Search

A recent paper by Lasker et al. provides a "gold standard" test for genetic causes of the US Black/white test score gap by simple regression estimation linking high-quality intelligence test scores to African/European genetic admixture proportions precisely measured with modern DNA technology. The paper gives new, empirically powerful evidence for a large genetic component to the gap. This note critically reviews some key findings of the paper from a social science perspective.

In this study, the risk hedge between the Morgan Stanley Taiwan stock index (MSTI) and its underlying futures is analyzed regarding hedging cost under various hedge states using the trend and volatility involved regime-switching models compared with OLS and the naive method. The correlation between MSTI spot and futures is very high and the cointegration test between them is very significantly. The hedging result is evaluated using out-of-sample data and the realized variances and covariances, and is really satisfying in the subprime period or when both spot and future stay in a down state. In this stock index context, the risk aversion is determined to be 1. The optimal hedge ratio on average is around 0.878. The White test favors the regime-switching models in prediction. The trend and volatility-switching model performs particularly well in wealth increase.

A test for time-varying correlation is developed within the framework of a dynamic conditional score (DCS) model for both Gaussian and Student t-distributions. The test may be interpreted as a Lagrange multiplier test and modified to allow for the estimation of models for time-varying volatility in the individual series. Unlike standard moment-based tests, the score-based test statistic includes information on the level of correlation under the null hypothesis and local power arguments indicate the benefits of doing so. A simulation study shows that the performance of the score-based test is strong relative to existing tests across a range of data generating processes. An application to the Hong Kong and South Korean equity markets shows that the new test reveals changes in correlation that are not detected by the standard moment-based test.

Currently, the black/white preference test has been used to evaluate anxiety-like behaviors in zebrafish. However, several inconsistent results have been reported across literature. Since animal behavior can be influenced by several environmental factors, the main goal of the present study was to investigate the influence of different water column depths and light intensities on zebrafish behavioral responses in the black/white test. On a 4cm water column depth, animals spent more time in the black than in the white compartment. However, when animals were tested in an 8cm water column, no significant difference was found. Using an inclined acrylic floor inside the aquarium, animals spent more time in the deep compartment when this was black. However, there is no difference in time spent in each compartment when the deeper compartment was white. For light intensity test, animals showed preference for the white compartment only when both compartments were illuminated with 100lx. For the others illumination settings, there was no difference in the compartment preference. In conclusion, our results suggest that variations in water column depth and light intensity can modulate zebrafish preference in the black/white test. These variations may be implicated in the discrepancies observed in literature.

The black–white test score gap remains a measurable phenomenon in the United States. Up to this point the literature has primarily focused on the black–white achievement gap without taking into account the underlying mobility patterns of individual students as they progress from one grade to the next. However, the degree to which policy makers and educators should be concerned about the black–white test score gap should be tied to how mobile the two groups of students are through the distribution of test scores from one grade to the next. In this paper I apply two nonparametric estimators of distributional mobility to data on test scores and track black–white differences in mobility across the entire distribution of achievement. When compared to whites, blacks tend to be less upwardly mobile and more downwardly mobile for both math and reading. This pattern is particularly prominent for reading in the very early years of schooling.

In the paper, a residual-based test is developed for variance components in LMM. It is distribution-free, tractable, consistent and suitable for clustered designs and crossed designs. Numerical analysis is also conducted.

We propose an encompassing test for non-nested linear quantile regression models and show that it has an asymptotic χ2 distribution. It is also shown that the proposed test is a regression rank score test in a comprehensive model under conditional homogeneity. Our simulation results indicate that the proposed test performs very well in finite samples.

Does the race of interviewers introduce a bias in estimating the test score gap between blacks and whites in the United States? To answer this question. I use an adult sample from the General Social Survey (GSS) in which vocabulary testing involves face-to-face and one-on-one interaction between the respondent and the interviewer. I find that black respondents perform better when tested by a black interviewer as opposed to a white interviewer. For white respondents, however, the race of the interviewer does not have a significant impact on test performance. Because most black respondents are tested by white interviewers in the GSS, the test performance of black respondents is downward biased, and the black-white test score gap is overestimated.

Racial segregation is often blamed for some of the achievement gap between blacks and whites. We study the effects of school and neighborhood segregation on the relative SAT scores of black students across different metropolitan areas, using large microdata samples for the 1998–2001 test cohorts. Our models include detailed controls for the family background of individual test-takers, school-level controls for selective participation in the test, and city-level controls for racial composition, income, and region. We find robust evidence that the black–white test score gap is higher in more segregated cities. Holding constant family background and other factors, a shift from a highly segregated city to a nearly integrated city closes about one-quarter of the raw black–white gap in SAT scores. Specifications that distinguish between school and neighborhood segregation suggest that neighborhood segregation has a consistently negative impact while school segregation has no independent effect, though we cannot reject equality of the two effects. Additional tests indicate that much of the effect of neighborhood segregation operates through neighbors' incomes, not through race per se . Data on enrollment in honors courses suggest that within-school segregation increases when schools are more highly integrated, potentially offsetting the benefits of school desegregation and accounting for our findings.

We show the bootstrap procedure of Jeong and Lee [Jeong, J. and Lee, K., 1999. Bootstrapped White's test for heteroskedasticity in regression models. Economics Letters, 63, 261–267.] leads to the same bootstrapped distribution of the White's test as that based on a standard bootstrap procedure when there exists an intercept in the underlying linear regression model.

An extension of the Shapiro-Wilk test to verify the hypothesis of normality in the presence of nuisance regression and scale has been previously considered. Such a test is typically based on the pair of the maximum likelihood and BLUE estimators of the standard deviation in the linear regression model. It has been shown that the asymptotic null distribution of the test criterion, extended to the regression model, is equivalent to that of the original Shapiro-Wilk test for the location-scale model. A simulation study is performed in order to show that both criteria are close under the normality hypothesis for moderate as well for large data sets. The power of the test against various alternative distributions of the model errors is illustrated. Furthermore, it is shown that the probabilities of errors of both the first and second kinds do not depend on the design matrix or on the parameters of the linear model.

This paper reviews evidence on the family origins of racial differences in young children’s test scores and considers how much of the gap is due to differences in the economic and demographic conditions in which black and white children grow up. Our review of the literature finds that the estimated size of the gaps varies considerably across studies. However, a surprisingly consistent result is that a collection of measures related to family socioeconomic resources appears to account for a little less than half a standard deviation of the black–white test score gap, regardless of the assessments used or the populations studied. We discuss the policy implications of these findings and suggest avenues for future research.

In recent years concern about the black–white test score gap has grown. Yet, little attention has been given to the differential impact black and white families might have on academic achievement. The purpose of this paper is to fill this void by examining the impact of family sociodemographic and interpersonal process characteristics on the academic achievement of black and white youth. I address two questions: (1) do black and white families parent their children differently; and (2) does the size of the impact of family traits on academic achievement differ among these adolescents. Using data from Prince George's County, Maryland, as a case study, I find that black and white families employ different parenting strategies. Also, different family characteristics influence black and white achievement. I conclude with a discussion of the implications these findings have for lessening the black–white test score gap.

In the presence of heteroskedasticity, conventional standard errors (which assume homoskedasticity) can be biased up or down. The most common form of heteroskedasticity leads to conventional standard errors that are too small. When Wald tests based on these standard errors are insignificant, heteroskedasticity ro- bust standard errors do not change inference. On the other hand, inference is conservative in a setting with upward-biased conventional standard errors. We discuss the power gains when using robust standard errors in this case and also potential problems of heteroskedasticity tests. As a solution for the poor performance of the usual heteroskedasticity tests in this setting, we propose a modification of the White test which has better properties. We illustrate our findings using a study in labor economics. The correct standard errors turn out to be around 15 percent lower, leading to different policy conclusions. Moreover, only our modified test is able to detect heteroskedasticity in this application.

This study investigates the behaviour of test statistics for heteroscedasticity of the disturbances in a simple regression model when the regressor is measured with error. By means of simulation, the performance of the test statistics are studied when applied to least squares residuals and residuals obtained from instrumental variables estimation. The results show that the least squares residuals could be used for diagnostic checking even if the estimation method is based on instrumental variables. We also found that great care has to be taken when applying the frequently used White test.

Race is often viewed as a causal variable and “race effects” found from regression analyses are sometimes given causal interpretations. I argue that this is a mistaken way to proceed. Race is not a causal variable in a very important sense of the word, and yet it does have a significant role in causal studies. The key role that race plays is to help our understanding of the effects of causes or interventions through the statistical “interaction” of race with causal variables, rather than as “the main effect of race.” These ideas are briefly illustrated using data from a study of tests constructed to manipulate the distribution of scores of Black and White test takers.

Several different test signals with flat power spectrum, such as white noise, Schroeder-phased waveform, and Galois noise sequences were generated and used to adaptively model the error path in an active sound cancellation (ASC) controller. The standard filtered-X LMS (FXLMS) algorithm was used with a Finite Impulse Response (FIR) model of the error path and an FIR controller structure. Both adaptive FIR filters were operated during the active sound cancellation of 80 and 125 Hz tones. The residual modeling error for different test signal mean power spectral densities (PSD) was determined. It was discovered that the residual error decreased with an increase in the mean PSD, until a minimum residual error was achieved. When the mean PSD was increased beyond this value, no further decrease in residual error occurred. Each test signal was distinguished by the minimum mean PSD that achieved the minimum residual error. All three test signals achieved approximately the same residual error at approximately the same mean PSD for both the 80 and 125 Hz tone. Therefore, the best test signal was selected as the signal with the lowest peak factor, in this case the Schroeder-phased waveform. Given a low peak factor, power can be injected into the test waveform without significantly increasing the size of the time domain envelope.

This paper tabulates significance points for a Lagrange multiplier (LM) test for normality. We find the points to be accurate in regression models, including models where exact critical values cannot be obtained by simulation. We illustrate the test using macroeconomic time series.

We present a new test when there is a nuisance parameter λ under the alternative hypothesis. The test exploits the p-value occupation time [PVOT], the measure of the subset of λ on which a p-value test based on a test statistic Tn(λ) rejects the null hypothesis. The PVOT has only been explored in Hill and Aguilar (2013) and Hill (2012) as a way to smooth over a trimming parameter for heavy tail robust test statistics. Our key contributions are: (i) we show that a weighted average local power of a test based on Tn(λ) is identically a weighted average mean PVOT, and the PVOT used for our test is therefore a point estimate of the weighted average probability of PV test rejection, under the null; (ii) an asymptotic critical value upper bound for our test is the significance level itself, making inference easy (as opposed to supremum and average test statistic transforms which typically require a bootstrap method for p-value computation); (iii) we only require Tn(λ) to have a known or bootstrappable limit distribution, hence we do not require √n-Gaussian asymptotics as is nearly always assumed, and we allow for some parameters to be weakly or non-identified; and (iv) a numerical experiment, in which local asymptotic power is computed for a test of omitted nonlinearity, reveals the asymptotic critical value is exactly the significance level, and the PVOT test is virtually equivalent to a test with the greatest weighted average power in the sense of Andrews and Ploberger (1994)We give examples of PVOT tests of omitted nonlinearity, GARCH effects and a one time structural break. A simulation study demonstrates the merits of PVOT test of omitted nonlinearity and GARCH effects, and demonstrates the asymptotic critical value is exactly the significance level.

Edgeworth expansions to the null distributions of three classical test statistics in the multivariate regression model were derived by Rothenberg (University of California at Berkeley, Working Paper IP-225, 1977) and Phillips ( Journal of the Japan Statistical Society , 1984, 14, 107–124) for the purpose of obtaining size-corrected critical values for such tests. We combine their results with the results of Cordeiro and Ferrari ( Biometrika , 1991, 78, 573–582) to obtain corrections to be applied to the test statistics directly. Simulation results are also given.

A statistically sound formulation of variance propagation for correlated parameters is introduced. Two general purpose statistical tests (the Wald test and the likelihood ratio test) based on this formulation are then presented. It is shown how one can (a) test single or multiple hypotheses about regression parameters, (b) test the validity of constraints on the parameters, (c) decide whether one peakshape or background is better than another, and (d) determine the number of peaks required by the data.

Local school districts often stagger daily start times for their schools in order to reduce busing costs. This paper uses data on all middle school students in Wake County, NC from 1999 to 2006 to identify the causal effect of daily start times on academic performance. Using variation in start times within schools over time, the effect is a two percentile point gain in math test scores – roughly fourteen percent of the black–white test score gap. I find similar results for reading scores and using variation in start times across schools. The effect is stronger for students in the lower end of the distribution of test scores. I find evidence supporting increased sleep as a mechanism through which start times affect test scores. Later start times compare favorably on cost grounds to other education interventions which result in similar test score gains.

Analysts often examine the black-white test score gap conditional on family income. Typically only a current income measure is available. We argue that the gap conditional on permanent income is of greater interest, and we describe a method for identifying this gap using an auxiliary data set to estimate the relationship between current and permanent income. Current income explains only about half as much of the black-white test score gap as does permanent income, and the remaining gap in math achievement among families with the same permanent income is only 0.2 to 0.3 standard deviations in the CNLSY and ECLS samples. When we add permanent income to the controls used by Fryer and Levitt (2006), the unexplained gap in 3rd grade shrinks below 0.15 SDs, less than half of what is found with their controls.

We investigate the behavior of various standard and modified F, LR and LM tests in linear homoskedastic regressions, adapting an alternative asymptotic framework where the number of regressors and possibly restrictions grows proportionately to the sample size. When restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared irrespective of whether there are many or few regressors. However, when restrictions are numerous, standard asymptotic versions of classical tests are invalid. We propose and analyze asymptotically valid versions of the classical tests, including those that are robust to the numerosity of regressors and restrictions. The local power of all asymptotically valid tests under consideration turns out to be equal. The "exact" F test that appeals to critical values of the F distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions.

Using results from an asymptotic expansion of the likelihood ratio criterion the paper derives a small sample correction factor to be applied to the likelihood ratio statistic when testing for homoskedasticity of the error variance in the single equation linear model.

This paper evaluates the performance of the Breusch-Pagan LM test and the White test for heteroskedasticity in fixed-effects one-way error components models. It contrasts the behavior of these tests under the fixed-effects model with the first differences model for different variance functional forms, degrees of heteroskedasticity and sample sizes. Monte Carlo results indicate both tests perform equally well in large samples. They are very sensitive to overall sample size, as changes in T or N do not affect the performance if overall sample size is held constant. The White test seems to be more reliable for identifying heteroskedasticity than the Breusch-Pagan test, even if we are able to identify the actual functional form of the variance. The performance of either test in small samples is poor.

In this paper, we derive an exact test for linear restrictions on regression coefficients in seemingly unrelated regressions with the same regressors in each equation. The test statistic is distributed as the T 2 distribution, and thus critical values can be obtained from the F distribution. Since the test for symmetry in demand systems is a special case of the test for linear restrictions, our test gives an exact test for symmetry.

In this paper we provide considerable Monte Carlo evidence on the finite sample performance of several alternative forms of White's [1982] IM test. Using linear regression and probit models, we extend the range of previous analysis in a manner that reveals new patterns in the behavior of the asymptotic version of the IM test - particularly with respect to curse of dimensionality effects. We also explore the potential of parametric and nonparametric bootstrap methods for reducing the size bias that characterizes the asymptotic IM test. The nonparametric bootstrap is of particular interest because of the weak conditions it imposes, but the results of our Monte Carlo experiments suggest that this technique is not without limitations. The parametric bootstrap demonstrates good size and power in reasonably small samples, but requires assumptions that may be auxiliary from the standpoint of a QMLE. We observe that the effects of violating one of these auxiliary assumptions has a non-trivial impact on the size of IM tests that employ this technique.

This paper is concerned with testing for first-order autoregressive disturbances in the linear regression model and recommends an alternative test to the Durbin-Watson test. The new test is most powerful invariant in a given neighbourhood of the alternative hypothesis parameter space. An empirical power comparison indicates that the test is generally more powerful than the Durbin-Watson test. The comparison also suggests that for many economic applications, the difference in power will be small, although circumstances do exist in which the power advantage of the new test is very real. Selected bounds for the test's significance points are tabulated.

In the spirit of diagnostic testing, this study proposes a simple Lagrange multiplier test for the appropriateness of the lognormal regression model. The alternative hypothesis covers the class of Box-Cox truncated regression models considered by Poirier (1978). The simplicity of the test arises from the absence of any truncation under the null hypothesis.

Making use by the recent work by Harris, this paper provides the formula for size correction to the Lagrange multiplier test for heteroskedasticity. Monte Carlo experiments indicate that our size correction is effective in improving the accuracy of the size of the test. Since the Lagrange multiplier test tends to have a true size less than the nominal size in our experiments, the application of the test at a higher true significance level tends to increase the power of the test as well. Reasonable results in our numerical experiments also give a partial check on the validity of the derived formula.

In order to test the null hypothesis that a continuous distribution is symmetric about zero, the absolute values of observations are arranged in ascending order of magnitude. We consider tests based on the runs of the original observations occuring in this ordered sequence. The well known sign test can be regarded as such a test, but it is really a test of the median and not of symmetry. As another example, a one-sample analogue of the Wald-Wolfowitz run test is obtained. It is shown that this test is consistent against a much wider class of non-symmetric alternatives, possibly with the same median.

The main example of the class of problems considered below is that of testing whether a subset of regression coefficients are jointly zero assuming knowledge of the coefficients' signs. If this knowledge is ignored, the likelihood ratio, Wald, and Lagrange multiplier tests are each equivalent to the F -test. We propose a new test which can be applied as a one-sided t -test and which is UMPI in a subspace of the parameter space. Empirical power comparisons with the power envelope, the F -test, and the exact one-sided likelihood ratio test show that the new test can have exceptionally good power over a wide range of the parameter space.

In this paper we generalize the R procedure to test a null linear regression model against a separate alternative in the context of generalized instrumental variable estimation, and thereby motivate the use of the standard F test. The relations between the F test and several one-degree-of-freedom separate tests are examined under the null, and the asymptotic distributions of the statistics are evaluated under local alternatives. It is shown that the one-degree-of-freedom tests can be more powerful than the F test under a Pesaran-type local alternative, and that the F test is more widely consistent than the one-degree-of-freedom tests.

Savin and White [14] suggested a simultaneous test for two sources of specification error. In this paper we generalize their test to cover all four common sources of errors in specification: functional form, autocorrelated disturbances, heteroscedasticity, and missing variables. The Savin-White test, as well as the standard tests for only one source of error, are special cases of the test developed. The generalized test is applied to data in an illustrative example.

In this paper we propose a simplified method of a calculating the information matrix test in the normal linear regression model. A simulation study demonstrates that our test has considerably better size properties than the Chesher (1983)-Lancaster (1984) version of this test. Our test converges to its asymptotic distribution by n = 600, whereas for the same model Taylor (1987) reports the Chesher-Lancaster test statistic has not converged to its asymptotic distribution by n = 8000.

Following adaptation to a black/white rectangular-wave grating, the black and white bars of a square wave of the same period no longer appear equal. Black bars are shifted in apparent width away from the width of the black adaptation bars, and white bars appear to be shifted away from the width of the white adaptation bars. Tests with single adaptation and test bars (rather than gratings) confirm the contrast specificity of the effect—i.e. white test bars are reliably affected only by white adaptation bars. This suggests separate processing of black and white size-specific information, or phase specificity of spatial frequency channels.

The most commonly used functional forms in measuring market response functions are the linear and log-linear (double-log) specifications. Although the two models are mutually non-nested, they are both nested within the class of Box-Cox regression models. This enables one to test the statistical validity of these two models using nested tests, the power characteristics of which are better established relative to non-nested hypotheses tests, at least in large samples. In this paper, an application of the Lagrange multiplier (LM) test to determine the validity of linear, log-linear, and attraction-type formulations of market share models is illustrated using marketing data. The test is easy to compute and involves running only one extra linear regression. A Monte Carlo simulation is performed to study the properties of the test for samples of varying size and different levels of error variance. The simulation results indicate that the LM test should not be used with samples of less than 100 observations. We also compare the performance of the LM test to that of the PE test developed by MacKinnon, White, and Davidson for non-nested models. The results show that the PE test has a lower probability of a type 1 error for all sample sizes and different error levels. The power of the LM test, however, is greater when the error variance of the true model is high, given a fixed sample size.

The problem of testing for multiplicative heteroskedasticity is considered and a large sample test is proposed. The test statistic is based upon ordinary least squares results, so that only estimation under the null hypothesis of homoskedasticity is required. The test is, however, asymptotically equivalent to the likelihood ratio test and so has good asymptotic power properties. The finite sample behaviour of the test statistic is examined using Monte Carlo experiments which indicate that the test works well for quite small samples.

An exact small-sample point-optimal test is developed for testing the hypothesis that a regression coefficient is constant against the alternative that it is generated by a first-order autoregressive process. In addition, it is shown how Watson and Engle's (1985) asymptotic test can be modified so that its small-sample level can be computed and its small-sample power properties investigated. Simulation results show that the point-optimal test developed in this paperoutperforms the small-sample Watson–Engle test as well as other tests given in the literature. A point-optimal test is also constructed for a stochastic coefficient generated by an ARIMA (1,1,0) process.

The distance of the center of the blind spot from the center of the field of vision for the achromatic and chromatic stimuli averaged 16.5 degrees and ranged from 14.5 to 17.5 degrees. The blind spot was larger for a black test object on a white field than for a white test object on a black field. The blind spots for chromatic stimuli were all much larger than for achromatic stimuli. Other findings relate to variations in size of the blind spot for different colors as seen upon backgrounds of varying brightness. As to satisfactory technique, gray of the brightness of the color as background gave the best and white the worst results.