## Vadim Marmer

I am an Associate Professor in the Vancouver School of Economics at UBC. I came to UBC in 2005 after completing my Ph.D. at Yale University. My main area of research is Econometrics, where I have worked on estimation and inference for auctions, weak identification, misspecification, and time series.

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**PUBLISHED PAPERS**

We consider inference on the probability density of valuations in the first-price sealed-bid auctions model within the independent private value paradigm. We show the asymptotic normality of the two-step nonparametric estimator of Guerre, Perrigne, and Vuong (2000) (GPV), and propose an easily implementable and consistent estimator of the asymptotic variance. We prove the validity of the pointwise percentile bootstrap confidence intervals based on the GPV estimator. Lastly, we use the intermediate Gaussian approximation approach to construct bootstrap-based asymptotically valid uniform confidence bands for the density of the valuations.

This paper considers tests and confidence sets (CSs) concerning the coefficient on the endogenous variable in the linear IV regression model with homoskedastic normal errors and one right‐hand side endogenous variable. The paper derives a finite‐sample lower bound function for the probability that a CS constructed using a two‐sided invariant similar test has infinite length and shows numerically that the conditional likelihood ratio (CLR) CS of Moreira (2003) is not always “very close,” say 0.005 or less, to this lower bound function. This implies that the CLR test is not always very close to the two‐sided asymptotically‐efficient (AE) power envelope for invariant similar tests of Andrews, Moreira, and Stock (2006) (AMS).

On the other hand, the paper establishes the finite‐sample optimality of the CLR test when the correlation between the structural and reduced‐form errors, or between the two reduced‐form errors, goes to 1 or −1 and other parameters are held constant, where optimality means achievement of the two‐sided AE power envelope of AMS. These results cover the full range of (nonzero) IV strength.

The paper investigates in detail scenarios in which the CLR test is not on the two‐sided AE power envelope of AMS. Also, theory and numerical results indicate that the CLR test is close to having the greatest average power, where the average is over a specified grid of concentration parameter values and over a pair of alternative hypothesis values of the parameter of interest, uniformly over all such pairs of alternative hypothesis values and uniformly over the correlation between the structural and reduced‐form errors. Here, “close” means 0.015 or less for k ≤ 20, where k denotes the number of IVs, and 0.025 or less for 0 < k ≤ 40.

The paper concludes that, although the CLR test is not always very close to the two‐sided AE power envelope of AMS, CLR tests and CSs have very good overall properties.

The standard real-options model predicts that increased uncertainty discourages investment. When projects are large and take time to build, however, that prediction can be reversed. We investigate the investment/uncertainty relationship empirically using historical data on opening dates of new U.S. copper mines – large, irreversible projects with substantial construction lags. Both the timing of the decision to go forward and the price thresholds that trigger that decision are assessed. In particular, we build upon a reduced form analysis to construct a structural model of entry. We find that, in this market, greater uncertainty encourages investment and lowers the price thresholds for many mines.

In fuzzy regression discontinuity (FRD) designs, the treatment effect is identified through a discontinuity in the conditional probability of treatment assignment. We show that when identification is weak (i.e., when the discontinuity is of a small magnitude), the usual t-test based on the FRD estimator and its standard error suffers from asymptotic size distortions as in a standard instrumental variables setting. This problem can be especially severe in the FRD setting since only observations close to the discontinuity are useful for estimating the treatment effect. To eliminate those size distortions, we propose a modified t-statistic that uses a null-restricted version of the standard error of the FRD estimator. Simple and asymptotically valid confidence sets for the treatment effect can be also constructed using this null-restricted standard error. An extension to testing for constancy of the regression discontinuity effect across covariates is also discussed.

In this paper, we argue that limited asset market participation (LAMP) plays an important role in explaining international business cycles. We show that when LAMP is introduced into an otherwise standard model of international business cycles, the performance of the model improves significantly, especially in matching cross-country correlations. To perform formal evaluation of the models we develop a novel statistical procedure that adapts the statistical framework of Vuong (1989) to DSGE models. Using this methodology, we show that the improvements brought out by LAMP are statistically significant, leading a model with LAMP to outperform a representative agent model. Furthermore, when LAMP is introduced, a model with complete markets is found to do as well as a model with no trade in financial assets – a well-known favorite in the literature. Our results remain robust to the inclusion of investment specific technology shocks.

We develop a selective entry model for first-price auctions that nests two polar models often estimated in the empirical literature on auctions, Levin and Smith (1994), and Samuelson (1985). The selective entry model features a pro-competitive selection effect. The selection effect is shown to be nonparametrically identifiable, and a nonparametric test for its presence is proposed. This test can be used to discriminate between the two polar models.

Suppose that the econometrician is interested in comparing two misspecified moment restriction models, where the comparison is performed in terms of some chosen measure of fit. This paper is concerned with describing an optimal test of the Vuong (1989) and Rivers and Vuong (2002) type null hypothesis that the two models are equivalent under the given measure of fit (the ranking may vary for different measures). We adopt the generalized Neyman–Pearson optimality criterion, which focuses on the decay rates of the type I and II error probabilities under fixed non-local alternatives, and derive an optimal but practically infeasible test. Then, as an illustration, by considering the model comparison hypothesis defined by the weighted Euclidean norm of moment restrictions, we propose a feasible approximate test statistic to the optimal one and study its asymptotic properties. Local power properties, one-sided test, and comparison under the generalized empirical likelihood-based measure of fit are also investigated. A simulation study illustrates that our approximate test is more powerful than the Rivers–Vuong test.

This paper proposes several testing procedures for comparison of misspecified calibrated models. The proposed tests are of the Vuong-type ( and ). In our framework, the econometrician selects values for model’s parameters in order to match some characteristics of data with those implied by the theoretical model. We assume that all competing models are misspecified, and suggest a test for the null hypothesis that they provide equivalent fit to data characteristics, against the alternative that one of the models is a better approximation. We consider both nested and non-nested cases. We also relax the dependence of models’ ranking on the choice of a weight matrix by suggesting averaged and sup-norm procedures. The methods are illustrated by comparing the cash-in-advance and portfolio adjustment cost models in their ability to match the impulse responses of output and inflation to money growth shocks.

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in first-price sealed-bid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre et al. (2000), and is also asymptotically normal with an appropriate choice of the bandwidth.

[go to paper] [go to MATLAB codes] [go to supplement] [Working paper version with corrected typos]

This paper introduces a rank-based test for the instrumental variables regression model that dominates the Anderson–Rubin test in terms of finite sample size and asymptotic power in certain circumstances. The test has correct size for any distribution of the errors with weak or strong instruments. The test has noticeably higher power than the Anderson–Rubin test when the error distribution has thick tails and comparable power otherwise. Like the Anderson–Rubin test, the rank tests considered here perform best, relative to other available tests, in exactly identified models.

Implications of nonlinearity, nonstationarity, and misspecification are considered from a forecasting perspective. Our model allows for small departures from the martingale difference sequence hypothesis by including a nonlinear component, formulated as a general, integrable transformation of the I(1) predictor. We assume that the true generating mechanism is unknown to the econometrician and he is therefore forced to use some approximating functions. It is shown that in this framework the linear regression techniques lead to spurious forecasts. Improvements of the forecast accuracy are possible with properly chosen nonlinear transformations of the predictor. The paper derives the limiting distribution of the forecasts’ mean squared error (MSE). In the case of square integrable approximants, it depends on the L2-distance between the nonlinear component and approximating function. Optimal forecasts are available for a given class of approximants.

This paper presents tests for the null hypothesis of no regime switching in Hamilton’s (Econometrica 57:357–384, 1989) regime switching model. The test procedures exploit similarities between regime switching models, autoregressions with measurement errors, and finite mixture models. The proposed tests are computationally simple and, contrary to likelihood based tests, have a standard distribution under the null. When the methodology is applied to US GDP growth rates, no strong evidence of regime switching is found.

In this paper, we suggest a simple econometric procedure for identification of bottlenecks in the US natural gas pipelines network. We claim that there is a bottleneck between two nodes of the network if their spot gas prices are not co-integrated. Existence of bottlenecks is attributed to insufficient pipeline capacity between two such nodes. We find that the network is separated into three local markets: Northeast, Midwest and California.

This paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d0 are included. The results establish that the bootstrap provides higher-order improvements over the delta method. Analogous results are given for tests. The CIs and tests are based on one or other of two approximate maximum likelihood estimators. The first estimator solves the first-order conditions with respect to the covariance parameters of a “plug-in” log-likelihood function that has the unknown mean replaced by the sample mean. The second estimator does likewise for a plug-in Whittle log-likelihood.

The magnitudes of the coverage probability errors for one-sided bootstrap CIs for covariance parameters for long-memory time series are shown to be essentially the same as they are with iid data. This occurs even though the mean of the time series cannot be estimated at the usual n1/2 rate.

WORKING PAPERS

This paper considers a general form of network dependence where dependence between two sets of random variables becomes weaker as their distance in a network gets longer. We show that such network dependence cannot be embedded as a random field on a lattice in a Euclidean space with a fixed dimension when the maximum clique increases in size as the network grows. This paper applies Doukhan and Louhichi (1999)'s weak dependence notion to network dependence by measuring dependence strength by the covariance between nonlinearly transformed random variables. While this approach covers examples such as strong mixing random fields on a graph and conditional dependency graphs, it is most useful when dependence arises through a large functional-causal system of equations. The main results of our paper include the law of large numbers, and the central limit theorem. We also propose a heteroskedasticity-autocorrelation consistent variance estimator and prove its consistency under regularity conditions. The finite sample performance of this latter estimator is investigated through a Monte Carlo simulation study.

We propose a new nonparametric estimator for first-price auctions with independent private values that imposes the monotonicity constraint on the estimated inverse bidding strategy. We show that our estimator has a smaller asymptotic variance than that of Guerre, Perrigne and Vuong's (2000) estimator. In addition to establishing pointwise asymptotic normality of our estimator, we provide a bootstrap-based approach to constructing uniform confidence bands for the density function of latent valuations.

We develop a fully nonparametric identification framework and a test of collusion in ascending bid auctions. Assuming efficient collusion, we show that the underlying distributions of values can be identified despite collusive behaviour when there is at least one known competitive bidder. We propose a nonparametric estimation procedure for the distributions of values and a bootstrap test of the null hypothesis of competitive behaviour against the alternative of collusion. Our framework allows for asymmetric bidders, and the test can be performed on individual bidders.

Extending the L_{1}-IV approach proposed by Sakata (1997, 2007), we develop a new method, named the ρ_{τ}-IV estimation, to estimate structural equations based on the conditional quantile restriction imposed on the error terms. We study the asymptotic behavior of the proposed estimator and show how to make statistical inferences on the regression parameters. Given practical importance of weak identification, a highlight of the paper is a proposal of a test robust to the weak identification. The statistics used in our method can be viewed as a natural counterpart of the Anderson and Rubin's (1949) statistic in the ρ_{τ}-IV estimation.