## Abstract

This article shows that the seasonality of food consumption during childhood, conditional on average consumption, affects long-run human capital development. We develop a model that distinguishes differences in average consumption levels, seasonal fluctuations, and idiosyncratic shocks, and estimate the model using panel data from early 1990s Tanzania. We then test whether the mean and seasonality of a child’s consumption profile affect height and educational attainment in 2010. Results show that the negative effects of greater seasonality are 30 % to 60 % of the magnitudes of the positive effects of greater average consumption. Put differently, children expected to have identical human capital based on annualized consumption measures will have substantially different outcomes if one child’s consumption is more seasonal. We discuss implications for measurement and policy.

## Introduction

In this article, we address whether a consistently seasonal diet during childhood has long-run effects on human capital formation. Consider two children who have the same level of consumption over the course of a year. These children are indistinguishable using standard measures of poverty, which rely on annualized consumption. Suppose the first child has smooth consumption over all 12 months, while the second consumes substantially more in the months after harvest (the harvest season) than in later months (the lean season). The goal of our study is to empirically examine whether the second child is worse off in the long run—and if so, by how much. That is, our aim is to determine whether the seasonality of consumption affects child development, conditional on the average level.

Our question is motivated by two lines of prior research. The first is the large literature on the connection between nutrition during childhood and later-life outcomes (Alderman et al. 2009; Behrman 2016; Bleakley 2010; Case et al. 2005; Currie and Almond 2011; Cunha and Heckman 2007; Glewwe et al. 2001; Victora et al. 2008). Many of these studies use shocks to consumption from droughts, wars, nutrition programs, or other exogenous events to study the long-run effects of changes in consumption levels on health or educational attainment (Akresh et al. 2012; Alderman et al. 2006; Baez 2011; Bundervoet et al. 2009; Dercon and Porter 2014; Hoddinott and Kinsey 2001; Hoyne et al. 2016; Maluccio et al. 2009; Singh et al. 2013). Emphasis is on long-term effects of variation in consumption levels, not on seasonality.

A second body of work studies the link between seasonal fluctuations in consumption and short-term measures of well-being (Abay and Hirvonen 2016; Behrman 1993; Bengtsson 2010; Bhagowalia et al. 2011; Egata et al. 2013). This topic is central to recent research on the effects of income volatility on child development in wealthy countries (Hill et al. 2013) and is especially important in low-income agrarian countries, where the composition and level of consumption typically fluctuate with the agricultural cycle (Arsenault et al. 2014; Branca et al. 1993; Chikhungu and Madise 2014; Hirvonen et al. 2016; Miller et al. 2013; Mitchikpe et al. 2009). In many agricultural countries, households use coping strategies to survive the lean season: meal skipping, selectively reducing some members’ consumption, or increasing dependence on starchy staple foods (Adams 1995; Behrman 1988a, b; Sahn 1989; Shetty 1999). These can lead to measurable lean-season deficits in weight, mid–upper arm circumference, and other measures of wasting and stunting (Maleta et al. 2003).

It is not ex ante obvious that the effects of consumption seasonality will persist in the long run. Seasonal fluctuations around a high enough level of average consumption may not impede child development.1 Also, slow growth in the lean season may be offset by catch-up growth after harvest (Alderman et al. 2006; Martorell et al. 1994). Current debates in epidemiology and nutrition center on the extent to which full catch-up is possible (Behrman 2016; Hirvonen 2014; Leroy et al. 2013; Prentice et al. 2013). Because our analysis conditions on average consumption, two children with different degrees of seasonality will not be consistently ranked in terms of daily consumption. In some months, one child will consume more; in other months, the other child will.

In a sample from Tanzania, we study the effects of consumption seasonality during childhood on height and educational attainment measured 19 years later. These outcomes have substantial precedent in the literature on nutrition and child development. As we discuss in the next section, the theoretical rationale linking height and education to consumption seasonality involves biological pathways (due to seasonal interruptions in physical or cognitive development) as well as behavioral pathways (e.g., pulling older children from school during the lean season).

We use data from the Kagera Health and Development Survey (KHDS), a 19-year panel survey. Prior work with an intermediate wave of KHDS data has shown a link between child nutritional status and educational outcomes (Alderman et al. 2009). The KHDS data meet the key challenge for this research question in that they include both measures of seasonal consumption during childhood and long-term follow-up measures of human capital. Although our findings are informative for Kagera and Tanzania specifically, our motivating question has broad applicability. A large share of the world’s poor live in regions with pronounced intra-annual cycles of agricultural production because of the cycle of wet and dry seasons associated with the climates of African savannahs and monsoon-affected zones of Asia (Chambers et al. 1981). Hence, the findings and the method used here are informative for other low-income countries.

Our empirical analysis proceeds in two stages. First, we develop a model of daily consumption with variation in average consumption, seasonal fluctuations, and idiosyncratic shocks. We estimate the model using data from 1991–1994, and show that the standard deviation of the projected consumption sequence is a tractable measure of household-level consumption seasonality, purged of nonseasonal idiosyncratic variation. In the second step we use estimates of average consumption and seasonality, from the projected childhood consumption sequence, as explanatory variables in regressions with 2010 height or educational attainment as the dependent variable. We provide an extensive discussion of identification, and estimate a series of robustness checks to verify that the seasonality measure is not mistakenly capturing other nonlinear relationships between household characteristics and long-run outcomes.

Across specifications, we find a robust, negative relationship between consumption seasonality and human capital formation, conditional on average consumption. The negative relationship between seasonality and human capital is 30 % to 60 % of the magnitude of the positive relationship between average consumption and human capital (in the same units). When we allow for heterogeneous effects by age, the effects of seasonality on height are greatest for children in utero and in infancy, during the critical first 1,000 days of life. Effects on education are most pronounced for older children, suggesting that behavioral channels—such as dropping out of school to help on the farm—are more important in this sample than early-life effects on cognitive development. When we further allow for heterogeneity by both age and gender, we see that the height effects during infancy are concentrated among girls, while the education effects during adolescence are largely driven by boys.

We conclude with a discussion of these findings, including an interpretation of the magnitudes of estimated effects relative to the literature. We suggest ways that current consumption and poverty measures could be augmented to incorporate information about seasonality and reflect on policies to provide countercyclical consumption support.

## Background and Theoretical Motivation

The outcomes studied here—namely, height and education—share an important common feature: both are stock variables accumulated gradually throughout childhood and adolescence. These outcomes also differ in key ways. For example, height is directly influenced by a range of factors that are unobserved in socioeconomic data (such as genetic endowment), while educational attainment over the range considered here is the consequence of a sequence of choices over which agents have control. Hence, we develop the theoretical motivations separately.

### Seasonality and Height

Linear growth leading to the accumulation of height depends on a complex set of environmental, genetic, health, and nutritional factors. A large literature has demonstrated that chronic undernutrition or negative shocks during childhood can lead to height deficits that persist into adulthood (Almond and Currie 2011; Attanasio, 2015; Victora et al. 2008). There is some evidence of “catch-up growth”—that is, higher-than-average growth rates by previously disadvantaged children when they experience a shift to receive adequate nutritional support (Alderman et al. 2006; Martorell et al. 1994). The literature has not settled on a definitive answer for whether full catch-up is possible (Behrman 2016; Hirvonen 2014; Leroy et al. 2013; Prentice et al. 2013). Yet, even if full catch-up is biologically possible, negative effects will persist for individuals who do not access the nutritional and medical resources required for catch-up.

The link between persistent seasonal variation in consumption and the accumulation of height can be thought of in two ways. The first is direct. Other things being equal, receipt of a sufficient diet during any period enables a child to grow in accordance to her or his genetic potential. Seasonal reductions in caloric and nutritional intake can undercut that growth. A child whose consumption falls below critical thresholds for a regular period each year will then experience repeated minor interruptions in growth. For children experiencing acute malnutrition, lean-season deprivations are obvious. For other children, each seasonal episode of undernourishment and slow growth may be small enough to elude detection, while the cumulative effect leads to a measurable height deficiency in adulthood.2

A second set of pathways arises through the possibility of dynamic interactions (Cunha and Heckman 2007; Foster 1995). For some aspects of cognitive and physical development, early deprivations make a person less responsive to future investments (dynamic complementarities). For example, early-life malnutrition can delay the onset and shorten the duration of the adolescent growth spurt, resulting in lower adult height (Limony et al. 2015; Martorell 1999). However, dynamic forces may also mitigate the effect of seasonality on height (dynamic substitution). Catch-up growth may occur through biological mechanisms that increase the efficiency with which consumption is translated into growth, or through adaptation by the household to provide more nutrients to an underfed child. If such dynamic factors are present, the question of whether lean-season deprivations aggregate into measurable differences during adulthood rests on the net effects.

Although children can grow continuously from infancy through late adolescence, faster growth occurs during key periods. Particularly important spells include the years from conception through age 2 (the first 1,000 days) and the adolescent growth spurt. The latter typically occurs from age 11–15 for girls and 13–17 for boys in well-nourished populations (Rogol et al. 2000) but can be delayed to persist beyond age 17 (Simondon et al. 1998). To accommodate this variation, we allow for heterogeneity by age group in the empirical analysis. We also estimate specifications in which we allow for heterogeneity by age and gender because prior work has shown both biological and behavioral channels by which nutrition variation can affect boys and girls differently (Maluccio et al. 2009; Mancini and Yang 2009).

### Seasonality and Educational Attainment

The mechanisms linking seasonal consumption to educational attainment are more numerous than those for height. The additional complexity arises from the nature of the education production function, which takes both cognitive ability and child time as inputs.

Effects on education that occur through cognitive ability are similar in some ways to the mechanisms described for height. Cognition develops in stages. Basic functions, such as the regulation of sight, are established in infancy; language processing is mostly developed by age 5; and the capacity for higher-order cognition develops through adolescence (Grantham-McGregor et al. 2007). Annually recurring periods of low nutrition can impede or slow the pace of cognitive development. Evidence from other settings suggests that dynamic complementarities are particularly important in this domain (Heckman 2008). Interventions to improve children’s nutritional circumstances—in this setting, analogous changes would be the return to harvest season levels of consumption or changes in household circumstances that reduce consumption seasonality—are not as effective if delivered later in childhood, after the accumulation of previous deficits. Because cognitive ability affects success in school and the probability of continuation, consumption seasonality may reduce educational attainment through the accumulated negative impacts of lean-season deprivation on cognitive development (Currie and Thomas 1999; Grantham-McGregor et al. 2007; Peet et al. 2015).

Consumption seasonality can also affect educational attainment through two behavioral channels. First, there is evidence that children who are hungry at school have difficulties paying attention and completing tasks, and score lower on standardized tests than nonhungry children (Gennetian et al. 2015; Kristjansson et al. 2007; Pollitt et al. 1982; Powell et al. 1998; Rampersaud et al. 2005; Wisniewski 2010). It is plausible that children who experience periods of acute hunger during the lean season are less likely to succeed in school during that period, resulting in poorer performance, reduced attendance, and earlier dropout within or between school years. The second behavioral channel is through competing demands on child time. In Tanzania, children assist with a range of household tasks, such as fetching water, collecting firewood, preparing meals, tending to animals, caring for smaller children, assisting on the farm, or working off-farm for a family enterprise or in the market (Beegle et al. 2006). For some households, lean-season deprivation may be severe enough that the marginal value of child time outside of school exceeds the expected marginal return to schooling, leading to dropout. Evidence from the KHDS suggests that households view child labor as a means to smooth consumption in the face of unexpected shocks (Beegle et al. 2006). Effects operating through this mechanism are most likely to be present for the oldest children, for whom the opportunity cost of time in school is greatest.

In sum, the literature suggests a number of mechanisms through which seasonal variation in consumption might affect height and educational attainment in the long run. Of course, the same mechanisms also indicate an important role for the average level of consumption in determining these outcomes. Any empirical model linking seasonal consumption variation with human capital outcomes must condition on average consumption.

## Data and Descriptive Statistics

The data for this project are from the Kagera Health and Development Survey (KHDS). Kagera is a hilly, rainy region in the far northwest corner of Tanzania, bordered on the east by Lake Victoria, the north by Uganda, and the west by Rwanda. In some respects, Kagera is not the ideal place to study seasonal consumption. The region has relatively high annual rainfall and two rainy seasons (October–December and March–May), which is not typical for much of sub-Saharan Africa. This likely dampens seasonal fluctuations in consumption because some foods can be harvested multiple times per year. Nevertheless, as we discuss later, the data indicate a strong seasonal pattern to food consumption in Kagera.

The KHDS consists of three surveys, resulting in a 19-year panel data set. The first set of surveys, KHDS 1, consists of four panel rounds collected from late 1991 to early 1994. The sample includes 6,353 individuals, in 915 households, in 51 communities. Researchers interviewed 759 households in all four rounds.3 The survey covered a wide range of topics, including demographics, consumption, health, child anthropometry, agriculture, time use, labor supply, shocks, credit, and other topics common to the Living Standards Measurement Surveys (LSMS) format. The KHDS survey team worked continuously, spacing each household’s interviews by roughly six months.

Follow-up surveys with initial respondents, new family members, and any out-migrants or split-off households were conducted in 2004 (KHDS 2) and 2010 (KHDS 3). We do not use the 2004 data. In 2010, the team interviewed someone from 706 of the initial 759 households (93 %). At the individual level, the reinterview rate among the nondeceased was 85 %. The remarkably low attrition rate for a long-term sample in this setting is due to the team’s extensive efforts to track respondents, including those who had migrated long distances.

### Consumption and Household Characteristics, 1991–1994

The KHDS 1 consumption model is of the representative consumption format. For a wide range of foods, respondents were asked whether members consumed that item in the previous 6 to 12 months as well as how much was consumed in a typical month of positive consumption. We assign responses for a given survey date to the previous month’s consumption and deflate expenditure using a Laspeyres price index that accounts for both spatial and temporal price variation. Further details regarding the consumption data are described in Online Resource 1, section A.

Figure 1 shows the histogram of KHDS 1 survey dates (lower panel) and a local polynomial regression of consumption on the interview day (upper panel). In the lower panel, the broad temporal coverage of the survey is clear. The survey team worked continuously during the study. Although this is not reflected in the figure, the team also distributed its work evenly across districts; thus, survey timing and location do not covary. In the analysis to follow, the quasi-random assignment of interview dates will be helpful for power, although not necessary for identification.

In the upper panel of Fig. 1, seasonality is clear. Consumption begins to rise in September as some crops are harvested, peaks in January-February shortly after beans are harvested and just as the primary maize crop comes in, and drops off substantially through the following months as households exhaust crop stores and food prices rise. The lean season starts in April–May and persists for three to six months. In real terms, peak average consumption is greater in the first full survey year than in the second; minimum average consumption is similar across years.

Figure 2 shows annual consumption trends by food group. Bars indicate the average number of different items consumed; lines show the average real value of consumption. We note three takeaways. First, seasonality is not apparent in the number of different food items consumed per month. Within each group, except perhaps grains, there is little evidence of a seasonal pattern in the bars. Second, for the four food groups that represent the largest shares of consumption—starches, animal products, fruits, and grains—there is substantial seasonal variation in real consumption value.4 During the lean season, the typical household reduces its intake of both macro- and micronutrients (e.g., protein from animal products, micronutrients from fruits and vegetables). Taken together, these two observations indicate that seasonality in Kagera manifests primarily through seasonal reductions in consumption within categories rather than through periodic unavailability of some food categories. In other settings, these patterns could be different. Third, in all food categories, the trough in consumption occurs around May.

The upper panel of Table 1 shows summary statistics for the 758 households interviewed in all four rounds of KHDS 1, pooled across rounds.5 The average household is headed by a 50-year-old male with four years of formal education, who owns roughly five acres of land and the livestock equivalent of nearly 1.5 head of cattle (in tropical livestock units). The asset index is a relative measure of wealth that captures ownership of durable assets and household dwelling characteristics (Filmer and Pritchett 2001; Sahn and Stifel 2003). Although agriculture represents the primary livelihood strategy in this region, 40 % of households engage in some form of nonfarm enterprise. To the extent that diversification of income sources is a consumption-smoothing strategy, this is a possible source of between-household variation in the degree of consumption seasonality.

### Sample and Outcome Variables in 2010

We include in the estimation sample all respondents who were aged 17–36 in 2010, which is equivalent to ages –2 to 17 in 1991. We define age groups and eligibility by working backward from age reported in 2010 because we expect less misreporting from adults stating their own age than from proxy respondents answering for children in KHDS 1. In total, 2,859 respondents who were children during KHDS 1 were successfully tracked during KHDS 3. Respondent height was directly measured by KHDS 3 enumerators. The height measure is available for 2,578 individuals, or 90.2 % of the sample. The other primary outcome variable—years of education completed through 2010—is available for 2,633 of the age-eligible respondents (92.1 %). Nine respondents indicated only “Adult education” or “Koranic school,” both of which we coded as 0 years of formal education.

The lower panel of Table 1 provides summary statistics for the outcome variables, overall and by age and gender subgroups. The age group categories are based on the theoretical discussion provided earlier. Age Groups 2 and 3—representing children aged 1–10 and 11–17 in 1991, respectively—account for the majority of the sample. The youngest group, children in the first 1,000 days of life, represent 12 % of the sample. Across the sample, the average height is 162.5 cm, and the average years of education is 7.6. Slight differences between age groups in average height are likely because of variation in the number of remaining growth years as of 2010. We also find slight differences in educational attainment, with younger children acquiring more education. This reflects trends in Tanzania toward increased enrollment in primary and secondary education, similar to much of sub-Saharan Africa.

## Identification and Estimation

In this section, we explain the identification and estimation of a model linking consumption seasonality during childhood to human capital development. We first develop the model and show how we estimate a household-level measure of seasonality. We then present the empirical model linking seasonality in 1991–1994 to height and educational attainment in 2010. The final subsection addresses identification and robustness.

### Modeling Consumption

Consider the following model of daily household consumption.6 Let c(d, Xydh) be food consumption by household h on day d in year y, where d = 1, . . . , 365; y = 1, . . . , Y; and the matrix Xydh consists of household characteristics that affect consumption. We can write a simple linear model of consumption as follows:
$cdXydh=Xydhϕ+vydh,$
1
where ϕ is a coefficient vector, and νydh is a stochastic component. Xydh can include a trend term or time dummy variables if necessary. When there is a seasonal component to consumption, νydh can be decomposed into that component and a statistical error term:
$cdXydhZydh=Xydhϕ+ΓdZydh+ψydh,$
2
where Γ is a function that maps household characteristics on day d into a day-specific seasonal innovation, and ψydh is an independent and identically distributed error term with a mean of 0 and a variance of $σψ2$.7 The matrix Zydh consists of household characteristics and may contain some, all, or none of the same elements as Xydh. Assume for now that Xydh and Zydh are constant over all d and y (we relax this assumption later). The approach in Eq. (2) nests the case with no seasonality, which would have Γ(d, Zydh) = 0 for all d. Suppose that Γ(d, Zydh) can be represented as the product of two components, Γ(d, Zydh) = γ(d) f(Zydh). The term γ(d) represents a sequence of day-specific innovations common to all households. This sequence has a mean of γ and a variance of $σγ2$. The effect of the daily innovation is attenuated or exacerbated by household characteristics through the function f(Zydh). The conditional variance of Γ(d, Zydh) can be written as $σγh2≡σγ2fZydhσγh2≡σγ2fZydh2$. If we assume Cov(γ, ψ) = 0, the conditional variance of the household consumption sequence cydh = c(d, Xydh, Zydh) is given by
$VarcydhXZ=Ecydh−Ecydh2XZ=EXydhϕ+γdfZydh+ψydh−Xydhϕ+γ¯fZydh2XZ=σγh2+σψ2.$
3
Equation (3) makes an intuitive point: as long as stochastic consumption shocks are orthogonal to regularly occurring seasonal fluctuations, the variance of the consumption sequence is the sum of the conditional variance due to seasonality and the common variance due to unexpected shocks. It follows immediately that
$VarEcydhXZ=σγh2.$
4
That is, the variance of the sequence of expected consumption realizations is simply the conditional variance of the seasonal component. This suggests a straightforward empirical strategy for isolating and estimating a household-specific measure of the seasonal component of consumption variation: estimate the model, project consumption on every day of the year as a function of observable household characteristics, and then take the variance of that sequence.
To complete the model for estimation, we must structurally represent the seasonal component γ(d) f (Zydh). We write the household-specific term as a linear function of household characteristics, f(Zydh) = Zydhρ, where ρ is a coefficient vector. This term allows the amplitude of seasonality to vary across households. In deciding how to model the common seasonal component γ(d), we use the wave-like shape of the aggregate consumption path from Fig. 1 as our guide and adopt a sine function representation. To allow the data—rather than the functional form—to divide the calendar year into periods above/below Day 1 consumption, we generalize the sine function to allow for asymmetric periods above and below 0 by adding the parameter τ for the day d on which consumption returns to its Day 1 level (equivalent to the standard sine function crossing the horizontal axis at x = π). The full model then becomes
$cydh=Xydhϕ+sinπdτId≤τ+sinπ+πd−τ365−τId>τZydhρ+ψydh=Xydhϕ+wdτZydhρ+ψydh,$
5
where w(d,τ) is a weight, and the parameter vector consists of τ, ϕ, and ρ.

We estimate the model in Eq. (5) using maximum likelihood with Gaussian errors. The data for estimation are from KHDS 1. For each KHDS 1 household, we observe cydh on four randomly selected days over a 28-month period. In our main specifications, we use the variables reported in the upper panel of Table 1, with the addition of district effects, for both Xydh and Zydh. Because the components of Zydh are weighted by a function of the interview date, no exclusion restriction is required for identification. We discuss this further in the upcoming section, Identification. The quasi-random assignment of interview dates is not necessary for identification, but it is useful for power because it ensures that the variation in the components of Xydh and Zydh is well represented across months of the year.

With an estimate in hand of $ϕ̂ρ̂τ̂$, projected consumption on day d of year y for household with characteristics Xydh and Zydh is given by $ĉydh=Xydhϕ̂+wdτ̂Zydhρ̂$. This projection requires values for Xydh and Zydh on every day. Here, we must relax the assumption that the variables in Xydh and Zydh are fixed over the study period. Although many of the variables in the upper panel of Table 1 are constant, some are not. To smoothly accommodate intertemporal variation in household characteristics, we interpolate to noninterview days using the weighted average of the variables from the nearest surveys before and after each date d.8 The variance of the resulting sequence of household-specific consumption projections, $ŝh2$, is our empirical estimate of Eq. (4). The mean of the sequence, $m̂h$, is an estimate of the average level of consumption by household members.9

### Linking Seasonality to Human Capital Outcomes

In the Background and Theoretical Motivation section, we outlined a number of channels by which consumption seasonality may negatively affect child development, conditional on average consumption. To test the hypotheses suggested by that discussion, we estimate regressions of the following form:
$lnOutcomeih2010=α+β1lnm^h+β2lns^h+γWih+δ+εih,$
6
where i indexes individuals; h indexes households from KHDS 1; $Outcomeih2010$ is either height or educational attainment; Wih is a vector of individual controls for age, gender, and other variables used in robustness checks; $δ̂$ is a vector of district effects; and εih is a stochastic error term. The variables $m̂h$ and $ŝh$ are as defined in the previous subsection; all other variables are from KHDS 3 (in 2010).10 We adopt a double log specification for the estimated consumption statistics so that we can interpret coefficient estimates as elasticities and so that results do not depend on whether we use the estimated variance ($ŝh2$) or the estimated standard deviation ($ŝh$) to characterize consumption seasonality.

Because Eq. (6) includes projected values, we bootstrap the full estimation procedure across Eqs. (5) and (6). See Online Resource 1, section C, for a description of the bootstrap procedure. The point estimates and pattern of statistical significance from the bootstrapped estimates are the same as those from estimation in two separate steps with ordinary least squares (OLS) standard errors clustered at the level of the 1991–1994 household.

The earlier theoretical discussion suggests clear predictions for the signs of the key parameters in Eq. (6). We expect to find β1> 0 because higher average consumption is generally associated with better outcomes in an undernourished population. The prediction that seasonality reduces human capital is implemented by testing whether β2 is negative—that is, by attempting to reject the null hypothesis H0: β2 0.

We also estimate specifications that include interactions of age or age × gender with the consumption statistics, using the age groups from Table 1. This allows us to test specific mechanisms laid out in the earlier theoretical discussion. A negative relationship between seasonality and educational attainment for children in utero or during infancy (Age Group 1) would indicate a causal pathway through cognitive development, whereas a similar finding only for children in Age Group 3 would more likely indicate a behavioral mechanism through reduced school attendance. Likewise, negative effects of seasonality on height for Age Group 1 would indicate persistent deficits acquired during infancy, while such effects for children in Age Group 3 would represent deficits acquired during the adolescent growth spurt.

One challenge in interpreting any differences between age groups is that we cannot distinguish cohort effects from age-specific effects.11 Hence, while any age-specific findings remain valid, because they are based on within-age-group variation in $m̂h$ and $ŝh$, interpretation must be undertaken with caution. Heterogeneous effects by age are only suggestive evidence of differential effects of seasonality on child development.

A related issue is that genuine (as opposed to cohort-related) heterogeneity by age group is detectable only if household circumstances sometimes change during childhood. If the degree of seasonality to which a child is exposed is fixed throughout childhood, then the age at which we observe that child would not affect our estimate of the link between seasonality and human capital. Yet, we know that many households’ circumstances change over time, resulting in intertemporal variation in household capacity to smooth consumption. In this sense, our measures $m̂h$ and $ŝh$ are proxies for the distribution of average and seasonal consumption profiles experienced throughout childhood.

An attractive feature of this approach is that by projecting consumption on every day of the year and then calculating statistics from the projected values, the estimated moments are conditionally independent of unobservable household characteristics. Hence, in Eq. (6), measurement error in $m̂h$ and $ŝh$ is not driven by unobserved household factors that might lead a household to have consumption that is higher or lower than expected. Unobservable characteristics can lead to bias in Eq. (6) only indirectly, through correlation with elements of Xydh and Zydh. That is the rationale for a series of robustness checks that we describe in the next subsection.

### Identification

The empirical approach developed in the previous two subsections partially relies on the structure of the consumption model to identify the effects of seasonality. Clearly, it would be preferable if seasonality were randomly assigned. In this subsection, we discuss whether even exogenous assignment of seasonal variation could identify the effect of interest, without additional controls. We then explain some robustness checks and components of the design that give us confidence in the identification strategy.

The central identification challenge stems from our interest in seasonality, which is related to the second moment of consumption. Yet, the first moment of consumption—the average level—is also an input to child development. We think it unlikely that an instrument or experimental design exists that could generate exogenous variation in seasonality without also affecting average consumption. The approach most likely to succeed would be in a lab, where researchers could assign participants to 2 × 2 factorial subgroups with {High, Low} mean consumption and {High, Low} seasonality of consumption. This approach is clearly infeasible in practice, not least because of the ethical barriers to running a food restriction study of this nature with children. Other alternatives—such as randomly assigning a treated group of households to receive countercyclical consumption support at key times of year, or providing all households with the same annual food transfer but randomizing the seasonality of transfers—would generate confounding variation in average consumption, would be relevant only for populations receiving regular consumption support, or both.

A related identification challenge stems from the conceptualization of seasonality as a treatment. Households are not assigned a consumption path; they choose it, at least in part. And although food consumption might be exogenous from the child’s perspective, it is possible that parents who exhibit a strong preference for consumption smoothing, or who have greater capacity to smooth, differ in important ways from parents who do not. This could lead to biased estimation of Eq. (5) and misattribution of variation in long-run human capital outcomes to seasonality.12

A consequence of these inherent challenges is that the structure of the consumption model plays a role in identification. Thus, we use a functional form that is reflective of the wave-like shape of the aggregate consumption cycle. It is also helpful that the model allows projected consumption to be a smooth function of a large set of household characteristics. All observations contribute to the estimation of all parameters of Eq. (5) and thereby to the consumption projections for all other households on all days. And it is critical that we condition on average consumption because this controls for the first-order effects of consumption variation on human capital outcomes.

Otherwise, these identification issues amount to a concern that $ŝh$ could pick up the effects of other seasonally varying characteristics that are not accounted for by $m̂h$ or, relatedly, that we are loading all nonlinear relationships between variables in Xydh and human capital outcomes into our estimates of $ŝh$. To check the robustness of our results to these concerns, we sequentially reestimate the model in Eq. (5) after dropping one variable at a time from Xydh and Zydh and including the dropped variable and its square as control variables in Eq. (6). Our aims with these robustness checks are to demonstrate only that no single variable is driving the results, and that $ŝh$ is not picking up other nonlinear effects outside the scope of the model. Further details on the implementation of this test are available in Online Resource 1, section E.

Despite these efforts, we cannot definitively rule out that some part of the association we find between seasonality and human capital could be due to an omitted variable. The nature of this problem may be such that no single study can establish beyond doubt a causal link between consumption seasonality and child development. In that case, our contribution is to document and measure an important risk factor for low human capital outcomes. However, for reasons described in this subsection, we believe both that omitted variables bias is unlikely, given our design, and that our approach rivals other feasible solutions to the identification challenges that are inherent to this research question.

## Results

We now turn to the empirical results. We first present the estimates of Eq. (5) and the associated estimates of $m̂h$ and $ŝh$. We then show the estimates of human capital models based on Eq. (6) and conclude with an examination of robustness.

### Modeling Consumption: Estimation Results

Estimates of the parameter vector for Eq. (5) are not of specific interest. The model is for projection purposes, and we made no attempt to exclude correlated variables.13 Hence, interpreting the individual coefficient estimates is of little value. To demonstrate the search process for one key parameter, panel a of Fig. 3 plots the log likelihood against the 365 possible choices of τ. The likelihood is a smooth function of τ and is maximized at $τ̂$ = 151. Because we set the start date of the annual cycle to a point in late November corresponding visually to x = 0 for a standard sine function, this indicates that average consumption rises at the end of the year, falls back to its November level in April, and remains below the November reference level for 214 days.

Panel b of Fig. 3 shows observed and projected consumption for two households. The ×s and dots are observed values; the lines show the projected consumption path (the ×s are associated with the dashed line; the dots, with the solid line). Three findings are noteworthy. First, the projected values preserve the ordering of both average consumption and the degree of seasonality (although this need not always be the case): the ×s have a higher mean and higher variance than the dots, and this is also clearly true for the dashed line relative to the solid line. Second, the projected values for the × household are all below the observed values, but the projected values for the dot household are all above the observed values. This indicates that based on household characteristics, we would expect the × (dot) household to have slightly lower (higher) consumption than observed. In this way, the model is purging idiosyncratic variations in observed consumption. Third, the projected sequence for the × household has a noticeably lower variance than the sample variance of the four × observations, suggesting that the especially high first value for the × household—which lies far above expectations—is due partly to measurement error or to an unexpected positive shock.

We further assess model performance by comparing the means of $m̂h$ and $ŝh$ with the mean and standard deviation of observed consumption. The empirical mean of daily consumption per adult equivalent is 121.8 Tanzanian shillings (TZS); the mean of $m̂h$ is 121.2 TZS. This close match is reassuring because the model is intended to center average consumption on its empirical mean. The empirical standard deviation of daily consumption per adult equivalent is 62.1 TZS, while the mean of $ŝh$ is 23.7 TZS. The mean of $ŝh$ is lower than the raw standard deviation because $ŝh$ isolates the seasonal variation, whereas the observed standard deviation includes both seasonality and idiosyncratic shocks. The relative magnitudes suggest that seasonal variation accounts for approximately 36 % of variation around mean consumption.14

In Fig. 4, we examine how the seasonality parameter ($ŝh$) varies with the level parameter ($ŝh$). Panel a shows $ŝh$ plotted against $ŝh$; panel b shows the coefficient of variation $ŝh/m̂h$ plotted against $m̂h$. Clearly, heterogeneity exists in the degree of seasonality at all levels of consumption. Hence, the seasonality effect is not identified only by the experience of a subgroup of low- or high-consumption households. Also, the degree of seasonality is slightly increasing in average consumption, even when the coefficient of variation is used. In these data, a high value of $ŝh$is not a proxy for being poor.15

### Main Results

We now turn to the main results. Baseline estimates of Eq. (6), without age-gender interactions, are shown in column 1 (height) and column 5 (education) of Table 2. All regressions include level controls for gender and age groups. In column 1, a 10 % increase in the mean of consumption is associated with 0.21 % greater height, which is the expected positive association between the level of consumption during childhood and adult height. By contrast, an increase of 10 % in the seasonality term is associated with 0.07 % lower height, conditional on the mean. The relative magnitude of the coefficients is the most striking. In absolute value, the seasonality coefficient is one-third of the mean coefficient. In other words, reducing the standard deviation of the seasonal component of consumption by 10 % would have equivalent effects on height to those of a 3.3 % increase in mean consumption.

Column 5 of Table 2 shows the estimates with the log of years of education as the dependent variable. Once again, the coefficients on the level and seasonality terms are statistically significant and in the expected direction. A 10 % increase in $m̂h$ is associated with a 4 % increase in educational attainment, and a 10 % increase in $ŝh$ is associated with a 0.98 % decrease in educational attainment. The absolute magnitudes of both elasticities are substantially greater than those for height, although the relative magnitude is similar. In the case of educational attainment, a 10 % decrease in the standard deviation of consumption is equivalent to a 2.5 % increase in the mean.

Earlier, we discussed the possibility of critical windows for human capital development, particularly during the first 1,000 days of life and during adolescence. Columns 2 and 6 of Table 2 show estimates of Eq. (6) with interactions between the consumption statistics and dummy variables for age groups. Results are based on regressions with the same controls as columns 1 and 5. Here, an intriguing pattern emerges. In column 2, the seasonality term is associated with the most substantial decreases in height for infants and children in utero and is statistically significant only for the two youngest age groups.16 In this sample, a seasonally varying diet has the greatest effect on linear growth when it occurs during the formative period at the start of life. In contrast, the effect of seasonality on educational attainment is greatest for children aged 11–17 and is statistically significant only for this group (column 6). The difference across age groups is not as robust as that for height: the coefficients for Age Groups 1 and 2 are substantial in magnitude and too imprecise for us to reject that they are the same as the coefficient for Age Group 3. However, the interpretation suggested by the magnitude and precision of the Age Group 3 coefficient is that seasonality affects education by raising the opportunity cost of school for older children or by making it harder for students to focus and apply effort in school.17 Another possible interpretation is that when the lean season corresponds with labor-intensive periods of the agriculture cycle, the marginal value of child work on the farm is greater for households experiencing more intense lean-season deprivation.

Finally, in columns 3–4 and 7–8 of Table 2, we show similar results disaggregated by age group and gender. Columns 3 and 4 show marginal effects by age and gender from a single regression, with height as the dependent variable; columns 7-8 are for a similar regression with education as the dependent variable. The aim of these specifications is to examine whether there are important differences for boys and girls that suggest biological or behavioral channels by which seasonality has gender-differentiated effects. This level of disaggregation asks a lot from the data in terms of statistical power. Nevertheless, we see interesting patterns that align with theory. Column 3 reveals that the effect of seasonality on height both in utero and during infancy is statistically different from 0 for girls only. This is consistent with parents favoring male infants more than female infants during the lean season, or with gender-specific biological channels regulating development. This finding is consistent with prior research showing girls to be particularly responsive to early-life shocks (Mancini and Yang 2009). In contrast, the effects on educational attainment for school-aged children are statistically significant for boys only (column 8), suggesting either that seasonal hunger has a greater effect on boys’ ability to pay attention and perform in school or that boys are more likely to be pulled from school during the lean season to assist in the household.18

### Robustness

In the Identification section, we described the rationale for a series of robustness checks in which variables are dropped from the consumption model and included with their square in the 2010 regressions (leave-one-out models). Detailed results of that exercise are provided in Online Resource 1, section E. The takeaway is that these regressions provide overwhelming support for the main findings. For height, all the leave-one-out estimates are statistically significant, and all but two are greater in magnitude than the main estimate from column 2 of Table 2 (Fig. 5). For education, all the leave-one-out coefficients are again statistically significant. Eight are greater in magnitude than the main estimate from column 6 of Table 2; two are the same; and seven are smaller (Fig. 6).

A separate robustness concern relates to the possibility of nonrandom attrition in the long-term tracking of respondents from the 1991–1994 sample. Although differential attrition would not invalidate our main findings, it would raise questions about their generalizability. In Table 3, we test the statistical significance of any differences between KHDS 1 respondents who were and were not located in 2010. We find a small number of statistically significant differences, but they work against our hypotheses. Sample individuals come from households with less variable consumption and land and livestock holdings that are slightly higher than average. Hence, if anything, our results may understate the true population effect of consumption variability on human capital.

## Discussion

We conclude with a discussion of two issues: the magnitudes of the estimated effects, and the implications for measurement and policy.

### Magnitudes of the Estimated Effects

Across columns 1–2 and 5–6 of Table 2, our findings indicate that a 10 % increase in average consumption during childhood leads to a 0.017 % to 0.026 % increase in height and a 3.9 % to 4.0 % increase in educational attainment; a 10 % increase in consumption seasonality during childhood leads to a 0.05 % to 0.16 % decrease in height and a 0.74 % to 1.29 % decrease in educational attainment. These magnitudes are smaller than some in the literature. For example, Maluccio et al. (2009) reported that children receiving a 10 % increase in caloric support in Guatemala experienced increases of 1.2 years of schooling attainment (for girls) and 2.5 additional cm of height at age 3 (for all children).19 Those effects are 4–10 times larger than the effects of $m̂h$ measured here and 12–15 times larger than the effects of $ŝh$ (although directly comparing the height effects is problematic because we look at much longer-term effects).

We think there are two main reasons for this difference. The first is that our findings are based on a short window of observation. Children acquire height and education over two decades; we use consumption statistics from just over two years. Household consumption profiles can and do change, both gradually over the medium term and sharply from one year to the next (Barrett 2005; Baulch and Hoddinott 2000; Dercon and Krishnan 2000; Duncan 1988; Ligon and Schechter 2003). Hence, our measures of $m̂h$ and $ŝh$ are noisy and subject to attenuation bias due to measurement error. Possible changes in consumption profiles also explain why we see different effects by age group. If consumption profiles were fixed throughout childhood, then the age at which we observe a child would not matter for estimating the link between seasonality and human capital.

The second reason for the difference in magnitudes relates to features of the KHDS. As described earlier, Kagera has more abundant rainfall and likely less seasonality than neighboring regions and countries. Also, the KHDS sample is relatively homogeneous. Kagera has a single major ethnic group, a single agroclimatic zone, and a common set of primary crops. The standard deviation of height in the nationally representative Tanzania LSMS-ISA data is nearly 25 % greater than the comparable statistic from the KHDS sample. The effects in a more heterogeneous population facing greater seasonality may be substantially larger than those estimated here.

For these reasons, our results may greatly understate the true effect of seasonality on human capital. If we assume that the seasonality effects are attenuated by the same degree as the average consumption effects, then scaling up the magnitude of the seasonality effects by 7 (the midpoint of the 4 to 10 range, noted earlier) gives an indication of how large the negative consequences of seasonal consumption might be. With this rescaling, a 10 % increase in seasonality would lead to a 0.35 % to 1.12 % decrease in height (0.6–1.8 cm) and a 5.18 % to 9.03 % decrease in educational attainment (0.4–0.8 years). At these levels, chronic seasonality has effects similar to those of droughts or major conflicts. Although this is only a back-of-the-envelope exercise, it is still a useful way to understand how detrimental seasonal consumption might be to human capital development.

### Implications for Measurement and Policy

At present, poverty lines are set with reference to average annual consumption. Resources are often targeted to households or geographical areas with the lowest annualized consumption measures. We have shown that two children who have similar levels of food consumption when averaged over the year will have markedly different human capital outcomes if one child’s consumption profile is more seasonal than the other’s. One implication of this finding is that current approaches to measuring poverty would have greater relevance to long-term child well-being if augmented with a measure of seasonality. This is an important finding regardless of whether the association we document is causal.

Current consumption measures could be augmented to account for seasonality in at least two ways. First, for consumption surveys conducted over 12 months, analysts could estimate a model of seasonal consumption similar to that in the first stage of our analysis. In targeting a food security intervention, the case could then be made that two households with similar values of $m̂h$ but different levels of $ŝh$ should receive different levels of intervention. A second approach would involve adapting the Food Consumption Score or other widely used measures of food security to include questions about seasonality. Most such measures do not account for seasonal consumption fluctuations, although they may be implemented during the lean season because of this concern. Proposing a specific redesign of such measures would take us beyond the scope of this article. Yet, our findings suggest a new and important rationale for incorporating some information about seasonality into these tools.

In broader terms, it would be incorrect to argue that policymakers neglect the issue of seasonal food security. Food aid is often implicitly countercyclical. Programs such as the Famine Early Warning Systems Network (FEWSNET) provide drought and food security forecasting tools. Government programs such as the Productive Safety Net Programme in Ethiopia provide seasonally varying access to transfers and employment opportunities explicitly to combat lean-season deprivation. Yet, the finding that persistent seasonal consumption has long-term consequences, distinct from those related to shocks, introduces a separate rationale for intervening to promote consumption smoothing. Based on our findings, one might argue for seasonally varying any form of consumption support, such as a subsidy for food purchases or a food transfer through a conditional program. Depending on management costs, seasonally varying support could have a substantially larger effect on human capital than providing uniform transfers throughout the year, even if total resources are constant.

Finally, our findings demonstrate a specific channel by which structural transformation influences human development. When the employment shares of manufacturing and services increase relative to agriculture, income and consumption become less seasonal. Our results suggest that this reduction in seasonality will have a meaningful effect on child development, independent of that due to income growth.

## Acknowledgments

We are grateful to the African Development Bank, World Bank, and Cornell University for funding through the STAARS program. We thank the Editors, three anonymous referees, Abraham Abebe Asfaw, Chris Barrett, Anirban Basu, Jere Behrman, Leah Bevis, Joshua Blumenstock, Jennifer Burney, Michael Carter, Arun Chandrasekhar, Norma Coe, Alison Cullen, Joachim De Weerdt, Andrew Foster, Rachel Heath, Heather Hill, Kalle Hirvonen, Martijn Huysmans, Nathan Jensen, Arianna Legovini, Mark Long, Linden McBride, Tyler McCormick, Ellen McCullough, Craig McIntosh, Robert Plotnick, Jenny Romich, Jacob Vigdor, and seminar participants at Cornell, KU Leuven, the World Bank, the University of Washington, the Second Annual Global Food Security Conference, the STAARS conference in Addis Ababa, the 2017 Pacific Development Conference, and the 2017 Annual Bank Conference on Africa for helpful discussions and comments. We are joint first authors on the article. Any errors are our responsibility.

## Notes

1

Wealthy country consumers also eat seasonal diets, although the fluctuations seem to be less pronounced and occur around a greater average level than in low-income countries (de Castro 1991; Ma et al. 2006).

2

It is unclear whether something about a variable diet itself, at any level of consumption, impedes growth. We found little discussion of this in the literature. The mechanism discussed here suggests that seasonal fluctuations around high levels of consumption will not impede growth if lean-season consumption never falls below the threshold required for a child to reach his or her potential. In section Modeling Consumption: Estimation Results and in section D of Online Resource 1, we discuss heterogeneity in seasonality across the consumption distribution.

3

In the first round, 840 households were surveyed; 81 of these did not appear in the last round, the majority of which had moved outside the study area. Seventy-five households were selected as replacements for the 81 that dropped out, leading to 915 total unique households included across rounds.

4

For clarity of presentation, we exclude Nuts/Pulses and Beverages from Fig. 2. These represent a very small share of consumption in this population.

5

Of the 758 households interviewed in all four rounds of KHDS 1, 23 did not complete the full food consumption and expenditure modules in all four rounds. The 736 with complete consumption data constitute the main analysis sample.

6

This model was informed by our reading of Ligon and Schechter (2003) and Arndt et al. (2006).

7

This decomposition does not rule out the possibility that the drivers of seasonality could be stochastic. The key distinction is between those stochastic factors whose distributions vary systematically across the days of the year and those whose distributions do not. For example, the rain cycle is an annual event that introduces some seasonality, but the timing and duration of the rainy season in any given year is partly stochastic. The seasonality term in our model captures the average contribution of all seasonally varying factors, on any day of the year, to the consumption cycle.

8

For this reason, we use data from only those households surveyed in all four rounds, so as not to extrapolate to dates more than a year before or after the most recent interview.

9

Because we allow Zydh to evolve over time, $ŝh2$ is not exactly analogous to $σγh2$ from Eq. (4). We could fully align the two if we took the additional steps of modeling the evolution of the variables in Zydh and added the appropriate adjustment to Eq. (4). We elect not to do this because it would introduce complexity with little value. The important point is that $σγh2$ need not be constant over time because it is a function of some time-varying household characteristics. Hence, $ŝh2$ measures the average seasonal component for the household over the study period.

10

We also estimated specifications using the observed values of mh and sh, calculated directly from the four observations in KHDS 1. The pattern of results from those specifications is similar to what we report in the Results section. However, this alternative approach is clearly misspecified because the raw statistics mh and sh contain both seasonal and idiosyncratic variation. Results are available upon request.

11

Average differences in outcomes across cohorts are not problematic because they are controlled for by age group effects. The question is whether confounding trends in the seasonality of consumption allowed the different age groups to consume at significantly different levels of seasonality during the unobserved years. We know of no ancillary evidence suggesting that consumption in Kagera became markedly more or less seasonal during the decade before or after 1991–1994.

12

The specific reasons for the persistence of seasonal fluctuations in food prices and consumption across much of sub-Saharan Africa, even to this day, remain a puzzle. See Basu and Wong (2015), Burke (2014), Dillon (2017), Fink et al. (2014), Kaminski et al. (2014, 2016), and Stephens and Barrett (2011).

13

Parameter estimates are provided in Online Resource 1, Table S1.

14

This is an approximation because some allowance must be made for suppressed variation in the projected variable $ŝh$—hence, the rationale for bootstrapping standard errors.

15

In Online Resource 1, section D, we show that there is no statistically significant heterogeneity across $m̂h$ in the effects of seasonality on human capital.

16

For height, we can reject the hypotheses that the Age Group 2 coefficient is less than the Age Group 1 coefficient (p value = .067) and that the Age Group 3 coefficient is less than the Age Group 1 coefficient (p value = .056).

17

Unfortunately, we cannot determine in the KHDS 1 data whether attendance drops during the lean season, which would have aided in the interpretation of this result. During every KHDS 1 survey month, a majority of respondents answered “Yes” when asked whether a child was attending school “now,” even though school was not in session during some of those months. Hence, respondents clearly interpreted the question about current attendance to be more about recent enrollment or general attachment to school.

18

For Age Groups 1 and 3, p values for the one-sided comparisons between boys (column 8) and girls (column 7) are below .10.

19

For more details on the Guatemala study, see Stein et al. (2008).

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