Econometric approach

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suggests that it is necessary to simultaneously account for the proximity to and size of proximate urban areas. The next section focuses on these issues⁴⁴.

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potentially endogenous road networks. The second instrument is an interaction between the first instrument, the Euclidian distance, and altitude. All else equal, locations that are on extreme altitudes (very high or very low) are more likely to have higher transportation cost compared to areas at average altitudes (Stifel, Minten, and Koru 2016). While initial construction costs of infrastructure tend to be higher at extreme altitudes, the average fuel cost per passenger is also likely to be higher in these locations⁴⁵. To isolate extreme altitude areas, a dummy variable is generated that takes a value of zero when altitude is within two standard deviations from the mean, one otherwise⁴⁶.

The validity of the IV strategy rests on two criteria. The first is the relevance criterion that demands that the instruments should be good predictors of transportation cost. To formally test for this criterion, transportation cost is estimated as a function of the instruments and other relevant household and community characteristics, including several household wealth measures. Table 3.2 shows the first-stage regression results. The first column presents a result of the more parsimonious model where only the instrumental variables and the town size indicator dummy variables are included. From this result, it is evident that the instruments are relevant. That is, the instruments are good predictors of transportation cost. The model's partial F-statistic is larger than 10, the minimum threshold value of the rule of thumb for valid instruments (Staiger and Stock 1997). The second column of Table 3.2 presents the results with more covariates related to household and location characteristics. In this more elaborate model with zonal fixed effects, the coefficients on both instruments are statistically significant and appear with an a priori expected sign. Moreover, the additional IV diagnostic tests presented at the bottom of the Table affirm the relevance of the instruments.

45 One reason for this could be that on extreme altitudes, population density and hence the number of commuters tends be very low. Public transportation facilities often charge a higher fare per person in order to compensate for missing revenues owing to vacant seats.

46 Rather than 2 standard deviation, the sensitivity of the results with 1 standard deviation and over the whole range of altitude is also tested. The basic results, available from authors upon demand, remained qualitatively the same.

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Table 3.2. First Stage regression result: determinants of transportation cost

Explanatory variables a0 a1

ln(Distance to nearest market town) 0.844*** 0.822***

(0.010) (0.014)

(Distance to nearest town)*(village is at extreme altitude) 0.045* 0.047*

(0.025) (0.026)

Large town, yes=1 -0.238*** -0.218***

(0.038) (0.043)

Household and location characteristics No Yes

Zonal Fixed Effects No Yes

Constant 0.324*** -2.887

(0.037) (2.558)

Number of observations 14,139 14,036

R2 0.852 0.889

Adjusted R2 0.852 0.889

F test of excluded instruments:

F( 1, 432) 3,617.4 1,873.0

Prob > F 0.00 0.00

Weak-identification tests:

Cragg-Donald F-statistic: 3,617 1,873

Kleibergen-Paap rk Wald F statistic: 204 157

---p-value 0.00 0.00

Over-identification test

Hansen-J 0.01 0.98

---p-value 0.93 0.32

Source: Author’s calculation based on LSMS-ISA (2012, 2014 & 2016)

Note: Standard errors clustered at the village level in parentheses. Statistical significance indicated by: *** p<0.01, **

p<0.05, * p<0.1; Coefficients on household and location characteristics omitted to preserve space

The second criterion for good instruments is the exclusion restriction which requires that instruments should not affect the outcome variable (i.e. the nutritional status) other than through the transportation cost. One specific concern against this exclusion restriction is that the distance variable might not be exogenous. It might be possible, for example, that households concerned about their welfare may relocate to areas better connected to urban areas. If so, this would violate the exclusion restriction. However, this is not likely to pose a serious threat as the cost of migration is prohibitively high in Ethiopia, especially so for rural households because of absent private land markets (Deininger et al. 2003). Land is owned by the state and individual farmers have only user rights. Securing land use rights is contingent on permanent physical residence in the community.

Therefore, it is too costly for households seeking to enhance their welfare to do so by changing their place of residence in the short run, which reduces the likelihood of selection bias.

Nevertheless, as a sensitivity test, the model is re-estimated by restricting the sample to those households remaining in the village for the whole period⁴⁷. This last step helps account for endogenous dynamic migration decisions.

Another potential concern with the exclusion restriction is that the altitude indicator variable might directly affect households’ nutritional status as it is correlated with agro-ecological factors

47 This analysis produced similar results and is available from the authors on demand.

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(Niermeyer, Mollinedo, and Huicho 2009; Singh et al. 1977). Altitude could also be correlated with other unobserved variables that are correlated with the outcome variables. If either of these two conditions holds, then the exclusion restriction would be violated. To address this issue, the altitude indicator variable is also included as a right-hand-side variable- 𝑋𝑖𝑡. Furthermore, mean annual temperature and zonal fixed effect are controlled for to ensure that this instrument is not simply picking up differences in agro-ecological factors.

Another concern in the estimation of equation (3.1) is that there might be selection bias because households might systematically self-select to live in and around large towns. If this is the case, 𝛽₂ cannot be estimated consistently. Indeed, the descriptive result in Table 1 shows that there might be spatial sorting into large towns based on the human capital endowment. The Table shows that while about 26.4 percent of large-town household heads attained secondary or tertiary level education, only 9 percent of small-town household heads attained a similar level of education.

Though not as extreme, one can observe a systematic difference between households residing in the two locations based on asset ownership, housing quality, land size, and access to health and social services.

To address this potential selection bias, we apply a double robust regression approach (Rosenbaum 2012; Rosenbaum and Rubin 1984). This method first involves the estimation of the probability of residing in a large town and then adjusting the regression estimation based on a weight generated from the predicted value of the selection equation. Based on the literature, the selection equation includes variables that are likely to affect the probability of residing in large towns such as household characteristics (age, gender, education, and household size), asset ownership, and housing quality. Table A3.2 in the appendix presents the result from the estimation of the selection equation using a probit model.

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