Econometrics Commons^™

Singapore As A Sustainable City: Past, Present And The Future, Tomoki Fujii, Rohan Ray

Research Collection School Of Economics

Singapore has achieved impressive economic growth over the last half-century. This chapter provides an overview of the major sustainability challenges Singapore has experienced and the policies that have been adopted to address them, particularly in the areas of land use, transportation, waste management, water, and energy. It argues that Singapore has been successful in addressing these challenges owing to sound long-term vision and planning as well as flexibility in the implementation of the policies to tackle them. The chapter provides some discussion on policy options, challenges, and opportunities for making Singapore more sustainable and liveable. Leaders of Singapore have recognised …

Entrepreneurship In Singapore, Jungho Lee

Research Collection School Of Economics

Singapore has completed its catch-up growth phase and needs to find a new growth engine. Entrepreneurship can contribute to a nation’s productivity growth. The purpose of this chapter is twofold. First, a theoretical framework is presented, along with empirical evidence, to understand government interventions aimed at boosting entrepreneurship. Second, using the framework, the chapter discusses whether Singapore’s current policies are suitable for helping entrepreneurship. The theory demonstrates four reasons why government intervention is needed: (1) resource misallocation, (2) positive externality, (3) entrepreneurial human capital, and (4) tax and default policies. Singapore’s government has implemented various policies that potentially fix market …

Wild Bootstrap For Instrumental Variable Regressions With Weak And Few Clusters, Wenjie Wang, Yichong Zhang

Research Collection School Of Economics

We study the wild bootstrap inference for instrumental variable (quantile) regressions in the framework of a small number of large clusters, in which the number of clusters is viewed as fixed and the number of observations for each cluster diverges to infinity. For subvector inference, we show that the wild bootstrap Wald test with or without using the cluster-robust covariance matrix controls size asymptotically up to a small error as long as the parameters of endogenous variables are strongly identified in at least one of the clusters. We further develop a wild bootstrap Anderson-Rubin (AR) test for full-vector inference and …

Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu

Research Collection School Of Economics

We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Hölder classes as special cases. The general Glivenko-Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.

Volatility Coupling, Jean Jacod, Jia Li, Zhipeng Liao

Research Collection School Of Economics

This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting. Specifically, we propose uniform confidence bands for spot volatility, beta, idiosyncratic variance processes, and their nonlinear transforms. The theory is also applied to address an open question concerning the inference of monotone nonsmooth integrated …

Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics, Jia Li, Yunxiao Liu

Research Collection School Of Economics

We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.

Generalized Local-To-Unity Models, Liyu Dou, Ulrich K. Müller

Research Collection School Of Economics

We introduce a generalization of the popular local‐to‐unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local‐to‐unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and …

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

Research Collection School Of Economics

This article obtains the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein–Uhlenbeck process when a continuous record is available. The exact distribution is asymmetric, trimodal, dependent on the initial condition. These three properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models. Motivated by these observations, the article then develops an in-fill asymptotic theory for the LS estimator of structural break point in the AR(1) coefficient. The in-fill asymptotic distribution is also asymmetric, tri-modal, dependent on the initial condition, and delivers …

On Factor Models With Random Missing: Em Estimation, Inference, And Cross Validation, Sainan Jin, Ke Miao, Liangjun Su

Research Collection School Of Economics

We consider the estimation and inference in approximate factor models with random missing values. We show that with the low rank structure of the common component, we can estimate the factors and factor loadings consistently with the missing values replaced by zeros. We establish the asymptotic distributions of the resulting estimators and those based on the EM algorithm. We also propose a cross validation-based method to determine the number of factors in factor models with or without missing values and justify its consistency. Simulations demonstrate that our cross validation method is robust to fat tails in the error distribution and …

Boosting: Why You Can Use The Hp Filter, Peter C. B. Phillips, Zhentao Shi

Research Collection School Of Economics

We propose a procedure of iterating the HP filter to produce a smarter smoothing device, called the boosted HP (bHP) filter, based on L2-boosting in machine learning. Limit theory shows that the bHP filter asymptotically recovers trend mechanisms that involve integrated processes, deterministic drifts, and structural breaks, covering the most common trends that appear in current modeling methodology. A stopping criterion automates the algorithm, giving a data-determined method for data-rich environments. The methodology is illustrated in simulations and with three real data examples that highlight the differences between simple HP filtering, the bHP filter, and an alternative autoregressive approach.

Business Cycles, Trend Elimination, And The Hp Filter, Peter C. B. Phillips, Sainan Jin

Research Collection School Of Economics

Trend elimination and business cycle estimation are analyzed by finite sample and asymptotic methods. An overview history is provided, operator theory is developed, limit theory as the sample size n → ∞ is derived, and filtered series properties are studied relative to smoothing parameter (λ) behavior. Simulations reveal that limit theory with λ =O(n4) delivers excellent approximations to the HP filter for common sample sizes but fails to remove stochastic trends, contrary to standard thinking in macroeconomics and thereby explaining ‘spurious cycle’ effects of the HP filter. The findings are related to the long run effects of the GFC.

A Hybrid Equity Release Plan For Retirement Financing, Koon Shing Kwong, Yiu Kuen Tse, Junxing Chay

Research Collection School Of Economics

There are two main equity release plans for retirement financing: reverse mortgage plan and home reversion plan. Both plans entitle the homeowners not only to release cash from their properties but also to allow them living there for life. In the lease buyback scheme (LBS) recently introduced in Singapore, the home owner sells the tail-end of the property lease to the government in exchange for a cash payment upfront. Unlike the two main equity release plans, the LBS only allows the owner to stay in the property for the front part of the lease but not for life.

In this …

Spatial Dynamic Panel Data Models With Correlated Random Effects, Liyao Li, Zhenlin Yang

Research Collection School Of Economics

In this paper, M-estimation and inference methods are developed for spatial dynamic panel data models with correlated random effects, based on short panels. The unobserved individual-specific effects are assumed to be correlated with the observed time-varying regressors linearly or in a linearizable way, giving the so-called correlated random effects model, which allows the estimation of effects of time-invariant regressors. The unbiased estimating functions are obtained by adjusting the conditional quasi-scores given the initial observations, leading to M-estimators that are consistent, asymptotically normal, and free from the initial conditions except the process starting time. By decomposing the estimating functions …

Mildly Explosive Autoregression With Anti-Persistent Errors, Yiu Lim Lui, Weilin Xiao, Jun Yu

Research Collection School Of Economics

An asymptotic distribution is derived for the least squares (LS) estimate of a first‐order autoregression with a mildly explosive root and anti‐persistent errors. While the sample moments depend on the Hurst parameter asymptotically, the Cauchy limiting distribution theory remains valid for the LS estimates in the model without intercept and a model with an asymptotically negligible intercept. Monte Carlo studies are designed to check the precision of the Cauchy distribution in finite samples. An empirical study based on the monthly NASDAQ index highlights the usefulness of the model and the new limiting distribution.

Determining The Number Of Communities In Degree-Corrected Stochastic Block Models, Shujie Ma, Liangjun Su, Yichong Zhang

Research Collection School Of Economics

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio. For estimation, we consider a spectral clustering together with binary segmentation method. This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted. We also derive its limiting distribution when the model is under-fitted. Based on these properties, we establish the consistency of our estimator for the true number of communities. Developing these theoretical properties require a mild condition on the average degree: growing at a rate faster than log(n), where n is the number …

Mildly Explosive Autoregression With Anti-Persistent Errors, Yui Lim Lui, Jun Yu, Jun Yu

Research Collection School Of Economics

An asymptotic distribution is derived for the least squares (LS) estimate of a first-order autoregression with a mildly explosive root and anti-persistent errors. While the sample moments depend on the Hurst parameter asymptotically, the Cauchy limiting distribution theory remains valid for the LS estimates in the model without intercept and a model with an asymptotically negligible intercept. Monte Carlo studies are designed to check the precision of the Cauchy distribution in finite samples. An empirical study based on the monthly NASDAQ index highlights the usefulness of the model and the new limiting distribution.

Change In Outbreak Epicentre And Its Impact On The Importation Risks Of Covid-19 Progression: A Modelling Study, Oyelola A. Adegboye, Adeshina I. Adekunle, Anton Pak, Ezra Gayawan, Denis H. Y. Leung, Diana P. Rojas, Emma S. Mcbryde, Damon P. Eisen

Research Collection School Of Economics

Background: The outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) that was first detected in the city of Wuhan, China has now spread to every inhabitable continent, but now the attention has shifted from China to other epicentres. This study explored early assessment of the influence of spatial proximities and travel patterns from Italy on the further spread of SARS-CoV-2 worldwide. Methods: Using data on the number of confirmed cases of COVID-19 and air travel data between countries, we applied a stochastic meta-population model to estimate the global spread of COVID-19. Pearson's correlation, semi-variogram, and Moran's Index were used to …

Identifying Latent Group Structures In Nonlinear Panels, Wuyi Wang, Liangjun Su

Research Collection School Of Economics

We propose a procedure to identify latent group structures in nonlinear panel data models where some regression coefficients are heterogeneous across groups but homogeneous within a group and the group number and membership are unknown. To identify the group structures, we consider the order statistics for the preliminary unconstrained consistent estimators of the regression coefficients and translate the problem of classification into the problem of break detection. Then we extend the sequential binary segmentation algorithm of Bai (1997) for break detection from the time series setup to the panel data framework. We demonstrate that our method is able to identify …

House Prices And Affordability, R. Greenaway-Mcgrevy, Peter C. B. Phillips

Research Collection School Of Economics

The decade following the global financial crisis (GFC) has witnessed rampant house price appreciation in many cities of the developed world. The metropolitan centres of New Zealand showcase this phenomenon with house price appreciation persistently outpacing income growth. In Auckland, the ratio of prevailing median house prices to median household income rose from 6.4 in 2010 to 10.0 in 2016 (Demographia, Citation2011, Citation2017), before declining to 8.6 by 2019 as house prices flat-lined while household incomes increased (Demographia, Citation2020). However, a strong resurgence in house prices during 2020 means that this ratio has resumed its upward trajectory, with an increase …

Joint Tests For Dynamic And Spatial Effects In Short Dynamic Panel Data Models With Fixed Effects And Heteroskedasticity, Zhenlin Yang

Research Collection School Of Economics

Simple and reliable tests are proposed for testing the existence of dynamic and/or spatial effects in fixed-effects panel data models with small T and possibly heteroskedastic errors. The tests are constructed based on the adjusted quasi scores (AQS), which correct the conditional quasi scores given the initial differences to account for the effect of initial values. To improve the finite sample performance, standardized AQS tests are also derived, which are shown to have much improved finite sample properties. All the proposed tests are robust against nonnormality, but some are not robust against cross-sectional heteroskedasticity (CH). A different type of adjustments …

Causal Change Detection In Possibly Integrated Systems: Revisiting The Money-Income Relationship, Shuping Shi, Stan Hurn, Peter C. B. Phillips

Research Collection School Of Economics

This paper re-examines changes in the causal link between money and income in the United States over the past half century (1959-2014). Three methods for the data-driven discovery of change points in causal relationships are proposed, all of which can be implemented without prior detrending of the data. These methods are a forward recursive algorithm, a rolling window algorithm, and a recursive evolving algorithm all of which utilize subsample tests of Granger causality within a lagaugmented vector autoregressive framework. The limit distributions for these subsample Wald tests are provided. Bootstrap methods are developed to control family-wise size in the implementation …

Testing For Structural Changes In Factor Models Via A Nonparametric Regression, Liangjun Su, Xia Wang

Research Collection School Of Economics

We propose a model-free test for structural changes in factor models. The basic idea is to regress the data on commonly estimated factors by local smoothing and compare the fitted values of time-varying factor loadings with those of time-invariant factor loadings estimated via principal component analysis. By construction, the test is designed to be powerful against both smooth structural changes and sudden structural breaks with a possibly unknown number of breaks and unknown break dates in the factor loadings. No restrictions on the form of alternatives or trimming of boundary regions near the beginning or end of the sample period …

Quasi-Bayesian Inference For Production Frontiers, Xiaobin Liu, Thomas Tao Yang, Yichong Zhang

Research Collection School Of Economics

We propose a quasi-Bayesian method to conduct inference for the production frontier. This approach combines multiple first-stage extreme quantile estimates by the quasi-Bayesian method to produce the point estimate and confidence interval for the production frontier. We show the asymptotic properties of the proposed estimator and the validity of the inference procedure. The finite sample performance of our method is illustrated through simulations and an empirical application.

Point Optimal Testing With Roots That Are Functionally Local To Unity, Anna Bykhovskaya, Peter C. B. Phillips

Research Collection School Of Economics

Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from unit roots. The present paper shows how to generalize LUR asymptotics to cases where the localized departure from unity is a time varying function rather than a constant. Such a functional local unit root (FLUR) model has much greater generality and encompasses many cases of additional interest that appear in practical work, …

Asymptotic Properties Of Least Squares Estimator In Local To Unity Processes With Fractional Gaussian Noises, Xiaohu Wang, Weilin Xiao, Jun Yu

Research Collection School Of Economics

This paper derives asymptotic properties of the least squares estimator of the autoregressive parameter in local to unity processes with errors being fractional Gaussian noises with the Hurst parameter H. It is shown that the estimator is consistent when H ∈ (0, 1). Moreover, the rate of convergence is n when H ∈ [0.5, 1). The rate of convergence is n^2H when H ∈ (0, 0.5). Furthermore, the limit distribution of the centered least squares estimator depends on H. When H = 0.5, the limit distribution is the same as that obtained in Phillips (1987a) for the local to …

Diagnostic Tests For Homoskedasticity In Spatial Cross-Sectional Or Panel Models, Badi K. Baltagi, Alain Pirotte, Zhenlin Yang

Research Collection School Of Economics

We propose an Adjusted Quasi-Score (AQS) method for constructing tests for homoskedasticity in spatial econometric models. We first obtain an AQS function by adjusting the score-type function from the given model to achieve unbiasedness, and then develop an Outer-Product-of-Martingale-Difference (OPMD) estimate of its variance. In standard problems where a genuine (quasi) score vector is available, the AQS-OPMD method leads to finite sample improved tests over the usual methods. More importantly in non-standard problems where a genuine (quasi) score is not available and the usual methods fail, the proposed AQS-OPMD method provides feasible solutions. The AQS tests are formally derived and …

Persistent And Rough Volatility, Xiaobin Liu, Shuping Shi, Jun Yu

Research Collection School Of Economics

This paper contributes to an ongoing debate on volatility dynamics. We introduce a discrete-time fractional stochastic volatility (FSV) model based on the fractional Gaussian noise. The new model has the same limit as the fractional integrated stochastic volatility (FISV) model under the in-fill asymptotic scheme. We study the theoretical properties of both models and introduce a memory signature plot for a model-free initial assessment. A simulated maximum likelihood (SML) method, which maximizes the time-domain log-likelihoods obtained by the importance sampling technique, is employed to estimate the model parameters. Simulation studies suggest that the SML method can accurately estimate both models. …

Uniform Nonparametric Inference For Time Series, Jia Li, Zhipeng Liao

Research Collection School Of Economics

This paper provides the first result for the uniform inference based on nonparametric series estimators in a general time-series setting. We develop a strong approximation theory for sample averages of mixingales with dimensions growing with the sample size. We use this result to justify the asymptotic validity of a uniform confidence band for series estimators and show that it can also be used to conduct nonparametric specification test for conditional moment restrictions. New results on the validity of heteroskedasticity and autocorrelation consistent (HAC) estimators with increasing dimension are established for making feasible inference. An empirical application on the unemployment volatility …

Forecasting Large Covariance Matrix With High-Frequency Data: A Factor Approach For The Correlation Matrix, Yingjie Dong, Yiu Kuen Tse

Research Collection School Of Economics

We apply the factor approach to the correlation matrix to forecast large covariance matrix of asset returns using high-frequency data, using the principal component method to model the underlying latent factors of the correlation matrix. The realized variances are separately forecasted using the Heterogeneous Autoregressive model. The forecasted variances and correlations are then combined to forecast large covariance matrix. Our proposed method is found to perform better in reporting smaller forecast errors than some selected competitors. Empirical application to a portfolio of 100 NYSE and NASDAQ stocks shows that our method provides lower out-of-sample realized variance in selecting global minimum …

Unconditional Quantile Regression With High-Dimensional Data, Yuya Sasaki, Takuya Ura, Yichong Zhang

Research Collection School Of Economics

Credible counterfactual analysis requires high-dimensional controls. This paper considers estimation and inference for heterogeneous counterfactual effects with high-dimensional data. We propose a novel doubly robust score for double/debiased estimation and inference for the unconditional quantile regression (Firpo, Fortin, and Lemieux, 2009) as a measure of heterogeneous counterfactual marginal effects. We propose a multiplier bootstrap inference for the Lasso double/debiased estimator, and develop asymptotic theories to guarantee that the bootstrap works. Simulation studies support our theories. Applying the proposed method to Job Corps survey data, we find that i) marginal effects of counterfactually extending the duration of the exposure to the …