# The Moorish Wanderer

## 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
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)

## 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 |
--------------------------------------

## The Big Picture – Part 3

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on May 7, 2012

Looking back at the latest two posts, I must admit I had spent too much time trying to identify the deep parameters needed to build Morocco’s RBC model. But it was a blessing in disguise; indeed, when the standard methods of calibration are applied, the necessary structural parameters fit very well with the regressed/estimated results earlier; no harm done there.

This means a lot: calibrated parameters are usually constructed by means of steady state, and as far as academic modus operandi goes, there are no particular standard methods to follow (or in my case, by computing long-term trends for the variables of interest) – and the fact that econometric computations, however rudimentary and based upon a relatively small sample, tend to be vindicated by calibration method, does point out to the existence of some steady-state (that is yet to be determined) and the superiority of a long-term sample, compared to that of HCP’s forecast model.

The deep parameters’ vector encompasses the following values:

$\eta$ – time fraction allocated to labour activities : 1/3

$\alpha$ – Capital share output : .03414 (homogeneity of degree one is acquired, and Labour share is thus $1-\alpha$

$\theta$ – a measure for risk aversion : .0370

$\delta$ – depreciation rate of Capital (annual) : 2.905%

$\beta$ – household discount rate : .9198

$\rho$ – persistence of structural exogenous shocks: .923611

$\sigma$ – ‘white noise’ standard deviation : .00177

These figures are computed from stead-state identities:

1/$\alpha=\left[\frac{\delta+\frac{1}{\beta}-1}{\delta}\right]\frac{i_{lt}}{y_{lt}}$

2/$\theta=\frac{\delta+\hat{\beta}}{\delta}$ with $\beta=\frac{1}{1+\hat{\beta}}$

3/$\eta=\theta^{\alpha}$

4/$\phi=\frac{1}{1+\frac{2(1-\alpha)}{c_{lt}/y_{lt}}}$

Finally, the remaining figure to compute is $k_0$ which is derived from Capital motion law at steady state, with

$\frac{k_{lt}}{y_{lt}}=\frac{i_{lt}}{\delta y_{lt}}$

The subscript ‘lt’ refers to the steady-state proxy, i.e. long-term mean. As for the initial stock of capital (a figure nowhere to be found I am afraid) the idea is to use properties of the balanced growth path, with $y_0$ as the initial state for output, thus ensuring a ‘calibrated’ $k_0$

While these figures are not strictly equal to the estimates described before, they do fit in all of 95% Confidence Interval for each of their estimates, in fact they fit for all of them in the 99% CI. The simple difference being here that these parameters are fixed values, while estimates provided in the two last posts are in essence random variables, centred around the OLS estimates; it will be helpful in estimating the persistence factor of exogenous shocks. Indeed, the standard recipe to compute it is to consider it as the formula most able to capture the Solow Residual, defined such:

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

recall the first post for the log-linear argument; exogenous shocks are thus defined as AR(1) process, with a fixed term that denotes of long-term shocks;

$\log(z_t)=\rho\log(z_{t-1}) + (1-\rho)\log(z_{lt}) + \epsilon_{t-1}$

the next step is to compute $z_t$ just like all other aggregates with HP-filters, then regress the trend -i.e. $\log(z_{lt}$– on a index time to find $(1-\rho)$ which yields the following results:

      Source |       SS       df       MS              Number of obs =      62
-------------+------------------------------           F(  1,    60) = 2753.20
Model |  115.862298     1  115.862298           Prob > F      =  0.0000
Residual |  2.52497013    60  .042082836           R-squared     =  0.9787
Total |  118.387268    61  1.94077489           Root MSE      =  .20514
------------------------------------------------------------------------------
HP_z_t_sm_1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
index |    .076389   .0014558    52.47   0.000     .0734769    .0793011
_cons |   22.80177   .0527426   432.32   0.000     22.69627    22.90727
------------------------------------------------------------------------------

The reader can observe that the coefficient .076389 means parameter rho is therefore has a value of .923611. Furthermore, the model’s mean (MS) square residual also allows for ‘white noise’ estimate, a zero-centred normal distribution with $\sigma=.00177$

We propose the following system of identities to solve Morocco’s RBC:

Households maximize and smooth their utilities over time according to the following:

$U\left(c_t;1-h_t\right)=E\sum\limits_{0}^{\infty}\beta^t\left[\frac{c_t^\gamma(1-h_t)^{(1-\gamma)}}{1-\phi}\right]^{1-\phi}$

the function is maximized subject to the following constraints:

$k_{t+1}=i_t+(1-\delta)k_t$

$y_t=z_t k_t^\alpha n_t^{1-\alpha}$

$i_t=s_t+\exp(z_t)tb_t$

$tb_t$ refers to the trade balance, the aggregate explanation for discrepancies between domestic savings and actual investment.

(next piece will deal with a first set of simulation and comparison with HP-filtered data in the first post)