# The Moorish Wanderer

## The Big Picture – Part 2

Consumption smoothing is a reality in view of empirical data, and in this particular occasion, HCP’s own PRESIMO model is at faults in terms of specification and reliability on estimated coefficients, and the model specification themselves can be gainsaid as to their robustness.

Consider their proposed model for household consumption:

$\log(c_t)=.73\log(rw_t)+.87\log\left[\frac{rw_{t-1}}{c_{t-1}}\right]-.84\left[\frac{u_t}{l+u_t}\right]-0,82icv_t-.01(r_{t_0}-icv_t)$

La variable la plus importante dans la détermination de la consommation est le revenu disponible des ménages. Dans le modèle, cette variable est endogène et résulte d’un ensemble de composantes : la masse salariale, l’excédent brut d’exploitation (EBE), les revenus de la propriété, les impôts sur les revenus, les transferts courants, les prestations sociales et les cotisations sociales.

The reported t-values indicate a pretty large standard deviation attached to each of the computed coefficients in this formula (just divide the estimated coefficients by their corresponding t-values below) Not to mention the fact that inflation and short-term interest rates tend to make the model dependent on contingent data, hence the relatively high R², though it comes at the expenses of a long-term, structural explanation of how households smooth their consumption across time and variations in income.

Consumption smoothing can be traced back to the consumption cycle – whose absolute and relative to GDP’s volatility are both second only to labour work. The proposed alternative does away with inflation and short-term interest rates, as well as unemployment; The idea behind it is can be broken down into two sub-parts:

– long-term trends: inflation and distortionary interest rates do not stay for long, and are eventually factored in by households. The fact that there is little (genuine) concern over subsidies provided by the Compensation Fund, as well as the short-lived effects of Bank Al Maghrib’s decision to cut its policy rate by 25bps are two illustrative examples of the simple intuition behind the idea: households rationalize a lot more than what they let on, and decisions of short-term consequences (including inflation and unexpected shifts in monetary policy) are eventually factored in, and their effect tends to fade away as time goes by. And in this particular issue, we are interested in real consumption behaviour over a very long period of time. Finally, because most of the aggregates are expressed in real terms,

– unemployment is a bit more difficult to gauge from aggregate macroeconomic data; furthermore, because the model is based on household units instead of individuals, there is a mechanism of risk-sharing that alleviates the effects of unemployment and the attached uncertainty to it.

We therefore consider the following model:

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

where: $\beta$: the discount time factor and $\gamma$: time fraction allocated to leisure.

While the formula might look baffling, it displays interesting computational properties in terms of inter-temporal behaviour – the trade-offs households face in deciding their present and immediate future consumption; for $\phi = 1$ we get:

$E\sum\limits_{0}^{\infty}\beta^t\left[\gamma\log(c_t)+(1-\gamma)(1-h_t)\right]$

(the ‘curvature’ of the proposed utility function denotes of the ‘intensity’ of inter-temporal arbitrage)

PWT provides dataset with consumption per capita, GDP per capita as well as GDP per effective worker; Consumption per capita is then computed back into an aggregate of Consumption per household, so as to preclude uncertainty around unemployment. Worked hours are then computed on the basis of the 40-hours, as the result is based on Moroccan labour laws.

When computed, First Order Conditions on that utility function yield the following, which is then regressed to provide estimates for the parameters described above:

. reg C k_h
Source |       SS       df       MS              Number of obs =      56
-------------+------------------------------           F(  1,    54) =    1.48
Model |  .000169425     1  .000169425           Prob > F      =  0.2283
Residual |  .006162348    54  .000114118           R-squared     =  0.0268
Total |  .006331773    55  .000115123           Root MSE      =  .01068
------------------------------------------------------------------------------
C |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
k_h |    .247134   .2028243     1.22   0.228    -.1595042    .6537721
_cons |   .9015001   .0882337    10.22   0.000     .7246021    1.078398
------------------------------------------------------------------------------

with: $C=\frac{c_{t+1}}{c_{t}}$
$k_h= \frac{\beta}{1-\gamma}\left[\alpha\left(\frac{k}{h}\right)^{\alpha-1}+1-\delta\right]$
Households’ own $\beta_t$ is therefore .9015 which does square with estimates from academic (and a lot more serious) papers.

These deep (structural) parameters are now all identified, next step is to build Morocco’s RBC model.