# Data Analysis Critique Essay

To analyze the time series data, a statistical software (STATA) was used. In time series data analysis important required condition is stationarity of the data set. To test whether the time series is stationary or not, the two tests are used; the ADF (Augmented Dickey Fuller) test and Zivot and Andrews test for unit root.

Both of these tests have same null hypothesis that the series is non-stationary (unit root process). For ADF unit root test we need lag length for the given time series variables. The lag length is selected by using information criteria (HQIC, AIC, SBIC) mentioned in section. We performed the unit root tests with both trend and constant.

It is important because the graphs of the time series variables gives an indication, whether we will include the trend term in the model or not. We can check the t value as well for inclusion of trend term in the model. The graph of immigration, unemployment and inflation shows that these series have time trend, but GDP growth rate series has no trend.

The results obtained from Zivot and Andrews test of unit are shown table 6. GDP growth rate has same results like in previous tests which is stationary at level with constant and trend and without trend. Unemployment rate and immigration are non-stationary series with or without trend.

The inflation rate is stationary without trend but non-stationary when including trend term in the model. Zivot and Andrews test was reformed after taking first difference of the three non-stationary time series. The unemployment, immigration and inflation rate have a strong evidence to reject the null hypothesis of unit root at first difference.

Zivot and Andrew unit root test for structural break (at first difference)Variables With intercept With trend and intercept Test statistics Z(t) Test statistics Z(t)D.

The empirical results of vector autoregressive model are investigated in the form of Granger causality test and Impulse response function. In this thesis, the time series variables used on levels to perform VAR model, because GDP growth rate is stationary on level and the remaining three variables (IMMIG, UNEMP and INF) are stationary at first difference.

As mentioned in section, various studies have indicated that vector auto regressive model can be estimated on levels of variables.The information criterion is used to select the lag length for a vector autoregressive model with four time series variables. The three information criterion (HQIC, AIC, SBIC) gives same lag length, which is two. But we preferred SBIC for selecting the lag length.

After computing the results of vector autoregressive model, there is need to test for autocorrelation of residuals and stability of the model. The LM Test for Residual Autocorrelation is used to test for autocorrelation. The results of the test shows that there is no evidence of autocorrelation found between the residuals.

The resulting VAR model gives all eigenvalues less than one and these eigenvalues lies inside the unit circle, which confirms that estimated VAR model is stable.The Granger causality test is performed by using the results of VAR model. Table 8 shows the results of Granger-causality.

The next two columns give test statistics value and p-value. We set the level of significance to be at 5%. The degree of freedom for all pairs is used 2, because the estimated VAR model has lag length 2. The results obtained from granger causality test for first null hypothesis have p-value 0.194, which is a clear evidence that we cannot reject null hypothesis. It showed that immigration does not granger cause unemployment rate.

For hypothesis about effect of immigration on GDP growth rate, the p-value is 0.35, which means again that we cannot reject the null hypothesis and conclude that the immigration does not granger cause GDP growth rate. The same results found in case of immigration and inflation rate hypothesis, where the p-value is 0.186. It is found that immigrations do not granger cause inflation rate. In these three cases we cannot reject the null hypothesis.

In this study unemployment rate, GDP growth rate and inflation rate are considered as the economic variables. The annual data for period 1970-2014 is used to examine the relationship between these variables in Sweden. We estimated VAR model for a short run relationship. The estimated VAR model satisfied the stability condition and by using Lagrange Multiplier (LM) test for autocorrelation, it was made sure that there is no autocorrelation between the residuals at any lag order 2.

The granger causality analysis performed by using the results of VAR model. The granger causality results shows that the immigration does not effect the unemployment rate, growth rate and inflation rate in Sweden during the study period. It is concluded that immigration has no short run relationship with these three macro-economic variables.

The results obtained from impulse response function shows that the immigration has short run positive relationship with the unemployment rate after first few years. On the other hand, the immigration have negative effect on growth rate in first three periods, but after these periods, the reverse effect has been observed.

There is a positive relationship found in first two years between immigration and inflation rate. But after two years it has negative relationship between immigration and inflation rate. The impulse response function results shows that immigration affect these economic variables for five to six periods and after that it have no such effect.

This indicates that in the beginning the immigrants does not participate in the economic growth. One probable cause of this could be the exposure to a new language in Sweden, which produces language barriers. Which also verifies that the GDP growth rate becomes static relative to the immigrations after few years, since language barrier is a temporary effect.

However, considering more economic variables which could be affected by the immigration may lead to more findings in Sweden’s economic growth. Moreover, increasing the sample size of the study variables could yield more improved results.

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