Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note

doi:10.2307/1913018

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Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note

Journal Article•DOI•

Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note

01 Mar 1970-Econometrica (Econometric Society)-Vol. 38, Iss: 2, pp 361-366

About: This article is published in Econometrica.The article was published on 1970-03-01. It has received 1350 citations till now. The article focuses on the topics: Proper linear model & General linear model.

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Journal Article•DOI•

Oil and the Macroeconomy since World War II

[...]

James D. Hamilton

01 Apr 1983-Journal of Political Economy

TL;DR: The authors found that all but one of the U.S. recessions since World War II have been preceded, typically with a lag of around three-fourths of a year, by a dramatic increase in the price of crude petroleum.

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Abstract: All but one of the U.S. recessions since World War II have been preceded, typically with a lag of around three-fourths of a year, by a dramatic increase in the price of crude petroleum. This does not mean that oil shocks caused these recessions. Evidence is presented, however, that even over the period 1948-72 this correlation is statistically significant and nonspurious, supporting the proposition that oil shocks were a contributing factor in at least some of the U.S. recessions prior to 1972. By extension, energy price increases may account for much of post-OPEC macroeconomic performance.

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3,391 citations

Journal Article•DOI•

Oil and the Macroeconomy When Prices Go Up and Down: An Extension of Hamilton's Results

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Knut Anton Mork

01 Jun 1989-Journal of Political Economy

TL;DR: This paper investigated whether Hamilton's results continue to hold when the sample is extended to include the recent oil market collapse and the oil price variable is corrected for the effects of price controls, and they found that the correlation persists in periods of price decline.

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Abstract: In an important paper, Hamilton (1983) demonstrated a strong correlation between oil price changes and gross national product growth in U.S. data. However, his study pertained to a period in which all the large oil price movements were upward, and thus it left unanswered the question whether the correlation persists in periods of price decline. Moreover, the price variable he used was somewhat distorted by price controls in the 1970s. This note investigates whether Hamilton's results continue to hold when the sample is extended to include the recent oil market collapse and the oil price variable is corrected for the effects of price controls. Particular attention is given to the possibility of asymmetric responses to oil price increases and decreases, as suggested in the structural employment literature (Loungani 1986; Davis 1987; Hamilton 1988). Like Hamilton, I based my investigation on the GNP equation in Sims's (1 980b) six-variable quarterly vector autoregressive model,

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1,560 citations

Journal Article•DOI•

Tests of Conditional Predictive Ability

[...]

Raffaella Giacomini¹, Halbert White¹•Institutions (1)

University of California, Los Angeles¹

01 Nov 2006-Econometrica

TL;DR: This paper proposed a framework for out-of-sample predictive ability testing and forecast selection designed for use in the realistic situation in which the forecasting model is possibly misspecified, due to unmodeled dynamics, unmodelled heterogeneity, incorrect functional form, or any combination of these.

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Abstract: We propose a framework for out-of-sample predictive ability testing and forecast selection designed for use in the realistic situation in which the forecasting model is possibly misspecified, due to unmodeled dynamics, unmodeled heterogeneity, incorrect functional form, or any combination of these. Relative to the existing literature (Diebold and Mariano (1995) and West (1996)), we introduce two main innovations: (i) We derive our tests in an environment where the finite sample properties of the estimators on which the forecasts may depend are preserved asymptotically. (ii) We accommodate conditional evaluation objectives (can we predict which forecast will be more accurate at a future date?), which nest unconditional objectives (which forecast was more accurate on average?), that have been the sole focus of previous literature. As a result of (i), our tests have several advantages: they capture the effect of estimation uncertainty on relative forecast performance, they can handle forecasts based on both nested and nonnested models, they allow the forecasts to be produced by general estimation methods, and they are easy to compute. Although both unconditional and conditional approaches are informative, conditioning can help fine-tune the forecast selection to current economic conditions. To this end, we propose a two-step decision rule that uses current information to select the best forecast for the future date of interest. We illustrate the usefulness of our approach by comparing forecasts from leading parameter-reduction methods for macroeconomic forecasting using a large number of predictors.

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1,248 citations

Journal Article•DOI•

Has the u.s. economy become more stable? a bayesian approach based on a markov-switching model of the business cycle

[...]

Chang-Jin Kim, Charles R. Nelson¹•Institutions (1)

University of Washington¹

01 Nov 1999-The Review of Economics and Statistics

TL;DR: In this article, the authors employ a Bayesian approach to identify a structural break at an unknown changepoint in a Markov-switching model of the business cycle, with the posterior mode of the break date at 1984.

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Abstract: We hope to answer three questions: Has there been a structural break in postwar U.S. real GDP growth towards stabilization? If so, when? What is the nature of this structural break? We employ a Bayesian approach to identify a structural break at an unknown changepoint in a Markov-switching model of the business cycle. Empirical results suggest a break in GDP growth toward stabilization, with the posterior mode of the break date at 1984:1. Furthermore, we find a narrowing gap between growth rates during recessions and booms that is at least as important as any decline in the volatility of shocks.

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1,225 citations

Cites background or result from "Tests of Equality Between Sets of C..."

...Within the context of a Markov-switching model, one can distinguish between two important sources of stabilization in real GDP growth: a decline in the variance of shocks and a narrowing gap between growth rates during booms and recessions. Within the context of a linear model, one cannot distinguish between the two sources, and a narrowing gap between growth rates would show up as a decline in volatility. Empirical results suggest both sources of stabilization may not be ignored, even though we find stronger sample evidence in favor of a narrowing gap between growth rates during booms and recessions. In addition, the posterior mode of the break date turned out to be 1984:I. This is consistent with McConnell and Quiros (1999), who document a structural decline in the volatility of U....
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...1 Goldfeld and Quandt (1973) introduced Markov-switching models for serially uncorrelated data, and Hamilton (1989) for serially correlated data. Kim (1994) extends the approach to general state-space models....
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...1 Goldfeld and Quandt (1973) introduced Markov-switching models for serially uncorrelated data, and Hamilton (1989) for serially correlated data....
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...economy toward more stabilization: a narrowing gap between the mean growth rates during booms and recessions and a decline in the volatility of real GDP growth. To further investigate the nature of the structural break in real GDP growth, we need to compare models (II), (III), and (IV). Model (II) with a structural break in the mean growth rates is most preferred, suggesting that a narrowing gap between the mean growth rates during booms and recessions is at least as important as a decline in the volatility of real GDP growth. 5 Notice that, within the context of a linear model, a narrowing gap between the mean growth rates will show up as a decline in the volatility. Thus, within the linear model, one may not be able to distinguish between the two sources of stabilization in real GDP growth. In figures 2.A, 3.A, and 4.A, the posterior distributions of the changepoint ( t) for models (II), (III), and (IV) are depicted against real GDP growth. In all three cases, the posterior mode of the changepoint is 1984.I, as in McConnell and Quiros (1999), even though the posterior distribution is more widely spread for model (II) than for the other models....
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Posted Content•

Tests of conditional predictive ability

[...]

Raffaella Giacomini¹, Halbert White¹•Institutions (1)

University of California, Los Angeles¹

01 Apr 2003-Research Papers in Economics

TL;DR: The authors proposed an alternative framework for out-of-sample comparison of predictive ability based on conditional expectations of forecasts and forecast errors rather than the unconditional expectations that are the focus of the existing literature.

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Abstract: We argue that the current framework for predictive ability testing (e.g.,West, 1996) is not necessarily useful for real-time forecast selection, i.e., for assessing which of two competing forecasting methods will perform better in the future. We propose an alternative framework for out-of-sample comparison of predictive ability which delivers more practically relevant conclusions. Our approach is based on inference about conditional expectations of forecasts and forecast errors rather than the unconditional expectations that are the focus of the existing literature. We capture important determinants of forecast performance that are neglected in the existing literature by evaluating what we call the forecasting method (the model and the parameter estimation procedure), rather than just the forecasting model. Compared to previous approaches, our tests are valid under more general data assumptions (heterogeneity rather than stationarity) and estimation methods, and they can handle comparison of both nested and non-nested models, which is not currently possible. To illustrate the usefulness of the proposed tests, we compare the forecast performance of three leading parameter-reduction methods for macroeconomic forecasting using a large number of predictors: a sequential model selection approach, the "diffusion indexes" approach of Stock and Watson (2002), and the use of Bayesian shrinkage estimators.

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1,151 citations

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References

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Journal Article•DOI•

Tests of equality between sets of coefficients in two linear regressions

[...]

Gregory C. Chow

01 Jul 1960-Econometrica

5,143 citations

Book•

The design and analysis of experiments.

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Oscar Kempthorne¹•Institutions (1)

Iowa State University¹

15 Jan 1952

TL;DR: In this article, Monterey describes a books design and analysis of experiments, and the pronouncement as without difficulty as perspicacity of this design and analyses of experiments montgomery can be taken as skillfully as picked to act.

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Abstract: Yeah, reviewing a books design and analysis of experiments montgomery could mount up your close associates listings. This is just one of the solutions for you to be successful. As understood, achievement does not suggest that you have wonderful points. Comprehending as skillfully as covenant even more than extra will have enough money each success. next-door to, the pronouncement as without difficulty as perspicacity of this design and analysis of experiments montgomery can be taken as skillfully as picked to act. Page Url

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1,064 citations

Book•

An introduction to linear statistical models.

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Franklin Arno Graybill

20 Jul 2013

897 citations

Journal Article•DOI•

The Design and Analysis of Experiments

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Oscar Kempthorne¹•Institutions (1)