Heckman procedure against the instrumental variable approach<sup>36</sup> is that it provides a direct test for selection bias. If the Mills ratio, λ, is not statistically different from zero, it indicates that there is no selection problem due to unobserved heterogeneity and the PSM results are reliable. Results are reported in table 9.

**_<u>Table 9: Robustness Check: Endogenous Treatment Effects Model</u>_**

|<br>**Variable**|<br>**(1)**<br>**Random**<br>**sample**|<br>**(2)**<br>**Purposive**<br>**sample**|<br>**(3)**<br>**Random**<br>**sample**|<br>**(4)**<br>**Purposive**<br>**sample**|**(5)**<br>**Random**<br>**sample**|**(6)**<br>**Purposive**<br>**sample**|
|---|---|---|---|---|---|---|
||**Labor pr**|**oductivity**|**Process u**|**pgrading**|**Product u**|**pgrading**|
|Contract|0.178|0.0882|0.0551*|-0.0108|0.132***|0.0319|
||(0.144)|(0.0836)|(0.0334)|(0.0228)|(0.0469)|(0.0248)|
|GVC|2.382|-45.48|0.0474|2.352|-0.239|3.532|
||(3.611)|(36.36)|(0.463)|(2.471)|(1.080)|(4.023)|
|Observations|1,203|2,249|1,203|2,249|1,179|2,165|
|rho|-0.883|1|-0.244|-1|0.312|-1|
|sigma|1.331|22.81|0.183|1.232|0.310|1.827|
|lambda|-1.175|28.60|-0.0447|-1.483|0.0966|-2.237|
|se(lambda)|1.160|88.58|0.219|4.783|0.397|4.605|

_Note:_ Columns 1 and 2: OLS regression; columns 3 to 6: probit regression. Bootstrapped standard errors are in parentheses. Country, region, and crop fixed effects are always included.

Using the selection model, we generally confirm that value chain participation has no effect on structural transformation. Most importantly, the Mills ratio lambda is not significant, irrespective of the model and selection variable. Because of that, the results are similar to the ones obtained with the OLS estimator. We carefully argue that we do not face a severe selection bias based on unobservables, and that our PSM results are unbiased and reliable. However, multicollinearity may be an issue here because of some implausible coefficient estimates. Additional variables that could serve as an instrument for value chain participation were also tested. Although the results are similar, farmers’ motivation, experience in farming, and satisfaction with their buyer (complaints) are not shown to be valid instruments either.

# <u>Model Variations</u>

Based on the discussion of the baseline regression results, the effect of value chain participation on structural transformation is likely to be higher when the product is sold to a value chain under a contract, because a formal or informal agreement regulates the provision of inputs into production, such as fertilizer, technology, extension services, market information, and so forth. To test this hypothesis, we employ an alternative specification where the main variable of interest is the interaction term of value chain participation and contract farming (equation 2).

# Yi � f �VCi#Contracti, Contracti, Xi, dj, cn, pk, εi, θ� **(2)**

The results are provided in tables 10 and 11 in annex A. Compared with table 6, columns 1 and 2, the interaction of value chain participation with contract farming is indeed larger and also significant in the random sample (0.480**) using simple OLS. However, there is still no positive

> 36 The <mark>instrumental variable approach and Heckman selection model would generally produce similar estimates. However, the Mills ratio is derived under the normality assumption. In the absence of normality, instrumental variables should be preferred.</mark>

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