This system has only 6 equations, three of which must be fitted in order to assess the coefficients. \(\alpha_i, \beta_j, \gamma_k\) are coefficient to be estimated. \(G\) as government expenditure plus net exports \(Time\) as an index of the passage of time, e.g. 1931 = zero \(WG\) as wage bill of the government sector \(WP\) as wage bill of the private sector (demand for labor)
\(CN\) as private consumption expenditure In this post, we will show how to do structural equation modeling in R by working through the Klein Model of the United States economy, one of the oldest and most elementary models of its kind. For example, one might want to account for an error auto-correlation of some degree in the regression, or force linear restrictions modeling coefficients. Moreover, they often require combining time series and regression equations in ways that are well beyond what the ts() and lm() functions were designed to do. Structural Equation Models (SEM), which are common in many economic modeling efforts, require fitting and simulating whole system of equations where each equation may depend on the results of other equations.
Andrea Luciani is a Technical Advisor for the Directorate General for Economics, Statistics and Research at the Bank of Italy, and co-author of the bimets package.