# 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 [2.2]. 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 Table 4 summarizes the results of ADF test at levels. The given table consists of test statistics value and p-value. In case of variable GROWTH, the hypothesis was rejected and we can say that GDP growth rate is stationary at levels. The remaining variables IMMIG, UNEMP and INF are non-stationary at levels. All these three variables are non-stationary, when ADF test is performed with trend and intercept in the model.
Table 4: Augmented Dickey-Fuller Test for Unit Root at levelsVariables With intercept With trend and intercept Test statistics Z(t) P-value Test statistics P-valueIMMIG -0.838 0.8077 -2.825 0.1881UNEMP -1.398 0.5833 -2.503 0.3265GROWTH -5.671 0.0000 -5.587 0.0000INF -1.313 0.6231 -3.163 0.1032Since the series (IMMIG, UNEMP and INF) are not-stationary at levels, we take first difference for these three series.
After taking the first differenced for IMMIG, UNEMP and INF series, the ADF test are then performed, as shown in table 5. Now these three variables are stationary at the first difference and they are said to be integrated of first order. Table 5: Augmented Dickey-Fuller Test for Unit Root at first differenceVariables With intercept With trend and intercept Test statistics Z(t) P-value Test statistics P-valueIMMIG -6.516 0.0000 -6.520 0.0000UNEMP -4.582 0.0001 -4.523 0.0014INF -7.967 0.0000 -7.891 0.0000
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.Table 6.
Zivot and Andrew unit root test for structural break (at levels)Variables With intercept With trend and intercept Test statistics Z(t) Break Year Test statistics Z(t) Break YearIMMIG -4.167 2006 -3.698 2002UNEMP -5.313 1992 -3.841 1997GROWTH -6.001*** 1994 -5.180*** 2005INF -5.025** 1992 -3.830 1977Note:
significant at 10% level, **significant at 5% level, *** significant at 1% level Table 7.
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.
IMMIG -7.032*** -6.413***D.UNEMP -5.600*** -4.632**D.INF -7.092*** -6.896***
Note: *significant at 10% level, **significant at 5% level, *** significant at 1% level
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 [2.1], 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 shown in appendix [A4], 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 null and alternative hypotheses is used for immigration variable are H_0: Immigration does not Granger cause unemployment rateH_1: Immigration granger causes the unemployment rate H_0: Immigration does not granger cause GDP growth rate H_1: Immigration granger causes the GDP growth rate ? H?_0: Immigration does not Granger cause inflation rate H_1: Immigration granger causes the inflation rateIn first column of table 8 the null hypothesis is shown and degree of freedom is in 2nd column.
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.
Table 8: Engle-Granger test for Causality:Null Hypothesis df Chi-sq Prob > chi-sq decision IMMIG does not granger cause UNEMP 2 3.2787 0.194 Do not reject H0IMMIG does not granger cause GROWTH 2 2.1011 0.350 Do not reject H0IMMIG does not granger cause INF 2 3.3626 0.186 Do not reject H0The impulse response function obtained from vector autoregressive model results are presented in figures (6-9).
The impulse response function in the figure (7) shows the response of unemployment rate after a shock in the immigration. At first two steps, the resulting effect is negative, but after two steps it has a positively increasing trend till the fourth step. At the fourth step it has a maximum value near 2 and after fourth step it goes down, which eventually disappeared at sixth step.
The impulse response function in this case build an idea that immigrations have positive short run relationship with unemployment.The figure (8) displays the response of growth rate to a shock in immigrations. It shows the negative relation in first three years. After the third year, it tends towards positive side and after sixth year it fades away.
In figure (9) the response of inflation rate to a shock in immigration show that in first three years it has positive value. But after third years, it is going towards negative side till sixth year and after sixth year it has no effect. It shows that in first years immigration and inflation have positive significance short run relationship and after this period it has negative relation till sixth year.
Figure 6: Graph of Impulse Response Function Figure 7: Response of UNEMP to a shock in IMMIG Figure 8: Response of GROWTH to a shock in IMMG Figure 9: Response of INF to a shock in IMMG ? ConclusionsThe main objective of this thesis is to investigate the effect of immigration on macro-economic variables in Sweden.
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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