The Desire for (Danish) Quality in High and Low Income Countries

We estimate the correlation between firm prices and sales within a CN8 product-country-year market. We do this for every market to which at least 16 different Danish firms exported between 1999 and 2006. Approximately 60% of Danish exports are to markets in which the price is negatively correlated with sales. These correlations are significantly different across destination countries within product categories, but across years for a given product-destination pair. While some existing theories perform better than others at predicting these patterns, none can reconcile the variation across countries. To fully explain the patterns, We introduce a model in which the price-sales correlation can be interpreted as the market's desire for high quality goods over low cost substitutes. We discover an inverted U shaped relation between a country's desire for quality and its per capita GDP, which we term a Quality Kuznets Curve. This curve has a turning point around 10 000 Euros for Danish exports. The Quality Kuznets Curve appears both when looking across products and within products.exports; firm heterogeneity; quality; productivity; Kuznets

Demand Uncertainty: Exporting Delays and Exporting Failures

This paper presents a model of trade that explains why firms wait to export and why many exporters fail. Firms face uncertain demands that are only realized after the firm enters the destination. The model retools the timing of uncertainty resolution found in productivity heterogeneity models. This retooling addresses several shortcomings. First, the imperfect correlation of demands reconciles the sales variation observed in and across destinations. Second, since demands for the firm's output are correlated across destinations, a firm can use previously realized demands to forecast unknown demands in untested destinations. The option to forecast demands causes firms to delay exporting in order to gather more information about foreign demand. Third, since uncertainty is resolved after entry, many firms enter a destination and then exit after learning that they cannot profit. This prediction reconciles the high rate of exit seen in the first years of exporting. Finally, when faced with multiple countries in which to export, some firms will choose to sequentially export in order to slowly learn more about its chances for success in untested markets.firm heterogeneity; exporting; trade failures; trade delay

Extreme statistics of non-intersecting Brownian paths

We consider finite collections of $N$ non-intersecting Brownian paths on the line and on the half-line with both absorbing and reflecting boundary conditions (corresponding to Brownian excursions and reflected Brownian motions) and compute in each case the joint distribution of the maximal height of the top path and the location at which this maximum is attained. The resulting formulas are analogous to the ones obtained in [MFQR13] for the joint distribution of $\mathcal{M}={\rm max}_{x\in\mathbb{R}}\{\mathcal{A}_2(x)-x^2\}$ and $\mathcal{T}={\rm argmax}_{x\in\mathbb{R}}\{\mathcal{A}_2(x)-x^2\}$, where $\mathcal{A}_2$ is the Airy$_2$ process, and we use them to show that in the three cases the joint distribution converges, as $N\to\infty$, to the joint distribution of $\mathcal{M}$ and $\mathcal{T}$. In the case of non-intersecting Brownian bridges on the line, we also establish small deviation inequalities for the argmax which match the tail behavior of $\mathcal{T}$. Our proofs are based on the method introduced in [CQR13,BCR15] for obtaining formulas for the probability that the top line of these line ensembles stays below a given curve, which are given in terms of the Fredholm determinant of certain "path-integral" kernels.Comment: Minor corrections, improved exposition. To appear in Electron. J. Proba

Instabilities in the mean field limit

Consider a system of $N$ particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a $\mathcal{C}^2$ smooth potential in any dimension. We prove that in the mean field limit $N \to + \infty$, the $N$ particles system displays instabilities in times of order $\log N$ for some configurations approximately distributed according to unstable homogeneous equilibria.Comment: minor typos corrected; Journal of Statistical Physics, accepte

Ill-posedness of the hydrostatic Euler and singular Vlasov equations

In this paper, we develop an abstract framework to establish ill-posedness in the sense of Hadamard for some nonlocal PDEs displaying unbounded unstable spectra. We apply it to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov-Dirac-Benney system