estimate a fixed effects model for these whereas presence of a non-trivial fraction of zero observations for fertilizer leads us to choose a random effects tobit model. Throughout, the key variable of interest is _γ_ , the estimated difference in output or input intensity between owned and sharecropped plots not accounted for by other factors. A positive and significant value of this variable would indicate Marshallian inefficiency.

# **_C. Optimality of Adjustment through Rental Markets_**

Irrespectively of whether the principal’s inability to enforce the optimum level of effort by the agent will lead to sharecropping being inefficient, it is important to explore whether land rental allows households to attain their desired or ‘optimum’ cultivated land size. A number of factors including the transaction costs (e.g. for search of partners and contract enforcement) associated with land rental or imperfections in other markets, e.g. those for labor and draught animals (Bliss and Stern 1982, Bell and Sussangkarn 1988), may prevent attainment of desired holding sizes. Ethiopian studies take _prima facie_ evidence on the failure of rental markets to equalize factor ratios as an indicator for rental markets allowing only partial adjustment (Teklu and Lemi 2004). Together with large rates of non-participation, this is often interpreted as an indication for presence of friction in land rental markets (Ghebru and Holden 2006, Holden and Bezabih 2006) although the methodology does not allow quantification of magnitudes involved. At the same time, the only study that formally tests factor adjustment, albeit for a small sample of households renting out land only, is unable to reject the hypothesis of land markets facilitating full and frictionless adjustment to the desired land size (Pender and Fafchamps 2006). Other empirical evidence suggests that imperfections in land rental markets lead to large productivity differentials that are not gender neutral: not only is female-headed households’ land used much less productively than that cultivated by male-headed ones (Holden, Shiferaw, and Pender 2001), female headed households also tend to rent-out their land to tenants with much lower productivity (Bezabih and Holden 2006, Holden and Bezabih 2006).

To formally test for such friction in land rental markets, let _k_ be the amount of net land leased which is itself a function of the difference between desired cultivated area ( _DCA_ ), defined as the amount of land that matches the household’s resource endowment in the absence of friction in the tenancy market, and total owned area ( _K_ ).<sup>8</sup> Letting _h_ be an the adjustment function which depends on the size and type of transaction costs in the rental market (Skoufias 1995), this relationship can be written as where, by assumption, _DCA_ is a function of the household’s endowment with oxen power _O_ and family labor _L._ With the adjustment function _h_ being non-decreasing in ( _DCA – K_ ) and _h_ (0)=0, i.e., a household that owns its desired cultivated area will not participate in the tenancy market, and _f_ non-decreasing in both of its arguments, a first-order Taylor series expansion of equation (2) yields

> 8 See Bliss and Stern (1982) and Skoufias (1985) for graphical exposition of some of the possible forms of the adjustment function, _h_ .

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