Conference Agenda

This paper develops integrated modified ordinary and generalized least squares estimation for systems of cointegrating multivariate polynomial regressions, i.e., systems of regressions that include deterministic variables, integrated processes and (cross-)products of non-negative integer powers of these variables as regressors. The stationary errors are allowed to be correlated across equations, over time and with the regressors. The necessity to consider integrated modified generalized least squares estimation arises in case of estimation under restrictions, which in general implies that ordinary and generalized least squares estimators cease to be identical. We discuss in detail hypothesis testing for the unrestricted and restricted estimators. Furthermore, we develop asymptotically pivotal fixed-b inference, shown to be available only in special cases. A brief illustration to modelling output and emissions as a Translog cointegrated production system with TFP, capital and labor as inputs indicates the potential usefulness of the developed methods.

Integrated modified ordinary least squares (IM-OLS) estimation, introduced for cointegrating linear regressions in Vogelsang and Wagner (2014), has several key advantages compared to other modified least squares estimators used in cointegrating regression analysis: First, estimation is tuning-parameter-free. IM-OLS requires the estimation of a conditional long-run covariance matrix for inference only. Second, IM estimation allows performing fixed-b inference in cointegrating regressions (see Vogelsang and Wagner, 2014, Section 5). Fixed-b inference is designed to capture the impact of kernel and bandwidth choices, required for estimating the above-mentioned conditional long-run covariance matrix, on the sampling distributions of test statistics. Third, and this is a very important conceptual advantage, IM estimation can be extended directly to allow for the inclusion not only of powers of integrated processes as regressors (the CPR case), but also of arbitrary non-negative integer products of integrated processes as regressors, i. e., to the SCMPR setting considered in this paper.

Considering systems of equations, useful to, e. g., analyze Translog cost or production function systems with several outputs (or systems for different sectors or countries), adds some aspects compared to the single equation setting discussed in Vogelsang and Wagner (2024). First, see also the corresponding discussion in Wagner (2023), systems of equations necessitate a detailed consideration of generalized least squares estimators, in this paper integrated modified generalized least squares (IM-GLS). This stems from the well-known fact that OLS- and GLS-type estimators coincide in general only (for any positive definite symmetric weighting matrix) in systems with identical regressors in all equations and without parameter constraints. Second, the scope of fixed-b inference needs to be investigated in more detail than in the single equation case. It turns out that - in addition to full design, required also in Vogelsang and Wagner (2024) - fixed-b inference is only available for up-to-the-intercept-identical hypotheses tested in all equations in systems with identical regressors in all equations. Whilst this is, of course, restrictive it includes, e. g., fixed-b RESET-type specification testing for systems of equations with identical regressors in all equations under both the null specification and in the augmented test regression.

The empirical illustration demonstrates the potential usefulness of the developed methods. The chosen examples indicates that the methods allow for a step forward in moving the modelling of the relationships between emissions and output from a reduced-form single-equation EKC setting to a more structural production-systems setting. Taking the results at face value, whilst stressing the exemplary and incomplete character of the illustration, the evidence for Translog-type cointegrating relationships for emissions appears to be limited; but the question deserves a deeper and more detailed investigation. A deeper investigation is beyond the scope of this methods-oriented paper, but can be undertaken with the tools developed.

This paper derives new asymptotic results for the adaptive

LASSO estimator in cointegrating regressions, allowing for uncertainty

about whether the regressors are exact unit root processes. We study

model selection probabilities, estimator consistency, and limiting

distributions under standard and moving-parameter asymptotics. We also

derive uniform convergence rates and the fastest local-to-zero rates

detectable by the estimator under conservative and consistent tuning.

In the consistently tuned case, we provide confidence regions that are

easy to construct, uniformly valid over the parameter space, and

asymptotically achieve sure coverage without requiring any

knowledge or estimation of local-to-unity or long-run covariance

parameters. Our simulation results reveal that the finite-sample

distribution of the adaptive LASSO estimator deviates substantially

from the oracle property, whereas moving-parameter asymptotics provide

much more accurate approximations. Consequently, oracle-based

confidence regions are often too small to achieve adequate coverage in

empirically relevant scenarios with small but non-zero coefficients.

In contrast, our confidence regions achieve adequate coverage across

the entire parameter space, making them a useful tool for quantifying

uncertainty around adaptive LASSO estimates in empirical applications.

We propose computationally inexpensive and efficient estimators for multivariate stochastic volatility (MSV) models with cross-dependence, Granger causality, and higher-order persistence in latent volatilities. The proposed class of estimators is based on a few moment equations derived from the VARMA representations of MSV models. Except for cross-dependence parameters, closed-form expressions for the other parameters are derived where no numerical optimization procedure or choice of initial parameter values is required. To increase the stability and efficiency of volatility persistence parameter estimates, we suggest shrinkage-type VARMA estimators where averaging or matrix-variate regression (MVR) is employed. We derive the asymptotic distribution of these estimators. Due to their computational simplicity, VARMA estimators allow one to make reliable -- even exact -- simulation-based inferences by applying Monte Carlo test techniques. In empirically realistic setups, simulation results show that the proposed shrinkage estimator based on MVR is superior to Bayesian and QML estimators in terms of bias and root mean square error. We examine the precision of the shrinkage estimator using large-scale simulated data where models up to 1,500 dimensions and 4,503,000 parameters are fitted and studied. The proposed estimators are applied to stock return data, and the effectiveness of the proposed estimators is assessed in two ways. First, we show the usefulness of the proposed models and methods in estimating high-frequency returns with many assets and observations. Second, in the context of dynamic minimum variance portfolio strategy, we find unrestricted higher-order MSV models outperform existing alternatives, including multivariate GARCH-type models.