Spurious Regression Research Articles

Linear Lagged Relationship Between Inflation, Unemployment and Labor Force Change Rate in France: Cointegration Test

A linear and lagged relationship between inflation, unemployment and labor force change rate, ?(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+A2 (where A0, A1, and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for France is characterized by A0=-1, A1=4, A2=0.095, t0=4 years, and t1=4 years. For GDP deflator, it provides a root mean square forecasting error (RMFSE) of 1.0% at a four-year horizon for the period between 1971 and 2004. The relationship is tested for cointegration. All three variables involved in the relationship are proved to be integrated of order one. Two methods of cointegration testing are used. First is the Engle-Granger approach based on the unit root test in the residuals of linear regression, which also includes a number of specification tests. Second method is the Johansen cointegration rank test based on a VAR representation, which is also proved to be an adequate one via a set of appropriate tests. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds together with statistical estimates of goodness-of-fit and RMSFE. Relationships between inflation and labor force and between unemployment and labor force are tested separately in appropriate time intervals, where the Banque de France monetary policy introduced in 1995 does not disturb the long-term links. All the individual relationships are cointegrated in corresponding intervals. The VAR and vector error correction (VEC) models are estimated and provide just a marginal improvement in RMSFE at the four-year horizon both for GDP deflator (down to 0.9%) and CPI (~1.1%) on the results obtained in the regression study. The VECM approach also allows re-estimation of the coefficients in the individual and generalized relationship between the variables both for cointegration rank 1 and 2. Comparison of the standard cointegration approach to the integral approach to the estimation of the coefficients in the individual and generalized relationships between the studied variables demonstrates the superiority of the latter. The cumulative inflation curve or inflation index, which is the actually measured evolution of price level, is much better predicted in the framework of the integral approach, which is a powerful tool for revealing true relationships between non-stationary variables and can be potentially used for rejection of spurious regression. The cumulative curves allow avoiding obvious drawbacks of the VECM representation and cointegration tests - increasing signal to noise ratio after differentiation and severe dependence on statistical properties of error terms. The confirmed validity of the linear lagged relationship between inflation, unemployment and labor force change indicates that since 1995 the Banque de France has been wrongly applying the policy fixing the monetary growth to the reference value around 4.5%. As a result of the policy, during the last ten years unemployment in France was twice as large as the one dictated by its long-term equilibrium link to labor force change. This increased unemployment compensates the forced price stability.

ANALISIS MODEL DINAMIS DAMPAK INFLASI TERHADAP SEKTOR PERTANIAN INDONESIA TAHUN

Agriculture sector have positive growth while national growth have been negative, and its function in GDP still significant when economic crisis occurred. For more accurated analysis, economic growth can be devide in to sectoral activities. Using macro economic theories through relationship between prices and real growth would be faced agriculture real growth through consumer’s price index, general prices in the agriculture sector within prices received and prices paid, and agriculture wage as an indicator for supply aggregate and dummy variable to vanish effect of economic crisis in the model. This study use time series data. To solve spurious regression, we use error correction model. The conclusion are: first, factors that influenced GDP of agriculture sector are long run variables of consumer’s price index, general prices in the agriculture sector within prices received and prices paid, and agriculture wage; second, inflation is faster than agriculture growth, that must be followed by fiscal and monetary policy to affect supply aggregate, to increase productivity of agriculture sector, for instance by increasing technology in to agriculture sector, and more qualified human resource with education. Or can be combined between fiscal policy and income policy, withn labor intensive program to develop agriculture project, so government expenditure and agriculture asset increases all at once.

Testing for spurious regression in a panel data model with the individual number and time length growing

This article shows a test for the spurious regression problem in a panel data model with a growing individual number and time series length. In the estimation, tapers are used and the integrated order for the remainder disturbance is extended to a real number; at the same time, the spurious regression problem can be detected without prior knowledge. Through Monte Carlo experiments, we examine the consistent estimators by various sizes of time length and individual number, in which the remainder disturbance is assumed to be either stationary or non-stationary. In addition, the asymptotic normality properties are discussed with a quasi log-likelihood function. From the power tests we can see that the estimators are quite successful and powerful.

Monetary policy and dividend growth in Germany: long-run structural modelling versus bounds testing approach

This study examines the long-run relationship between monetary policy and dividend growth in Germany. For this purpose, cointegration is tested for between both variables in the period 1974 to 2003. However, problems related to spurious regression arise from the mixed order of integration of the series used, from mutual causation between the variables and from the lack of a long-run relationship among the variables of the model. These problems are addressed by applying the bounds testing approach to cointegration in addition to a more standard long-run structural modelling approach. In principle, both procedures are capable of dealing with the controversial issue of the exogeneity of monetary policy vis-à-vis dividend growth. However, the structural modelling approach still leaves a certain degree of uncertainty about the integration properties of the interest rate and the dividend growth. Hence, one feels legitimized to refer to the bounds testing procedure and to conclude that in the longer term short-term rates drive stock returns but not vice versa.

Quality Quandaries: Studying Input-Output Relationships, Part I

In this column we demonstrate with a simulated example the problem of spurious regression for autocorrelated data. This is another problem quality engineers may encounter when investigating possible input-output relationships. For example, suppose the process is an industrial furnace and we want to see if there is a possible relationship between an input variable xt, such as fuel rate at a given time t, and the temperature yt in the furnace.

Spurious Regression Under Broken‐Trend Stationarity

Abstract. We study the phenomenon of spurious regression between two random variables, when the generating mechanism of individual series is assumed to follow a stationary process around a trend with (possibly) multiple breaks in the level and slope of trend. We develop the relevant asymptotic theory and show that the phenomenon of spurious regression occurs independent of the structure assumed for the errors. In contrast to previous findings, the presence of a spurious relationship will be less severe when breaks are present in the generating mechanism of individual series. This is true whether the regression model includes a linear trend or not. Simulations confirm our asymptotic results, and reveal that in finite samples, the phenomenon of spurious regression is sensitive to the presence of a linear trend in the regression model and to the relative location of breaks within the sample.

Estimating the long memory granger causality effect with a spectrum estimator

AbstractThis paper discusses the Granger causality test by a spectrum estimator which allows the transfer function to have long memory properties. In traditional methodology the relationship among variables is usually assumed to be short memory or contemporaneous. Hence, we have to make sure they are of the same integrated order, else there might be a spurious regression problem. In practice, not all the variables are fractionally co‐integrated in the economic model. They may have the same random resources, but under a different integrated order. This paper focuses on how to capture the long memory Granger causality effect in the transfer function. This does not necessarily assume the variables are of the same fractional integrated order. Moreover, by the transfer function we construct an estimator to test the long memory effect with the Granger causality sense. Copyright © 2006 John Wiley & Sons, Ltd.

Spurious correlation of I(0) regressors in models with an I(1) dependent variable

Hassler [Hassler, U., 1996. Spurious regressions when stationary regressors are included, Economics Letters, 50, 25–31] shows that t- and F-tests for zero restrictions on I(0) regressors in equations with an I(1) dependent variable do not diverge to infinity asymptotically. He concludes that there is no spurious significance for these regressors. Using Monte Carlo simulation we demonstrate that spurious correlation generally occurs in such regressions.

Testing for cointegration in the presence of mis-specified structural change

The finite-sample properties of cointegration tests incorporating structural change are derived when applied to independent unit root processes subject to changes in innovation variance. It is shown that decreases in innovation variance can result in severe size distortion, with the extent of spurious rejection dependent upon which series experiences a break and when the break occurs. Mis-specified structural change is therefore shown to result in spurious regression, the very problem cointegration analysis attempts to overcome.

The Nexus between IT Investment and Banking Performance in Korea

This paper explores the nexus between the information technology (IT) investment of Korean banks and their management performance, employing panel cointegration testing and estimation techniques. Annual panel data on the financial statements and IT investment measures of banks are exploited in empirical analysis. Various panel unit root tests demonstrate that the data variables are integrated processes with unit roots. It suggests that the existing researches that do not consider panel unit roots suffer reduced reliability in their estimation and inference results due to the spurious regression problem. Three distinct panel cointegration techniques are used to estimate the profitability equation. The relationship between ROE and the capital budget ratio is found to be the strongest, which implies that the capital budget has had the greatest effects on enhancing bank returns. The IT investment of large banks shows a stronger positive influence on improving bank returns than that of small banks. The IT investment of wholesale banks specializing in corporate loans produces greater positive effects on bank profitability than that of retail banks. Several elucidations are provided for the above findings.

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.

Type I Spurious Regression in Econometrics

In applied econometrics researchers often infer the relation among nonstationary time series by regression of their differences. The aim of this paper is to show that in some circumstances regression of differenced time series tends to reject the relation among their levels. This phenomenon is known as type I spurious regression. Time series are dynamic processes, and the ignored system dynamics will become the systematic errors in regression equations. Differencing does not preserve the underlying relation among time series in regression due to systematic errors. This paper will outline how regression of differenced time series tends to reject the relation between their levels, and so potentially to incur type I spurious regression.

Solving the Price-Earnings Puzzle

Accounting and finance professionals have empirically known that in the long run stock prices are roughly proportional to earnings. However, econometric testing could not been able to verify this expected contribution of earnings to stock prices, thus formed the price-earnings (PE) puzzle in the accounting literature. This paper seeks to solve this puzzle by allowing the earnings response coefficient to be a variable instead of a constant, and shows that the PE puzzle turns out to be a phenomenon of type I spurious regression in econometrics.

Vztah deficitu běžného účtu platební bilance a rozpočtového deficitu - analýza panelových dat

Panel data are increasingly being used in both macro- and micro-level studies of economic problems. Macro-panel data (i denotes countries) are characteristic by sufficiently long time series to be able to analyze panel spurious regression and panel cointegration. According to the main stream of the economic theory the budget deficits leads to deterioration in the current account balance. The panel long-run causal relation is examined in the case of the four groups of countries. For the Granger causality test the panel cointegration analysis is needed. The panel cointegration relationships were not found in any case. Some similarities in the panels were found in the case of Latin America countries but they are not significant.

Using HP Filtered Data for Econometric Analysis: Some Evidence from Monte Carlo Simulations

The Hodrick-Prescott (HP) filter has become a widely used tool for detrending integrated time series. Even if the methodological literature sums up an extensive catalogue of severe criticism against an econometric analysis of HP filtered data, the original Hodrick and Prescott (1980, 1997) suggestion to measure the strength of association between economic variables by a regression analysis of corresponding HP filtered time series appears to be very popular. This might be justified if HP induced distortions were quantitatively negligible in empirical applications. However, the simulated regression analyses presented in our paper demonstrate that any attempts of inference based on HP prefiltered series are challenged by a serious risk of spurious regression results.

THE BILATERAL J‐CURVE: AUSTRALIA VERSUS HER 23 TRADING PARTNERS

Several studies have tested the J‐curve phenomenon for Australia using non‐stationary aggregate trade data and have provided mixed results. They not only suffer from the ‘aggregation bias problem’ but also from the ‘spurious regression problem’. To overcome these problems, in this paper we investigate the short‐run and the long‐run effects of real depreciation of the Australian dollar on the trade balance between Australia and each of her 23 trading partners using quarterly data over the 1973–2001 period and recent advances in cointegration analysis. The results from the bound testing approach for cointegration and error‐correction modeling does not provide much support for the J‐curve phenomenon.

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.

Higher Taxa as Surrogates of Plant Biodiversity in a Megadiverse Country

Abstract: An important question in conservation biology is the extent to which the number of taxonomic supraspecific categories can serve as surrogates of species richness. This issue has been little explored in highly diverse areas. We used 113 floristic inventories from throughout Mexico, a megadiverse country, to evaluate the potential of higher‐taxon richness for predicting local species richness of vascular plants. This large biodiversity data set includes the main vegetation types found across the country. In all, 247 families, 2,398 genera, and 11,890 species were used for the analysis, representing 99.6%, 90.2%, and 53.2% of the respective totals recorded in the country. We hypothesized that the number of genera and species would be accurately predicted by the richness of the higher taxon. To avoid getting spurious regressions resulting from the logical increase in lower‐taxon richness as a higher taxon becomes richer, we calculated new response variables by subtracting from the number of elements in the lower taxon group the number of those in the higher taxon; these variables were “excess species” (number of species minus number of genera or families) and “excess genera” (number of genera minus number of families). Our results indicate that genera provide very effective surrogates for estimation of local species richness (R2= 0.85), whereas families have a more limited potential for this purpose (R2= 0.64). The predictive capacity of the diversity of higher taxon increased when the analyses were constrained to particular vegetation types (maximum R2= 0.95 for genera). This surrogate method may be a valuable tool in locating and designing representative systems of protected areas for vascular plant diversity, especially in megadiverse countries, where conservation efforts are hindered by the lack of complete inventories and insufficient resources.

Dividend Persistence and Return Predictability

Evidence of dividend yield return predictability has been presented so widely and consistently that the result has tended to be generally accepted. This paper provides strong evidence that return predictability of the dividend yield is a spurious result, even when the dividend yield definition is broadened to include share repurchases. The paper demonstrates how a spurious regression problem that is due to dividend persistence is compounded when the dependent and independent variables in return predictability regressions are ratios composed of common component variables, and it utilizes a simulation procedure to take account of this problem. The paper's results therefore imply that extreme care should be taken when using ratios as predictor or explanatory variables in time series regression. The paper finds that standard dividend behaviour explanatory models are also affected by the spurious regression problem, and introduces a reformulated Lintner first difference dividend behaviour model that is not subject to spurious regression.

Consistent Testing of Cointegrating Relationships

In this paper we investigate methods for testing the existence of a cointegration relationship among the components of a nonstationary fractionally integrated (NFI) vector time series. Our framework generalizes previous studies restricted to unit root integrated processes and permits simultaneous analysis of spurious and cointegrated NFI vectors. We propose a modified F-statistic, based on a particular studentization, which converges weakly under both hypotheses, despite the fact that OLS estimates are only consistent under cointegration. This statistic leads to a Wald-type test of cointegration when combined with a narrow band GLS-type estimate. Our semiparametric methodology allows consistent testing of the spurious regression hypothesis against the alternative of fractional cointegration without prior knowledge on the memory of the original series, their short run properties, the cointegrating vector, or the degree of cointegration. This semiparametric aspect of the modelization does not lead to an asymptotic loss of power, permitting the Wald statistic to diverge faster under the alternative of cointegration than when testing for a hypothesized cointegration vector. In our simulations we show that the method has comparable power to customary procedures under the unit root cointegration setup, and maintains good properties in a general framework where other methods may fail. We illustrate our method testing the cointegration hypothesis of nominal GNP and simple-sum (M1, M2, M3) monetary aggregates.