distribution of the residual term. These were therefore added to the equation as dummy variables. It is not clear whether these can be justified as useful explanatory variables or not: neither the PEFA reports nor IMF reports describe policies or events in the context of compositional expenditure deviations.

The Jarque-Bera test fails to reject the null hypothesis of a normally distributed error term when the two dummy variables are included. The null hypothesis of no heteroskedasticity is not rejected by White’s test. The Ramsey RESET test, however, does reject the null of no mis-specification using squared fitted values of the dependent variable.

One possible solution to the RESET test outcome is to substitute a non-linear relationship between _fb_ and | _e_ | for the hypothesized linear relationship found in 11b. This is motivated by the idea that it might become progressively more difficult to increase the share of ministries absorbing a shock, even though the demand to do so would increase as the strength of the shock increased. This might occur because political and/or administrative frictions increase as the number of ministries involved rises. To test this idea, a number of alternatives were tested: _e_<sup>2</sup> , | _e_ |<sup>0.5</sup> and _ln_ | _e_ |. All were found to be acceptable substitutes in terms of statistical significance but only the latter was found to cure the RESET problem. The result is equation 11c in Table 12.

**<u>Table 12—Fraction of Budget Accurately Spent,</u>** **_<u>fb</u>_**

||<br>**Equation **|<br>**11b**|<br>**Equatio **|<br>**n 11c**|**Equatio **|**n 11d**|
|---|---|---|---|---|---|---|
||**Coeff.**|**Coeff.**|**Coeff.**|**Prob. **|**Coeff.**|**Prob. **|
||**6**|**7**|**8**|**9**|**10**|**11**|
|_Constant_|20.144|**0.007**|25.978|**0.001**|-2.453|0.741|
|Aggregate Deviations, |_e_||-0.741|**0.000**|..|**..**|..|..|
|Aggregate Deviations,_ln_|_e_||..|**..**|-6.062|**0.000**|..|..|
|Aggregate Deviations,_ln_|_e_| when_e_< 0|..|**..**|..|**..**|-5.365|**0.000**|
|Aggregate Deviations,_ln_|_e_| when_e_> 0|..|**..**|..|**..**|-5.883|**0.000**|
|_H01 FCTN_ETHN_|-0.224|**0.000**|-0.202|**0.000**|-0.215|**0.000**|
|_H05 MPP_|0.189|**0.000**|0.138|**0.010**|0.142|**0.008**|
|_H08 PEFA_|9.292|**0.001 **|8.471|**0.002 **|9.495|**0.001 **|
|Burundi 2005|49.740|**0.000**|49.233|**0.000**|48.476|**0.000**|
|Uganda 2006-07|51.093|**0.000**|51.891|**0.000**|50.319|**0.000**|
|Observations|144||144||144||
|R-squared|0.479||0.505||0.512||
|Adjusted R-squared|0.456||0.484||0.487||
|S.E. of regression|13.110||12.769||12.725||
|Sum squared resid|23,55||22,336||22,023||
|Log likelihood|-571||-567||-566||
|F-statistic|20.949|**0.000**|23.323|**0.000**|20.404|**0.000**|
|Normal error term 1/|**0.752**||**0.518**||**0.730**||
|Heteroskedasticity Test 2/|**0.849**||**0.636**||**0.429**||
|Omitted VariableTest 3/|0.001||**0.426**||**0.593**||

1. Jarque-Bera probability.

2. White n∙R<sup>2</sup> probability (without cross terms).

3. Ramsey RESET F-statistic probability (1 term).

The results reject most of the hypothesized relationships but those included in equation 11c are all robust and conform to expectations. Overall, the fraction of budget heads that are accurately spent _fb_ tends to fall as aggregate expenditure deviations move away from zero in either direction. The rate of decline slows as aggregate deviations move further away from zero. Equation 11d shows there is little to be gained by dividing aggregate expenditure deviations into negative and positive observations: the coefficients suggest the response is essentially symmetrical. This, of course, may not be the case within specific countries across time.

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