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Recent Developments in Cointegration

by Katarina Juselius

Econometrics 2018, 6(1), 1; https://doi.org/10.3390/econometrics6010001 - 31 Dec 2017

Cited by 4 | Viewed by 6978

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(This article belongs to the Special Issue Recent Developments in Cointegration)

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638 KiB

Open AccessArticle

Formula I(1) and I(2): Race Tracks for Likelihood Maximization Algorithms of I(1) and I(2) Cointegrated VAR Models

by Jurgen A. Doornik, Rocco Mosconi and Paolo Paruolo

Econometrics 2017, 5(4), 49; https://doi.org/10.3390/econometrics5040049 - 20 Nov 2017

Viewed by 9026

Abstract

This paper provides some test cases, called circuits, for the evaluation of Gaussian likelihood maximization algorithms of the cointegrated vector autoregressive model. Both I(1) and I(2) models are considered. The performance of algorithms is compared first in terms of effectiveness, defined as [...] Read more.

This paper provides some test cases, called circuits, for the evaluation of Gaussian likelihood maximization algorithms of the cointegrated vector autoregressive model. Both I(1) and I(2) models are considered. The performance of algorithms is compared first in terms of effectiveness, defined as the ability to find the overall maximum. The next step is to compare their efficiency and reliability across experiments. The aim of the paper is to commence a collective learning project by the profession on the actual properties of algorithms for cointegrated vector autoregressive model estimation, in order to improve their quality and, as a consequence, also the reliability of empirical research. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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966 KiB

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Short-Term Expectation Formation Versus Long-Term Equilibrium Conditions: The Danish Housing Market

by Andreas Hetland and Simon Hetland

Econometrics 2017, 5(3), 40; https://doi.org/10.3390/econometrics5030040 - 04 Sep 2017

Cited by 2 | Viewed by 7899

Abstract

The primary contribution of this paper is to establish that the long-swings behavior observed in the market price of Danish housing since the 1970s can be understood by studying the interplay between short-term expectation formation and long-run equilibrium conditions. We introduce an asset [...] Read more.

The primary contribution of this paper is to establish that the long-swings behavior observed in the market price of Danish housing since the 1970s can be understood by studying the interplay between short-term expectation formation and long-run equilibrium conditions. We introduce an asset market model for housing based on uncertainty rather than risk, which under mild assumptions allows for other forms of forecasting behavior than rational expectations. We test the theory via an I(2) cointegrated VAR model and find that the long-run equilibrium for the housing price corresponds closely to the predictions from the theoretical framework. Additionally, we corroborate previous findings that housing markets are well characterized by short-term momentum forecasting behavior. Our conclusions have wider relevance, since housing prices play a role in the wider Danish economy, and other developed economies, through wealth effects. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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284 KiB

Open AccessArticle

Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models

by Søren Johansen and Morten Nyboe Tabor

Econometrics 2017, 5(3), 36; https://doi.org/10.3390/econometrics5030036 - 22 Aug 2017

Cited by 6 | Viewed by 7557

Abstract

A state space model with an unobserved multivariate random walk and a linear observation equation is studied. The purpose is to find out when the extracted trend cointegrates with its estimator, in the sense that a linear combination is asymptotically stationary. It is [...] Read more.

A state space model with an unobserved multivariate random walk and a linear observation equation is studied. The purpose is to find out when the extracted trend cointegrates with its estimator, in the sense that a linear combination is asymptotically stationary. It is found that this result holds for the linear combination of the trend that appears in the observation equation. If identifying restrictions are imposed on either the trend or its coefficients in the linear observation equation, it is shown that there is cointegration between the identified trend and its estimator, if and only if the estimators of the coefficients in the observation equations are consistent at a faster rate than the square root of sample size. The same results are found if the observations from the state space model are analysed using a cointegrated vector autoregressive model. The findings are illustrated by a small simulation study. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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379 KiB

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Using a Theory-Consistent CVAR Scenario to Test an Exchange Rate Model Based on Imperfect Knowledge

by Katarina Juselius

Econometrics 2017, 5(3), 30; https://doi.org/10.3390/econometrics5030030 - 07 Jul 2017

Cited by 12 | Viewed by 6749

Abstract

A theory-consistent CVAR scenario describes a set of testable regularieties one should expect to see in the data if the basic assumptions of the theoretical model are empirically valid. Using this method, the paper demonstrates that all basic assumptions about the shock structure [...] Read more.

A theory-consistent CVAR scenario describes a set of testable regularieties one should expect to see in the data if the basic assumptions of the theoretical model are empirically valid. Using this method, the paper demonstrates that all basic assumptions about the shock structure and steady-state behavior of an an imperfect knowledge based model for exchange rate determination can be formulated as testable hypotheses on common stochastic trends and cointegration. This model obtaines remarkable support for almost every testable hypothesis and is able to adequately account for the long persistent swings in the real exchange rate. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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Modeling Real Exchange Rate Persistence in Chile

by Leonardo Salazar

Econometrics 2017, 5(3), 29; https://doi.org/10.3390/econometrics5030029 - 07 Jul 2017

Cited by 4 | Viewed by 8444

Abstract

The long and persistent swings in the real exchange rate have for a long time puzzled economists. Recent models built on imperfect knowledge economics seem to provide a theoretical explanation for this persistence. Empirical results, based on a cointegrated vector autoregressive (CVAR) model, [...] Read more.

The long and persistent swings in the real exchange rate have for a long time puzzled economists. Recent models built on imperfect knowledge economics seem to provide a theoretical explanation for this persistence. Empirical results, based on a cointegrated vector autoregressive (CVAR) model, provide evidence of error-increasing behavior in prices and interest rates, which is consistent with the persistence observed in the data. The movements in the real exchange rate are compensated by movements in the interest rate spread, which restores the equilibrium in the product market when the real exchange rate moves away from its long-run benchmark value. Fluctuations in the copper price also explain the deviations of the real exchange rate from its long-run equilibrium value. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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251 KiB

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Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems

by H. Peter Boswijk and Paolo Paruolo

Econometrics 2017, 5(3), 28; https://doi.org/10.3390/econometrics5030028 - 29 Jun 2017

Cited by 6 | Viewed by 6973

Abstract

Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood [...] Read more.

Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood estimation are presented, and asymptotic properties sketched. The techniques are illustrated using the analysis of the PPP and UIP between Switzerland and the US. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

384 KiB

Open AccessArticle

Sustainable Financial Obligations and Crisis Cycles

by Mikael Juselius and Moshe Kim

Econometrics 2017, 5(2), 27; https://doi.org/10.3390/econometrics5020027 - 22 Jun 2017

Cited by 3 | Viewed by 6778

Abstract

The ability to distinguish between sustainable and excessive debt developments is crucial for securing economic stability. By studying US private sector credit loss dynamics, we show that this distinction can be made based on a measure of the incipient aggregate liquidity constraint, the [...] Read more.

The ability to distinguish between sustainable and excessive debt developments is crucial for securing economic stability. By studying US private sector credit loss dynamics, we show that this distinction can be made based on a measure of the incipient aggregate liquidity constraint, the financial obligations ratio. Specifically, as this variable rises, the interaction between credit losses and the business cycle increases, albeit with different intensity depending on whether the problems originate in the household or the business sector. This occurs 1–2 years before each recession in the sample. Our results have implications for macroprudential policy and countercyclical capital-buffers. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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416 KiB

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Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles

by Massimo Franchi and Søren Johansen

Econometrics 2017, 5(2), 25; https://doi.org/10.3390/econometrics5020025 - 14 Jun 2017

Cited by 2 | Viewed by 6623

Abstract

It is well known that inference on the cointegrating relations in a vector autoregression (CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have rejection probabilities under the null, which vary from the [...] Read more.

It is well known that inference on the cointegrating relations in a vector autoregression (CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have rejection probabilities under the null, which vary from the nominal size to more than 90%. This paper formulates a CVAR model allowing for multiple near unit roots and analyses the asymptotic properties of the Gaussian maximum likelihood estimator. Then two critical value adjustments suggested by McCloskey (2017) for the test on the cointegrating relations are implemented for the model with a single near unit root, and it is found by simulation that they eliminate the serious size distortions, with a reasonable power for moderate values of the near unit root parameter. The findings are illustrated with an analysis of a number of different bivariate DGPs. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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367 KiB

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Maximum Likelihood Estimation of the I(2) Model under Linear Restrictions

by Jurgen A. Doornik

Econometrics 2017, 5(2), 19; https://doi.org/10.3390/econometrics5020019 - 15 May 2017

Cited by 8 | Viewed by 9328

Abstract

Estimation of the I(2) cointegrated vector autoregressive (CVAR) model is considered. Without further restrictions, estimation of the I(1) model is by reduced-rank regression (Anderson (1951)). Maximum likelihood estimation of I(2) models, on the other hand, always requires iteration. This paper presents a new [...] Read more.

Estimation of the I(2) cointegrated vector autoregressive (CVAR) model is considered. Without further restrictions, estimation of the I(1) model is by reduced-rank regression (Anderson (1951)). Maximum likelihood estimation of I(2) models, on the other hand, always requires iteration. This paper presents a new triangular representation of the I(2) model. This is the basis for a new estimation procedure of the unrestricted I(2) model, as well as the I(2) model with linear restrictions imposed. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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301 KiB

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Panel Cointegration Testing in the Presence of Linear Time Trends

by Uwe Hassler and Mehdi Hosseinkouchack

Econometrics 2016, 4(4), 45; https://doi.org/10.3390/econometrics4040045 - 01 Nov 2016

Cited by 7 | Viewed by 7114

Abstract

We consider a class of panel tests of the null hypothesis of no cointegration and cointegration. All tests under investigation rely on single-equations estimated by least squares, and they may be residual-based or not. We focus on test statistics computed from regressions with [...] Read more.

We consider a class of panel tests of the null hypothesis of no cointegration and cointegration. All tests under investigation rely on single-equations estimated by least squares, and they may be residual-based or not. We focus on test statistics computed from regressions with intercept only (i.e., without detrending) and with at least one of the regressors (integrated of order 1) being dominated by a linear time trend. In such a setting, often encountered in practice, the limiting distributions and critical values provided for and applied with the situation “with intercept only” are not correct. It is demonstrated that their usage results in size distortions growing with the panel size N. Moreover, we show which are the appropriate distributions, and how correct critical values can be obtained from the literature. Full article

(This article belongs to the Special Issue Recent Developments in Cointegration)

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