Back Matter

References

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1/

The paper was completed while the author was in the Middle Eastern Department.

2/

I am thankful, without implication, for discussions with and comments from M. El-Erian, B. Short, A. Furtado, and K. Wajid

1/

The assumption that the velocities of the underground and formal economies are the same is a strong assumption. There is no theoretical or empirical consensus, however, as to which velocity is higher if they differ.

2/

For the purpose of this paper it is more appropriate to use the currency to bank deposits ratio, rather than M2 as in Tanzi’s model, since the model is attempting to capture the effects of the independent variables on the public’s decision regarding their portfolio choice of currency vis-a-vis non-currency forms of money.

1/

Taxes that are difficult to evade such as, surcharges, property and motor vehicle taxes were excluded.

1/

D-F t-statistic for Dif and GDf (both differenced once) are significant at 1 percent and 5 percent respectively.

1/

For complete review of the cointegration technique see Granger (1986).

1/

Since the data in this paper is annual, the long term is defined to cover the whole sample period while short term is defined in limited number of years.

1/

A statistically significant error term could be interpreted as an evidence of causality (Granger (1988, p.203)).

2/

as follow: First, each series is regressed on its own lagged values and for every lag structure the corresponding FPE is calculated using the following formula:

FPEm=T+m+1Tm1QmT,(1)

where (T) is the number of observations, (m) is the order of lags varying from 1 to M, and Qm is the associated sum of squared residuals. The value of m, such as ∗, that minimizes FPE is the optimum number of lags for the variable. In the second step, each series is set as the controlled variable, with the order of lags set at ∗, and the other series is treated as the manipulated variable, with the order of lags n varying from 0 to N. The corresponding two dimensional FPE is calculated for each lag structure:

FPEm,n=T+m*+n+2Tm*n2Qm*,nT,(2)

the number of lags of the second series is chosen at the value of n, such as ∗, that minimizes FPE(m, n). If FPE(∗, ∗) FPE(∗) then causality is established.

1/

The following F test is used to test the significance of causality results:

F=(SSEcSSEu)/nSSEu/(T(m*+n*+2))(1)

where SSEc is the sum of squared residuals in the constrained equation, and the SSEu is the sum of squared residuals in the unconstrained equation.

1/

These conclusions pertain only to fiscal policy and UE relation and do not exclude other important measures such as liberalization and market oneness.

2/

No significant short term relations between private investment and either the formal output or the underground output were detected, therefore, the results of the tests on long term relations only are reported.

1/

These results could be a factor contributing to the anomalies detected in the private investment behavior in Pakistan.

The Underground Economy: Estimation, and Economic and Policy Implications: The Case of Pakistan
Author: Mr. Ghiath Shabsigh