Academic research
Research in econometric theory: GMM and GEL inference with singular moment variance, identification-robust inference, weak instruments, and applied microeconometrics.
A brief, plain-English summary of the doctoral thesis (supervised by Professor Richard J. Smith) and the three papers it contains. Read the full thesis (PDF). The thesis is also catalogued by the British Library: EThOS record. Presented at RJS@65, the conference in honour of Professor Smith's 65th birthday (Cambridge, May 2014): programme and abstracts.
The thesis · University of Cambridge · 2013
Supervised by Professor Richard J. Smith, the thesis asks one unifying question: how do you still draw trustworthy conclusions from economic data when the standard textbook assumptions quietly break down? It gathers three self-contained papers, each tackling a different way those assumptions fail. All three are summarised below.
Paper 1 · Identification-robust inference
Estimating a relationship from data relies on the data carrying a strong enough signal to pin the answer down. Popular "robust" tests assume that signal never fully collapses. This paper works out what happens when it does, using higher-order matrix perturbation theory. It finds new conditions under which a widely used test, the Generalised Anderson-Rubin statistic, still behaves correctly, and identifies a failure case, "moment-singularity bias", where the test blows up and gives badly misleading answers. A simulation of an instrumental-variables model demonstrates the problem. Why it matters: it warns applied researchers when a trusted method can silently fail.
Paper 2 · Weak instruments · Published, Advances in Econometrics 2012
When economists use "instruments" to separate cause from correlation, having many weak ones biases the result. A common fix compresses the instruments using principal components, keeping the "biggest" combinations. This paper shows that fix can throw away exactly the information that matters, because the biggest variation is not the same as the most relevant. It proposes "Normalized Principal Components" (NPC), which rank instrument combinations by genuine relevance, and shows in simulations they beat the standard method. Applied to Angrist and Krueger's well-known Vietnam-draft study of the returns to schooling, the method finds the effect of education on earnings to be much lower than the standard estimates suggest. Why it matters: better instrument choice means more credible cause-and-effect estimates.
Paper 3 · Partial identification · With Richard J. Smith
Sometimes economic theory only tells you a quantity is "at least" or "no more than" something, not its exact value, so the data pin down a range of possibilities rather than a single number (this is called partial identification). This paper, joint with Professor Richard J. Smith, develops generalised empirical likelihood (GEL) methods for that setting, and shows that dropping one seemingly harmless technical assumption is actually essential to the results. It proves the method reliably recovers the whole plausible range and pins down how quickly it does so. Why it matters: it strengthens the toolkit for modern applied work where models are only partially identified.
Nicky L. Grant (University of St Andrews) & Richard J. Smith (University of Cambridge)
Constructs a confidence region with pointwise asymptotically correct size for a parameter of interest using the generalised Anderson-Rubin (GAR) statistic when the moment variance matrix is singular. The large-sample behaviour of the GAR statistic is analysed via a Laurent series expansion around points of moment variance singularity. Under a condition termed first-order moment singularity, the GAR statistic is shown to have a limiting chi-square distribution on parameter sequences converging to the true value. Violation of this condition renders the GAR statistic unbounded asymptotically. The paper details an appropriate discretisation of the parameter space to implement a feasible GAR-based confidence region with pointwise asymptotically correct size. No regularisation or pre-testing is required. Simulation evidence demonstrates the efficacy of the approach.
Keywords: Laurent series expansion · moment indicator · parameter sequences · singular moment matrix · JEL: C13, C31, C51, C52
Journal article · 2019
How sensitive is the average taxpayer to changes in the tax-price of giving?
International Tax and Public Finance, Vol. 26(2), pp. 317-356, Springer
Shows that standard estimates of the price elasticity of giving for the average US taxpayer, which include non-itemisers, are biased downwards, so the literature over-states the elasticity in absolute value. Proposes a consistent and more efficient estimator under a testable restriction, estimates the bias at around -1, and finds an inelastic price response for the average taxpayer, with an elastic response only for households in the top income decile. Published online 26 June 2018 and open access. An earlier version circulated as University of Manchester Economics Discussion Paper EDP-1606 (October 2016), "Consistent Estimation of the Tax-Price Elasticity of Charitable Giving with Survey Data".
Journal article · 2016
Correlated Random Effects Quantile Estimation of the Tax-Price Elasticity of Charitable Donations
Economics Bulletin, Vol. 36(3), pp. 1729-1736
Estimates the tax-price elasticity of charitable donations across the distribution of giving using a Correlated Random Effects quantile estimator, controlling for unobserved heterogeneity. Elasticities for small-to-mid-level donors are found to be substantially smaller in absolute size than pooled quantile estimates suggest.
CeMMAP working paper · 2018 · CWP23/18
GEL-based inference with unconditional moment inequality restrictions
Centre for Microdata Methods and Practice, Institute for Fiscal Studies
Studies generalised empirical likelihood (GEL) methods for estimation of and inference on partially identified parameters in models specified by unconditional moment inequality constraints. Establishes large-sample equivalence with GMM and proposes simple conservative confidence regions for the identified set. Includes simulation evidence comparing GEL and non-diagonal GMM procedures.
Working paper · 2018
GMM Estimation and Inference with (Asymptotically) Singular Moment Variance
University of Manchester
Studies efficient 2-Step GMM estimation from strongly identified linear moment functions with (asymptotically) singular moment variance at the true parameter. Shows the 2-Step GMM estimator converges at rate √n to a non-standard limit distribution, with rate-n convergence in certain directions when the null space of the moment variance matrix does not lie within that of the outer product of the expected Jacobian. Provides examples of (almost) singular moment variance and discusses implications for inference of common empirical methods used to remove singularities.
Working paper · 2014 · EDP-1417
GMM with Weakly-Singular Variance
Economics Discussion Paper Series EDP-1417
Studies two-step GMM when moment functions are highly correlated at the true parameter, so that a subset of eigenvalues of the moment variance matrix is local to zero ("weakly-singular" variance). GMM remains consistent and asymptotically Gaussian but converges faster than root-n in certain directions of the parameter space, and the analysis clarifies where the Nearly-Singular Design results of Caner (2008) break down.
Working paper
Comment on Caner (2008): Nearly-Singular Design in GMM and Generalised Empirical Likelihood Estimators
University of Manchester
Identifies and corrects errors in the main results of Caner (2008) on GMM and GEL estimators with nearly-singular moment variance. Shows that mistakes in key lemmas invalidate the proofs of the main theorems. A corrected version of the 2-Step GMM results is provided under minimal modifications to Caner's assumptions. Also shows that the identification setup in Caner (2008) is overly restrictive, ruling out OLS as a special case, and proposes a more general identification assumption.
Book chapter · 2012
Overcoming the Many Weak Instrument Problem Using Normalized Principal Components
Essays in Honor of Jerry Hausman, Advances in Econometrics, Vol. 29, pp. 107-47. Eds: Baltagi, Hill, Newey, White. Emerald Publishing.
Introduces "normalized principal components" (NPCs) for IV estimation in the presence of many weak instruments. Shows that standard principal component reduction methods produce poor small-sample performance, and demonstrates through simulation that NPC-based selection substantially outperforms the standard approach.
Teaching notes
Linear Models in Econometrics
University of Manchester, Department of Economics.
Lecture notes covering the linear model, OLS, the zero conditional mean assumption, identification, consistency and asymptotic normality. Written as a pre-course note for the MSc econometrics course (ECON61001) at the University of Manchester.
Full publication record on CeMMAP. For questions about any of this work, get in touch.
Conference presentations
2025
GAR-Based Inference with Singular Moment Variance
With Richard J. Smith (Cambridge)
University of St Andrews
2024
Efficient GMM Estimation with (Almost) Singular Variance
Two-step efficient GMM when the moment variance is (almost) singular: non-normal limit, super-consistency, a DSGE simulation, and the case against regularisation
2019
GEL-Based Inference with Moment Inequality Restrictions
CeMMAP working paper CWP23/18 · With Richard J. Smith (Cambridge)
CeMMAP, IFS, London
2018
GMM Estimation and Inference with Singular Moment Variance
Identification-robust inference with singular moment variance matrix
Cambridge Faculty of Economics
University of St Andrews
2016
Bias in Estimating the Tax-Price Elasticity of Charitable Donations with Survey Data
Session 32, ESEM Topics in Applied Micro: Taxes · With Peter Backus (Manchester)
2016
Efficient Estimation and Inference from GMM with Singular Variance
Properties of 2-Step GMM with asymptotically singular moment variance; ad-hoc methods for removing singularities in applied work
2014
Efficient Estimation & Inference from GMM in Linear Models with Singular Moment Variance
Presented at RJS@65, the conference in honour of the 65th birthday of Professor Richard J. Smith, supervisor of the PhD thesis
2012
Overcoming the Many Weak Instrument Problem Using Normalized Principal Components
NPC-based IV selection for many weak instrument settings
Econometrics conference
Advances in Econometrics Vol. 29
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