The relationship between macroeconomic indicators and economic development based on time-series model in the case of Australia Boqijonov Adxamjon Ikromjon o’g’li

Step-1
Checking for the condition


Step-3
Checking for Heteroskedastic

Step-2
Checking for second condition

Step-4
Autocorrelation among model residuals

Step-5
Normal distributions of residuals







Approaches
Shapiro-Wilk and Skewness Kurtosis tests for normality



Approaches
Durbin-Watson and Breusch-Godfrey test

Approaches
Breusch-Pagan test





Forecasting of model that successfully passed the tests

Results, discussion, and recommendations

In our study, we used a quantitative method by implementing a multi-factor time series model to assess the relationship between GDP per capita (dependent variable) and inflation, unemployment, FDI, exchange rate, industry, and export (independent variables) in the case of Australia between 1981 and 2021. During this time, we developed an econometric model and equations by recording economic equations using multi-factor time series.

There are seven hypotheses in the research:
H0: There is no link between other economic factors and economic development.
H1: There is a link between inflation and economic development.
H2: There is a link between unemployment and economic development.
H3: There is a link between FDI and economic development.
H4: There is a link between exchange rate and economic development.
H5: There is a link between industry and economic development.
H6: There is a link between export and economic development.

The following models have been developed to investigate the relationship between economic factors and Australia's economic development:

Log-log models

𝐺𝐷𝑃𝑝𝑒𝑟𝑐𝑎𝑝𝑖𝑡a_i = 𝛽₀ + 𝛽₁Inflation_i + 𝛽₂Unemployment_i + 𝛽₃FDI_i + 𝛽₄ExchangeRate_i + 𝛽₅Industry_i + 𝛽₆Export_i + 𝜀_i. (1)
ln𝐺𝐷𝑃𝑝𝑒𝑟𝑐𝑎𝑝𝑖𝑡a_i = 𝛽₀ + 𝛽₁lnInflation_i + 𝛽₂lnUnemployment_i + 𝛽₃lnFDI_i + 𝛽₄lnExchangeRate_i + 𝛽₅lnIndustry_i + 𝛽₆lnExport_i + 𝜀_i. (2)

Where:
ln𝐺𝐷𝑃𝑝𝑒𝑟𝑐𝑎𝑝𝑖𝑡a_i : natural logarithm of 𝐺𝐷𝑃 𝑝𝑒𝑟 𝑐𝑎𝑝𝑖𝑡a

lnInflation_i : natural logarithm of Inflation
lnUnemployment_i : natural logarithm of Unemployment
lnFDI_i : natural logarithm of FDI
lnExchangeRate_i : natural logarithm of Exchange rate
lnIndustry_i : natural logarithm of Industry
lnExport_i : natural logarithm of Export
𝛽₀ : the intercept of the model
𝜀_i : error term.

The VAR model specification is given as follows:

𝑌_t = 𝑎 + 𝛽₁𝑌_t-1 + 𝛽₂𝑌_t-2 + ⋯ + 𝛽_p𝑌_t-p + 𝜀_i . (3)
where α is the intercept, a constant and β1, β2 till βp are the coefficients of the lags of Y till order p.
Order ‘p’ means, up to p-lags of Y is used and they are the predictors in the equation.
The ε_{t} is the error, which is considered as white noise.
The ARDL (p, 𝑞₁ , 𝑞₂ ……, 𝑞_k) model specification is given as follows:
Ф(L,p) 𝑦_t =∑ _I=1^k 𝛽_i (L, 𝑞_i) 𝑥_it + δ𝑤_t + u_t . (4)
Where:
Ф(L,p) = 1- Ф₁L - Ф₂𝐿² - … - Ф_p𝐿^p
β(L,q) = 1- β₁L - β₂𝐿² - … - β_q𝐿^q, for i=1,2,3 ……k, 𝑢𝑡~iid(0; δ²).
L is a lag operator such that 𝐿⁰y_t = X_t , 𝐿¹y_t= y_t-1, and 𝑤_t is a s x₁ vector of deterministic variables such as the intercept term, time trends, seasonal dummies, or exogenous variables with the fixed lags. P=0,1,2…, m, q=0,1,2…., m, i=1,2…., k: namely a total of (m+1) 𝑘+1 different ARDL models. The maximum lag order, m, is chosen by the user. Sample period, t = m+1, m+2…., n.
In our study, we additionally forecasted chosen indicators using multi-factor time series models such as VAR and ARDL. We used the Stata 16 program to model and forecast, which is currently widely used by scholars all around the world.

To achieve the aforementioned purpose, the variables are subjected to three major requirements of cointegration dependence:

In multi-factor time series, the cointegration relationship was performed in the following steps:

-indicators were logged;
-time series were checked for stationary;
-a regression model was built;
-the residue was checked for stationary.

Stationary Test

A unit root is tested with Augmented Dickey-Fuller (ADF) test. Do the variables observed have a tendency to return to the long-term trend following a shock or the variables follow a random walk? If the variables follow a random walk after a temporary or permanent shock, the regression between variables is spurious. Hence, the OLS will not produce consistent parameter estimates. All series should be stationary at the same level. ADF test can be determined as in Equation.

The hypothesis tested:

H0: δ = 0 (contains a unit root, the data are not stationary)
H1: δ < 0 (does not contains a unit root, the data are stationary)
H2: δ < 0 (does not contains a unit root, the data are stationary)
H3: δ < 0 (does not contains a unit root, the data are stationary)
H4: δ < 0 (does not contains a unit root, the data are stationary)
H5: δ < 0 (does not contains a unit root, the data are stationary)
H6: δ < 0 (does not contains a unit root, the data are stationary).

The parameter can be presented in the form of Vector Autoregressive Error

Correction Mechanism:

Where vector β = (-1, 𝛽2, …, 𝛽𝑛) that contain r cointegration vectors, and speed of adjustment parameter is given as α = (𝑎, 2, …, 𝑎𝑛) when rank β=rFurthermore, before making the analysis of the model, five conditions of Gaus Markov have been used in finding the direction and density of the indicators, heteroskedastic problem, model residual autocorrelation problem, regression models.


RESULT

Table 1 shows a large growth in GDP per capita, from $42744 to $80987 between 1981 and 2021, indicating that GDP per capita increased by 189% in Australia during this period. The inflation rate was 9.49 in the first year of this era and 2.86 in the last year, despite large variations in the rate of inflation during the period. Australia was unable to achieve unemployment rate stability; as seen in the table below, it was 5.78% in 1981, climbed for the next two years, and then declined. However, in the final years of that period, the unemployment rate was lower than at the start of this period. We can conclude that the Export of Australia rose significantly from 1981 to 2021.