This study finds that investors price firms' greenhouse gas (GHG) emissions as a negative component of equity value, and this valuation discount does not differ between firms that voluntarily disclose to the Carbon Disclosure Project (CDP) and nondisclosing firms. We derive the GHG emissions for nondisclosers from an estimation model that incorporates firm characteristics and industry. The finding that investors view CDP amounts and estimates of emissions as equally value-relevant suggests that equity values reflect GHG information from channels other than the CDP. An event study of investors' response to emission-related information in firms' 8-K filings further supports this finding. Economically, our results suggest that, for the median S&P 500 firm, GHG emissions impose a market-implied equity discount of $79 per ton, representing about one-half of 1 percent of market capitalization. * Accepted

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The human visual system is proficient in perceiving three-dimensional shape from the shading patterns in a two-dimensional image. How it does this is not well understood and continues to be a question of fundamental and practical interest. In this paper we present a new quantitative approach to shape-from-shading that may provide some answers. We suggest that the brain, through evolution or prior experience, has discovered that objects can be classified into lower-dimensional object-classes as to their shape. Extraction of shape from shading is then equivalent to the much simpler problem of parameter estimation in a low-dimensional space. We carry out this proposal for an important class of three-dimensional (3D) objects: human heads. From an ensemble of several hundred laser-scanned 3D heads, we use principal component analysis to derive a low-dimensional parameterization of head shape space. An algorithm for solving shape-from-shading using this representation is presented. It works well even on real images where it is able to recover the 3D surface for a given person, maintaining facial detail and identity, from a single 2D image of his face. This algorithm has applications in face recognition and animation.

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