Teaching Note 6

Analyzing the Business Environment

Econometric Modeling

An Example: Klein's Model I of U.S. Economy

Econometric modeling is an advanced application of multivariate regression in which there are more than one independent variable. In this course we can only illustrate its application, as advanced techniques are required for solution. A model of an economy is constructed using several equations each representing a characteristic or factor that is assumed to influence economic behavior. Such a model is termed a simultaneous equation analysis because several equations are evaluated at the same time in the model. The model is more of a system of interdependent equations that are solved. Econometric models are usually characterized by:

• the use of time-series data
• dynamic states, in which changes over time play an important role, are moideled by sets of equations, called identities, by which important factors are specified or defined by equations

Klein's Model I of the U.S. economy is a typical textbook illustration of econometric models. It models the U.S. economy in the period between the two World Wars as a system of 8 equations (all variables except Atime _t are measured in billions of 1934 dollars):

Outcome (y) variables that are statistical relationships:

y₁ : Aggregate Consumption, C_t. = a₁P_t + a ₂P_t-1 + a ₃ W_t + e₁
y₂ : Net Investment, I_t = b₁P_t + b₂P_r-1 + b₃K_t-1 + e₂

y₃ : Private Wage Bill, W_t^* = c₁E₁ + c₂ E_t-1 + c₃A_t + e₃

Outcome (y) variables that are identities or defined by mathematic relationships:

y₄ : Total Profits, P_t = Y_t - W_t
y₅: Total Income, Y_t = C_t + I_t + G_t - T_t
y₆ : End-of-Year Capital Stock, K_t = K_t-1 + I_t
y₇ : Total Wage Bill, W_t = W_t^* + W_t^**
y₈ : Total Production of Private Industry, E_t = Y_t + T_t - W_t^**

x₁: Government Wage Bill, W_t^**
x₂: Taxes, T_t
x₃: Government Non-Wage Expenditures, G_t
x₄: Time in Years from 1931, A_t

The system of equations is used to estimate the 9 parameters: a₁ , a₂, a₃ , b₁ , b₂, b₃ , c₁ , c₂, c₃