Econometrics Commons^™

Bubble Testing Under Deterministic Trends, Xiaohu Wang, Jun Yu

Research Collection School Of Economics

This paper develops the asymptotic theory of the ordinary least squares estimator of the autoregressive (AR) coefficient in various AR models, when data is generated from trend-stationary models in different forms. It is shown that, depending on how the autoregression is specified, the commonly used right-tailed unit root tests may tend to reject the null hypothesis of unit root in favor of the explosive alternative. A new procedure to implement the right-tailed unit root tests is proposed. It is shown that when the data generating process is trend-stationary, the test statistics based on the proposed procedure cannot find evidence of …

Non-Separable Models With High-Dimensional Data, Liangjun Su, Takuya Ura, Yichong Zhang

Research Collection School Of Economics

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and penalized conditional density estimation, respectively, where control variables are selected via a localized method of L1-penalization at each value of the continuous treatment. In the second stage we estimate the average and the marginal distribution …

Domestic Liquidity Conditions And Monetary Policy In Singapore, Hwee Kwan Chow-Tan

Research Collection School Of Economics

Singapore has an unusual exchange rate-centered monetary policy framework that has served the economy well over the past decades. Monetary policy operations are carried out by the central bank through the management of the Singapore dollar against a currency basket. As is well recognized, such foreign exchange interventions do have an impact on domestic liquidity conditions. However, in the case of Singapore, this tends to be counteracted by the liquidity impact of public sector operations related to the fiscal position and the national pension scheme. The central bank takes into account the net liquidity impact these and other autonomous money …

Adaptive Estimation Of Continuous-Time Regression Models Using High-Frequency Data, Jia Li, Viktor Todorov, George Tauchen

Research Collection School Of Economics

We derive the asymptotic efficiency bound for regular estimates of the slope coefficient in a linear continuous-time regression model for the continuous martingale parts of two Itô semimartingales observed on a fixed time interval with asymptotically shrinking mesh of the observation grid. We further construct an estimator from high-frequency data that achieves this efficiency bound and, indeed, is adaptive to the presence of infinite-dimensional nuisance components. The estimator is formed by taking optimal weighted average of local nonparametric volatility estimates that are constructed over blocks of high-frequency observations. The asymptotic efficiency bound is derived under a Markov assumption for the …

Structural Inference From Reduced Forms With Many Instruments, Peter C. B. Phillips, Wayne Yuan Gao

Research Collection School Of Economics

This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testing even in cases of uniformly weak instruments. Comparisons are made with methods based on unrestricted reduced forms, and numerical computations showing finite sample performance of the tests are reported. Some new results are obtained on inequalities between noncentral chi-squared distributions with different degrees of freedom that assist in analytic power comparisons.

Indirect Inference In Spatial Autoregression, Maria Kyriacou, Peter C. B. Phillips, Francesca Rossi

Research Collection School Of Economics

Ordinary least-squares (OLS) is well known to produce an inconsistent estimator of the spatial parameter in pure spatial autoregression (SAR). In this paper, we explore the potential of indirect inference to correct the inconsistency of OLS. Under broad conditions, it is shown that indirect inference (II) based on OLS produces consistent and asymptotically normal estimates in pure SAR regression. The II estimator used here is robust to departures from normal disturbances and is computationally straightforward compared with quasi-maximum likelihood (QML). Monte Carlo experiments based on various specifications of the weight matrix show that: (a) the II estimator displays little bias …

Indirect Inference In Spatial Autoregression, Maria Kyriacou, Peter C. B. Phillips, Francesca Rossi

Research Collection School Of Economics

Ordinary least-squares (OLS) is well known to produce an inconsistent estimator of the spatial parameter in pure spatial autoregression (SAR). In this paper, we explore the potential of indirect inference to correct the inconsistency of OLS. Under broad conditions, it is shown that indirect inference (II) based on OLS produces consistent and asymptotically normal estimates in pure SAR regression. The II estimator used here is robust to departures from normal disturbances and is computationally straightforward compared with quasi-maximum likelihood (QML). Monte Carlo experiments based on various specifications of the weight matrix show that: (a) the II estimator displays little bias …

A Martingale Difference-Divergence-Based Test For Specification, Liangjun Su, Xin Zheng

Research Collection School Of Economics

In this paper we propose a novel consistent model specification test based on the martingale difference divergence (MDD) of the error term given the covariates. The MDD equals zero if and only if error term is conditionally mean independent of the covariates. Our MDD test does not require any nonparametric estimation under the alternative and it is applicable even if we have many covariates in the regression model. We establish the asymptotic distributions of our test statistic under the null and a sequence of Pitman local alternatives converging to the null at the usual parametric rate. Simulations suggest that our …

Singapore’S Life Program: Actuarial Framework, Longevity Risk And Impact Of Annuity Fund Return, Koon Shing Kwong, Yiu Kuen Tse, Wai-Sum Chan

Research Collection School Of Economics

The Central Provident Fund (CPF) is a defined-contribution savings plan forming the key pillar of the pension system in Singapore. The CPF Lifelong Income For the Elderly (LIFE) program, which provides lifetime income for retirees, is a mandatory pension scheme for all Singapore residents. In this paper we construct an actuarial framework to analyze the LIFE program. We use this framework to study the plan payout outcomes with respect to changes in mortality and annuity fund return assumptions. We also examine the effects of some possible changes in the program on the payouts and bequests.

In-Fill Asymptotic Theory For Structural Break Point In Autoregression: A Unified Theory, Liang Jiang, Xiaohu Wang, Jun Yu

Research Collection School Of Economics

This paper obtains the exact distribution of the maximum likelihood estimatorof structural break point in the OrnsteinñUhlenbeck process when a continuousrecord is available. The exact distribution is asymmetric, tri-modal, dependenton the initial condition. These three properties are also found in the önite sampledistribution of the least squares (LS) estimator of structural break point inautoregressive (AR) models. Motivated by these observations, the paper then developsan in-öll asymptotic theory for the LS estimator of structural break point inthe AR(1) coe¢ cient. The in-öll asymptotic distribution is also asymmetric, trimodal,dependent on the initial condition, and delivers excellent approximationsto the önite sample distribution. Unlike …

On Time-Varying Factor Models: Estimation And Testing, Liangjun Su, Xia Wang

Research Collection School Of Economics

Conventional factor models assume that factor loadings are fixed over a long horizon of time, which appears overly restrictive and unrealistic in applications. In this paper, we introduce a time-varying factor model where factor loadings are allowed to change smoothly over time. We propose a local version of the principal component method to estimate the latent factors and time-varying factor loadings simultaneously. We establish the limiting distributions of the estimated factors and factor loadings in the standard large N and large T framework. We also propose a BIC-type information criterion to determine the number of factors, which can be used …

A Specification Test Based On The Mcmc Output, Yong Li, Jun Yu, Tao Zeng

Research Collection School Of Economics

A test statistic is proposed to assess themodel specification after the model is estimated by Bayesian MCMC methods. Thenew test is motivated from the power enhancement technique of Fan, Liao and Yao(2015). It combines a component (J1) that tests anull point hypothesis in an expanded model and a power enhancement component (J0) obtained from the null model. It is shown that J0 converges to zero when the null model is correctly specified anddiverges when the null model is misspecified. Also shown is that J1 is asymptotically X2-distributed, suggesting that theproposed test is asymptotically pivotal, when the null model is correctlyspecified. …

Improved Likelihood Inferences For Weibull Regression Model, Yan Shen, Zhenlin Yang

Research Collection School Of Economics

A general procedure is developed for bias-correcting the maximum likelihood estimators (MLEs) of the parameters of Weibull regression model with either complete or right-censored data. Following the bias correction, variance corrections and hence improved t-ratios for model parameters are presented. Potentially improved t-ratios for other reliability-related quantities are also discussed. Simulation results show that the proposed method is effective in correcting the bias of the MLEs, and the resulted t-ratios generally improve over the regular t-ratios.

Robust Jump Regressions, Jia Li, Viktor Todorov, George Tauchen

Research Collection School Of Economics

We develop robust inference methods for studying linear dependence between the jumps of discretely observed processes at high frequency. Unlike classical linear regressions, jump regressions are determined by a small number of jumps occurring over a fixed time interval and the rest of the components of the processes around the jump times. The latter are the continuous martingale parts of the processes as well as observation noise. By sampling more frequently the role of these components, which are hidden in the observed price, shrinks asymptotically. The robustness of our inference procedure is with respect to outliers, which are of particular …

Granger Causality And Structural Causality In Cross-Section And Panel Data, Xun Lu, Liangjun Su, Halbert White

Research Collection School Of Economics

Granger noncausality in distribution is fundamentally a probabilistic conditional independence notion that can be applied not only to time series data but also to cross-section and panel data. In this paper, we provide a natural definition of structural causality in cross-section and panel data and forge a direct link between Granger (G-) causality and structural causality under a key conditional exogeneity assumption. To put it simply, when structural effects are well defined and identifiable, G-non-causality follows from structural noncausality, and with suitable conditions (e.g., separability or monotonicity), structural causality also implies G-causality. This justifies using tests of G-non-causality to test …

Asymptotic Theory For Estimating Drift Parameters In The Fractional Vasicek Model, Weilin Xiao, Jun Yu

Research Collection School Of Economics

This paper develops the asymptotic theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model is assumed to be driven by the fractional Brownian motion with a known Hurst parameter greater than or equal to one half. It is shown that the asymptotic theory for the persistent parameter depends critically on its sign, corresponding asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered. When the persistent parameter is positive, …

Econometric Reviews Honors Esfandiar Maasoumi, Peter C. B. Phillips, Aman Ullah

Research Collection School Of Economics

This Special Issue of Econometric Reviews (ER) is a tribute to Esfandiar Maasoumi for his longstanding contributions to the econometrics profession as an outstanding researcher, a revered teacher and supervisor, and a journal editor of three decades, all of which manifests his extraordinary devotion to the discipline of econometrics and to its growing community of students and scholars. Essie, as he is universally known to his friends, colleagues, and the international community, took on the editorship of ER in 1987. At that point, as (very) senior members of the profession will remember, the journal had a paperback cover, no formal …

Reduced Forms And Weak Instrumentation, Peter C. B. Phillips

Research Collection School Of Economics

This paper develops exact finite sample and asymptotic distributions for a class of reduced form estimators and predictors, allowing for the presence of unidentified or weakly identified structural equations. Weak instrument asymptotic theory is developed directly from finite sample results, unifying earlier findings and showing the usefulness of structural information in making predictions from reduced form systems in applications. Asymptotic results are reported for predictions from models with many weak instruments. Of particular interest is the finding that, in unidentified and weakly identified structural models, partially restricted reduced form predictors have considerably smaller forecast mean square errors than unrestricted reduced …

Lag Length Selection In Panel Autoregression, Chirok Han, Peter C. B. Phillips, Donggyu Sul

Research Collection School Of Economics

Model selection by BIC is well known to be inconsistent in the presence of incidental parameters. This article shows that, somewhat surprisingly, even without fixed effects in dynamic panels BIC is inconsistent and overestimates the true lag length with considerable probability. The reason for the inconsistency is explained, and the probability of overestimation is found to be 50% asymptotically. Three alternative consistent lag selection methods are considered. Two of these modify BIC, and the third involves sequential testing. Simulations evaluate the performance of these alternative lag selection methods in finite samples.

Joint Spatial Time Series Epidemiological Analysis Of Malaria And Cutaneous Leishmaniasis Infection, O. A. Adegboye, M. Al-Saghir, Denis H. Y. Leung

Research Collection School Of Economics

Malaria and leishmaniasis are among the two most important health problems of many developing countries especially in the Middle East and North Africa. It is common for vector-borne infectious diseases to have similar hotspots which may be attributed to the overlapping ecological distribution of the vector. Hotspot analyses were conducted to simultaneously detect the location of local hotspots and test their statistical significance. Spatial scan statistics were used to detect and test hotspots of malaria and cutaneous leishmaniasis (CL) in Afghanistan in 2009. A multivariate negative binomial model was used to simultaneously assess the effects of environmental variables on malaria …

Deviance Information Criterion For Bayesian Model Selection: Justification And Variation, Yong Li, Jun Yu, Tao Zeng

Research Collection School Of Economics

Deviance information criterion (DIC) has been extensively used for making Bayesian model selection. It is a Bayesian version of AIC and chooses a model that gives the smallest expected Kullback-Leibler divergence between the data generating process (DGP) and a predictive distribution asymptotically. We show that when the plug-in predictive distribution is used, DIC can have a rigorous decision-theoretic justification under regularity conditions. An alternative expression for DIC, based on the Bayesian predictive distribution, is proposed. The new DIC has a smaller penalty term than the original DIC and is very easy to compute from the MCMC output. It is invariant …

Giving Economic Data A Voice, Singapore Management University

Research@SMU: Connecting the Dots

Professor Su Liangjun is developing new techniques in econometrics to provide a more realistic understanding of the economy.

See the papers:

• Testing homogeneity in panel data models with interactive fixed effects
• Identifying latent structures in panel data
• Shrinkage estimation of dynamic panel data models with interactive fixed effects

The Race Against Time, Singapore Management University

Research@SMU: Connecting the Dots

Professor Tse Yiu Kuen is developing econometric models that can provide us with a clearer picture of global markets.

See the papers:

• Estimation of high-frequency volatility: An autoregressive conditional duration approach
• Intraday periodicity adjustments of transaction duration and their effects on high-frequency volatility estimation;
• Intraday value-at-risk: An asymmetric autoregressive conditional duration approach

On Estimating Market Microstructure Noise Variance, Yingjie Dong, Yiu Kuen Tse

Research Collection School Of Economics

We study the market microstructure noise-variance estimation of high-frequency stock prices. Based on the Hansen and Lunde (2006) approach, we propose estimates using subsampling method at different time scales. We conduct a Monte Carlo study to compare our method against others in the literature. Our results show that our proposed estimates have lower (absolute) mean error and root mean-squared error, and their performance is quite stable at different time scales.

A Multivariate Stochastic Unit Root Model With An Application To Derivative Pricing, Offer Lieberman, Peter C. B. Phillips

Research Collection School Of Economics

This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (STUR) models to a multivariate case including asymptotic theory for estimation of the model's parameters. The extensions are useful for applications of STUR modeling and because they lead to a generalization of the Black-Scholes formula for derivative pricing. In place of the standard assumption that the price process follows a geometric Brownian motion, we derive a new form of the Black-Scholes equation that allows for a multivariate time varying coefficient element in the price equation. The corresponding formula for the value of a European-type call option …

Changes In Depressive Symptoms Among Older Adults With Multiple Chronic Conditions: Role Of Positive And Negative Social Supports, Sangnam Ahn, Seonghoon Kim, Hongmei Zhang

Research Collection School Of Economics

Depression severely affects older adults in the United States. As part of the social environment, significant social support was suggested to ameliorate depression among older adults. We investigate how varying forms of social support moderate depressive symptomatology among older adults with multiple chronic conditions (MCC). Data were analyzed using a sample of 11,400 adults, aged 65 years or older, from the 2006–2012 Health and Retirement Study. The current study investigated the moderating effects of positive or negative social support from spouse, children, other family, and friends on the association between MCC and depression. A linear mixed model with repeated measures …

Reducing Extreme Poverty Through Skill Training For Industry Job Placement, Abu S. Shonchoy, Selim Raihan, Tomoki Fujii

Research Collection School Of Economics

Vocational training programs aimed at rapidly growing sectors have the potential to reduce skills gaps, improve income and employment potentials. Such programs often been unsuccessful, because they are not driven by industry-demand and market-linkages, and they are not well targeted. Our rigorous RCT-based impact study shows that a targeted training-program offered to poor rural households in northwest Bangladesh has significant effects on employment in garment factories. Data from a follow-up — six and twelve months’ after the intervention — shows a statistically significant and large employment effect of the training program when it is combined with the stipend or internship.This …

Efficient Augmented Inverse Probability Weighted Estimation In Missing Data Problems, Jing Qin, Biao Zhang, Denis H. Y. Leung

Research Collection School Of Economics

When analyzing data with missing data, a commonly used method is the inverse probability weighting (IPW) method, which reweights estimating equations with propensity scores. The popularity of the IPW method is due to its simplicity. However, it is often being criticized for being inefficient because most of the information from the incomplete observations is not used. Alternatively, the regression method is known to be efficient but is nonrobust to the misspecification of the regression function. In this article, we propose a novel way of optimally combining the propensity score function and the regression model. The resulting estimating equation enjoys the …

Estimating Smooth Structural Change In Cointegration Models, Peter C. B. Phillips, Degui Li, Jiti Gao

Research Collection School Of Economics

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to reorient coordinates and …

Determining Individual Or Time Effects In Panel Data Models, Xun Lu, Liangjun Su

Research Collection School Of Economics

In this paper we propose a jackknife method to determine individual and time e⁄ects in linear panel data models. We rst show that when both the serial and cross-sectional correlation among the idiosyncratic error terms are weak, our jackknife method can pick up the correct model with probability approaching one (w.p.a.1). In the presence of moderate or strong degree of serial correlation, we modify our jackknife criterion function and show that the modied jackknife method can also select the correct model w.p.a.1. We conduct Monte Carlo simulations to show that our new methods perform remarkably well in nite samples. We …