What is the cost of low participation in French timber auctions?

Abstract

How much is the standing timber from public forests worth? To estimate the value of a timber lot, we adopt the transaction evidence appraisal approach using data from timber auctions in Lorraine (Eastern France) accounting for the facts that: (i) the seller's reserve prices are secret, (ii) there remain many unsold lots and (iii) the number of bidders varies across auctions. Taking into account the endogenous participation in our hedonic price equation for the highest bid, we estimate that, compared to lots that receive two bids, the highest bid is 22% lower when there is only one bid and 37% higher when there are three or more bids.

Notes

¹ See Poirier and Tobias (2007) for a general introduction on this topic. The idea is to replace methods based on maximum likelihood that often do not converge in complicated settings.

² The Herfindahl index is the sum of the square volume proportion of each species. Here, the number of species is seven. The more homogeneous the lot, the closer is the index to one.

³ Indeed, latent variables can be simulated and conditional on these variables, the model is a simple Seemingly Unrelated Regression (SUR) model that is easy to deal with. We use a Metropolis step to draw from the conditional posterior distribution of the elements of the covariance matrix of the unobservable variables.

⁴ The Gibbs algorithm is an MCMC algorithm that iteratively draws from the conditional posterior distributions of the parameters and always accepts such draws.

⁵ We propose a slightly different MCMC algorithm for the sample selection part of the model than Van Hasselt (2005). We write the latent model as a SUR model with an unequal number of observations; and thus inference on the coefficients of the observed equation only relies on observations that are not censored.

⁶ We decompose the ordinal variable in a set of binary variables so that our results do not depend on the way we have coded the ordinal variable. This is not an issue in Equation 2 since the methodology automatically determines the cut-off points regardless of the values of the ordinal variable.

⁷ See Wooldridge (2002) or any other textbook on the econometrics of qualitative dependant variable.

⁸ The econometric model identifies all parameters associated with x ₁, x ₂ and x ₃ because of the nonlinearity of the Mill's ratio. However, in most sample selection specifications, some variables are usually not available for the censored observations, which means that the set of variables in x ₁ is usually smaller than in x ₂ and x ₃.

⁹ Since each stage contains different number of observations and generally different sets of explanatory variables, we cannot estimate the SUR model with Ordinary Least Squares (OLS) regression applied to each latent equation separately.

¹⁰ To conclude this methodological section, one could wonder if we need three equations. Our model could have been written within an ordered probit framework if one only uses one latent variable for the number of bidders (lots without bids are interpreted as censored observations). However, this specification is not as flexible, because it implies that the unobservable variable that determines whether a lot receives at least one bid is perfectly correlated with the unobservable variable that determines the number of bidders conditional on a lot receiving at least one bid. There are indeed good reasons to believe that these unobservable variables are not perfectly correlated.

¹¹ Convergence of the MCMC algorithm was reached quickly. We removed the first 100 000 iterations and kept the next 1 000 000 iterations for inference.

¹² Results of these preliminary estimations are available upon request.

¹³ Such a model is available upon request.