Spurious regressions driven by excessive volatility

This paper shows that the excessive volatility results in spurious regressions. The spuriousness can be driven by persistency in the error variances unlike the conventional spurious regressions that are generated by the persistency in the level of regression errors.     

A comment on ‘Is the spurious regression problem spurious?’

McCallum (2010) presented evidence that the spurious regression problem can be solved by standard means. We show using finite-sample evidence that the spurious regression problem cannot always be fixed using standard autocorrelation correction procedures and remains, therefore, a not-so-spurious problem.     

Spurious regression: A higher-order problem

This paper investigates solving the spurious regression problem using an autocorrelation correction. It is shown that if the relevant data generation processes contain higher-order terms, this solution is not as effective as in the first-order case.     

季节平稳过程间的虚假回归

本文推导了当数据生成过程是独立的季节平稳过程情形下,OLS参数估计及检验统计量的极限分布。发现序列中的自相关性会导致虚假回归现象的发生。     

Engineering robust instruments for GMM estimation of panel data regression models with errors in variables: a note

Econometricians have long recognized the need to account in some way for measurement errors, specification errors and endogeneity to ensure that the ordinary least squares estimator is consistent. This article introduces a new generalized method of moments estimator that relies on robust instruments to estimate panel data regression models containing errors in variables. We show how this GMM approach can be generalized for the panel data framework using higher moments and cumulants as instruments. The new instruments, engineered for greater robustness, are proposed to tackle the pervasive problem of weak instruments.     

ROLLING REGRESSION VERSUS TIME‐VARYING COEFFICIENT MODELLING: AN EMPIRICAL INVESTIGATION OF THE OKUN'S LAW IN SOME EURO AREA COUNTRIES

During the last decade, economists have shown that the inverse relationship between economic growth and unemployment rate varies over time. Rolling regression has been the main tool used to quantify such a relationship. This methodology suffers from several well‐known problems which lead to spurious non‐linear patterns in the Okun's coefficient behaviour over time. Here, we take a penalized regression spline approach to estimate the Okun's time‐varying effects. As a result, spurious non‐linearities are suppressed and hence important time‐varying coefficient features revealed. Our empirical results show that the inverse relationship in some Euro area countries is spatially heterogeneous and time‐varying. The findings are complemented by the calculation of the rate of output growth needed for a stable unemployment rate, as proposed by Knotek.     

Is the spurious regression problem spurious?

So-called “spurious regression” relationships are generally accompanied by clear signs of residual autocorrelation. A conscientious researcher would likely re-estimate with an autocorrelation correction. Simulations indicate that resulting test statistics are close to true values, so do not yield spurious results.     

Spurious regressions between stationary generalized long memory processes

This paper shows that a spurious regression can occur between two stationary generalized fractional processes, as long as their generalized fractional differencing parameters sum up to a value greater than 0.5 and their spectral densities have poles at the same location. This theoretical finding is supported by simulations.     

Building growth and value hybrid valuation model with errors-in-variables regression

Growth value model (GVM) considers stock intrinsic value as the synergy of book value and return on equity (ROE), which contains two parameters, value factor and growth factor. This study addresses the problem of independent variables having measurement errors by utilizing errors-in-variables regression to estimate accurate model parameters. Research findings show the following: (1) The regression curve derived by traditional regression analysis exhibits severe bias. Errors-in-variables regression is capable of correcting the bias. (2) Large-scale firms exhibit lower value factor and higher growth factor, which indicates that large-scale firms possess better profit persistence.     

The seasonal unit root structure in New Zealand Macroeconomic variables

ADF unit root tests are generally applied to macroeconomic data prior to testing theoritical models to ensure that all relevant variables are integrated of the same order. Not only is it important to test that these variables are integrated of the same order but also that a cointegrating relationship exists; failure to do so raise the specture of false inference associated with the spurious regression problem. The seasonal nature of quarterly data adds a further proplem which has generally been overcome by seasonally adjusting the data using procedure such as the census X-11 rather than suppressing it, have attempted to determine whether the seasonal component in each variable exhibits stochastic non-stationary. This paper analysisunit roots in a seasonal setting and compares the recently developed tests for seasonal unit roots as well as the standard augmented Dickey-Fuller zerop frequency unit root tests. Of the variables tested relatively few paper to be integrated at the seasonal frequenciues and, as other studies suggest,determinstic seasonal effects are typically more important than stochastic ones.     

Spurious regressions with stationary series

A spurious regression occurs when a pair of independent series, but with strong temporal properties, are found apparently to be related according to standard inference in an OLS regression. Although this is well known to occur with pairs of independent unit root processes, this paper finds evidence that similar results are found with positively autocorrelated autoregressive series or long moving averages. This occurs regardless of the sample size and for various distributions of the error terms.     

State dependence,serial correlation and heterogeneity in the union membership dynamics

In order to distinguish the true and spurious state dependence from the complicated dynamics of union membership, the simulation estimators incorporating the lagged dependent variables, unobserved individual heterogeneity and correlations among the errors are implemented in this article to study union membership dynamics. It is found that the true state dependence of union membership under multivariate t assumption is much higher than the standard dynamic panel probit estimators which are under multivariate normal assumptions. On the other hand, the spurious state dependence (the variance of the unobserved individual heterogeneity) is estimated to be higher when using the standard dynamic panel probit estimators than under multivariate t assumption. Moreover, blacks and married men are found to have higher union membership true state dependence than whites and unmarried men.     

Stability of the money demand function in Asian developing countries

Previous studies that estimated the money demand function in Asian developing countries either employed traditional estimation techniques or recently popularized cointegration technique. While the first group suffers from ‘spurious regression’ problems, the second group interpreted their finding of cointegration as a sign of stability of estimated parameters. This study, after incorporating the CUSUM and CUSUMSQ tests into cointegration analysis, shows that in some Asian countries even though real M1 or M2 monetary aggregates are cointegrated with their determinants, the estimated parameters are unstable.     

Time series dynamics of US State unemployment rates

This paper examines the time series properties of state and national unemployment rates. Based upon unit root, variance ratio, and cointegration tests, as well as Granger-causality and error-correction model results, several important conclusions can be made. First, forecasting models that include only levels of unemployment rates may produce spurious regression results. Second, in the vast majority of cases, there is no long run co-movement between the aggregate US unemployment rate and individual state unemployment rates. Third, models that are specified in first-differences generally yield reliable insights into state-national unemployment relationships.     

Using monthly returns to model conditional heteroscedasticity

This empirical study examines the extent of non–linearity in a multivariate model of monthly financial series. To capture the conditional heteroscedasticity in the series, both the GARCH(1,1) and GARCH(1,1)–in–mean models are employed. The conditional errors are assumed to follow the normal and Student– t distributions. The non–linearity in the residuals of a standard OLS regression are also assessed. It is found that the OLS residuals as well as conditional errors of the GARCH models exhibit strong non–linearity. Under the Student density, the extent of non–linearity in the GARCH conditional errors was generally similar to those of the standard OLS. The GARCH–in–mean regression generated the worse out–of–sample forecasts.     

EstimatingJ (>1) quarterly time series in fulfilling annual and quarterly constraints

This paper addresses the problem of joint disaggregating a group of time series when their temporal aggregation values and their contemporaneous aggregation are known and when a number of related series in the desired frequency are available. The focus is on temporal distribution of annual series. This problem was treated before by other authors but they did not solve the problem of spurious steps which usually emerge in this framework. Proposed here is the simplest hypothesis congruent with reality that solves this difficulty. An algorithm is proposed to use these hypotheses in empirical works.     

A note on spurious significance in regressions involving <Emphasis Type="BoldItalic">I</Emphasis>(0) and <Emphasis Type="BoldItalic">I</Emphasis>(1) variables

We demonstrate that t ratios (the F statistic) for I(1) regressors in a model with an I(0) dependent variable will generally be oversized. This indicates that spurious significance occurs in a situation where it was not previously identified. We also compare the asymptotic rejection rates of t ratios for various combinations of I(1) and I(0) variables in the two-variable linear regression model. These rejection rates systematically increase with the degree of autocorrelation, yielding spurious significance, when both variables are either positively or negatively autocorrelated. In contrast, when one variable is negatively autocorrelated and the other is positively autocorrelated the rejection rates systematically fall and are undersized.     

A REAPPRAISAL OF THE INCIDENCE OF EMPLOYER CONTRIBUTIONS TO SOCIAL SECURITY IN JAPAN

This paper reappraises Tachibanaki and Yokoyama (2008)—an empirical analysis indicating no apparent backward shifting of employer social insurance contributions—by modifying their empirical strategy. First, we control for a spurious positive correlation between wages and employers' contribution rates by trend variables. Second, we utilize a cross‐sectional variation in the contribution rate of workers' compensation insurance. Third, we exclude two industries from our sample to remove sampling errors in wages. Our results indicate that the social insurance burden shifts back onto employees to some extent, contrary to Tachibanaki and Yokoyama (2008). Our finding is consistent with other existing studies.     

A note on spurious nonlinear regression

This paper explores the power of two tests for nonlinearity against spurious nonlinear regression. Results show that while the BDS test is susceptible to spuriousness, an approach introduced by Peña and Rodriguez [Peña, D. and Rodriguez, J., 2005, Detecting nonlinearity in time series by model selection criteria, International Journal of Forecasting 21, 731–748.] is powerful, regardless of sample size.     

Does inflation uncertainty increase with the level of inflation?

This paper presents evidence that if agents forecast inflation rationally, using an estimate of the reduced form equation which generated the data, then the size of their forecast errors is positively correlated with the level of inflation. Forecast errors are measured first as the residuals from a full sample OLS regression, and secondly from one period ahead, outside sample, forecasts using a regression estimated from only data available at the time of the forecast. Thus, agents who form rational expectations about the variance, as well as the mean, of inflation should form conditional variances dependent on the level of inflation, at the date of the forecast.