Food Policy 67 (2017) 119–132
Contents lists available at ScienceDirect
Food Policy
journal homepage: www.elsevier.com/locate/foodpol
Food price seasonality in Africa: Measurement and extent
Christopher L. Gilbert a,⇑, Luc Christiaensen b, Jonathan Kaminski c,1,2
a
SAIS Bologna Center, Johns Hopkins University, Bologna, Italy
b
World Bank, Brussels, Belgium
c
Geneva, Switzerland
a r t i c l e i n f o a b s t r a c t
Article history: Everyone knows about seasonality. But what exactly do we know? This study systematically measures
Available online 27 October 2016 seasonal price gaps at 193 markets for 13 food commodities in seven African countries. It shows that
the commonly used dummy variable or moving average deviation methods to estimate the seasonal
gap can yield substantial upward bias. This can be partially circumvented using trigonometric and saw-
tooth models, which are more parsimonious. Among staple crops, seasonality is highest for maize (33
percent on average) and lowest for rice (16½ percent). This is two and a half to three times larger than
in the international reference markets. Seasonality varies substantially across market places but maize is
the only crop in which there are important systematic country effects. Malawi, where maize is the main
staple, emerges as exhibiting the most acute seasonal differences. Reaching the Sustainable Development
Goal of Zero Hunger requires renewed policy attention to seasonality in food prices and consumption.
Ó 2016 The World Bank. Published by Elsevier Ltd. This is an open access article under the CC BY IGO
license (http://creativecommons.org/licenses/by/3.0/igo/).
1. Introduction is that, although ‘‘we all know about seasonality”, it is very unclear
precisely what it is we know.3
It is well-known that agricultural prices vary across seasons, Knowing the extent of food price seasonality matters for a num-
typically peaking just before the harvest, and dropping substan- ber of reasons. First, when food prices display high seasonality, so
tially immediately thereafter. Despite this, there exists little sys- may also be dietary intake and nutritional outcomes, with episodes
tematic research on the extent of this seasonal variation across of nutritional deﬁciencies during the ﬁrst 1000 days of life partic-
food commodities, countries, or markets within countries. The only ularly detrimental for cognitive development and future earnings
comprehensive analysis that systematically applies the same (Dercon and Portner, 2014). The 2015 adoption of Sustainable
methodology across commodities and countries is Sahn and Development Goal II of Zero Hunger4 adds pertinence.5 When pro-
Delgado (1989). This is by now somewhat dated. The consequence duction is cyclical, some seasonality in prices is normal; intertempo-
ral arbitrage is needed and storage costs ensue, which drive a wedge
between prices before and after the harvest.6 This gap can be
3
A number of country-speciﬁc studies exist but these stop short of quantifying the
extent of seasonal price variation. Examples include Allen (1954), who analyzed
⇑ Corresponding author. seasonality in UK food prices over the immediate post-war decade, and Statistics New
E-mail addresses: christopher.gilbert@jhu.edu (C.L. Gilbert), lchristiaensen@ Zealand (2010), which reviewed seasonality in New Zealand fruit and vegetable
worldbank.org (L. Christiaensen), kaminski.jonathan@gmail.com (J. Kaminski). prices. Recent country case studies from Sub-Saharan Africa, where food price
1
The paper forms part of the project ‘‘Agriculture in Africa – Telling Facts from seasonality is expected to be highest, include Manda (2010) (maize, Malawi), Aker
Myths” – see http://www.worldbank.org/en/programs/africa-myths-and-facts. A (2012) (millet, Niger), Gitonga et al. (2013) (maize, Kenya), and Hirvonen et al. (2015)
preliminary version of the paper was presented at the Società Italiana degli (food price index, Ethiopia).
4
Economisti dello Sviluppo, Florence, Italy, 10–11 September, 2014. Shamnaaz Sufrauj http://www.un.org/en/zerohunger/challenge.shtml.
5
and Lina Datkunaite assisted with calculations. The authors thank a referee, Daniel The need for reviving attention to the reality of seasonality in African livelihoods
Gilbert, Denise Osborn and Wouter Zant for useful discussion. The ﬁndings, among development scholars and practitioners is also highlighted by Devereux et al.
interpretations, and conclusions expressed are entirely those of the authors, and do (2011).
6
not necessarily represent the view of the World Bank, its Executive Directors, or the Price seasonality may also follow from seasonal patterns in demand such as those
countries they represent. related to festivities, e.g. high sugar demand in preparation of the Eid festival, or
2
Gauss programs for the empirical analysis conducted in this paper are available celebration of the New Year and Orthodox religious festivities (Meskel) in September
at: https://sites.google.com/site/christopherlesliegilbert/data. in Ethiopia (Hirvonen et al., 2015).
http://dx.doi.org/10.1016/j.foodpol.2016.09.016
0306-9192/Ó 2016 The World Bank. Published by Elsevier Ltd.
This is an open access article under the CC BY IGO license (http://creativecommons.org/licenses/by/3.0/igo/).
120 C.L. Gilbert et al. / Food Policy 67 (2017) 119–132
compounded by poorly integrated markets and trade restrictions, variable approach may still perform better, because it is more
market power along the marketing chain, and sell-low, buy-back- ﬂexible.
high behavior among liquidity and credit constrained households To select the preferred speciﬁcation and minimize the upward
(Stephens and Barrett, 2011). They can push up the seasonal price bias when estimating the seasonal gap, a three step procedure is
gap well beyond the levels expected in settings with well- advanced. Systematically applying this three step approach, the
functioning markets. extent of price seasonality is measured by market place (typically
Excess seasonality in prices may further translate into seasonal major provincial centers) for 13 food commodities in seven Sub-
variation in dietary intake and nutrition, for example, when house- Saharan African countries, or a total of 1053 market place-
holds are credit constrained or ill-equipped with other coping commodity pairs. In each case, there are between six and 13 years
strategies, as has been documented in Ethiopia (Dercon and of monthly data depending on the country, market place and
Krishnan, 2000), Bangladesh (Khandker, 2012), and Tanzania commodity.
(Kaminski et al., 2016).7 Moderation of seasonal price variation The ﬁndings indicate that seasonality in African food markets
(for example through facilitation of storage or access to credit) could remains sizeable. The seasonal gap is highest among vegetables
then be a way to increase overall food and nutrition security. (60.8 percent for tomatoes) and fruits, and lowest among com-
A second reason for refocusing attention to food price seasonal- modities which are produced throughout the year (eggs) and/or
ity relates to the sharply increased volatility of world food prices in whose harvest is not season bound (cassava). Among staple grains,
the immediate aftermath of the 2007–08 world food crisis (Gilbert seasonality is highest for maize (33.1 percent on average) and low-
and Morgan, 2010, 2011) although volatility levels appear to have est for rice (16.6 percent). These gaps are two and a half to three
dropped back since that time (Minot, 2014). This volatility was times higher than on the international reference markets, pointing
transmitted to a greater or lesser extent to food prices in develop- to substantial excess seasonality. While excess seasonality is
ing countries and attracted considerable government attention observed in virtually all the maize and rice markets studied, there
(Galtier and Vindel, 2012; World Bank, 2012; Ceballos et al., is wide heterogeneity within and across countries. Seasonality is
2015). Food price volatility arises from both international and especially high in Malawi, where maize is also the main staple,
domestic shocks to production (harvest shocks) or consumption causing a double seasonality burden for most households.
(changes in purchasing power). However, seasonality (i.e. known In what follows, Section 2 sets the stage by reviewing general
ﬂuctuations) also contributes to price volatility (especially domes- considerations on the data, seasonality metrics and the overall esti-
tically) and would require different policy instruments to address mation approach. Section 3 looks at the commonly used methods
it. Little is known on the extent of this possibility. for estimating the seasonal gap and shows that these can result
The third reason relates to the measurement and analysis of in upwardly biased estimates when data samples are short. The
poverty (the focus of the ﬁrst Sustainable Development Goals). performance of alternative and more parsimonious seasonality
Poverty measurement relies heavily on food expenditure informa- models is examined in Section 4. Section 5 introduces the price
tion which is typically collected only once for each household dur- data from the thirteen commodities and seven African countries
ing at a particular point during the year (with a 7–30 day recall examined here and discusses the ﬁndings. Section 6 concludes.
period). The annual expenditures measures derived from these sur-
veys will be incorrect when food price seasonality is substantial
and not corrected for, as is mostly the case in current practice 2. Material, metrics and method – general considerations
(Muller, 2002; Van Campenhout et al., 2015).
The seasonal gap—the difference between the high price imme- Many developing country governments publish monthly prices
diately prior to the harvest and the low price following the harvest, for staple food commodities for major locations in their territories.
averaged across years—is the standard measure used to measure These prices are obtained by sending observers to markets in these
the extent of seasonality. It is common to estimate this gap from locations, who record the prices at which the different commodi-
a (monthly) dummy variables regression on trend-adjusted prices ties are transacted. It is unclear how much intra-month averaging
or simply from the (monthly) mean price deviation around a mov- is undertaken, but at least for some countries (e.g. Uganda), the
ing average trend (Goetz and Weber, 1986, Chapter IV). monthly prices derive from weekly observations. Much of this
Using Monte Carlo simulations, this paper shows that, when price information results from the FEWSNET initiative, supported
samples are short (5–15 years), these approaches can seriously by USAID, and the FAO’s GIEWSNET initiative.
overestimate the extent of seasonality, especially when there is Three features of these price data stand out. First, the price data
either little seasonality or where the seasonal pattern is poorly collection initiatives are relatively recent so that the time series
deﬁned. Although the coefﬁcients of individual monthly dummy available are usually short. Second, in many of the price series,
variables, or the monthly price averages, are individually unbiased, the frequent occurrence of missing observations compounds the
the seasonal gap, which is obtained as the difference between the short duration of the series. Gaps may arise for example because
maximum and the minimum dummy coefﬁcient, each identiﬁed the observers did not see transactions in the foods in question
from the data, is upwardly biased. This problem has hitherto not when they visited the markets. In some other instances, prices
been noted despite the relatively short samples typically used in are missing for all locations in a particular month suggesting an
the development literature on seasonality. administrative explanation. Finally, in most countries, only a small
It is shown that the problem can be mitigated by using trigono- number of (mainly urban) locations (ﬁve to ﬁfteen) are covered,
metric or sawtooth models. These more parsimonious models though some governments (Malawi in our sample) attempt to be
impose some structure on the nature of seasonality, thereby sub- more comprehensive. These features of the data are important to
stantially reducing the number of parameters to be estimated keep in mind when measuring seasonality in developing countries.
and providing more observations per estimated parameter. This They also caution against overgeneralization based on a small
substantially reduces the upward bias in the estimated gap. When number of market locations within countries, as seasonality will
there is more than one season, which is less common, the dummy prove to differ substantially from place to place.
In agriculture, seasonality measures attempt to capture the part
7
Few studies explicitly study the link between food price seasonality and
of the intra-annual variability of the monthly observations that is
seasonality in diets and nutrition. Related studies include Chambers et al. (1981) speciﬁcally related to the crop cycle. The simplest case is that of
and Dostie et al. (2002), and Stephens and Barrett (2011). a subsistence crop with a single annual harvest and for which
C.L. Gilbert et al. / Food Policy 67 (2017) 119–132 121
imports and exports are unimportant within a wide price band. X
Y
The price of such a commodity will be lowest immediately after sm ¼ Y
1
ðpym À lym Þ ðm ¼ 1; . . . ; 12Þ ð6Þ
y¼1
the harvest and will then rise steadily until the following harvest
to reﬂect (at a minimum) storage and deterioration costs. The most This is the approach adopted in Allen (1954) and Goetz and Weber
widely used seasonality measure for such products is the seasonal (1986).
gap (also used here), which is the expected (or average) fall in price While straightforward to apply and widely used in the agricul-
over the pre- and post-harvest period.8 tural and development literature, this moving average deviation
The basic structural representation of seasonality in a price ser- (MAD) procedure also comes with important disadvantages. First,
ies considers three components: trend, seasonal factors and irreg- calculation of the moving average price trend sacriﬁces the initial
ular variation: and ﬁnal six months of the dataset. If the available sample is short,
pym ¼ lym þ sm þ eym ð 1Þ this can be a major loss. Second, estimation of the moving average
price trend requires interpolation of the missing data points. In the
where pym is the logarithm of the food price in month m of year y, absence of clear conceptual guidance on the appropriate informa-
lym is the trend, s1 ; . . . ; s12 are a set of twelve seasonal factors satis- tion base for interpolation, this poses a concern.10 Third, the proce-
P dure of taking deviations from the moving average trend induces a
fying 12 9
j¼1 sj ¼ 0 and eym is a disturbance. In this framework, the
complicated moving average error into the disturbance term associ-
standard measure of the seasonal gap is the difference between
ated with the price deviations. This does not affect the calculation of
the highest and the lowest seasonal factor:
seasonal factors but will invalidate standard statistical inference.
gap ¼ max sm À min sm ð 2Þ The alternative approach, which we adopt in what follows, is to
suppose that the price trend is stochastic. Even if price series are
There are three issues: the speciﬁcation of the trend component
non-trend-stationary, they will generally be difference stationary
lym , the estimation of the seasonal factors s1 ; . . . ; s12 , and the treat-
(Nelson and Kang, 1984). This yields the stochastic trend model
ment of missing values. The choice of trend speciﬁcation affects
(Stock and Watson, 2003, chapter 12). Like the MAD procedure,
ﬂexibility in dealing with missing values. These two issues are dis-
the stochastic trend model allows for a trend which varies over
cussed together. The simplest trend estimation procedure is to
time, albeit with a constant annual increment. It sets
specify a linear trend. The seasonal factors can be estimated from
the regression: lym ¼ ly;mÀ1 þ c þ mym ð7Þ
X
11 As in the linear trend model (3), c is the monthly trend incre-
pym ¼ j þ ct þ dj zmj þ eym ð 3Þ ment. Differencing Eq. (1) and substituting Eq. (7) yields
j¼ 1
Dpym ¼ c þ Dsm þ uym ð8Þ
where the trend t ¼ 12 Ã ðy À 1Þ þ m and zmj is the dummy variable
1 j¼m where uym is a compound error term. The estimating equation
deﬁned by zmj ¼ . Normalizing d12 = 0 gives seasonal
0 j–m becomes
factors: X
11
Dpym ¼ c þ dj Dzmj þ uym ð9Þ
X
12
j¼1
sm ¼ d m À 1
12
dj ðm ¼ 1; . . . ; 12Þ ð 4Þ
j¼1 where the differenced dummies11 Dzmj (j = 1,. . .,11) are deﬁned by
8
Sahn and Delgado (1989) adopt this approach. <1 m¼j
Dzmj ¼ À1 m ¼ j À 1 .
The linear trend approach assumes that prices are trend station- :
0 otherwise
ary, i.e. that they revert to a deterministic trend. However, eco-
nomic theory does not provide any basis to suppose that food The approach set out in Eq. (9) has important advantages over
price trends are constant. One way to allow for a variable trend the MAD procedure. First, only a single observation is lost through
is to estimate the trend as a centered moving average, which can differencing compared with twelve in the MAD procedure. Second,
vary from month to month: there is no requirement for interpolation over gaps.12 If there is a
" # gap of k months prior to observation (y,m), Eq. (9) can be replaced by
1 X 5
1
lym ¼ p þ ðp þ py;mÀ6 Þ ð 5Þ X
kÀ1
12 j¼À5 y;mþj 2 y;mþ6 Dk pym ¼ pym À py;mÀkÀ1 ¼ kc þ smÀi þ wym ð10Þ
i¼0
Using this approach, seasonal factors can be estimated as aver-
age deviations from the detrended price series so that where wym is a new compound error term.13
8
A number of alternative measures of intra-annual price variability are available,
3. Bias in seasonal gap estimates
all based on the month price means. However, these measures do not relate directly
to the harvest cycle and so are better regarded as general measures of intra-annual Regression on a set of constants, as in Eqs. (3) and (9), yields
price variability than of seasonality. This is true of both the intra-annual price unbiased and consistent coefﬁcient estimates. It follows that the
standard deviation and the intra-annual Gini coefﬁcient, both of which compare
prices in every month and not just those pre- and post-harvest.
9 10
See Harvey (1990, chapter 1). In a large sample, one might wish to include an Interpolation requires a model which will need to contain seasonal factors. This
autoregressive component in the decomposition deﬁned by Eq. (1) such that the induces circularity into the gap estimation.
11
disturbance term becomes innovational. In a short sample, this runs the risk of Eq. (9) can be equivalently re-expressed in terms of the undifferenced dummy
confusing the autoregressive and seasonal components. Seasonality patterns may also variables and differenced coefﬁcients.
12
vary over time, either in an evolutionary manner, perhaps in relation to climate In an earlier draft of this paper, we reported estimates in which we had
change, or randomly if harvest dates are random. These issues are important but interpolated over gaps in the series. These results differed sharply from those we now
cannot easily be examined with short data samples. The analysis presented here report in those cases in which the gaps were substantial.
13
abstracts from time varying seasonality. For notational simplicity we suppose that the Differencing will induce a serially correlated disturbance term. This is the same
data cover complete years so that the ﬁrst observation p11 represents the price in problem which arises in the MAD model where the serial correlation arises from the
January of year 1 and the ﬁnal observation pY,12 is the price in December of year Y. For trend estimation procedure. Serial correlation will not result in any bias in the
m þ j > 12, py;mþj ¼ pyþ1;mþjÀ12 and for m À j < 1, py;mÀj ¼ pyÀ1;mÀjþ12 . estimated seasonal factors but will complicate inference.
122 C.L. Gilbert et al. / Food Policy 67 (2017) 119–132
estimated seasonal factors s1 ; . . . ; s12 are also unbiased. If we know, number of annual observations will yield an imprecise (high vari-
a priori, that the seasonally high pre-harvest price is in month hi ance) gap estimate but this estimate is as likely to be too low as too
and the seasonally low post-harvest price in month lo, then the high. In the opposite case, in which the actual gap is low and/or the
seasonal gap as measured by gap ¼ shi À slo will also be unbiased. peak and trough months are poorly deﬁned, the dummy variables
In this circumstance, the dummy variables estimator of the sea- gap estimator will select those peak and trough months which
sonal gap works well. However, the exact timing of seasonal peaks happen, in the sample available, to give the highest gap estimate.
and troughs varies across crop-location pairs, even within coun- The estimator will be consistent since, given a sufﬁciently long
tries. Even knowledgeable observers, but especially the analyst sit- sample, the correct peak-trough identiﬁcation will be made and
ting in London, Paris or Washington, may well be unfamiliar with the probability of a seasonal reversal will approach zero. However,
harvest patterns in all locations and may wish to estimate these with the sample sizes typically available in an African context, the
from the price data. probability of bias is high.
In these circumstances, the analyst will use the gap estimate To illustrate, two sets of Monte Carlo experiments are reported.
deﬁned by Eq. (2), gap ¼ max sm À min sm : This is biased upwards, The ﬁrst set of experiments (Table 1) estimates the seasonal gaps
even though consistent, when identiﬁed from the data. Intuitively, using the dummy variable regression (9), based on a stochastic
while the empirical estimates of the seasonal factors (or monthly trend model. The second set (Table 2) uses the MAD procedure
dummies) are each unbiased, each empirical estimate of a seasonal where the moving average trend estimate is deﬁned by Eq. (5)
factor represents a draw from a distribution, which usually devi- and estimation using Eq. (6). In each set of experiments, the data
ates slightly from its true point value. As a result, by taking each were generated according to Eq. (9). The disturbances uym were
time the maximum and minimum values of all seasonal factors, are independently distributed N ð0; 0:152 Þ.
the gap will be overestimated. There are three sub-cases:
In statistical terms, while a linear transformation of two unbi-
ased statistics remains unbiased, this does not hold when the (a) Columns 1–3: Data generated with no seasonality.
transformation is non-linear. The estimated gap measure deﬁned (b) Columns 4–6. Data generated with a clear and regular saw-
by Eq. (2) is a non-negative and a nonlinear function of the sea- tooth (i.e. non-symmetric) seasonal pattern. On average,
sonal factors and therefore (upwardly) biased.14 By contrast, the prices fall by 10 percent in each of January and February
gap measure shi À slo for known peak and trough months is a differ- and rise by 2 percent in the remaining eleven months imply-
ence between two unbiased statistics and will itself be unbiased. In a ing a 20 percent gap (more on sawtooth seasonal patterns
particular sample, this gap measure for a known harvest month may below).
either be positive or negative, although it is likely to be positive. The (c) Columns 7–9. Data generated by a diffuse and less well-
difference between the maximum and the minimum, deﬁned seasonal pattern. On average, prices fall by 4 percent
max sm À min sm , is necessarily positive. in each of January and February and rise by 0.8 percent in
The problem arises because the peak and trough months identi- the remaining ten months implying a 4 percent gap. How-
ﬁed in any particular sample may differ from those deﬁned by the ever, one year in ﬁve, the harvest is retarded by one month
harvest pattern. This misrepresentation is more likely in short sam- such that the price falls in February instead of January. Tak-
ples and with data where the harvest cycle contributes only a small ing into account the fact that January prices continue to rise
proportion of total price variation. To appreciate the conceptual and one year in ﬁve, this gives a seasonal gap of 8.16 percent.
empirical importance of this insight, consider the extreme case in
which there is no seasonality (i.e. no price difference between the In each case, four samples are considered, of length 5, 10, 20 and
pre- and postharvest months). Picking the largest and the smallest 40 years of monthly data. The results reported are based on 100,000
monthly estimates necessarily yields a positive seasonal gap, sug- replications. The tables also report the average regression R2 (i.e.
gesting spurious evidence of seasonality. This is despite the fact that share of the price variation in the sample on average ‘‘explained”
each of the seasonal factor estimates is unbiased. by the seasonal factors) and the proportion of simulations in which
In sum, bias in the dummy variables gap estimate arises from the regression F statistic rejects the hypothesis of no seasonality.
three separate factors which interact with each other: The dummy variable estimates for the stochastic trend model
(Table 1) are considered ﬁrst.
peak and trough months are identiﬁed from the data;
the estimated gap is a nonlinear function of the (unbiased) (a) When there is no seasonality, the gap measure shows sub-
dummy variable coefﬁcients; stantial upward bias. The estimated gap is 21 percent and
the small number of observations typically used to estimate the 15 percent using ﬁve and ten years of data respectively.
coefﬁcients of the peak and trough month dummy variables. The R2 statistics indicate that around 19 percent and 9 per-
(What is relevant here is the number of years of data in the cent of the sample price variation respectively are ‘‘ex-
sample, not the number of monthly observations). plained” by seasonality. However, the F tests correctly
show that, at the 5 percent level, only around 5 percent of
In samples in which the peak and trough months are clearly the estimates reject the null of no seasonality.
deﬁned or the gap is large, it is unlikely that the procedure will (b) In the case of clear seasonality, the dummy variables gap
make an incorrect peak-trough identiﬁcation or that the estimated estimator remains upwardly biased, but by much less (8 per-
coefﬁcient of the trough month dummy will exceed that of the cent on ﬁve years data and 4 percent on ten years data).
peak month dummy (an apparent ‘‘seasonal reversal”). A small Unsurprisingly, the R2 statistics are higher than in the no
seasonality case but with ten years data, the null of no sea-
sonality is only rejected in approaching half the cases.
14
The maximum value of a set of numbers is a nonlinear function of the data – a (c) The third case, diffuse seasonality, generates intermediate
particular observation, that corresponding to the maximum, gets a weight of one and results. The bias is substantial in short samples (14½ percent
all other observations have zero weight. Crucially, the identity of this maximal value
is determined by the sample. The same is true of the minimum. The range, here
and 8 percent respectively using ﬁve and ten years data) and
interpreted as the seasonal gap, which is the difference between the maximum and the regression F statistic does a poor job in conﬁrming the
minimum values, is a linear function of two nonlinear functions of the data and is presence of seasonality.
therefore itself a nonlinear function of the data.
C.L. Gilbert et al. / Food Policy 67 (2017) 119–132 123
Table 1
Dummy variable bias.
Years No seasonality Clear seasonality Poorly deﬁned seasonality
2 2
Bias R Statistical signiﬁcance (%) Bias R Statistical signiﬁcance (%) Bias R2 Statistical signiﬁcance (%)
5 0.2126 0.1866 5.1 0.0828 0.2522 22.9 0.1425 0.1959 6.7
10 0.1504 0.0926 5.0 0.0410 0.1662 51.3 0.0843 0.1028 9.0
20 0.1062 0.0460 5.1 0.0182 0.1238 88.9 0.0459 0.0569 14.6
40 0.0752 0.0230 5.0 0.0069 0.1027 99.8 0.0213 0.0341 28.0
Estimated bias in gap estimation from dummy variables regression based on 100,000 replications. Price changes are normally and independently distributed with mean and
variance equal to 0.01. The data for the estimates reported in the ﬁrst block (columns 1–3) do not show any seasonality, those in the second block (columns 4–6) exhibit a
clearly deﬁned seasonal peak and trough with a gap of 20% and those in the ﬁnal block (columns 7–9) show a diffuse and poorly deﬁned seasonal pattern with a gap of 8%. R2
indicates share of the price variation in the sample on average ‘‘explained” by the seasonal factors and the proportion of simulations in which the regression F statistic rejects
the hypothesis of no seasonality is reported under ‘‘statistical signiﬁcance”.
Table 2
Bias for Moving Average Deviations Procedure.
Years No seasonality Clear seasonality Poorly deﬁned seasonality
Bias R2 Statistical signiﬁcance (%) Bias R2 Statistical signiﬁcance (%) Bias R2 Statistical signiﬁcance (%)
5 0.2183 0.2001 7.8 0.0689 0.2692 29.7 0.1441 0.2104 10.3
10 0.1544 0.1003 8.2 0.0212 0.1791 59.9 0.0830 0.1116 13.5
20 0.1093 0.0502 8.2 À0.0093 0.1339 92.4 0.0415 0.0620 20.6
40 0.0772 0.0250 8.0 À0.0301 0.1113 99.9 0.0145 0.0372 36.1
Estimated bias in gap estimation from dummy variables regression of deviations from a centered moving average trend based on 100,000 replications. Price changes are
normally and independently distributed with mean and variance equal to 0.01. The data for the estimates reported in the ﬁrst block (columns 1–3) do not show any
seasonality, those in the second block (columns 4–6) exhibit a clearly deﬁned seasonal peak and trough with a gap of 20% and those in the ﬁnal block (columns 7–9) show a
diffuse and poorly deﬁned seasonal pattern with a gap of 8%. R2 indicates share of the price variation in the sample on average ‘‘explained” by the seasonal factors and the
proportion of simulations in which the regression F statistic rejects the hypothesis of no seasonality is reported under ‘‘statistical signiﬁcance”.
The third set of results (those for diffuse seasonality) are in high. If, when using a short sample, the test fails to reject the
some respects the most disturbing. The results in the no seasonal- hypothesis of no seasonality it will be difﬁcult to know whether this
ity case suggest discarding the dummy variable estimates when is because the data are not seasonal or because the test lacks power
the estimates fail to reject the hypothesis of no seasonality. Yet to reject that. (Tests for the signiﬁcance of the seasonal factors are
that rule would often lead to an estimate of zero seasonality in correctly sized when the stochastic trend model is estimated, though
cases of diffuse seasonality. Finally, note that the R2 statistics in they lack power when the sample size is short.) Third, on the extent
short samples tend to attribute much more explanatory power to of seasonality, the empirical monthly dummy based estimated range
seasonality than it actually has, as becomes apparent when the measure of the seasonal gap tends to exaggerate the extent of sea-
sample size increases. The seemingly high degree of explanation sonality on samples of the typical size available in Africa (5–
obtained in short samples is entirely spurious in the ‘‘no seasonal- 15 years). The upward bias is larger the shorter the sample and the
ity” experiments and largely so in the other two experiments. less well deﬁned the seasonal pattern. Given that long monthly price
The biases obtained using the MAD procedure are similar to time series will not be generally available in the foreseeable future
those using the stochastic trend model (Table 2). They are slightly (including for many other seasonal phenomena), there are important
higher when there is no seasonality, slightly lower with clear sea- gains from procedures that can mitigate the estimated bias.
sonality, and virtually the same when seasonality is poorly deﬁned.
The notable difference is that the MAD estimates exaggerate the
statistical signiﬁcance of the results. For large samples, the R2 4. More parsimonious models
statistics converge to the values obtained with the stochastic trend
model, though they are systematically higher for shorter samples. The dummy variable approach to measuring the seasonal gap is
Second, in the case of no seasonality, exactly 5 percent of experi- highly parametrized. This has the advantage that it does not pose
ments should reject the hypothesis of no relationship. Instead, many restrictions on the data, but it comes at the expense of hav-
absence of seasonality is rejected in around 8 percent of cases ing to estimate a large number of parameters (eleven with monthly
using the MAD procedure (compared with 5 percent using the data). The alternative is a more parsimonious seasonality model
stochastic trend model) (Tables 1 and 2, column 3). This indicates which exploits the fact that seasonality in agricultural markets is
mild over-sizing, arising from autocorrelation in the error terms generated by the crop cycle. By imposing a harvest-based pattern
generated by the moving average transformation. on the pattern of monthly seasonality factors, parsimonious sea-
Overall, three conclusions emerge. First, on model choice, the sonality models reduce the inﬂuence of any single monthly mean
stochastic trend model is slightly preferred. It is more reliable in price. Consequently, there is a much lower probability of an incor-
its statistical inference. It is also more parsimonious in its data rect peak-trough identiﬁcation (for example through an error of a
use, which the analysis above has abstracted from.15 Second, on single month in either direction). Intuitively, with Y years of data
the matter of whether there is seasonality or not, if a standard F test (say Y = 10), there are in essence only 10 observations from which
rejects the hypothesis of no seasonality, one can be conﬁdent that each monthly effect is estimated in the monthly dummy regression
the data are seasonal even if the gap measure will tend to be too (despite there being 120 price data points). In contrast, by smooth-
ing out the variation through the imposition of a tighter parametric
structure, the degrees of freedom increase and so does estimation
15
It remains that the MAD procedure uses up twelve monthly observations in efﬁciency.
estimating the trend. The estimates reported in Table 2 relay on 5, 10, 20 and 40 years
of detrended data equivalent to 6, 11, 21 and 41 years of raw data. The close
Nevertheless, parsimonious speciﬁcations have a cost. The gap
correspondence in the two sets of Monte Carlo results is ensured by use of a common estimates should be more accurate so long as the actual seasonal
random number seed in the two sets of experiments. structure conforms to the imposed structure. But if the actual
124 C.L. Gilbert et al. / Food Policy 67 (2017) 119–132
Fig. 1. Tomato price seasonality, Morogoro, Tanzania.
structure differs, the estimates will be misleading and the gap esti- This is a case in which seasonality is high and well-deﬁned so
mate may be less accurate than the biased estimate from the the dummy variables procedure also works well. The estimated
dummy variable model. We consider two alternative parametric seasonal gap is 56% using the trigonometric speciﬁcation, but
speciﬁcations. The simplest is trigonometric seasonality – in which 60% on the basis of the dummy variable estimates.
the seasonal pattern is deﬁned by a pure sine wave. The simplest Although, the trigonometric speciﬁcation is parsimonious, it is
two parameter sinusoidal trigonometric seasonality representation restrictive in that the post-harvest price decline is symmetric with
is respect to the pre-harvest price rise. In practice, for many crops,
mp mp prices drop more rapidly post-harvest than that they rise in the
sm ¼ a cos þ b sin ð11Þ remainder of the crop year. An alternative parametric speciﬁcation
6 6
is a sawtooth function in which prices fall sharply post-harvest and
With trending data, the estimating equation is then rise at a steady rate through the remainder of the crop year –
see Samuelson (1957) and, for an application, Statistics New
Dpym ¼ c þ Dsm þ uym
mp mp Zealand (2010). Suppose the peak seasonal factor of k occurs in
¼ c þ aD cos þ bD sin þ uym ð12Þ month m⁄ and that the price falls by the seasonal gap of 2k to –k
6 6 in the harvest month m⁄ + 2. The seasonal factor then rises steadily
k
Eq. (12) is estimable by least squares. The seasonal factor sm may be by an amount 5 over the reminder of the year. Conditional on
re-expressed as a pure cosine function: knowing the peak price month m⁄, the amplitude parameter k
mp may be estimated from the regression
sm ¼ k cos Àx ð13Þ
6 Dpym ¼ c þ Dsm þ uym ¼ c þ kDzm ðmÃ Þ þ uym ð14Þ
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
where k ¼ a2 þ b2 and x ¼ tanÀ1 a . The parameter k measures Here Dzm ðmÃ Þ is equal to À1 if m ¼ mÃ þ 1 or m ¼ mÃ þ 2 and 1 5
b
otherwise. We estimate by performing a grid search choosing the
the amplitude of the seasonal cycle and implies a seasonal gap of
value for m⁄ which gives the maximum R2 ﬁt statistic.17
2k. If the speciﬁcation is valid, least squares estimation of Eq. (11)
Fig. 2 illustrates a sawtooth seasonal pattern for tomato prices
yields unbiased and consistent estimates of the a and b coefﬁcients
in Lira, an administrative center in northern Uganda. The estimated
in Eq. (12). However, the implied seasonal gap 2k is a nonlinear
seasonal gap is 40 percent, again somewhat lower than the 52 per-
non-negative function of these estimates and will therefore also
cent using the dummy variables model.
be biased upwards. Ghysels and Osborn (2001) provide a general
Different seasonal speciﬁcations perform better in different cir-
discussion of trigonometric representations of seasonality.16
cumstances. The trigonometric and sawtooth speciﬁcations both
The trigonometric approach is illustrated by comparing the esti-
suppose a single annual harvest. Fig. 3 illustrates the dummy vari-
mated seasonal pattern with the estimated dummy variable coef-
able seasonality estimates for wholesale maize in the Uganda cap-
ﬁcients for tomato prices in Morogoro, a provincial capital in
ital, Kampala. Close to the equator, Kampala beneﬁts from maize
central southern Tanzania – see Fig. 1. Tomatoes, which are annu-
ally cropped and perishable, tend to exhibit acute price seasonality
and therefore provide good illustrations of seasonality proﬁles.
17
Strictly, if the peak month m⁄ is estimated, Eq. (14) is not nested within the
dummy variables representation (9). If m⁄ were known, it would be nested and
impose 10 restrictions on the dummy variables coefﬁcients in Eq. (9). In what follows,
16
The dummy variable model, which contains 11 parameters, can be expressed in we perform F tests against the dummy variables speciﬁcation as if the two equations
terms of six sinusoidal functions as in Eq. (12) with frequencies of 12, 6, 4, 3 and 12 5 were estimated but adjust the degrees of freedom associated with the sawtooth
months respectively – see Ghysels and Osborn (2001). This representation also representation to obtain correctly sized tests under the null hypothesis of no
contains 11 parameters. Eq. (12) restricts 9 of these parameters to zero. It follows that seasonality. See Meyer and Woodroofe (2000). Monte Carlo experiments led us to
the trigonometric Eq. (12) is nested within the dummy variables Eq. (6) and can be associate 4.1 degrees of freedom with the speciﬁcation in Eq. (14). This number is
tested against it using a standard F test. reﬂected in the results reported in column 3 of Table 4 (below).
C.L. Gilbert et al. / Food Policy 67 (2017) 119–132 125
Fig. 2. Tomato price seasonality, Lira, Uganda.
Fig. 3. Maize price seasonality, Kampala, Uganda.
from two annual harvests – in January (17% peak to trough gap) The third block of statistics relates to a poorly deﬁned seasonal
and July (25% peak to trough gap). Neither the trigonometric nor process. This may be the most realistic in practical applications.
the sawtooth models are able to account for this pattern. Both estimators generate substantial bias reductions relative to
We repeated the Monte Carlo experiments reported for the the dummy variables procedure – reductions of the order of 70
dummy variables and MAD estimators in Section 3. The results percent for the trigonometric estimator and 50 percent for the
for the trigonometric estimator are reported in Table 3 and those sawtooth estimator. With short data samples on poorly deﬁned
for the sawtooth estimator in Table 4. When there is no seasonality seasonal processes, the greater parsimony of these estimators
in the process under investigation (left hand block), the bias falls leads to more reliable estimation. However, even with samples as
by about 40% for trigonometric estimator and 25% for the sawtooth long as 40 years, statistical signiﬁcance tests have low power
estimator. When there is clear seasonality (second blocks), the against the hypothesis of no seasonality – see the ﬁnal column in
sawtooth estimator eliminates almost all the bias while the each of Tables 3 and 4.
trigonometric estimator shows only a small (and negative) bias. In summary, parsimonious seasonal models are likely to be
Given that the data in this example were generated by a sawtooth preferable to the standard dummy variable procedure for estimat-
process, it is unsurprising that the sawtooth estimator has the ing the extent of seasonality when data samples are short or sea-
superior performance. The negative bias in the trigonometric pro- sonal processes are poorly deﬁned. These are typical
cess arises from the fact that the sinusoidal functional form circumstances in data on prices for developing country food crops.
imposes smooth peaks and troughs whereas the data generating These procedures substantially reduce the bias resulting from use
process is spiked. The ranking would be reversed if we had used of dummy variable estimators of the seasonal gap. Signiﬁcance
a trigonometric seasonal process to generate the data. tests on the presence of seasonality remain correctly sized (i.e. they
126 C.L. Gilbert et al. / Food Policy 67 (2017) 119–132
Table 3
Bias for the trigonometric seasonality estimator.
Years No seasonality Clear seasonality Poorly deﬁned seasonality
2 2
Bias R Statistical signiﬁcance (%) Bias R Statistical signiﬁcance (%) Bias R2 Statistical signiﬁcance (%)
5 0.1325 0.0339 5.0 À0.0082 0.0614 19.4 0.0614 0.0386 7.1
10 0.0938 0.0168 5.0 À0.0300 0.0458 37.9 0.0261 0.0216 9.5
20 0.0662 0.0083 5.0 À0.0401 0.0381 68.6 0.0037 0.0133 15.1
40 0.0469 0.0042 5.1 À0.0457 0.0343 94.8 À0.0096 0.0092 26.4
Estimated bias in gap estimation from trigonometric regression based on 100,000 replications. Price changes are normally and independently distributed with mean and
variance equal to 0.01. The data for the estimates reported in the ﬁrst block (columns 1–3) do not show any seasonality, those in the second block (columns 4–6) exhibit a
clearly deﬁned seasonal peak and trough with a gap of 20% and those in the ﬁnal block (columns 7–9) show a diffuse and poorly deﬁned seasonal pattern with a gap of 8%.
Table 4
Bias for the sawtooth seasonality estimator.
Years No seasonality Clear seasonality Poorly deﬁned seasonality
2 2
Bias R Statistical signiﬁcance (%) Bias R Statistical signiﬁcance (%) Bias R2 Statistical signiﬁcance (%)
5 0.1618 0.0641 4.9 0.0026 0.1131 31.7 0.0887 0.0699 7.1
10 0.1145 0.0318 5.0 0.0054 0.0920 67.7 0.0445 0.0380 10.2
20 0.0809 0.0158 5.2 0.0006 0.0856 96.4 0.0160 0.0228 18.5
40 0.0572 0.0019 5.1 0.0001 0.0835 100 À0.0006 0.0156 37.4
Estimated bias in gap estimation from sawtooth regression based on 100,000 replications. Price changes are normally and independently distributed with mean and variance
equal to 0.01. The data for the estimates reported in the ﬁrst block (columns 1–3) do not show any seasonality, those in the second block (columns 4–6) exhibit a clearly
deﬁned seasonal peak and trough with a gap of 20% and those in the ﬁnal block (columns 7–9) show a diffuse and poorly deﬁned seasonal pattern with a gap of 8%.
incorrectly reject the hypothesis of no seasonality in the expected series, where nearly one in ﬁve intermediate data points are
proportion of cases) but they may have low power (they fail to cor- absent.19 In those cases in which gaps are present, we use the skip
rectly reject the hypothesis of no seasonality in a large proportion estimation procedure deﬁned by Eq. (10).
of cases). Their limitation is that they will perform poorly for crops The stochastic trend model is applied to estimate the seasonal
in which there are two harvests per year. gap and a three step procedure is followed to identify the appropri-
ate speciﬁcation (dummy variable, trigonometric, or sawtooth). In
5. Seasonality in African food crop prices the absence of precise information for all crop-location pairs on the
existence of multiple growing seasons (and the exact month of har-
The extent of seasonality in food prices is examined for seven vest), it is a priori not clear whether parsimonious models are pre-
African countries: Burkina Faso, Ethiopia, Ghana, Malawi, Niger, ferred over the dummy variable model, nor which of the two
Tanzania and Uganda. Monthly price series for 13 crops and food parsimonious models is more appropriate. Overall, the trigonomet-
products in local markets over the period 2000–2012 were ric and sawtooth gap estimates have correlations of 0.94 and 0.92
obtained from national statistical ofﬁces and from a private mar- with the dummy variable estimates and 0.8 with each other. More
keting agency in Uganda. The crops covered the main staple cereals particularly,
(maize, millet, rice, sorghum and teff) together with cassava and a
number of important fruits and vegetables, as well as eggs. The (a) The estimates of the trigonometric and sawtooth speciﬁca-
number of markets varies across countries. In four countries (Burk- tions, which are nested within the dummy speciﬁcation
ina Faso, Niger, Tanzania and Uganda), prices are reported both at (see Section 4), are compared against those of the dummy
the retail and wholesale level, although not always for the same variable model. If the F test rejects both models, the dummy
marketplaces. For the other three countries there are only whole- variables estimates are retained.
sale prices. This dataset yields a total of 1053 location-food crop (b) If the F test rejects one but not both of the parsimonious pro-
pairs. Table 5 provides more detailed information. cedures, the non-rejected parsimonious model is taken as an
Prices are all expressed in nominal terms and local currency. acceptable simpliﬁcation of the dummy procedure, reducing
There has been substantial inﬂation during the sample period in bias in the seasonal gap estimates.
some of the countries. Deﬂation of the price of a major food staple (c) Finally, if the F test fails to reject the trigonometric and saw-
by the local CPI would, however, remove part of the variation of tooth model, one of them is selected based on ﬁt, as mea-
interest. We rely on the trend in Eq. (1) to account for the impact sured by the R2 statistic.
of inﬂation and other trend-associated factors. Estimation is based
on the stochastic trend model deﬁned by Eqs. (9), (12) and (14), Using this rule, the dummy variables speciﬁcation is preferred
depending on the seasonal speciﬁcation.18 in 168 instances, the trigonometric speciﬁcation in 625, and the
For some of the series, missing data points are a potential prob- sawtooth speciﬁcation in the remaining 260. The trigonometric
lem. These take two forms. Some series start later or ﬁnish earlier and sawtooth speciﬁcations are quite similar and there is little pat-
than others. With thirteen years of data, there will be a maximum tern in whether one or the other gives the better ﬁt. We only adopt
of 156 data points in each series. We only have this full number of the dummy speciﬁcation if both are rejected against the dummy
observations for wholesale prices in Uganda and (with some alternative. This will happen if two conditions are satisﬁed – the
exceptions) Tanzania - see Table 5. Sample start and end dates
therefore differ across series. The more serious problem is gaps
19
within the series. This is most acute in the Burkinabe retail price We dropped a number of series from the analysis on the basis of insufﬁcient data.
We require (a) at least 24 observations, with (b) at least one observation for each
month (otherwise the dummy variables estimator ceases to be identiﬁed) and (c) a
18
In Kaminski et al. (2016) we apply these methods to deﬂated Tanzanian maize maximum of 50% missing intermediate (gap) observations. We also dropped both the
and rice data using slightly longer samples. The results are comparable to those wholesale and retail rice price series for Niger – these only changed intermittently,
reported here. suggesting that they might be administered or ofﬁcial prices.
C.L. Gilbert et al. / Food Policy 67 (2017) 119–132 127
Table 5
Data availability.
Commodities Locations Pairs Start date End date Observations Gaps
Burkina Faso Wholesale 3 11 31 Jan-00 Sep-11 24–144 5.1%
Retail 3 49 126 Jul-04 Sep-11 38–96 19.3%
Ethiopia Wholesale 11 11 71 Jan-03 Dec-12 49–120 None
Ghana Wholesale 11 14 149 Jul-06 Aug-11 46–68 1.9%
Malawi Wholesale 4 68 253 Apr-05 Dec-12 26–93 11.7%
Niger Wholesale 2 8 10 Jan-02 Dec-12 94–131 1.8%
Retail 3 14 22 Jan-02 Dec-12 95–132 1.3%
Tanzania Wholesale 5 20 86 Jan-00 Dec-12 27–155 5.8%
Retail 8 20 160 Jan-02 Dec-12 33–132 0.1%
Uganda Wholesale 7 8 56 Jan-00 Dec-12 64–156 0.8%
Retail 12 8 89 Jul-05 Dec-12 90 None
Total Wholesale 43 140 656
Retail 26 91 397
In many countries, price data are either not reported for all commodity-location pairs or are insufﬁcient for analysis.
The start dates and end dates reported in the table give the maximum extent of the series. The actual number of data points is less than this maximum number because of a
later start, earlier ﬁnish or gaps in the series. The ﬁnal column reports the overall proportion of gaps in the data series.
seasonal pattern must be well deﬁned and is not well reﬂected in a
sinusoidal or sawtooth pattern. A two harvest pattern meets these Table 6
Average estimated seasonal gap and seasonal R2 by food crop.
two requirements but there can be other instances. Many of the
cases in which the dummy speciﬁcation is preferred relate to Seasonal gap Seasonality signiﬁcant Seasonal
Uganda (beans, maize, matoke, oranges and tomatoes), an equato- (%) (%) R2
rial country where double cropping is possible for many crops. Tomatoes 60.8 64.0 0.21
There are relatively few instances in which this speciﬁcation is pre- Plantain/matoke 49.1 66.7 0.32
Oranges 39.8 50.0 0.16
ferred for cassava, millet and sorghum where seasonal patterns are
Maize 33.1 93.2 0.25
less well deﬁned – see Table 6, column 3. Bananas 28.4 39.1 0.13
Based on these preferred speciﬁcations for each commodity- Teff 24.0 100.0 0.15
location pair crude seasonal gaps are calculated in the wholesale Beans 22.9 81.7 0.21
and retail markets and averaged by crop across all locations in Sorghum 22.0 48.2 0.15
Millet 20.1 41.3 0.16
the country (Appendix Tables A1 and A2). We report the propor- Cassava 18.8 26.9 0.08
tion of cases in which the seasonality is statistically signiﬁcant Rice 16.6 68.2 0.17
(i.e. null hypothesis of no seasonality rejected at the 5% level) in Cowpeas 17.6 27.8 0.09
parentheses. These tests are correctly sized and a high proportion Eggs 14.1 64.0 0.18
of locations in which seasonality is signiﬁcant can be taken as an Average 28.3 59.3 0.17
indication of the existence of seasonality.20 Yet, potential overesti- The table reports the regression estimates of the average seasonal gap in wholesale
mation of the extent of that seasonality cannot be fully excluded, markets, the proportion of locations for which the preferred gap estimate is based
especially for commodity-locations pairs where samples are short. on coefﬁcients which are signiﬁcant at the 95% level and seasonal R2 by crop. The
The predominant use of parsimonious speciﬁcations helps mitigate averages reported in the bottom row of the table are the unweighted averages
across crops.
against such bias.
Because the sample size mainly varies by country (Table 5), the
spective. Yet substantial price seasonality could still ensue, for
seasonality estimates for the different commodities can be par-
example if their consumption is mainly countercyclical (high when
tially purged from potential overestimation by regressing the
other staple foods are expensive and low when they are cheap) and
1053 estimated gaps for each commodity-location pair on the
storage is difﬁcult.
commodity type, the nature of the market (retail/wholesale), and
Among the cereals, maize shows the highest seasonal gap (33.1
a set of country dummies.21 The average estimated seasonal gaps
percent on average), and rice the lowest (16.6 percent). Seasonality
for each commodity are reported in Table 6 (controlling for the nat-
is signiﬁcant in the vast majority of the markets in both cases, con-
ure of the market and country effects), together with the share of
ﬁrming the existence of seasonality. Moreover, with peak prices
locations in which the null of no seasonality is rejected.
across locations on average 33.1 percent higher than during the
Fruits and vegetables (tomatoes, plantain and oranges) display
trough, seasonality in maize prices is substantial, and about twice
the highest seasonal gaps (60.8, 49.1 and 39.8 percent respec-
as high as this of rice, whose seasonal gap is estimated at 16.6 per-
tively). This is intuitive, especially for tomatoes and oranges. They
cent. Higher seasonality of maize among the cereals could also be
are highly perishable and their production is season-bound. Cas-
expected, given lower storability and greater post-harvest loss
sava and eggs, which are produced throughout the year, are among
than millet and sorghum (World Bank, 2011). With Africa a grow-
the commodities with the lowest seasonality. Furthermore, cassava
ing importer of rice (which is becoming more important in the
can be stored underground and harvested throughout the year, as
urban diets), rice markets are more closely linked with the interna-
needed. The high seasonal gap for plantain (and also bananas),
tional markets. Part of African rice production is also irrigated. The
which are also perennials, is somewhat surprising from this per-
other cereals (teff, sorghum, millet) have seasonal gaps of around
20–24 percent. They tend to store better—they have smaller grains
20
That said, a high rejection rate of seasonality may follow also from small sample and are cultivated in dryer areas. On average, seasonal gaps are 3.4
size (false negatives).
21
percent higher in wholesale than in retail markets. This is in line
We also experimented by adding a variable measuring the number of observa-
tions available for the estimation of the seasonal gap. This variable is correlated with
with experience in developed economies where a substantial pro-
the country dummies making it difﬁcult to extract country effects. The results portion of the value of retail products is generated by transport
reported here omit this sample size variable. costs and by labor costs in retailing.
128 C.L. Gilbert et al. / Food Policy 67 (2017) 119–132
Table 7 further shows the estimated country effects, with the Table 7
caveat that they reﬂect both the country effects and potential short Average estimated seasonal gap and seasonal R2 by country.
sample bias.22 Niger, Burkina Faso, Malawi and Ghana are associated Seasonal gap (%) Seasonality signiﬁcant (%) Seasonal R2
with the highest average seasonal gaps, all in excess of 30 percent at Burkina Faso 33.2 54.8 0.21
the wholesale level. Ethiopia has the lowest average gap at approx- Ethiopia 14.5 77.5 0.15
imately 15 percent. Tanzania and Uganda, which also have the long- Ghana 31.4 36.9 0.13
est samples, are intermediate at around 25 percent. The ﬁndings for Malawi 34.0 70.8 0.19
Niger 36.6 64.5 0.28
Niger and Burkina are intuitive and consistent with other studies.23 Tanzania 24.4 59.8 0.09
Dryland agriculture is predominant in both countries and the raining Uganda 23.7 65.5 0.16
season short (and erratic). The large gap observed in Ghana is less Average 28.3 61.4 0.17
expected, however, and may be related to the short duration of the
price series (only 6 years at most) implying higher potential bias. The table reports the regression estimates of the average seasonal gap in wholesale
markets, the proportion of locations for which the preferred gap estimate is based
Ghana also displays the largest proportion of locations where its sea-
on coefﬁcients which are signiﬁcant at the 95% level and seasonal R2 by country.
sonality is not statistically signiﬁcant (Appendix Tables A1 and A2). The averages reported in the bottom row of the table are the unweighted averages
Seasonal gaps measure the extent of seasonality. A second ques- across crops.
tion posed in the introduction was that of the share of monthly
price variation attributable to seasonality. This share is measured African seasonal R2 coefﬁcients for maize and rice are an order
by the seasonal R2 which is simply the standard regression R2 in higher than those for the corresponding world markets (6.0 percent
Eqs. (9), (12) or (14), depending on the speciﬁcation. Among crops, for SAFEX maize and 2.2 percent for Bangkok rice).
plantain/matoke and maize show the largest (0.32 and 0.25 respec- Fourth, how widespread is excess seasonality? Figs. 4 and 5 give
tively) and cassava and cowpeas the lowest seasonal R2s (0.08 and a visual summary of the maize and rice seasonal gap distributions
0.09 respectively) – see Table 6. Across countries seasonality in each of the seven countries relative to the respective interna-
appears to explain around 17 percent of overall price variability.24 tional reference market. The vertical lines measure the range of
It increases to 27.7 and 21.3 percent in Niger and Burkina Faso seasonal gaps across markets in each country, i.e. the distance
respectively, where agriculture is also mainly rain-fed and highly between the largest and smallest gap, while the rectangles demar-
seasonal. While the bulk of intra-annual price variability is not cate the interdecile range between the 20 percent and 80 percent
related to seasonal ﬂuctuations, for a number of crops (maize) and points in the gap distribution. Seasonality is larger than in the
countries (especially in the Sahel), its contribution appears nonethe- international reference market in virtually all of the 133 wholesale
less non-negligible. maize and 107 wholesale rice markets examined. There are only
Thirdly, we ask whether the seasonality we ﬁnd in African food two centers where the estimated gap for maize is lower than the
markets is excessive? Some seasonality in prices is to be expected SAFEX gap of 12.2 percent (Ho in Ghana and Niamey in Niger)
when production is seasonal, given storage costs. But what should and three where the gap is lower than the 5.1 percent gap in the
count as excessive? Most of the products considered are non- Bangkok spot market for rice (Santhe, Lizulu and Neno, in Malawi).
traded in the sense that only small quantities cross national bor- The occurrence of excess seasonality is widespread. Nonetheless,
ders. However, this is not true of either maize or rice and for these there is also substantial variation in the extent of seasonality
two commodities the national seasonal gaps can be compared with across locations within countries, as in Malawi, Ghana and Tanza-
those on the relevant international market. White maize predom- nia (for both maize and rice). This counsels caution against over-
inates in human consumption through most of Africa rather than generalization from case studies and underscores the need for
the yellow maize typically consumed in the developed world. differentiated and targeted interventions.
The Johannesburg futures market (SAFEX) provides the reference Fifth, at 50.6 percent on average (Table A1), maize price season-
price for white maize in southern and east Africa. This price is ality is particularly striking in Malawi. Households appear to suffer
quoted in rand. For rice, the most commonly used reference price a double seasonality impact – the main staple food is maize which
is the Bangkok spot price (5 per cent broken) which is quoted in has the highest seasonal gap among the cereals (Table 6) and there
US dollars. In both cases, we use monthly prices over the 13 year is a large country effect (Table 7). From this perspective, the atten-
period 2000–12.25 tion in the seasonality literature to this speciﬁc country-crop pair
Seasonality is well deﬁned in both price processes, with the does not surprise– see for example Manda (2010), Chirwa et al.
dummy variables speciﬁcation preferred in each case. The esti- (2011) and Ellis and Manda (2012).
mated seasonal gaps are 12.2 percent for SAFEX white maize and But is the Malawi effect an exception? Put differently, to what
5.1 percent for Bangkok rice.26 These statistics are to be compared extent is the variability of seasonal gaps affected by national
with the average maize and rice seasonal gap estimate of 33.1 per- boundaries (to be distinguished from overall country effects). An
cent and 16.6 percent respectively. In both cases, seasonality is on analysis of variance exercise, reported in Table 8, casts light on this
average two and a half to three times as acute in local African mar- question. This shows that 30.4 percent of the variation of the pre-
kets as on the relevant international market. Moreover, the local ferred seasonal gap measure is attributable to the crop, 14.5 per-
cent to the (market) location and only 0.5 percent to the country
and 0.4 percent to the market level (wholesale or retail).
22
The average statistics reported in the ﬁnal row of Table 7 may differ from those in Country-speciﬁc variation is not statistically signiﬁcant.
the ﬁnal row of Table 6 because of differences in the number of reporting locations in Looking at each crop separately we ﬁnd statistically signiﬁcant
each country and for each food crop. country differences only for maize and plantain, while most
23
Using simple monthly averages of the 1996–2006 real prices, Aker (2012) also
seasonality is attributable to market location.27 This suggests that
reports a high seasonal gap of for millet in Niger (44%).
24
These statistics may show an upward bias in small samples (Section 3), though differences in seasonality arising from geographical location are
the country ﬁxed effects also helped control for this. likely to be caused more by transport factors than by differences
25
Sources: Johannesburg Stock Exchange, https://www.jse.co.za/downloadable-
ﬁles?RequestNode=/Safex/PriceHistory/Spot%20Months%20on%20all%20Grain%
27
20Products and IMF, International Financial Statistics. This analysis requires data at both the retail and the wholesale level for at least
26
In Kaminski et al. (2016) we used a slightly different model selection criterion one country. This prevents our performing this analysis for bananas, eggs, oranges,
which favored the dummy speciﬁcation for these two price series. This gave slightly teff and tomatoes. For maize, we have gap estimates for all seven countries under
narrower seasonal gaps. analysis while for plantain information is conﬁned to Ghana and Uganda.
C.L. Gilbert et al. / Food Policy 67 (2017) 119–132 129
Fig. 4. Seasonal gaps for wholesale maize.
Fig. 5. Seasonal gaps for wholesale rice.
in government policies at the national level, the single important meteorological conditions are similar. Mbeya, which is the capital
exception being for maize where, controlling for the market level of the Tanzanian region (mkoa) of the same name contiguous with
(wholesale versus retail) the Malawian seasonal gap averages 23 the border with Malawi, exhibits a maize seasonal gap of 22.8 per-
percent higher than the average of the other countries. cent. Chitipa (143 km from Mbeya, maize seasonal gap 48.3 percent),
We performed two exercises in order to further explore the Karonga (161 km, 74.8 percent) and Misuku (180 km, 71.6 percent)
Malawian maize seasonal gap. First, using real local maize are the closest locations on the Malawian side of the border.29 Maize
prices for Malawi spanning 23 years (1989–2012) instead of 8 price seasonality appears to change dramatically over these relatively
(2005–2012), the preferred seasonal gap estimate is 39.5 percent short cross-border differences.
(instead of 50.6 percent, Table A1).28 The lower ﬁgure may in part The prevalence of high seasonal gaps throughout Malawi
reﬂect the use of deﬂated prices. Irrespectively, it remains higher together with the sharp drop in the gap as one moves north into
than the wholesale estimates for all the other countries in our sam- Tanzania suggests that the high Malawian gaps are the results of
ple. Second, we compared the maize gaps across locations on both political or institutional factors speciﬁc to the country rather than
sides of the Malawian and Tanzanian borders where cultivation and agroeconomic factors. To that extent, it should be possible to
reduce some of the more extreme instances of seasonal price vari-
28
The price data are from the dataset used by Dana et al. (2006). Given rapid
inﬂation in Malawi during the 1990s, prices were deﬂated by the CPI (IMF,
29
International Financial Statistics). Quoted distances are the distances for the fastest road connections.
130 C.L. Gilbert et al. / Food Policy 67 (2017) 119–132
Table 8
Analysis of variance.
Crop Retail/wholesale Country Market location Observations R2
⁄⁄⁄ ⁄⁄ ⁄⁄⁄
All 30.4% 0.4% 0.5% 14.5% 1053 52.2%⁄⁄⁄
Beans – 5.2%⁄⁄⁄ 0.6% 76.3%⁄⁄⁄ 121 76.3%⁄⁄⁄
Cassava – 0.3% 0.1% 91.7%⁄ 106 91.7%⁄
Maize – 0.7%⁄⁄ 3.7%⁄⁄⁄ 50.8%⁄⁄⁄ 202 96.4%⁄⁄⁄
Millet – 0.3% 2.0% 40.2% 131 40.2%
Plantain – – 13.0%⁄⁄ 71.0% 28 98.1%⁄
Rice – 0.3% 0.2% 88.5%⁄⁄⁄ 135 88.5%⁄⁄⁄
Sorghum – 0.5% 0.5% 51.0%⁄ 106 51.0%⁄⁄
The ﬁrst row of the table reports a four way analysis of variance of the preferred measure of the seasonal gap for the complete set of food commodities analyzed in the paper
(the listed commodities plus bananas, eggs, oranges, teff and tomatoes). The remaining rows report the three way analysis of variance (two way for plantain) for those
commodities there is sufﬁcient variation to calculate signiﬁcance tests. In each case, the reported statistic is the proportion of the variance attributable to the factor.
⁄⁄⁄ ⁄⁄
, and ⁄ indicate signiﬁcance at the 99%, 95% and 90% levels respectively.
ation in Malawi, including by facilitating cross-country trading, and which can be stored in the ground (cassava). Among the cere-
which would also beneﬁt Tanzania.30 als, seasonality is highest for maize (33.1 percent), about half this
for rice (16.6 percent), which is more irrigated and traded interna-
6. Concluding remarks tionally, and around 20–24 percent on average for millet, sorghum
and teff (which store better than maize). These averages hide sub-
As development practitioners and economists, we are all well stantial differences across markets within countries, cautioning
aware of seasonality in African livelihoods, much of it originating against generalizations from non-representative samples, and
from seasonality in food prices. At the same time, it is unclear what highlighting the need for targeted interventions (e.g. when provid-
exactly it is we know. The issue has somewhat disappeared to the ing better storage facilities).
background during the 2000s and an updated and systematic Third, African seasonal price variability appears substantially
review of its extent, especially in the African context, has been higher than this observed internationally. Looking at both maize
missing. In addition, most of our empirical knowledge has been and rice, for which there are well-deﬁned international reference
based on very short samples and (purposively sampled) case stud- prices, the seasonal price gap is two and a half to three times
ies, often confounding intra-annual variation with seasonality and higher than on the international reference markets. This suggests
generalizing from a non-representative base. substantial scope for reduction.
This paper has contributed to extending what we know about Fourth, price seasonality explains on average about 17 percent of
seasonality, both by revealing some of the shortcomings in the domestic staple crop volatility, rising to 25 percent for maize.
standard practice of measuring it, as well as by systematically Clearly, domestically, there is substantial regularity in price volatil-
examining the extent of price seasonality in Africa using a uniform ity, especially for maize. Internationally, the share is only 6 percent.
methodological approach. In total, the seasonal price gap was esti- Finally, seasonal gaps vary more according to the identity of the
mated across thirteen staple and non-staple crops/products in crop than the location at which the price is measured. Looking at
seven countries from across southern, eastern and western Africa each food crop separately, there is only evidence of statistically sig-
during the 2000s and early 2010s, yielding a total of 1053 niﬁcant country-speciﬁc variation in seasonal gaps for maize and,
location-commodity pairs. Five key insights emerge, with impor- to a lesser extent, plantain. Speciﬁcally, Malawi stands out as hav-
tant implications for further empirical work and policy orientation. ing the highest maize seasonal gaps both in terms of statistical cri-
First, on methodology, the simple, most widely used (monthly) teria and in cross-border comparisons with neighboring locations
dummy variables and moving average deviation approaches to in Tanzania.
measuring the seasonal price gap overestimate the extent of price Together these ﬁndings indicate that the current neglect of sea-
seasonality. This holds especially when the samples are short (up sonality in the policy debate is premature. First, the results under-
to 15 years), when the peak and trough months are not known a score the importance of correcting for seasonality in food prices
priori and when the seasonal pattern is either unclear or absent. when constructing welfare and poverty measures, a largely ignored
With short samples of data, the trigonometric and sawtooth mod- issue among poverty measurement practitioners so far – see Muller
els, which are less ﬂexible, but more parsimonious, can produce (2002) and Van Campenhout et al. (2015). Second, they suggest
substantially more accurate estimates of the seasonal gap (8–9 important welfare losses for the large share of (often poor) net food
percent lower than those found using the dummy variable model, buying households even in the rural areas, where they frequently
as illustrated through Monte Carlo simulations). Caution is war- engage in sell-low, buy-back high behavior (Stephens and Barrett,
ranted in using dummy variable models in future empirical work 2011; Palacios-Lopez et al., 2015). Third, this suggests important
to estimate the seasonal gap, especially when less than 15 years gains from better post-harvest storage techniques through
of (monthly) price data are available and the peak and trough exploitation of the seasonal price differentials (Gitonga et al., 2013).
months are not a priori known. Whether food price seasonality also translates into seasonal
Second, turning to the ﬁndings, food price seasonality in Africa declines in the quantity and quality of diets and nutritional
remains substantial (despite the somewhat lower estimates than outcomes, will depend on a series of other factors such as the sub-
those reported in the literature). It is also quite diverse across stitutability among crops, the net marketing position of house-
crops, regions and market places. Looking across commodities holds, their access to ﬁnancial markets, and their capacity to
and countries, the average seasonal gap is 28.3 percent. It is highest store crops. Establishing the link between price and consumption
for fruits and vegetables (60.8 percent for tomatoes) which are seasonality was beyond the scope of this paper. Yet the levels of
highly perishable and whose production is seasonal, and lowest staple price seasonality documented here, the recent reconﬁrma-
for eggs and cassava, which are harvested throughout the year tion of continued seasonality in African diets (Savy et al., 2006;
Becquey et al., 2012; Hirvonen et al., 2015) and the adoption of
30 the Zero Hunger goal provide an important impetus as well as
For Tanzania, Baffes et al. (2015) demonstrate for example an adverse effect on its
own maize markets of its intermittent imposition of its export bans. building blocks for further research into these topics.
C.L. Gilbert et al. / Food Policy 67 (2017) 119–132 131
Appendix A
See Tables A1 and A2.
Table A1
Seasonal gap estimates and statistical signiﬁcance (wholesale markets).
Burkina Faso Ethiopia Ghana Malawi Niger Tanzania Uganda
Bananas (sweet) 9.1% (20%) 48.6% (54%)
Beans 27.7% (77%) 23.2% (90%) 28.1% (100%)
Cassava 19.2% (8%) 26.6% (28%) 20.1% (50%)
Cowpeas 14.5% (7%) 47.5% (100%)
Eggs 14.3% (100%) 7.2% (36%)
Maize 26.9% (56%) 19.8% (100%) 38.0% (71%) 50.6% (100%) 20.1% (100%) 29.4% (100%) 31.1% (88%)
Matoke/Plantain 61.5% (69%) 28.8% (63%)
Millet 23.4% (64%) 9.2% (21%) 20.2% (23%) 19.0% (75%)
Oranges 21.0% (51%) 33.6% (46%)
Rice 18.4% (15%) 19.9% (73%) 19.9% (85%) 12.5% (75%)
Sorghum 24.7% (45%) 13.6% (80.0%) 11.8% (21%) 14.5% (23%) 22.6% (100%)
Teff 10.3% (100%)
Tomatoes 36.3% (73%) 98.0% (57%)
The table reports averages of the seasonal gap estimates for each country-commodity pair in wholesale markets irrespective of statistical signiﬁcance using the preferred gap
estimates Numbers in parentheses show the proportion of locations for which the preferred gap estimate is based on coefﬁcients which are signiﬁcant at the 95% level.
Ethiopia: teff refers to white teff.
Ghana: rice refers to locally produced rice; plantain is ap’tu plantain; bananas are ap’em plantain.
Table A2
Seasonal gap estimates and statistical signiﬁcance (retail markets).
Burkina Faso Niger Tanzania Uganda
Bananas (sweet) 16.1% (20%) 12.9% (25%)
Beans 12.4% (60%) 28.7% (100%)
Cassava 18.9% (20%) 10.0% (13%)
Cowpeas 41.3% (100%) 5.7% (100%)
Eggs 4.6% (13%)
Maize 62.4% (80%) 22.8% (50%) 13.5% (75%)
Matoke/ Plantain 42.1% (100%)
Millet 30.9% (95%) 28.5% (100%) 10.1% (0%) 8.6% (38%)
Oranges 37.2% (80%) 40.2% (100%)
Rice 17.3% (95%) 13.4% (75%)
Sorghum 33.2% (88%) 20.6% (100%) 40.4% (100%)
Tomatoes 42.2% (75%) 36.8% (63%)
The table reports averages of the seasonal gap estimates for each country-commodity pair irrespective of statistical signiﬁcance in retail markets using the preferred gap
estimates. Numbers in parentheses show the proportion of locations for which the preferred gap estimate is based on coefﬁcients which are signiﬁcant at the 95% level.
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