where _Yij_ is the outcome of interest -either value of gross or net revenue excluding family labor and level of input use per acre or an indicator of investment having been made during the past- on plot _j_ by cultivator _i_ ; _αi_ captures unobserved determinants of productivity by _i_ including farming skills, access to technology and credit etc; _Rij_ is an indicator variable for sharecropped plots; and _Xij_ is a vector of observable plot characteristics including size, soil type or quality, access to irrigation and drainage, and distance from the operator’s homestead.<sup>5</sup> Empirically, identification and truncation issues need to be considered.

On the first set of concerns, as _αi_ will be correlated with _Rij_ (or _E(αi|Rij=1) ≠ 0_ ), OLS estimation of _β_ will be biased. To deal with this, we follow other studies using plot level data (Jacoby and Mansuri 2009; Shaban 1987) and limit our sample to owner-cum-tenants so that _β_ can be identified from within household variation.<sup>6</sup> A second source of bias is that E( _εij_ |Rij=1) _≠_ 0; in fact sharecropped plots are often assumed to be of lower quality than owned ones. Two factors alleviate concerns that such bias may affect our estimates. First, we control for a wide range of observable plot attributes. Second, many unobserved soil quality attributes such as texture, capillarity, drainage, and salinity, respond to farmers’ management decisions over longer periods of time and can thus be considered an investment. As acquisition of new _barga_ plots came to a virtual standstill after 1978, differences in these attributes can at least partly be attributed to tenants’ actions since receiving the plot as an indicator of tenure-induced under-investment. If there were still unobserved differences in soil quality, they would likely lead us to overestimate the magnitude of the Marshallian inefficiency. Although such bias will be unlikely in our setting, it will be useful to bound the potential magnitude of such bias under rather extreme assumptions. To do so, we use the methodology developed by Altonji, Elder, and Taber (2005) for categorical variables.<sup>7</sup> The lower bounds are estimated based on the assumption of equality of selection on observables and selection on unobservables. Specifically, they are obtained by estimating a bivariate probit model for investment decision and tenancy status of plot _j_ by imposing ρ=Cov(X’β, X’γ)/Var(X’γ), where ρ is the correlation between the error components in the investment decision equation I=1(X’γ+α*T+ε>0) and the share tenancy equation (T=1(X’β+u>0)).

We also note that our data will include a large amount of zeros for investment and some types of inputs. We thus adopt the semi-parametric trimmed LAD approach (Honore 1992) to estimate a fixed-effect tobit to complement the linear probability model to ascertain the probability of any investment being made. If

> 5 In the private irrigation regression only public irrigation is included and all irrigation dummies are excluded in the public irrigation regression. 6 Although an assessment of overall welfare effects would require information on the cost of supervision, landlord monitoring can limit the efficiency loss associated with share tenancy. In a Pakistani sample, the Marshallian inefficiency, estimated to be about 18%, very close to the 17% obtained by Shaban’s study, is virtually eliminated for tightly monitored share tenants (Jacoby and Mansuri 2009).

> 7 The bounding technique is suitable to estimate bivariate probit model and we have not seen any application to continuous variables in the literature so far, we are limited to estimate the lower bounds on impact of share tenancy on investment decisions (namely, the likelihood to make any land improvement in the past 8 years and the likelihood of using family labor in 2008). For more details see Altonji, Elder and Taber (2005).

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