DSGE With Oil Production in Stata

Introduction:

The Real Business Cycle (RBC) model is a cornerstone of macroeconomic analysis, providing insights into the fluctuations of real output and economic growth. The model, however, is often criticized for its simplicity and lack of consideration for certain real-world factors. One such factor that significantly impacts the global economy is the role of oil. In this article, we explore how to enhance the basic DSGE RBC model by incorporating oil into the production function, providing a more nuanced understanding of economic dynamics.

Adding Oil to the Basic RBC Model:

The standard RBC model assumes a simplified production function where output is solely a function of capital and labor. To incorporate oil into this framework, we modify the production function to reflect the contribution of oil to the overall output. The augmented production function now takes the form:

y= a*k^alpha1*L^alpha2*O^alpha3

• Y is output,

• A is the technology shock,

• K is the capital stock,

• L is the labor input,

• O​ is the oil input,

• α1is the capital share in output,

• α2 is the labor share in output.

• α3 is the oil share in output.

Exogenous Oil Supply:

In this extended model, the oil supply is considered exogenous and follows an Auto Regressive process of order 1 (AR(1)). This assumption allows us to capture the persistence and stochastic nature of oil supply shocks, adding a layer of realism to the model.

Demand shock in the Model

The technology shock in the oil production function follows an exogenous behavior, signifying that its evolution over time is not influenced by the endogenous variables of the model. This exogeneity allows us to model the unpredictability and external nature of technological advancements in oil extraction.

The model distinguishes between supply shocks and demand shocks. A demand shock is identified as a productivity shock affecting firms, leading them to demand more capital, more labor, and more oil. When there is an increase in the productivity of firms (positive demand shock), the demand for oil rises. This increase in demand for oil then influences oil prices, reflecting the fundamental economic principle of supply and demand.

Oil Supply Shock in the Model

Conversely, when there is an oil supply shock resulting from an increase in the productivity of oil producers, the price of oil decreases. This reflects a simple demand and supply relationship: an increase in oil supply leads to a surplus, putting downward pressure on oil prices.