# The Moorish Wanderer

## Growth and Technological Change

Posted in Dismal Economics, Morocco, Read & Heard by Zouhair ABH on November 16, 2012

Capital accumulation exhibits significantly low levels of growth compared to output growth, and remarkably enough, TFP.

For all its simplistic setting, the 1957 Solow paper provides enough of a case to support the following claim: accumulation of physical capital per capita does not create growth. And as far as the domestic economy goes, this is what comes out:

   Y  |   H   |   K  | TFP
------+-------+------+-------
1.40% | 0.07% | 0.22% | 0.83%
| 5.12% | 15.68%| 59.38%

(Quarterly growth. Y: Output, H: Labour, K: Capital, TFP: Solow Residual)

Over the past half a century, capital accumulation accounted for only 15.7% of the average GDP growth in the Moroccan economy, three times as much as demographic growth (actually, growth in the labour force) but most of the observed growth (in real terms) comes from TFP, Total Factor Productivity, or commonly known as ‘The Solow Residual’.

TFP accounts for almost 60% of the long-run average GDP growth. It does a lot more than that: it is more aligned with GDP growth, more correlated, and most importantly, a 1% increase in the Solow residual accounts for .96% in output growth, even as 1% in Capital growth accounts for only .08% in output What can the policy-maker learn from this very simple yet robust model? First, that accelerated accumulation of capital is unlikely to get output to grow faster. In the universe of our government’s commitment to get the 5.5% growth over their legislature, they need to generate a mind-boggling 23% increase in gross capital formation – i.e. an annual additional investment of 9.42 Bn dirhams above the current trend.

Impulse response graph to a 1%, one-period increase in productivity. Capital (k) decreases 4.43% the first period, and recovers only 60% of its initial return 5 years after the shock. Investment (x) on the other hand, increases substantially, even if it does not exhibit comparable strong persistence.

The findings are easy to sum up: what drives most of economic growth is not physical capital accumulation, but rather those things policy makers in Morocco care little about: research & development, labour and capital efficiency (a sad story I can recall from a lecturer in my Alma Mater, about a project of diesel-powered desalt water plant in Laayun, a wasteful process the Moroccan officials were reportedly proud of) and most important of all, institutional changes. These of course do not refer exclusively to political reforms, it encompasses labour market regulation and rigidities, rule of law and enforcement of contracts.

What is the real effect of this ‘technological change?’ first, a 1% sustained increase in innovation (such as it is) over 4 periods (or one year) results in boosting investment productivity 4.24%, with spillover effects going up to 3.2% on average over a 5-year period. Just think of it: this is sustained investment over just the first year in office. In budget terms, this means a relatively low investment of 50 Million dirhams in efficiency programs can increase investment efficiency by 4.24%, hence contributing an additional 12.5 Bn dirhams a year, a net contribution to growth by 360 basis points in one year – that is, an additional 3 Bn in added value, jobs and economic activity.

In fact, the accrued effect of  a one-year investment produce a marginal effect of almost one percentage point of GDP growth. And it is only right GDP grows thanks to technological change – because these resources when allocated to capital accumulation have a much lower return (one observes in the second graph capital accumulation declines by similar amounts (4.43% the first period). I argue this provides good evidence that accumulated investment for its own sake (which is about anything when it comes to some of the ongoing Grand Design workshops)

One last thing; since the mid-1970s, a particular component I have not described here accounted for the remaining 20% in real growth: even the impact of foreign trade (or perhaps just foreign productivity spillover effects) generates more growth than capital accumulation.

Technical note:

See Cooley & Prescott for the model used to generate the IRF graphs. Steady-state values have been used to calibrate the deep parameters.

## 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
-------------+------------------------------           Adj R-squared =  0.9783
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)