Relationship between Volatility of Economics Variables and Economics Growth

Economic growth of an economy is defined as the steady state path through which the productivity of an economy is improved and increases the levels of national output and income. The government consumption expenditures and investment play a key role in the process of investigating the macroeconomic performance of an economy and determinants of economic growth. The countries which grow quickly, invest a substantial fraction of their GDP for consumption expenditures as well for the sources which encourage private investment. The objective of this study to calculate the volatility in economics growth in Pakistan. The annual time series data are used from 1975 to 2014 from WDI, Economics survey of Pakistan and Hand Book of Statistics. GARCH model has been used to measure volatility of all variables. The empirical results of the study confirmed that the volatility of the different variables (volatility of inflation, volatility of interest rate, volatility of political instability, volatility of GDP, and volatility of foreign direct investment) significant affect the government consumption expenditures and private investment in the economy of Pakistan. The study analyzed data by using the autoregressive distributive lag model which is mainly used in time series data Econometrics to estimate the non-stationary models with mix order of integration. The estimated results of the study evaluated that volatility of the inflation lead to uncertainty which is also suggested by the Able (1980) and negatively affect the economy consumption expenditures as well as private investment in the economy of Pakistan. Because uncertainty directly affects the cost of capital as well as reduce private investor confidence.


Introduction
Economic growth of an economy is defined as the steady state path through which the productivity of an economy is improved and increases the levels of national output and income. The government consumption expenditures and investment play a key role in the process of investigating the macroeconomic performance of an economy and determinants of economic growth. The countries which grow quickly, invest a substantial fraction of their GDP for consumption expenditures as well for the sources which encourage private investment. While slowly developing countries are those which fail to invest. It makes clear that investment and government consumption expenditures are the key components of economic growth of an economy. The changes in the share of government consumption and investment expenditures can affect the economic growth of the economy due to the uncertainty (Bloom et al., 2007).
Traditional Solow Swan (1956) growth model shows that an increase in the government consumption expenditures shifts the economy toward a new steady state equilibrium which is also increasing the saving and investment that only have transitory effects on the rate of growth, so economy move toward the new higher steady-state equilibrium. Following figure shows that any change in the investment will change the output of the economy and consumption expenditures of the economy while on the other side government fulfill their expenditures by increase the taxation. The following diagram shows that equilibrium takes place at point E1, due to the increase in the government consumption expenditures steady state equilibrium shift upward at point E2.

Subhead
The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is one of the popular models for estimating stochastic volatility of the macroeconomics series. GARCH model assumed that the randomness of the variance process varies with the variance of the series, as opposed to the square root of the variance as in the Heston model.
In empirical work with ARCH models, high q is often required, a more parsimonious representation is the Generalized ARCH model. This is an ARMA (max (p, q), p) model for the squared innovations.
The standard GARCH (1, 1) model has the following form for the variance differential: The GARCH model has been extended via numerous variants, including the NGARCH, TGARCH,   IGARCH, LGARCH, EGARCH, GJR-GARCH, etc. Strictly, however, the conditional volatilities from GARCH models are not stochastic since at time t the volatility is completely pre-determined (deterministic) given previous values.

Unit Root Test:
The unit root test has been highly popular to test for stationary. To explain this test we start with the following equation.
In this equation, we regress Yt its lagged value Yt-1 and find out if the estimated is statically equal to I, stationary.
Now subtract Y t-1 from both sides of the equation and obtain Now we estimate the above equation and test the null hypothesis δ = 0. If δ=0 then ρ = 1 which means that the time series under consideration is non-stationary and for stationary, ρ should be less than 1.
Then examine the significance of the empirical results, which test we should use if the estimated coefficient of Y t-1 in equation (3.4) is zero or not. Firstly, we may tend to use usual t test, but unfortunately, under the null hypothesis that δ = 0 (ρ = 1), the t value of the estimated coefficient of Y t-1 does not follow the t distribution even in the large sample. Alternatively, Dickey and Fuller considered that under the null hypothesis that δ = 0, the estimated t value of the coefficient of Y t-1 follows the τ (tau) statistics. Dickey and Fuller computed the critical values of the tau statistics on the basis of Monte Carlo Simulation. Generally, tau statistics is known by the name of Dickey and Fuller statistics.
The Dickey and Fuller estimated co-efficient of Y t-1 in three different specifications like ∆ Y t = β 1 + β 2t + δY t-1 + µ t …………… (3.5) Y t is the Random Walk with drift around a stochastic trend.
The procedure of actual estimation is that first, estimates these equations by OLS, divide he estimated coefficient of Y t-1 by its standard error to calculated tau statistics and move toward Dickey and Fuller value, we reject H 0 , that is, δ = 0, in such case, the time series will be stationary. On the other hand, if the computed absolute value of the tau statistics is less than the Dickey and Fuller critical value, we don't reject the null hypothesis δ = 0, in such case, the time series is non-stationary.
There are two types of unit root test:

Result
Empirical results of the macroeconomic volatility, which is closely linked with the macroeconomic uncertainty by using Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The

Discussion
The fundamental objective of the study was to evaluate the Macroeconomic Uncertainty, Consumption Econometrics to estimate the non-stationary models with mix order of integration.
The estimated results of the study evaluated that volatility of the inflation lead to uncertainty which is also suggested by the Able (1980) and negatively affect the economy consumption expenditures as well as private investment in the economy of Pakistan. Because uncertainty directly affects the cost of capital as well as reduce private investor confidence.
Political thinkers and policy makers believe that the volatility of the macroeconomic and political variables may lead to uncertainty in the developing economy which has significant impact on government consumption expenditures and private investment.
The foreign capital inflow plays a key role in the development of an economy in the form of resource flows between the industrial and developing economies in the form of infrastructure development and technological advancement which lead to improve productivity growth of the economy. Foreign direct investment is the one of the form of capital inflow from the host countries. The estimated results of the study confirm the statistically significant adverse effect of the volatility of the foreign direct investment on the government consumption expenditure and private investment in the economy. Because the domestic political and security situation affects foreign direct investment with negative trend throughout the world. So there is a need for a policy which reduces the volatility of foreign direct investment.
The overall findings of our study concluded that macroeconomic uncertainty due to the volatility of the macroeconomic variables significantly matters for the determination of government consumption expenditures as well as private investment in the developing countries like Pakistan. We observed in our study that Pakistan experiences more volatility in macroeconomics variables caused more fluctuation in government consumption expenditures and private investment.