Robertson-AER-2000

Title: Wage Shocks and North American Labor-Market Integration

Notes: Develops 3 sector model of international labor markets and bases empirical model from it.  Sees lagged wage in the US affecting labor demand in US. Begins with a linear labor demand equation and suppy equations for Mexico.Solves labor market equilibrium such that Mexican wages are based on lagged American wages. Using the final difference equilibrium equation they test two parameter estimates to check on hypotheses that American and US wages respond to same shocks and that they are converging. 

Robust vs. Clustered Errors

A constant problem is the homoscedasticity of error terms assumption is required to validate the Gauss-Markov Theorem (making straight foward OLS the BLUE). As the assumption can often be violated leading to funky standard error estimates, and therefore inference, the two most common corrections are estimating error variances and covariances (VCs) as a function of observables.  So now instead of estimating the error VCs unconditionally as in the basic OLS formulation an additional step is taken whereby the VCs are estimated with an additional preceding auxilliary regression whereby error components are a function of individual terms or cluster terms.  For example,the equation { error = individual (or group) effect + random component }. So while the error term was originally not homoscedastic the assumption here is that the random component is since the heterocedasticity was derived from the individual or group effects and these are controlled for.  Modeling the error structure as having an individual or group effect is what makes the error estimator as either robust (former) and clustered (the latter).  This method was introduced by White (1980), hence the name White estimator (among others), and is within the family of GLS methods.

Here are some helpful links:
http://www.stata.com/support/faqs/stat/cluster.html
http://sekhon.berkeley.edu/causalinf/sp2010/section/week7.pdf

Fafchamps, Shilpi-EJ-2005

Title: Cities and Specialization: Evidence from South Asia

Notes: No theoretical model. Uses non-parametric method called roughness penalty (Silverman 1982 referenced).  Specialization is basically measured by a Simpson Index-essentially Sum of squared number of hours in each occupation divided by squared number of total hours. City proximity is basically an integral of the product of urban households and distance to a specific household. They analyze how a household's and village specialization indexes are affected by city proximity. 

Emran, Shilpi-IIEPWP#11-undated(after 2008)

Title: The Extent of the Market and Stages of Agricultural Specialization

Notes: Applies gravity equations where specialization (in terms of a herfindal index of  concentration of crop-land use at the village-level) is regressed on a market size measure and controls. It uses Nepalese household survey data.

Key, Sadoulet, De Janvry-AJAE-2000

Title: Transactions Costs and Agricultural Household Supply Response

Notes: Build on an AHM of household supply to either market or home consumption and estimate it for only maize using Mexican data. It does allow for a simultaneous choice of production and consumption. They jointly estimate three regimes of (buyer, seller, autarky) by tacking on errors to the three theoretically derived equations.  They estimate the parameters by maximum likelyhood by assuming the errors in the 5 equations they end up with are ~ I.N.D. Funny to see them refer to identification in this paper as the ability to identify separate parameters within a model (as oppose to producing estimates of their product for example) while the now it seems identification is more associated with causation.  See Angrist and Pischke's book for a good discussion.

Their Abstract: "We develop and estimate a model of supply response when transactions costs create a situation where some producers buy, others sell, and others do not participate in markets. We present two rationales for why producing households may have different relationships to the market: proportional and fixed transactions costs. Using data on Mexican corn producers, we estimate an empirical model that allows for separate tests of the significance of both types of transactions costs, revealing that both fixed and proportional transactions costs matter for the estimation. The results provide consistent estimates of supply elasticity and measures of the relative importance of factors determining both proportional and fixed transactions costs."

Bowlus and Sicular-JDE-2003

Title: Moving toward markets? Labor allocation in rural China

Notes: Tests for separation property of AHM with Chinese Data uses Benjamin's (1992) approach.