Asymmetric Power Distribution: Theory and Applications to Risk Measurement

Theoretical literature in finance has shown that quantifying the risk of financial time series amounts to measuring their expected shortfall, also known as tail Value at Risk. Unfortunately, little empirical work has been devoted to the problem of modeling and inference of such risk measures and, in particular, to their estimation. In this paper, we construct a parametric estimator for the expected shortfall based on a new family of densities, which we call the Asymmetric Power Distribution (APD). The APD family extends the Generalized Power Distribution to cases where the data exhibits asymmetry. We provide a detailed description of the properties of an APD random variable, such as its quantiles, moments and moment related parameters. Moreover, we discuss the problem of simulation of such random variables and provide maximum likelihood estimates of the APD density parameters. The study of asymptotic properties of the latter falls outside the standard framework due to the non-differentiability of the APD log-likelihood. An empirical application to six daily financial market series reveals that returns tend to be asymmetric, with innovations which cannot be modeled by either Laplace (double-exponential) or Gaussian distribution, even if we allow the latter to be asymmetric. Under a more general assumption that the return innovations are APD, we are able to compute expected shortfalls and corresponding confidence intervals and thus compare the riskiness of the series examinedexpected shortfall, value-at-risk, generalized power distribution

What Goods Do Countries Trade? New Ricardian Predictions

Though one of the pillars of the theory of international trade, the extreme predictions of the Ricardian model have made it unsuitable for empirical purposes. A seminal contribution of Eaton and Kortum (2002) is to demonstrate that random productivity shocks are sufficient to make the Ricardian model empirically relevant. While successful at explaining trade volumes, their model remains silent with regards to one important question: What goods do countries trade? Our main contribution is to generalize their approach and provide an empirically meaningful answer to this question.

Biases in Macroeconomic Forecasts: Irrationality or Asymmetric Loss?

Survey data on expectations frequently find evidence that forecasts are biased, rejecting the joint hypothesis of rational expectations and symmetric loss. While the literature has attempted to explain this bias through forecasters' strategic behavior, we propose a simpler explanation based on asymmetric loss. We establish that existing rationality tests are not robust to even small deviations from symmetry and hence have little ability to tell whether the forecaster is irrational or the loss function is asymmetric. We propose new and more general methods for testing forecast rationality jointly with flexible families of loss functions that embed quadratic loss as a special case. An empirical application to survey data on forecasts of nominal output growth shows strong evidence against rationality and symmetric loss. There is considerably weaker evidence against rationality once asymmetric loss is permittedrationality testing, forecasting, asymmetric loss

Testing Models with Multiple Equilibria by Quantile Methods

We derive an econometric test for the presence of monotone comparative statics in models with multiple equilibria. The test applies to many economic models, such as single-person decision, industrial organization, macroeconomic and game-theory models. These models have complementarities between exogenous and endogenous variables. We show that, as a result, extreme (large and small) conditional quantiles of the endogenous variable are increasing in the exogenous variable. We develop a likelihood-ratio test based on estimates for the conditional quantiles of the endogenous variable, which is an asymptotic extension of Bartholomew's (1959a,b) "chi-bar squared" test. Our assumptions are weak; we remain agnostic about the cardinality, location and probabilities of the equilibrium set, and make no restrictions on the equilibrium-selection procedure

Nonparametric Identification and Estimation of Transformation Models

This paper derives sufficient conditions for nonparametric transformation models to be identified and develops estimators of the identified components. Our nonparametric identification result is global, and is derived under conditions that are substantially weaker than full independence. In particular, we show that a completeness assumption combined with conditional independence with respect to one of the regressors suffices for the model to be identified. The identification result is also constructive in the sense that it yields explicit expressions of the functions of interest. We show how natural estimators can be developed from these expressions, and analyze their theoretical properties. Importantly, it is demonstrated that the proposed estimator of the unknown transformation function converges at the parametric rate.nonparametric identification; transformation models; kernel estimation

What Goods Do Countries Trade? A Quantitative Exploration of Ricardo's Ideas

The Ricardian model predicts that countries should produce and export relatively more in industries in which they are relatively more productive. Though one of the most celebrated insights in the theory of international trade, this prediction has received virtually no attention in the empirical literature since the mid-sixties. The main reason behind this lack of popularity is the absence of clear theoretical foundations to guide the empirical analysis. Building on the seminal work of Eaton and Kortum (2002), the present paper offers such foundations and uses them to quantify the importance of Ricardian comparative advantage. Using trade and productivity data from 1997, we estimate that, ceteris paribus, the elasticity of bilateral exports with respect to observed productivity is 6.53. From a welfare standpoint, however, the removal of Ricardian comparative advantage at the industry level would only lead, on average, to a 5.5% decrease in the total gains from trade.

Evaluation and combination of conditional quantile forecasts

We propose an encompassing test for comparing conditional quantile forecasts in an out-of-sample framework. Our test provides a basis for forecast combination when encompassing is rejected. Its central features are (1) use of the "tick" loss function, (2) a conditional approach to out-of-sample evaluation, and (3) derivation in an environment with asymptotically nonvanishing estimation uncertainty. Our approach is valid under general conditions; the forecasts can be based on nested or nonnested models and can be obtained by general estimation procedures. We illustrate the test properties in a Monte Carlo experiment and apply it to evaluate and compare four popular value-at-risk models

New Trade Models, Same Old Gains?

Micro-level data have had a profound influence on research in international trade over the last ten years. In many regards, this research agenda has been very successful. New stylized facts have been uncovered and new trade models have been developed to explain these facts. In this paper we investigate to what extent answers to new micro-level questions have affected answers to an old and central question in the field: how large are the welfare gains from trade? A crude summary of our results is: "So far, not much." (JEL F11, F12)