3rd meeting of young researchers at UP 1 - IJUP - Universidade do ...

Numerical solution of short-term macroeconomic models
J. Mendes 1 , O. Afonso 2 and P.B. Vasconcelos 3
1 Faculty of Economy, University of Porto, Portugal.
2 Faculty of Economy and CEF.UP, University of Porto, Portugal.
3 Faculty of Economy and CMUP, University of Porto, Portugal.
Macroeconomics examines the economy as a whole, proceeding from the aggregation of
similar activities conducted by different agents; in particular, households, firms and
government. It is traditionally interested in the path of the aggregate output (usually measured
by GDP), as well as in employment and prices. Short-term macroeconomic analysis is focused
on the conjuncture, and its central aim is to smooth the path of the three relevant variables. As
a strong cyclical stability does not guarantee a fast and sustainable economic growth, long-term
macroeconomic analysis is concerned with the economic growth. In this work, we consider
mathematical models to model the short-term macroeconomic performance; i.e., Keynesian
and IS/LM (linear models), AD/AS (nonlinear model) and SP/DG (dynamical model). These
models require the consideration of functional forms, and thus the consideration of endogenous
and exogenous variables and parameters. In order to solve these models, to extend them and to
be able to tackle more complex ones, where an analytical solution does not explicitly exist or is
difficult to obtain, a numerical approach is mandatory. For this purpose, it is necessary to
implement computationally the model, and calibrate the parameters and the exogenous
variables taking into account both empirical and theoretical literature.
The mathematics required for models construction and resolution, the exposition to some of the
most widely used numerical methods to solve such problems and the economic understanding
and forecast make this interdisciplinary work of great importance. The sensitivity analysis due
to perturbation of exogenous variables can be rapidly accessed and graphically represented,
favoring the policy maker to influence the
economic development. The Philips (Sp) curve
represented in the picture shows the relationship
between inflation (π) and the output ratio ( )
given a fixed expected rate of inflation ( ).
Initially the economy is in equilibrium with π=6
and =0, the occurrence of a positive shock in
the growth of the nominal GDP induces the
economy in long run adjustment.
The speed and the concrete path of the
adjustment depend on the inflation expectations:
, ; the
bigger λ is, the greater is the speed adjustment to
the new long term equilibrium.
References:
[1] Gordon, R.J.(2008), Macroeconomics, 11th Edition,
Pearson, Addison-Wesley.
[2] Burda, M. and Wyplosz, C. (2005), Macroeconomics – a European text, 4th Edition, Oxford University Press.
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