A General Framework of Dual Certificate Analysis for Structured Sparse Recovery Problems

This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work, due to the lack of a general and coherent theory, the analysis has so far only been carried out in limited scopes for specific problems. In this context the current paper makes two contributions. First, we introduce a general definition of dual certificate, which we then use to develop a unified theory of sparse recovery analysis for convex programming. Second, we present a class of structured sparsity regularization called structured Lasso for which calculations can be readily performed under our theoretical framework. This new theory includes many seemingly loosely related previous work as special cases; it also implies new results that improve existing ones even for standard formulations such as L1 regularization

The External Impact of China's Exchange Rate Policy: Evidence from Firm Level Data

We examine the impact of renminbi revaluation on firm valuations, considering two surprise announcements of changes in China’s exchange rate policy in 2005 and 2010 and data on 6,050 firms in 44 countries. Renminbi appreciation has a positive effect on firms exporting to China but little positive or even a negative impact on those providing inputs for China’s processing exports. Stock prices rise for firms competing with China in their home market while falling for firms importing Chinese products with large imported-input content. Renminbi appreciation also reduces the valuation of financially-constrained firms, particularly in more financially integrated countries.

Is China's FDI Coming at the Expense of Other Countries?

We analyze how China's emergence as a destination for foreign direct investment is affecting the ability of other countries to attract FDI. We do so using an approach that accounts for the endogeneity of China's FDI. The impact turns out to vary by region. China's rapid growth and attractions as a destination for FDI also encourages FDI flows to other Asian countries, as if producers in these economies belong to a common supply chain. There is also evidence of FDI diversion from OECD recipients. We interpret this in terms of FDI motivated by the desire to produce close to the market where the final sale takes place. For whatever reason -- limits on their ability to raise finance for investment in multiple markets or limits on their ability to control operations in diverse locations -- firms more inclined to invest in China for this reason are corresponding less inclined to invest in the OECD. A detailed analysis of Japanese foreign direct investment outflows disaggregated by sector further supports these conclusions.

Does Trade Globalization Induce or Inhibit Corporate Transparency? Unbundling the Growth Potential and Product Market Competition Channels

How does increasing globalization affect corporate transparency? Freer trade represents different facets and in theory has ambiguous effects on corporate transparency. On the one hand, by exposing firms to more product market competition, it could discourage discretionary disclosure. On the other hand, by opening up foreign markets and enhancing firms’ growth opportunities, it may promote more transparency. Rather than simply estimating a net effect, this paper pursues an approach that allows separate estimation of the two potentially opposing channels. We employ three different measures of corporate transparency and track their evolutions for 4061 firms in 49 countries during 1992-2005. By using detailed product-level tariff schedules for these countries, we construct a measure of growth opportunities enabled by foreign tariff liberalizations at the sector-country-year level, and a second measure of globalization-induced product market competition based on a country’s own tariff liberalization (again at the sector–country-year level). We find strong evidence that higher growth opportunities engendered by globalization promotes corporate transparency, especially in industries that depend heavily on external financing. At the same time, we find somewhat weaker evidence that greater product market competition engendered by globalization discourages corporate transparency. The results demonstrate the importance of disentangling the multiple and potentially conflicting effects of globalization.

Sparse Recovery with Very Sparse Compressed Counting

Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt very sparse Compressed Counting for nonnegative signal recovery. Our design matrix is sampled from a maximally-skewed p-stable distribution (0<p<1), and we sparsify the design matrix so that on average (1-g)-fraction of the entries become zero. The idea is related to very sparse stable random projections (Li et al 2006 and Li 2007), the prior work for estimating summary statistics of the data. In our theoretical analysis, we show that, when p->0, it suffices to use M= K/(1-exp(-gK) log N measurements, so that all coordinates can be recovered in one scan of the coordinates. If g = 1 (i.e., dense design), then M = K log N. If g= 1/K or 2/K (i.e., very sparse design), then M = 1.58K log N or M = 1.16K log N. This means the design matrix can be indeed very sparse at only a minor inflation of the sample complexity. Interestingly, as p->1, the required number of measurements is essentially M = 2.7K log N, provided g= 1/K. It turns out that this result is a general worst-case bound