The Engle-Granger Methodology

The Engle-Granger Methodology
Application on the Austrian Economy Data


Martin Fukač
(martin.fukac@cerge-ei.cz)


Abstract
In this paper I test for two theoretical relationships using the cointegration approach. First, I test whether growth of nominal wages is a function of the growth of aggregate price level. I find there is a quite close relationship. This fact suggests that theinflation phenomenon is anticipated in the wage policy. Second relationship I test for is the relationship given by the Friedman’s rule, i.e., in equilibrium inflation grows at the same rate as the real output does. I find that this is not the case of Austrian economy, although there is certain causality between inflation and output growth.



Introduction
I focus in this paper on testing twocausal relationships expected by the economic theory. Testing is done on the quarterly economic data of the Austrian economy. In the first case, a microeconomic one, I try to find out whether the nominal wage adjusts for the aggregate price level changes. In other words, I try to test, whether there is a tendency in the economy to keep real wage at least non-decreasing. In the second case, amacroeconomic one, I try to indirectly check whether there is a tendency of the monetary policy to follow the Friedman’s rule. The employed testing procedure is based on the Engle-Granger methodology described in Enders (1995).
The paper proceeds as follows. In the next part I describe the data sources and the relevant data transformation for testing. In the second section I briefly sketch the hypothesisto be tested. The methodology of is in the third part. The fourth part presents results and the discussion about them, and the fifth part concludes.
1 Data description
The source of data is the Osterreichisches Institut fur Wirtschaftsforschung (www.wifo.ac.at). The description of quarterly time series I use for this paper is contained in the following Table 1.

Table 1 Original time seriesTime series of Denotation Units Data span Note
Real Gross Domestic Product GDPr mill. of ATS (base year 1985) 1980:Iq – 1999:IVq seasonally unadjusted
Consumer price index CPI %
(base year 1995) 1980:Iq – 1999:IVq seasonally unadjusted
Average Nominal Wage W ATS 1980:Iq – 1999:IVq seasonally unadjusted

For the testing purposes I have to transform the original data. The transformation andthe new variables are described in the Table 2.


Table 2 Transformed time series (relevant for testing)
Time series of Denotation Units Data span Transformation form
Year-to-Year Real GDP growth g % 1981:Iq – 1999:IVq

Year-to-Year CPI inflation  % 1981:Iq – 1999:IVq

Year-to-Year Nominal Wage growth w % 1981:Iq – 1999:IVq

Note: Using the described transformation none of theseries exhibits a seasonal pattern.



In the following figures, I plot the graphs of transformed time series which will be used for testing later on. The Figure 1 shows the real GDP growth, Figure 2 shows the yearly inflation path, and the Figure 3 presents the growth of nominal wages.



Figure 1 Year-to-Year growth of Real GDP



Figure 2 Year-to-Year inflation of CPIFigure 3 Year-to-Year growth of Average Nominal Wage


2 Test Hypothesis



Hypothesis H1: The inflation rate is anticipated in wage contracts

The first hypothesis to be tested expects that if economic agents are rational they adjust their wage appropriately to the changes in product prices, i.e., they will tend to keep their real earnings at least constant. If this is actually true Ishould be able to find cointegration in the growth of nominal wage and aggregate price level inflation. I assume the following long-run relationship between price inflation and the growth of nominal wage:

,
( 1 )

where w is the growth rate of the aggregate nominal wage,  is the aggregate price level inflation, and e is iid process.





Hypothesis H2: The monetary policy follows...