nep-ecm New Economics Papers
on Econometrics
Issue of 2020‒10‒19
25 papers chosen by
Sune Karlsson
Örebro universitet

  1. Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection—rejoinder By Fryzlewicz, Piotr
  2. Inference with a single treated cluster By Andreas Hagemann
  3. Identifying Marginal Treatment Effects in the Presence of Sample Selection By Bartalotti, Otávio; Kedagni, Desire; Possebom, Vitor
  4. Consistent Specification Test of the Quantile Autoregression By Anthoulla Phella
  5. Conditional asymmetry in ARCH(8) models By Julien Royer
  6. A Simple Instrument for Proxy Vector Autoregressive Analysis By Lukas Boer; Helmut Lütkepohl
  7. Nonclassical Measurement Error in the Outcome Variable By Christoph Breunig; Stephan Martin
  8. Jump or kink: note on super-efficiency in segmented linear regression break-point estimation By Chen, Yining
  9. Local Regression Distribution Estimators By Matias D. Cattaneo; Michael Jansson; Xinwei Ma
  10. Identification of Treatment Effects with Mismeasured Imperfect Instruments By Kedagni, Desire
  11. Adaptive Doubly Robust Estimator By Masahiro Kato
  12. Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices By Nadja Klein; Michael Stanley Smith; David J. Nott
  13. Discovering general and sectorial trends in a large set of time series By Espasa Terrades, Antoni; Carlomagno Real, Guillermo
  14. Sharp Bounds on Treatment Effects for Policy Evaluation By Sukjin Han; Shenshen Yang
  15. Interpreting Unconditional Quantile Regression with Conditional Independence By David M. Kaplan
  16. A Class of Time-Varying Vector Moving Average Models: Nonparametric Kernel Estimation and Application By Yayi Yan; Jiti Gao; Bin Peng
  17. A Note on the Importance of Normalizations in Dynamic Latent Factor Models of Skill Formation By Del Bono, Emilia; Kinsler, Josh; Pavan, Ronni
  18. Generalized instrumental inequalities: testing the instrumental variable independence assumption By Kedagni, Desire; Mourifié, Ismael
  19. Robust and Efficient Estimation of Potential Outcome Means under Random Assignment By Akanksha Negi; Jeffrey M. Wooldridge
  20. DoubleEnsemble: A New Ensemble Method Based on Sample Reweighting and Feature Selection for Financial Data Analysis By Chuheng Zhang; Yuanqi Li; Xi Chen; Yifei Jin; Pingzhong Tang; Jian Li
  21. The characteristic function of Gaussian stochastic volatility models: an analytic expression By Eduardo Abi Jaber
  22. Prediction intervals for Deep Neural Networks By Tullio Mancini; Hector Calvo-Pardo; Jose Olmo
  23. A primer on p-value thresholds and α-levels – two different kettles of fish By Hirschauer, Norbert; Gruener, Sven; Mußhoff, Oliver; Becker, Claudia
  24. Hierarchical PCA and Modeling Asset Correlations By Marco Avellaneda; Juan Andr\'es Serur
  25. Difference-in-Differences for Ordinal Outcomes: Application to the Effect of Mass Shootings on Attitudes toward Gun Control By Soichiro Yamauchi

  1. By: Fryzlewicz, Piotr
    Abstract: Many existing procedures for detecting multiple change-points in data sequences fail in frequent-change-point scenarios. This article proposes a new change-point detection methodology designed to work well in both infrequent and frequent change-point settings. It is made up of two ingredients: one is “Wild Binary Segmentation 2” (WBS2), a recursive algorithm for producing what we call a ‘complete’ solution path to the change-point detection problem, i.e. a sequence of estimated nested models containing 0 , … , T- 1 change-points, where T is the data length. The other ingredient is a new model selection procedure, referred to as “Steepest Drop to Low Levels” (SDLL). The SDLL criterion acts on the WBS2 solution path, and, unlike many existing model selection procedures for change-point problems, it is not penalty-based, and only uses thresholding as a certain discrete secondary check. The resulting WBS2.SDLL procedure, combining both ingredients, is shown to be consistent, and to significantly outperform the competition in the frequent change-point scenarios tested. WBS2.SDLL is fast, easy to code and does not require the choice of a window or span parameter.
    Keywords: adaptive algorithms; break detection; jump detection; multiscale methods; randomized algorithms; segmentation; EP/L014246/1
    JEL: C1
    Date: 2020–09–16
  2. By: Andreas Hagemann
    Abstract: I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in difference-in-differences estimation but the test developed here applies more generally. I show that the test controls size and has power under asymptotics where the number of observations within each cluster is large but the number of clusters is fixed. The test combines weighted, approximately Gaussian parameter estimates with a rearrangement procedure to obtain its critical values. The weights needed for most empirically relevant situations are tabulated in the paper. Calculation of the critical values is computationally simple and does not require simulation or resampling. The rearrangement test is highly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.
    Date: 2020–10
  3. By: Bartalotti, Otávio; Kedagni, Desire; Possebom, Vitor
    Abstract: This article presents identification results for the marginal treatment effect (MTE) when there is sample selection. We show that the MTE is partially identified for individuals who are always observed regardless of treatment, and we derive sharp bounds on this parameter under four sets of assumptions. The first identification result combines the standard MTE assumptions without any restrictions to the sample selection mechanism. The second result imposes monotonicity of the sample selection variable with respect to the treatment, considerably shrinking the identified set. Third, we incorporate a stochastic dominance assumption which tightens the lower bound for the MTE. Finally, we provide a set of conditions that allows point identification for completeness. Our analysis extends to discrete instruments and distributional MTE. All the results rely on a mixture reformulation of the problem where the mixture weights are identified. We therefore extend the Lee (2009) trimming procedure to the MTE context. We propose some preliminary estimators for the bounds derived, provide a numerical example and simulations that corroborate the bounds feasibility and usefulness as an empirical tool. In future drafts, we plan to highlight the practical relevance of the results by analyzing the impacts of managed health care options on health outcomes and expenditures, following Deb, Munkin, and Trivedi (2006).
    Date: 2019–09–15
  4. By: Anthoulla Phella
    Abstract: This paper proposes a test for the joint hypothesis of correct dynamic specification and no omitted latent factors for the Quantile Autoregression. If the composite null is rejected we proceed to disentangle the cause of rejection, i.e., dynamic misspecification or an omitted variable. We establish the asymptotic distribution of the test statistics under fairly weak conditions and show that factor estimation error is negligible. A Monte Carlo study shows that the suggested tests have good finite sample properties. Finally, we undertake an empirical illustration of modelling GDP growth and CPI inflation in the United Kingdom, where we find evidence that factor augmented models are correctly specified in contrast with their non-augmented counterparts when it comes to GDP growth, while also exploring the asymmetric behaviour of the growth and inflation distributions.
    Date: 2020–10
  5. By: Julien Royer (CREST, ENSAE, Institut Polytechnique de Paris)
    Abstract: We consider an extension of ARCH(8) models to account for conditional asymmetry in the presence of high persistence. After stating existence and stationarity conditions, this paper develops the statistical inference of such models and proves the consistency and asymptotic distribution of a Quasi Maximum Likelihood estimator. Some particular specifications are studied and tests for asymmetry and GARCH validity are derived. Finally we present an application on a set of equity indice store examine the preeminence of GARCH (1,1) specifications. We find strong evidences that the short memory feature of such models is not suitable for lightly traded assets.
    Keywords: ARCH(8) models, conditional asymmetry, Quasi Maximum Likelihood Estimation
    JEL: C22 C51 C58
    Date: 2020–07–07
  6. By: Lukas Boer; Helmut Lütkepohl
    Abstract: A major challenge for proxy vector autoregressive analysis is the construction of a suitable instrument variable for identifying a shock of interest. We propose a simple proxy that can be constructed whenever the dating and sign of particular shocks are known. It is shown that the proxy can lead to impulse response estimates of the impact effects of the shock of interest that are nearly as efficient as or even more efficient than estimators based on a conventional, more sophisticated proxy.
    Keywords: GMM, heteroskedastic VAR, instrumental variable estimation, proxy VAR, structural vector autoregression
    JEL: C32
    Date: 2020
  7. By: Christoph Breunig; Stephan Martin
    Abstract: We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a special regressor type restriction and monotonicity in the nonlinear relationship between the observed and unobserved true outcome. Nonparametric identification is then obtained under a normalization of the unknown link function, which is a natural extension of the classical measurement error case. We propose a novel sieve rank estimator for the regression function. We establish a rate of convergence of the estimator which depends on the strength of identification. In Monte Carlo simulations, we find that our estimator corrects for biases induced by measurement errors and provides numerically stable results. We apply our method to analyze belief formation of stock market expectations with survey data from the German Socio-Economic Panel (SOEP) and find evidence for non-classical measurement error in subjective belief data.
    Date: 2020–09
  8. By: Chen, Yining
    Abstract: We consider the problem of segmented linear regression with a single breakpoint, with the focus on estimating the location of the breakpoint. If $n$ is the sample size, we show that the global minimax convergence rate for this problem in terms of the mean absolute error is $O(n^{-1/3})$. On the other hand, we demonstrate the construction of a super-efficient estimator that achieves the pointwise convergence rate of either $O(n^{-1})$ or $O(n^{-1/2})$ for every fixed parameter value, depending on whether the structural change is a jump or a kink. The implications of this example and a potential remedy are discussed.
    Keywords: change-point; minimax rate; Pointwise rate; Structural break
    JEL: C1
    Date: 2020–09–19
  9. By: Matias D. Cattaneo; Michael Jansson; Xinwei Ma
    Abstract: This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample distributional approximation in a unified way, allowing for both boundary and interior evaluation points simultaneously. Using this result, we study the asymptotic efficiency of the estimators, and show that a carefully crafted minimum distance implementation based on "redundant" regressors can lead to efficiency gains. Second, we establish uniform linearizations and strong approximations for the estimators, and employ these results to construct valid confidence bands. Third, we develop extensions to weighted distributions with estimated weights and to local $L^{2}$ least squares estimation. Finally, we illustrate our methods with two applications in program evaluation: counterfactual density testing, and IV specification and heterogeneity density analysis. Companion software packages in Stata and R are available.
    Date: 2020–09
  10. By: Kedagni, Desire
    Abstract: In this article, I develop a novel identification result for estimating the effect of an endogenous treatment using a proxy of an unobserved imperfect instrument. I show that the potential outcomes distributions are partially identified for the compliers. Therefore, I derive sharp bounds on the local average treatment effect. I write the identified set in the form of conditional moments inequalities, which can be implemented using existing inferential methods. I illustrate my methodology on the National Longitudinal Survey of Youth 1979 to evaluate the returns to college attendance using tuition as a proxy of the true cost of going to college. I find that the average return to college attendance for people who attend college only because the cost is low is between 29% and 78%.
    Date: 2019–06–03
  11. By: Masahiro Kato
    Abstract: We propose a doubly robust (DR) estimator for off-policy evaluation (OPE) from data obtained via multi-armed bandit (MAB) algorithms. The goal of OPE is to evaluate a new policy using historical data. Because the MAB algorithms sequentially updates the policy based on past observations, the generated samples are not independent and identically distributed (i.i.d.). To conduct OPE from dependent samples, we propose an OPE estimator with asymptotic normality even under the dependency. In particular, we focus on a DR estimator, which consists of an inverse probability weighting (IPW) component and an estimator of the conditionally expected outcome. The proposed adaptive DR estimator only requires the convergence rate conditions of the nuisance estimators and the other mild regularity conditions; that is, we do not impose a specific time-series structure and Donsker's condition. We investigate the effectiveness by using benchmark datasets compared to a past proposed DR estimator with double/debiased machine learning and an adaptive version of an augmented IPW estimator.
    Date: 2020–10
  12. By: Nadja Klein; Michael Stanley Smith; David J. Nott
    Abstract: Recurrent neural networks (RNNs) with rich feature vectors of past values can provide accurate point forecasts for series that exhibit complex serial dependence. We propose two approaches to constructing deep time series probabilistic models based on a variant of RNN called an echo state network (ESN). The first is where the output layer of the ESN has stochastic disturbances and a shrinkage prior for additional regularization. The second approach employs the implicit copula of an ESN with Gaussian disturbances, which is a deep copula process on the feature space. Combining this copula with a non-parametrically estimated marginal distribution produces a deep distributional time series model. The resulting probabilistic forecasts are deep functions of the feature vector and also marginally calibrated. In both approaches, Bayesian Markov chain Monte Carlo methods are used to estimate the models and compute forecasts. The proposed deep time series models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian National Electricity Market, we show that our models provide accurate probabilistic price forecasts. Moreover, the models provide a flexible framework for incorporating probabilistic forecasts of electricity demand as additional features. We demonstrate that doing so in the deep distributional time series model in particular, increases price forecast accuracy substantially.
    Date: 2020–10
  13. By: Espasa Terrades, Antoni; Carlomagno Real, Guillermo
    Abstract: The objective of this research note is to extend the pairwise procedure studied by Car- lomagno and Espasa (ming) to the case of general and sectorial trends. The extension allows to discover subsets of series that share general and/or sectorial stochastic trends between a (possible large) set of time series. This could be useful to model and forecast all of the series under analysis. Our approach does not need to assume pervasiveness of the trends, nor impose special restrictions on the serial or cross-sectional idiosyncratic correlation of the series. Additionally, the asymptotic theory works both, with finite N and T ! 1, and with [T;N] ! 1. In a Monte Carlo experiment we show that the extended procedure can produce reliable results in finite samples.
    Keywords: Heteroskedasticity; Pairwise Tests; Disaggregation; Factor Models; Cointegration
    JEL: C53 C32 C22 C01
    Date: 2020–09–29
  14. By: Sukjin Han; Shenshen Yang
    Abstract: For counterfactual policy evaluation, it is important to ensure that treatment parameters are relevant to the policies in question. This is especially challenging under unobserved heterogeneity, as is well featured in the definition of the local average treatment effect (LATE). Being intrinsically local, the LATE is known to lack external validity in counterfactual environments. This paper investigates the possibility of extrapolating local treatment effects to different counterfactual settings when instrumental variables are only binary. We propose a novel framework to systematically calculate sharp nonparametric bounds on various policy-relevant treatment parameters that are defined as weighted averages of the marginal treatment effect (MTE). Our framework is flexible enough to incorporate a large menu of identifying assumptions beyond the shape restrictions on the MTE that have been considered in prior studies. We apply our method to understand the effects of medical insurance policies on the use of medical services.
    Date: 2020–09
  15. By: David M. Kaplan
    Abstract: This note provides additional interpretation for the counterfactual outcome distribution and corresponding unconditional quantile "effects" defined and estimated by Firpo, Fortin, and Lemieux (2009) and Chernozhukov, Fern\'andez-Val, and Melly (2013). With conditional independence of the policy variable of interest, these methods estimate the policy effect for certain types of policies, but not others. In particular, they estimate the effect of a policy change that itself satisfies conditional independence.
    Date: 2020–10
  16. By: Yayi Yan; Jiti Gao; Bin Peng
    Abstract: Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics, this paper proposes a wide class of multivariate dynamic models with time-varying coefficients, which have a general time-varying vector moving average (VMA) representation, and nest, for instance, time-varying vector autoregression (VAR), time-varying vector autoregression moving-average (VARMA), and so forth as special cases. The paper then develops a unified estimation method for the unknown quantities before an asymptotic theory for the proposed estimators is established. In the empirical study, we investigate the transmission mechanism of monetary policy using U.S. data, and uncover a fall in the volatilities of exogenous shocks. In addition, we find that (i) monetary policy shocks have less influence on inflation before and during the so-called Great Moderation, (ii) inflation is more anchored recently, and (iii) the long-run level of inflation is below, but quite close to the Federal Reserve's target of two percent after the beginning of the Great Moderation period.
    Date: 2020–10
  17. By: Del Bono, Emilia (ISER, University of Essex); Kinsler, Josh (University of Georgia); Pavan, Ronni (University of Rochester)
    Abstract: In this paper we highlight an important property of the translog production function for the identification of treatment effects in a model of latent skill formation. We show that when using a translog specification of the skill technology, properly anchored treatment effect estimates are invariant to any location and scale normalizations of the underlying measures. By contrast, when researchers assume a CES production function and impose standard location and scale normalizations, the resulting treatment effect estimates are biased. Interestingly, the CES technology with standard normalizations yields biased treatment effect estimates even when age-invariant measures of the skills are available. We theoretically prove the normalization invariance of the translog production function and then produce several simulations illustrating the effects of location and scale normalizations for different technologies and types of skills measures.
    Keywords: children, human capital, dynamic factor analysis, measurement, policy
    JEL: C13 C18 I38 J13 J24
    Date: 2020–09
  18. By: Kedagni, Desire; Mourifié, Ismael
    Abstract: This paper proposes a new set of testable implications of the instrumen- tal variable (IV) independence assumption: generalized instrumental inequalities. In our leading case with a binary outcome, we show that the generalized instrumen- tal inequalities are necessary and sufficient to detect all observable violations of the IV independence assumption. To test the generalized instrumental inequalities, we propose an approach combining a sample splitting procedure and intersection bounds inferential methods. This idea allows one to easily implement the test using the Stata package of Chernozhukov, Kim, Lee, and Rosen (2015).We apply our pro- posed strategy to assess the validity of the IV independence assumption for various instruments used in the returns to college literature.
    Date: 2020–02–29
  19. By: Akanksha Negi; Jeffrey M. Wooldridge
    Abstract: We study efficiency improvements in estimating a vector of potential outcome means using linear regression adjustment when there are more than two treatment levels. We show that using separate regression adjustments for each assignment level is never worse, asymptotically, than using the subsample averages. We also show that separate regression adjustment improves over pooled regression adjustment except in the obvious case where slope parameters in the linear projections are identical across the different assignment levels. We also characterize the class of nonlinear regression adjustment methods that preserve consistency of the potential outcome means despite arbitrary misspecification of the conditional mean functions. Finally, we apply this general potential outcomes framework to a contingent valuation study for estimating lower bound mean willingness to pay for an oil spill prevention program in California.
    Date: 2020–10
  20. By: Chuheng Zhang; Yuanqi Li; Xi Chen; Yifei Jin; Pingzhong Tang; Jian Li
    Abstract: Modern machine learning models (such as deep neural networks and boosting decision tree models) have become increasingly popular in financial market prediction, due to their superior capacity to extract complex non-linear patterns. However, since financial datasets have very low signal-to-noise ratio and are non-stationary, complex models are often very prone to overfitting and suffer from instability issues. Moreover, as various machine learning and data mining tools become more widely used in quantitative trading, many trading firms have been producing an increasing number of features (aka factors). Therefore, how to automatically select effective features becomes an imminent problem. To address these issues, we propose DoubleEnsemble, an ensemble framework leveraging learning trajectory based sample reweighting and shuffling based feature selection. Specifically, we identify the key samples based on the training dynamics on each sample and elicit key features based on the ablation impact of each feature via shuffling. Our model is applicable to a wide range of base models, capable of extracting complex patterns, while mitigating the overfitting and instability issues for financial market prediction. We conduct extensive experiments, including price prediction for cryptocurrencies and stock trading, using both DNN and gradient boosting decision tree as base models. Our experiment results demonstrate that DoubleEnsemble achieves a superior performance compared with several baseline methods.
    Date: 2020–10
  21. By: Eduardo Abi Jaber (Université de Paris 1 Panthéon Sorbonne (Université de Paris))
    Abstract: Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample paths. This is made possible by virtue of the flexibility introduced in the choice of the covariance function of the Gaussian process. The price to pay is that, in general, such models are no longer Markovian nor semimartingales, which limits their practical use. We derive, in two different ways, an explicit analytic expression for the joint characteristic function of the log-price and its integrated variance in general Gaussian stochastic volatility models. Such analytic expression can be approximated by closed form matrix expressions stemming from Wishart distributions. This opens the door to fast approximation of the joint density and pricing of derivatives on both the stock and its realized variance using Fourier inversion techniques. In the context of rough volatility modeling, our results apply to the (rough) fractional Stein-Stein model and provide the first analytic formulae for option pricing known to date, generalizing that of Stein-Stein, Schöbel-Zhu and a special case of Heston.
    Keywords: Gaussian processes,Volterra processes,non-Markovian Stein-Stein/Schöbel- Zhu models,rough volatility
    Date: 2020–09–22
  22. By: Tullio Mancini; Hector Calvo-Pardo; Jose Olmo
    Abstract: The aim of this paper is to propose a suitable method for constructing prediction intervals for the output of neural network models. To do this, we adapt the extremely randomized trees method originally developed for random forests to construct ensembles of neural networks. The extra-randomness introduced in the ensemble reduces the variance of the predictions and yields gains in out-of-sample accuracy. An extensive Monte Carlo simulation exercise shows the good performance of this novel method for constructing prediction intervals in terms of coverage probability and mean square prediction error. This approach is superior to state-of-the-art methods extant in the literature such as the widely used MC dropout and bootstrap procedures. The out-of-sample accuracy of the novel algorithm is further evaluated using experimental settings already adopted in the literature.
    Date: 2020–10
  23. By: Hirschauer, Norbert; Gruener, Sven; Mußhoff, Oliver; Becker, Claudia
    Abstract: It has often been noted that the “null-hypothesis-significance-testing” (NHST) framework is an inconsistent hybrid of Neyman-Pearson’s “hypotheses testing” and Fisher’s “significance test-ing” approach that almost inevitably causes misinterpretations. To facilitate a realistic assessment of the potential and the limits of statistical inference, we briefly recall widespread inferential errors and outline the two original approaches of these famous statisticians. Based on the under-standing of their irreconcilable perspectives, we propose “going back to the roots” and using the initial evidence in the data in terms of the size and the uncertainty of the estimate for the pur-pose of statistical inference. Finally, we make six propositions that hopefully contribute to im-proving the quality of inferences in future research.
    Date: 2020–09–23
  24. By: Marco Avellaneda; Juan Andr\'es Serur
    Abstract: Modeling cross-sectional correlations between thousands of stocks, across countries and industries, can be challenging. In this paper, we demonstrate the advantages of using Hierarchical Principal Component Analysis (HPCA) over the classic PCA. We also introduce a statistical clustering algorithm for identifying of homogeneous clusters of stocks, or "synthetic sectors". We apply these methods to study cross-sectional correlations in the US, Europe, China, and Emerging Markets.
    Date: 2020–10
  25. By: Soichiro Yamauchi
    Abstract: The difference-in-differences (DID) design is widely used in observational studies to estimate the causal effect of a treatment when repeated observations over time are available. Yet, almost all existing methods assume linearity in the potential outcome (parallel trends assumption) and target the additive effect. In social science research, however, many outcomes of interest are measured on an ordinal scale. This makes the linearity assumption inappropriate because the difference between two ordinal potential outcomes is not well defined. In this paper, I propose a method to draw causal inferences for ordinal outcomes under the DID design. Unlike existing methods, the proposed method utilizes the latent variable framework to handle the non-numeric nature of the outcome, enabling identification and estimation of causal effects based on the assumption on the quantile of the latent continuous variable. The paper also proposes an equivalence-based test to assess the plausibility of the key identification assumption when additional pre-treatment periods are available. The proposed method is applied to a study estimating the causal effect of mass shootings on the public's support for gun control. I find little evidence for a uniform shift toward pro-gun control policies as found in the previous study, but find that the effect is concentrated on left-leaning respondents who experienced the shooting for the first time in more than a decade.
    Date: 2020–09

This nep-ecm issue is ©2020 by Sune Karlsson. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
General information on the NEP project can be found at For comments please write to the director of NEP, Marco Novarese at <>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.