# Economic growth and fiscal policy

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## Abstract

Having explicitly examined the influence of fiscal policy on short-term interest rate dynamics and the term structure of interest rates in the last two chapters, we now want to turn to the second main question to be addressed within our model: how do fiscal policy and financial market interactions influence the evolution of output, income and hence economic growth? Since we already mentioned in Chapter 3 that our production function is known to produce endogenous growth, the question here is not whether growth reaches a steady state or not. The question is rather: does the interaction between interest rate dynamics and fiscal policy imply positive or negative growth rates in average? And are growth rates accelerating like in the deterministic setting (which did not automatically imply that they are positive)? Recalling the discussion in the introductory chapter, it is our aim to show that growth does not evolve independent of financial markets and fiscal policy settings.

## Keywords

Interest Rate Lyapunov Exponent Fiscal Policy Effective Dimension Stationary Probability Distribution## Preview

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## Notes

- 1.We assume k to start with a positive value so that it will start indeed within [0, ∞]. Later on, we will show that k can never leave this interval i.e. can never get negative.Google Scholar
- 2.See Arnold (1998) for a complete discussion of all questions regarding random dynamic systems which contains SDEs in the Ito sense as a special case.Google Scholar
- 3.This assumption can be shown to be true when the drift and diffusion terms of all components of the multidimensional diffusion are also C
^{-}-functions.Google Scholar - 4.For a recent survey of the method of Gröbner Bases and its field of application, see Buchberger/Winkler (1998).Google Scholar
- 5.See Schuss (1980, Chapter 5.4) for a derivation of the respective PDE.Google Scholar
- 6.This calculation was done using the ‘FindRoot’ function from the computer algebra package ‘Mathematica 3.0’ As starting values we used 0.5(1-z) which guarantees convergence since we have already shown that in the interval (0, 1-z) there is only one root.Google Scholar
- 7.The linear regression statistics involved with (5.28) are of a similar quality than in the regression (5.24).Google Scholar
- 8.Note that a’ stationary solution’ in a deterministic context always corresponds to a fixed or equilibrium point. However, this concept is too narrow for stochastic processes since’ stationary solution’ can now also mean that the probability distribution induced by the process becomes time independent and thus stationary. A stationary solution can hence exist even if no fixed points are present. This is important for our model since we have seen in Chapter 3 that the short-term interest rate process has no fixed point. But owing to the fact that we have shown the process to move on an open interval with zero probability of reaching the interval boundaries, one knows by a theorem of Skorokhod (1989) that the process must converge to a stationary solution if and only if its probability density exists and is integrable over the corresponding interval. In the further context, we use the fact that such a stationary solution for the short-term interest rate process exists.Google Scholar
- 9.It will soon become clear why it is allowed to treat S
_{1}as a quasi-constant in carrying out this integration.Google Scholar