This paper studies Structural Vector Autoregressions that impose equality and/or inequality restrictions to set-identify a single shock (e.g., a monetary shock). We make three contributions to the literature. (i) We present an algorithm to compute -- for each horizon, each variable, a fixed vector of reduced-form parameters, and a given collection of equality and/or inequality restrictions -- the largest and smallest value of the coefficients of the structural impulse-response function. (ii) We provide conditions under which the largest and smallest value of the structural parameters are directionally differentiable functions of the reduced-form parameters. (iii)We propose a computationally convenient delta-method confidence interval for the set-identified coefficients of the structural impulse-response function. We present sufficient conditions to guarantee the pointwise consistency in level of the suggested inference approach. To illustrate our results, we use a monetary Structural Vector Autoregression estimated with monthly U.S. data. We set-identify an unconventional monetary policy shock that decreases the two-year government bond rate upon impact, but has no effect over the nominal federal funds rate. We impose two additional sign restrictions on the contemporaneous responses of inflation and output. We use our confidence bands to assess the effects of the announcement of the second part of the so-called Quantitative Easing program in August 2010. (JEL-Classification: C1, C32, E47).
2015 11th World Congress Econometric Society, Montreal, Canada
2015 22nd International Symposium on Mathematical Programming, Pittsburgh, USA
2015 PSU-Cornell Macro Workshop, Pennsylvania State University, State College, USA
2015 Annual Conference of the Royal Economic Society, University of Manchester, UK
2015 Higher School of Economics, Moscow, Russia
2014 Latin American Meeting of The Econometric Society, University of São Paulo, Brazil
All finite single-agent choice problem with ordinal preferences admit a compatible utility function such that: strict dominance by pure or mixed actions coincides with dominance by pure actions in the sense of Börgers (1993). With asymmetric preferences, Börgers’ notion of dominance reduces to the classical notion of strict dominance by pure strategies. The result extends to some infinite environments satisfying different assumptions. In all cases, the equivalence holds whenever the agent is sufficiently risk averse.
Working Papers
Conditional quantile estimators: A small sample theory
This paper studies small sample properties and bias of just-identified instrumental variable quantile regression (IVQR) estimators, nesting order statistics and classical quantile regression. We propose a theoretical framework for analyzing small sample properties based on a novel approximation of the discontinuous sample moments with a Hölder continuous process. Using this approximation, we derive remainder bounds for the asymptotic linear expansions of exact and k-step estimators of IVQR models. Furthermore, we derive a bias formula for exact IVQR estimators up to order o(1/n). The bias contains components that cannot be consistently estimated and depend on the particular numerical estimation algorithm. To circumvent this problem, we propose a novel 1-step adjustment of the estimator, which admits a feasible bias correction. Monte Carlo evidence suggests that our formula removes a substantial portion of the bias for sample sizes as small as n=50. We suggest using exact estimators, when possible, to achieve the smallest bias. Otherwise, applying 1-step corrections may improve the higher-order bias and MSE of any consistent estimator.
Inference in high-dimensional set-identified linear models
This paper proposes both point-wise and uniform confidence intervals (CIs) for an element theta_1 of a parameter vector theta in R^d which is partially identified by affine moment equality and inequality conditions. The CIs are based on an estimator of a regularized support function of the identified set and have closed–form. I provide examples in which my CIs are shorter than those in the existing literature. Unlike much of the existing literature, the proposed CIs can be computed as a solution to a convex optimization problem, which leads to a substantial decrease in computation time. My approach can be used, for instance, to compute a CI for the return to schooling using income bracket data without strong distributional assumptions.
We study the properties of projection inference for set-identified Structural Vector Autoregressions. A nominal 1-alpha projection region collects the structural parameters that are compatible with a 1-alpha Wald ellipsoid for the model's reduced-form parameters (autoregressive coefficients and the covariance matrix of residuals). We show that projection inference can be applied to a general class of stationary models, is computationally feasible, and it produces regions for the structural parameters and their identified set with both frequentist coverage and robust Bayesian credibility of at least 1- alpha.
A drawback of the projection approach is that both coverage and robust credibility may be strictly above their nominal level. Following the work of Kaido, Molinari, and Stoye (2016), we calibrate the radius of the Wald ellipsoid to guarantee that the robust Bayesian credibility of the projection method is exactly 1 - alpha. If the bounds of the identified set are differentiable, our calibrated projection also covers the identified set with probability 1 - alpha. We illustrate the main results of the paper using the demand/supply-model for the U.S. labor market in Baumeister and Hamilton (2015).
2015 11th World Congress Econometric Society, Montreal, Canada
2015 22nd International Symposium on Mathematical Programming, Pittsburgh, USA
2015 PSU-Cornell Macro Workshop, Pennsylvania State University, State College, USA
2015 Annual Conference of the Royal Economic Society, University of Manchester, UK
2015 Higher School of Economics, Moscow, Russia
2014 Latin American Meeting of The Econometric Society, University of São Paulo, Brazil
We present a signalling theory of Quantitative Easing (QE) at the zero lower bound on the short term nominal interest rate. QE is effective because it generates a credible signal of low future real interest rates in a time consistent equilibrium. We show these results in two models. One has coordinated monetary and fiscal policy. The other an independent central bank with balance sheet concerns. Numerical experiments show that the signalling effect can be substantial in both models.
2015 Annual Conference of the Royal Economic Society, University of Manchester, UK
2014 Latin American Meeting of The Econometric Society, University of São Paulo, Brazil
2014 Workshop on non-standard monetary policy measures, European Central Bank, Frankfurt
2014 EconCon 2014 conference, Princeton University, USA
2014 Higher School of Economics, Moscow, Russia
2014 Annual Meeting of the Society for Economic Dynamics, University of Toronto, Canada
2013 Second Prospects in Economic Research Conference, Pennsylvania State University, USA
Identification in dynamic models using sign restrictions
Sign restrictions on impulse response functions are used in the literature to identify structural vector autoregressions and structural factor models. I extend the rank condition used for exclusion restrictions and provide a necessary and sufficient conditions for point identification for sign restrictions in this class of models. The necessary condition for point identification implies that as the number of sign restrictions grows a subset with sufficient number of sign restrictions becomes binding in the limit. However, one does not need to possess information about this subset to achieve point identification. So when exclusion restrictions are not justified by theory, sign restrictions can provide an alternative way to get point-identified impulse response functions. Also further, I present a closed form representation of the set of all impulse response functions satisfying a set of sign restrictions. I demonstrate that restrictions on responses to all shocks can dramatically shrink this set when compared to restrictions only on a small number of shocks.
2013 23rd Annual Meeting of the Midwest Econometrics Group, Indiana University, Bloomington
What drives heterogeneity in retail price-setting behavior? Using weekly scanner data on household goods covering hundreds of stores in 24 markets, we construct standard measures of nominal rigidity at the store-product level and uncover several new facts. First, we find that product-level factors accounts for 23% of total variation in nominal rigidity. However, we document substantial within-product variation driven by stores, which accounts for 18 to 28% of the non-residual variation (or 5 to 10% of total variation). We use three observable factors to describe how sensitive store profits are to mispricing errors for each product. These factors not only explain across-product variation, but can also account for some fraction of within-product variation due to differences in responsiveness to these factors across stores. Specifically, stores that price more flexibly on average are also more sensitive to observables when setting pricing policies. A model of rational attention, in which heterogeneity is driven by variation in both product characteristics and manager information capacity, provides a compelling explanation for these findings.
2015 11th World Congress Econometric Society, Montreal, Canada
2015 Annual Conference of the Royal Economic Society, University of Manchester, UK
A Simulation-Based Toolbox for Solving High-Dimensional Dynamic Models
We develop a simulation-based toolbox for solving high-dimensional dynamic economic models basedon the generalized stochastic simulation algorithm (GSSA) proposed in Judd, Maliar, and Maliar (2011). GSSA is a global solution method that solves dynamic economic models on a set of simulated points. The main innovations introduced in GSSA elative to the previous stochastic simulation approaches | linear regressions with regularization and quadrature and monomial integration | make GSSA a stable and accurate solution method. In developing our toolbox based on GSSA we pursue two major goals. First, we provide a user with an interface to specify an economic model, while shielding him or her from the implementation details of the algorithm (i.e., we provide a solver-like functionality). Second, we design the toolbox in a modular way, such that users can choose between options for different parts of the algorithm and new parts can be added without rewriting the whole solver. We further improve the original GSSA (as it is introduced in Judd et al, 2011) along several dimensions. First, we allow a user to divide the list of model unknowns into those which are approximated by polynomials and those which are solved exactly from a system of non-linear equations. Second, we introduce parallelization into several parts of the algorithm. As a next step, we plan to implement curve tting with parameter restrictions (e.g., shape restrictions) and to introduce an option to approximate solutions with local basis functions. The toolbox can be used under both Windows and Unix systems and it is available upon request from the authors.
Do unobserved components models forecast inflation in Russia?
Based on my undergraduate thesis, featured in Deutsche Bank's Quantitative Strategy Academic Insights newsletter issue 10.11.2013 Open PDF
I apply the model with unobserved components and stochastic volatility (UC-SV) to forecast the Russian consumer price index. I extend the model which was previously suggested as a model for inflation forecasting in the USA to take into account a possible difference in model parameters and seasonal factor. Comparison of the out-of-sample forecasting performance of the linear AR model and the UC-SV model by mean squared error of prediction shows better results for the latter model. Relatively small absolute value of the standard error of the forecasts calculated by the UC-SV model makes it a reasonable candidate for a real time forecasting method for the Russian CPI.
