Impact of Design Changes on Economic Analyses Project

Daniel K. Yang, Jeffrey M. Gonzalez∗

Office of Survey Methods Research

U.S. Bureau of Labor Statistics

December 12, 2013

Executive Summary

The Impact of Design Changes on Economic Analysis Project (EAP) for the Consumer Expenditure Surveys is a research project conducted by the Office of Survey Methods Research

(OSMR) and the Division of Consumer Expenditure Survey (DCES) of the Bureau of Labor

Statistics (BLS). In this project, we analyzed various statistical models in economic analysis under a simple random subsample condition. The simple random subsample condition is akin to

implementing a split questionnaire design. We selected the first quarter of Consumer Expenditure Survey (CE) 2011 Phase III data (CEQ 2011 Q1) data for this study.

The primary objective of this research is to identify specific sensitivities of the economic

models when utilizing a simple random subsample to conduct the various economic analyses.

The basic question is: are there particular parameters of the economic models that are compromised?

We want to evaluate the numerical impact of a simple random subsample condition on

various economic analyses. To explore economic analyses of varying sophistication (basic,

medium, refined and advanced models approved and/or chosen by stakeholders), we consider

descriptive statistics, regression analysis, generalized logistic regression, two-stage analysis,

and hierarchical modeling to identify potential sensitivities in these analyses. Recommendations are then provided for design changes and statistical methods in collecting and analyzing

the CE data.

The analysis results indicate specific sensitivities in the following:

1. First, in simple univariate statistics estimation (e.g. means, percentages and standard

errors or SE):

(a) 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;

∗Currently work as a Survey Statistician in 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

1
(b) 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. Second, in linear regression and generalized logistic regression models, 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. Third, in a two-stage regressions Cragg’s model, we found that:

(a) 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;

(b) the second stage estimates, such as marginal propensity to consume and elasticity,

from the simple random subsample deviate from the full sample.

4. Finally, 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; and

(c) Compared to the classic two-stage Cragg’s, the two-stage hierarchical generalized

linear mixed Cragg’s model generally produces higher probabilities of purchase and

elasticity estimates.

To improve the estimation precision of marginal propensity to consume and elasticity under

simple random sampling without replacement subsample (SRSWORSS) with a 0.5 probability

of selection, we also recommend preliminary steps:

1. First, oversample groups that might result in small effective sample sizes due to the subsampling;

2. Second, implement a dynamic interview, 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;

3. Third, consider pooling extra quarters of data to offset the individual quarterly impact;

4. In addition, apply bootstrap methodology as an option with a large number of simple

random subsamples to obtain stable variance estimators with sufficient degrees of freedom and stable second stage estimates;

5. Finally, consider implementing a hierarchical model with random components as an alternative approach for a complex CE data.

2
Contents

1 Introduction 6

2 Literature Reviews 7

2.1 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Food . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Medical and Health Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5 Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Data set construction 11

3.1 Discrepancies in variable definitions and limitations of the data source . . . . . . . . 12

3.1.1 Variable definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.2 Differences in data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.3 Other discrepancies and and limitations . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Description of expenditure variables comparing to Omori (2010): Table 2 . . . . . . . 13

4 Basic analysis 13

4.1 Basic demographic and expenditure estimates: Table 3 . . . . . . . . . . . . . . . . . 14

4.1.1 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1.2 Expenditures on children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Medium analysis 15

5.1 Model specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

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

scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.3 Comparing the logistic regression results for reporting nonzero expenditures on

children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.4 Comparing the linear regression results for nonzero expenditures on children . . . . 17

5.4.1 Under the SRSWORSS condition . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.4.2 Reduced SE under the SRSWORSS . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.4.3 Potential contributing factors for the discrepancies could be: . . . . . . . . . . 18

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3
6 Refined analysis 18

6.1 Data set construction for Cragg’s model . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.2 Model specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.3 Comparing the Cragg’s model results for children’s expenditures . . . . . . . . . . . 20

6.3.1 First stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.3.2 Second stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.3.3 Small groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

7 Advanced analysis 21

7.1 Data set construction for HGLMM Cragg’s model . . . . . . . . . . . . . . . . . . . . 22

7.2 Model specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7.3 Comparing the HGLMM Cragg’s model results for children’s expenditures . . . . . 22

7.3.1 First stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7.3.2 Second stage estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7.3.3 Small groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7.3.4 Impacts of accounting for the variation among geographical regions . . . . . 23

7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8 Conclusion 24

8.1 Summary of potential sensitivities from the above economic analyses under a simple random subsample condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

8.2 Preliminary recommendations for improvement of expenditure estimates precision . 25

8.2.1 D/A. Oversampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8.2.2 D/A. Dynamic interview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8.2.3 A. Pooling additional quarters/years of data . . . . . . . . . . . . . . . . . . . 26

8.2.4 A. Implement Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

8.2.5 A. Hierarchical modeling with random components . . . . . . . . . . . . . . . 26

8.3 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

List of Tables

1 Level of analyses, methods and variables for expenditure types . . . . . . . . . . . . 33

2 Expenditure variables description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3 Household expenditures on children and demographic descriptive statistics for the

Consumer Expenditure Interview Survey, CEQ 2011 Q1 and its SRSWORSS. (weighted) 35

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

CEQ 2011 Q1 and its SRSWORSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4
5 Logistic regression results: likelihood of expenditures on items in selected categories, CEQ 2011 Q1 and its SRSWORSS (weighted) . . . . . . . . . . . . . . . . . . . 37

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) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7 Number of observations and number of reporting expenditures by household types 39

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

propensity to consume and elasticity, and so forth under “ceteris paribus” . . . . . . 40

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” . . . . . . . . . . . . . . . . . . . . 41

List of Figures

1 Household incomes before tax, poverty threshold among family size . . . . . . . . . 31

2 Box Plot of Expenditures on Children: Original Scale vs. Natural Log Scale . . . . . 32

5
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 other DCES teams and provide beneficial inputs to the CE redesign.

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.

6
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 document is the final deliverable in a series 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, 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.

7
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) fastfood-dominated, (4) meat-eater, (5) miscellaneous-food-dominated, (6) alcohol-dominated, (7) beveragesdominated, 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

8
of being in the FAFH group. Younger consumers have a higher probability of being in fast-fooddominated 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 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 outof-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)).

9
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.

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

10
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

11
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.

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.

12
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 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

13
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

14
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.

4.2 Summary

We found that the simple random subsample produces similar demographic estimates in terms

of percentage and mean as compared to the full sample, with larger SE. One exception is the single

father group which is likely due to the small initial sample size of this group and the subsequent

subsampling. The simple random subsample produces different expenditure estimates on children in terms of means and SE as compared to the full sample, with larger SE.

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

15
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 categoryspecific 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 condition is smaller than that of the full sample. This

16
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.

17
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.

5.5 Summary

We found that (1) the simple random subsample produces different coefficient estimates and

generally higher SE as compared to the full sample; and, (2) the simple random subsample produces a few coefficients SE are smaller than the full sample.

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,

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

18
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

19
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:

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).

6.4 Summary

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.

20
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.

21
7.1 Data set construction for HGLMM 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). This was because we wanted the procedure of

our analyses from basic to the highest level of sophistication to be as consistent as possible. And

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 regression models 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 in Yang and Gonzalez 2013a). For reference, we also described discrepancies in

variable definitions and limitations of the data source in Section Three.

7.2 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, 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.

7.3 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

22
sample and SRSWORSS condition. We describe these findings as follows:

7.3.1 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.

7.3.2 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.

7.3.3 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).

7.3.4 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).

7.4 Summary

After accounting for the variation among geographical regions, we found that:

1. 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

23
for predicted expenditures (buyers only), i.e. sometimes higher, sometimes lower than the

full sample;

2. the second stage estimates, marginal propensities to consume and elasticities, from the simple random subsample deviate from the full sample;

3. under the simple random subsample, we were not able to produce hierarchical linear mixed

model eatimtes of predicted expenditures (buyers only) and second stage estimates for the

single father group due to small sample sizes; and

4. comparing 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 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

24
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. We have identified two broad classes of approaches –

design-based (denoted as D, i.e. modifications to the data collection processes) and analysis-based

(denoted as A, i.e. modifications to the methods used to process, analyze and produce official estimates from the collected data)

8.2.1 D/A. 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.

8.2.2 D/A. 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 subse25
quent phase, then apply modified weights to the data in the subsequent process to produce valid

official estimates.

8.2.3 A. 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 A. 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 A. 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.

26
References

[1] Raghunathan, T. E. and Grizzle, J. E. (1995). A Split Questionnaire Survey Design. Journal of

the American Statistical Association, 90, 54-63

[2] Gonzalez, J. M., Hackett, C., To, N., and Tan, L. (2009). Definition of Data Quality for the Consumer Expenditure Survey: A Proposal. http://www.bls.gov/cex/ovrvwdataqualityrpt.pdf

(visited April 13, 2012)

[3] Brackstone, G. (1999). Managing Data Quality in a Statistical Agency. Survey Methodology, 25,

139-149.

[4] Groves, R. M., Fowler, J., Couper, M. P., Lepkowski, J. M., Singer, E., and Tourangeau, R.

(2004). Survey Methodology. New York: Wiley.

[5] Henderson S., Brady, V., Brattland, J., Creech, B., Garner, T., and Tan, L. (2010). Consumer

Expenditure Survey Data Users’ Needs. //Filer6/dces/dces-public/Teams/Gemini/5 User

Needs/Deliverables/DUFreport Final 12Aug2010.docx (Internal report, visted April 13,

2012)

[6] Henderson S. (2012). Sample of CE data analyses by economic researchers.

//Filer1/dces/Projects - In Progress/Economic Analyses/Literature reviews/List of

CE data analyses by economic researchers.docx (Internal report, visited April 13, 2012)

[7] Abbot, C. (2008). An Analysis of Southern Energy Expenditures and Prices, 1984-2006.

Monthly Labor Review, 133(4), 3–18.

[8] Bureau of Labor Statistics, U.S. Department of Labor, Consumer Expenditure Survey Comparisons with National Health Expenditures and the Current Population Survey (2002, 2003, 2004, and

2005), Consumer Expenditure Survey, 2004–2005, Report 1008. http://www.bls.gov/cex/

twoyear/200405/csxnhecps.pdf (visited June 27, 2012).

[9] Bureau of Labor Statistics, U.S. Department of Labor, Consumer Expenditure Survey Compared with National Health Expenditure Accounts (years compared–2004, 2005, 2006, and 2007),

Consumer Expenditure Survey, 2006–2007, Report 1021. http://www.bls.gov/cex/twoyear/

200607/csxnhe.pdf (visited June 27, 2012).

[10] Bureau of Labor Statistics, U.S. Department of Labor, (2010). Health Care Spending: 1998,

2003, and 2008, Focus on Prices and Spending, Consumer Expenditure Survey, 2008, 1(8).

[11] Bureau of Labor Statistics, U.S. Department of Labor, (2010). Household Energy Spending:

Two Surveys Compared, Focus on Prices and Spending, Consumer Expenditure Survey, 2008,

1(12).

27
[12] Bureau of Labor Statistics, U.S. Department of Labor, (2011). Do Two Live as Cheaply as One?

Evidence from the Consumer Expenditure Survey, Focus on Prices and Spending, Consumer

Expenditure Survey, 2009, 2(4).

[13] Bureau of Labor Statistics, U.S. Department of Labor (2011). Part D Prescription Drug Coverage and Health Care Spending by Seniors on Medicare, Focus on Prices and Spending, Consumer

Expenditure Survey, 2009, 2(8).

[14] Bureau of Labor Statistics, U.S. Department of Labor. (2011). Consumer Spending in 2010,

Focus on Prices and Spending, Consumer Expenditure Survey, 2010, 2(12).

[15] Ethridge, V. (2009). Preliminary Examination of Expenditure Patterns and Higher Gasoline

Prices, A paper presented at the Academy of Business Economics MBAA International 2009 Conference, College of Business, University of St. Francis.

[16] Fan, J. X., Brown, B. B., Kowaleski-Jones, L., Smith, K. R., and Zick, C. D. (2007). Household

Food Expenditure Patterns: A Cluster Analysis. Monthly Labor Review, 130(4), 38–51.

[17] Foster, A. C. (2010). Out-of-Pocket Health Care Expenditures: A Comparison. Monthly Labor

Review, 133(2), 3–19.

[18] Gicheva, D., Hastings, J., and Villas-Boas, S. (2010). Investigating Income Effects in Scanner

Data: Do Gasoline Prices Affect Grocery Purchases? American Economic Review: Papers and

Proceedings, 100, 480–4.

[19] Hong, G-S, Kim, S. Y. (2000). Out-of-Pocket Health Care Expenditure Patterns and Financial

Burden across the Life Cycle Stages. The Journal of Consumer Affairs, 34(2), 291–313.

[20] Lino, M. (1998), Expenditures on Children by Families, 1997, Family Economics and Nutrition

Review, vol. 11, no. 3, 1998, pp. 25–43.

[21] McLanahan, S. S. and Sandefur, G. D. (1994), Growing Up with a Single Parent, Cambridge,

MA, Harvard University Press

[22] Omori, M. (2010). Household Expenditures on Children. Monthly Labor Review, 133(9), 3–16.

[23] Paulin, G. (2008). Expenditure Patterns of Young Single Adults: Two Recent Generations

Compared. Monthly Labor Review, 131(12), 19–50.

[24] Paulin, G. D. and Lee, Y. G. (2002), Expenditures of single parents: how does gender figure

in? Monthly Labor Review (MLR), July 2002, Vol. 125, No. 7

[25] Powell, B., Steelman, L. C. and Carini, R. M. (2006), Advancing Age, Advantaged Youth:

Parental Age and the Transmission of Resources to Children, Social Forces, March 2006, pp.

1359–90.

28
[26] Short, K. and Garner, T. I. (2002). Experimental Poverty Measures: Accounting for Medical

Expenditures. Monthly Labor Review, 125(8), 3-13.

[27] Zan, H. and Fan, J. X. (2010). Cohort Effects of Household Expenditures on Food Away from

Home. The Journal of Consumer Affairs, 44(1), 213-233.

[28] Melzer, B. T. (2012). Mortgage Debt Overhang: Reduced Investment by Homeowners with

Negative Equity. http://www.kellogg.northwestern.edu/faculty/melzer/Papers/ (visited

May 30, 2012)

[29] Gonzalez, J. M. (2012). The Use of Responsive Split Questionnaires in a Panel Survey. Ph.D.

Thesis, Joint Program in Survey Methodology (JPSM), University of Maryland.

[30] Valliant, R. and Fay, R. (2012). Inference from Complex Surveys (SURV 742) Lecture Notes

Chapter 7. The Bootstrap (pp. 7-1, 2, 11, 15), JPSM, University of Maryland.

[31] Yang, D. K. and Gonzalez J. M. (2012a). Impact of Design Changes on Economic Analyses

Project: Basic. Second Deliverable, Office of Survey Methods Research, U.S. Bureau of Labor

Statistics.

[32] Yang, D. K. and Gonzalez J. M. (2012b). Impact of Design Changes on Economic Analyses

Project: Medium. Third Deliverable, Office of Survey Methods Research, U.S. Bureau of Labor Statistics.

[33] Yang, D. K. and Gonzalez J. M. (2012c). Impact of Design Changes on Economic Analyses

Project: Literature Review, Office of Survey Methods Research, U.S. Bureau of Labor Statistics.

[34] Yang, D. K. and Gonzalez J. M. (2013a). Impact of Design Changes on Economic Analyses

Project: Refined. Fourth Deliverable, Office of Survey Methods Research, U.S. Bureau of Labor Statistics.

[35] Yang, D. K. and Gonzalez J. M. (2013b). Impact of Design Changes on Economic Analyses

Project: Advanced analysis. Fifth Deliverable, Office of Survey Methods Research, U.S. Bureau of Labor Statistics.

[36] Paulin, Geoffrey D. and Duly, Abby L. (2002), Planning ahead: consumer expenditure patterns in retirement. Monthly Labor Review, 133(9), 38-58.

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

Analysis.

29
[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.

30
Figure 1: Household incomes before tax, poverty threshold among family size

31
Figure 2: Box Plot of Expenditures on Children: Original Scale vs. Natural Log Scale

32
Table 1: Level of analyses, methods and variables for expenditure types

Types of ExpendituresLevel of

Analyses

Sophistication

Methods Variables

Education Basic,

Medium

mean, linear regression, logistic regressioneducation 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 regressionhealth care expenditure, health

insurance expenditure, medical

services expenditure, income-topoverty-threshold ratio, prescription drugs expenditure, health

insurance coverage status

Demographics Basic,

Refined

mean, two-stage regressiontuition 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

33
Table 2: Expenditure variables description

Primary expenditure

categories

Omori (2010) descriptionEAP 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)Condition: for non-gift (CLOGFTA=2) and child or

adopted child (CU CODE=3); Include: purchase price of

clothing (CLOTHXA)

CLA, CLB

“Infants’ clothing” 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)

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.

34
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) 1,574 336 59 293

SRSWORSS (wt) 786 175 24 146

Percent reporting non-zero expenditure:2

Education CEQ 2011 Q1 (wt) 43.5 29.5 30.5 23.9

SRSWORSS (wt) 42.0 35.4 37.5 21.2

Entertainment CEQ 2011 Q1 (wt) 49.9 31.0 40.7 29.0

SRSWORSS (wt) 50.1 34.3 54.2 27.4

Books2 CEQ 2011 Q1 (wt) 39.3 22.6 28.8 27.0

SRSWORSS (wt) 38.0 24.6 41.7 26.7

Children’s Apparel CEQ 2011 Q1 (wt) 42.5 40.2 39 30.7

SRSWORSS (wt) 43.8 40.6 37.5 30.8

Quarterly expenditure (dollars):3

Education CEQ 2011 Q1 (wt) 887.38 (700.28, 1074.49) 95.29 453.60 (271.73, 635.47) 91.65 282.56 (103.39, 461.72) 84.92 445.85 (264.50, 627.19) 90.90

SRSWORSS (wt) 931.71 (658.32, 1205.09) 138.97 334.06 (210.39, 457.74) 61.85 295.77 (-46.65, 638.19) 148.49 403.91 (219.70, 588.12) 90.20

Entertainment CEQ 2011 Q1 (wt) 212.35 (174.68, 250.02) 19.19 108.65 (78.41, 138.88) 15.25 229.78 (114.36, 345.21) 55.80 127.25 (86.95, 167.55) 20.27

SRSWORSS (wt) 192.89 (167.12, 218.65) 13.11 113.50 (64.90, 162.11) 24.29 277.53 (87.14, 467.92) 87.38 129.14 (79.69, 178.59) 24.45

Books2 CEQ 2011 Q1 (wt) 70.79 (64.13, 77.44) 3.39 42.05 (30.68, 53.42) 5.71 61.84 (18.61, 105.07) 20.39 51.05 (36.74, 65.37) 7.19

SRSWORSS (wt) 66.54 (58.07, 75.01) 4.30 49.62 (31.43, 67.80) 9.01 49.68 (4.96, 94.39) 19.77 63.81 (37.78, 89.84) 12.86

Children’s apparel CEQ 2011 Q1 (wt) 211.97 (189.64, 234.30) 11.37 169.21 (135.25, 203.18) 17.17 328.45 (179.12, 477.77) 72.00 179.50 (143.88, 215.11) 17.92

SRSWORSS (wt) 217.95 (181.99, 253.91) 18.28 172.58 (119.55, 225.61) 26.59 303.66 (-50.12, 657.45) 153.42 169.96 (124.64, 215.29) 22.49

Income percentile CEQ 2011 Q1 (wt) 57.35 (55.93, 58.76) 0.72 24.35 (22.06, 26.65) 1.17 42.14 (34.93, 49.34) 3.59 36.64 (33.64, 39.63) 1.52

SRSWORSS (wt) 57.47 (55.49, 59.45) 1.01 24.29 (21.03, 27.55) 1.65 40.07 (28.27, 51.87) 5.67 35.66 (31.53, 39.80) 2.09

Education (%):

Less than high school CEQ 2011 Q1 (wt) 13.0 18.1 7.7 23.5

SRSWORSS (wt) 11.8 19.6 4.1 27.4 High school CEQ 2011 Q1 (wt) 21.7 28.1 26.2 26.8

SRSWORSS (wt) 23.4 26.4 32.6 21.6

Some college CEQ 2011 Q1 (wt) 29.6 38.4 44.7 36.2

SRSWORSS (wt) 29.9 37.5 36.4 38.7

College and higher CEQ 2011 Q1 (wt) 35.6 15.4 21.5 13.5

SRSWORSS (wt) 34.9 16.6 26.9 12.3

Occupation (%):

Managerial/professional CEQ 2011 Q1 (wt) 27.2 17.9 31.2 15.9

SRSWORSS (wt) 26.7 20.2 42.3 15.6

Administrative CEQ 2011 Q1 (wt) 5.5 12.4 3.4 6.5

SRSWORSS (wt) 6.0 12.4 0.0 7.0

Other occupation CEQ 2011 Q1 (wt) 67.3 69.8 65.5 77.5

SRSWORSS (wt) 67.3 67.4 57.7 77.4

Race/ethnicity (%): White CEQ 2011 Q1 (wt) 64.9 41.3 71.6 48.1

SRSWORSS (wt) 63.9 41.7 71 43.8

African American CEQ 2011 Q1 (wt) 8.7 33.4 17.6 27.1

SRSWORSS (wt) 8.7 32.4 22.1 29.8 Hispanic CEQ 2011 Q1 (wt) 19.8 21.1 9.7 20.5

SRSWORSS (wt) 20.9 19.6 6.6 21.0

Other CEQ 2011 Q1 (wt) 6.6 4.2 1.1 4.4

SRSWORSS (wt) 6.5 6.3 0.4 5.4

Age, years CEQ 2011 Q1 (wt) 40.93 (40.46, 41.40) 0.24 35.83 (34.83, 36.83) 0.51 43.55 (41.50, 45.60) 1.02 41.36 (39.73, 42.99) 0.83

SRSWORSS (wt) 40.70 (40.04, 41.36) 0.34 35.26 (33.84, 36.68) 0.72 44.59 (41.56, 47.61) 1.46 39.80 (37.60, 42.00) 1.11 Number of children:

Ages 0–5 CEQ 2011 Q1 (wt) 0.63 (0.59, 0.67) 0.02 0.59 (0.50, 0.67) 0.04 0.21 (0.09, 0.33) 0.06 0.71 (0.61, 0.80) 0.05

SRSWORSS (wt) 0.65 (0.60, 0.71) 0.03 0.66 (0.54, 0.78) 0.06 0.22 (0.01, 0.43) 0.10 0.77 (0.63, 0.91) 0.07

Ages 6–12 CEQ 2011 Q1 (wt) 0.73 (0.69, 0.77) 0.02 0.71 (0.61, 0.81) 0.05 0.54 (0.36, 0.72) 0.09 0.60 (0.51, 0.69) 0.05

SRSWORSS (wt) 0.73 (0.67, 0.79) 0.03 0.66 (0.52, 0.80) 0.07 0.54 (0.23, 0.85) 0.15 0.67 (0.54, 0.80) 0.07

Ages 13–18 CEQ 2011 Q1 (wt) 0.65 (0.60, 0.69) 0.02 0.54 (0.47, 0.61) 0.04 0.74 (0.54, 0.94) 0.10 0.56 (0.47, 0.64) 0.04

SRSWORSS (wt) 0.63 (0.57, 0.69) 0.03 0.49 (0.39, 0.60) 0.05 0.80 (0.45, 1.15) 0.17 0.46 (0.34, 0.58) 0.06

Region (%): Northeast CEQ 2011 Q1 (wt) 18.3 18.1 8.3 17.2

SRSWORSS (wt) 18.9 14 8.7 19.0

South CEQ 2011 Q1 (wt) 35.0 44.3 44.2 38.7

SRSWORSS (wt) 33.6 45.6 34.9 39.9 Midwest CEQ 2011 Q1 (wt) 21.6 21.1 19.8 20.2

SRSWORSS (wt) 21.9 20.3 13.3 16.2 West CEQ 2011 Q1 (wt) 25.0 16.5 27.6 24.0

SRSWORSS (wt) 25.6 20.2 43.1 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 1s t quarter sample

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

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

35
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 2281.238 11.377 168.436 1.533 -0.181 0.131

SRSWORSS 432 2340.502 11.975 184.435 1.479 -0.203 0.297

Entertainment CEQ 2011 Q1 999 479.475 18.150 448.323 1.158 0.029 0.080

SRSWORSS 507 264.734 3.363 14.353 1.168 -0.078 -0.150

Books CEQ 2011 Q1 791 79.717 3.073 12.613 1.085 -0.260 0.123

SRSWORSS 391 73.887 2.769 10.936 1.083 -0.243 -0.025

Apparel CEQ 2011 Q1 917 276.346 5.227 52.159 1.089 -0.122 -0.216

SRSWORSS 469 310.571 6.097 60.694 1.109 -0.103 -0.098

SD: Standard Deviation

36
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) 1.023 (1.021, 1.026) 0.987 (0.985, 0.989) 0.935 (0.933, 0.938) 1.090 (1.088, 1.092)

SRSWORSS (wt) 1.438 (1.433, 1.442) 1.081 (1.078, 1.085) 0.971 (0.967, 0.974) 1.144 (1.141, 1.148)

Single father CEQ 2011 Q1 (wt) 0.756 (0.753, 0.760) 0.582 (0.580, 0.585) 0.613 (0.610, 0.616) 0.943 (0.939, 0.947)

SRSWORSS (wt) 1.138 (1.130, 1.145) 1.040 (1.033, 1.047) 1.083 (1.076, 1.090) 0.750 (0.745, 0.755)

Cohabiting CEQ 2011 Q1 (wt) 0.640 (0.638, 0.641) 0.697 (0.695, 0.699) 0.907 (0.905, 0.909) 0.690 (0.689, 0.692)

SRSWORSS (wt) 0.607 (0.605, 0.609) 0.686 (0.683, 0.688) 1.069 (1.066, 1.073) 0.699 (0.697, 0.701)

Income percentile CEQ 2011 Q1 (wt) 1.012 (1.012, 1.012) 1.020 (1.020, 1.020) 1.016 (1.016, 1.017) 1.008 (1.008, 1.008)

SRSWORSS (wt) 1.011 (1.011, 1.011) 1.016 (1.016, 1.016) 1.012 (1.012, 1.012) 1.009 (1.009, 1.009)

Education:3

High school CEQ 2011 Q1 (wt) 1.391 (1.387, 1.395) 1.509 (1.505, 1.513) 1.232 (1.229, 1.235) 1.202 (1.200, 1.205)

SRSWORSS (wt) 1.840 (1.832, 1.847) 1.306 (1.301, 1.310) 1.327 (1.322, 1.332) 1.120 (1.117, 1.124)

College and higher CEQ 2011 Q1 (wt) 2.443 (2.437, 2.449) 2.412 (2.406, 2.418) 1.750 (1.746, 1.755) 1.084 (1.082, 1.086)

SRSWORSS (wt) 3.574 (3.561, 3.588) 2.623 (2.613, 2.632) 1.538 (1.533, 1.544) 1.106 (1.103, 1.110)

Occupation:4

Managerial/professional CEQ 2011 Q1 (wt) 1.285 (1.283, 1.287) 1.546 (1.544, 1.549) 1.411 (1.409, 1.413) 0.933 (0.931, 0.934)

SRSWORSS (wt) 1.466 (1.463, 1.470) 1.562 (1.559, 1.566) 1.442 (1.438, 1.445) 0.992 (0.990, 0.994)

Administrative CEQ 2011 Q1 (wt) 0.916 (0.914, 0.919) 1.088 (1.085, 1.091) 0.928 (0.925, 0.931) 1.156 (1.153, 1.159)

SRSWORSS (wt) 0.971 (0.967, 0.974) 1.259 (1.254, 1.264) 0.956 (0.952, 0.960) 0.892 (0.888, 0.895)

Race/ethnicity:5

African American CEQ 2011 Q1 (wt) 0.630 (0.629, 0.631) 0.449 (0.448, 0.450) 0.608 (0.606, 0.609) 0.864 (0.862, 0.866)

SRSWORSS (wt) 0.718 (0.716, 0.721) 0.470 (0.468, 0.471) 0.543 (0.541, 0.545) 0.803 (0.801, 0.805)

Hispanic CEQ 2011 Q1 (wt) 0.567 (0.566, 0.569) 0.646 (0.644, 0.647) 0.514 (0.512, 0.515) 1.052 (1.050, 1.054)

SRSWORSS (wt) 0.689 (0.687, 0.691) 0.830 (0.828, 0.833) 0.567 (0.565, 0.569) 0.910 (0.908, 0.912)

Other CEQ 2011 Q1 (wt) 1.290 (1.286, 1.294) 0.306 (0.305, 0.307) 0.766 (0.764, 0.768) 1.064 (1.061, 1.067)

SRSWORSS (wt) 1.968 (1.960, 1.976) 0.323 (0.322, 0.325) 1.320 (1.315, 1.326) 0.793 (0.790, 0.796)

Age CEQ 2011 Q1 (wt) 1.007 (1.007, 1.007) 1.004 (1.004, 1.004) 1.013 (1.013, 1.013) 0.989 (0.989, 0.989)

SRSWORSS (wt) 1.015 (1.015, 1.016) 1.009 (1.009, 1.009) 1.005 (1.005, 1.005) 0.990 (0.990, 0.990)

Number of children:

Ages 0–5 CEQ 2011 Q1 (wt) 1.251 (1.249, 1.252) 0.772 (0.771, 0.773) 0.924 (0.922, 0.925) 0.842 (0.841, 0.842)

SRSWORSS (wt) 1.205 (1.203, 1.207) 0.740 (0.739, 0.741) 0.889 (0.887, 0.890) 0.773 (0.772, 0.774)

Ages 6–12 CEQ 2011 Q1 (wt) 1.116 (1.115, 1.117) 1.017 (1.016, 1.018) 1.024 (1.023, 1.025) 1.002 (1.001, 1.003)

SRSWORSS (wt) 1.062 (1.060, 1.063) 0.949 (0.948, 0.950) 0.921 (0.920, 0.922) 1.077 (1.076, 1.078)

Ages 13–18 CEQ 2011 Q1 (wt) 0.965 (0.964, 0.966) 1.037 (1.036, 1.038) 0.986 (0.985, 0.987) 1.108 (1.107, 1.109)

SRSWORSS (wt) 0.892 (0.890, 0.893) 1.059 (1.057, 1.060) 1.048 (1.046, 1.049) 1.105 (1.103, 1.106)

Region:6

South CEQ 2011 Q1 (wt) 0.822 (0.820, 0.823) 0.877 (0.875, 0.879) 0.901 (0.899, 0.903) 0.745 (0.743, 0.746)

SRSWORSS (wt) 0.811 (0.809, 0.813) 0.762 (0.760, 0.764) 1.111 (1.108, 1.114) 0.679 (0.677, 0.681)

Midwest CEQ 2011 Q1 (wt) 0.898 (0.896, 0.900) 1.074 (1.071, 1.076) 1.018 (1.015, 1.020) 0.833 (0.831, 0.835)

SRSWORSS (wt) 0.724 (0.722, 0.726) 0.994 (0.990, 0.997) 1.481 (1.476, 1.485) 0.761 (0.759, 0.763)

West CEQ 2011 Q1 (wt) 0.948 (0.946, 0.950) 1.333 (1.330, 1.336) 1.013 (1.011, 1.016) 0.708 (0.706, 0.709)

SRSWORSS (wt) 0.870 (0.867, 0.872) 1.048 (1.045, 1.052) 1.067 (1.064, 1.071) 0.666 (0.664, 0.668)

N CEQ 2011 Q1 2,262 2,262 2,262 2,262

SRSWORSS 1,131 1,131 1,131 1,131

1

Including other reading materials, such as magazines and newspapers. 4 Reference class: other occupations.

2 Reference class: married-couple households. 5 Reference class: White.

3 Reference class: less than high school. 6 Reference class: Northeast.

37
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) 4.456 70.378 3.145 70.268 2.558 70.291 4.106 70.265

SRSWORSS (wt) 4.950 70.502 3.164 70.367 3.035 70.395 4.365 70.375

Household type:2

Single mother CEQ 2011 Q1 (wt) -0.337 90.165 -0.228 0.119 -0.164 0.135 0.056 0.111

SRSWORSS (wt) -0.634 80.210 -0.200 0.161 -0.047 0.182 0.115 0.162

Single father CEQ 2011 Q1 (wt) -0.659 0.340 0.210 0.235 -0.146 0.269 0.608 80.229

SRSWORSS (wt) -0.938 90.442 0.321 0.312 -0.488 0.353 0.491 0.384

Cohabiting CEQ 2011 Q1 (wt) -0.229 0.181 -0.237 0.124 -0.069 0.130 0.083 0.126

SRSWORSS (wt) -0.171 0.250 -0.175 0.176 0.079 0.179 0.081 0.183

Income percentile CEQ 2011 Q1 (wt) 0.006 80.002 0.006 70.001 0.009 70.002 0.004 80.001

SRSWORSS (wt) 0.007 80.002† 0.006 70.002 0.008 70.002† 0.003 0.002

Education:3

High school CEQ 2011 Q1 (wt) 0.494 90.218 0.118 0.156 0.169 0.167 0.085 0.127

SRSWORSS (wt) 0.154 0.318 0.285 0.220 0.040 0.225 0.091 0.188

College and higher CEQ 2011 Q1 (wt) 0.971 70.200 0.378 90.146 0.240 0.153 0.076 0.121

SRSWORSS (wt) 0.736 80.293 0.443 90.207 0.157 0.210 0.024 0.176

Occupation:4

Managerial/professional CEQ 2011 Q1 (wt) 0.317 80.110 0.287 70.077 0.096 0.084 0.105 0.088

SRSWORSS (wt) 0.183 0.146 0.401 70.110 0.204 0.122 0.242 0.125

Administrative CEQ 2011 Q1 (wt) -0.053 0.205 0.052 0.138 -0.014 0.158 -0.037 0.137

SRSWORSS (wt) -0.194 0.269 -0.099 0.187 -0.042 0.218 0.045 0.202

Race/ethnicity:5

African American CEQ 2011 Q1 (wt) -0.153 0.166 -0.241 0.127 -0.202 0.136 0.070 0.114

SRSWORSS (wt) -0.398 0.216 -0.328 0.176 -0.161 0.195 0.025 0.163

Hispanic CEQ 2011 Q1 (wt) -0.517 80.157 -0.014 0.107 -0.163 0.124 0.075 0.101

SRSWORSS (wt) -0.565 80.199 0.037 0.143 -0.131 0.169 -0.032 0.142

Other CEQ 2011 Q1 (wt) 0.196 0.185 0.035 0.172 0.155 0.157 -0.100 0.150

SRSWORSS (wt) 0.125 0.231 0.380 0.239 0.137 0.198 -0.128 0.220

Age CEQ 2011 Q1 (wt) 0.005 0.006 0.012 80.004 0.011 90.004 0.005 0.005

SRSWORSS (wt) 0.001 0.008 0.008 0.006 0.004 0.006 0.002 0.006

Number of children:

Ages 0–5 CEQ 2011 Q1 (wt) 0.174 90.076 0.119 0.062 0.022 0.063 0.093 0.059

SRSWORSS (wt) 0.233 80.101 0.097 0.086 -0.030 0.087 0.061 0.089

Ages 6–12 CEQ 2011 Q1 (wt) -0.120 90.060 0.182 70.044 0.006 0.048 0.114 90.046

SRSWORSS (wt) -0.126 0.083 0.185 80.062 -0.082 0.067 0.108 0.063

Ages 13–18 CEQ 2011 Q1 (wt) -0.034 0.069 0.207 70.050 0.095 0.056 0.227 70.051

SRSWORSS (wt) -0.073 0.097 0.198 80.069 0.136 0.076 0.284 70.072

Region:6

South CEQ 2011 Q1 (wt) -0.338 90.138 -0.130 0.099 -0.300 80.108 -0.198 90.098

SRSWORSS (wt) -0.162 0.186 -0.150 0.140 -0.376 90.163 -0.213 0.142

Midwest CEQ 2011 Q1 (wt) -0.346 90.150 -0.087 0.106 -0.292 90.115 -0.275 90.108

SRSWORSS (wt) -0.417 90.207 -0.087 0.149 -0.380 90.166 -0.511 80.155

West CEQ 2011 Q1 (wt) -0.385 80.148 0.008 0.103 -0.087 0.114 -0.342 80.109

SRSWORSS (wt) -0.251 0.196 -0.018 0.143 -0.044 0.168 -0.455 80.152

N CEQ 2011 Q1 871 999 791 917

SRSWORSS 432 507 391 469

R

2 CEQ 2011 Q1 (wt) 0.159 0.135 0.132 0.064

SRSWORSS (wt) 0.191 0.162 0.144 0.090

1

Including other reading materials, such as magazines and newspapers. 6 Reference class: Northeast.

2 Reference class: married-couple households. 7 p < 0.001.

3 Reference class: less than high school. 8 p < 0.01.

4 Reference class: other occupations. 9 p < 0.05.

5 Reference class: White. † SE(SRSWORSS) < SE(CEQ 2011 Q1).

38
Table 7: Number of observations and number of reporting expenditures by household types

Expenditure Analysis Married couple Single mother Single father Cohabiting

Overall CEQ 2011 Q1 1367 304 52 254

SRSWORSS 682 155 22 129

Education CEQ 2011 Q1 612 91 15 59

SRSWORSS 287 58 8 26

Entertainment CEQ 2011 Q1 703 100 21 77

SRSWORSS 342 57 11 37

Books CEQ 2011 Q1 566 73 14 72

SRSWORSS 270 41 8 35

Apparel CEQ 2011 Q1 610 131 20 76

SRSWORSS 311 68 7 38

39
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.

40
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)

41