# Three Dimensions of Time: An Age-Period-Cohort Analysis of U.S. Spending Patterns

## 1 Introduction

It is no stretch to suggest that the elderly tend to consume a different mix of products than younger generations. From casual observation, this would appear to hold true both within product categories and for the weight each of those categories is given in the overall consumption basket. Yet there are multiple potential explanations for why purchasing patterns might change over time. A critical question, therefore, is how much of the temporal change is actually due to the aging process, and how much is due to something else—for instance, the particular moment in history being analyzed, or the particular time and circumstances in which an individual aged. Disentangling these separate effects can help us answer important questions related to aging, consumption, and preference formation. By analyzing long-term consumption patterns along these dimensions, we can identify trends that explain broader purchasing patterns and illuminate our understanding of well-known American generations.

To test for the existence of generational or “cohort” effects in U.S. spending behavior, I incorporate Age-Period-Cohort (APC) modeling, which disentangles three distinct time-related effects on changes in behavior, into Deaton and Muellbauer’s Almost Ideal Demand System (AIDS). The result is an empirical model that accounts for these nuanced time effects but is also consistent with the principles of consumer theory. Estimation of the model using data from the Consumer Expenditure Survey suggests that household budget allocations exhibit significant cohort effects, and that including cohort effects significantly improves on demand models that account only for age. The existence of these effects suggests that cohort membership can influence spending patterns across the life course.

The analysis proceeds as follows: In the following section, I draw insights from literature in sociology, history, and economics to demonstrate the importance of accounting for cohort or generational effects while analyzing time- or age-related changes in behavior or consumption patterns, and I survey prior work that has addressed these issues. In Section 3, I propose explanations for why cohort membership could have an effect on macro spending behavior above and beyond changes related to aging or the particular period being examined. In Section 4, I offer an economic model of utility-maximizing consumers, which forms the groundwork for the construction of a demand framework that is consistent with microeconomic theory. In Section 5, I describe the particular sample of Consumer Expenditure Survey data that I use in this paper’s analysis. In Section 6, I combine two existing models from the literature—APC models and AIDS—into a single empirical model that I use to estimate the effect of cohort membership on consumer behavior. Additionally, I confront the fundamental identifiability problem inherent in building APC models, and I propose a solution to combat that problem in my model. In Section 7, I discuss some limitations of this analysis, and I propose several directions for future research in this field. In Section 8, I conclude by reiterating my main findings and emphasizing the importance of cohort effects in demand analysis.

## 2 Background

Sociologists and historians have repeatedly tackled the concept of birth cohort and what distinguishes one cohort from another. Cohorts, or generations, are shaped and defined by their particular age-related involvement in prominent historical events during their lifetime (Strauss and Howe 1992). The same historical event can have extremely different effects on two generations that experience that event at different ages and in different life stages (Strauss and Howe 1992). For example, it is easy to imagine that the Great Depression would influence toddlers, the middle-aged, and the elderly quite differently. Similarly, it is easy to fall into what Strauss and Howe (1992) label the “life-course fallacy,” in which we attempt to explain a life-cycle by looking at the different age groups that are alive at a particular moment in time.

The fact that today’s elderly demonstrate certain preferences doesn’t mean that tomorrow’s elderly will express those same preferences. Rather, groups follow a diagonal trajectory, experiencing each age at one unique time. As a result, no two groups experience an event or period in the same way, nor do two groups experience being a particular age in the same way. Tracking individuals by age location, rather than age or time period alone, allows us to see how historical events and trends shape different age groups differently (Strauss and Howe 1992). Such analysis becomes particularly meaningful when we define groups not just as uniformly sized cohorts, but as “historical generations” whose boundaries are demarcated by prominent historical events (Carlson 2008). Moreover, we can hypothesize that not only do historical events differentially affect different age groups, but that those effects may continue to influence those groups throughout the life course.

This sociological premise can be tested and examined in the realm of economics. Treating consumption patterns as one dimension along which this generational logic can operate allows us to test whether different generations really do act (and spend) differently, and whether those differences coincide with our prior understandings of American history and culture. Moreover, disentangling how age, period, and cohort differentially affect consumption patterns will help us understand the consequences of an ever-changing population age composition on aggregate demand (Howden and Meyer 2011).

Age-period-cohort (APC) analysis formally captures these sociological concepts in estimable models. Its primary aim is to disentangle age, period, and cohort effects to determine which is dominant in driving behavioral variations over time (Chen et al. 2001). Age effects are variations resulting from the biological and social processes of aging specific to individuals, such as physiological changes and the buildup of social experience (Reither, Hauser, and Yang 2009). Period effects are defined as external variations across time periods that simultaneously influence all age groups, and encompass a wide range of historical, social, and environmental factors, such as wars, technological innovation, and economic crises (Reither et al. 2009), as well as changes in income and relative prices. Cohort effects, the focus of this paper’s analysis, capture a number of concepts and interpretations. At the most fundamental level, these effects convey the idea that different age groups were born at different times, that they experience a unique collection of environmental forces as they age, and that they could therefore develop distinctive patterns of behavior above and beyond changes in their age or in prices and income in a given period (Chen et al. 2001). In other words, a birth cohort experiences the same historical, social, and environmental events at the same age, potentially giving rise to unique, cohort- specific values, attitudes, and preferences. Of course, there is also potential interaction among age, period, and cohort effects. For instance, one’s cohort membership might affect the process of aging. The focus of this paper, however, will be to isolate distinct effects, and, as such, interactions will not be estimated.

Cohort analysis has been more widely applied in the field of sociology than in economics (Chen et al. 2001), though a number of studies have used it to analyze changing consumption patterns for a variety of goods. Chen et al. (2001) employed cohort analysis using a constrained multiple regression model to examine the U.S. life insurance purchase pattern between 1940 and 1996, and found that baby boomers’ tendency to purchase less life insurance than their earlier counterparts—a cohort effect particular to the baby boom generation—was driving the recent decline in insurance purchases. The cohort analysis method has also been used to examine not just single-product consumption, but variations in product mixes. For instance, Kerr et al. (2003) analyzed age, period, and cohort effects not only on total alcohol consumption, but on beverage-specific trends in the composition of individuals’ alcohol intake. Their findings suggest that cohort effects do affect drinking patterns, not just in quantity, but in compositional makeup, and that the aging and mortality of high-consumption cohorts influence economy-wide, beverage-specific demand, as well as trends in medical conditions typically associated with particular types of alcohol consumption. It is possible that this finding, which points to the existence of cohort effects on the compositional makeup of certain forms of consumption, can be generalized to the compositional makeup of all nondurable expenditures.

This paper will examine broad U.S. consumption patterns and see whether underlying cohort effects influence not just specific product preferences, but consumer behavior on a macro scale. Indeed, understanding what drives the changing tastes of individuals as they age not only provides a richer knowledge of different groups of consumers, but it also provides us with a more thorough comprehension of aggregate demand and how it will change with shifting demographics. Age, period, and cohort effects on consumption patterns could have economy-wide implications for understanding aggregate spending behavior and key drivers of demand. In sum, by looking at how individuals across age groups and across time choose to allocate their money among these different product groups, we can come away with a better understanding of consumer preferences and how product- specific demand will change over time as different cohorts reach different life milestones and differentially experience history.

## 3 Hypothesis

Given the evidence in prior literature that age, period, and cohort effects can and do separately influence demand for specific products, it seems reasonable to think that age, period, and/or cohort could each affect the broad compositional makeup of household budget allocations over time. Determining the relative size of these different effects will be the aim of this paper’s empirical analysis. It seems both possible and likely that the magnitude of each effect would vary with the time period and cohort being analyzed. Flexible interpretations of each time- related variable convey the different mechanisms by which these effects might occur.

Physiological changes coinciding with the aging process would certainly seem to influence product demand and, by extension, budget allocation. Age effects need not be physiological; age-related household roles or stages in life could similarly affect marketplace behavior. Research suggests that bachelors tend to allocate their money to used furniture and automobiles, restaurant meals, entertainment, and recreation; newlyweds prepare more meals at home and purchase new furniture and autos; and the birth of a first child generally leads to more home-oriented leisure activities (Shaninger and Danko 1993). As households age, we would expect their consumption decisions to align with these physiological and socio-cultural changes.

One way to interpret period effects at a given moment in history is as the combination of price and income effects. In the simplest microeconomic terms, we might imagine that, if people today are richer than they were 100 years ago, they might demand different goods and different quantities of those goods; in particular, they might come to cultivate tastes for higher-quality or luxury goods. Price effects similarly align with intuition: if apples today are cheaper than they were 100 years ago, we can imagine that people today would demand more apples. As average incomes have risen over the past century (Chao and Utgoff 2006), we can anticipate that households’ optimal allocation of expenditures will shift toward more income-elastic, “luxury” goods—for instance, clothing and personal care, and food away from home. Similarly, we expect that own-price elasticities will be negative, and that elasticities for necessity items will have lower magnitudes.

We can also think of period effects as trends or fads, in that the proliferation and popularity of a certain product or behavior is the result of a particular time, and it affects all individuals living in that time. Of course, the idea of fads can easily become confounded with age and cohort. For instance, it is unlikely that 80-year-olds and 20-year-olds would be equally affected by a bell- bottoms trend; rather, fads might differentially affect different age-cohort groups. Like Rentz, Reynolds, and Stout (1983), we can look for any fad-related effects that persist over time and label those as cohort effects. We can also generalize the idea of a “fad” beyond specific products to see whether fads emerge in broader spending patterns.

We can interpret cohort effects—and justify their existence—in a number of other ways as well. First and foremost, we can think of them as the direct consequence of an individual being a certain age at a certain point in history. Any number of stories can be constructed along these lines. We might hypothesize, for example, that individuals who passed through young adulthood during Prohibition might have different lifetime consumption patterns of alcohol than other cohorts (Levenson, Aldwin, and Spiro 1998). Similarly, children or young adults of the Great Depression might demonstrate distinct lifetime purchasing patterns of luxury goods, even in expansionary periods. It is unclear, however, whether such effects would be positive or negative for any given cohort and product.

The “learning and habit formation” interpretation of cohort effects could be relevant in the food away from home (FAFH) category, in which the U.S. has seen a dramatic proliferation of convenience foods, fast-food establishments, and food marketing. Given the vast evidence suggesting that children are highly susceptible to external influences on eating behavior, the changing face of the FAFH market could have a life-long effect on the cohorts of children it influenced. Similarly, we might look for trends in food consumption both at and away from the home as cultural understandings of gender and family roles evolved over time.

In sum, strong cases can be made for why age, period, and/or cohort could each affect the particular broader compositional makeup of household budget allocations over time.

## 4 Economic Model

In my model, I assume that individuals solve a standard utility maximization problem over a range of product categories {$$x_i,..,x_k$$} and all other forms of consumption $$x_z$$ given individuals’ age A, birth cohort C, and the time period of the decision P. At any given time, individuals choose a bundle of goods so as to maximize their utility subject to their overall budget constraint. Individual utility functions take into account the changes that occur in the marginal utility of each good when age, period, and cohort vary. Individuals therefore face the following problem:

\underset{\left \{ x_i,..., x_k \right \}, x_z}{max}U\left ( x_i,..., x_k, x_z \mid A, P, C \right )

s.t.\; y= p_1x_1 + ... + p_kx_k + p_zx_z

Solving the utility maximization problem yields the individual's optimal demand functions $$x_i^{\ast }$$ as a function of all the available goods' prices $$p_i$$, as well as the individual's age, birth cohort, and the time period.

x_i^{\ast } = x_i^{\ast }\left ( p_1, ..., p_z, A, P, C \right )

All consumption good prices must enter the demand function to account for the possibility of substitution and complementarity between goods. We can imagine past prices indirectly affecting the preferences of particular cohorts—for instance, if the price for good X was low during an individual’s childhood, that person was more likely to cultivate a taste for X, and that effect stays with that individual through the life-course.

With these optimal demand functions, total nondurable expenditures $$y_n$$ can be calculated in absolute terms as:

y_n = \sum_{i=1}^{k} p_ix_i^{\ast }

Since the set $$\left \{ x_i,...,x_k \right \}$$ is taken to represent different product categories (e.g., food consumed at home, clothing and personal care, etc.), and their $$x_i^{\ast }$$ to represent optimal consumption of that category, optimal budget composition can be calculated by product group. As such,

{\omega _{i}}^{\ast } = \frac{p_i{x_{i}}^{\ast } }{\sum_{i=1}^{k} p_i{x_{i}}^{\ast }}

represents the utility-maximizing share $$\omega_i$$ of an individual's budget allocated to product $$i$$.

While the economic model is fairly straightforward, the more interesting contribution of this paper lies in the empirical analysis, whereby the individual effects are disentangled and estimated. The empirical method is a direct extension of Deaton and Muellbauer’s (1980) Almost Ideal Demand System (AIDS), which is based on a classical consumption model like the one described in this section, though without accounting for the effects of age, period, and cohort. The AIDS framework allows us to take standard, individual utility functions and derive demand functions for utility-maximizing individuals. I outline and construct the empirical method more thoroughly in Section 6.

## 5 Data

Analysis of age, period, and cohort requires the collection of data from multiple time periods due to the fact that each of these factors fundamentally relates to changes over time. Mason and Wolfinger (2001) explain that both longitudinal and repeated cross-sectional data can be used for cohort analysis. Clearly, single-period (i.e., cross-sectional) datasets must be ruled out, since any difference in the dependent variable with age could be interpreted as either an age or a cohort effect, with no clear basis for choosing (Mason and Wolfinger 2001).

The data selected for analysis come from the Consumer Expenditure Survey (CEX), a Bureau of Labor Statistics (BLS) survey that collects information on the expenditure habits of U.S. consumers at the household—or “consumer unit”—level, as well as income data and household characteristics. In particular, this analysis uses data from the Diary survey component of the CEX, in which respondents fill out a detailed diary of expenses for two consecutive one-week periods. The Diary survey is intended to gather data on small, frequently-purchased items like food or clothing that respondents are unlikely to recall over time, as opposed to much larger purchases like property or vehicles. Each week-long diary is divided into seven days, and each day is divided into four parts based on expenditure type: food and drinks away from home; food and drinks for home consumption; clothing, shoes, jewelry, and accessories; and all other products, services, and expenses. Each category is broken down into more detailed product subcategories that are explained to survey respondents.

The CEX gathers data at the level of the consumer unit, which it defines as all members of a household who are related by blood, marriage, adoption, or other legal arrangements; a person living alone or sharing a household with others who is financially independent (determined by spending behavior on housing, food, and other living expenses); or two or more persons living together who use their incomes to make joint expenditure decisions. For a given consumer unit, the reference person is the first member mentioned by the respondent when asked to “Start with the name of the person or one of the persons who owns or rents the home.” All other consumer unit members’ relationships are determined relative to this person. Throughout this analysis, any mention of individual characteristics (age, birth year, etc.) will refer to this reference person unless otherwise specified.

I use a cleaned version of the CEX data compiled by Aguiar and Hurst (2012), who use NBER CEX extracts (compiled and harmonized across years by Harris and Sabelhaus) including all survey waves from 1980 through 2003. Aguiar and Hurst restrict the sample to include only those households that report expenditures in all four quarters of the survey (which they sum to calculate annual expenditures), record non-zero expenditures on six key sub-components of the consumption basket (food, entertainment, transportation, clothing and personal care, utilities, and housing/rent), and have a head between the ages of 25 and 75 (inclusive). They take additional measures to account and correct for the possibility of zero expenditures on smaller consumption categories, including food away from home, alcohol and tobacco, etc. The authors also limit their analysis of expenditures and budget shares to nondurables, excluding health and education expenditures; they define a measure of nondurables consisting of expenditures on food (at and away from home), alcohol, tobacco, clothing and personal care, utilities, domestic services, nondurable transportation, airfare, nondurable entertainment, net gambling receipts, business services, and charitable giving. Cumulatively, these categories comprise roughly 75% of household annual expenditures. This nondurables measure will be employed in this paper’s analysis. Unless otherwise specified, expenditures are nondurable, and budget shares are expressed as a fraction of nondurable expenditure.

The Aguiar and Hurst data consolidate expenditures into broader product categories, four of which will be the focus of this analysis. They include: food consumed at home, food consumed away from home, clothing and personal care, and alcohol and tobacco. The fifth category of this analysis includes all other nondurable (“Other ND”) expenditures not included in the first four categories. That is:

Other ND = Total ND - FAH - FAFH - CPC - AT

Aguiar and Hurst calculate composite price indexes for the former four categories using weighted CPI data, which they use to convert nominal expenditures into real ones; I used these calculations along with overall price level data to calculate a price index for all “other” nondurables. In addition to the sample restrictions imposed by Aguiar and Hurst, I have reduced the sample to households of size 1 or 2 and without children, so as to reduce the need for household equivalence scaling (explained in Section 6). The resulting data sample contains 23,987 observations.

## 6 Empirical Method

The main contribution of this research lies in the empirical method, the aim of which is to disentangle, identify, and estimate sources of change in demand that result from time- related preferences distinct from changes in price and income (Poray et al. 2000). These effects can then be incorporated into designing and estimating a demand system that more thoroughly and satisfactorily explains consumer behavior along the dimensions of age, period, and cohort, while also staying true to fundamental tenets of consumer theory (Deaton and Muellbauer 1980). Understanding and modeling the true origins of demand poses significant difficulties, as changes in observed equilibrium prices and quantities of goods over time can be the result of shifts in both supply and demand (Shafrin 2009). I aim to build a model that adequately reflects changes in observed demand over time and identifies the sources of that change. Such a model can be used to improve standard demand analysis and derive greater insights into individual and aggregate demand.

To construct this model, I combine specifications from two existing, but largely separate, models from the literature: the Almost Ideal Demand System (AIDS) proposed by Deaton and Muellbauer (1980), and APC modeling. The following sub- sections describe each of the models in further detail. I combine the models to incorporate APC variables into a single demand system consistent with consumer preferences.

### 6.1Almost Ideal Demand System (AIDS)

Deaton and Muellbauer’s AIDS model is derived from Muellbauer ’s “price independent generalized linearity,” or PIGL/PIGLOG model, which allows aggregation over consumers as if they were the outcome of decisions by a single, utility- maximizing consumer (Muellbauer 1975). Deaton and Muellbauer begin with a classical theoretical model of consumer behavior very much like the economic model presented in section 4 of this paper, but not including age, period, or cohort. From this model they derive AIDS demand functions for utility-maximizing consumers in terms of budget shares. Within this framework, household demand is approximated as (Deaton and Muellbauer 1980):

w_ih = a_i + \sum_{j}\gamma_{ij}\log p_j + \beta_i\log \left \{ \frac{x_h}{k_hp} \right \}

where $$w_ih$$ is household $$h$$'s budget share of good $$i$$, $$x$$ is total expenditure, $$p$$ is a price index, and $$k_h$$ is a sophisticated measure of household size that can account for other household characteristics, such as economies of household size, and which is used to deflate budget.  For the sake of simplicity, I assume $$k$$ = 1. Because this analysis is limited to small households, this should be a reasonable assumption. Deaton and Muellbauer's demand system also accounts for price and expenditure changes, with changes in relative prices working through $$\gamma_{ij}$$ terms and changes in real expenditure operating through $$\beta_i$$ coefficients.

A number of restrictions are imposed on the model to make it consistent with the theory of demand (Deaton and Muellbauer 1980). The first of these restrictions is additive, whereby all of a household's budget shares sum to 1 (i.e., $$\sum \omega \equiv 1$$); this restriction is imposed so that all the categories, as we've defined them, sum to total expenditures. Homogeneity of the system says that $$\sum \gamma_{ij} = 0$$. That is, if all prices rise or fall by the same amount, none of the demand functions should change, and therefore budget shares should not change. This homogeneity restriction is imposed on a per-regression basis. A third restriction, the Slutsky symmetry restriction, ensures that cross-price elasticities are symmetric between goods, such that the change in demand for good $$i$$ in response to a change in price for good $$j$$ is equal to the change in demand for $$j$$ in response to a price change for $$i$$ (i.e., $$\gamma_{ij} = \gamma_{ji}$$) (Deaton and Muellbauer 1980).

Additionally, AIDS models must account for household size and composition in order to approximate behavior accurately and consistently, as emphasized by Deaton (1997). He argues that household consumption must be adjusted to account for economies of scale and variations in individual needs. To remove the need for equivalence scaling, I modify the data to include only those households with 1 or 2 members and no children, and I control for household size while estimating the AIDS model. While this limitation on the sample might prevent our results from generalizing to larger households with children, it could be generalized to the elderly.

### 6.2Age-Period-Cohort Models

While original applications of APC analysis tended to rely on innovative graphical presentations of data, recent work in sociology and statistics has explored more formal quantitative modeling of individual effects (Holford 2005). However, any attempt to quantify the three effects must work around a fundamental “identifiability problem,” in that age, period, and cohort are linearly dependent according to the following relationship:

Cohort = Period - Age

and therefore cannot be uniquely and simultaneously estimated (Holford 2005). It is consequently logically impossible to hold two effects constant and then vary the third in the way we typically understand and interpret regression coefficients (Mason et al. 1973). Indeed, Mason et al. (1973) conclude that if we assume that all age groups, time periods, and birth cohorts have unique effects on the dependent variable, it is impossible to estimate a difference between the effects of any two categories. Finding techniques to combat this fundamental problem is the primary aim of subsequent research in cohort analysis (Mason and Wolfinger 2001).

The simplest and most straightforward solution to the identifiability problem is to drop one of the effects altogether and fit a two-factor model (Holford 2005). In situations for which there is reason to expect minimal or no contribution from one of the effects, or in which a two-factor model fits the data well, this approach seems reasonable (Holford 2005). However, the appropriateness of two-way cohort analysis depends entirely on whether we consider age, period, and birth cohort to have causally distinct effects on the dependent variable (Mason et al. 1973). Unfortunately, the possibility of each factor having a distinct causal relationship to the dependent variable is very strong in most archival data. Mason et al. (1973) explain how age, period, and cohort could all intuitively and independently affect a number of observable trends, including men’s earnings over time and party identification. Similarly, in the budget composition story, there is no such reason to expect a priori that any of the three effects would be negligible, and in fact, logical cases can be made for why each factor might have a significant effect.

In cases where all three effects are deemed essential to the analysis, the linear dependency must be eliminated by some other restriction on effect coefficients (Mason and Wolfinger 2001). Rather than equate all effects for one of the model factors to zero, a second approach to nonidentifiability is to equate just two of the effects for one of the three factors. However, the validity of this approach relies on making a reasonable assumption for the equality constraint. Typically, there is no more solid basis for equating two effects beyond reasonable intuition (Holford 2005). Nevertheless, the resulting parameter estimates can vary significantly for two equally logical assumptions and still fit the data equally well, and therefore any analysis of the results depends critically on the assumptions that are made (Mason and Wolfinger 2001).

Mason and Wolfinger (2001) propose yet another solution to the identifiability problem. The idea behind this alternate method is that, while APC analysis studies time trends (since age, period, and cohort are all time measures), the effect of time is not itself causal, but rather is instead related to some other factor or factors that will affect the outcome. Therefore, one way to conduct the analysis and avoid the identifiability problem altogether is to include a more direct measure of the underlying factor for which time is a surrogate measure (Mason and Wolfinger 2001). For instance, if we had reason to believe that a cohort’s size was the only way it meaningfully contributed to the dependent variable, we could substitute cohort size for cohort membership to eliminate collinearity in the regression (Mason et al. 1973).

The aim of the analysis presented here is to estimate each of the three factors’ effects on expenditures, according to

y_{apc},_i = \beta_0 + \beta_1a_a + \beta_2p_p + \beta_3c_c + \varepsilon

where the dependent variable $$y_{apc},_i$$ is the expenditure in period $$p$$ on product category $$i$$ by a household whose respondent is of age $$a$$ and was born in cohort $$c$$, and where $$\varepsilon$$ controls for demographic factors. Given its relative flexibility and the fact that no equality restriction on two age, period, or cohort effects can reasonably be defended \emph{a priori}, the Mason and Wolfinger underlying-factor method will be used in this analysis. Period effects will be taken to be the sum of price and income effects: the effect of a specific time period on budget allocation is reflected and generated by prevailing price levels and trends in income for that period.

Clearly, changes in price and income over time will change the way people spend their money. The AIDS framework controls both for changes in relative prices (via the $$\gamma_i$$ terms) and for changes in income (through the $$\beta_i$$ terms), and their cumulative effects are taken to be the predominant influence of a given time period on an individual's purchasing decisions. For the sake of simplicity, I will avoid introducing more complexity via additional macroeconomic measures.

### 6.3Building a Demand System Including APC Variables

Combining Deaton and Muellbauer’s flexible demand system with APC analysis of expenditure data allows us to determine how temporal preferences come to affect demand within the framework of a theory-consistent model. Though the two models are largely separate in existing literature, Gustaven and Rickertsen (2009) included APC variables in a demand system that they applied to Norwegian purchases of non-alcoholic beverages. Inserting age, period, and cohort dummies into an AIDS framework gives them a model that can be simplified as

\begin{align}
w_{ih} &= a_{i0} + \sum_{k=1}^{K}\pi_{ik}A_k + \sum_{l=2}^{L}\delta_{il}P_l + \sum_{m=2}^{M}\eta_{im}C_m + \sum_{j}\gamma_{ij}\log p_j \nonumber \\
&+ \beta_i\log \left \{ \frac{x_h}{P} \right \}
\end{align}

where one age, period, and cohort dummy variable is dropped due to singularity, and $$K-1$$ age dummies, $$L-1$$ period dummies, and $$M-1$$ cohort dummies remain. (To ease interpretation of variables, I will drop the first of each: i.e., youngest age group, earliest birth cohort).

Taking period effects to be the result of price effects ($$\sum_j \gamma_{ij}$$) and income effects ($$\beta_i$$) leaves us with the following:

\begin{align}
w_{ih} = &a_{i0} + \sum_{k=2}^{K}\pi_{ik}A_k + \sum_{m=2}^{M}\eta_{im}C_m + \sum_{j}\gamma_{ij}\log p_j \nonumber \\
&+ \beta_i\log \left \{ \frac{x_h}{P} \right \}
\end{align}

Dummies for age and cohort are broken into 5-year intervals,[1] resulting in 10 age groups (25-29, 30-34, etc.) and 11 birth cohorts (beginning with 1916-20). As mentioned before, the age 25-29 and cohort 1916-20 dummies are dropped from the regression due to singularity and the remaining dummy coefficients can be interpreted as digression from those reference groups.

### 6.4 Estimation

In my main analysis, I estimate a set of linear simultaneous equations for the five different product categories (food at home, food away from home, clothing and personal care, alcohol and tobacco, and other nondurables) using the method of seemingly unrelated regressions. This method allows for the simultaneous estimation of separate linear regressions whose error terms are allowed to be correlated across equations. Estimating the model as a set of simultaneous equations is also required for the imposition of the symmetry constraint, which requires equality of cross-price elasticities across regressions.

In addition, because the dependent variable in question is a budget share (rather than traditional) quantity demanded and price, therefore appears on both sides of the demand equation, extra work must be done to interpret price coefficients in the model; that is, they cannot be interpreted as elasticities directly as they appear in the model. I follow the steps taken by Fujii, Khaled, and Mak (1985) to calculate elasticities from the model parameters as follows:

• Own-price elasticity (uncompensated): $$-1-\beta_i + \gamma_{ij}/\omega_i$$

• Own-price elasticity (compensated): $$-1-\omega_i + \gamma_{ij}/\omega_i$$

• Income: $$1 + \beta_i/\omega_i$$

## 7 Results and Discussion

Estimation of my AIDS-APC model (Table 2), a constrained multiple regression model in which all AIDS restrictions are imposed and period effects are approximated by price and income effects, suggests the existence of distinct age, period, and cohort effects among households.

As mentioned in the previous section, because the dependent variable in question is a budget share (rather than traditional quantity demanded) and price therefore appears on both sides of the demand equation, price coefficients in the model need to be translated into elasticities before we can make sense of them. Table 3 contains own-price and income elasticities for the five expenditure categories as calculated from the fully AIDS- constrained model. Four of the five elasticities are significantly negative and fit within ranges suggested by prior research on expenditure data, though elasticity estimates vary widely in the literature. Cramer (1973) calculates a price elasticity for beer (the largest single component of alcohol expenditures in recent CEX data) of -2.00, extremely close to the alcohol elasticity of -2.06 calculated in the model. Food at home elasticity falls generally within the range suggested by Nayga and Capps (- 0.428), Craven and Haidacher (-0.455), and Lamm (-0.630). That FAFH appears less elastic than FAH is surprising and somewhat counterintuitive, though the number calculated here still fits in the lower range calculated by Andreyeva, Long, and Brownell (2010). The positive own-price elasticity for clothing and personal care is also somewhat unexpected, though it is just barely positive, and much smaller in magnitude than all other elasticities.[2]

Income elasticities largely fit with our expectation. Across categories, income elasticities are positive—i.e., total expenditures rise with income. Income elasticities between 0 and 1 denote necessities, for which total expenditures rise with income but budget share falls. In this analysis, food at home falls within that range, as we might expect. Interestingly, alcohol and tobacco also falls within the necessity range, perhaps contrary to expectations. Those goods with income elasticities greater than 1 (food away from home, clothing and personal care, and other nondurables) are considered luxuries, for which budget share increases with income. This finding is consistent with the findings of Leser (1941).

Both FAH and FAFH are correlated with household size in agreement with economies of scale in both categories. In terms of FAH, for instance, we might intuit that once an individual goes through the trouble of cooking at home, it becomes less costly to cook extra for a second person, and that larger households will therefore choose to eat at home more often. This outcome is consistent with the findings of Nelson (1988), who finds significant economies of scale in household food consumption and points to discounts from bulk purchasing as a possible source of such economies.

Food at home demonstrates highly significant and increasing age effects, meaning that increasingly older age groups allocate increasingly greater portions of their budgets to food at home. Regression results indicate that the 70-75 age group allocates roughly 9.8 additional percentage points of its nondurable expenditures to FAH, compared to 25-29-year-olds. This does not suggest that older individuals have greater absolute FAH expenditures, which would be in disagreement with Aguiar and Hurst (2005), who suggest that absolute food expenditures fall at retirement. Rather, it merely suggests that as people age, a greater share of their nondurable expenditures is devoted to FAH, and they reallocate money from other—perhaps more conspicuous or luxury-related—product categories into food at home. Simply put, it appears that as individuals age, their taste for food at home rises relative to, say, their taste for clothing and personal care items.

Cohort effects for food at home are also highly significant and also increasing in later cohorts. Interestingly, this makes net effects in any given period ambiguous, as increasing age necessarily implies belonging to earlier cohorts, and demonstrates how conventional cross-sectional analysis cannot sufficiently distinguish between effects. The results suggest that the 1966- 70 cohort allocates an additional 6.1 percentage points of its budget to FAH compared to the 1916-20 reference cohort. Given that research suggests that childhood is a crucial period in the formation of life-long food preferences (Birch and Fisher 1998), it is not surprising that food expenditures demonstrate significant cohort effects. The increasing nature of these cohort effects could be interpreted in a number of ways: as an increase in absolute quantity of food (i.e., households are purchasing more food), an increase in food quality (i.e., households are purchasing better food), or a substitution away from FAFH expenditures. Our results eliminate the latter explanation, since FAFH budget shares also demonstrate increasing cohort effects, but distinguishing between the first two is impossible given our data, and both seem plausible.

Nevertheless, it is not difficult to speculate as to why more recent cohorts might prefer to spend more of their budgets on food than the cohorts before them, regardless of whether those changes are a reflection of shifting quantities or qualities. For instance, the development and proliferation of supermarkets and specialty food stores over time has made food more widely available, including gourmet and specialty items (Chao and Utgoff 2006). As availability of items and overall household incomes increased, households may have formed tastes for higher quality (i.e., more expensive) grocery items, coinciding also with a rising gourmet movement throughout the twentieth century (Strauss 2011). On the other hand, the American diet has also risen in calories in recent decades, driven in part by technological innovations that have facilitated mass production of food items and lowered time costs of production (Culter, Glaeser, and Shapiro 2003), potentially accounting for some of the additional FAH budgeting. Additionally, we might imagine that as overall prosperity rises, households’ propensity to waste perishable food might also be increasing, and increased expenditures on food might not necessarily imply increased consumption.

The increasing cohort effect appears highly linear across successive cohorts. Interestingly, this is also true of many of the cohort effects (as well as age effects) examined in this analysis. While the explanation behind this phenomenon is unclear, it suggests that there might be a cumulative aspect to cohort effects. In other words, my cohort prefers to allocate more to a given good than our parents did, but our parents preferred to allocate more to that good than their parents did, leading to semi-linear, largely monotonic cohort effects.

In contrast to food at home, FAFH consumption has no significant age effects. Cohort effects, however, are highly significant, with younger cohorts allocating an increasing portion of their budgets to food away from the home. This isn’t surprising, given the proliferation of sit-down and fast-food restaurants, the increasing availability of take-out, ready-made, or convenience foods (Guthrie, Lin, and Frazao 2002), and the rising popularity of gourmet food establishments (Strauss 2011) throughout the twentieth century, all of which could be influencing the lifelong eating habits of young cohorts experiencing those changes.

A number of other explanations can account for these highly significant cohort effects. Individuals of later cohorts entered the labor market at a time in which women were increasingly participating in the workforce, attending school, and establishing careers (Guthrie, Lin, and Frazao 2002). We might imagine that as women entered the workplace and shed their roles as full- time housekeepers, American households became increasingly dependent on ready-made or convenience foods.

Fast food—and different cohorts’ differential exposure to it— could also be contributing to the rising cohort effects observed in the data. The earliest cohorts in this analysis were already approaching middle age during the advent of the fast food industry and its period of phenomenal growth. More recent cohorts, on the other hand, were highly exposed to fast food and its marketing campaigns. These cohorts demonstrate a markedly increased propensity to spend money on food away from home compared to prior cohorts, suggesting that different cohorts are differentially influenced by dramatic changes in the marketplace depending on their age at that moment in time. Children who grow up with exposure to fast food, for instance, might be disproportionately susceptible to its external influence on dietary habit formation.

It is also notable that the 1926-30 cohort is the only cohort without a significant cohort effect in FAFH. We could perhaps fit this finding into a larger narrative of the Great Depression, since research and intuition both suggest that families will scale back on eating out during recessionary times (Kumcu and Kaufman 2011). As such, we might expect that members of the 1926- 30 cohort, who were children and young adolescents during the Great Depression, grew up eating out less frequently than children raised in non-recessionary periods and never developed a life long taste for eating out (Birch and Fisher 1998). This finding, however, is far from conclusive, and is not significantly different than the other observed effects.

A great deal of research has pointed to the increasing importance of food away from home in the American diet (U.S. Department of Agriculture 2013). Overall, though, the main lesson from the FAFH analysis is that higher FAFH budget shares, which we might associate with young people who like the social aspect of eating out, are not so much a factor of youth as much as the cohort membership of the particular youths we’re studying. Their preferences for eating out, therefore, should stay with them even as they age. As a generation born and raised on convenience foods, fast food, and dining out, they have cultivated a taste for those forms of consumption that will persist beyond their youth and across the life course. This has tremendously different implications for demand forecasting than a cross-sectional analysis looking only at age profiles at a single moment in time.

Clothing and personal care consumption demonstrates yet another distinct pattern of time effects. Age effects are significant from the ages of 35-54, with successive age groups allocating smaller and smaller budget shares relative to the 25-29-year-old reference group. This finding suggests that older individuals might feel less of a need to purchase personal grooming products or other status-conferring goods as they enter married life and/or middle age. After the age of 55, however, age effects do not appear significant, suggesting an increase in CPC allocation back to pre-35 levels. Cohort effects are highly significant, with later cohorts spending increasingly large portions of their budgets on clothing and personal care items. This outcome aligns with the claim that those who experienced the hardship of the Great Depression cultivated a sense of “things that matter,” valuing things like hard work and the centrality of family over material possessions (Elder 1999). Cohort effects grow increasingly positive the further a cohort lies from the Depression and its lingering memory, possibly reflecting a loss of the values it imparted and a subsequent shift in preferences toward material goods. This suggests that cultural attitudes of status seeking, conspicuous consumption, and consumerism in America can be interpreted from a generational viewpoint. The existence of a cohort effect suggests that, holding income and all other variables constant, later generations exhibit a relative preference for more outwardly noticeable consumption goods.

Notably, by far the greatest jump in cohort effect occurs in the 1966-70 cohort; its difference is indeed statistically significant from the prior cohort. Interestingly, members of the 1966-70 cohort are considered the early portion of “Generation X.” Gen X has earned a reputation in sociology literature for being the first generation to put quality of personal life ahead of work life (Meredith and Schewe 1994). As such, the large cohort effect can be interpreted as an increased propensity to allocate money to personal care, luxury, or conspicuous-consumption items among members of that cohort.

The relative increase for the 1966 cohort could also be interpreted as a relatively less robust increase for the cohorts immediately preceding it—those born between 1956 and 1965. The results point to no statistically significant difference in cohort effects between the 1956-60 and 1961-65 cohorts, a deviation from the upward trend. Prior literature suggests that this “Boomers II” cohort, whose members came of age during the Arab oil embargo of 1973 and the subsequent economic slump, showed less optimism about their financial future than the cohorts on either side of them (Schewe and Noble 2010). As such, they might have been more cautious with discretionary spending and been less preoccupied with status-seeking consumerism throughout their lives, even in more stable economic times.

Age effects in alcohol and tobacco consumption are almost a mirror image of clothing consumption. Age effects are barely or not significant until the age of 55, at which point older individuals spend increasingly less on this consumption category, as we might expect for both health/physiological reasons as well as socio- cultural ones. Cohort effects, perhaps surprisingly, are largely insignificant, with one prominent exception: the 1931-35 cohort, whose members tend to allocate less of their budgets to alcohol and tobacco than other cohorts. These individuals were born immediately after the 1933 repeal of Prohibition, though it is difficult to justify why a changing alcohol environment would influence such young children, or even if it did, why the effect would be necessarily be negative. Instead, it might make sense to look later in history to account for this outcome. Individuals from this cohort approached legal drinking age in the very early 1950s. Interestingly, the federal government imposed a sharp tax increase on most forms of alcohol to raise revenues during the Korean War, bringing alcohol taxes to some of their highest real levels in American history (Mosher and Beauchamp 1983). While our regression analysis holds prices constant, it is possible that high taxes during the Korean War distorted preferences, and that those individuals who reached drinking age exactly at that time didn’t go on to cultivate a life long taste for alcohol. If this is true, it would imply that there is a critical age range at which one’s life- long consumption of alcohol is tremendously influenced. Similar to the idea that individuals’ life-long eating habits are cultivated in early childhood, it is possible that their life-long drinking habits are cultivated in young adulthood.

Other nondurables also demonstrate highly significant decreasing age and cohort effects, with older individuals and more recent cohorts allocating smaller and smaller budget shares to this category. Changes in other nondurables expenditures are difficult to interpret because the category is comprised of several very different types of goods and services, including utilities, domestic services, nondurable transportation, airfare, nondurable entertainment, net gambling receipts, business services and charitable giving. Our data does not distinguish among these categories, and therefore it is difficult to attribute a shift in other nondurables expenditures to any particular sub-category of goods. Indeed, any of its components could be driving the observed trends. However, the highly significant age and cohort effects, combined with the fact that this category comprises roughly 52% of all nondurable expenditures, means that these patterns are an important part of the story. Further research could be done into the individual components of this category to more thoroughly explain the roots of the observed effects.

This paper’s results are also undoubtedly affected by the exclusion of households with children. Childless households by definition do not experience many of the life phases experienced in households with children—early and late parenthood, empty nesting, and so on—and therefore exhibit different consumption behavior. Further work in household equivalence scaling could enable the inclusion of households with children into the sample. Additionally, the choice to use total nondurable expenditures as a basis for budget share analysis necessarily meant forgoing the study of expenditures on housing, education, and other durable goods. While examining nondurables still proved fruitful, searching for potential cohort effects in expenditures on, say, education, could also have valuable results. Moreover, budget share results in this paper’s analysis could be somewhat different when housing, durables, and education are included in expenditure totals. Future research could also address heterogeneity within cohorts, such as how race, gender, geography, or other differentiating features might differentially sensitize members of a common birth cohort to prominent events.

## 8 Conclusions

This paper makes two important contributions: one methodological and one substantive. On the methodological side, this paper constructs and estimates a model that accounts for distinct age, period, and cohort effects within the framework of a formalized demand system and confronts the fundamental identifiability problem in APC modeling. The inclusion of cohort effects significantly improves demand models that account only for age and allows for a far more nuanced understanding of consumer behavior, whether at the level of individual products or at the level of broader macro patterns in consumer spending.

The results suggest that cohort effects in spending patterns are both real and significant: different birth cohorts form generational preferences that affect their purchasing patterns over the life course, though these effects can easily be obscured when confounded with age and period effects. Relating these effects to notable historical occurrences suggests that individuals are not uniformly affected by events, but are instead distinctly shaped by their unique experience of history given their particular age at a particular time. Many of the results suggest that children and young adults can be particularly vulnerable to these effects, and therefore point to the importance of historical and cultural events during childhood and young adulthood in shaping future consumption patterns. This is particularly salient in the cases of food away from home expenditures, clothing and personal care expenditures, and alcohol and tobacco expenditures, all of which demonstrate highly significant cohort effects that increase over time and show large increases in particular cohorts occupying notable places in the evolution of the marketplace.

In sum, this paper confirms the body of work that suggests that individuals are inextricably linked to and shaped by their particular experience of history, and that the occurrence of certain events at certain developmental periods can have effects throughout the life course. The results here suggest that this idea applies not only to a generation’s values and attitudes, but also to its concrete, quantifiable changes in spending patterns. With their far-reaching implications in a vast array of fields, cohort effects ought to be more thoroughly studied and considered as an integral driver of demand.

## Footnotes

[1] Given the range of the data, some groups are one year larger or smaller.

[2] Of the five expenditure categories, however, CPC seems the most likely to approach a positive value, as it encompasses a number of commodities (clothing, jewelry) that convey status, for which price can serve as an indicator of quality, and for which preferences may thereby increase with price. Prior research suggests that some consumers demonstrate status motives when purchasing clothing (Leibenstein 1950) and women’s cosmetics (Chao and Schor 1998). Cramer (1973) calculated positive price elasticities for both shoes (1.83) and toilet articles (0.16).

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