Capital Humano

This section uses the integration and cointegration properties of the data to infer the strength of the link between the relations explained in Section 5.3 as potential long-run equilibrium relations. First, the appropriate lag length is determined for each model based on the Schwarz (SC) and the Hannan-Quinn (H-Q) criteria. The suggested criteria vary in terms of the strength of the penalty associated with the increase in model parameters due to adding more lags. The test criteria for different values of lags denoted by ‘p’ are calculated and accordingly the value of p corresponding to the smallest value is chosen. The results of the lag length determination tests, reported in Appendix 5C, suggested p = 2 for all the models. The Lagrange Multiplier (LM) tests in each VAR (p) are further used to check for left-over residual autocorrelation in each VAR (p) model (Juselius, 2006, p.72). These tests seem to accept absence of autocorrelation in the VAR (2). Following Juselius (2006), both multivariate and univariate misspecification tests are then implemented to test for the statistical adequacy of the chosen VAR models. These include tests of residual autocorrelation, residual heteroscedasticity and normality tests. The multi- and uni-variate test results, presented in Appendix 5D, suggest that the models are adequately specified with p = 2.72 Therefore, the analyses are carried out with VAR(2).

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The Johansen cointegration rank tests based on the Bartlett corrected trace test and the maximum eigenvalue test are then conducted on the data to determine the rank for each model. Appendix 5E reports the estimated eigenvalues (λi), the trace test (Trace), the Bartlett corrected

trace tests (Trace*) with p-values in brackets, and the 95% quantile from the asymptotic tables (Q.95), all of which are generated in CATS software. The trace tests analyses have been

corrected for small sample size.73 _{Statistically significant, the Bartlett corrected trace test results}

suggest the choice of r = 3 for both models. Appendix 5F reports the moduli of the roots of the companion matrix where the rank is chosen so that the largest unrestricted root is far from a unit root (i.e. it has modulus less than one).74 The findings are further confirmed by the graphs of the cointegration relations shown in in Figures 5G1-5G2 in Appendix 5G.

With estimation based on such a long time-series of data in a country that has undergone substantial political changes, it is crucial to test the stability of the model parameters. Therefore, the statistical adequacy of the models is investigated by conducting recursive stability tests, beginning with a sample of 1977-2003 and then adding observations until the full sample size is reached. The tests are based on the log-transformed eigenvalues demonstrated in Figures 5H1- 5H2 Appendix 5H, as these tests provide more detailed information about the constancy of the individual cointegration relations.75 The findings could suggest that there is no significant change in the model parameters over the period under study. Yet, it must be noted that the sample is small and not many observations are left for testing the constancy of the parameters.

Shown in Appendix 5I, the test results for a unit vector in β (variables’ stationarity), suggest that the variables are non-stationary, hence supporting the treatment of the main variables as being I(1). Appendix 5J presents tables from CATS’ short-run parameters output for weakly exogenous/fixed variables, time t-1 and t-2, dummy variables and constant, with their associated t-values. For each equation, Figures 5K1-K2 in Appendix 5K plot the residuals including the fitted and the actual values of Δxit, the residuals scaled by their standard deviation,

autocorrelations of the residuals and the histogram. On the whole, the graphs of the residuals

73 _{Juselius (2006) argues that for moderately-sized typical macro-economic samples (50-70 observations), the}

corrections can be substantial. This is because for a small sample, the asymptotic distributions often do not tend to be good approximations to the true distributions and using asymptotic tables can lead to size and power distortions.

74 _{It must be noted that the characteristic roots are reported without confidence bands and the discussion as whether}

a root is big or not is only indicative.

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illustrate that the estimated values capture the dynamic responses and follow the actual values reasonably closely.

Juselius (2006) suggests transforming the long-run matrix Π = αβ' by a non-singular r x r matrix Q as follows: Π = αQQ'β' = α̃β̃', where α̃ = αQ and β̃ = βQ'-1_{. The matrix Q imposes a total of}

r(r – 1) just-identifying restrictions on β and (r – 1) just-identifying restrictions on each βi.76 In

order to identify long-run structures, one approach is to first impose just-identifying restrictions on β vectors and then imposing over-identifying restrictions by setting the least significant coefficients in the just-identified model to zero one after another. The just-identifying restrictions do not change the likelihood function, whereas the over-identifying restrictions constrain the parameter space and change the likelihood function and therefore are testable. Another approach is to test sets of irreducible relations. This study takes the latter approach. The over-identification restriction tests are based on the log-likelihood ratio (LR) test procedures detailed in Juselius (2006, pp.209-12).

Accordingly, the cointegrating structures of the steady-state relations are formulated. In all of the models, further to equation (4.11ˈ), the first relation (β1) is normalized on the investment variable. Tables 5.2 and 5.3 illustrate the results of the over-identified cointegrating structures of the theoretically motivated relations in the data, where the reported over-identifying restrictions in all of the models are not rejected based on the p-values associated with the LR test statistics reported in the tables. Respectively, the β and α coefficients correspond to the long-run structures and the estimated adjustment dynamics. The statistically significant β estimates are in bold face to distinguish them from the α coefficients.77 _{Section 5.5.2 estimates the baseline}

model of investment incorporated with symmetric measures of oil for the Iranian economy.

76 _{The hypotheses tested are of the form β}c _{= (H}

1φ1, ψ1, ψ2) and implies that the test is for whether a single relation

is on sp(β). βc _{is the constrained cointegrating vector, H}

i, i = 1, … , r, are the design matrices of the long-run

structure of dimension p1 x s1, φi are si x 1 matrices of unrestricted coefficients, and ψ1 and ψ2 are the unrestricted

cointegration vectors. The cointegrating relationships which are not rejected are chosen for further identification by imposing just- and over-identified restrictions on them.

77 _{In this approach, for the just- and over-identified structures, the degree of freedom is computed employing the}

following formula, ν = ∑r

i=1 (mi – r + 1), where r is the cointegration rank and mi is the number of restrictions on βi

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