The Moorish Wanderer

Quarterly Data for the Moroccan Economy: A Shortcut

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on May 30, 2012

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.

(Ronald Coase)

Annual GDP is usually computed as follows: y_t = \sum_{q=1}^{4} y_q (adjusted for seasonal fluctuations). On the other hand, we might substitute this expression with a more probabilistic setting, with y_t 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.

The idea is to find a distribution across quarters so as to minimize differences in relative GDP over the considered period (graph depicts annual output)

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 N \left(\bar{y_{t,t+1}},\sigma_{229}\right) where \sigma_229 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.

Brand new Morocco’s Quarterly RBC, and HP-filtered.

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.

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From Hero to Zero: 7% – 5.5% – 5% … 4%?

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on May 27, 2012

Who cares really… Forecast in growth is usually a very tricky business, but it is interesting in assessing the government’s own projections of how the Moroccan economy will fare in the next couple of years.

For instance, by my account, the government’s claim to create enough growth for 2016, an average of 5.5% as a matter of fact. 2012 is off to a bad start, since the best estimates are 3-4%, which leaves them with a higher target – about 5.8% to 6.1% to meet by the end of their legislation. By Bank Al Maghrib‘s own projections, that means the economy has to perform 5.5% for the next couple of years. But then again, these are basic results: growth figures are computed as geometric means, with 1+\hat{y_t}=\sqrt[5]{\prod 1+y_t}

the lower the initial value, the higher the next growth figures will have to make up for it – that’s how averages work. But then again, I do not expect the government to delve into explaining the method by which they get their figures. So if the Moroccan economy does not perform very close to 5 or 5.5% every year, then they would lose their bet, and with it some of their spending commitment will be halved or shelved.

Potential Real GDP (computed with respect to demographic growth)

A quick word perhaps on projected growth: there is more to it than just delivering a 5.5% five years straight. for the last 20 years, the potential output growth for the economy has turned around 5% (4.98% to be precise) in real terms. To promise 5.5% on average over the next 5 years means they are expecting an expansionary cycles, which does not seem to be doable at this moment: ever since 1992, the potential GDP growth has been very steady, and the volatility of cycles have decreased by a third when compared to the 50-years trend, and has been hovering around 5.02% and 4.95%, regardless of economic performances (and these were not top notch during the 1990s with the benefit of hindsight)

An IMF report points out:
Growth has been lackluster and volatile, especially since the 1990s. The most recent years show some encouraging signs […] However, the performance of the economy still needs to improve to catch up with the recent trends of GDP […]

Let us look back to the RBC computations described in the Big Picture Series: I have recomputed the parameters in question, and introduced the changes below. It is worth pointing out that these changes, while not very significant, are solely based on how one deals with the labour aggregate; the standard modus operandi is to compute total hours worked by the potential working population; since I have based most of my computations on DeJong & Dave, this is the most proper way to proceed:

Title:              	Nonfarm Business Sector: Hours of All Persons
Series ID:          	HOANBS
Source:             	U.S. Department of Labor: Bureau of Labor Statistics
Release:            	Productivity and Costs
Seasonal Adjustment:	Seasonally Adjusted
Frequency:          	Quarterly
Units:              	Index 1992=100
Date Range:         	1947-01-01 to 2004-10-01
Last Updated:       	2005-03-03 8:36 AM CT

But since no such data exist for Morocco, I had to make do with the available material, and settle for the standard 2080 hours per productive worker.

1/ we first list the parameters of interest as follows:

\alpha Capital Share: 0.335966

\beta Households’ discount rate: 0.934257

\delta Capital annual depreciation rate: 2.909%

\epsilon_{z_t} White noise of structural shocks N(0,0.01019)

\upsilon_{bp_t} White noise of balance of payments N(0, 0.08656)

\tau cross-persistence between the balance of payments and structural shocks: 0.599035

\rho persistence of AR(1) process: 0.371501

\phi time share allocated to work, 8 hours per day: 1/3

2/ model specification

* Household utility function, defined such: U(c_t,h_t)=\sum_{t=0}^{\infty}\beta^t\left[\theta \log c_t +(1-\theta) \log (1-h_t)\right]

* Output production: y_t=\exp(z_t)k_t^\alpha h_t^{1- \alpha}

* Structural shock process: z_t = \rho z_{t-1} + \tau bp_{t-1} + \epsilon_{z}

* Balance of payments process: bp_t = \rho bp_{t-1} + \tau z_{t-1} + \upsilon_{bp}

* Capital accumulation: k_{t+1} = (1 - \delta) k_{t-1} + i_t

* Investment dynamics: i_t = \exp (bp_t) \frac{y_t}{c_t} the definition combines a measure of domestic savings (\frac{y_t}{c_t}) and inflows of Capital.

* National Accounting Identity: y_t = \exp (bp_t) g_t + c_t + i_t government expenditure factors in foreign shocks as well, so as to capture other constraints a government in a closed economy doesn’t usually face.

* Government dynamics: it is assumed the government funds itself by levying taxes on capital and labour, with no room for deficit. this assumption is dictated to by the reality of given data and not pure ideology: the time series on public debt are incomplete and do not go as far as the late 1950s. The government announces a sequence of taxes \left\{tax_k , tax_h \right\}

Taxes: g_t = tax_k.\alpha.\exp z_{t-1} \left[\frac{k_t}{h_t}\right]^{\alpha-1} + tax_h.(1-\alpha).\exp z_{t-1} \left[\frac{k_t}{h_t}\right]^{\alpha}

Substitution rates of taxes: \frac{tax_h}{tax_k}=\frac{h_t}{k_t} \left(\frac{1-\alpha}{\alpha}\right)

3/ Results:

the assumption behind a utilitarian rate of substitution precludes any activist policy; the idea is to figure out first how an optimal funding for government expenditure in an RBC setting, then consider other settings where taxes are selected according to a specific decision rule.

  V   | St.Dev | sj/sy|Cor(j,y)|
------+--------+------+--------+     
  Y   |0.060230|   1  |    1   |
------+--------+------+--------+       
  C   |0.042792|0.7105| 0.9636 |
------+--------+------+--------+
  K   |0.380672|6.3203| 0.8090 |
------+--------+------+--------+       
  I   |0.020965|0.3481| 0.8727 |
------+--------+------+--------+        
  H   |0.004720|0.0784|-0.5595 |
------+--------+------+--------+        
 tax_h|0.003165|0.0525| 0.4948 |
------+--------+------+--------+        
 tax_k|0.076674|1.2730| 0.3870 |
------+--------+------+--------+
  G   |0.009470|0.1572| 0.2632 |
------+------------------------+

the model is significantly less volatile than the data, but ultimately fields good prediction when the cycle is close to the trend.

(we can already say the tax sequence is not based on utilitarian principles, since volatility on tax_k is higher than total government expenditure, and a lot closer to that of empirical government aggregates – this means taxes on capital are either too distortionary, or that government decision rules are based on unknown parameters.

in terms of cycle projection, while issues of equity premium puzzle arise – the comparison between RBC-generated data and empirical cycles for investment and capital, broader results are in line with model predictions, in particular when the cycle is close to the trend; aside from the expected low volatility, deviations are mainly due to exogeneous shocks, which allows for some predictions without too much tampering with the broad aggregates’ identities.

At this point, the model predicts very narrow results for the next quarters in 2011, but it remains very ellusive: the graph below points out to the variations with respect to the potential GDP growth per capita – about 3,94%, or 4,98% in aggregates terms.

Growth will not go beyond 5% for the next half a decade; there are no particular exogeneous shocks to expect that might lift productivity up and thus push the boundary of potential growth. There are however many shocks to expect that might slow down growth: foreign demand for Moroccan exports is likely to weaken, and the need for imported goods – whose relative price is quite high- will grow and handicap the economy. This means growth projects are wider on the lower side than they are on the upper one; a growth target for 5%, the baseline scenario might very well look overly optimistic, let alone an average of 5.5% over the 2012-2016 period.

On the other hand, the model by itself predicts a higher boundary of 4.98% – the potential trend that is – and provides ample room for lower projections, in the region of 4%. For Q2-2012, the model forecasts between 3.951% and 3.936% per capita growth; this means, in real terms, the economy will grow between 4.05% and 4.03%; but based on historical volatility, it is likely to be closer to 4%. From then on, the model predicts only one quarter above the 4.98% trend and from 2012 to 2016, average real GDP growth per capita does not rise beyond an average of 4.02%, and could go down as low as 3.8% (within a 95% confidence interval, that is)

Mixed-bag agriculture

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on May 24, 2012

I have read it ever since I took interest in Moroccan economics: “advanced models matter very little because, in the final analysis, the Moroccan economy relies heavily on agriculture”;

This sector plays a substantial role in the macroeconomic balance of the country.

The quintessential argument behind any serious rationalization over quantitative predictions on the Moroccan economy has been the importance of agricultural output. While it is clear that particular sector is of vital interest to the Moroccan people and businesses, I would like to submit some pieces of evidence that challenge the conventional wisdom surrounding it. Because only too often do our government officials, elected and otherwise, get away with their failure to create the right conditions for growth and job creation by hiding behind the Agriculture Smoke-screen. My criticism doesn’t apply to a particular government, it is merely an observation.

First off, Agriculture as a percentage of GDP is decreasing at a steady pace since independence. I took the liberty to generate the missing decade from the World Bank Data and then retrofit it back into the PWT dataset; since 1955, while Agricultural GDP grew 4.31% on average (in real terms per capita) its share of total GDP fell a modest – 0.17% on annual average over the period, decreasing from 23.7% in 1955, to 13.84% in 2011.

We are interested in looking into the effect of agricultural output on the aggregate business cycles: if indeed correlation was strong, as strong as, say that of domestic consumption, then the official line holds: agriculture matters, it influences Morocco’s economic performance, and has to be taken care of. However flawed the tax exemption is, it would make sense as a policy in broad principle: a tax-pristine economic sector doesn’t usually experience fiscally induced distortions, and the main thing our agricultural sector would benefit from is a smoothing of an all-too volatile cycle. On the other hand, if the agricultural output doesn’t exhibit strong correlation indicators with GDP and the other significant aggregates, then we can say with a great deal of certainty that agriculture, while retaining its importance for a significant part of Morocco’s labour force, does not hold sway over Morocco’s economic performances, and as such makes it even harder to justify some policies and plans for that particular sector.

Let us consider these moments where the economy departs from its long-term trend; as per definition, an economy is on the expansionary phase if its cycle is above the long-term trend:

. sum HP_y_1 if HP_y_1>0
    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      HP_y_1 |        30    .0627514    .0426686    .005383   .1696304

and in recession when below

. sum HP_y_1 if HP_y_1<0
    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      HP_y_1 |        27   -.0697238    .0409879  -.1399502  -.0107043

when below potential output, recessions tend to be a little less volatile and a little deeper. “Boom” periods, on the other hand, are prone to be more volatile but with a weaker growth figure in absolute value. but overall there is a great deal of symmetry. Is this however due to agricultural output? We know both cycles exhibit a correlation coefficient of .62 but on the other hand, we get:

. . sum HP_y_1 if   HP_y_g_1>0
    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      HP_y_1 |        29    .0419493    .0648962  -.0682606   .1696304
. . sum HP_y_1 if   HP_y_g_1<0
    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      HP_y_1 |        28   -.0434474    .0677846  -.1399502   .102021

When the agriculture sector is in trouble, so is total GDP (hence the positive coefficient of correlation) but one can notice the virtual symmetry in their dynamics – as though the effects of agricultural fluctuations are ‘locked’ into a tunnel: however agriculture fares, the projected fluctuations conditioned by its state on GDP are located between – 4.2% and + 4.3% deviation from steady state, which is still less volatile than the total aggregate itself. In fact, the correlation in cycles is weak whenever agricultural GDP is in recession: .29 vs .414 when it is expansionary. the symmetry doesn’t carry beyond cycle statistics, which confirms the initial assumption agriculture is not a drag on the aggregate economy.

To sum up:

1/ Agricultural output is more volatile than GDP – respectively .113 and .0785 (in standard deviation).

2/ AGDP and GDP are more correlated in periods of expansionary cycles than they are in times of recession.

3/ GDP is more volatile when AGDP is in recession, but the average recession has a smaller magnitude and volatility compared to the broader aggregate.

The Big Picture – Part 6

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on May 19, 2012

This should be the last of “the Big Picture” series. My computations have reached a point where further effort needs to be fed more reliable figures – and get paid handsomely for it.

All previous results assumed no government intervention in the economy; But just as the initial results did not factor in foreign trade, the gradual adjustment of the RBC model shows our laborious business cycles accounting gets better as we introduce new elements.

Now consider government expenditure to be financed by taxes levied on labour and capital. These taxes are levied on ‘net’ income, and are defined as follows:

tax_{labour} = \tau_w (1-\alpha) z_t \left[\frac{k_t}{h_t}\right]^\alpha

tax_{capital} = \tau_k. \alpha .z_t \left[\frac{h_t}{k_t}\right]^{1-\alpha} +1 - \delta

both \tau_w .\ \tau_k are proportional to wages and capital rent. In terms of quantitative fiscal policy, these amount to a total fiscal pressure of about 14% GDP. Government expenditure is then added up to the National Accounting identity: Y = C + G + I

where Consumption, Investment and General government expenditure make up GDP.

Government taxation in this particular case is optimal – and as such might not fit exactly the general framework of fiscal policy-making: these are fluctuating rates within specified steady-state values (\tau_w .\ \tau_k are not fixed) and they levy fiscal income on factors paid at their marginal productivity, a strong assumption very difficult to verify with the data at hand. However, these government wedges, while they do not account for government cycles, do explain a lot of the observed volatility in other Business Cycles components. The new comparison table yields:

HP Data     |s      |sj/sy |Corr(y,j)|
------------+-------+------+----------
Y_GDP        |0.0803|   1  |    1    |
------------+-------+------+----------
Consumption |0.07013|0.8734|  0.8215 |
------------+-------+------+----------
Investment  |0.22035|2.7441|  0.8369 |
------------+-------+------+----------
Capital     |0.09167|1.1416|  0.4448 |
------------+-------+------+----------
Government  |0.24127|3.0046|  0.4997 |
------------+-------+------+----------
Labour      |0.04256|0.5300| -0.8670 |
--------------------------------------
RBC         |s      |sj/sy |Corr(y,j)|
------------+-------+------+----------
Y_GDP       |0.0734 |   1  |    1    |
------------+-------+------+----------
Consumption |0.0592 |0,8065|  0.9842 |
------------+-------+------+----------
Capital     |0.0826 |1,1253|  0.5972 |
------------+-------+------+----------
Government  |0.0045 |0,0613| -0.7591 |
------------+-------+------+----------
Labour      |0.0250 |0,3405| -0.9462 |
--------------------------------------

Government wedges do a very good work actually: the distortionary effects of labour taxes for instance, account for much of their deviation from steady-state and correlation with output. Same goes for Capital, but not investment: while corporations are taxed on their operational margins -minus a few policy incentives- they do not seem to have a significant impact on their investment decision. the model’s shortcomings are relatively easy to explain: the only exogeneous shock incorporated in the model comes from foreign trade (trade balance) and model specification restraints somewhat capital accumulation; this explains why capital is more correlated to output in the model compared to actual data: other (significant) factors have not been taken into account.

While government wedges do quite well in explaining absolute and relative volatility (to output), they are pretty weak at explaining the intrinsic volatility of government expenditure, nor do they succeed in capturing the pro-cyclical nature of empirical public finances; the RBC model matches the theoretical framework of government expenditure – anti-cyclical and designed to smooth business cycles over- actual data however, seem to indicate a relatively weak positive correlation between government expenditure and Morocco’s business cycles. One way to account for this result is the strong assumption underlying government expenditure and tax receipts: these are set to be balanced over the long run; this means public debt as a budget policy designed to fund some of the government’s expenditure in smoothing cycles – especially in recession phases- is not as efficient as one might think – efficiency, in this case, is not to be measured for the quarters following the immediate expansionary policy, but as a result taken over a long period of time, such as the one the data is based on.

In addition to the introduction of public finances dynamics, the standard output function has been specified with two incorporated shocks: the trade balance has been added as a distinct component – and this explains a lot the increased output volatility – not only does foreign capital account for much of Morocco’s own capital accumulation, but it seems other factors embedded in it – say foreign imported technical expertise – give a powerful explanation as to how output fluctuates over time, and these foreign (exogeneous) factors can be expected to be downplayed due to the stationary specification of the balance of trade process. Furthermore, the optimal tax sequences \left\{ \tau_w .\ \tau_k \right\} are computed on the steady-state assumption that primary fiscal pressure does not go beyond 17.4% of GDP, in real terms; this means the longer a budget deviates upwards from that threshold, the longer agents (households and businesses alike) will adjust their own behaviour accordingly; in essence, any major fiscal policy cannot count on permanent effects – computations show only 72% of an initial policy decision carries its effect over one period -assumed in this case to be a year. This means that for a government to set a policy for the legislature, the measure in effect carries only 25.16% of its initial intensity by end of the 5th year. On the other hand, any cut to the corporate tax is likely to maintain its effect on capital accumulation at 93% on average over two years; these results are based on the auto-correlation results listed below:

Order       1       2       3       4       5       
Y        0.7227  0.5081  0.3686  0.2668  0.1944
C        0.8179  0.6436  0.5124  0.4110  0.3323
K        0.9667  0.8984  0.8194  0.7363  0.6544
H        0.7328  0.5944  0.4930  0.4095  0.3417
z        0.7676  0.5310  0.3758  0.2646  0.1865
tb       0.6361  0.4593  0.3219  0.2272  0.1601
tax_l    0.6362  0.4593  0.3220  0.2272  0.1601
tax_k    0.6362  0.4593  0.3220  0.2272  0.1601
G        0.6361  0.4593  0.3220  0.2272  0.1601

There was one major difficulty I kept stumbling upon: no matter how careful my coding was, I failed to produce satisfactory results as to the differentiated impulse responses triggered by exogeneous shocks, those “white noises” from the structural shocks z_t .\ \epsilon_t and tb_t .\ \upsilon_t functions. Other than that, the final results are pretty straightforward in view of the described methodology.

The source code I have compiled to get the results can be found below. MATLAB “Dynare” add-in is a very powerful language that needs to be downloaded (for free) and installed on the MATLAB directory and run via the simple command line dynare YourFile.mod (alternatively, GNU Octave can do as well)

\\declaration of variables mainly Output, Consumption, Capital, Labour and Government,
var y, c, k, h, g, z, tb, tax_l,tax_k;
varexo e, u;
\\structural parameters computed by means of calibration
parameters theta, alpha, gamma, delta, beta, tau, rho, sigmae, sigmau;
theta = 0.037;
alpha = 0.3414;
gamma = 0.3351763958;
delta = 0.029;
beta = 0.9198;
rho = 0.27234;
tau = 0.43244;
sigmae = 0.0678233;
sigmau = 0.0959883;
\\the model is computed by building a matrix of First Order Conditions that capture agent's decision rules
model;
c = gamma*(1-tax_l)*(1-alpha)*exp(z)*(k(-1)/h)^alpha;
z = rho*z(-1) + tau*tb(-1) + e(-1);
tb = rho*tb(-1) + tau*z(-1) + u(-1);
y = exp(z)*exp(tb)*k(-1)^alpha*h^(1-alpha);
k = exp(tb(-1))*(y-c)+(1-delta)*k(-1);
exp(tb)*c^(gamma*(1-theta)-1)*((1-gamma)*h)^((1-gamma)*(1-theta))=
beta*(exp(tb(+1))*c(+1)^(gamma*(1-theta)-1)*((1-gamma)*h(+1))^((1-gamma)*
(1-theta))*((1-tax_k)*alpha*exp(z(+1))*(h(+1)/k)^(1-alpha)+1-delta));
g = (tax_l*(1-alpha)*exp(z)*(k(-1)/h)^alpha)+(tax_k*(alpha*exp(z)*
(h/k(-1))^(1-alpha)+1-delta));
y = exp(tb)*g + c + k - (1-delta)*k(-1);
tax_l/tax_k = (1-alpha)/alpha;
end;
\\steady-state values computed by the same methodology proposed for calibration
initval;
g = 0.0726936349;
tax_l = 0.0324716235289365;
tax_k = 0.0324716235306143;
h = 0.2663385236;
y = 0.465686322;
k = 1.3684021321;
c = 0.4259362416;
tb = 0;
z = 0;
e = 0;
u = 0;
end;
\\simulated shocks from exogeneous "white noises"
shocks;
var e; stderr sigmae;
var u; stderr sigmau;
var e, u = sigmae*sigmau;
end;
stoch_simul;

The Big Picture – Part 5

Posted in Dismal Economics, Flash News, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on May 16, 2012

evidence shown on my last piece points out to foreign trade as a major factor in output cycles and its growth. The initial proposed model has therefore to be readjusted accordingly, through the TFP process, and the relation it bears with the Balance of Payments; and so:

\log z_t = \rho z_{t-1} + \tau bp_{t-1} + \epsilon_{t-1}

\log bp_t = \rho bp_{t-1} + \tau z_{t-1} + \upsilon_{t-1}

where \rho is the persistence parameters, and \tau the cross-persistence parameter that captures transmission shocks between TFP and balance of payment; both processes displays the following properties:

E(z_t) = \rho E(z_{t-1}) + \tau E(bp_{t-1}) + E(\epsilon_{t-1}) = 0

and that is so because the empirical data shows it: the long-run shows both the Balance of payments and the Solow Residuals converge to a zero.

var(z_t) = \rho^2 var(z_{t-1})+\tau^2 var(bp_{t-1})+ var(\epsilon_{t-1})+ 2 cov(z_{t-1},bp_{t-1})

equivalently,

E(bp_t) = \rho E(bp_{t-1}) + \tau E(z_{t-1}) + E(\upsilon_{t-1}) = 0

and

var(bp_t) = \rho^2 var(bp_{t-1})+\tau^2 var(z_{t-1})+ var(\upsilon_{t-1})+ 2 cov(z_{t-1},bp_{t-1})

Both parameters \rho and \tau are then estimated by computing the TFP residuals on HP-filtered data. Recall:

\log y_t = \alpha \log k_t + (1- \alpha) \log n_t + z_t

we also have: cov(z_{t-1},bp_{t-1}) = corr(z_{t-1},bp_{t-1})\sigma_{z}\sigma_{bp}

Balance of Payments and the Exchange Rate exhibit a strong positive correlation, starting from the mid 1970s.

The graph makes the case for the constructed balance of payments to capture the effects of international trade – starting from the mid 1970s, the discrepancies between Investment and Savings captured by the Balance of Payments, and the exchange rate with the Dollar have locked up in a strong positive co-movement; the exchange rate isn’t set arbitrarily: it has real impact on input cost, on growth projections and consumption across the board. We have now a good insight on how foreign trade impacts growth performance. (The data still does not incorporate government expenditure)

Computations on parameters \left( \rho .\ \tau .\ \sigma_{z} .\ \sigma_{bp} \right) yield:

we get:

\tau = .4324

\rho = .2723

we observe the condition for \left| \rho+\tau \right| < 1 is acquired, and the results might, at this point, explain the discrepancies pointed out earlier: the persistence parameter is significantly weaker as the Balance of Payment shocks are incorporated into the structural process before they get into the economy; we observe the variance-covariance matrix displays the following values:

Variables       e         u         
e            0.004600  0.006510
u            0.006510  0.009214

It makes sense, since these in turns carry part of the unobservable shocks in a closed-economy, and because foreign inflows of capital are critical to the national investment, and thus to output growth, the cross-persistence parameter is more significant; yet another piece of evidence that any sensible public policy to boost growth is NOT to shut down foreign trade (a gentle wink to the protectionist left-wingers out there). We do notice that Capital accumulation in Morocco relies heavily on foreign inflows, and by implication, output growth as well. Structural shocks, to that effect, are a kind of a buffer between exogeneous, unexpected shocks, and the economy: transitory shocks are captured by structural shocks rather than those attached to the

the results are very much in line with prediction on standard RBC, only this time numbers fit a lot better, as they show below. There are still some problems on the Labour side, and public finances’ effects on cycles are yet to be estimated; but so far, the picture looks great 🙂

   Data   |σ       |σj/σy  |Corr(y,j)|
----------+--------+-------+----------
Y_GDP     |0,08030 |1       |1       |
----------+--------+-------+---------+
Con       |0,07013 |0,87339|0,82150  |
----------+--------+-------+---------+
Capital   |0,09167 |1,14159|0,4448   |
----------+--------+-------+---------+
Investment|0,24127 |3,00463|0,83690  |
----------+--------+-------+---------+
Labour    |0,09806 |0,81888|-0.8670  |
----------+--------+-------+---------+
Government|0,22035 |2,74415|0,49970  |
--------------------------------------
    RBC     |σ      |σj/σy |Corr(y,j)|
------------+-------+------+----------
Y_GDP       |0,06596|   1  |    1    |
------------+-------+------+----------
Consumption |0,04715|0,7148|  0,5092 |
------------+-------+------+----------
Investment  |0,20460|3,1018|  0,8766 |
------------+-------+------+----------
Government  |         No Data        |
------------+-------+------+----------
Labour      |0,00002|0,0003|  0,0238 |
--------------------------------------
  New RBC   |σ      |σj/σy |Corr(y,j)|
------------+-------+------+----------
Y_GDP       |0,0631 |   1  |    1    |
------------+-------+------+----------
Consumption |0,0455 |0,721 |  0,9515 |
------------+-------+------+----------
Capital     |0,1268 |2,009 |  0,7060 |
------------+-------+------+----------
Government  |         No Data        |
------------+-------+------+----------
Labour      |0,0126 |0,199 |  0,7183 |
--------------------------------------