🔎 Why This Matters

The spatial weights matrix W sits at the heart of spatial regression models, yet there are few techniques for validating a chosen specification of W. Reframing misspecification of W as a measurement error reveals a distinctive form of endogeneity that matters for spatial inference.

🧭 The Problem Identified

When W is inflated by a constant, a predictable form of endogeneity arises that does not affect ordinary regression contexts in the same way. Recognizing this structure makes it possible to both test for and control that specific misspecification.

🛠️ A New Test and Control: The K Test

A theoretically grounded test and corresponding control procedure—called the K test—are proposed to assess the validity of a specified W. The K test is constructed to be tractable for panel data applications and targets the endogeneity induced by constant inflation of the weights matrix.

📊 How It Was Evaluated

• Monte Carlo simulations are used to demonstrate the utility and behavior of the K test in controlled settings.

⭐ Key Findings

• Constant inflation of W produces a characteristic endogeneity in spatial regression models.
• That endogeneity can be detected and addressed using the K test in panel data.
• Simulations illustrate the test's practical performance and its use as a diagnostic and corrective tool.

⚖️ Why It Matters

The K test offers applied researchers a tractable diagnostic and adjustment for a common form of weights misspecification, strengthening confidence in inferences drawn from spatial regression models.