Dynamic linear error-components models are introduced. Issues of multi-dimensional asymptotics are discussed. Large sample properties of the instrumental variable estimator (IV), generalized method of moments estimator (GMM), and maximum likelihood estimator (MLE) when N is fixed and T goes to infinity, or T is fixed and N goes to infinity, or both N and T large, are examined. Bias correction estimators are introduced.

The use of a panel vector autoregressive model as a reduced form approximation to a panel dynamic system is introduced. Nonstationarity and cointegrations over time and across cross-sections are discussed. Identification conditions and MLE or GMM estimation of dynamic simultaneous equation models are considered.

To what extent does bias correction and downscaling increase the value of GCM outputs for regional-scale applications?This chapter provides an overview of the concept of added value for downscaling studies and discusses the methods and metrics used for evaluating the value that bias correction and downscaling, using an RCM and/or an ESDM, adds to climate projections for impact assessments

Empirical-statistical downscaling combines observations with global climate model outputs to generate high-resolution spatial and temporal projections. This chapter describes some of the common methods and models used in spatial and temporal disaggregation and bias correction, focusing on aspects of their design and performance that are relevant to their application for quantifying local to regional-scale impacts.