Rainfall variability and food crop portfolio choice: evidence from Ethiopia

Abstract

This paper concerns the patterns of food crop choice in a multicropping setting, in which production risk considerations and rainfall uncertainty are likely to be critical factors. The analysis employed plot level panel data from Ethiopia, combined with 30 year meteorological data corresponding to the survey villages used to construct seasonal and yearly rainfall variability. Using the single index approach, the riskiness of crop portfolio was constructed at a household level, taking into account the multicropping nature of the farming system. The combined riskiness of crops grown at a household level responded negatively to annual rainfall variability, with seasonal rainfall variability having a less consistent impact. Farmers are, therefore, more likely to select less risky crop portfolios even when intercrop interactions are taken into account.

Appendix: The single index method measuring the riskiness of crop portfolio at the household level

Equation 1a specifies the relationship between the reference portfolio revenue, and the individual crop revenue

$$ {S_K}=\sum\limits_{i=1}^n {x_i {S_i}} $$

(1a)

Where S _k is the reference portfolio, X _i is the weight of enterprise (crop) i, and S _i stand for the stochastic revenue of crop i.

Similarly, the revenue variance-covariance relationships between the reference portfolio and the individual crop revenues are given by:

$$ z_K^2=\sum\limits_{j=1}^m {\sum\limits_{i=1}^n {d_i {d_j}{z_{ij }}} } $$

(2a)

where z _K ² is variance of the revenue corresponding to the reference portfolio, z _ij and the covariance of the individual crop revenues. This equation captures the essence of the single index method—that the portfolio risk measures the proportionate contribution of an individual enterprise’s risk to the variance of the underlying index.

From Eq. 2a, the marginal risk—the contribution that each crop makes to portfolio variance is computed. This is given by:

$$ \frac{\partial V_K^2 }{{\partial {x_i}}}=2\sum\limits_{j=1}^n {d_i {V_{ij }}} $$

(3a)

Our parameter of interest, the anticipated changes in the revenues of a commodity in response to changes in portfolio returns, beta, is given in Eq. 4a.

$$ {\beta_i}=\frac{{{z_{ij }}}}{z_k^2 } $$

(4a)

This parameter is retrieved from regressions of S _ih on the underlying reference portfolio, S _kh , are the characteristic equations that determine systematic and non-systematic risk

$$ {S_{ih }}={\alpha_i}+{\beta_i}{S_{kh }}+{e_{ih }} $$

(5a)

Where α _i is the intercept and β _i is the regression coefficient, and e _it is the error term. For simplicity, the weights d _i are kept to 1 (equal weights).

The beta parameter estimated then measures the riskiness of each crop. Averaging over the beta coefficients estimated for each crop within the household gives the riskiness of the overall crop portfolio of the household.

In Turvey (1991), the basis of the empirical approach for our paper, the unit of analysis in their study is the county. Therefore, Eq. 5a is estimated using time-series data to generate, a county-beta. In our case, as we set out to estimate beta for each crop within the household, our unit of analysis is essentially the plot (crop type) within each household, for which we have a plot level observations for about 1,500 households over the four survey years. As a result, unlike Turvey (1991) OLS estimation of Eq. 5a using time series data, our estimation is an estimation of panel data (time subscripts representing years are suppressed for notational convenience). In order to take advantage of the panel feature of our data, (and to circumvent the effect of the beta coefficient picking up the effect of variation across households), we estimate Eq. 5a using a household fixed effects estimator.

In sum while we have the advantage of larger numbers of observations across households, our panel is short making time series estimation impossible. It should be noted that using time series data for such estimations is difficult in our setting and we are not aware of any such data at the plot level in a multicropping farm context in Ethiopia. Even our detailed plot level data collected over 4 years is very rare. This is the first step in trying to measure riskiness using this methodology. Future studies need to look into using much richer sources of data.