it increases the likelihood that our identifying assumptions hold, as discussed in Section 4. However, there is indisputably some degree of arbitrariness in deciding how long the effects of road improvements last on average.<sup>20</sup> In the case of rehabilitation, this definition (i.e., treatment lasting more than five years) is corroborated by broader literature. In the case of routine maintenance, the duration corresponds to the annual weather cycle. However, in the case of periodic maintenance, we rely solely on our own definition based on the judgment of transport experts on the project implementation team, DRVN, and TDSI. Given potential subjectivity, we test how robust our results are to modifications in the definition of treatment length for periodic maintenance. Increasing the length of treatment from one to two years does not result in any significant changes in the conclusions of our analysis.<sup>21</sup> Second, we check if our results are robust to an alternative functional form specification. We reestimate Equation 1 using an inverse hyperbolic sine (IHS) transformation of our dependent variables, expressed in Vietnamese dong (crops and livestock amounts traded and sold, income). We prefer to use an IHS transformation rather than a logarithmic one to avoid losing observations where these outcomes are equal to zero, which constitutes a non-trivial proportion of our sample.

The results from the robustness checks for the main results with the pooled treatment term are presented in Tables A.16 to A.19. While the direction of the effect remains the same, we lose significance of most of our results with IHS transformation. Only in the equations with income from sales of assets as a dependent variable, coefficients remain statistically significant for both the treatment variable and its interaction with the female-headed household dummy. Thus, our results are not fully robust to modifications in functional form. However, use of levels remains our preferred specification because of our interest in changes in the right tail of the distribution. Our qualitative work revealed that better roads triggered productive changes in agriculture, such as the increased use of machinery and switch towards more commercially lucrative crops. However, these changes take time and happened in the households that were more likely to invest in improved production processes and planting new crops. However, these types of changes may substantially increase production rather than trigger change in the margin. Consequently, we would like our estimates to be sensitive to the changes in the right tail of the distribution, which are likely to be subdued when IHS transformation is used.

# 6. Conclusion

Although accurately estimating the magnitude of global investment in transport is fraught with challenges, the estimates that exist point to a very large number—on the order of magnitude of US$1 trillion annually. Recent studies demonstrate that such investments play an important role in improving development outcomes ranging from crop diversification (Shamdasani, 2016) to higher educational enrollment (Garz

> 20 Our administrative data do not allow us to distinguish between activities carried out on sealed versus unsealed roads and the baseline conditions of roads, two data points which would narrow the range of life spans, we could reasonably expect. They also do not allow us to distinguish between upgrading and rehabilitation, but as we note in footnote 15, the impact of this is not as large given the short time frame of this study.

> 21 Results are available upon request.

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