Quarterly Data for the Moroccan Economy: A Shortcut
This is some heavy stuff: the post proposes to use statistical results from computations on cycles to develop, in turns, the broad aggregates and expand the level of details; we move from 56 years to 224 quarters (1 years = 4 quarters). Obviously, this gainsaid much of the computations performed in other posts: the HP filter does usually a lot better with quarterly data, and these do not come in hand – not so much a gainsay as it is a complete reformulation of any past doodling. On the other hand, the closer any official study got to it was the Finance Ministry’s 2009 study on Cycles, considered too short a time sequence – 1980 to 2008. This will explain some discrepancies in their results – it also explains why the Hodrick-Prescott filter works better, although I suspect any non-parametric filter would do equally fine.
If you torture the data long enough, it will confess.
Annual GDP is usually computed as follows: (adjusted for seasonal fluctuations). On the other hand, we might substitute this expression with a more probabilistic setting, with the cumulative density for quarterly GDP (with a normalized annual GDP to 1) this statistical device is needed to generate the moments needed for further computations: mean, standard deviation and perhaps skewness. Obviously, this denies the modelthe possibility of capturing outstanding fluctuations, but there is an arbitrage to be made: scarce data, persistent fluctuations and the easy in computations.
Scarce data: it is a pity HCP or any other public institution does not publish long time series pertaining to the Moroccan economy – reliable data goes as far as the early 1980s, and annual data is usually not available on domestic sources (I have yet to find some lonely pdf file on the Finance Ministry’s website with dates from the 1960s…)
Persistent fluctuations: to capture these means eliminating outliers; no doubt the process will underestimate negative shocks because of the constraints put on the model.
Handiness in computations: there are some models available, for which assumptions -sometimes strong ones- have to be made in order to make sense of it all. In that respect, the results are not supposed to be iron-cast; in uncharted territories, it is hardly the case, and Moroccan business cycles certainly are.
From the beginning of the year till its end, growth is somehow randomly distributed across quarters. Perhaps ‘random’ is not the right word: what matters here are the moments of interest; it matters little to ‘guess’ the appropriate form quarterly growth displays over the very long run, and these errors will cancel out over almost 230 quarters. the initial step is to adopt the overly simplistic assumption that growth is uniform across quarter, that is, growth adopts the cumulative density of a uniform distribution, from Q1 to Q4, while the assumption is indeed very strong, it has the convenience to present us with smoothness: uniformity means inter-quarter growth will be very close to the yearly trend growth. In that sense, those recorded disturbances around the trend will be considered as the historical volatility we need to compute for more advanced distributions.
How do we check the results make sense? There is a benchmark out there for us to see: Quarterly data for US GDP per Capita is available, as well as the annual data for the percentage of GDP the Moroccan economy represents with respect to that of the US. A successful estimation for quarterly growth in Morocco means the relative GDP to the US should be very similar to that in yearly setting. The idea is simply to compute both countries’ trends, and from then on the ration across the available 196 quarters (usable US Data runs from 1955:I to 2004:IV)
We proceed to generate a normal distribution at each year, with where is a measure of volatility derived for the time being from levels of annual growth, and centred around an average measure computed on annual growth values. We thus obtain the following results compared to annual data:
GDPY ------------------------------------------------------------- Percentiles Smallest 10% 6.252841 6.162857 Obs 57 25% 7.11526 6.189924 Sum of Wgt. 57 50% 8.232385 Mean 7.942243 Largest Std. Dev. .9970512 90% 9.121388 9.263059 Variance .9941111 95% 9.263059 9.275018 Skewness -.4843868 Quarterly_GDP ------------------------------------------------------------- Percentiles Smallest 10% 6.259518 6.089419 Obs 228 25% 7.096377 6.104532 Sum of Wgt. 228 50% 8.24034 Mean 7.941979 Largest Std. Dev. .9909281 90% 9.101249 9.296097 Variance .9819385 95% 9.253781 9.301066 Skewness -.4863844 99% 9.296097 9.343733 Kurtosis 1.9077
As one can see, the quarterly data does not distort the original series too much, the trade-off being at the cost of a marginally smaller volatility and average GDP.
The newly generated doesn’t look much like the earlier results I posted on. Simply put, the data was not fit for cycle-generation. Some short-term fluctuations were not taken into account precisely because the data was annual, and subsequently, some outstanding quarters (in both ways) were skipped or instead exacerbated because of their effects on annual growth.
Overall, the essential features of ‘yearly’ cycles can be found in the graph too: boom-and-bust in the second half of the 1960s, the boom of the 1970s, and then the quagmires in short cycles in the 1980s and 1990s.
Interestingly enough, volatility is much smaller compared to initial projections; in fact, 38% smaller, as we can observe on the descriptive statistics:
Variable |Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------- HP_Quarter_1 |228 2.28e-19 .048117 -.1296305 .1497003 HP_AnnualY_1 | 57 -7.30e-19 .078588 -.1399502 .1696304
(the difference in mean is not very significant, as both are very close to zero)
How does this cycle perform with respect to that computed by the Finances Ministry in their 2009 paper?
Les huit cycles d’affaires enregistrés durant les décennies 80 et 90 ont été marqués par la comptabilisation de 13 années de sécheresse entrainant de fortes oscillations de la production agricole et des secteurs de l’activité économique qui lui sont associés à l’amont et à l’aval. […] La phase expansionniste que connait aujourd’hui l’économie marocaine se démarque clairement de l’expérience des décennies précédentes […] Ce contexte d’évolution démontre distinctement dans quelle mesure l’économie nationale a réussi à amorcer un changement positif de structures économiques et à développer une grande capacité d’adaptation et d’amortissement des chocs. Les gains de stabilité et de durabilité enregistrés au cours de ces dernières années tiennent dans une grande partie à l’amélioration de la conduite de la politique économique et de la qualité des dispositifs institutionnels.
The findings about the expansionary cycle beginning from late 2000 are somewhat mitigated when one considers a longer time series: true, the average cycle has been less volatile (25% less than the 229 quarters-long time series) but these fluctuations are under-estimated in the MINEFI study because of the historical volatility they embed: the 1980s have been very volatile indeed, and the great moderation that followed makes cycles in the 2000s very moderate, hence the optimistic view held in the ministry’s findings. On the other hand, it seems the last 40 quarters have exhibited historically low volatility, which, when combined with those in the period 1980-2000, can be under-stated.