Economies compared: Italy vs Eurozone

Italy and Euro Area GDP trend

In order to understand better where the differences between Italy GDP and Euro Area one are, the two time series has been decomposed in their trend and cyclic part using a Hodrick-Prescott filter. The Hodrick-Prescott filter is used in macroeconomics, especially in real business cycle theory, to remove the cyclical component of a time series from raw data.

The trend part visualized below shows a significant difference in trend from 2008 onward. While Euro Area GDP maintains his upward trend. Italy GDP dropped till 2015 and then it went up without reaching the level before 2008 (not considering COVID-19 crisis).

GDP business cycles

The cyclic part of the time series highlights the overall economic cycle to which Europe has been subject to. Again the global financial crisis (2008), the national debt crisis (2011) and the COVID-19 one (2020) are clearly visible.

The business cycles of Euro Area and Italy are really similar. In statistics this is said that they are highly correlated.

The plot above, outcome of cross correlation analysis, identifies lags of the Italy GDP cycle that might be useful predictors of Euro Area business cycle at time t. With no lag the two series are almost collinear.

stationarity

One of the most important characteristic for time series to be modeled is their stationarity. A time series is said to be weakly stationary when it has constant mean and variance throughout the time.

The two time series under study seems not to be exactly weakly stationary as confirmed by the Philips-Perron test. This statistical test checks the null hypothesis that a unit root is present in a time series against the alternative that the series is stationary.

## 
##  Phillips-Perron Unit Root Test
## 
## data:  gdps_growth$IT_growth
## Dickey-Fuller = -2.8008, Truncation lag parameter = 3, p-value = 0.248

## 
##  Phillips-Perron Unit Root Test
## 
## data:  gdps_growth$EA18_growth
## Dickey-Fuller = -3.5242, Truncation lag parameter = 3, p-value =
## 0.04539

Reported p-values higher than 5% means that the null hypothesis of presence of a unit root cannot be rejected.

Getting rid of the last GDP quarter referring to COVID-19 crisis that is indeed a clear outlier, the time series become weakly stationary as confirmed by Philips-Perron test.

## 
##  Phillips-Perron Unit Root Test
## 
## data:  gdps_growth_st$IT_growth
## Dickey-Fuller = -4.3275, Truncation lag parameter = 3, p-value = 0.01

## 
##  Phillips-Perron Unit Root Test
## 
## data:  gdps_growth_st$EA18_growth
## Dickey-Fuller = -4.7402, Truncation lag parameter = 3, p-value = 0.01

Without 2020 the p-values are below 5% so the null can be rejected.

GDP growths distributions and statistics

The following plot compares the distributions of Italy growth towards de-Italianized Euro Area.

where such measures describe the probability distribution

• mean represents the average value for growth. Quarterly growth for Italy is 0.05 %, the figure for Euro Area without Italy is 6 times higher;

• standard deviation measures the amount of variation or dispersion of the growths values. Italy growth seems to be slightly more variable than Euro Area (18 country) one;

• skewness measures asymmetry in the distribution. Both distribution appears distorted or skewed to the left (towards low and negative value);

• kurtosis measures the “tailedness” of the distributions. Both distributions have more observations in tails than in a normal distribution (kurtosis = 3) with Euro Area distribution deviating significantly from normal.

last three years of GDP growth

In order to get a closer look at GDP growths the following plot visualizes the last 3 years (from 2017 to 2019).

vector autoregression

Starting from the hypothesis that GDP growth for Italy and for Euro Area not including Italy are somewhat interdipendent affecting each other intertemporally, the 2 GDP growth series can be modeled using vector autoregression (VAR). VAR models generalize the univariate autoregressive model (AR model) by allowing for more than one evolving variable. All variables in a VAR enter the model in the same way: each variable has an equation explaining its evolution based on its own lagged values, the lagged values of the other model variables, and an error term.

Properties of the VAR model are usually summarized using impulse response analysis which main purpose is to describe the evolution of a model’s variables in reaction to a shock in one or more variables. For our analysis purpose it is interesting to see how Italian GDP growth could react to a positive impulse in fictitious Euro Area at 18 country economy growth.

The interpretation of graph above is straightforward: an impulse (shock) to Euro Area at 18 country growth at time zero has small effect the next period and the effect become smaller and smaller as the time passes. The dotted lines show the 95 percent interval estimates of these effects that are clearly not statistically significant.

The variance decomposition indicates the amount of information each variable contributes to the other variables in the auto regression. It determines how much of the forecast error variance of each of the variables can be explained by exogenous shocks to the other variables.

The graph above shows that almost 100 percent of the variance in Italian GDP growth is caused by the Italian GDP growth itself despite the exogenous shock to Euro Area not including Italy.

## $Granger
## 
##  Granger causality H0: EA18_growth do not Granger-cause IT_growth
## 
## data:  VAR object var_mdl
## F-Test = 0.12253, df1 = 1, df2 = 150, p-value = 0.7268
## 
## 
## $Instant
## 
##  H0: No instantaneous causality between: EA18_growth and IT_growth
## 
## data:  VAR object var_mdl
## Chi-squared = 27.807, df = 1, p-value = 1.34e-07

forecasting Italy GDP growth (no COVID-19 crisis)

In order to predict future points in the Italy GDP growth series (forecasting), an ARIMA model could be fitted to data. Analyzing the series and the auto correlation and partial auto correlation plot it is possible to identify the model specification. The PACF shows a single spike at the first lag and the ACF shows a tapering pattern therefore an AR(1) model is indicated.

In order to assess the goodness of fit of the AR(1) model, the residuals against time, their autocorrelation and their distribution have been plotted. The ACF of the residuals show non-significant values at all lags except for a barely significant residual auto correlation at lag 9. Furthermore the residuals show a almost normal distribution. This confirm the goodness of the fit of the AR(1) model for the Italian GDP growth series.

It is now possible to forecast growth one year ahead (4 quarters horizon) If no COVID-19 pandemic occurred Italy GDP growth will likely recover a bit from a slightly negative value.

forecasting Euro Area GDP growth (no COVID-19 crisis)

Series against time, auto correlation and partial auto correlation plots for Euro Area GDP growth are shown below.
The PACF shows a single spike at the first lag and the ACF shows a tapering pattern: also in this case an AR(1) model is indicated.

The fitted auto regressive model of order 1 has the following parameters:

In order to assess the goodness of fit of the AR(1) model, the residuals against time, their autocorrelation and their distribution have been plotted. The residuals show a almost normal distribution and the ACF of the residuals shows non-significant values at all lags except for a barely significant residual autocorrelation at lag 8 thus confirming the goodness of the fit of the AR(1) model.

It is now possible to forecast growth one year ahead (4 quarters horizon) using the fitted model. If no COVID-19 crisis will occur, the Euro Area GDP without growth, not including Italy contribution, would have slightly raise but not reaching values of previous year.