# _7.1 Correlations from alternative cyclical components_

The Hedrick-Prescott filter employed in section 4.1 to estimate the correlation of the cyclical components of GDP and the different fiscal variables is often criticized for its so-called end-point problems and spurious dynamics. These issues seem to be especially important when real output is far from its potential value. Recently, Hamilton (2018) suggested an alternative procedure to filter variables that avoids many of the shortcomings of the Hedrick-Prescott filter while preserving many of its advantages. He proposes a “linear projection”, in which a variable at date _t+h_ is regressed on the four most recent values as of date _t_ , resulting in stationary residuals that represent a cyclical component. The value of _h_ is suggested to be 2 for annual data, given that the primary reasons for being wrong in predicting macro variables at a horizon of 2 years ahead are cyclical factors.

**Table** **<u>6</u>** <u>Correlation coefficients between differently filtered fiscal variables and GDP</u>

|**Country**||**Government**<br>**expenditure**|Obs.|**Inflation**<br>**tax**|<br>Obs.|**Tax**<br>**revenue**|Obs.|
|---|---|---|---|---|---|---|---|
|_Bangladesh_|HP filter|0.33*|26|-0.26|22|-0.08|26|
||Hamilton (2018)|0.30|26|0.13|22|-0.15|26|
|_Bhutan_|HP filter|0.35*|26|-0.33*|26|0.2|26|
||Hamilton (2018)|0.31|26|-0.48**|26|0.33*|26|
|_India_|HP filter|-0.23|26|0.03|26|0.66***|26|
||Hamilton (2018)|-0.11|26|0.20|26|0.68***|26|
|_Nepal_|HP filter|0.29|26|-0.33|26|0.46**|26|
||Hamilton (2018)|0.37*|26|-0.16|26|0.60***|26|
|_Pakistan_|HP filter|0.37**|26|0.14|26|0.19|26|
||Hamilton (2018)|0.43**|26|0.14|26|0.43**|26|
|_Sri Lanka_|HP filter|0.04|26|0.11|24|0.26|26|
||Hamilton(2018)|0.12|26|0.16|24|0.18|26|

**Note:** Based on annual data from 1990 to 2017. Cyclical components are calculated as the deviation of the actual data from a trend computed using the Hedrick-Prescott filter with the standard smoothing parameter for annual data (6.25). ***, **, * denote significance at the 1, 5 and 10 percent levels respectively.

**Sources:** ADB, IMF, World Bank, and own calculations.

In Table 6, we compare the correlations of the cyclical components from the Hedrick-Prescott filter and from the Hamilton (2018) procedure. We correct previously calculated values from the HedrickPrescott filter in order to match the sample size used for the Hamilton (2018) approach. For Bangladesh, Bhutan, and Nepal the correlation remains positive and of similar magnitude, but the statistical significance is either weakened or lost. For Pakistan, on the other hand, the correlation coefficient increases and remains statistically significant at the 5 percent level. For the inflation tax the correlation was statistically significant for Bhutan with the HP filter and remains so with the Hamilton (2018) procedure, whereas for Nepal it becomes insignificant in both cases. For the tax revenue, the results are again similar, though with some notable differences. The correlation coefficients increase in India and Nepal, where the relationship is significant at the 1 percent level. In Bhutan, the correlation becomes statistically significant, as well as in Pakistan, where the correlation is now significant at the 5 percent level and as strong as for the government expenditure. Overall, the Hamilton (2018) procedure results in quite similar cyclical correlations of government expenditure and in somewhat stronger correlations of tax revenue.

_7.2 Pooled mean-group rather than fixed-effect error correction model_ 13