Economic Dynamic Modeling: An Overview of Stability

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Berggoetz, Nathan
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Economics often focuses on the end result of changes in the economy. Forexample, it is important to know now, if increases in government spendingthis year will affect real income and interest rates in the long run. Economicdynamics seeks to understand the change in economic variables over time andwhether or not economic results can be predicted mathematically. In the aboveexample, an understanding of real income and interest rate changes overtimewould be observed. This analysis allows for better government policyrecom-mendations since recommendations can be tailored to the desired results suchas a fast increase in real income and a slow increase in interest rates orviceversa. The focus here will be to consider two dynamic macroeconomicmodels,the first uses the goods and money market to model the macroeconomy whichwe will call the IS-LM model, and the second uses the goods and bonds mar-ket to model the macroeconomy which we will call the IS-BB model.In thispaper we will determine the stability of these two models as a check for theirvalidity. If either model shows instability it must be reformulated. Since thereal world does not exhibit unstable markets in which economic variables movetoward economic ruin, the correct model for the economy must be stable. Ifboth models exhibit stability then a second check must be performed in orderto choose which model is best. The second check involves comparingthe timepaths for each model and empirical data. It is important to note that these models consider all variables to be in real terms. Money is in nominalterms,which means that it simply serves as a unit of account, and as such will alwaysprovide the same service. This implies that to convert money as a measure ofsomething such as income, expenditure, or the supply of money intoreal terms,the amount of money must be divided by the price level. We consider the pricelevel to be the price of a representative good from goods market, which can bethought of as an average of all prices.