given a unit change in income”and income elasticity is defined 

as “the percent change in expenditure for a specific good given a 1-percent increase in income.” In this analysis, we 

replicate Table 7: Elasticities, and so forth under “ceteris paribus” from Paulin and Duly (2002) using an HGLMM 

approach. The number of observations and number of reporting expenditures by household types remain the same as 

reported in Table 8 of Section Six (replicate of Table 5 in Paulin and Duly 2002). 

The second purpose is to characterize potential sensitivities in the differences found in this analysis under simple 

random subsample condition. For example, would some particular parameter estimates of the models be changed 

after utilizing a simple random subsample to conduct the various economic analyses? Based on these differences and 

sensitivities, we provide preliminary recommendations for general changes to the design and statistical methods used 

to collect and analyze the CE data in Section Eight. In this section, we use the same data set constructed in the refined 

analysis (Section 6.1) for HGLMM Cragg’s model. 

13 
7.1 Model specifications 

Similar to Paulin and Duly (2002), we compare the estimated averages of probability of purchase, predicted expenditure (buyers only), marginal propensity to consume and elasticity for each of the married couple, single mother, 

single father and cohabiting household type groups. In the first stage analysis, to account for the variation among geographical regions, we implement HGLMM logistic regression models to obtain probability of purchase, and HGLMM 

regression models to obtain predicted expenditure (buyers only). For each of the four expenditure categories (education, entertainment, books, and apparel), the outcome variable of the HGLMM logistic regression model is whether a 

household reported a nonzero expenditure on children, and the outcome variable of the HGLMM regression model is 

the natural log of category-specific nonzero expenditure on children. Both HGLMM logistic and regression models use 

the same set of socioeconomic and demographic characteristic covariates: natural logarithm household income, education attainment, occupation level, ethnicity, number of children in the household between age 0 and 5, between age 

6 and 12, between age 13 and 18, and geographic region. See Paulin and Duly (2002) Appendix B for computational 

details. 

7.2 Comparing the HGLMM Cragg’s model results for children’s expenditures 

In Table 9 we compare the HGLMM regression results for nonzero expenditures on children. From Table 9, we identify 

certain differences (or “sensitivities”) and similarities under the full sample and SRSWORSS condition. We describe 

these findings as follows: 

7.2.1 First stage estimates 

The simple random subsample produces estimates of the purchase probabilities that were close to the full sample 

estimates, but provides no consistent trends for predicted expenditures (buyers only), i.e. sometimes higher, sometimes 

lower than the full sample. 

7.2.2 Second stage estimates 

Marginal propensity to consume from the simple random subsample deviate from the full sample, more deviations are 

observed for elasticity. We conjecture that these may simply be anomalies from only drawing one subsample. One 

way to verify this conjecture would be to draw repeated subsamples and then calculate the empirical averages from 

multiple subsamples. 

7.2.3 Small groups 

Due to the small samples in the single father and cohabiting group, the HGLMM Cragg’s model estimates seem 

unreliable for both full sample and simple random subsample. We were not able to produce hierarchical linear mixed 

model eatimtes of predicted expenditures (buyers only) and second stage estimates for entertainment expenditure on 

children under the full sample, and for all children’s expenditures under the simple random subsample for the single 

father group. In addition, as evident from by Paulin and Duly (2002) Appendix B. (pp. 57-58), the negative coefficient 

estimates from HGLMM logistic and regression models may produce a negative estimate of marginal propensity to 

consume, and lead to a negative income elasticity of demand which is associated with an inferior good (whose demand 

reduces as consumer income increases). 

7.2.4 Impacts of accounting for the variation among geographical regions 

The HGLMM Cragg’s model generally produces higher probability of purchase and elasticity estimates when taking 

into account the random variations among U.S. regions of Northeast, South, Midwest and West, as compared to the 

classic two-stage Cragg’s model in refined analysis (Section Six). 

14 
8 Conclusion 

8.1 Summary of potential sensitivities from the above economic analyses under a simple 

random subsample condition 

Our primary research objective is to characterize the potential sensitivities (e.g., are there particular parameters of the 

economic models that are compromised?) of utilizing a simple random subsample to conduct the various economic 

analyses? I this study, we investigate a series of economic analyses under a simple random subsample condition. The 

results indicate the following: 

1. In simple univariate statistics estimation (e.g. means, percentages and SE), (1) for household demographic 

variables, the simple random subsample produces similar demographic estimates in terms of percentage and 

mean as compared to the full sample, with larger SE. The exception is the single father group which is likely 

due to the small initial sample size of this group and the subsequent subsampling. (2) For household expenditures 

on children, the simple random subsample produces different expenditure estimates on children in term of the 

mean as compared to the full sample, and generally larger SE (with a few exceptions). 

2. In linear regression and generalized logistic regression models, we found that the simple random subsample 

produces different coefficient estimates and generally higher SE as compared to the full sample. However, the 

SE for some of the coefficients from the simple random subsample are smaller than the full sample. 

3. In a two-stage regressions Cragg’s model, we found that (1) the simple random subsample produces close first 

stage estimates, such as probability of purchase and predicted expenditure (buyers only), as compared to the full 

sample; (2) the second stage estimates, such as marginal propensity to consume and elasticity, from the simple 

random subsample deviate from the full sample. 

4. In a two-stage Cragg’s model using generalized linear mixed regressions to account for geographical region 

variations, we found that: 

(a) For first stage estimates, the simple random subsample produces estimates of the purchase probabilities 

that were close to the full sample estimates, but produces no consistent trends for predicted expenditures 

(buyers only), i.e. sometimes higher, sometimes lower than the full sample; 

(b) The second stage estimates, marginal propensities to consume and elasticities, from the simple random 

subsample deviate from the full sample; 

(c) Under the simple random subsample, we were not able to produce hierarchical linear mixed model estimates of predicted expenditures (buyers only) and second stage estimates for the single father group due 

to small sample sizes; and 

(d) Compared to the classic two-stage Cragg’s model in refined analysis (Yang and Gonzalez 2013a), the 

HGLMM Cragg’s model generally produces higher probabilities of purchase and elasticity estimates. 

8.2 Preliminary recommendations for improvement of expenditure estimates precision 

Based on the inflation in 95% confidence intervals (CIs) and standard errors (SE), and differences in odds ratio (OR) 

estimates, coefficient estimates and mean estimates, and the Cragg’s model estimates between the CEQ 2011 Q1 and 

the SRSWORSS, we recommend following preliminary approaches to improve the estimation precision of expenditures, marginal propensity to consume and elasticity under SRSWORSS. 

8.2.1 Oversampling 

Oversample groups that might result in small effective sample sizes due to the subsampling. This would lead to an 

increase in the degrees of freedom for variance estimators. 

15 
8.2.2 Dynamic interview 

Implement a dynamic interview, such as, those proposed in Gonzalez (2012) in which groups are identified during an 

initial phase of data collection and oversample those groups in a subsequent phase, then apply modified weights to the 

data in the subsequent process to produce valid official estimates. 

8.2.3 Pooling additional quarters/years of data 

Researchers should consider pooling extra quarters of data to offset the individual quarterly impact (e.g. minimum of 

4 years data). This has the potential to result in “smoother” mean, coefficient and variance estimates, and second stage 

estimates, such as marginal propensity to consume and elasticity. 

8.2.4 Implement Bootstrap 

Researchers may consider bootstrap methodology as an option with a large number of simple random subsamples (e.g. 

500, from Valliant and Fay 2012) to obtain stable variance estimators with sufficient degrees of freedom and stable 

second stage estimates. 

8.2.5 Hierarchical modeling with random components 

CE data is collected from 90 primary sampling units (PSU) across four geographical regions. Implementing a hierarchical model with random components (e.g. HGLMM) is an alternative which might reflect the complexity of CE 

data for the analysis. If a HGLMM Cragg’s model is considered, in order to have enough households for estimation, researchers should combine at least, but not limited to one year of data to take into account the variation among 

geographical regions, or further to account for the variation among PSU within each region. 

8.3 Future research 

The results indicate sensitivities from various economic model estimations under a simple random subsample condition. The Gemini Steering Team recommend a new CE redesign proposal to collect data in two waves, 12 months 

apart. Each wave includes two household interview visits and a one-week electronic diary for all CU members age 

15 and older. Further studies are needed to evaluate those economic models under this proposed redesign condition. 

Future analyses might also include drawing repeated simple random subsamples and then obtain the model parameter estimates, empirical SE and two-stage model estimates from multiple subsamples. This will be implemented 

by simulations to provide information about distributions of economic model parameters. Furthermore, recent developments in economics research illustrate the interest of generating a composite statistic from multi-dimensional 

measurements (Garner and Short 2013). Therefore, future analyses will also consider evaluating a composite measure 

from economics interest perspective by simulating repeated simple random subsamples. 

16 
Acknowledgments 

I am sincerely grateful to Jeffrey M. Gonzalez (from the Division of Statistics and Research Methods, Center for 

Financing, Access, and Cost Trends, Agency for Healthcare Research and Quality, Department of Health and Human 

Services) for his assistance, advice and cooperation for this research, and for his comments to the draft of this paper. I would also like to thank the following researchers from the Bureau of Labor Statistics, Adam N. Safir, Laura 

A. Paszkiewicz (Branch of Research and Program Development, DCES), Steve W. Henderson, Geoffrey D. Paulin 

(Branch of Information and Analysis, DCES), John L. Eltinge and Wendy L. Martinez (from Office of Survey Methods Research) for their assistance and advice on this research. 

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Monthly Labor Review, 133(9), 38-58. 

[37] Heeringa, Steven G., West, Brady T. and Berglund Patricia A. (2010). Applied Survey Data Analysis. 

[38] Garner, Thesia I. and Short, Kathleen S. (2013), A Multi-dimensional Measure of Economic Well-Being for the 

U.S.: The Material Condition Index. Joint Statistical Meetings Proceedings in Progress, Business and Economic 

Statistics Section. 

19 
Figure 1: Household incomes before tax, poverty threshold among family size 

20 
Figure 2: Box Plot of Expenditures on Children: Original Scale vs. Natural Log Scale 

21 
Table 1: Level of analyses, methods and variables for expenditure types 

Types of Expenditures Level of 

Analyses Sophistication 

Methods Variables 

Education Basic, 

Medium 

mean, linear regression, logistic regression education expenditure, proportion of reporting nonzero expenditure, educational 

attainment, occupation level, race, age, geographic region, household type, mean income percentile 

Food Refined multivariate cluster analysis, 

multinomial logistic regression, multiple regression 

food expenditure, adjust-income (after 

tax), sex, employment status 

Medical and 

Health Care 

Basic, 

Medium 

mean, proportion, multiple 

regression 

health care expenditure, health insurance expenditure, medical services expenditure, income-to-poverty-threshold ratio, 

prescription drugs expenditure, health insurance coverage status 

Demographics Basic, Refined mean, two-stage regression tuition expenditure, household tenure, 

transportation spending, health care, personal insurance and pensions 

Assets Medium multiple regression mortgage principal payments, home improvements expenditure, home maintenance expenditure, for vehicles expenditure, furniture expenditure, appliances expenditure, equity indicator 

Energy Basic, 

Medium 

proportion, mean, time series generalized least square 

(GLS) model 

energy expenditure, gasoline expenditure, 

motor oil expenditure 

22 
Table 2: Expenditure variables description 

Primary expenditure categories Omori (2010) description EAP description Data files 

(RELN) 

Education All related educational 

expenses: “childcare, tuition, food and board at 

school, schoolbooks and 

supplies, and the broad 

category ‘other educational 

expenses.”’ 

Condition: for CU members (EDUCGFTC=1); Include: payments for 

educational expenses minus reimbursements (JEDUCNET) 

EDA 

Entertainment “Tickets and admissions to 

theaters, concerts, sporting 

events, health clubs, and 

swimming pools, as well 

as fees for participating in 

sports.” 

Include: participating sports fees (QPSF3MCX), spectator sports fees 

(QSSF3MCX), admissions paid to performances including service fees 

and surcharges (QEAD3MCX), admissions paid to other entertainment 

activities (QENT3MCX), reference period minus current month; Condition: for CU members (S17GFTCA=1); Subscriptions and memberships expenses, reference period minus current month (QSUB3MCX) 

for theater, concert, opera, or other musical series, season tickets; season tickets to sporting events; health clubs, fitness centers, swimming 

pools, weight loss centers or other sports and recreational organizations 

(S17CODEA=500, 600 or 830) 

ENT, SUB 

Books “Subscriptions to, and purchases of, newspapers, magazines, periodicals, books, 

and encyclopedias.” 

Include: book expenses including reference books (QBR3MCX), 

newspaper, magazine, and periodical expenses (QNMG3MCX); reference period minus current month; Condition: for CU members 

(S17GFTCA=1); Include: subscriptions and memberships expense, reference period minus current month (QSUB3MCX) for subscriptions to 

newspapers, magazines, or periodicals including online subscriptions; 

books purchased from a book club; encyclopedias or other sets of reference books (S17CODEA=150, 200 or 700) 

ENT, SUB 

Children’s apparel “Boys’ and girls’ clothing” 

(age ¡ 18) 

“Infants’ clothing” 

Condition: for non-gift (CLOGFTA=2) and child or adopted child 

(CU CODE=3); Include: purchase price of clothing (CLOTHXA) 

Condition: for CU members (CLOGFTB=2); Include: purchase price of 

infant clothing (CLOTHXB) except for watches, jewelry and hairpieces, 

wigs or toupees (CLOTHYB=360, 370 and 380) 

CLA, CLB 

1 We select CUs with children age < 18 in MEMB data set. 

2 Some childcare expenses are collected in Section questionnaire 19. 

3 Some combined expenditures also include infants clothing from CLA. Starting April 2011, all infants clothing is reported in CLA. 

23 
Table 3: Household expenditures on children and demographic descriptive statistics for the Consumer Expenditure 

Interview Survey, CEQ 2011 Q1 and its SRSWORSS. (weighted) 

Parameter Analysis Married Single mother Single father Cohabiting 

Mean 95% CI SE Mean 95% CI SE Mean 95% CI SE Mean 95% CI SE 

Number of households CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1,574 

786 

336 

175 

59 

24 

293 

146 

Percent reporting non-zero expenditure:2 

Education CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

43.5 

42.0 

29.5 

35.4 

30.5 

37.5 

23.9 

21.2 

Entertainment CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

49.9 

50.1 

31.0 

34.3 

40.7 

54.2 

29.0 

27.4 

Books2 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

39.3 

38.0 

22.6 

24.6 

28.8 

41.7 

27.0 

26.7 

Children’s Apparel CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

42.5 

43.8 

40.2 

40.6 

39 

37.5 

30.7 

30.8 

Quarterly expenditure (dollars):3 

Education CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

887.38 

931.71 

(700.28, 1074.49) 

(658.32, 1205.09) 

95.29 

138.97 

453.60 

334.06 

(271.73, 635.47) 

(210.39, 457.74) 

91.65 

61.85 

282.56 

295.77 

(103.39, 461.72) 

(-46.65, 638.19) 

84.92 

148.49 

445.85 

403.91 

(264.50, 627.19) 

(219.70, 588.12) 

90.90 

90.20 

Entertainment CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

212.35 

192.89 

(174.68, 250.02) 

(167.12, 218.65) 

19.19 

13.11 

108.65 

113.50 

(78.41, 138.88) 

(64.90, 162.11) 

15.25 

24.29 

229.78 

277.53 

(114.36, 345.21) 

(87.14, 467.92) 

55.80 

87.38 

127.25 

129.14 

(86.95, 167.55) 

(79.69, 178.59) 

20.27 

24.45 

Books2 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

70.79 

66.54 

(64.13, 77.44) 

(58.07, 75.01) 

3.39 

4.30 

42.05 

49.62 

(30.68, 53.42) 

(31.43, 67.80) 

5.71 

9.01 

61.84 

49.68 

(18.61, 105.07) 

(4.96, 94.39) 

20.39 

19.77 

51.05 

63.81 

(36.74, 65.37) 

(37.78, 89.84) 

7.19 

12.86 

Children’s apparel CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

211.97 

217.95 

(189.64, 234.30) 

(181.99, 253.91) 

11.37 

18.28 

169.21 

172.58 

(135.25, 203.18) 

(119.55, 225.61) 

17.17 

26.59 

328.45 

303.66 

(179.12, 477.77) 

(-50.12, 657.45) 

72.00 

153.42 

179.50 

169.96 

(143.88, 215.11) 

(124.64, 215.29) 

17.92 

22.49 

Income percentile CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

57.35 

57.47 

(55.93, 58.76) 

(55.49, 59.45) 

0.72 

1.01 

24.35 

24.29 

(22.06, 26.65) 

(21.03, 27.55) 

1.17 

1.65 

42.14 

40.07 

(34.93, 49.34) 

(28.27, 51.87) 

3.59 

5.67 

36.64 

35.66 

(33.64, 39.63) 

(31.53, 39.80) 

1.52 

2.09 

Education (%): 

Less than high school CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

13.0 

11.8 

18.1 

19.6 

7.7 

4.1 

23.5 

27.4 

High school CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

21.7 

23.4 

28.1 

26.4 

26.2 

32.6 

26.8 

21.6 

Some college CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

29.6 

29.9 

38.4 

37.5 

44.7 

36.4 

36.2 

38.7 

College and higher CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

35.6 

34.9 

15.4 

16.6 

21.5 

26.9 

13.5 

12.3 

Occupation (%): 

Managerial/professional CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

27.2 

26.7 

17.9 

20.2 

31.2 

42.3 

15.9 

15.6 

Administrative CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

5.5 

6.0 

12.4 

12.4 

3.4 

0.0 

6.5 

7.0 

Other occupation CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

67.3 

67.3 

69.8 

67.4 

65.5 

57.7 

77.5 

77.4 

Race/ethnicity (%): 

White CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

64.9 

63.9 

41.3 

41.7 

71.6 

71 

48.1 

43.8 

African American CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

8.7 

8.7 

33.4 

32.4 

17.6 

22.1 

27.1 

29.8 

Hispanic CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

19.8 

20.9 

21.1 

19.6 

9.7 

6.6 

20.5 

21.0 

Other CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

6.6 

6.5 

4.2 

6.3 

1.1 

0.4 

4.4 

5.4 

Age, years CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

40.93 

40.70 

(40.46, 41.40) 

(40.04, 41.36) 

0.24 

0.34 

35.83 

35.26 

(34.83, 36.83) 

(33.84, 36.68) 

0.51 

0.72 

43.55 

44.59 

(41.50, 45.60) 

(41.56, 47.61) 

1.02 

1.46 

41.36 

39.80 

(39.73, 42.99) 

(37.60, 42.00) 

0.83 

1.11 

Number of children: 

Ages 0–5 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.63 

0.65 

(0.59, 0.67) 

(0.60, 0.71) 

0.02 

0.03 

0.59 

0.66 

(0.50, 0.67) 

(0.54, 0.78) 

0.04 

0.06 

0.21 

0.22 

(0.09, 0.33) 

(0.01, 0.43) 

0.06 

0.10 

0.71 

0.77 

(0.61, 0.80) 

(0.63, 0.91) 

0.05 

0.07 

Ages 6–12 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.73 

0.73 

(0.69, 0.77) 

(0.67, 0.79) 

0.02 

0.03 

0.71 

0.66 

(0.61, 0.81) 

(0.52, 0.80) 

0.05 

0.07 

0.54 

0.54 

(0.36, 0.72) 

(0.23, 0.85) 

0.09 

0.15 

0.60 

0.67 

(0.51, 0.69) 

(0.54, 0.80) 

0.05 

0.07 

Ages 13–18 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.65 

0.63 

(0.60, 0.69) 

(0.57, 0.69) 

0.02 

0.03 

0.54 

0.49 

(0.47, 0.61) 

(0.39, 0.60) 

0.04 

0.05 

0.74 

0.80 

(0.54, 0.94) 

(0.45, 1.15) 

0.10 

0.17 

0.56 

0.46 

(0.47, 0.64) 

(0.34, 0.58) 

0.04 

0.06 

Region (%): 

Northeast CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

18.3 

18.9 

18.1 

14 

8.3 

8.7 

17.2 

19.0 

South CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

35.0 

33.6 

44.3 

45.6 

44.2 

34.9 

38.7 

39.9 

Midwest CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

21.6 

21.9 

21.1 

20.3 

19.8 

13.3 

20.2 

16.2 

West CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

25.0 

25.6 

16.5 

20.2 

27.6 

43.1 

24.0 

25.0 

1 No confidence interval was calculated for percentages. 

2 Including other reading materials, such as magazines and newspapers. 

3 Only for those who reported a nonzero expenditure in each category. 

CEQ 2011 Q1: CE interview survey 2011 1st quarter sample 

SRSWORSS: simple random sampling without replacement subsample (selection probability = 0.5) 

wt: weighted analysis using the final weight variable “FINLWT21” 

24 
Table 4: Selected original and logarithmic statistics for expenditures discussed in the text, CEQ 2011 Q1 and its 

SRSWORSS 

Expenditure category Analysis N Original value Natural logarithm of original value 

SD Skewness Kurtosis SD Skewness Kurtosis 

Education CEQ 2011 Q1 871 

432 

2281.238 

2340.502 

11.377 

11.975 

168.436 

184.435 

1.533 

1.479 

-0.181 

-0.203 

0.131 

SRSWORSS 0.297

Entertainment CEQ 2011 Q1 999 

507 

479.475 

264.734 

18.150 

3.363 

448.323 

14.353 

1.158 

1.168 

0.029 

-0.078 

0.080 

SRSWORSS -0.150

Books CEQ 2011 Q1 791 

391 

79.717 

73.887 

3.073 

2.769 

12.613 

10.936 

1.085 

1.083 

-0.260 

-0.243 

0.123 

SRSWORSS -0.025

Apparel CEQ 2011 Q1 917 

469 

276.346 

310.571 

5.227 

6.097 

52.159 

60.694 

1.089 

1.109 

-0.122 

-0.103 

-0.216 

SRSWORSS -0.098

SD: Standard Deviation 

25 
Table 5: Logistic regression results: likelihood of expenditures on items in selected categories, CEQ 2011 Q1 and its 

SRSWORSS (weighted) 

Parameter Analysis Education Entertainment Books1 Apparel 

Estimate 95% CI Estimate 95% CI Estimate 95% CI Estimate 95% CI 

Household type:2 

Single mother CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.023 

1.438 

(1.021, 1.026) 

(1.433, 1.442) 

0.987 

1.081 

(0.985, 0.989) 

(1.078, 1.085) 

0.935 

0.971 

(0.933, 0.938) 

(0.967, 0.974) 

1.090 

1.144 

(1.088, 1.092) 

(1.141, 1.148) 

Single father CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.756 

1.138 

(0.753, 0.760) 

(1.130, 1.145) 

0.582 

1.040 

(0.580, 0.585) 

(1.033, 1.047) 

0.613 

1.083 

(0.610, 0.616) 

(1.076, 1.090) 

0.943 

0.750 

(0.939, 0.947) 

(0.745, 0.755) 

Cohabiting CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.640 

0.607 

(0.638, 0.641) 

(0.605, 0.609) 

0.697 

0.686 

(0.695, 0.699) 

(0.683, 0.688) 

0.907 

1.069 

(0.905, 0.909) 

(1.066, 1.073) 

0.690 

0.699 

(0.689, 0.692) 

(0.697, 0.701) 

Income percentile CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.012 

1.011 

(1.012, 1.012) 

(1.011, 1.011) 

1.020 

1.016 

(1.020, 1.020) 

(1.016, 1.016) 

1.016 

1.012 

(1.016, 1.017) 

(1.012, 1.012) 

1.008 

1.009 

(1.008, 1.008) 

(1.009, 1.009) 

Education:3 

High school CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.391 

1.840 

(1.387, 1.395) 

(1.832, 1.847) 

1.509 

1.306 

(1.505, 1.513) 

(1.301, 1.310) 

1.232 

1.327 

(1.229, 1.235) 

(1.322, 1.332) 

1.202 

1.120 

(1.200, 1.205) 

(1.117, 1.124) 

College and higher CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

2.443 

3.574 

(2.437, 2.449) 

(3.561, 3.588) 

2.412 

2.623 

(2.406, 2.418) 

(2.613, 2.632) 

1.750 

1.538 

(1.746, 1.755) 

(1.533, 1.544) 

1.084 

1.106 

(1.082, 1.086) 

(1.103, 1.110) 

Occupation:4 

Managerial/professional CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.285 

1.466 

(1.283, 1.287) 

(1.463, 1.470) 

1.546 

1.562 

(1.544, 1.549) 

(1.559, 1.566) 

1.411 

1.442 

(1.409, 1.413) 

(1.438, 1.445) 

0.933 

0.992 

(0.931, 0.934) 

(0.990, 0.994) 

Administrative CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.916 

0.971 

(0.914, 0.919) 

(0.967, 0.974) 

1.088 

1.259 

(1.085, 1.091) 

(1.254, 1.264) 

0.928 

0.956 

(0.925, 0.931) 

(0.952, 0.960) 

1.156 

0.892 

(1.153, 1.159) 

(0.888, 0.895) 

Race/ethnicity:5 

African American CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.630 

0.718 

(0.629, 0.631) 

(0.716, 0.721) 

0.449 

0.470 

(0.448, 0.450) 

(0.468, 0.471) 

0.608 

0.543 

(0.606, 0.609) 

(0.541, 0.545) 

0.864 

0.803 

(0.862, 0.866) 

(0.801, 0.805) 

Hispanic CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.567 

0.689 

(0.566, 0.569) 

(0.687, 0.691) 

0.646 

0.830 

(0.644, 0.647) 

(0.828, 0.833) 

0.514 

0.567 

(0.512, 0.515) 

(0.565, 0.569) 

1.052 

0.910 

(1.050, 1.054) 

(0.908, 0.912) 

Other CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.290 

1.968 

(1.286, 1.294) 

(1.960, 1.976) 

0.306 

0.323 

(0.305, 0.307) 

(0.322, 0.325) 

0.766 

1.320 

(0.764, 0.768) 

(1.315, 1.326) 

1.064 

0.793 

(1.061, 1.067) 

(0.790, 0.796) 

Age CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.007 

1.015 

(1.007, 1.007) 

(1.015, 1.016) 

1.004 

1.009 

(1.004, 1.004) 

(1.009, 1.009) 

1.013 

1.005 

(1.013, 1.013) 

(1.005, 1.005) 

0.989 

0.990 

(0.989, 0.989) 

(0.990, 0.990) 

Number of children: 

Ages 0–5 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.251 

1.205 

(1.249, 1.252) 

(1.203, 1.207) 

0.772 

0.740 

(0.771, 0.773) 

(0.739, 0.741) 

0.924 

0.889 

(0.922, 0.925) 

(0.887, 0.890) 

0.842 

0.773 

(0.841, 0.842) 

(0.772, 0.774) 

Ages 6–12 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

1.116 

1.062 

(1.115, 1.117) 

(1.060, 1.063) 

1.017 

0.949 

(1.016, 1.018) 

(0.948, 0.950) 

1.024 

0.921 

(1.023, 1.025) 

(0.920, 0.922) 

1.002 

1.077 

(1.001, 1.003) 

(1.076, 1.078) 

Ages 13–18 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.965 

0.892 

(0.964, 0.966) 

(0.890, 0.893) 

1.037 

1.059 

(1.036, 1.038) 

(1.057, 1.060) 

0.986 

1.048 

(0.985, 0.987) 

(1.046, 1.049) 

1.108 

1.105 

(1.107, 1.109) 

(1.103, 1.106) 

Region:6 

South CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.822 

0.811 

(0.820, 0.823) 

(0.809, 0.813) 

0.877 

0.762 

(0.875, 0.879) 

(0.760, 0.764) 

0.901 

1.111 

(0.899, 0.903) 

(1.108, 1.114) 

0.745 

0.679 

(0.743, 0.746) 

(0.677, 0.681) 

Midwest CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.898 

0.724 

(0.896, 0.900) 

(0.722, 0.726) 

1.074 

0.994 

(1.071, 1.076) 

(0.990, 0.997) 

1.018 

1.481 

(1.015, 1.020) 

(1.476, 1.485) 

0.833 

0.761 

(0.831, 0.835) 

(0.759, 0.763) 

West CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.948 

0.870 

(0.946, 0.950) 

(0.867, 0.872) 

1.333 

1.048 

(1.330, 1.336) 

(1.045, 1.052) 

1.013 

1.067 

(1.011, 1.016) 

(1.064, 1.071) 

0.708 

0.666 

(0.706, 0.709) 

(0.664, 0.668) 

N CEQ 2011 Q1 

SRSWORSS 

2,262 

1,131 

2,262 

1,131 

2,262 

1,131 

2,262 

1,131 

1 Including other reading materials, such as magazines and newspapers. 

2 Reference class: married-couple households. 

3 Reference class: less than high school. 

4 Reference class: other occupations. 

5 Reference class: White. 

6 Reference class: Northeast. 

26 
Table 6: Ordinary least squares regression results: estimates of (the natural logarithm of) quarterly expenditures on 

items in selected categories, CEQ 2011 Q1 and its SRSWORSS (weighted) 

Parameter Analysis Education Entertainment Books1 Apparel 

Estimate SE Estimate SE Estimate SE Estimate SE 

Intercept CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

4.456 

4.950 

70.378 

70.502 

3.145 

3.164 

70.268 

70.367 

2.558 

3.035 

70.291 

70.395 

4.106 

4.365 

70.265 

70.375 

Household type:2 

Single mother CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.337 

-0.634 

90.165 

80.210 

-0.228 

-0.200 

0.119 

0.161 

-0.164 

-0.047 

0.135 

0.182 

0.056 

0.115 

0.111 

0.162 

Single father CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.659 

-0.938 

0.340 

90.442 

0.210 

0.321 

0.235 

0.312 

-0.146 

-0.488 

0.269 

0.353 

0.608 

0.491 

80.229 

0.384 

Cohabiting CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.229 

-0.171 

0.181 

0.250 

-0.237 

-0.175 

0.124 

0.176 

-0.069 

0.079 

0.130 

0.179 

0.083 

0.081 

0.126 

0.183 

Income percentile CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.006 

0.007 

80.002 

80.002† 

0.006 

0.006 

70.001 

70.002 

0.009 

0.008 

70.002 

70.002† 

0.004 

0.003 

80.001 

0.002 

Education:3 

High school CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.494 

0.154 

90.218 

0.318 

0.118 

0.285 

0.156 

0.220 

0.169 

0.040 

0.167 

0.225 

0.085 

0.091 

0.127 

0.188 

College and higher CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.971 

0.736 

70.200 

80.293 

0.378 

0.443 

90.146 

90.207 

0.240 

0.157 

0.153 

0.210 

0.076 

0.024 

0.121 

0.176 

Occupation:4 

Managerial/professional CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.317 

0.183 

80.110 

0.146 

0.287 

0.401 

70.077 

70.110 

0.096 

0.204 

0.084 

0.122 

0.105 

0.242 

0.088 

0.125 

Administrative CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.053 

-0.194 

0.205 

0.269 

0.052 

-0.099 

0.138 

0.187 

-0.014 

-0.042 

0.158 

0.218 

-0.037 

0.045 

0.137 

0.202 

Race/ethnicity:5 

African American CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.153 

-0.398 

0.166 

0.216 

-0.241 

-0.328 

0.127 

0.176 

-0.202 

-0.161 

0.136 

0.195 

0.070 

0.025 

0.114 

0.163 

Hispanic CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.517 

-0.565 

80.157 

80.199 

-0.014 

0.037 

0.107 

0.143 

-0.163 

-0.131 

0.124 

0.169 

0.075 

-0.032 

0.101 

0.142 

Other CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.196 

0.125 

0.185 

0.231 

0.035 

0.380 

0.172 

0.239 

0.155 

0.137 

0.157 

0.198 

-0.100 

-0.128 

0.150 

0.220 

Age CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.005 

0.001 

0.006 

0.008 

0.012 

0.008 

80.004 

0.006 

0.011 

0.004 

90.004 

0.006 

0.005 

0.002 

0.005 

0.006 

Number of children: 

Ages 0–5 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.174 

0.233 

90.076 

80.101 

0.119 

0.097 

0.062 

0.086 

0.022 

-0.030 

0.063 

0.087 

0.093 

0.061 

0.059 

0.089 

Ages 6–12 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.120 

-0.126 

90.060 

0.083 

0.182 

0.185 

70.044 

80.062 

0.006 

-0.082 

0.048 

0.067 

0.114 

0.108 

90.046 

0.063 

Ages 13–18 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.034 

-0.073 

0.069 

0.097 

0.207 

0.198 

70.050 

80.069 

0.095 

0.136 

0.056 

0.076 

0.227 

0.284 

70.051 

70.072 

Region:6 

South CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.338 

-0.162 

90.138 

0.186 

-0.130 

-0.150 

0.099 

0.140 

-0.300 

-0.376 

80.108 

90.163 

-0.198 

-0.213 

90.098 

0.142 

Midwest CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.346 

-0.417 

90.150 

90.207 

-0.087 

-0.087 

0.106 

0.149 

-0.292 

-0.380 

90.115 

90.166 

-0.275 

-0.511 

90.108 

80.155 

West CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

-0.385 

-0.251 

80.148 

0.196 

0.008 

-0.018 

0.103 

0.143 

-0.087 

-0.044 

0.114 

0.168 

-0.342 

-0.455 

80.109 

80.152 

N CEQ 2011 Q1 

SRSWORSS 

871 

432 

999 

507 

791 

391 

917 

469 

R

2 CEQ 2011 Q1 (wt) 

SRSWORSS (wt) 

0.159 

0.191 

0.135 

0.162 

0.132 

0.144 

0.064 

0.090 

1 Including other reading materials, such as magazines and newspapers. 

2 Reference class: married-couple households. 

3 Reference class: less than high school. 

4 Reference class: other occupations. 

5 Reference class: White. 

6 Reference class: Northeast. 

7 p < 0.001. 

8 p < 0.01. 

9 p < 0.05. 

† SE(SRSWORSS) < SE(CEQ 2011 Q1). 

27 
Table 7: Number of observations and number of reporting expenditures by household types 

Expenditure Analysis Married couple Single mother Single father Cohabiting 

Overall 

Education 

Entertainment 

Books 

Apparel 

CEQ 2011 Q1 

SRSWORSS 

CEQ 2011 Q1 

SRSWORSS 

CEQ 2011 Q1 

SRSWORSS 

CEQ 2011 Q1 

SRSWORSS 

CEQ 2011 Q1 

SRSWORSS 

1367 

682 

612 

287 

703 

342 

566 

270 

610 

311 

304 

155 

91 

58 

100 

57 

73 

41 

131 

68 

52 

22 

15 

8 

21 

11 

14 

8 

20 

7 

254 

129 

59 

26 

77 

37 

72 

35 

76 

38 

28 
Table 8: Cragg’s model probability of purchase, predicted expenditure (buyers only), marginal propensity to consume 

and elasticity, and so forth under “ceteris paribus” 

Expenditure, Ceteris paribus criteria Analysis Married couple Single mother Single father Cohabiting 

Education 

Probability of purchase CEQ 2011 Q1 0.45 0.30 0.29 0.23 

SRSWORSS 0.42 0.37 0.36 0.20 

Predicted expenditure (buyers only) CEQ 2011 Q1 336.91 203.54 329.97 220.81 

SRSWORSS 394.8 190.57 319.75 350.61 

Marginal propensity to consume CEQ 2011 Q1 0.06 0.01 0.05 0∗

SRSWORSS 0.01 0.01 0.01 0 

Elasticity CEQ 2011 Q1 0.15 0.11 0.64 0.1 

SRSWORSS 0.22 0.24 0.66 -0.03 

Entertainment 

Probability of purchase CEQ 2011 Q1 0.51 0.33 0.40 0.30 

SRSWORSS 0.50 0.37 0.50 0.29 

Predicted expenditure (buyers only) CEQ 2011 Q1 120.81 73.9 153.1 80.86 

SRSWORSS 125.7 79.8 231.82 93.85 

Marginal propensity to consume CEQ 2011 Q1 0.05 0 0 0 

SRSWORSS 0.01 0 -0.03 0 

Elasticity CEQ 2011 Q1 0.30 0.06 0.09 0.13 

SRSWORSS 0.30 0.14 -2.56 0.31 

Books 

Probability of purchase CEQ 2011 Q1 0.41 0.24 0.27 0.28 

SRSWORSS 0.40 0.26 0.36 0.27 

Predicted expenditure (buyers only) CEQ 2011 Q1 47.61 28.4 50.28 33.66 

SRSWORSS 47.38 30.14 54.13 47.49 

Marginal propensity to consume CEQ 2011 Q1 0.01 0 0 0 

SRSWORSS 0 0 -0.01 0 

Elasticity CEQ 2011 Q1 0.21 0.13 -0.07 0.09 

SRSWORSS 0.16 0.27 -3.18 0.18 

Apparel 

Probability of purchase CEQ 2011 Q1 0.45 0.43 0.38 0.30 

SRSWORSS 0.46 0.44 0.32 0.29 

Predicted expenditure (buyers only) CEQ 2011 Q1 128.15 111 303.01 126.76 

SRSWORSS 127.06 116.4 382.57 136.83 

Marginal propensity to consume CEQ 2011 Q1 0.01 0 0.01 0 

SRSWORSS 0 0 -0.14 0 

Elasticity CEQ 2011 Q1 0.09 0.01 0.14 -0.03 

SRSWORSS 0.10 0.04 -8.75 -0.02 

∗ Rounded at two decimal places. 

29 
Table 9: Hierarchical Generalized Linear Mixed (HGLMM) Cragg’s model probability of purchase, predicted expenditure (buyers only), marginal propensity to consume and elasticity, and so forth under “ceteris paribus” 

Expenditure, Ceteris paribus criteria Analysis Married couple Single mother Single father Cohabiting 

Education 

Probability of purchase CEQ 2011 Q1 0.61 0.57 0.57 0.56 

SRSWORSS 0.60 0.59 0.59 0.55 

Predicted expenditure (buyers only) CEQ 2011 Q1 335.6 198.31 305.60 220.17 

SRSWORSS 389.45 178.52 – 339.98 

Marginal propensity to consume CEQ 2011 Q1 0.05 0.01 0.08 0.01 

SRSWORSS 0.01 0.01 – -0.01 

Elasticity CEQ 2011 Q1 0.17 0.18 1.05 0.22 

SRSWORSS 0.27 0.33 – -0.16 

Entertainment 

Probability of purchase CEQ 2011 Q1 0.62 0.58 0.60 0.57 

SRSWORSS 0.62 0.59 0.62 0.57 

Predicted expenditure (buyers only) CEQ 2011 Q1 120.54 72.60 – 79.03 

SRSWORSS 124.95 76.93 – 92.95 

Marginal propensity to consume CEQ 2011 Q1 0.04 0∗ – 0 

SRSWORSS 0 0 – 0 

Elasticity CEQ 2011 Q1 0.32 0.10 – 0.17 

SRSWORSS 0.33 0.21 – 0.49 

Books 

Probability of purchase CEQ 2011 Q1 0.60 0.56 0.57 0.57 

SRSWORSS 0.60 0.57 0.59 0.57 

Predicted expenditure (buyers only) CEQ 2011 Q1 47.39 27.94 50.42 33.07 

SRSWORSS 46.94 29.91 – 46.66 

Marginal propensity to consume CEQ 2011 Q1 0.01 0 0 0 

SRSWORSS 0 0 – 0 

Elasticity CEQ 2011 Q1 0.26 0.25 -0.03 0.13 

SRSWORSS 0.20 0.48 – 0.29 

Apparel 

Probability of purchase CEQ 2011 Q1 0.61 0.61 0.59 0.57 

SRSWORSS 0.61 0.61 0.57 0.57 

Predicted expenditure (buyers only) CEQ 2011 Q1 127.49 110.67 289.03 126.15 

SRSWORSS 125.78 115.29 – 133.27 

Marginal propensity to consume CEQ 2011 Q1 0.01 0 0.01 0 

SRSWORSS 0 0 – 0 

Elasticity CEQ 2011 Q1 0.10 0.02 0.18 -0.04 

SRSWORSS 0.11 0.07 – -0.05 

∗ Rounded at two decimal places. 

– Not Avaliable. (The estimate is not able to be produced for a hierarchical linear mixed model) 

30