Bootstrap Critical Values Research Articles

Improved Inference on the Rank of a Matrix

This paper develops a general framework for conducting inference on the rank of an unknown matrix \Pi_0. A defining feature of our setup is the null hypothesis of the form H_0: rank(\Pi_0)\leq r. The problem is of first order importance because the previous literature focuses on H_0': rank(\Pi_0)= r by implicitly assuming away rank(\Pi_0), which may lead to invalid rank tests due to over-rejections. In particular, we show that limiting distributions of test statistics under H_0' may not stochastically dominate those under rank(\Pi_0) < r. A multiple test on the nulls rank(\Pi_0)=0,...,r, though valid, may be substantially conservative. We employ a testing statistic whose limiting distributions under H_0 are highly nonstandard due to the inherent irregular natures of the problem, and then construct bootstrap critical values that deliver size control and improved power. Since our procedure relies on a tuning parameter, a two-step procedure is designed to mitigate concerns on this nuisance. We additionally argue that our setup is also important for estimation. We illustrate the empirical relevance of our results through testing identification in linear IV models that allows for clustered data and inference on sorting dimensions in a two-sided matching model with transferrable utility.

Stationary bootstrapping for common mean change detection in cross-sectionally dependent panels

Stationary bootstrapping is applied to a CUSUM test for common mean break detection in cross-sectionally correlated panel data. Asymptotic null distribution of the bootstrapped test is derived, which is the same as that of the original CUSUM test depending on cross-sectional correlation parameter. A bootstrap test using the CUSUM test with bootstrap critical values is proposed and its asymptotic validity is proved. Finite sample Monte-Carlo simulation shows that the proposed test has reasonable size while other existing tests have severe size distortion under cross-section correlation. The simulation also shows good power performance of the proposed test against non-cancelling mean changes. The simulation also shows that the theoretically justified stationary bootstrapping CUSUM test has comparable size and power relative to other, theoretically unjustified, moving block or tapered block bootstrapping CUSUM tests.

Energy consumption promotes economic growth or economic growth causes energy use in China? A panel data analysis

This study tries to examine the causal relationship between energy consumption and economic growth for twenty-nine provinces of China by employing the panel Granger causality analysis. The econometric methodology used in this paper allows us to untangle the causal nexus between energy consumption and economic growth and helps us to discriminate between competing theories on which hypothesis is applicable to China. Among the main results, it is found that there is no causality in two out of twenty-nine provinces and bidirectional causality is observed in sixteen out of twenty-nine provinces. Unidirectional causality is observed in eleven out of twenty-nine provinces of China. When bootstrap critical values are used, our empirical findings indicate that there is an unidirectional causal link running from real output to energy use for China, implying that economic growth significantly affects energy consumption, and hence, the conservation hypothesis is applicable to China.

Sequential change detection and monitoring of temporal trends in random-effects meta-analysis.

Temporal changes in magnitude of effect sizes reported in many areas of research are a threat to the credibility of the results and conclusions of meta‐analysis. Numerous sequential methods for meta‐analysis have been proposed to detect changes and monitor trends in effect sizes so that meta‐analysis can be updated when necessary and interpreted based on the time it was conducted. The difficulties of sequential meta‐analysis under the random‐effects model are caused by dependencies in increments introduced by the estimation of the heterogeneity parameter τ 2. In this paper, we propose the use of a retrospective cumulative sum (CUSUM)‐type test with bootstrap critical values. This method allows retrospective analysis of the past trajectory of cumulative effects in random‐effects meta‐analysis and its visualization on a chart similar to CUSUM chart. Simulation results show that the new method demonstrates good control of Type I error regardless of the number or size of the studies and the amount of heterogeneity. Application of the new method is illustrated on two examples of medical meta‐analyses. © 2016 The Authors. Research Synthesis Methods published by John Wiley & Sons Ltd.

Testing identifying assumptions in nonseparable panel data models

Recent work on nonparametric identification of average partial effects (APEs) from panel data require restrictions on individual or time heterogeneity. Identifying assumptions under the “generalized first-differencing” category, such as time homogeneity (Chernozhukov et al., 2013), have testable equality restrictions on the distribution of the outcome variable. This paper proposes specification tests based on these restrictions. The bootstrap critical values for the resulting Kolmogorov–Smirnov and Cramer–von-Mises statistics are shown to be asymptotically valid and deliver good finite-sample properties in Monte Carlo simulations. An empirical application illustrates the merits of testing nonparametric identification from an empiricist’s perspective.

Inference in semiparametric conditional moment models with partial identification

This paper develops inference methods for conditional moment models in which the unknown parameter is possibly partially identified and may contain infinite-dimensional components. For a conjectured restriction on the parameter, we consider testing the hypothesis that the restriction is satisfied by at least one element of the identified set. We propose using the sieve minimum of a Kolmogorov–Smirnov type statistic as the test statistic, derive its asymptotic distribution, and provide consistent bootstrap critical values. In this way a broad family of restrictions can be consistently tested, making the proposed procedure applicable to testing the model specification and constructing confidence set for any given component or some feature of the parameter. Our methods are robust to partial identification, and allow for the moment functions to be nonsmooth. As an illustration, we apply the proposed inference methods to study the quantile instrumental variable Engel curves for gasoline in Brazil. A Monte Carlo study demonstrates finite sample performance.

Current account sustainability in Middle East and Africa (MEA) countries: Evidence from panel data

Countries in the Middle East and Africa (MEA) have diverse economic structures. Some countries are oil exporters, some are oil importers and some countries are very poor, dependent on agriculture. Since current account is an important indicator of an economy’s health, it is of interest to examine if current account balances in MEA region are sustainable. However, empirical research paid scant attention to this issue. No study has been conducted before to examine this issue. The present paper makes an attempt to fill this research gap by employing panel data model over the period from 1995 to 2014 to examine current account sustainability in MEA countries. We follow intertemporal budget constraint approach and examine long-run relationship between export and import plus interest on net foreign debt. As we work with panel data, we pay special attention to cross-section dependence. We use annual data collected from World Development Indicators. All data (exports, imports and interest on long-term external borrowing) are in current US dollar and expressed as percentage of GDP. Interest payment on long-term external borrowing (also in current US dollar) is used as a proxy for interest on net foreign debt. Panel unit root test to cross-section dependence indicate variables are first-difference stationary. We next use panel cointegration and bootstrap critical values under null hypothesis to accommodate cross-section dependence. Panel cointegration result suggests that current account is sustainable. However, panel cointegrating regression estimation indicates that the value of sustainability coefficient is less than 1 (one), which implies that current account is weakly sustainable. As current account is weakly sustainable, it is desirable to make policy intervention at macro level to ensure strong sustainability. This may be achieved by accelerating ongoing trade reforms in MEA countries to boost export earnings and hence ensure the sustainability of external debt in the long run.

Energy Consumption and Health Outcomes in Africa

We examine causal links between energy consumption and health indicators (Mortality rate under-5, life expectancy, greenhouse effect, and government expenditure per capita) for a sample of 16 African countries over the period 1971-2010 (according to availability of countries' data). We use the panel-data approach of Konya (2006), which is based on SUR systems and Wald tests with country specific bootstrap critical values. Our results show that health and energy consumption are strongly linked in Africa. Unilateral causality is found from energy consumption to life expectancy and child under-5 mortality for Senegal, Morocco, Benin, DRC, Algeria, Egypt, and South Africa. At the same time, we found a bilateral causality between energy consumption and health indicators in Nigeria. In particular, our findings suggest that electricity consumption Granger causes health outcomes for several African countries.

CO2 emissions and human development in OECD countries: granger causality analysis with a panel data approach

Carbon dioxide (CO2) is a major greenhouse gas emitted through human activities resulting from energy use. This study examines the causal relation between the logarithms of the human development index and CO2 emissions in 33 Organization for Economic Co-operation and Development countries for 1992–2011. Moreover, it applies a new panel data approach developed by Konya (2006). This approach is based on the seemingly unrelated regression system and Wald tests with country-specific bootstrap critical values. The results obtained from the Granger causality analysis support the growth hypothesis for Denmark, Ireland, Israel, Italy, Japan, Korea, Luxembourg, Poland, Spain, Slovakia, Turkey, and the U.S. In addition, they support the conservation hypothesis for Chile, Czech Republic, Estonia, Finland, France, Greece, New Zealand, and Mexico. The feedback hypothesis is observed for Iceland, Norway, Portugal, and Switzerland as well as the neutrality hypothesis of the other countries (Australia, Austria, Belgium, Canada, Hungary, Netherlands, Slovenia, Sweden, and the UK). This implies that conservation policies that are related to coal, gas, electricity, and oil consumption can reduce CO2 emissions but may simultaneously hinder economic growth and human living standards. However, if conservation policies are not implemented, the detrimental effects of environmental degradation could also affect human living standards. Therefore, policymakers must develop strategic plans to reduce carbon emissions that do not negatively impact their constituents. One possible way to achieve this is by increasing the efficiency of energy use.

Simultaneous likelihood-based bootstrap confidence sets for a large number of models

The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics, and for adjusting the confidence level for multiplicity. Theoretical results state the bootstrap validity in the following setting: the sample size \(n\) is fixed, the maximal parameter dimension \(p_{\textrm{max}}\) and the number of considered parametric models \(K\) are s.t. \((\log K)^{12}p_{\max}^{3}/n\) is small. We also consider the situation when the parametric models are misspecified. If the models' misspecification is significant, then the bootstrap critical values exceed the true ones and the simultaneous bootstrap confidence set becomes conservative. Numerical experiments for local constant and local quadratic regressions illustrate the theoretical results.

Remittances and financial development in Sub-Saharan African countries: A system approach

This paper investigates the causality between remittances and financial sector development in Sub-Saharan African (SSA) countries. To this end, we employ the panel Granger causality testing approach that is based on Seemingly Unrelated Regressions (SUR) multivariate systems and Wald tests with country specific bootstrap critical values. Using annual data over the 1980–2010 period for 19 SSA countries, the study gives the following results. Based on liabilities as a proxy for financial sector development, remittances positively influence financial development only in four countries (Niger, Senegal, Sierra Leone and Sudan) and financial development positively impacts remittances only in Gambia. On the contrary, considering credit to measure financial depth, the results show that remittances positively affect financial development only in Sudan and financial development does not influence remittances in any country. Consequently, there is no strong evidence supporting the view that remittances promote financial development in SSA countries and financial development seems not to be a relevant determinant of remittances received in SSA countries.

LM tests of spatial dependence based on bootstrap critical values

To test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, in finite samples, the LM test referring to asymptotic critical values may suffer from the problems of size distortion and low power, which become worse with a denser spatial weight matrix. In this paper, residual-based bootstrap methods are introduced for asymptotically refined approximations to the finite sample critical values of the LM statistics. Conditions for their validity are clearly laid out and formal justifications are given in general, and in detail under several popular spatial LM tests using Edgeworth expansions. Monte Carlo results show that when the conditions are not fully met, bootstrap may lead to unstable critical values that change significantly with the alternative, whereas when all conditions are met, bootstrap critical values are very stable, approximate much better the finite sample critical values than those based on asymptotics, and lead to significantly improved size and power. The methods are further demonstrated using more general spatial LM tests, in connection with local misspecification and unknown heteroskedasticity.

Testing the Causality between Electricity Consumption, Energy Use and Education in Africa

We investigate the existence of causal relationships between energy consumption and education (enrollment in primary secondary and higher education) for a sample of 16 African countries over the period 1971-2010 (according to availability of countries' data). We use the panel-data approach of Konya (2006), which is based on SUR systems and Wald tests with country specific bootstrap critical values. Our results show that education and energy use are strongly linked in Africa. There is bidirectional causality between primary, secondary and higher education and energy use for several countries. Moreover, electricity consumption plays a crucial role in the energy-education links in Africa.

Testing for structural stability of factor augmented forecasting models

Mild factor loading instability, particularly if sufficiently independent across the different constituent variables, does not affect the estimation of the number of factors, nor subsequent estimation of the factors themselves (see e.g. Stock and Watson (2009)). This result does not hold in the presence of large common breaks in the factor loadings, however. In this case, information criteria overestimate the number of breaks. Additionally, estimated factors are no longer consistent estimators of “true” factors. Hence, various recent research papers in the diffusion index literature focus on testing the constancy of factor loadings. However, forecast failure of factor augmented models can be due to either factor loading instability, regression coefficient instability, or both. To address this issue, we develop a test for the joint hypothesis of structural stability of both factor loadings and factor augmented forecasting model regression coefficients. Our proposed test statistic has a chi-squared limiting distribution, and we are able to establish the first order validity of (block) bootstrap critical values. Empirical evidence is also presented for 11 US macroeconomic indicators.

Testing asymmetric correlations in stock returns via empirical likelihood method

Purpose – This study aims to propose a model-free statistic that tests asymmetric correlations of stock returns, in which stocks move more often with the market when the market goes down than when it goes up, and then empirically analyze the asymmetric correlations of the China stock market and international stock markets, respectively. Design/methodology/approach – Using empirical likelihood method, this study designs and conducts a model-free test, which converges to χ2 distribution under regulated conditions and performs well in the finite sample using bootstrap critical value method. Findings – By analyzing the authors' model-free test, the authors find that compared with Hong et al.'s test that closely relates to the authors, both of the tests are under rejected using asymptotic critical value. However, using the bootstrap critical value method can greatly improve the performance of the two tests. Second, investigating the power of the two tests, the authors find that the proportion of rejections of the authors' test is roughly 10-20 percent larger than Hong et al.'s test in mixed copula model setting. The last finding is the authors find evidence of asymmetric for small-cap size portfolios, but no evidence for middle-cap and large-cap size portfolios in the China stock market. Besides, the authors test asymmetric correlations between the USA and Japan, France and the UK; the asymmetric phenomenon exists in international stock markets, which is similar to Longin and Solnik's findings, but they are not significant according to both the authors' test and Hong et al.'s test. Research limitations/implications – The findings in this study suggest that both the authors' test and Hong et al.'s test are under rejected using asymptotic critical value. When applying these statistics to test asymmetric correlations, the authors should take care with the choice of critical value. Practical implications – The empirical analysis has a significant practical implication for asset allocation, asset pricing and risk management fields. Originality/value – This study constructs a model-free statistic to test asymmetric correlations using empirical likelihood method for the first time and corrects the size performance by bootstrap method, which improves the performance of Hong et al.'s test. To the authors' knowledge, this is the first study to test the asymmetric correlations in the China stock market.

Untangling the causal relationship between government budget and current account deficits in OECD countries: Evidence from bootstrap panel Granger causality

This study examines the causal relationship between the current account deficit and government budget deficit for eleven OECD countries by employing the panel Granger causality analysis. The econometric methodology used in this paper allows us to untangle the causal nexus between the current account deficit and government budget deficit and helps us to discriminate between competing theories on which hypothesis is applicable to these OECD countries. Among the main results, it is found that the Barro–Ricardo Equivalence hypothesis is applicable to France and the UK. When bootstrap critical values are used, our empirical findings indicate that there is bi-directional causality between the current account deficit and the government budget deficit for eleven OECD countries. The twin deficits hypothesis is supported either through the Keynesian hypothesis or through the current account targeting hypothesis.

Optimal Test for Markov Switching Parameters

This paper proposes a class of optimal tests for the constancy of parameters in random coefficients models. Our testing procedure covers the class of Hamilton's models, where the parameters vary according to an unobservable Markov chain, but also applies to nonlinear models where the random coefficients need not be Markov. We show that the contiguous alternatives converge to the null hypothesis at a rate that is slower than the standard rate. Therefore, standard approaches do not apply. We use Bartlett-type identities for the construction of the test statistics. This has several desirable properties. First, it only requires estimating the model under the null hypothesis where the parameters are constant. Second, the proposed test is asymptotically optimal in the sense that it maximizes a weighted power function. We derive the asymptotic distribution of our test under the null and local alternatives. Asymptotically valid bootstrap critical values are also proposed.

Bootstrapped Durbin– Watson Test of Autocorrelation for Small Samples

The Durbin-Watson (DW) test is the most widely used test for autocorrelation of a first order in regression analysis. The critical value of DW test depends on X matrix. As a result, the DW test statistic falls sometime in the inconclusive region. For large sample, the DW test can be used for normal distribution. In this paper, we proposed a bootstrap critical value for small sample and compared the power properties with other procedures. Monte-Carlo study shows that the bootstrapped DW test performs better than the usual DW test with the help of power.

A test for bivariate normality with applications in microeconometric models

In this paper, we propose a test for bivariate normality in imperfectly observed models, based on the information matrix test for censored models with bootstrap critical values. In order to evaluate its properties, we run a comprehensive Monte Carlo experiment, in which we use the bivariate probit model and Heckman sample selection model as examples. We find that, while asymptotic critical values can be seriously misleading, the use of bootstrap critical values results in a test that has excellent size and power properties even in small samples. Since this procedure is relatively inexpensive from a computational viewpoint and is easy to generalise to models with arbitrary censoring schemes, we recommend it as an important and valuable testing tool.

Immigration, unemployment and GDP in the host country: Bootstrap panel Granger causality analysis on OECD countries

This paper examines the causality relationship between immigration, unemployment and economic growth of the host country. We employ the panel Granger causality testing approach of Kònya (2006) that is based on SUR systems and Wald tests with country specific bootstrap critical values. This approach allows one to test for Granger-causality on each individual panel member separately by taking into account the contemporaneous correlation across countries. Using annual data over the 1980–2005 period for 22 OECD countries, we find that, only in Portugal, unemployment negatively causes immigration, while in any country, immigration does not cause unemployment. On the other hand, our results show that, in four countries (France, Iceland, Norway and the United Kingdom), growth positively causes immigration, whereas in any country, immigration does not cause growth.