## The Big Picture – Part 6

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:

both 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 ( 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 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 and 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;

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