Estimating the LQAC model with I(2) variables

Journal of Econometrics, 2000

This paper generalizes the existing cointegration analysis literature in two respects. Firstly, the problem of e$cient estimation of vector error correction models containing exogenous I(1) variables is examined. The asymptotic distributions of the (log-)likelihood ratio statistics for testing cointegrating rank are derived under di!erent intercept and trend speci"cations and their respective critical values are tabulated. Tests for the presence of an intercept or linear trend in the cointegrating relations are also developed together with model misspeci"cation tests. Secondly, e$cient estimation of vector error correction models when the short-run dynamics may di!er within and between equations is considered. A re-examination of the purchasing power parity and the uncovered interest rate parity hypotheses is conducted using U.K. data under the maintained assumption of exogenously given foreign and oil prices.

Journal of Economic Dynamics and Control, 2006

In this paper we focus on the econometric analysis of the linear quadratic adjustment cost model with rational expectations and cointegrated variables considering the case where agents optimize with respect to a vector of decision variables rather than a scalar. The method we propose is based on the idea of nesting the system of interrelated Euler equations stemming from agent's optimization problem within a cointegrated Vector Equilibrium Correction Model (VEqCM) for the observable variables. In contrast to previous practise a likelihood-based procedure can be set out without implementing numerical optimization algorithms. Cointegration techniques and generalized least squares (GLS) are required to estimate and test the model with remarkable advantages for practitioners.

Journal of Economic Surveys, 1998

The paper addresses the practical determination of cointegration rank. This is difficult for many reasons: deterministic terms play a crucial role in limiting distributions, and systems may not be formulated to ensure similarity to nuisance parameters; finite-sample critical values may differ from asymptotic equivalents; dummy variables alter critical values, often greatly; multiple cointegration vectors must be identified to allow inference; the data may be I(2) rather than I(1), altering distributions; and conditioning must be done with care. These issues are illustrated by an empirical application of multivariate cointegration analysis to a small model of narrow money, prices, output and interest rates in the UK.

Journal of Policy Modeling, 1997

In the money demand literature the Linear Quadratic Adjustment Cost (LQAC) model is often considered to explain the observed slow adjustment in agents' money holdings. In this paper we propose a new method of estimating and testing the LQAC model of money demand. In an empirical application to U.K. money demand, we reject the LQAC model defined from a loss function expressed in terms of real money balances. This is in sharp contrast to the results obtained by Cuthbertson and Taylor (1990) in a previous article in this journal using similar techniques on an equivalent data set. In order to explain the discrepancies we point out some pitfalls in the empirical methodology adopted by Cuthbertson and Taylor. We also consider a specification of the LQAC model in terms of nominal money and, despite statistical rejection, we find that if the LQAC model should have any empirical content such a specification should be preferred to the real money specification.

Econometric Theory, 2007

This note presents estimation and simulation results to compare the likelihood ratio (LR) test and the Two-Step based test for cointegration ranks in the I(2) model. Three empirical examples are considered: Banerjee, Cockerell, and Russell (2001), Rahbek, Kongsted, and Jørgensen (1999), and Nielsen (2002). A final simulation study generates more DGPs to cover a broader range of the parameter space of the I(2) model. Details on the implementation, e.g. the treatment of initial values, are given in the main paper.

Econometric Theory, 2013

We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap versions that are simple to compute. A simulation study shows that the finite-sample pr...

2010

In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are potentially useful in general for analysis of nonstationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. With respect to testing, this makes implementation of testing involved, and...

Journal of Applied Econometrics, 1994

In this paper we demonstrate a new way of testing the linear quadratic adjustment cost (LQAC) model under rational expectations. We illustrate how the parameter restrictions arising from this model can be formally specified and we use these restrictions to extent the technique of Campbell and Shiller (1987) to a wider class of models based on present value relations. Potentially the demand for labour is an area in which the LQAC model can find applicability in practice and subsequently we analyse sectoral labour demand in Danish manufacturing. We find, however, that for our data set the quadratic adjustment cost model under rational expectations can be rejected.

Economics Letters, 1998

Tests of cointegrating coefficients in vector autoregressive error correction models ignore the Cauchy-like behavior of the 2 estimator's finite-sample distribution. This causes excessive rejections of the null in standard x tests. We propose a 2 Cauchy-based x test, and show, via simulation, that it yields adequate rejection rates.