Question

where ?#! and ?$! are two unrelated white noise error terms, ln ???! is the natural logarithm of tax revenue and ln ??? is the natural logarithm of government expenditure.

a) Carefully explain how she would test for Granger-causality between tax revenue and expenditure within this framework.

Answer 1

Granger-casuality between tax revenue and expenditure:-The nexus between government revenue and government expenditure always wins the
attention of policy makers and think tanks while they work four making fiscal policies for
an economy. This paper is an empirical investigation on the unidirectional causality
between government expenditures and the revenues, which government collects from
public in shape of various levied taxes. Annual data for Pakistan from the period of 1979 to
2010 for governmental expenditures and its tax revenue have been collected. While, the
unidirectional and bidirectional causality were interrogated via applying Granger causality
for the outlined variables. The results indicate that there is an uni-directional causality
between the expenditures and revenues, which runs from tax revenues to govt.
expenditures, that is the previous lags of tax revenue has a causal impact on the current government spending.

In this study, the relationship between tax revenue, government expenditure, and economic growth has been examined for Canada, France, Germany, Italy, Japan, UK, and the USA—the G7 countries using annual data from 1980 to 2016. The study used two different panel causality approaches in order to make a comparison. According to the time domain panel causality test results, there are a bidirectional causality between economic growth and government expenditure but unidirectional causality between tax revenue and government expenditure. Moreover, there is no causal relationship between economic growth and tax revenue. On the other hand, frequency domain causality results show that there are a bidirectional short- and long-run causality between economic growth and tax revenue, and long-run causality between economic growth and government expenditure. The main finding is that the taxation policies to be implemented on the basis of the economic conjuncture of G7 countries are a powerful financial tool, with the potential to serve the economic objectives to be achieved.

Methods for test:-

Since the Granger causality test is relevant only when the variables involved are either
stationary or nonstationary but cointegrated,2 the Augmented Dickey-Fuller (1981, hereafter
ADF) unit root test has been performed for government revenues (REV) and government
expenditures (EXP).
The regression equation for ADF test is as follows.
where indicates the first differenced series of , is a time trend, and denotes
either REV or EXP at time . Since we do not know a priori whether the intercept and
the time trend should be included in Equation (1), we need some statistical criteria. In this
paper, both Akaike (1974) criterion (hereafter, AIC) and Schwarz (1978) criterion (hereafter,
SC) are adopted.3 The functional form to be selected is the one where both AIC and SC
are minimized. And the lag length p is chosen such that the error term, , is white noise.
  the null hypothesis is and the alternative hypothesis
is . If we cannot reject , then the variable has a unit root and it is a nonstationary
series. If all variables have been proven to be nonstationary and integrated of order 1,