A Bounds Approach to Inference Using the Long Run Multiplier

2019 ◽  
Vol 27 (3) ◽  
pp. 281-301 ◽  
Author(s):  
Clayton Webb ◽  
Suzanna Linn ◽  
Matthew Lebo
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Small Sample ◽  
Stochastic Simulations ◽  
Upper And Lower Bounds ◽  
Test Statistics ◽  
Test Statistic ◽  
Independent Variables ◽  
Long Run ◽  
Presidential Success

Pesaran, Shin, and Smith (2001) (PSS) proposed a bounds procedure for testing for the existence of long run cointegrating relationships between a unit root dependent variable ($y_{t}$) and a set of weakly exogenous regressors $\boldsymbol{x}_{t}$ when the analyst does not know whether the independent variables are stationary, unit root, or mutually cointegrated processes. This procedure recognizes the analyst’s uncertainty over the nature of the regressors but not the dependent variable. When the analyst is uncertain whether $y_{t}$ is a stationary or unit root process, the test statistics proposed by PSS are uninformative for inference on the existence of a long run relationship (LRR) between $y_{t}$ and $\boldsymbol{x}_{t}$. We propose the long run multiplier (LRM) test statistic as a means of testing for LRRs without knowing whether the series are stationary or unit roots. Using stochastic simulations, we demonstrate the behavior of the test statistic given uncertainty about the univariate dynamics of both $y_{t}$ and $\boldsymbol{x}_{t}$, illustrate the bounds of the test statistic, and generate small sample and approximate asymptotic critical values for the upper and lower bounds for a range of sample sizes and model specifications. We demonstrate the utility of the bounds framework for testing for LRRs in models of public policy mood and presidential success.

TESTING FOR SEASONAL UNIT ROOTS IN PERIODIC INTEGRATED AUTOREGRESSIVE PROCESSES

2008 ◽  
Vol 24 (4) ◽  
pp. 1093-1129 ◽  
Author(s):  
Tomas del Barrio Castro ◽  
Denise R. Osborn
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Finite Sample ◽  
Test Statistic ◽  
Important Special Case ◽  
Frequency Unit ◽  
Annual Frequency ◽  
Fixed Order ◽  
Fuller Distribution ◽  
Zero Frequency

This paper examines the implications of applying the Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) (HEGY) seasonal root tests to a process that is periodically integrated. As an important special case, the random walk process is also considered, where the zero-frequency unit root t-statistic is shown to converge to the Dickey–Fuller distribution and all seasonal unit root statistics diverge. For periodically integrated processes and a sufficiently high order of augmentation, the HEGY t-statistics for unit roots at the zero and semiannual frequencies both converge to the same Dickey–Fuller distribution. Further, the HEGY joint test statistic for a unit root at the annual frequency and all joint test statistics across frequencies converge to the square of this distribution. Results are also derived for a fixed order of augmentation. Finite-sample Monte Carlo results indicate that, in practice, the zero-frequency HEGY statistic (with augmentation) captures the single unit root of the periodic integrated process, but there may be a high probability of incorrectly concluding that the process is seasonally integrated.

THE LIMITING PROPERTIES OF THE CANOVA AND HANSEN TEST UNDER LOCAL ALTERNATIVES

2002 ◽  
Vol 18 (5) ◽  
pp. 1197-1220
Author(s):  
Eiji Kurozumi
Keyword(s):  
Monte Carlo ◽  
Characteristic Function ◽  
Spectral Density ◽  
Unit Root ◽  
Null Hypothesis ◽  
Inverse Function ◽  
Unit Roots ◽  
Local Alternatives ◽  
Test Statistic ◽  
Economic Statistics

This paper investigates the limiting properties of the Canova and Hansen test, testing for the null hypothesis of no unit root against seasonal unit roots, under a sequence of local alternatives with the model extended to have seasonal dummies and trends or no deterministic term and also only seasonal dummies. We derive the limiting distribution of the test statistic and its characteristic function under local alternatives. We find that the local limiting power is an inverse function of the spectral density at frequency π (π/2) when we test against a negative unit root (annual unit roots). We also theoretically show that the local limiting power of the Canova and Hansen test against a negative unit root (annual unit roots) does not increase when the true process has annual unit roots (a negative unit root) but not a negative unit root (annual unit roots), which has been observed in Monte Carlo simulations in such research as Caner (1998, Journal of Business and Economic Statistics 16, 349–356), Canova and Hansen (1995, Journal of Business and Economic Statistics 13, 237–252), and Hylleberg (1995, Journal of Econometrics 69, 5–25).

Unit Root Tests of Structural Break with GARCH-Error Process

2012 ◽  
Vol 452-453 ◽  
pp. 986-990
Author(s):  
Jing Yong Wang ◽  
Li Da Xue
Keyword(s):  
Sample Size ◽  
Unit Root ◽  
Structural Breaks ◽  
Structural Break ◽  
Unit Roots ◽  
Test Statistic ◽  
Test Power ◽  
Nominal Size ◽  
Parameter Test ◽  
Garch Process

This paper studies the effect of GARCH process on the robustness and reliabilities of unit roots test with structural breaks. It gives that, as the GARCH process approaches integratedness, the test statistic’ the proportion of rejections reported actually increases as the sample size increases. Consequently, we can see that the standard asymptotic theory is inapplicable in this case. The statistic , their actual test size on the whole is accordant to nominal size in unit root and no break as the volatility parameter is small, =0 or approach to 0. The statistic exists a serious over sizing of null hypothesis as integratedness in all structural break type. The statistic test power increases as the sample size increases, but test power do not increases as the sample size increase under AR parameter. Test power increases as integratedness increases, and decreases as volatility parameter increases.

scholarly journals Relationship between Remittance and Economic Growth in Nepal

2019 ◽  
Vol 32 (2) ◽  
pp. 249-266 ◽  
Author(s):  
Raghu Raj Kaphle
Keyword(s):  
Economic Growth ◽  
Unit Root ◽  
Policy Formation ◽  
Growth Study ◽  
Policy Makers ◽  
Effective Utilization ◽  
Independent Variables ◽  
Long Run ◽  
Error Correction Mechanism ◽  
Short Run

For the period between 1976 and 2017, this study investigates the relation from remittances and trade to economic growth. Study applied time series econometric techniques; unit root, cointegration and error correction mechanism to examine long-run and short-run association between dependent and independent variables. Outcome confirms a long-run relationship between remittance, trade and economic growth. However, no short-run causal relationship exists between remittances and economic growth, but trade showed significant influence even in the short run in GDP for the period of analysis. The paper also discusses about the effective utilization of remittances. It is hoped that the study would be helpful to government and policy makers for domestic policy formation in the area of utilization of remittances and management of migration from Nepal.

The random walk in the stock prices of 18 OECD countries

2016 ◽  
Vol 43 (4) ◽  
pp. 598-608
Author(s):  
Hassan Shirvani ◽  
Natalya V. Delcoure
Keyword(s):  
Unit Root ◽  
Stock Prices ◽  
Unit Roots ◽  
Oecd Countries ◽  
Unit Root Tests ◽  
Panel Unit Root Tests ◽  
Cross Sectional ◽  
Panel Unit Root ◽  
Content Type ◽  
Long Run

Purpose The purpose of this paper is to examine the presence of unit roots in the stock prices of 16 OECD countries. Design/methodology/approach Heterogeneous panel unit root tests developed by Im et al. (1997/2003) and Pesaran (2007). Findings Under the assumption of cross-sectional independence across the panel, the authors find no evidence of unit roots, thus failing to reject mean reversion in the stock prices for all the countries in the sample. However, under the assumption of cross-sectional dependence, an assumption borne out by the diagnostic test results, the authors find support for the presence of unit roots in the stock prices. Practical implications Thus, the use of more robust panel unit root tests seems to raise questions about the long-run predictability of the stock market, at least in the context of the OECD countries. Originality/value Thus, it seems that in the long run, an investment policy of buy and hold has still much to offer.

scholarly journals Characterizing growth instability: new evidence on unit roots and structural breaks in countries’ long run trajectories

2021 ◽  
Author(s):  
Emanuele Russo ◽  
Neil Foster-McGregor
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
Structural Changes ◽  
Alternative Hypothesis ◽  
Unit Root Test ◽  
Unit Roots ◽  
Finite Sample ◽  
Aggregate Shocks ◽  
Long Run ◽  
Finite Sample Properties

AbstractIn this paper we investigate whether long run time series of income per capita are better described by a trend-stationary model with few structural changes or by unit root processes in which permanent stochastic shocks are responsible for the observed growth discontinuities. For a group of advanced and developing countries in the Maddison database, we employ a unit root test that allows for an unspecified number of breaks under the alternative hypothesis (up to some ex ante determined maximum). Monte Carlo simulations studying the finite sample properties of the test are reported and discussed. When compared with previous findings in the literature, our results show less evidence against the unit root hypothesis. We find even fewer rejections when relaxing the assumption of Gaussian shocks. Our results are broadly consistent with the implications of evolutionary macro models which posit frequent growth shifts and fat-tailed distribution of aggregate shocks.

ON THE PROPERTIES OF SOME TESTS FOR COMMON STOCHASTIC TRENDS

2002 ◽  
Vol 18 (6) ◽  
pp. 1336-1349
Author(s):  
Jörg Breitung ◽  
Carsten Trenkler
Keyword(s):  
Monte Carlo ◽  
Correlation Analysis ◽  
Canonical Correlation Analysis ◽  
Canonical Correlation ◽  
Asymptotic Properties ◽  
Small Sample ◽  
Test Statistics ◽  
Test Statistic ◽  
Stochastic Trends ◽  
Small Sample Properties

We study the asymptotic properties of the tests suggested by Choi and Ahn (1995, Econometric Theory 11, 952–983) in the case of a (nearly) improper normalization of the cointegration vectors. To overcome the size problems in such situations we suggest a test statistic that is based on the eigenvalues of a canonical correlation analysis. Using Monte Carlo simulations, the small sample properties of our test are compared to various other test statistics recently suggested in the literature.

scholarly journals Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

2021 ◽  
Author(s):  
Anna L Tyler ◽  
Baha El Kassaby ◽  
Georgi Kolishovski ◽  
Jake Emerson ◽  
Ann E Wells ◽  
...  
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Genetic Interaction ◽  
Recombinant Inbred Lines ◽  
Test Statistics ◽  
Test Statistic ◽  
Kinship Matrix ◽  
Main Effect ◽  
Main Effects ◽  
Interaction Test

Abstract It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied, are the effects of kinship on genetic interaction test statistics. Here we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using a LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

Multiple structural breaks in cointegrating regressions: a model selection approach

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Schmidt ◽  
Karsten Schweikert
Keyword(s):  
Structural Breaks ◽  
Penalized Regression ◽  
Adaptive Lasso ◽  
Test Statistics ◽  
New Approach ◽  
Multiple Structural Breaks ◽  
Long Run ◽  
Model Selection Approach ◽  
Regression Techniques ◽  
Lasso Estimator

Abstract In this paper, we propose a new approach to model structural change in cointegrating regressions using penalized regression techniques. First, we consider a setting with known breakpoint candidates and show that a modified adaptive lasso estimator can consistently estimate structural breaks in the intercept and slope coefficient of a cointegrating regression. Second, we extend our approach to a diverging number of breakpoint candidates and provide simulation evidence that timing and magnitude of structural breaks are consistently estimated. Third, we use the adaptive lasso estimation to design new tests for cointegration in the presence of multiple structural breaks, derive the asymptotic distribution of our test statistics and show that the proposed tests have power against the null of no cointegration. Finally, we use our new methodology to study the effects of structural breaks on the long-run PPP relationship.

scholarly journals Dynamic Relationship Between Real Export, Real Import, Real Exchange Rate, Labor Force and Real Gross Domestic Product in Malaysia

2019 ◽  
Vol 10 (5) ◽  
pp. 20
Author(s):  
Emilda Hashim ◽  
Norimah Rambeli ◽  
Asmawi Hashim ◽  
Norasibah Abdul Jalil ◽  
Shahrun Nizam Abdul Aziz ◽  
...  
Keyword(s):  
Exchange Rate ◽  
Labor Force ◽  
Open Economy ◽  
Unit Root ◽  
Correction Term ◽  
Unit Root Test ◽  
Real Effective Exchange Rate ◽  
Global Changes ◽  
Real Gdp ◽  
Long Run

This study examined short run and long run relationship between endogenous and exogenous variables. Specifically, it studied the relationship between real export, real import, labor force participation and real effective exchange rate (REER) and real GDP in Malaysia from 1988 to 2017. These variables were tested in various tests, namely, unit root test, granger causality test, vector autoregressive (VAR), Johansen Juselius test and Error Correction Term (ECT). The result revealed that all variables were non-stationary at the level form and stationary at first difference in ADF unit root test. The findings also exhibited the existence of bilateral relationships between real export and real GDP, real import and real GDP, as well as labor and real GDP. Nonetheless, there were no relationship found between REER and real GDP. On the other hand, in VAR, the lag optimum was lag 10 because it indicated the smallest value of AIC. Moreover, for Johansen Juselius cointegration test, it showed two cointegrated vector at both, 5% and 1%, level in trace test. In addition, Max-Eigen value test indicated two cointegrated vector at 0.05 and one cointegrated vector at 0.01. As for the Wald test, there were long run cointegration relationship between real GDP and its determinants, namely real export, real import, labor and REER. Apparently, Malaysia, as a small open economy, has relied heavily on foreign trade. Consequently, our domestic economic performance is susceptible to the changes in international markets and exchange rate. Therefore, suitable international policy implementation is vital to ensure Malaysian economy will be able to adjust to current global changes.

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