Salubridad

In this section we present the results of the estimation of supply elasticities for food and coffee, demand elasticities for staple food, other food and non-food goods and the wage income elasticity. These set of elasticities permits a complete analysis of output, consumption and income response to price changes. A summary of the full set of elasticities is reported in table 4.4.

We first estimate (see chapter two and three) supply elasticities for staple food and coffee. Estimation of the food and coffee supply elasticities permits taking into account the output response to prices and thus an important part of the income effect of price changes. In fact, food and coffee production on average account for around 35% of total income as we shall see in figure 4.1 below. How important the behavioural response will be depends on the supply elasticities which in our case are quite low. We estimated two models of supply response for food, a “wrong” pooled model which does not take

into account different regimes of market participation and a second one in chapter three which instead estimates the supply function conditional on the market participation regime and takes into account the unresponsiveness of self-sufficient households. We are thus in a position to first look at the effect on welfare using the wrong model and then compare this results with the one obtained using the correct model.

Demand elasticities

We estimate demand elasticities using the AIDS proposed by Deaton and Muellbauer (1980) which derives an econometric specification consistent with a constrained maximization of a single-period utility function.

In the AIDS the expenditure shares of the j^th commodity group sj are a function of total expenditure E and prices p:

ln ln( / ) , commodity groups

j j ji i j j j

i

s =α +

∑

P is the composite price index obtained as:

ln ln 1 ln ln

j j 2 ij ij ij

j j i

P= +α

∑

∑∑

and _j 1

j

s =

∑

With this system in place we can impose the theoretical restrictions of adding-up, symmetry and homogeneity:

Adding-up: _j 1 _ij 0 _j 0

The adding-up and homogeneity restrictions are imposed by dropping one of the share equations from the system and obtaining the remaining parameters using the adding-up restrictions. The symmetry restrictions are obtained by restricting the parameters of the equations.

Income elasticity is then obtained from the estimated parameters as:

1 ^j

j

sj

η = +δ

Where s is the sample average expenditure share of commodity group j. _j

Uncompensated Marshallian own and cross price elasticities are obtained respectively as:

Compensated Hicksian own and cross price elasticities are:

(0.0) geographical and time price variation³⁵. The households’ consumption module collects information on a wide range of food and non-food commodities. We exploit the presence of a market price survey which collects prices in each of the 51 clusters for the main commodities to avoid the issues involved in using unit values as a proxy for market prices (Deaton 1987). Expenditures are grouped into staple food, other food and non-food items³⁶. We adopt this aggregation to be consistent with the supply estimations and to exploit fully the market price module of the survey. The group prices are then calculated as the weighted average of the individual good prices using the cluster average of the budget shares of each good in the group expenditure as weights.

Total expenditure is the sum of households’ expenditure on the three commodity aggregates.

As controls we use a number of variables able to capture the demographic composition of the households that can influence preferences. These variables are the age of the head, year of education of the head, the size of the household, a dummy for female

35 As a robusteness check we repeat also the estimation exploiting the time variation only. Results for the elasticity show no significant difference with respect to the pooled estimation presented above.

36 Staple food comprise bananas, beans, maize and cassava; Other food comprises other cereals, roots, fruits and vegetables, dairy products, meats, oils, sugar and salt. Non-food comprises kerosene, charcoal, firewood, batteries, soap, linen and utensils.

head, the proportion of adults and elder for both genders and the proportion of children, year and district dummies.

The system is estimated as a Non-Linear Seemingly Unrelated Regressions (NLSUR).

NLSUR is the non-linear extension of Zellner’s seemingly unrelated regression model (Zellner 1962). The non-linearity results from the composite price index which is not linear in the parameters. Formally, the model fit by nlsur is:

1 1 1

with m equations commodity and n × t observations. A multivariate normal distribution is assumed for the error term as the errors for the i^th observation may be correlated and thus fitting the m equations jointly may lead to more efficient estimates. Moreover, fitting the equations jointly allows us to impose cross-equation restrictions on the parameters.

Results of the estimation are reported in table 4.1. Table 4.2 shows the price and income elasticities of demand obtained from the estimated coefficients using the above formulas (0.0) to (0.0).

Table 4.1 : Almost Ideal Demand System

Staple food Other food Non-food

Price staple food -0.103*** 0.0558*** 0.0470***

(0.0119) (0.00825) (0.00498)

Price other food 0.0558*** -0.0284*** -0.0274***

(0.00825) (0.00686) (0.00336)

Price non-food 0.0470*** -0.0274*** -0.0196***

(0.00498) (0.00336) (0.00269)

Expenditure -0.0649*** 0.0395*** 0.0254***

(0.00442) (0.00294) (0.00204)

HHD Size 0.00838*** -0.00491*** -0.00347***

(0.00134) (0.000890) (0.000617)

Age head -0.000790 0.00122* -0.000431

(0.00105) (0.000697) (0.000483)

Age squared 1.08e-05 -1.22e-05* 1.36e-06

(1.00e-05) (6.65e-06) (4.61e-06)

Female head 0.0292*** -0.0244*** -0.00474

(0.00906) (0.00599) (0.00416)

Education head -0.00621*** 0.00368** 0.00253**

(0.00218) (0.00144) (0.00100)

Edu squared -6.69e-05 0.000124 -5.67e-05

(0.000173) (0.000114) (7.93e-05)

Prprimemale -0.0240 0.0177 0.00630

(0.0223) (0.0147) (0.0102)

Prprimefemale -0.0531** 0.0168 0.0363***

(0.0236) (0.0156) (0.0108)

Preldermale -0.0385 0.0245 0.0140

(0.0351) (0.0232) (0.0161)

Prelderfemale -0.0641** 0.0329* 0.0312**

(0.0288) (0.0190) (0.0132)

Note: The table reports results from the Almost Ideal Demand System estimation. Demand own and cross elasticities are derived from a transformation of the above coefficients (see table 4.2). The estimation uses the five waves of the KHDS. Additional controls not reported in the table are dummies for the six Kagera districts and time dummies.

Table 4.2: Own, cross-price and income elasticities

Note: Elasticities are derived from a transformation of the AIDS coefficients using formulas (0.0) to (0.0) All elasticities are computed at the sample mean expenditure share.

Agricultural wage elasticity

The effect on wages and income is accounted for by estimating the agricultural wage income elasticity as proposed by Porto (2007). Agricultural wage income accounts on average for 6% of total expenditure but it has higher weight for households at the bottom of the distribution which thus rely more on off-farm wage income and other agricultural income generating activities as shown in Figure 4.1 below.

We estimate a simple model of agricultural wage income determinants to obtain the estimates used to compute the income effect of price changes. By agricultural wage income we mean sources of income related to agriculture but different from coffee and food sales which we account for through the estimation of demand and supply elasticities. These income sources are agricultural wages from off-farm labour, sales of products derived from crops, sales of livestock and dairy products and sales of crops different from food and coffee. By estimating an aggregate agricultural wage relationship without distinguish between the different agricultural activities where these wages are earned we are able to identify only the average response to prices weighted by the shares of each type of activity on total labour supply.

We estimate the wage elasticity to tradable goods prices only as these prices are exogenously set on the international markets unlikely other non-traded goods prices.

The reduced form estimation is:

lnw_ij = +α βX_ij+ηlnp_ij+ϕ ε_j+ _ij

where the dependent variable is the logarithm of the agricultural wage income of household i in cluster j,p is a vector of prices of coffee and food faced by household i _ij in cluster j; X is a vector of controls including age, education, size of the household, gender of the head, the proportion of children and men in the household, average rainfall and seasonal dummies. ϕ_jis a vector of cluster fixed effects and εij is a normally distributed error term. The sample is composed of 1215 households which report earnings from these activities and is restricted to the fifth wave of the survey.

Results of the above estimation are reported in table 4.3. The elasticities of the agricultural wage income to the coffee and food prices are both positive and higher for the coffee price than the food price.

Table 4.3 : Wage-income elasticity

Table 4.4 : Demand, Supply and wage income elasticities

Demand¹ (ε^c) Supply² (ε^q) Wage

1. Demand elasticities are estimated through an AIDS using the full KHDS panel.

2. Supply elasticities are estimated in chapter 2 for coffee and food using the full KHDS panel. Food supply elasticity derives from the pooled “wrong” model.

3. Agricultural wage income elasticities are estimated through OLS using only 2004 KHDS data.