Descriptive statistics and regression analysis The data were analyzed to obtain the descriptive statistics and multiple linear regression analysis was used to assess the factors influencing milk yield, loss and annual milk income. Factors included in the model were training, age, education, experience, forage land, lactating crossbred cow, family size and location. The effect of training on the milk income of participant dairy households in the study area was modeled explicitly as: Y = b0 + b1x1 + b2x2 + b3x3 + b4x4 … + u ……………………. (Equation 1) Where Y= Annual milk income; x1= Training received (1 if trained, 0 otherwise); x2 = Age of the farm head (years); x3 = Education level of the farm head (1 if attended formal school, 0 otherwise); x4 = Experience in dairy production (years); x5 = Size of land allocated to forage production (ha); x6 = Milking crossbred cows owned (number); x7 = Members of household (number); x8 = Location (1 if Cheliya, 0 otherwise); b0 = Constant term; b1 – b8 = Estimated coefficients of the independent variables; u = Error term. 3.5.2.

Calculation of milk incomeThe cost of milk production was assumed to be the cost of labor for feed production and cost of supplemental feed purchased. The opportunity cost of family labor was calculated based on the reported market wage rate of labor in the study area. Thus milk income from milk and milk products was calculated as the difference between gross milk income (mean revenue) and cost of production (expenditure on labor for feed production and cost of supplemental feeds). Revenue = price of milk (ETB/kg) * milk volume (kg) + price of butter (ETB/kg) * volume of butter (kg) + price of cheese (ETB/kg) * volume of cheese (kg) Variable cost = price of concentrate (ETB/kg) * volume of concentrate (kg) + cost of feed production. Milk Income = Revenue – Variable costOpportunity cost of family labor for feed production was calculated at the rate of 2 ETB/hour (4 ETB/0.1 ha of land) 3.5.3.

Econometric analysis 3.5.3.1 Propensity Score Matching (PSM)We used propensity score matching (PSM) technique (Dehejia and Wahba, 2002; Heckman et al., 1997; Rosenbaum and Rubin, 1985) to test our general hypothesis that farmers who are trained on dairy husbandry practices could apply the knowledge to improve milk yield and income.

In the case of the non-experimental method the presence of selection bias which arises due to differences in observable characteristics can be avoided by the use of PSM model. In this technique, participant dairy farmers, both trained and non-trained groups are matched based on their observable characteristics. To measure the average treatment effect on the treated (ATT) for the intended outcome variables, a logit model was used in order to get the propensity scores. The first step in PSM was to estimate and classify the propensity score.

Propensity score matching constructs a statistical comparison group that is based on a model of the probability of participating in the dairy husbandry training, using observable characteristics. Propensity score matching is expected to provide a weighting scheme that yields unbiased estimates of the impact of the treatment. The next step was the selection of matching estimator that best fit the data. Then, based on the propensity score determined and matching estimator selected, matching between treatment and control group was done to find out the impact of training on the mean values of the outcome variables.

The PSM technique is therefore used to control selection bias since it accounts between the outcomes of the treatment and control groups (Fancesconi and Heerink, 2010). This provides an unbiased estimate by controlling observable factors and reduces matching problems (Becker and Ichino, 2002). The section below describes the required methods and models to calculate the average treatment effect on the treated, which helps us to identify the impact of dairy husbandry training on the milk income.

Prior to the estimation of PSM, all the explanatory covariates included in the model were checked for the existence of multicollinearity and hetroscedasticity problems using Variation Inflation Factor (VIF) and Breusch-pagan/cook-Weisberg test respectively. These tests were done before running the logit model. Multicollinearity problem arises when at least one of the independent variable is a linear combination of the others that is greater than 10. On the other hand, heteroscedasticity problem arise when p-value is significant. The estimation process for dairy husbandry training on milk yield and income was done using psmatch2 in STATA 13.1.

Covariates included in the model should be the one that is unaffected by participation. The following 12 explanatory variables were selected for the model: sex, age of household head, education status of the household head, years of experience in dairying, family size, extension service obtained, access to credit, area of land allocated to forage production, cooperative membership, veterinary service obtained, number of lactating crossbred cows owned and distance to market. The propensity score for each observation was calculated using a logit model and the predicted value indicates the likelihood of the dairy household being included in the training. In the present study, we focus on the following specific variables as outcome indicator: (1) average annual milk income from milk and milk products; (2) average milk production; (3) average milk sold (4) average milk processed; and (5) average milk consumed. The average treatment effect (ATT) of the training is then calculated as the mean difference in outcomes across the trained and non-trained groups.

The validity of PSM depends on two conditions. The first one is conditional independence (unobserved factors do not affect participation) and the second one is common support or overlap in propensity scores across the participants and non-participant samples (Khandker et al., 2010). The assumption in the first condition is that treatment needs to fulfill the criterion of being exogenous, implying that any difference in outcome between the trained and non-trained groups with the same value of characteristics can be attributed only due to the dairy husbandry training. This assumption can be denoted as Y1, Y0 ? D|X………………………… (Equation 2) where ? denotes independence, D|X is an assignment to treatment (D equals 1 for trained and 0 for non-trained) conditional on characteristics X, Y1 and Y0 are the outcomes for the treatment and control groups, respectively. The second assumption, common support, ensures that individuals/groups with the same values for characteristics X have a positive probability of being both participant and non-participant of a treatment (Heckman et al., 1999).

This assumption is denoted as 0