The Frequency of Consumer Expenditure: An Empirical Analysis

Julie A. Nelson

Working Paper Series No. 94-08

April 1994

Note: The Working Papers of the Department of Economics, University of California, Davis, art preliminary materials circulated to invite 

discussion and critical comment. These papers may be freely circulated but to protect their tentative character they are not to be 

quoted without the permission of the author.
ABSTRACT

How does the observed pattern of household purchases vary, as we extend or shorten the 

period of observation? Over the course of a year, how often do households tend to purchase 

certain goods? These questions have implications for the empirical measurement of 

consumption, for the econometric treatment of zero expenditures, and for survey design and 

data imputation. An empirical analysis of data from the U.S. Consumer Expenditure Survey, 

Interview Survey, from 1987-1989, reveals that there is considerable heterogeneity across 

disaggregate goods and across households in the frequency of expenditure. Issues of data 

quality are discussed.

KEY WORDS: consumption, demand, frequency of expenditure, zero expenditures, U.S. 

Consumer Expenditure Survey, data quality
I. Why Study the Frequency of Expenditure?

Most economic studies of consumer behavior focus on how much people spend on 

particular goods, over a given period of time. In this paper, in contrast, the question of the 

level of expenditure is temporarily set aside, in order to turn attention to the period of time 

over which expenditure is defined. Looking only at the question of whether individual 

households do or do not purchase particular goods during a given time span, how does this 

pattern vary as we change the observation period from one month to three months, or to a 

year? Over the course of a year, in how many months or quarters, on average, do households 

spend on a particular good? These questions will be investigated using Consumer Expenditure 

(CE) Survey, Interview Survey, data from 1981-1989.

While the frequency of expenditure is of interest in its own right, in describing one 

dimension of household behavior, it also has implications for the study of a wider range of 

economic and statistical issues.

First, economic and econometric interpretation of expenditure data depends on the time 

period of observation. Most theoretical economic models are formulated in terms of an agent's 

consumption, not an agent's expenditure. While consumption is usually conceived of as a 

relatively smooth flow, expenditure events are discrete and take place at specific points in 

time. As the time period of observation of expenditure gets longer, we are more likely to get a 

less noisy measure of consumption. This point is illustrated in Nelson ( 1994), which shows, 

using CE data, how the use of a three-month measure of consumption as contrasted to a 

one-month measure dramatically reduces the estimated standard errors associated with a 

measure of the effect of changes in income on changes in consumption. Lengthening the time 

period is not costless,
2

however, even in a modeling sense. As the time period gets longer, we risk losing the ability 

to analyze changes in the economic fundamentals which create changes in consumption 

behavior.

Second, econometric problems arise when we observe non-purchase of a good, that is, 

expenditure on any particular good equal to zero. Such a zero expenditure may be due to 

misreporting, or may represent a "corner solution" where a consumer chooses not to consume 

at given prices and income, or may represent underlying tastes, such that a consumer would not 

consume the particular good at any price or income. But it may also represent infrequency of 

purchase, that is, the case in which a household usually consumes the item, but is not recorded 

as making expenditures for it within the constraints of the length and timing of the survey. For 

example, a household might be asked about something they normally purchase every other 

month during a nonspending month, or asked in the winter about something they normally 

purchase in the summer. Appropriate econometric treatment of observed zeros depends on 

which of these many factors is thought to be the cause (e.g., Blundell and Meghir 1987; Deaton 

and Irish 1984; Kay, Keen, and Morris 1984). Yet in the literature to date, the decision about 

how to categorize observed zeros has nearly always been made on a priori rather than 

data-informed grounds. The information in this paper will help to empirically distinguish the 

infrequency of purchase case from the cases of misreporting, corner solutions, or underlying 

tastes, in one data source.

Third, the frequency of expenditure should be, and often is, a factor in survey design. A 

critical number of observations (for statistical purposes) of purchases of a certain type can be 

gathered. with a shorter survey, the more frequently the purchases are commonly made. 

Infrequent purchases require a longer time frame. The U.S.
3

Consumer Expenditure Survey is already divided into two parts, for this reason. While the 

Diary Survey collects data on many frequently purchased goods (like specific food items) 

using a two-week diary, the Interview Survey collects data on less-frequently purchased goods 

(as well as global estimates of some smaller items such as food expenditure) using interviews 

that cover three months, and which are repeated for up to a year. In contrast, the United 

Kingdom's Family Expenditure Survey largely uses a two-week diary, but supplements this 

with information on certain goods known to be purchased less frequently.

Lastly, the frequency of purchase presents problems for the data user who would like to 

impute missing observations. For example, some households do not complete the full set of CE 

interviews which would yield data on a complete year of expenditures. While many users of 

this data exclude households that are not full-year (which may lead to certain biases), some 

researchers estimate full-year expenditure by appropriately grossing up those interviews which 

are reported (see for example, Betson 1990, Ferreira and Buse 1993, Rubin et al. 1990). While 

this grossing-up procedure is probably not misleading for goods whose purchase is frequent 

and habitual, applying this to goods which are purchased infrequently is more problematic. To 

take an example, while it is plausible that the household's purchases of food during a missing 

interview quarter are much like its purchases in non-missing interviews, it is less plausible that 

its purchases of automobiles or seasonal vacation travel can plausibly be so imputed. This 

paper provides information for finer distinctions along these lines, for goods somewhere on the 

continuum between food and vacations or automobiles.

Section II describes the CE survey data used in this study. Section III contains the 

results of the empirical study. Section IV investigates the extent to which certain
4

data problems may add qualifications to the analysis. Section V concludes.

II. The U.S. Consumer Expenditure Survey

The data used in this paper are from the Interview portion of the Consumer 

Expenditure Survey (CE), conducted by the U.S. Department of Labor, Bureau of Labor 

Statistics (BLS). Beginning in 1980, this survey has been conducted on an ongoing basis, with 

households introduced into the sample every month, interviewed up to five times, and then 

dropped from the sample on a rotating basis. The first interview is used solely for bounding 

purposes (that is, to prevent the respondent from "helping out" the interviewer by reporting 

purchases that occur before the desired sample period), and the data from this interview is not 

released for research use. Each of the subsequent four interviews collects data on expenditure 

types and amounts on a threemonth recall basis. For some categories of goods, households are 

also asked to report the specific month of purchase. Households who complete the full 

sequence of surveys, then, have recorded a full year of information on expenditures in 

three-month, and for some goods, monthly, increments. Increments finer than one month are 

not available in these data. Because the households begin and end at different times, survey 

years and interviews do not usually correspond to calendar years and calendar quarters. In 

addition to information on expenditures, the survey gathers information. on the composition of 

the "consumer unit" (roughly equivalent to, and henceforth referred to, as a "household"), 

employment, income, and other socio-economic variables.

Roughly 7,000 households begin the survey during a calendar year; of these, 

somewhat more than half usually complete all the interviews. A recent reorganization of the 

publicly released data for 1980-1989 allows household-level data to be easily
5

followed across interviews (Nelson 1992). Because the number of disaggregate expenditure 

records exceeds one million for each year, for tractability this paper uses data only from 

households whose last interview took place in 1988 or 1989 (so their expenditures may have 

taken place in 1987, 1988, or 1989). There were 7667 households in this period who completed 

all interviews, and hence provide information on a full year of expenditures.

For coding purposes, the types of goods purchased are matched with a set of over four 

hundred Universal Classification Codes. Such codes can be very fine, as for example, 

distinguishing between portable and non-portable dishwashers and between pants and shorts. 

For the purposes of this study, goods are more highly aggregated into sixty categories, and 

then into nine categories, following the categorization scheme used in preparation of the U.S. 

Consumer Price Index.' Data on gift purchases (for persons inside or outside the household) are 

included in each category.

III: Expenditure Frequencies

Table 1 presents summary statistics on household purchases on sixty categories of 

goods. Column (a) shows the percentage of the 7667 households who made a purchase in the 

category sometime during their survey year. The percentage of households who report a 

purchase during as interview (3-month) period is also of interest. Column (b) reports the 

average, over interviews two through five, of the percentage of households reporting a 

purchase in this part of their interview sequence.

The categories are listed in order of "habitualness," which is defined as the ratio of column (b) 

to column (a). That is, given that one purchases the item during the year,

1

A complete description of the aggregation scheme can be found in Nelson (1992).
6

"habitualness' is higher the more regularly purchases are made during the year. Looking at line 

3, for example, 99.2% of households report paying for piped gas and electricity during the 

year, and nearly everyone who purchases these at all, reports purchasing them at every 

interview (on average, 98.3% in each interview). Line 6, rent of dwelling, is an example of a 

service which is not purchased by the majority of the sampled households (only 29.5% of the 

sample purchase over the year), but which is a habitual purchase for the minority who 

constitute purchasers (28.1% of the sample report payment in an average interview). Moving 

to the end of the table, it is no surprise that purchases of new vehicles are distinctly 

non-habitual. While 11.9% of the households surveyed report a purchase in this category over 

a twelve-month period, only 2.9% (on average) report such a purchase over a three-month 

period. Major household appliances and used vehicles, the other major consumer durables, 

also appear as particularly low on the "habitualness" ranking. (Personal care appliances is a 

very small category).

For the goods for which information on the month of purchase is available, Columns 

(c), (d), and (e) report on the average, minimum, and maximum number of households 

reporting purchases in each calendar month. 3 In addition, columns (f) and (g) name the highest 

two months of expenditure, for goods for which a seasonal pattern is discernible. If only one 

month is named, it is a particular outlier; if the data is collected by month but no month is 

named, the distribution is close to uniform.4 The

2

The average is shown rather than the percentage for each interview, since there is 

relatively little variation across interviews. Since interviews many cover any three consecutive 

months, this measure has no seasonality implications. The calculation for interview two, for 

example, is the percentage of households who report a purchase in their second interview, no 

matter when--in calendar time--that interview took place.

3

In contrast to the calculations for the interview column, the monthly columns use 

calendar time in order to bring out seasonal effects. No distinction is made as to whether the 

calendar month fell in 1987, 1988, or 1989.
7

table indicates that monthly payments are the norm for "other utilities and public services," 

piped gas and electricity, mortgage interest, and auto finance' charges. Presumably this is also 

true for some other items such as rent, for which only quarterly data is available. For most 

other goods for which monthly data are available, the likelihood of observing a household 

making payment for it during a month is substantially lower than the likelihood of observing a 

payment during a three-month period or a year. Strong seasonal increases can be observed for 

various reasons: December holiday buying (for example, for all of the apparel and footwear 

categories, other housefurnishings, watches and jewelry); winter weather (for fuel oil); 

summer vacations (lodging while out of town); and the beginning of school terms (girl's and 

boy's apparel and footwear, tuition, lodging at school). The reasons for other seasonal swings, 

such as the upswing in property taxes (line 47) in October and November, or in car sales (lines 

57 and 60) in spring and summer, are less obvious, though there may be behavioral or 

institutional reasons far this not known to the author.

Tables 2 and 3 examine the data from a slightly different perspective. Rather than 

taking the time period as the unit of analysis and counting up households, the household is 

taken as the unit of analysis, and the number of purchase occasions is counted up.5 Taking only 

those households who purchased at some time during the year, what can we say about the 

frequency of purchase?

4

Specifically, the two highest months containing at least 9% of the total purchase 

occasions in the year are named. A uniform distribution would have 100%/12 or 8.33% in 

every month.

5

The number of purchase occasions" is defined here in terms of the shortest 

observable time frame, rather than in terms of numbers of actual market transactions. Since we 

do not observe the timing of transactions over periods shorter than a quarter (some categories) 

or a month (other categories), it makes no difference to the analysis whether a "purchase" 

required one or twenty checks or trips to the store. A household can report a maximum of tour 

quarterly or twelve monthly "purchases," as the term is used here.
8

Table 2 reports on the number of interviews in which a purchase was reported, for 

households who reported some purchase during their survey year. Column (a) reports the mean 

number of interviews in which a purchase was recorded. The listing of goods is ordered by this 

column, and is nearly identical to the ordering of the same goods by "habitualness" in Table 1. 

The modal number of interview-purchases is reported in column (b), dropping from a value of 

four for the more habitual goods, though a short mixed section, to a value of one for less 

frequently purchased goods. Public transportation (line 23), it can be noted, includes not only 

intra-city transportation that might be expected to be purchased frequently, but also airfares 

and inter-city bus and train, for which a modal interview-purchase of one is not unbelievable.

Columns (c) through (f) exhaustively describe the frequency of purchases, measured at 

the interview level. For example, only .1% of household record purchasing food at home (line 

1) during only one interview, while recording no purchases in that category for the remaining 

three interviews. This .1% case probably reflects bad data. Small percentages report food 

purchases in only two or only three interviews. More comfortingly, 98.8% of food at home 

purchasers report purchasing food in all four interviews. Column (g), which reports the number 

of households reporting purchase at some point during the year, confirms, at line 1, that 100% 

of the 7667 households in the sample report food at home purchase at some time during the 

survey year.6 Scanning down the table, one gets an impression of how the patterns of 

purchasing vary by household. While more than half the (purchasing) households report 

purchasing the goods represented by lines 1-10 in every interview, a smaller percentage 

purchase in only

6

The number in column (g) of Table 2 is the denominator for Table 2, columns 

(c)-(f), and the numerator for Table 1, column (a).
9

three interviews. While it is not a monotonic decrease in all cases, the distribution tends to be 

skewed to the left: in many cases a few less households reports purchases in two interviews 

than in three. and still fewer in only one interview than in two. Starting with line 11 (alcoholic 

beverages at home), less than half the purchasers purchase in all four interviewers. Continuing 

down the table, the distribution across columns (c)-(f) becomes progressively more uniform, 

and then finally more skewed towards the right as a single purchase becomes the mode. Except 

for at the extreme top and bottom rows of the tables, households appear to be heterogeneous in 

their behavior with respect to purchase frequency.

Table 3 performs a similar analysis for goods categories for which monthly data is 

available. Columns (a) and (b) present the mean and modal number of months in which 

purchases were reported. To save space, the frequencies of purchase are reported for only 

selected numbers of months (one, three, six, nine, and twelve) in columns (c)-(g). Column (h) 

reports the number of households reporting at least one purchase at any time during the year. 

With one exception, column (b) indicates that the modal number of months in which a 

purchase is recorded is either twelve or one. The case of women's apparel, for which the modal 

number of purchases is five, seems to be exceptional, both in having a mode in the middle of 

the distribution and in having a higher mean number of purchases than all the other apparel 

categories. While, as in the previous table, it is only at the very top and bottom that households 

act in anything like a homogeneous manner, purchasing in a single month out of the year 

appears to dominate for most of the middle section of the table, with a dramatic trailing off for 

number of purchases above three.

Tables 4 and 5 report the same information as Tables 1 and 2; except with the
10

expenditures now aggregated into only nine categories. Transportation, for example, includes 

vehicle purchases and rentals, motor fuel and motor oil, repairs, auto insurance and finance 

charges, miscellaneous charges such as tolls and registration, and public transportation. Shelter 

includes rent (for renters), household or tenants' insurance, expenditures on home maintenance, 

household fuels and utilities, lodging out of town, mortgage interest (for owners) an a few 

minor other categories. 7 As one would of course expect, non-purchase is less frequently 

observed the broader one defines the category. Yet even for the broad category of household 

furnishings and operations (which includes furniture and appliances, textile and non-textile 

housefurnishings, home business machines, TV and sound equipment, and housekeeping 

services) where 95.6% of households report some purchase over the survey year, only 80.3% 

report a purchase over an average interview quarter, and only 61.6% report purchases in all 

four interview quarters.

IV. Data issues

Tables 1 to 5 are only a valid indicator of consumer behavior to the extent that 

Consumer Expenditure Survey data, as publicly released, accurately captures this behavior. 

The (usual) problems of data gathering and dissemination suggest some caveats and cautions in 

regard to the above analysis.

7

Person who own homes without mortgages probably make up most of the 

nonpurchasers of "shelter," since mortgage interest is the major component of shelter costs for 

homeowners by the definition used here. This is obviously not an accurate way of measuring 

shelter consumption. The CE survey also contains information that can be used to calculate 

estimates of annual rental equivalence for many households, for studies where a measure of 

consumption rather than of expenditure is required.
11

Data, Processing

As with most large data sets, the CE Interview data gathered on the questionnaires is 

put through a series of edits and checks prior to public release. While a thorough explanation of 

the processes applied to the CE data is beyond the scope of this paper, it should be noted that 

these processes may be influencing the frequency of expenditures, and especially monthly

expenditures, reported in these tables. In fact, for a few cases (mortgage interest and auto 

finance charges among them) monthly payments are actually computed by BLS from other 

information (the date and terms of the loans). While for the vast majority of "monthly" goods, 

the month of expenditure is explicitly asked, if a respondent is vague about an amount spent, or 

the month in which it was spent, or the specific goods category on which an expenditure was 

made, the BLS will often impose (plausible) assumptions. A substantial percentage of 

expenditure records are flagged to note modification by computation (simple calculation), 

allocation (assignment of a vague response to more specific disaggregate groups), or (more 

rarely) imputation (of an expenditure value). While these processes may include assigning 

vaguely reported expenditures to random months (or one-third to each month) within an 

interview, a study by researchers at the BLS showed that such imputations of reference months 

occur in less than 1% of the expenditures recorded by month (Silberstein and Jacobs 1989). 

These data processing concerns should have. less effect on the reporting by interview quarter, 

however, since allocations are made only within, and not across, interviews.

Sample Selection

The use in this study of only those households who completed all interviews
12

means that the frequencies may not be representative of the full sample. Households may fail 

to complete all interviews if they decide not to cooperate, if they move, or if they are away on 

a trip at the time of an interview. A comparison of full-year vs. partyear participants (Nelson 

1992) shows that full-year reference persons are more likely to be older, to be homeowners 

and to have somewhat higher income than are part-year reference persons. It is unclear what 

biases, if any, this selection has imposed on Tables 1 to 3.

Quality of Response

The way in which the data are released makes it impossible to distinguish true zero 

expenditures from non-response. If the household reports purchasing the good then there is a 

record reporting this purchase; if the household does not report the good, either because they 

did not purchase it or because they have forgotten about it or are not taking the survey 

seriously, then there is simply no record. This may be one factor underlying the dramatic 

difference between reported numbers of purchases of women's apparel vs. other types of 

apparel: women are more likely to be the respondents to the survey (Silberstein 1937) and so 

may have better information about purchases for themselves.

There is little one can do, once the data is gathered, to remedy this problem." If it is 

thought that poor responses to expenditure questions might be correlated with poor responses 

to questions about income sources, a variable reporting on quality of income response might be 

used to select the better responders. The Bureau of Labor Statistics.

8

The BLS also releases files ( "EXPN" ) that are more detailed than the general files 

("MTAB") that form the base for this study, but these files are not standardized across goods 

categories and the non-response flags are often still difficult to interpret.
13

codes a household as a "complete income respondent" if they report values for their major 

components of income. When Tables 1 to 3 were rerun using a subsample of "complete" 

income reporters only (N=6696), results change only slightly. For example, 86.3% of 

"complete" income respondents report purchasing entertainment services, compared to 86.2% 

of the full sample (Table 1); 57.3% of the purchasers in the "complete" subset report 

purchasing entertainment services in all four interviews, compared to 56.1% ( Table 2 ) in the 

full sample. A slight shift towards more reporting is observed for some goods, and towards 

less reporting for others. It seems, then, that income response and frequency of reported 

purchase are not closely related.

The fact that monthly expenditures are recovered using recall over a three month 

period may also influence the observed frequency of expenditure. Expenditures three or two 

months prior to an interview may be more difficult for respondents to remember, than 

expenditures in the month immediately prior to an interview. This may lead to underreporting 

in the early months in each interview period. Indeed, in these data a disproportionate number 

of purchase occasions are recorded as taking place in the last month of each interview quarter, 

as can be seen for selected categories in Table 6. The first month is the one farthest in the past 

from the interview date; the third month is the most recent. The sample used is the same as in 

Table 3, and the percentages are for the sample as a whole. If respondents are reporting 

entirely accurately, there is no reason to expect more purchases, in the aggregate, in one month 

than in any other. Note that calendar time is not an issue here, since these months are defined 

in regard to their relationship to an interview, and an interview can take place any time of the 

year. In the utilities categories, where the respondents are explicitly asked about monthly bills 

received, the upward trend with proximity of the interview is
14

slight. For large irregular purchases, such as vehicles and major home appliances, the trend is 

somewhat greater, while for smaller irregular purchases the trend can be dramatic. Only 24.5% 

of purchases of boy's and girl's footwear, for example, are reported as taking place three 

months prior to the interview, while 45.9% are reported as taking place in the most recent 

month. Since it is highly unlikely that people tailor their consumption patterns around their 

interview schedule, poor recording seems to be the cause.

The poor reporting may not always imply underreporting, however. Instead of (or in 

addition to) forgetting earlier purchases, respondents may "telescope" into the most recent 

months) expenditures that actually happened earlier. If the problem were pure telescoping, 

then the expenditure reporting for the quarter as a whole would still be accurate (that is, there 

would be no overall underreporting) even though the monthly reports are inaccurate. Whether 

the problem is recall or telescoping, it is likely that the frequencies in the first and second 

months are underreported, especially the smaller and more irregular the purchase. The reports 

in the third month may be close to accurate (if there the pattern is due to recall bias) or be 

overly high (if there is telescoping). The patterns of spending described earlier in Table 3, 

then, probably in all underestimate the number of months in which many purchases, and 

especially small and infrequent purchases, occur.

A study by BLS researchers Silberstein and Jacobs (1989) found similar evidence of 

recall bias and/or telescoping by month, looking at mean expenditures aggregated over 

households in 1952-33 CE Interview data. They also investigated whether respondents tended 

to report more or less expenditure as their length of time in the sample increased. The time in 

the survey may affect the responses, as respondents
15

progressively learn how to do the survey and/or tire of doing the survey. Silberstein and 

Jacobs found that the variation in expenditure reporting with the interview sequence was 

statistically insignificant in over half the goods categories they examined. For those categories 

in which aggregate expenditures significantly increased or decreased with the interview 

number, a variety of patterns (rising with interview number, falling, rising then falling... ) was 

observed, and the degree of change was at most "moderate" (300). The quarterly patterns 

reported in Table 2, then, are unlikely to be much influenced by time in sample effects.

V. Conclusion

While the CE survey is designed to capture expenditures at monthly intervals for many 

goods, an analysis of the data suggests that such monthly reports may be unreliable for small 

and infrequently purchased goods. For economic analysis, then, the data should probably be 

treated as a panel of monthly observations only for larger purchases. In regards to survey 

design, there is evidence that three months may be too long a recall period for some goods. 

Whether or not there is underreporting in expenditures reported at, or aggregated to, a quarterly 

basis is less clear, depending on whether recall bias or telescoping predominates.

The examination of the reported frequencies of purchase (at either the interview, of 

more questionable monthly, levels) reveals considerable heterogeneity across goods. An 

overview of the tables may suggest a multiplicity of (sometimes overlapping) reasons for these 

varying frequencies of expenditure. Some goods for which there is a steady stream of 

expenditure correspond to fixed, regular bills (e.g., utilities, insurance, rent); others are 

necessary nondurables (food at home). The most irregular purchases
16

are for durable goods (e.g. vehicles, major appliances). In between, we find irregular 

purchases of semi-durables (e.g. apparel, textile housefurnishings), luxury nondurables (food 

away, alcohol away, lodging away from home), and goods whose purchase may represent 

shocks to consumption (e.g. hospital services, home repair services). While the data on 

monthly purchases was found to be suspect, whether or not a non-purchase in a given quarter 

represents non-consumption (over a year) or simply infrequency of purchase can probably be 

reasonably inferred from the tables presented.

The analysis also reveals considerable heterogeneity among households. Goods may be 

on average purchased with more or less frequency, but within any goods category some 

households report purchases much more frequently than others. This empirical finding is 

interesting, since in the (small) frequency-of-expenditure econometric literature (e.g. Blundell 

and Meghir 1987; Deaton and Irish 1984; Kay, Keen and Morris, 1984), a single, exogenous 

purchase probability is assumed to be common to all households. Further analysis of this point, 

at yet at a very preliminary stage, suggests that the usual sharp distinction between corner 

solutions and infrequency of purchase, which leads to separate treatment of the two issues in 

econometric theory, may not be empirically helpful. This distinction is itself intimately

related to the question of the time period of observation..







24

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