Regression models and Vector Autoregressive Models (VARs) play crucial roles in econometrics by allowing the analysis of multiple variables simultaneously. Despite their utility, these models face challenges like underfitting and overfitting, especially when determining the optimal model specification, which can lead to significant computational costs. To address these challenges, econometricians often rely on widely adopted model selection criteria such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). These criteria help balance model complexity and goodness of fit, aiding in the selection of the most suitable model specification for the given data. Nonetheless, there is a notable gap in existing research concerning the correct specification of these models, particularly in determining the optimal number of states a system can assume. Addressing this gap, we introduce a combinatorial framework designed to calculate the potential number of states in such econometric models. Our approach involves delineating four distinct stages in model development, each offering a range of specifications. This method enables a comprehensive combinatorial calculation of all possible states. The aim of this paper is to highlight this overlooked aspect of model specification and to spark a constructive dialogue within the empirical research community. By doing so, we hope to inspire further research that enhances the precision and applicability of econometric models. A theoretical complexity criterion is necessary to elucidate fundamental limitations and propose new objectives to pursue.

翻译：回归模型和向量自回归模型（VARs）在计量经济学中扮演关键角色，它们能够同时分析多个变量。尽管效用显著，但这类模型面临欠拟合与过拟合的挑战，尤其在确定最优模型设定时，可能招致高昂的计算成本。为应对这些挑战，计量经济学家常依赖广泛采用的模型选择准则，例如赤池信息准则（AIC）和贝叶斯信息准则（BIC）。这些准则有助于平衡模型复杂度与拟合优度，从而为给定数据选择最合适的模型设定。然而，现有研究在模型正确设定方面存在显著空白，特别是在确定系统可能假设的最优状态数量上。针对这一空白，我们引入一个组合框架，旨在计算此类计量经济学模型中潜在的状态数量。我们的方法包含模型开发的四个不同阶段，每个阶段提供一系列设定方案。此方法使得对所有可能状态进行全面组合计算成为可能。本文旨在强调这一被忽视的模型设定方面，并在实证研究界激发建设性对话。通过此举，我们希望激励进一步研究，以提升计量经济学模型的精确性与适用性。理论复杂度准则对于阐明基本局限性并提出新的追求目标是必要的。