9.2 Market participation as an adoption decision
9.3 A standard double hurdle model of the supply decision
9.5 The complicating presence of fixed costs
Our last application investigates the consequences for milk sales and distance-to-market estimates of viewing the entry decision as a two-step procedure. This type of framework has recently garnered support for modelling diverse consumption decisions and is motivated by the possibility that the factors affecting the participation decision (e.g. whether to smoke cigarettes) may be different from the factors affecting the decision about quantities (e.g. how many cigarettes to smoke per day).
As we did in the previous chapter, we focus much of our attentions towards the fixed costs issue. Households commonly incur fixed costs in making the decision to trade in a market. These costs can involve pecuniary expenditures, such as a fixed fee to enter a market in order to sell product. More commonly, the fixed costs of market participation involve time spent in search for and screening of counterpart transactors and in negotiating and enforcing contracts. Such costs are known to exist irrespective of transactions volume and surely affect the logically subsequent decision over how much quantity to supply to the market. Yet the standard estimation of market supply equations fails to account for these fixed costs. In this chapter we demonstrate a method for estimating the double hurdle model of market participation and supply volume determination in the face of unobservable fixed costs.
Over the past decade or so, economists have begun to treat market supply decisions as a sequence of two steps, a market participation decision followed by a supply volume decision (Goetz 1992; Key et al. 2000). The notion of two-step decision-making can be motivated in the following way. Let i = 1, 2, …, N denote the households in question. Each household compares the level of utility derived from market participation, ypi*, against its reservation utility attainable without market participation, yri*. Here, we use an asterisk (*) to denote the fact that both levels of utility are latent (unobservable) random variables. We will follow this convention below.
We assume that the difference between the utility levels is determined by a vector of characteristics specific to each household, xpi. Without loss of generality, we set yri* = 0 and denote the difference between the incurred and reserve utility levels ypi, and their relationship to the characteristics by the function fi(Y). The condition characterising the discrete choice about whether to participate in the market can then be written as:
with participation when ypi > 0 and non-participation otherwise. We now let the indicator variable δi = 1 when ypi > 0 and the household participates in the market, with δi = 0 under non-participation.
Statistical implementation depends on the information structure of this choice problem, in particular whether the discrete participation decision occurs before a corresponding quantity decision is undertaken about the intensity of participation, in this case, as to how much quantity to supply to the market. As is customary, we assume the participation decision is made first and that, conditional on that decision, the household now faces a corresponding quantity decision.
In introducing the multivariate econometric model, below, it will be useful to conserve on notation. Hence, in presenting the sales decision, we continue to use y to reference the endogenous variable of interest, but distinguish the sales quantity from the latent participation variable through subscripts, the former denoted ysi and the latter denoted ypi. Let Φi( · ) denote the level of a maximand—e.g. profit or utility—defined over the supply quantity, ysi, and let ji( · ) denote its first-order partial derivative with respect to this quantity. Naturally, this decision will also be affected by a set of household characteristics, which may be the same or may differ from the ones affecting the participation action. Let xsi denote these characteristics. Across each of the households i = 1, 2, …, N, we are concerned, once again, with the problem:
and the associated first-order conditions for a maximum; namely the derivative condition on the objective function,
the non-negativity restriction on choice,
and the complementary-slackness condition,
Equations (43)–(47) form the basis for a double hurdle interpretation of the household’s supply decision, on which we now expand.
Assume that the households, i = 1, 2, …, N generate a sample (of size N) independent supply decisions. For each household in the sample the decision as to how much quantity to supply is a double hurdle problem with three components. Observed sales are:
where δi is the market participation indicator variable and ysi** refers to a potentially censored target sales quantity. A linear version of the participation equation (equation 43) has the form:
where δi = 1 if ypi > 0 and δi = 0 otherwise, where βp is a vector of unknown coefficients controlling the relationship between household-specific characteristics and market participation, and upi is a random error. Finally, the model is completed by inclusion of a sales equation:
where we observe ysi** = max {0, ysi*}; ysi* is the latent (random) optimal sales volume, which is related to the household-specific covariates, xsi, by the vector βs, with usi a random error.
Equations (48)–(50), along with their restrictions, combine to yield the double hurdle motivation for participation. This notion is exhibited clearly in equation (48), which states that two conditions must be met in order for positive sales to be observed. First, the indicator variable, δi, must be positive. In other words, the condition ypi > 0 must prevail in equation (49). Second, the latent quantity ysi* must exceed zero in equation (50). Hence, both the participation- and the sales-equations ‘constraints’ must be satisfied in order for positive sales to arise.
Equation (49) is simply a linear, statistical interpretation of the participation decision in equation (43) and, when the error is normal, has the important connotation of a probit equation. Equation (50) follows from relaxing the non-negativity constraint in equation (46), ignoring the complementary-slackness condition in equation (47) and acknowledging that, when one does so, a latent, censored (Tobit) regression is implied in which observed sales are left-censored at zero.
Because two conditions must be met in order for positive sales to arise, the likelihood of observing a positive observation is simply the conditional data density for that observation multiplied by the joint probability that the two events occur, or
Consequently, the likelihood for observing zero sales is the probability that neither of the two conditions in question prevail, or
If the errors in the participation and sales equations (upi and usi, respectively) are independent, then the joint probability of the two events occurring (δi = 1 and ysi* > 0) can be factored into the product of marginal probabilities. Other recent work has used that simplifying restriction (Key et al. 2000). Less restrictively, one can assume that the errors in (49) and (50) follow a multivariate-normal distribution. In this context, equation (49) depicts a traditional probit regression, equation (50) depicts a traditional Tobit regression, and the multivariate-normal assumption allows correlation between the errors, as in Nelson (1977), Cogan (1981) and Goetz (1992). By combining results in Chib (1992) and in Albert and Chib (1993), some algebra (available upon request) reveals that the full conditional distributions for the unknown quantities have simple forms, wherein a Gibbs sampling, data augmentation algorithm can be constructed in order to simulate from the joint posterior distribution for the system parameters.
More precisely, stacking (49) and (50) as:
where y ≡ (yp', ys')', yp ≡ (yp1, yp2, …, ypN)', ys ≡ (ys1, ys2, …, ysN)'; x ≡ (x1, x2)', x1 ≡ (xp, 0s)', x2 ≡ (0p, xs)', xp ≡ (xp1, xp2, …, xpN)', xp1≡ (xp11, xp12, …, xp1kp), xp2 ≡ (xp21, xp22, …, xp2kp), …, xpN ≡ (xpN1, xpN2, …, xpNkp), xs≡ (xs1, xs2, …, xsN)', xs1≡ (xs11, xs12, …, xs1ks), xs2≡ (xs21, xs22, …, xs2ks), …, xsN (xsN1, xsN2, …, xsNks); β ≡ (βp', βs')', βp≡ (βp1, βp2, …, βpkp)', βs≡ (βs1, βs2, …, βsks)'; 0p and 0s are null vectors of dimensions N × ks and N × kp, respectively; and the 2N vector u ≡ (up', us')', up≡ (up1, up2, …, upN), us≡ (us1, us2, …, usN)', is assumed to have a multivariate normal distribution with mean the 2N null vector and covariance ∑ÄIN. The parameters of the 2 × 2 covariance matrix ∑ are important because they indicate the degree to which errors in the discrete- and continuous-choice components of the double hurdle decision are correlated.
The system in (53) is in the form of Zellner’s (1996 seemingly unrelated regressions model equations 8.72–8.78). As such, the model plays an important role in another discrete-choice setting that has received considerable attention of late, namely the multinomial-probit model (see, for example, Geweke et al. 1994; Dorfman 1996; Geweke et al. 1997; McCulloch et al. 2000). In those situations, a Gibbs sampling, data augmentation algorithm is used to simulate from the joint posterior. We demonstrate below that this estimation strategy also proves successful in the double hurdle context. However, in the double hurdle case, the two-step decision implies additional restrictions. In this regard, note that the 2N × 1 vector y contains both observed and latent components. The first N components, yp, are all latent and some proportion of the second component, ys, will also be unobserved. In particular, define c≡ { i | ysi = 0 } as the censor set corresponding to the households for which zero supply (market sales) is observed. For each household belonging to the censor set a latent (non-positive) quantity of sales is implied. These quantities facilitate estimation—a point that is demonstrated to great effect in the seminal paper, Chib (1992)—but they are also interesting in a policy context, conveying the notion of a ‘distance’ at which these non-participating households stand from the market. But restrictions dictated by the double hurdle representation must be placed on these latent quantities during estimation. There are several variants of these restrictions. The variants arise in correspondence to the investigator’s interpretation of the hurdling sequence in the two-step decision-making process. The respective variants can be characterised with reference to the probability masses of the four, respective events: E1≡ event (δi = 1 and ysi* > 0), E4 ≡ the event (δi = 1 and ysi* £ 0), E3 ≡ the event (δi = 0 and ysi* > 0) and E4 ≡ the event (δi = 0 and ysi* ≤ 0). These four events are mutually exclusive and exhaustive and motivate four alternative specifications of the sampling model.
The first and most natural interpretation, due to its links with standard Tobit and probit formulations, is to consider the joint restrictions δi = 1 and ysi* > 0 as perfectly correlated. This interpretation, in effect, assigns zero probability to events E2 and E3 (prob(di = 1 and ysi* ≤ 0) = prob(δi = 0 and ysi* > 0) = 0). Then, according to the restrictions implied by the probit model in equation (49) all N elements of yp are latent with ypi truncated to the positive (negative) part of the real line according to δi = 1 (δi = 0) and, in addition, the censored components of ys are all constrained to be negative.
The second model assigns zero mass to event E2 but not to E3. Here prob(δi = 1 and ysi* ≤ 0) = 0 but prob(δi = 0 and ysi* > 0) ≠ 0. Accordingly, we model this situation by simulating a draw from the probit model (as above) but now do not constrain the draws for the latent supplies to be negative.
The third model assigns zero mass to event E3 but not to E2. Here prob(δi = 0 and ysi* > 0) = 0 but prob(δi = 1 and ysi* ≤ 0) ≠ 0. By analogy to the previous case, we simulate this situation by constraining the draws in the Tobit regression to be negative but do not constrain the corresponding draws in the probit regression. Other variants of the basic set-up are possible, but the three presented appear to be the ones that have attracted most attention in the literature (see, for example, Cragg 1971; Fin and Schmidt 1984; Jones 1989).
A particularly attractive feature of the estimation algorithm that we are about to present is the ease with which these variants of the basic model can be simulated and tested as part of a model selection exercise. Because the three variants imply a set of nested restrictions on the most general specification, this comparison is performed robustly and intuitively by imposing the implied restrictions and computing at each round of the Gibbs sequence the relative number of violations.
Experiments in the present setting suggest that the first variant (model one) strongly dominated the other two variants (models two and three) and, hence, reports are made only for the model 1 specification. In addition, further experiments led to the conclusion that the same covariates were significant in explaining both the participation and the supply decisions.
In this case, the seemingly-unrelated regressions model in equation (54) reverts to the traditional multivariate regression system (Zellner 1996, p. 224, equation 8.1) and estimation is slightly simplified. In terms of equation (53), the modifications implied are y ≡ (yp, ys); x ≡ xp ≡ xs; x has dimensions N × k; b ≡ (bp, bs); and u ≡ (up, us) is now assumed to have a multivariate normal distribution with mean the N × 2 null vector and covariance ∑ÄIN. Additionally, due to the facts that the vector yp is latent, and a subset of the components of ys is also latent, we use the symbols zp and zs to signify the corresponding observed vectors with the latent components included. Hence, z ≡ (zp, zs). Finally, in a conventional notation, we note that there are m = 2 equations in the system.
With this notation at hand, under a non-informative prior π(∑, β, zp, zs) µ|∑|–(m + 1)/2, the full conditional distributions comprising the joint posterior for the unknown parameters and the latent data, π(∑, β, zp, zs | y, x), have the following forms:
where Ezp ≡ x βp + ∑ps ∑ss–1 (zs – x βs), Vzp ≡ ∑pp – ∑ps ∑ss–1∑sp; Ezs ≡ x βs + ∑sp ∑pp–1 (zp – x βs), Vzs ≡ ∑ss – ∑sp ∑pp–1∑ps; Eβ ≡ (x'x)–1z, Vβ ≡ ∑Ä (x'x)–1; W ≡ (z – x β)'(z – x β), v ≡ N–k + m + 1; and the 2 × 2 matrix ∑ has (scalar) components ∑pp, ∑ps, ∑sp and ∑ss. Consequently, simulations from the joint posterior can be undertaken through a Gibbs sampling, data augmentation algorithm that samples sequentially through the distributions in (54), and the outputs {∑(s) s = 1, 2, …, S}, {β(s) s = 1, 2, …, S}, {zp(s) s = 1, 2, …, S} and {zs(s) s = 1, 2, …, S} can be used to derive inferences about policy measures of interest.
However, unlike the previous algorithms, three additional features are necessary for convergence. First, due to identification problems, the draw from the inverted-Wishart in step 2 is normalised on the parameter ∑pp so that the variance implied in the probit equation is one. This is the traditional restriction imposed in univariate settings. Second, only a subset of the vector zs, corresponding to the households in the censor set, are drawn from the conditional normal distribution and the draws for both zp and zs are made in accordance with the restrictions implied by the various models. Finally, the samples collected in the last step can be used to draw inferences about any of the unknown quantities of interest. In the results reported below, the algorithm is run for a ‘burn-in phase’ of S1 = 2000 observations followed by a ‘collection phase’ of S2 = 2000 observations.
In closing this section it seems natural to ask the extent to which the well-known problem of sample selection bias (see, for example, Greene (2000), pp. 926–33) may be problematic and whether there is need to apply correction procedures, such as those outlined in Heckman (1976, 1979) and applied in Goetz (1992). Sample selection could arise in our context, in considering the effect upon sales of an increase in a level of a covariate, where some individuals who possess the covariate do not sell product. Had those individuals who do not sell been excluded from the sample then a selection bias exists due to the fact that only those respondents selling product are used to form an estimate of the response to the covariate. For example, if the covariate in question is related positively to sales, then only those respondents with a relatively strong response to the covariate will be included, leading to an upwards bias in the corresponding parameter estimate. However, because a latent (negative) sales quantity is simulated for each of the non-selling households and used as the dependent variable in a subsequent estimation step, no such bias exists. In short, the problem of sample selection bias is conveniently circumvented through the data augmentation step in the Gibbs sampling algorithm double hurdle model. In addition, related identification problems arising in frequentist applications, like the need to include non-identical covariate matrices in the probit and Tobit equations as, for example, in Goetz (1992) are similarly circumvented. Hence the proposed algorithm appears to offer a number of attractive features compared with more traditional methodology.
Until now, we have said very little about the issue of fixed costs nor about their impact on the sales decision and an appropriate estimation strategy. With the layout for the traditional model firmly in place, and the results of the previous chapter, these issues can now be handled with relative ease.
Basic theory of the firm tells us that in the presence of fixed costs there is some minimum quantity below which it is unprofitable for any economic unit—be it a firm or a household—to supply to the market. This implies that the true censoring point in the Tobit regression will not be zero but, rather, will be some unknown, positive quantity, θ > 0. This quantity is important in the context of household’s decisions to enter the market because it circumscribes a minimum-efficient scale of operations measured in terms of a sales quantity. This quantity can be conceptualised in the context of the decision-making model (equations 43–47), the statistical description of the hurdle model (equations 48–50) and the estimation model (equations 51–54), as follows.
The presence of fixed costs, may or may not influence the participation decision but, we conjecture, they are likely to influence the quantity decision. This is perhaps most apparent in the observation that, at the household level, trade is commonly discontinuous in time, with individual households selling in some periods and not selling in others. Plainly, such a household is a market participant, although it opts for zero sales volume in some periods. Put differently, the good it sells is tradable from its perspective even if it is not always traded. This is conceptually akin to households adopting a new technology, then discontinuing its use at some future date(s) when it proves unprofitable (Cameron 1999).
Hence, in the sales optimisation problem in (44), the constraint ysi ≥ 0 is replaced by the condition ysi ≥ q. This modification leads, in turn, to the notion that the observed data on sales, ysi**, are actually the maximum of the latent sales quantity, ysi*, as specified in (50), and the unknown quantity θ > 0. Consequently, θ is now the censoring point in the Tobit regression. As such θ becomes an additional parameter in the model and must be estimated, along with the system parameters ∑ and β, the latent zp and the latent components of zs.
All that remains is to derive the fully conditional distribution for the unknown censoring value, θ, and append this distribution to the sampling algorithm implied by (54). From the results established in the previous chapter we note that this distribution is:
implying a few modifications to the algorithm in (54). The first modification is to select a starting value θ(s). We select the minimum sales quantity observed, i.e. the upper boundary of the feasible range for θ. Second, the subsequent draws in the algorithm are now conditional on the chosen value θ(s). Third, at the end of the algorithm we insert the additional step: Draw θ(s + 1) from the uniform distribution with bounds [max{zsi(s + 1), i c}, min{zsi, i c}], where max{zsi(s + 1), i c} implies conditioning on the maximum component of zs(s + 1) and where min{zsi, i c} denotes the minimum sales quantity observed in the data.
Results of the Gibbs sampling, data augmentation algorithm applied to the 204 observations are presented in Table 9. The first column presents definitions and the remaining columns present the posterior means of the parameters in the multivariate probit–Tobit systems under traditional and non-zero censoring, respectively. Auxiliary statistics are reported in the lower portion of Table 9. The mnemonics in the first column refer, respectively, to θ (‘Censor value’); return time (in minutes) to transport fluid milk to the milk co-operative (‘Distance’); years of formal schooling by the household head (‘Education’); the number of crossbreed cows being milked at the survey date (‘Crossbred’); the number of indigenous cows milked at the survey date (‘Local’); the total number of visits in the twelve months prior to the survey date by an extension agent discussing production and marketing practices (‘Extension’); a binary variable corresponding to the Ilu-Kura survey site (equals 1 if respondent is from Ilu-Kura and equals 0 otherwise); and a binary variable corresponding to the Mirti survey site (equals 1 if respondent is from the Mirti survey site and equals 0 otherwise). Numbers in parentheses below the parameter estimates are lower and upper bounds for the 95% highest-posterior density regions.
Table 9. Double-hurdle equation estimates.
|
Model | |||
Zero censoring |
Non-zero censoring |
|||
Participation |
Sales |
Participation |
Sales | |
Censor value |
5.26 | |||
(3.75, 5.97) | ||||
Distance |
–0.02 |
–0.46 |
–0.02 |
–0.31 |
(–0.03, –0.01) |
(–0.76, –0.17) |
(–0.05, –0.01) |
(–0.51, –0.12) | |
Education |
0.17 |
4.21 |
0.22 |
2.59 |
(0.08, 0.26) |
(1.60, 7.35) |
(0.08, 0.40) |
(0.94, 4.53) | |
Crossbred |
0.80 |
28.61 |
1.02 |
21.68 |
(0.48, 1.20) |
(20.45, 39.00) |
(0.58, 1.64) |
(16.18, 29.00) | |
Local |
0.29 |
12.75 |
0.40 |
10.00 |
(0.04, 0.55) |
(5.59, 19.77) |
(0.07, 0.80) |
(5.64, 14.81) | |
Extension |
0.16 |
4.39 |
0.20 |
2.87 |
(0.06, 0.27) |
(1.58, 7.37) |
(0.09, 0.35) |
(1.24, 4.49) | |
Ilu-Kura |
–1.68 |
–64.82 |
3.12 |
–38.12 |
(–2.53, –0.87) |
(–98.00, –38.51) |
(1.65, 4.31) |
(–58.71,–22.51) | |
Mirti |
–3.08 |
–102.57 |
1.33 |
–61.95 |
(–3.97, –2.18) |
(–150.09, –67.92) |
(–0.98, 2.70) |
(–91.09, –41.36) | |
Covariance |
||||
Participation |
1.00 |
9.42 |
1.00 |
6.29 |
(4.60, 14.99) |
(3.46, 9.64) | |||
Sales |
(symmetric) |
1047.40 |
(symmetric) |
345.08 |
(475.38, 2045.15) |
(154.72, 686.32) | |||
Auxiliary statistics |
||||
Non-participants |
||||
R2 |
0.97 |
0.91 |
0.98 |
0.87 |
Positive predictions |
3.00 |
4.00 |
2.00 |
8.00 |
Negative predictions |
176.00 |
175.00 |
177.00 |
171.00 |
Participants |
||||
R2 |
0.92 |
0.33 |
0.84 |
0.39 |
Positive predictions |
11.00 |
11.00 |
25.00 |
13.00 |
Negative predictions |
14.00 |
14.00 |
0 |
12.00 |
Note: Figures in parentheses are 95% confidence intervals (highest posterior density values).
Considering, first, the traditional formulation with zero censoring in the Tobit regression, each of the parameter estimates are significant at the 5% significance level. (None of the 95% highest posterior density regions contains zero.) The signs of the posterior means all have the expected impact. Participation is promoted by education, cow ownership and the level of extension services, but is mitigated by distance to market. Sales are also increased by the intellectual capital stock (education and visits by extension agents) and the animal stock (local and crossbreed animals) but reduced by distance to market.
An important result in the context of two-step decision-making is the possibility that errors are correlated. Previous work (most notably, Key et al. 2000) assumes independence. The estimated covariance parameters suggest strongly that the participation and the sales decisions are correlated. Other features of the traditional model are the relatively large degree of variability in the sales equation error variance (posterior mean estimate of 1047.40 litres of milk per household per week); outstanding predictive performance among the non-participating ‘households’ (179 of the 204 total observations); but less satisfactory fit in the participating sample (25 observations in total). Because 85% of the sample observations are censored, the poor prediction in the participating sample is somewhat expected due to small sub-sample size. But the large error variance in the sales equation suggests that a number of other omitted factors may be responsible for weekly sales variability.
Before turning to examine differences between the first formulation and the formulation that does not restrict the censoring value to be zero, a word about the covariate ‘Distance’ seems in order. Recall that the purpose of relaxing the zero-restriction on the censoring value is to attempt to capture the importance of fixed costs and their affect on the minimum efficient supply quantity. But there may be grounds for suspecting double counting with reference to some of the covariates. For example, it is certainly true that there is a fixed cost related to distance (e.g. the cost of transporting the individual, not the milk, to market). In this case, it may be argued that the covariate ‘Distance’ is capturing both proportional and fixed transactions costs. Put differently, θ understates the fixed cost of market participation because of the distance-related fixed cost. Identification of proportional costs and separating them out from their corresponding contributions to fixed costs is problematic. This point is made by Key et al. (2000) who attempt to distinguish between the two components, empirically. Whether it is possible to perform a similar decomposition using the current estimation strategy remains an interesting issue for possible extensions of the current effort.
Turning to the second, non-zero censoring formulation, the most interesting comparisons are three. First, the posterior mean estimate of the censor value suggests that the minimum efficient scale of operations for the household is a resource base consistent with delivery of 5.26 litres of milk per week for a household located at the market delivery point. Note, also that this estimate is measured at a considerable degree of precision (with 95% highest-posterior-density bounds of 3.75 and 5.97, respectively). Hence, one important conclusion emerging from the exercise is that a significant bias could result from restricting the censor value to zero. Evidence of this potential bias is encountered in comparisons of the covariate estimates between the two models, which is the second important feature of comparison. In both the participation and supply equations, each of the continuous covariate (i.e. other than the site dummies) coefficient estimates has the same sign across the two models. But the magnitudes of the means estimates in the two equations exhibit an interesting pattern. In the participation equation each of the estimates in the random-censor model is greater (in absolute value) than the corresponding estimate in the traditional model and in the supply equation each of the estimates is smaller (in absolute value) than the corresponding estimate in the traditional, zero censoring model. Furthermore, in both the participation and supply equations, the site-specific dummy coefficients are greater under random censoring than in the traditional formulation. Hence, having concluded that the true point of censoring is not zero, these results suggest that ignoring the importance of potential fixed costs in the supply decision has three impacts on the double hurdle estimates. First, it biases downwards both estimates of the impact of the covariates on participation and the impact of ‘other factors’ as depicted by the constant terms. Second, it biases upwards estimates of the impacts of the covariates on supply but biases downwards estimates of the impacts of ‘other factors’ on supply as evidenced in reports of the coefficients of the site-specific dummies. In short, the net impacts of ignoring fixed costs are a lower prediction about likelihood of participation and a higher prediction about supply potency. Further evidence that the second formulation is a better description of the data is evidenced by the reports of dramatically lower error variances and the improved predictive statistics in the lower part of Table 9. This is not just an idle methodological point. The practical implication is that increasing market participation is central to expanded aggregate supply, so traditional price policy prescriptions that rest upon the assumption of ubiquitous market participation may not be the most effective means of increasing market supply.
Collectively, these results demonstrate the importance of allowing for non-negligible fixed costs in market participation (adoption) studies. When these costs are ignored but are non-negligible, a significant bias in participation and supply estimation appears to exist. In the context of examining this issue, we have presented a Bayesian approach to estimation of the double hurdle model, which is popular because it allows for a potentially diverse set of factors to influence participation and supply decisions. Our analysis, however, suggests that in these data on highland Ethiopian milk producers, the same factors influence both participation and supply and that the intellectual capital stock (education and visits by extension agents) is a vital complement to the physical capital stock (both local and crossbred animals) in effecting market entry among formerly subsistence households. With the intent of expanding the density of milk market participation in peri-urban settings, extension agents and policy makers should target these inputs with a view to expanding household capacities above a minimum of 5.26 litres of milk per household per week.
