LM Statistics Research Articles

Instability of Factor Strength in Asset Returns

We study the problem of detecting structural instability of factor strength in asset pricing models for financial returns with observable factors. We allow for strong and weaker factors, in which the sum of squared betas grows at a rate equal to and slower than the number of test assets, respectively: this growth rate determines the strength of the corresponding factor. We propose LM and Wald statistics for the null hypothesis of stability and derive their asymptotic distribution when the break fraction is known, as well as when it is unknown and has to be estimated. We corroborate our theoretical results through a comprehensive series of Monte Carlo experiments. An extensive empirical analysis uncovers the dynamics of instability of factor strength in financial returns from equity portfolios.

The Trajectory of Energy-Growth Relationships Revisited: A Multi-Sectoral Analysis with Relevance of Time Inclinations in Europe

This study examines the multidimensional impact of energy intensity (EI) and sectoral energy consumption on economic performance (EP). A sample of dataset includes European economies consisting of three decades from 1990 to 2020 is analyzed by employing several estimators and an inclusive estimation strategy for empirical robustness. This component of research is concerned with determining the trajectory of energy-growth relationships in order to explain changes in magnitude and intensity through time. This study is required in order to make an accurate comparison across time periods that how the change dimension is increasing or decreasing. Econometric practice is panel two step GMM. This study estimated by using GMM estimation and the results have been reported on the basis of probability values of F-statistics. The Kleibergen-Paap rk LM statistic with chi-square p-values of under-identification test are used to check the identification of the model. The chi-square probability values of Kleibergen-Paap rk LM statistics in all of the models of current study are highly significant which shows that model are identified. Moreover, Hansen J statistics are included to check validity of instruments. Our key findings suggest that energy intensity and energy mix on economic performance for European countries varies depending on the time era and degree of development. Results predict that economic expansion tends to be acutely susceptible to EI after 1990, and the lower the amount of income per capita, greater the sensitivity. It is also obvious that a broader approach is required.

SOCIO-ECONOMIC AND INSTITUTIONAL DETERMINANTS OF FOREIGN DIRECT INVESTMENT IN SOUTH ASIA

Determinants of foreign direct investment (FDI) is the key area of research in development economics. Earlier studies did not give due weight to the segregation of analysis across economic, social, and institutional factors for FDI. This study specifically attempts to explore the intervening role of social and institutional factors which affects the relationship between economic factors and inward FDI. For this purpose, three segregate models relating to economic, social, and institutional factors along with a composite model comprised of all these factors are taken into consideration in this study. Panel data utilized is related to South Asian countries from 2008 to 2016. In the light of Breusch-Pagan LM Statistics, Pooled OLS estimates are preferred for analyses. This study leads to the conclusion that in segregation analysis economic factors and institutional factors have an important role in attracting FDI, but social factors have no significant role in this regard. The intervening role of social and institutional factors is not found in this study. The only factors which are recognized in the composite analysis are economic. Enlarged market size having an efficient financial market with no inflationary pressure is found to be an economic environment in the South Asian region which is helpful for attracting FDI. The rule of law is not found to be an effective characteristic for inward FDI.

OECD Ülkelerine Ait Çeşitli Enerji Tüketimleri ve Ekonomik Büyüme Arasındaki İlişkinin Panel Eşbütünleşme Analizi ile İncelenmesi

One of the important parameters showing the development level of the countries is energy consumption. In general terms, in the countries that show developed as industry are consuming more energy. In this context, countries with high energy needs are turning to different alternative energy sources in order not to be dependent on foreign sources. In this study, the relationship between various energy types’ consumption and economic growth belonging to 36 OECD countries was analyzed by Westerlund (2007) panel cointegration test. Before Cointegration test, the heterogeneity of the data was tested, various cross-section dependency tests were applied to the data and the dependency of crosssections forming the panel was examined. In addition, it was determined whether the data is stationary by using CIPS test. According to the LM, LMadj and CDLM statistics (p <0.05), cross-sectional dependence was determined. Thus, it was decided that it would be appropriate to use the second generation unit root tests. According to CIPS test, it was determined that the variables were not stationary. The first differences of the non-stationary data were taken and again the stationary analysis was applied to the data and it was observed that the data were made stationary. The results showed that there is cointegration between energy consumption and economic growth. In addition, as a result of long-term cointegration test, it was determined that there is a positive relationship between hydroelectric and renewable energy consumption and economic growth, and a negative relationship between thermal energy consumption and economic growth.

Inference in second-order identified models

We explore the local power properties of different test statistics for conducting inference in moment condition models that only identify the parameters locally to second order. We consider the conventional Wald and LM statistics, and also the Generalized Anderson–Rubin (GAR) statistic (Anderson and Rubin, 1949; Dufour, 1997; Staiger and Stock, 1997; Stock and Wright, 2000), KLM statistic (Kleibergen, 2002; Kleibergen, 2005) and the GMM extension of Moreira (2003) (GMM-M) conditional likelihood ratio statistic. The GAR, KLM and GMM-M statistics are so-called “identification robust” since their (conditional) limiting distribution is the same under first-order, weak and therefore also second order identification. For inference about the model specification, we consider the identification-robust J statistic (Kleibergen, 2005), and the GAR statistic. Interestingly, we find that the limiting distribution of the Wald statistic under local alternatives not only depends on the distance to the null hypothesis but also on the convergence rate of the Jacobian. We specifically analyse two empirically relevant models with second order identification. In the panel autoregressive model of order one, our analysis indicates that the Wald test of a unit root value of the autoregressive parameter has better power compared to the corresponding GAR test which, in turn, dominates the KLM, GMM-M and LM tests. For the conditionally heteroskedastic factor model, we compare Kleibergen (2005) J and the GAR statistics to Hansen (1982) overidentifying restrictions test (previously analysed in this context by Dovonon and Renault, 2013) and find the power ranking depends on the sample size. Collectively, our results suggest that tests with meaningful power can be conducted in second-order identified models.

External Debt and Economic Growth in Nigeria

External credits have been received from various sources including bilateral and multilateral arrangements but the country’s debt is a source of worry since the projects for which these loans were contracted cannot finance the credit facilities. This paper focused on the impact of external debt on economic growth in Nigeria within the period of 1980 to 2016. Thus, secondary data on gross domestic product and external debt were sourced from CBN statistical bulletin and debt management office fact book. The econometric method of Generalized Method of Moments(GMM) test was used. Priori the GMM test is the Kwiatkowski, Phillips, Schemidt and Shin, (KPSS) unit root test to ascertain the stationarity of the variables. Based on the empirical results; the KPSS stationarity test for each of the series showed that all the variables were stationary at order one as their respective LM statistics was less than the critical value at 5%. The GMM test shows that external debt and economic growth has positive and significant relationship with R2 of 54 percent. Therefore, to achieve long-term solution to the problem of external debts burden, government should stimulate domestic production to liberate the Nigerian economy from the shackles of wants and excessive dependence on external economics, which build up debt. Also, government should avoid unnecessary and unproductive borrowing that will serve as a leakage to the economy. This to a large extent will enhance the growth of the Nigerian economy.

Residual bootstrap tests in linear models with many regressors

This paper is concerned with bootstrap hypothesis testing in linear regression models with many regressors. I show that bootstrap F, LR and LM tests are asymptotically valid even when the numbers of estimated parameters and tested restrictions are not asymptotically negligible fractions of the sample size. One of the conditions for these results is that the regressors come from an asymptotically balanced design. Depending on the number of restrictions tested and on the errors’ distribution, violation of that condition might render the bootstrap tests asymptotically invalid. In that case, I propose bootstrapping Calhoun’s (2011) G statistic or modified versions of the LR and LM statistics, and show that these procedures remain asymptotically valid.Monte Carlo simulations indicate that the bootstrap tests often outperform asymptotic ones. However, analyzing the approximate third cumulant of the F statistic reveals that the bootstrap test does not generally provide the usual higher order asymptotic refinements. Nevertheless, it is found that the bootstrap third cumulant partially matches the population third cumulant, which might explain the bootstrap’s good finite sample performances, especially when the errors come from a symmetric distribution.

TRENDS AND DETERMINANTS OF POVERTY AND INEQUALITY IN NIGERIA

The study analyzed the determinants of poverty and income inequality in Nigeria. The objectives of the study are to examine the impact of population growth on poverty and income inequality in Nigeria and to examine the impact of unemployment on poverty and income inequality in Nigeria. To achieve the stated objectives, secondary data from NBS and CBN statistical bulletin were collected on poverty, income inequality, population growth and unemployment. The study used descriptive statistics and Generalized Method of Moments GMM test as the estimation techniques of data analysis. The Kwiatkowski, Phillips, Schemidt and Shin, KPSS unit root test preceded the GMM test in order to establish the stationarity of the variables the variables are platykurtic in nature, implying their distributions are higher than normal. The KPSS stationarity test of the series showed that the variables were stationary at first difference as their respective LM statistics are less than 5 percent critical values. The GMM results show that the coefficient of population growth POP is positively related with poverty and statistically significant at 5 percent level. Similarly the coefficient of unemployment UEM is negatively related with poverty but statistically not significant at 5 percent level. Moreover, the coefficient of population growth POP is positively related with income inequality and statistically significant at 5 percent level. Also, the coefficient of unemployment UEM is negatively related with poverty and statistically significant at 5 percent level. The study concludes that there is significant prevalence of poverty and income inequality among the Nigerian citizen. Based on findings of the study recommends implementation of a sound government programme and welfare package in order to check growing rate of poverty and inequality in Nigeria.

Significance test in nonstationary logit panel model with serially correlated dependent variable

We derive the asymptotic distribution of the overall significance/LM test in logit panel models with nonstationary covariates when the binary dependent variable is serially correlated. The asymptotic distribution of LM statistic is shown proportional to Chi-square distribution. Spurious logit link could arise if one fails to take into account the serial correlation.

Testing for Sphericity in a Two-Way Error Components Panel Data Model

ABSTRACTThis article is concerned with sphericity test for the two-way error components panel data model. It is found that the John statistic and the bias-corrected LM statistic recently developed by Baltagi et al. (2011)Baltagi et al. (2012, which are based on the within residuals, are not helpful under the present circumstances even though they are in the one-way fixed effects model. However, we prove that when the within residuals are properly transformed, the resulting residuals can serve to construct useful statistics that are similar to those of Baltagi et al. (2011)Baltagi et al. (2012). Simulation results show that the newly proposed statistics perform well under the null hypothesis and several typical alternatives.

Testing for sphericity in a two-way error components panel data model

ABSTRACTThis article is concerned with sphericity test for the two-way error components panel data model. It is found that the John statistic and the bias-corrected LM statistic recently developed by Baltagi et al. (2011)Baltagi et al. (2012, which are based on the within residuals, are not helpful under the present circumstances even though they are in the one-way fixed effects model. However, we prove that when the within residuals are properly transformed, the resulting residuals can serve to construct useful statistics that are similar to those of Baltagi et al. (2011)Baltagi et al. (2012). Simulation results show that the newly proposed statistics perform well under the null hypothesis and several typical alternatives.

Estimating export potential for a small open economy using a gravity model approach: evidence from Namibia

Exports are the drivers of economic growth in Namibia. Given their importance in the economy, it is necessary to analyse factors that are determining export flows between Namibia and its trading partners. A gravity model is very important in the analysis of bilateral trade flows, and has proven to be a useful tool in determining trade or export potential of a country. The purpose of this study is to investigate factors that determine exports of Namibia using a gravity model approach. Panel data econometric technique was used to estimate the gravity model for Namibia. The analysis covers the period 1998–2012 and uses annual data. Pooled effects, fixed effects and random effects models were estimated. The LM and F-test statistics were used to test for poolability of the cross-sections. Poolability was rejected in favour of heterogeneity among the cross-sections. Haussman test was used to determine whether fixed or random effects is the appropriate model. The results showed that fixed effect is the appropriate model. The analysis indicates that increases in importer’s GDP and Namibia’s GDP cause exports to increase, while distance and importer’s GDP per capita are associated with a decrease in exports. Namibia’s GDP per capita and real exchange rates do not have an impact on export. Namibia exports more to countries where it shares a common border and SADC as well as to the European Union. The study shows that there is unexploited export potential to among others, Australia, Belgium, Kenya, Mauritius, Netherlands, Portugal, South Africa and Switzerland. These results are important for trade policy formulation in order ensure that Namibia’s export potential is exploited in order to enhance economic growth and generates employment. Trade promotion activities should be directed to that have unexploited potential.

Inference and Testing on the Boundary in Extended Constant Conditional Correlation GARCH Models

We consider inference and testing in extended constant conditional correlation GARCH models in the case where the true parameter vector is a boundary point of the parameter space. This is of particular importance when testing for volatility spillovers in the model. The large-sample properties of the QMLE are derived together with the limiting distributions of the related LR, Wald, and LM statistics. Due to the boundary problem, these large-sample properties become nonstandard. The size and power properties of the tests are investigated in a simulation study. As an empirical illustration we test for (no) volatility spillovers between foreign exchange rates.

Fixed-Smoothing Asymptotics in a Two-Step GMM Framework

The paper develops the …xed-smoothing asymptotics in a two-step GMM framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic and the LM statistic remain asymptotically pivotal. It is shown that critical values from the …xedsmoothing asymptotic distribution are high order correct under the conventional increasingsmoothing asymptotics. When an orthonormal series covariance estimator is used, the critical values can be approximated very well by the quantiles of a noncentral F distribution. A simulation study shows that the new statistical tests based on the …xed-smoothing critical values are much more accurate in size than the conventional chi-square test.

LM tests for spatial correlation in spatial models with limited dependent variables

Models of limited dependent variables are of great interest in econometrics. This paper focuses on the specification and hypothesis test of spatial models which have a Tobit structure. We derive an extended central limit theorem for statistics of a linear–quadratic form with multivariate random variables. We consider the LM statistics for testing spatial correlation and establish their asymptotic distributions. The tests are applied to an empirical example: we detect the presence of competition among school districts on school district income tax in Iowa.

산업생산지수 변동성과 외국인 직접투자의 선도-지연 관계

Foreign direct investment(FDI) not only increases output and employment, but also transfers advanced technologies. That is, FDI may promote economic growth and enhance competitiveness. One of the most important determinants of FDI is the market size. Larger market size offers opportunities to realize economies of scale. Market size is a proxy for product demand the potential for growth. This study uses industrial production index(IPI) as a proxy to market size, and examines the relationship between industrial production index volatility and foreign direct investment. That is, this paper investigates whether the uncertainty of real economy activity of the host country influences the decision-making of foreign investors. Previous studies on this subject focus mainly on the relationship between IPI in level and FDI. On the contrary, this study is distinguished from prior studies in that it investigates the relationship between IPI volatility and FDI. When decisions have an irreversible factor, uncertainty about future outcomes plays a key role in the decision to invest. Because FDI generally involves irreversible costs in the foreign country, foreign companies wait for a more favorable economic environment before investing abroad. Therefore, irreversibility of investment expenditures renders the investment decisions of foreign companies sensitive to economic uncertainty. The descriptive statistics show excess kurtosis, and the Jarque-Bera test statistic rejects the null hypothesis of normality for the unconditional distribution of the monthly IPI changes. To test ARCH effects in the residuals, we employ ex ante ARCH LM test. The null hypothesis of ARCH LM test is that there is no ARCH up to q order in the residuals. This is a regression of the squared residuals on a constant and lagged squared residuals up to order q. Ex ante ARCH LM tests show that there are ARCH effects in the residuals. Therefore, GARCH type model is appropriate for analyzing this data. The procedure used in this paper involves the following steps. First, to determine IPI volatility, I use the exponential generalized autoregressive conditional heteroskedasticity model proposed by Nelson. EGARCH model has a distinctive feature, namely, conditional variance is modeled to capture the asymmetry effect of volatility. The return series of IPI shows the serial correlation. This causes the distortion of parameter estimates in GARCH type model. To account for serial correlation in the returns, I include a MA(1) process for the residuals in the mean equation. According to the results, the asymmetric volatility effect is significant at 5% level. In this study, the asymmetry effect term is negative and statistically different from zero, indicating that the IPI volatility impact is asymmetric during the sample period. The economic implication of this sign of the leverage effect term is that a decrease in IPI would lead to a higher level of uncertainty when compared to the level of uncertainty generated by an increase in IPI. In estimated EGARCH model, the persistence parameter which is the coefficient of lagged conditional variance in the variance equation is smaller than one. Therefore, estimated conditional variance series is stationary. Ex post LM statistics test whether the residuals exhibit ARCH effect. If the EGARCH model is correctly specified, there should be no ARCH effect in the residuals. P-value indicates that there is not any ARCH effect up to order 5. Therefore, the EGARCH model is well specified. Second, a prerequisite in applying the Granger causality test is to test the unit root properties of the series. To examine the stationarity of the series, the Augmented Dickey-Fuller test is applied. The optimum lag order is determined by the SC. ADF test results show that the null hypothesis of a unit root is rejected in cases of IPI volatility and FDI, respectively.

Testing for structural breaks in dynamic factor models

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our Monte Carlo simulations) is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated. The proposed test procedures are applied to datasets from the US and the euro area.

Assessing the relative power of structural break tests using a framework based on the approximate Bahadur slope

Abstract We compare the asymptotic relative efficiency of the Exp, Mean, and Sup functionals of the Wald, LM and LR tests for structural change analyzed by Andrews [Andrews, D.W.K., 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821–856.] and Andrews and Ploberger [Andrews, D.W.K., Ploberger, W., 1994. Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414.]. We derive the approximate Bahadur slopes of these tests using large deviations techniques. These show that tests based on the Mean functional are inferior to those based on the Sup and Exp when using the same base statistic. Also, for a given functional, the Wald-based test dominates the LR-based test, which dominates the LM-based one. We show that the Sup- and Mean-type tests satisfy Wieand’s [Wieand, H.S., 1976. A Condition under which the Pitman and Bahadur approaches to efficiency coincide. Annals of Statistics 4, 1003–1011.] condition so that their slopes yield the limiting (as the size tends to zero) asymptotic relative Pitman efficiency (whether this holds for the Exp-type tests still remains a conjecture). Using this measure of efficiency, the Mean-type tests are also inferior to the Sup. We also compare tests based on the Wald and LM statistics modified with a HAC estimator. In this case, the inferiority of the LM-based tests is especially pronounced. The relevance of our theoretical results in finite samples is assessed via simulations. Our results are in contrast to those obtained by the authors–in the second reference cited above–based on a local asymptotic framework, and our analysis thereby reveals its potential weaknesses in the context of structural change problems.

A RESIDUAL-BASED LM-TYPE TEST AGAINST FRACTIONAL COINTEGRATION

Nonstationary integrated time series may be fractionally cointegrated. Here we propose a test for the null hypothesis of no cointegration. It builds on the asymptotically normal LM test against fractional alternatives applied to single equation residuals. It is shown that the LM test applied naively to residuals from a static level regression does not retain asymptotic normality. However, when the LM statistic is employed with residuals from a regression of difierenced variables, then the test statistic is shown to have a standard normal limiting distribution. Monte Carlo experiments establish its relevance in flnite samples.

Valid Confidence Intervals and Inference in the Presence of Weak Instruments

We investigate confidence intervals and inference for the instrumental variables model with weak instruments. Wald-based confidence intervals perform poorly in that the probability they reject the null is far greater than their nominal size. In the worst case, Wald-based confidence intervals always exclude the true parameter value. Confidence intervals based on the LM, LR, and Anderson-Rubin statistics perform far better than the Wald. The AndersonRubin statistic always has the correct size, but LM and LR statistics have somewhat greater power. Performance of the LM and LR statistics is improved by a degrees-of-freedom correction in the overidentified case. We show that the practice of “pre-testing” by looking at the significance of the first-stage regression leads to extremely poor results when the instruments are very weak.