Demand analysis for selected roots and tubers among urban households of Nakuru County, Kenya

Abstract

This study examines Kenya’s demand for selected roots and tubers (R&Ts). Data used for the analysis were collected from Nakuru Town East Sub-County. A sample unit of 385 urban households was interviewed at the market outlet immediately after purchasing R&Ts. Linear Approximated Almost Ideal Demand System (LA/AIDS) model was used to estimate demand elasticities, demographics and social-economic factors influencing the consumption patterns of R&Ts. Age, education, household size, and proportion of household members statistically and significantly explained the variations in R&Ts consumption patterns. Empirical results showed negative own-price elasticities for uncompensated and compensated demand analyses, therefore in line with utility theory. Cross-price elasticities had positive and negative signs, indicating the presence of substitutes and complements respectively among R&Ts. Expenditure (income) elasticities for R&Ts had mixed signs ranging from elastic to inelastic. Irish potato and sweet potato were inelastic with a positive sign classifying them as necessities goods. Cassava and yam were inelastic with a negative sign indicating they were inferior goods, while arrowroot was positive and elastic, therefore a luxury good. These results are broadly consistent with microeconomic theory; consequently, they could inform the formulation of effective policies and strategies that promote R&Ts consumption thereby contributing to food and nutritional security among households.

Keywords:

• Budget shares
• consumer demand
• household consumption
• linear approximated almost ideal demand system
• root and tuber crops

PUBLIC INTEREST STATEMENT

Roots and tubers (R&Ts) are affordable and cheap sources of carbohydrates, vitamins A, B, and C, and essential elements; iron, zinc, and calcium, and serve as staple foods worldwide. In this paper, we show the factors influencing demand for R&Ts among urban consumers who are most vulnerable. This is significant because it seeks to encourage their consumption, especially by the urban poor. We also believe that the findings presented in this paper will appeal to the general public to enhance R&Ts demand. The estimates in this paper add to the growing literature on root and tuber demand using the LA-AIDS framework. LA-AIDS model showed that the own-price elasticities of the selected five root and tubers are valued to be negative, meaning that every price increase will reduce the demand. Moreover, cross-price elasticities are a mixture of positive and negative values, implying the R&Ts are a mixture of substitutes and compliments.

1. Introduction

The importance of roots and tubers (R&Ts) in income generation, sustainable development, and food and nutrition security cannot be overemphasized, especially in tropical countries. In most developing countries, R&Ts are the second most important crop after cereals (Kennedy et al., 2019), contributing to the global food systems (Wijesinha-Bettoni & Mouillé, 2019). They are cheap sources of carbohydrates, vitamins A, B, and C, and essential elements; iron, zinc, and calcium, and serve as staple foods worldwide (Dotto et al., 2018). They store carbohydrates as starch in roots, tubers, corms, rhizomes, and stems consumed as human food, animal feeds, and raw materials in agro-based industries.

In the past few decades, R&Ts production has been increasing, especially in Sub-Saharan Africa (SSA) (Polar et al., 2022; Rusike et al., 2010; Scott, 2000). Moreover, by 2050, the global production of R&Ts is projected to increase by 50%, especially in developing countries (Rosegrant et al., 2017; Thiele & Friedmann, 2020). This increase will be driven by the ability of these crops (cassava, arrowroot, and sweet potato) to grow under harsh climatic conditions, which gives them a competitive edge over other foods therefore consumed as “famine reserve” crops (Petsakos et al., 2019). Their demand among households in many developing countries increases during the famine season as complements or substitutes to scarce staple cereals. The perception that R&Ts are healthy, nutritious, and supply high energy per unit consumed than cereals further increases their demand among the undernourished population who derive 50% of their daily calorie intake from R&Ts consumption (FAO, 2017). Further, the demand for R&T is fuelled by the increasing population growth, urbanisation, and shifts in lifestyles as households seek to bridge the nutritional gap created by the food demand deficit. R&T are often used as cheaper sources of carbohydrates, vitamins, and minerals (Rosegrant et al., 2017; ; Scott et al., 2000).

Despite the highlighted benefits from R&Ts in meeting food requirements, their demand in Kenya is still below the country’s potential (MoALFI, 2019). Moreover, there is insufficient data on current demand for R&Ts. Producers respond to market forces by reducing the production of agricultural commodities when the demand is low. For instance, proxy measures reveal that lack of market for cassava constrains its production by 13–23% (Githunguri & Njiru, 2021). This could be attributed to their bulkiness, perishability, fear of cyanide poisoning (a toxic substance) produced by cassava, and shifts in consumption trends from traditional meals favouring more conveniently prepared alternatives.

Several studies have been conducted on food demand patterns (Gabriel et al., 2017; Korir et al., 2020; Musyoka et al., 2010, 2014). Moreover, demand analysis in most studies has mainly been biased towards aggregate food items than single foods. Few of these studies have focussed on R&Ts demand (Rono et al., 2017; Rozi et al., 2021). Though R&Ts play a significant role in Kenya’s economic growth, development and food and nutrition security, systematic studies have not assessed demand for these crops among urban dwellers. Their actual contribution to the shift in demand among urban households remains unaccounted for due to a lack of consumption data. From the foregoing, this study intends to fill this knowledge gap by evaluating the effect of demographic variables, price, and expenditure elasticities on household demand for selected R&Ts among households. Irish potatoes (Solanum tuberosum L.), sweet potatoes (Ipomoea batatas L. Lam.), cassava (Manihot esculenta Crantz), arrowroots (Maranta arundinacea L.), and yams (Dioscorea alata L.) were selected for this study because they are the main R&Ts commonly produced and consumed in Kenya (MoALFI, 2019). This study’s findings could inform the formulation of relevant policies for the R&Ts subsector that promotes their consumption.

2. Materials and methods

2.1. Study area and sampling design

The study was conducted in Nakuru town east sub-county in Nakuru county, Kenya. Approximately, the sub-county covers an area of 230.9 square km with 193,926 inhabitants and a population density of 840 persons per square km (KNBS, 2019). The sub-county is subdivided into five wards¹ and enjoys a temperate climate all year round. The sub-county relies on food supplies from other regions since agriculture is not the mainstay activity and this was the main reason why the study area was selected.

Data were collected from selected urban dwellers using a stratified multistage sampling technique. The first stage purposively selected Nakuru County because of consumers’ heterogeneity. Nakuru Town East Sub-County was purposively selected in the second stage because it hosts the highest number of market outlets for R&Ts. In the third stage, the chosen market outlets were stratified into three (supermarkets, organised open-air markets, and roadside stalls) across all five wards of Nakuru Town East Sub County.

A mixed sampling technique was used in the fourth stage and conducted in two levels. Judgmental sampling was used in the first level because of the infinite population distribution of R&Ts consumers in the study area (Kothari, 2004). Respondents were deliberately and evenly distributed across selected market outlets in all wards. Random sampling was adopted in the second level, where an equal number of respondents were chosen from each market outlet across wards. Kothari (2004) approach was used to obtain 385 respondents distributed evenly across market outlets for all wards. Respondents were interviewed using semi-structured questionnaires at the market outlets immediately after purchasing R&Ts.

Information on gender, age, education level, household size, the proportion of household members 18 years and below, the proportion of household members 19 years and above, R&Ts real monthly expenditure, and R&Ts retail prices were obtained from the respondents. Using IBM SPSS Statistics 20 (IBMCorp, 2011) data analytical software, the collected data were coded and data entry errors removed. The data were transferred to Stata 12 (StataCorp, 2014) computer program for econometric analysis.

2.2. Demand systems estimation approach

Demand studies involve the use of either a single equation or systems approach. However, the systems approach has proved to be superior to single-equation approach. The systems approach consists of several equations, each representing one of the selected five R&Ts allowing for commodity substitution. The systems approach can be modelled as a Linear Expenditure System (LES), an Almost Ideal Demand System (AIDS), and Quadratic AIDS (QUAIDS) models. The AIDS model is preferred because it allows for approximate aggregation over consumers while at the same time retaining the theoretical features of flexibility (A. Deaton & Muellbauer, 1980) and its linear approximate version, the LA/AIDS is more flexible, easy to estimate, and interpret (Alston & Chalfant, 1993; Taljaard et al., 2004). Nonetheless, AIDS is criticised because it linearises Engel curves, but the Quadratic Almost Ideal Demand System (QUAIDS) solves this problem. However, the linear estimation systems have some advantages over the nonlinear systems in empirical works hence the main reason for the continued use of LA/AIDS. For instance, nonlinear parameters are problematic when taking differences to remove nonstationarity in time series (Matsuda, 2006). Unless linearly estimated, nonlinear models AIDS and QUAIDS cannot be used to analyse nonstationary variables such as cointegration (error correction model).

This study used a multistage budgeting approach where the household first allocates its income as per its total expenses over a broad category of commodities (food and non-food items). Thereafter, it allocates the respective income proportions to various subcategories of the previous broad categories (Bett et al., 2012; Edgerton, 1997). To estimate the demand for the selected R&Ts, this study adopts the linear approximated almost ideal demand system (LA/AIDS) model. During the demand analysis, the weak separability assumption was considered viable; therefore, tested. Further, R&Ts were considered a separable subcategory of the food category cascaded at the third budgeting stage. The LA/AIDS model follows the specification made by Deaton and Muellbauer (19).

The estimation was done in two stages because of the infrequent consumption of R&Ts in the data. The first stage estimated the decision to purchase within a Probit model, and the second stage estimated the inverse Mills ratios (IMRs) from Probit parameters. This is comparable to Heckman’s two-step model that corrects selectivity bias (Heckman, 2013). The AIDS model incorporated the estimated IMRs obtained from the first stage (of the Probit model) as an instrumental variable in the second stage of estimation. Demographic and socio-economic characteristics were added to the budget share equation to capture the differences in tastes and preferences across households (Deaton & Muellbauer, 1980; Pollak & Wales, 1981; Willemé, 2008). The share equation based on the AIDS model is specified in Equation 1(1) $w_i={\alpha }_i+\sum _j{\gamma }_{ij}\mathrm{I}\mathrm{n}\left(p_j\right)+{\beta }_i\mathrm{I}\mathrm{n}\left(\frac{x}{P}\right)+\sum _k{\gamma }_k{Z}_k+{\omega }_i\mathrm{I}\mathrm{M}{\mathrm{R}}_i+{\epsilon }_i,$(1) ;

(1) $w_i={\alpha }_i+\sum _j{\gamma }_{ij}\mathrm{I}\mathrm{n}\left(p_j\right)+{\beta }_i\mathrm{I}\mathrm{n}\left(\frac{x}{P}\right)+\sum _k{\gamma }_k{Z}_k+{\omega }_i\mathrm{I}\mathrm{M}{\mathrm{R}}_i+{\epsilon }_i,$(1)

where $(i,j)$ represents the five R&T crops, $w_i$ is the budget share of the $i^{th}$ R&T crop derived as $w_i=\frac{p_i{q}_i}{x},w_{i}isalreadydefined$, $q_i$ is the quantity of R&T $i$ purchased, $p_j$ is the price of $j^{th}$ R&T, and $x$ is the total expenditure of all R&Ts. $Z_k$ represents demographic and socio-economic characteristics, $\mathrm{I}\mathrm{M}{\mathrm{R}}_i$ is the inverse mills ratio, ${\epsilon }_i$ is random variable with zero mean and constant variance. The $P$ is Stones Price Index for aggregate food. This Stones Price Index was corrected for units of measurement invariance following Moschini (1995) approach shown in Equation 2(2) $\mathrm{I}\mathrm{n}\left(P\right)=\sum _i\bar{w}\mathrm{I}\mathrm{n}\left(p_i\right)$(2) ;

(2) $\mathrm{I}\mathrm{n}\left(P\right)=\sum _i\bar{w}\mathrm{I}\mathrm{n}\left(p_i\right)$(2)

where $\bar{w}$ represents the mean budget share. To comply with the basic demand theory, adding up, homogeneity, and Slutsky symmetry restrictions (Deaton & Muellbauer, 1980), are imposed as follows;

(3) $\sum _i\alpha =1\sum _i\gamma ij=0\sum _i{\beta }_i=0\sum _i{\omega }_i=0$(3)

(4) $\sum _i{K}_{ki}=0,\hspace{0.17em}j=1,\dots ,n\left(\mathrm{A}\mathrm{d}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{u}\mathrm{p}\right)$(4)

The adding-up restriction ensures that the expenditure shares always sum to one/unity.

(5) $\sum _k{\gamma }_{jk}=0,\hspace{0.17em}j=1,\dots ,n\left(\mathrm{H}\mathrm{o}\mathrm{m}\mathrm{o}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{i}\mathrm{t}\mathrm{y}\right)$(5)

Homogeneity restriction ensures that there is no “money illusion”, that is, if all prices and income change at the same rate, then the consumed quantities do not change.

(6) ${\gamma }_{ij}={\gamma }_{ji}\left(\mathrm{S}\mathrm{y}\mathrm{m}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{y}\right)$(6)

Also, negativity is tested after estimating the compensated own price elasticities (Green & Alston, 1990; Hayes et al., 1990). Therefore, the expenditure elasticity is estimated as shown in Equation 7(7) $e_i=1+\left(\frac{i}{{\bar{w}}_i}\right)\left(\frac{\mathrm{\partial }{\bar{w}}_i}{\mathrm{\partial }logx}\right)=1+\left(\frac{{\beta }_i}{{\bar{w}}_i}\right).$(7) ;

(7) $e_i=1+\left(\frac{i}{{\bar{w}}_i}\right)\left(\frac{\mathrm{\partial }{\bar{w}}_i}{\mathrm{\partial }logx}\right)=1+\left(\frac{{\beta }_i}{{\bar{w}}_i}\right).$(7)

The Marshallian/ Uncompensated Price Elasticities are estimated as;

(8) $s_{ii}^M=-1+\left(\frac{{\gamma }_{ii}}{{\bar{w}}_i}\right)-{\beta }_i\left(\mathrm{O}\mathrm{w}\mathrm{n}-\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\right)$(8)

(9) $\begin{array}{rl}& s_{ij}^M=-{\delta }_{ij}+\left(\frac{{\gamma }_{ij}}{{\bar{w}}_i}\right)-\left(\frac{{\beta }_{ij}}{{\bar{w}}_i}\right){\bar{w}}_j,\left(\mathrm{C}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}-\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\right)\\ & \mathrm{\forall }i,j=1,\dots ,n\end{array}$(9)

where ${\delta }_{ij}$ is a Kronecker delta that equals 1, for $i=j$, otherwise zero, while the Hicksian elasticities are obtained from, $s_{ij}^H=s_{ij}^M+e_i{\bar{w}}_i$ and $s_{ij}^H=s_{ij}^M+e_i{\bar{w}}_j$ is as follows;

(10) $s_{ii}^H=-1+\left(\frac{{\gamma }_{ii}}{{\bar{w}}_i}\right)-{\bar{w}}_i\left(\mathrm{O}\mathrm{w}\mathrm{n}-\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\right)$(10)

(11) $\begin{array}{rl}& s_{ij}^H=-{\delta }_{ij}+\left(\frac{{\gamma }_{ij}}{{\bar{w}}_i}\right)\hspace{0.17em}j=1,\dots ,n\left(\mathrm{C}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}-\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\right)\\ & \mathrm{\forall }i,j=1,\dots ,n\end{array}$(11)

The estimation process was performed through seemingly unrelated regression (SURE), an iterative estimation model (Zellner, 1962). Because the budget shares add up to unity in the demand system, the share equation for cassava was dropped to avoid error covariance matrix singularity. The dropped equation was recovered from the imposed restrictions on the LA/AIDS model (1). The SURE system parameter estimates in this study were obtained using Stata 12 (StataCorp, 2014) econometric software under constrained iterated seemingly unrelated regression (ITSUR) procedure. The model’s variables and expected influence were selected from previous studies (Ashagidigbi et al., 2012; Bata et al., 2018; Bett et al., 2012; Gido, 2022; Iorlamen et al., 2014; Kostakis, 2014; Nuani et al., 2022; Tankari & Badiane, 2015).

3. Results

3.1. Descriptive results

Table 1 provides details of the variables used in empirical data analysis. The mean age of decision-makers was approximately 40 years, with an average of 13 years of schooling. Male decision-makers were 47.79%. Households had an average of four family members. Approximately 31% of the family members were below the age of 18 years while 69% were above. On average, 34% of the household’s monthly income was allocated towards purchase of food items.

Table 1. Description of variables and descriptive statistics

Variables	Description of variables and their measurements	Range	Mean
Continuous variables
Age	Average age of the decision-maker^2 in years	18.00–72.00	40.00
Education	Average years of education of the decision-maker	1.00–27.00	13.00
H_size	Average household size	1.00–12.00	4.00
Prop_house1	Proportion of household members 18 years and below	0.00–0.75	0.31
Prop_house2	Proportion of the household members 19 years and above	0.25–1.00	0.69
Prop_incfood	Proportion of monthly income allocated to food items	0.02–0.90	0.34
lnExp	Natural log of R&Ts real^3 monthly expenditure in KES^4	3.25–7.99	5.69
In (p1, … p5)	Natural log price per kilogram of Irish potatoes, Sweet potatoes, Cassava, Arrowroots, and Yams, respectively
IMR	Inverse Mills Ratios
Categorical variableCount Percentage
Gender	Average % of male decision-makers	184	48.00

The results presented in Table 2 show household expenditures on R&T crops. The expenditure share allocation for R&T crops was highest in Irish potato and least in cassava. Similarly, participation (consumption) rates were highest in Irish potato and least in cassava and yam. Sweet potato, arrowroot, and yam had fair shares within the remaining R&T crops. Adding up restriction is confirmed in Table 2, where the sum of mean budget shares for all R&Ts sums up to one.

Table 2. Household expenditure on R&Ts

R&T category	Mean budget shares	Mean expenditure (KES)	Participation rate
Irish potato	0.4211	628.26	77.40
Sweet potato	0.2514	380.52	60.52
Cassava	0.0683	128.70	22.34
Arrowroot	0.1867	394.55	41.56
Yam	0.0725	139.09	22.34

KES refers to Kenyan shilling (official Kenyan currency); exchange rate is 1 $US = KES. 113.05

3.2. Empirical results

3.2.1. Socio-economic and demographic effects

Table 3 presents maximum likelihood estimates for socio-economic and demographic effects. The Chi-square values for all R&Ts equations were significant. The R² for Irish potato, sweet potato, cassava, arrowroot, and yam were 31.67, 26.80, 66.57, 18.21, and 74.87%, respectively. The poor fit was probably due to irregular purchases of some R&Ts. As shown in Table 3, few variables had significant influences on R&Ts budget shares. Statistically significant variables influencing the consumption patterns of R&Ts among urban households of Nakuru Town East sub-county include; Age, education, household size, and proportion of household members.

Table 3. Maximum likelihood estimates of the household socio-economic and demographic effects using LA/AIDS

Share	Age	Gender	Education	H_size	Prop_house1	Prop_house2	Prop_incfood	IMR
Irish potato	−0.070(0.057)	0.033(0.027)	0.058(0.045)	0.007(0.036)	0.642(0.646)	0.857(0.841)	0.010(0.033)	0.275***(0.028)
Sweet potato	0.111**(0.048)	0.032(0.023)	0.064**(0.032)	−0.038(0.032)	0.752(0.562)	0.865(0.732)	0.017(0.028)	0.423***0.043
Cassava	−0.066***(0.020)	−0.005(0.009)	−0.054***(0.013)	−0.039***(0.013)	1.006***(0.233)	1.230***(0.303)	0.009(0.011)	−0.285***(0.011)
Arrowroot	0.049(0.052)	−0.000(0.024)	0.034(0.034)	−0.038(0.034)	0.019(0.603)	−0.058(0.785)	0.003(0.030)	−0.170***(0.028)
Yam	0.022(0.017)	0.009(0.008)	0.019*(0.011)	0.004(0.011)	−0.777***(0.199)	−1.080***(0.260)	0.002(0.010)	−0.316***(0.010)

***, **, * = Significant at 1%, 5%, and 10%, respectively.

The age of the decision-maker (Table 3) significantly influenced shares for sweet potato positively and negatively for cassava. Education significantly and positively influenced the budget shares for sweet potato and yam at 5%, and 10% significant levels respectively and negatively influenced shares for cassava at 1% significant level. Household size had a negative and significant effect on cassava shares at P ≤ 0.01. The proportion of household members aged 18 years and below significantly influenced shares of cassava positively and negatively for yam. The proportion of household members aged 19 years and above had a similar influence on cassava and yam shares at P ≤ 0.01. In contrast, all R&Ts (Irish potato, sweet potato, cassava, arrowroot, and yam) had significant inverse Mills’ ratios (IMRs). Therefore, ignoring non-consumers for these R&Ts during the LA/AIDS estimation would result in biased and inconsistent parameter estimates.

3.2.2. Price and expenditure coefficients

Table 4 presents maximum likelihood estimates for price and expenditure effects on R&Ts budget shares. Results indicate that own-price coefficients for Irish potato, sweet potato, cassava, and arrowroot were positive except for shares allocated to yam. The own prices did not significantly influence budget shares for all R&Ts. However, the cross-prices significantly influenced budget shares for arrowroot and sweet potato at P ≤ 0.05 conforming to the theoretical imposition of symmetry restriction a priori. That is, both cross prices had similar effects of −0.083 at P ≤ 0.05 (Table 4), following symmetry fashion (${\gamma }_{ij}={\gamma }_{ji}$). The expenditure coefficients negatively and significantly influenced budgetary allocations for Irish potato, sweet potato, cassava, and yam, while for arrowroot it was positive at P ≤ 0.01.

Table 4. Maximum likelihood estimates of the R&Ts categories price and expenditure effects using LA/AIDS

	${\alpha }_i$			Prices			${\beta }_{ij}$
R&Ts Shares		Price_irish potato	Price_sweet potato	Price_cassava Price_arrowroot		Price_yam	Expenditure
	(Intercept)	(P1)	(P2)	(P3) (P4)		(P5)	Coef.
Irish potato	0.311(0.624)	0.056(0.085)	0.021(0.046)	−0.028(0.036)	−0.041(0.068)	−0.008(0.032)	−0.127***(0.020)
Sweet potato	−0.589(0.533)	0.021(0.046)	0.065(0.047)	0.001(0.019)	−0.083**(0.042)	−0.004(0.017)	−0.108***(0.017)
Cassava	0.404*(0.214)	−0.028(0.036)	0.001(0.019)	0.023(0.042)	−0.003(0.036)	0.008(0.031)	−0.075***(0.007)
Arrowroot	−0.216(0.569)	−0.041(0.068)	−0.083**(0.042)	−0.003(0.036)	0.098(0.083)	0.028(0.033)	0.053***(0.017)
Yam	1.517***(0.194)	−0.008(0.032)	−0.004(0.017)	0.008(0.031)	0.028(0.033)	−0.025(0.041)	−0.077***(0.006)

***, **, * = Significant at 1%, 5%, and 10%, respectively.

3.2.3. Price and expenditure elasticities

The own prices, cross prices, and expenditure elasticities are presented in Table 5. The price elasticity matrices comprise Marshallian (uncompensated) and Hicksian (compensated) elasticities. Results indicate that all Marshallian own-price elasticities for various R&Ts were negative, less than zero, conforming to utility theory.

Table 5. Price and expenditure elasticities

Expenditure share category	Irish potato	Sweet potato	Cassava	Arrowroot	Yam
Marshallian/uncompensated elasticities
Irish potato	−0.739	0.125	−0.046	−0.041	0.003
Sweet potato	0.263	−0.635	0.033	−0.248	0.017
Cassava	0.048	0.288	−0.594	0.157	0.196
Arrowroot	−0.338	−0.514	−0.037	−0.526	0.131
Yam	0.337	0.216	0.182	0.588	−1.268
Hicksian/compensated elasticities
Irish potato	−0.446	0.301	0.001	0.090	0.054
Sweet potato	0.503	−0.492	0.072	−0.142	0.058
Cassava	0.008	0.264	−0.601	0.139	0.189
Arrowroot	0.202	−0.191	0.051	−0.287	0.224
Yam	0.314	0.202	0.179	0.578	−1.272
Expenditure elasticities
	0.698	0.570	−0.095	1.284	−0.056

*In bold diagonally are the Marshallian and Hicksian own-price elasticities*.

The Hicksian own-price elasticities for Irish potato, sweet potato, cassava, arrowroot, and yam were also negative and consistent with utility theory a priori. Yam had more than unity (>1) price elasticity (−1.272) for the Hicksian demand function, hence elastic. All remaining R&Ts categories had less than unity (<1) price elasticities, therefore inelastic. The negative compensated own-price elasticities for all R&Ts satisfies the concavity requirement of utility function; therefore, the Slutsky matrix conforms to the negative semidefinite requirement. The expenditure elasticities range from positive to negative across all R&Ts, implying the presence of normal and inferior R&Ts categories in Nakuru Town East sub-county, Kenya. Moreover, the elasticities were computed using the total expenditure of R&Ts; therefore, they are conditional elasticities.

4. Discussion

4.1. Demographics, price, and expenditure effects on budget shares

Age of the decision-maker was significant with a positive and negative influence on sweet potato and cassava shares respectively. The nutritional benefits associated with sweet potato makes it more preferred by the ageing population with compromised immunity (Tan & Norhaizan, 2019). Similarly, Ülger et al. (2018) revealed high consumption of yellow and orange-fleshed sweet potatoes among the ageing population and attributed it to their endowed medicinal properties. The low cassava budgetary allocation is probably due to the fear of cyanide poisoning (Oloya et al., 2017). Older households are prone to non-communicable diseases and are cautious of their dietary intake, consequently avoiding foods that could put their health at risk. In addition, age positively influenced the consumption patterns for the remaining R&Ts categories but was not significant. The inclusion of age in the analysis can capture variations in purchase behaviour occasioned by fluctuations in consumers’ biogenic and psychogenic needs as age changes over time (Aidoo, 2009).

Education of the decision-maker significantly and positively influenced shares for sweet potato and yam and negatively for cassava shares. Educated households are likely to be more informed about dietary benefits of sweet potato and yam; therefore, they allocate more expenditure shares, agreeing with Villano et al. (2016) and Aidoo (2009). Consequently, the low cassava budgetary shares could be explained by educated households’ higher nutritional knowledge that enables them to shift their consumption from cassava favouring more convenient alternatives through dietary diversity (Nuani et al., 2022; Zani et al., 2019).

Household size had a significant and negative effect on cassava budget share. Larger households buy foodstuff that is affordable and meets preferences for all members. Since some cassava varieties have a bitter taste (Bechoff et al., 2018), few household members are likely to consume them. Larger households are more likely to have a wider variation in taste and preferences, implying different R&Ts meals are prepared for various household members at the same time. This food preparation process could be tedious, expensive, and time-consuming. In this regard, households are more likely to allocate smaller expenditure shares on cassava in favour of alternative food items acceptable to all members. Contrary, Zani et al. (2019) found a positive and significant influence of family size on cassava expenditure attributed to its affordability and fit in feeding larger households.

Deaton and Muellbauer (1986) observed that household size affected the type of food products consumed, which varies according to the composition of household members. The proportion of household members aged 18 years and below positively and significantly influenced cassava budget share. Likely, this is due to the nutritional and medicinal benefits associated with cassava. For instance, cassava is rich in zinc and iron, enhancing healthy growth and cognitive development among children and the general younger population (Ghislain et al., 2019). Moreover, it provides therapeutic benefits against chronic diseases such as diabetes and cardiovascular ailments among older people (Onodu et al., 2018). Further results revealed that the proportion of household members aged 19 years and above negatively influenced the yam budget share. This could be attributed to its high retail price (Aidoo, 2009), which discourages larger households who are likely to purchase more yam and therefore opt for cheaper alternative R&Ts.

4.2. Effects of price and expenditure elasticities on households’ r&ts consumption behaviour

4.2.1. Marshallian/Uncompensated price elasticities

Generally, the elasticity coefficients found in this study conform to economic theory. All uncompensated (Marshallian) own price elasticities were negative as expected a priori, and most (Irish potato, sweet potato, cassava, arrowroot) were less than one, except for the yam share category. Arrowroot had the least own price elasticity in absolute terms, indicating that in case of a uniform general price increase in R&Ts, more income would be allocated to Arrowroot. The elasticities for Irish potato, sweet potato, cassava, and arrowroot lie between −0.526 and −0.739; therefore are price inelastic, which agrees with findings by Rono et al. (2017). The elasticities suggest that the quantity demanded for most R&Ts is not sensitive to price change. Every price increase for the R&T crop will reduce its demand either slightly or not at all. For instance, if the price of Irish potato falls by 10%, then its demand would grow by 7.3%, with the price effect accounting for 4.4% while the income effect as a result of price decrease contributing 2.9%. Consequently, a 10% increase in per capita income with a corresponding 10% decrease in Irish potato price would result in a 9.8% increase in its demand attributed to the addition of 2.9% to the corresponding expenditure elasticity in Table 5.

If the price of arrowroot, a luxury R&Ts category decreases by 10%, then its demand would grow by approximately 5.2% in absolute terms, with the price effect accounting for 2.8% while the income effect is due to price decrease contributing 2.4%. This implies that a 10% increase in per capita income alongside a 10% decrease in arrowroot price would result in a 15.2% increase in its demand attributed to the additional 2.4% (income effect) on the corresponding expenditure elasticity (12.8%) Table 5. This description applies to the demand for the remaining R&T crops.

All positive Marshallian cross-price elasticities indicate that two corresponding R&Ts are substitutes; that is, as the price of one R&T crop increases, demand for other competing R&T crop increases. In contrast, negative cross-price elasticities indicate that R&Ts are complements such that the demand for one R&T crop increases with a fall in the price of another R&T crop. Similarly, Gido (2022) found negative Marshallian and Hicksian cross-price elasticities for African indigenous vegetables implying that the crops were complimentary otherwise substitutes. Categorically, Irish potato substitutes sweet potato and yam while complementing the rest of the R&Ts. For instance, if the price of Irish potato falls by 10%, the demand for sweet potato would decrease by 1.2% in Table 5, while 30.1% of this decline would consist of pure price effect. Alternatively, for Irish potato complements like cassava, a 10% decrease in Irish potato price would result in a 5% rise in demand for cassava. The same assessment applies to other substitutes and complements. Therefore, all substitutes and complements in the Marshallian demand system are gross substitutes and complements, respectively (De Jaegher, 2009).

4.2.2. Hicksian/compensated price elasticities

The compensated own-price elasticities for all R&Ts in Nakuru Town East sub-county were negative as expected a priori. All R&Ts had elasticities less than unity; therefore, price inelastic, except yam, which had a more than unity elasticity, therefore, price elastic. Arrowroot had the least own price elasticity in absolute terms. The elasticities of Irish potato, sweet potato, cassava, and arrowroot lie between −0.287 and −0.601; therefore, price inelastic. However, yam has an elasticity of −1.272, hence price elastic. The finding conforms with Rono et al. (2017), who found negative own-price elasticities for all R&Ts as expected a priori. Contrary, Manyong et al. (2007) found a positive own price elasticity for cassava flour and fufu attributed to the crops’ consumption as substitutes and other factors.

For cross-price elasticities, the observations are similar to Marshallian demand. Positive cross-price elasticity indicates substitution effect, while negative cross-price elasticities imply complementarity. For instance, this study found a positive cross-price elasticity between Irish potato and sweet potato, meaning that the two R&Ts were substitutes, agreeing with Rono et al. (2017). The signs shift from negative to positive for some cross-price elasticities, implying greater income effects on households (Ansah et al., 2020). Therefore, considering substitution for different R&Ts categories, Hicksian demand is preferred because it provides the best estimates due to a purely substitution effect, unlike the Marshallian demand, which has substitution and income effects, giving less efficient estimates.

4.2.3. Expenditure elasticities

The results indicate that expenditure elasticities for the R&Ts in the study area had mixed signs. The expenditure elasticities for Irish potato, sweet potato, and arrowroot were positive, therefore normal⁵ foods. The expenditure elasticity for arrowroot was greater than unity (1.284), consequently elastic and considered luxurious⁶ food to R&Ts consumers. This means that consumption of arrowroot will more than proportionately increase with an increase in expenditure (income). The expenditure elasticities for Irish potato and sweet potato were less than unity (0.698 and 0.570 respectively), therefore inelastic and regarded as necessity⁷ foods. Similarly, Ikudayisi and Okoruwa (2021) found that R&Ts across urban categories were expenditure inelastic implying that a 1% rise in the households’ income was likely to reduce the demand for R&Ts by less than 1%. Therefore, consumption of these R&Ts categories will increase at a lower proportion than the proportionate increase in expenditure. Contrary, the expenditure elasticities for cassava and yam were negative and less than unity (−0.095 and −0.056, respectively); therefore, inelastic and inferior⁸ categories of R&Ts, where income increase results in a decrease in quantity demand. Probably, higher income levels give households higher purchasing power that enables them to diversify consumption patterns to; wheat products, fruits, meat products, and beverages which agrees with Rozi et al. (2021). The aforementioned decrease in cassava and yam consumption supports the conventional argument that urban households shift consumption towards soft cereals supported by increased preferences for alternative starch sources such as wheat as their income increases (Musyoka et al., 2014).

For necessary R&Ts (Irish potato and sweet potato), an expenditure elasticity of 0.698 and 0.570 respectively implies that an increase in income by 10% would increase demand for Irish potato by 6.9% and sweet potato by 5.7%. For luxury R&T (arrowroot), an expenditure elasticity of 1.284 implies that a 10% increase in household income would increase demand for arrowroot by 12.84%. Finally, for inferior R&Ts (Cassava and yam), expenditure elasticities of −0.095 and −0.056, respectively, would imply a 10% increase in income would decrease their demand by 0.9 and 0.6%, respectively.

These findings contradict Rono et al. (2017), who found positive expenditure elasticities for all R&Ts crops and possibly considered them as normal to luxury commodities as expected a priori. The observed variations in expenditure elasticities could be explained by socio-economic, institutional and cultural factors affecting households’ consumption behaviour (Bett et al., 2012). Theoretically, income elasticities range from positive to negative signs. The positive and negative signs imply the presence of normal and inferior commodities respectively (Browne et al., 2007; Lewbel, 2006). For instance, as income rises, households substitute the consumption of inferior commodities; in this case, cassava and yam for superior or normal alternatives. This shift in consumption is called the income effect (Nsabimana et al., 2020).

5. Conclusion and recommendations

The demand estimates in this study conform to economic theory, similar to many other studies that use the AIDS model. Findings reveal existence of varied interrelationships among R&Ts for Nakuru Town Eat sub-county. There is observed substitution between R&T crops, with Irish potato substituting sweet potato, while cassava substitutes Irish potato, sweet potato, and arrowroot. Irish potato and sweet potato are necessities among the available R&Ts. Arrowroot is a luxury R&T while cassava and yam exhibit characteristics of inferior commodities. Moreover, elasticity estimates are necessary to formulate policies and strategies that target the R&Ts industry in general to improve the country’s R&Ts production, thereby meeting local demand and exporting the surplus.

These results have important policy implications in the R&Ts sub-sector. Arrowroot was found to be a luxury R&T commodity, evidenced by its income/expenditure elasticity of more than unity (1.284) in absolute terms, while its corresponding Marshallian own-price elasticity was 0.526 in absolute terms. Household income is likely to impact more on its consumption than prices. The magnitudes of household income are higher than those of prices. Therefore, for arrowroot, income policy appears to be likely more effective than price policy. Current estimates indicate that policies such as a general increase in R&Ts prices seeking to protect producers would not significantly affect households’ consumption patterns as those favouring income growth. Formulating income-related policies such as those favouring income growth would imply that consumers are likely to purchase more R&Ts in particular arrowroot which is identified to have a higher expenditure elasticity and therefore considered a luxury good. Furthermore, Irish potato and sweet potato are a necessity and therefore play a significant role in households’ dietary diversity. In this regard, policy formulation should consider not imposing taxes on Irish potato and sweet potato products, making them affordable among households.

Data availability statement

The data that support the findings of this study are available from the corresponding author (FON) upon reasonable request.

Acknowledgements

The authors are very thankful for the financial support offered to the first author by the African Economic Research Consortium (AERC). The funding made the research study a success. In a big way, we would also thank and appreciate the positive cooperation received from the enumerators during the data collection exercise. We also recognise the cooperation of the interviewed consumers during the survey.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the African Economic Research Consortium (AERC) under thegrant [AE/TG/19-02 (Award 1310)].

Notes on contributors

Fredrick O. Nuani

Mr. Fredrick Ouma Nuani is an African Economic Research Consortium (AERC) scholar pursuing a Collaborative Master of Science degree in Agricultural and Applied Economics at Egerton University, Kenya and University of Pretoria, South Africa. Dr. Eric Obedy Gido has a PhD in Agricultural Economics and currently serves as a lecturer in the Department of Agricultural Economics and Agribusiness Management, Egerton University. His main area of interest is on consumer studies and has taught several courses over the years. Dr. Oscar Ingasia Ayuya is a senior lecturer in the Department of Agricultural Economics and Agribusiness Management, Egerton University. He holds a PhD in Agricultural Economics with teaching and research experience running for many years. Dr. Michael Philliph Musyoka has a PhD in Agricultural Economics and works as a private Economic Development Consultant and Technical Advisor County Government of Makueni (CGM), Kenya.

Notes

1. Bashara, Flamingo, Kivumbini, Menengai, and Nakuru East wards.

2. Decision-maker is the household member responsible for making food consumption decisions.

3. Real monthly expenditure refers to the index scaled expenditures (Stones price index).

4. KES refers to Kenyan shilling (official Kenyan currency); exchange rate is 1 $US = KES. 113.05.

5. Normal foods are food groups whose demand increases with an increase in income.

6. A luxury food is a normal food whose income elasticity of demand is greater than one.

7. Necessity foods are normal foods whose income elasticity of demand lies between zero and one.

8. Inferior foods are foods whose demand drops with an increase in consumer’s income.