Supplemental Fiscal Budget and Capita Gross Domestic Product

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Introduction

The government of developing nation X is prepared to allocate $2 billion in support of policy measures to grow per capita Gross Domestic Product (GDP) in the medium term, over a fifteen-year period. The two policy measures under scrutiny:

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  1. devote the earmarked funding to raising the secondary school enrolment rate (the percentage of the secondary school age population) from 55% to 61% in the same time span; or
  2. emergency loans for the banking sector to forestall a drastic drop in the ratio of Private Credit by Deposit Money Banks and Other Financial Institutions to GDP to 0.38 versus 0.52 currently.

For the rest of this paper, the task is to employ an empirical model to test which of the two policy measures will enable country X, ceteris paribus, to attain greater appreciation in per-capita GDP.

Data Transformations

Item 1

The compiled data is shown in Table 1.

Table 1: Compilation of Logged and Calculated Data

X country dlypc lypc90 lseced govgdp openk infl credit
1 Algeria 0.169 8.578 2.434 10.845 73.969 0.136 0.402
2 Australia. 0.391 10.052 3.570 13.462 28.849 0.279 0.946
3 Bangladesh 0.293 7.388 1.386 8.177 17.809 -0.117 0.213
4 Belgium 0.257 10.109 3.694 14.844 124.592 0.490 0.348
5 Brazil. 0.142 8.963 2.398 21.340 13.395 0.378 0.240
6 Burkina Faso 0.332 6.831 0.000 38.366 59.154 0.242 0.175
7 Cameroon -0.049 7.905 1.099 10.672 30.563 0.325 0.275
8 Canada 0.304 10.148 4.551 15.207 49.940 0.175 0.766
9 Chile. 0.675 9.064 3.045 16.175 47.405 0.056 0.469
10 China 1.212 7.565 1.065 20.266 23.820 -0.268 0.864
11 Cote d’Ivoire -0.222 7.969 12.738 63.446 0.372 0.402
12 Ecuador 0.164 8.494 2.996 21.280 41.555 -0.607 0.122
13 Egypt 0.375 8.187 2.766 7.409 62.326 -0.114 0.279
14 Ethiopia 0.113 6.757 0.000 18.382 27.949 -0.181 0.231
15 France. 0.196 10.071 3.679 16.863 32.711 0.467 0.916
16 Germany 0.183 10.110 3.523 12.017 40.659 0.487 0.934
17 Ghana 0.195 7.138 0.336 18.116 58.882 -0.399 0.047
18 Greece 0.403 9.742 3.584 14.127 36.714 0.489 0.346
19 Hungary 0.349 9.345 2.639 27.649 36.516 0.233 0.449
20 India 0.520 7.602 1.792 28.288 17.046 -0.132 0.256
21 Indonesia. 0.418 8.076 2.219 18.323 46.589 -0.238 0.368
22 Iran 0.512 8.647 2.303 13.883 75.757 1.137 0.287
23 Italy 0.182 10.051 3.466 13.320 42.577 0.574 0.481
24 Japan 0.121 10.181 3.388 10.712 16.859 0.384 1.916
25 Kenya -0.022 7.631 0.470 8.405 43.024 -0.194 0.298
26 Madagascar -0.217 6.977 1.131 12.085 57.227 -0.159 0.147
27 Malawi 0.232 6.841 -0.511 6.724 55.696 0.144 0.126
28 Malaysia 0.672 9.038 1.974 13.874 139.834 -0.141 0.670
29 Mali 0.354 6.781 -0.511 19.816 45.729 0.445 0.124
30 Morocco 0.124 8.412 2.398 10.704 44.929 0.294 0.133
31 Nepal. 0.260 7.282 1.649 16.316 31.530 -0.087 0.117
32 Netherlands 0.282 10.111 17.613 78.337 0.456
33 Nigeria 0.301 7.200 1.386 7.017 56.439 -0.933 0.119
34 Pakistan 0.298 7.794 1.065 18.531 32.088 -0.091 0.237
35 Peru. 0.354 8.300 3.401 12.710 24.542 0.697 0.042
36 Philippines 0.182 8.127 3.332 13.531 74.321 -0.085 0.196
37 Poland 0.566 8.881 3.077 20.195 27.716 -0.423 0.016
38 Saudi Arabia. -0.083 10.022 2.451 17.739 79.725 -0.238 0.638
39 South Africa 0.194 8.977 2.549 22.266 38.403 0.444 0.836
40 South Korea 0.616 9.385 3.653 10.157 32.559 0.290 0.904
41 Spain 0.422 9.858 3.603 11.871 27.621 0.646 0.751
42 Sri Lanka 0.525 8.056 1.526 23.417 54.796 -0.037 0.177
43 Sudan 0.718 6.863 1.099 6.409 29.332 1.138 0.059
44 Syria 0.357 7.505 2.901 23.836 71.297 -0.079 0.070
45 Thailand 0.472 8.595 2.944 11.931 90.503 0.072 0.724
46 Turkey. 0.285 8.588 2.573 15.270 24.631 0.411 0.131
47 Uganda 0.456 6.607 0.000 32.611 27.076 -0.832 0.024
48 UK 0.331 9.987 3.408 16.479 36.968 0.569 1.130
49 Venezuela 0.078 9.225 3.367 21.964 46.470 -0.021 0.231
50 Zimbabwe -0.791 8.463 1.649 13.315 56.761 -1.471 0.197

The Empirical Model and Tests of Hypotheses

The result of the specified model based on the calculated coefficients in Table 2 (below) is as follows:

dlypci = β1 + β2lypc90i + β3lsecedi + β4govgdpi + β5openi + β6infli + β7crediti + ui

dlypci = 1.59 – 0.92 (lypc90) + 0.58 (lseced) + 0.26 (govgdp)+ 0.10 (open)+ 0.38 (infl)+ 0.39 (credit)

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Table 2: Calculated Coefficients

Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B
B Std. Error Beta t Sig. Lower Bound Upper Bound
(Constant) 1.594 0.558 2.859 0.007 0.468 2.720
Ln PCI 1990 -0.231 0.084 -0.915 -2.749 0.009 -0.400 -0.061
Ln Secondary enrolment 1990 0.129 0.062 0.577 2.074 0.044 0.003 0.255
Govt share real PC GDP 1990 0.011 0.006 0.257 1.849 0.072 -0.001 0.023
Openness of the economy 0.001 0.002 0.095 0.686 0.496 -0.002 0.004
Inflation rate 1985 to 1990 0.227 0.086 0.383 2.640 0.012 0.053 0.401
Ratio private credit to GDP 1990 0.297 0.146 0.390 2.036 0.048 0.002 0.591

a. Dependent Variable: PCI ch 1990 to 2005

Item 2i

Table 3 (below) presents the ANOVA results for the model as a whole and therefore constitutes a test of the hypotheses H0:b2=b3=b4=b5=b6=b7=0 against H1:bj=0. The F value is so high as to yield a significance statistic p < 0.05. This means the non-zero beta coefficients could have occurred by chance alone perhaps three times in a hundred country data compilations. One must therefore reject the null hypothesis.

Table 3

ANOVAb
Sum of Squares df Mean Square F Sig.
Regression 1.047 6 0.174 2.561 0.03365
Residual 2.793 41 0.068
Total 3.840 47

a. Predictors: (Constant), Ratio private credit to GDP 1990, Openness of the economy, Govt share real PC GDP 1990, Inflation rate 1985 to 1990, Ln Secondary enrolment 1990, Ln PCI 1990

b. Dependent Variable: PCI ch 1990 to 2005

Item 2ii

When each of the independent variables is tested singly, the result for the variable lypc90 (the log transformation of per-capita GDP in 1990 for all countries involved in the analysis) is that β2 rises from -0.915 in the multiple-regression model to -0.036. However, the t test associated with this beta coefficient is so low (-0.25) that the significance statistic p = 0.81 fails the minimum hurdle of a 95% confidence level. The outcome for the single-IV hypothesis test (Table 4 overleaf) is at the same unsatisfactory level. The F value for β2 is so low that this result could have been obtained roughly once in every five times a random selection of nations is compiled. This means that we cannot reject the null hypothesis. The log transformation of per-capita GDP in 1990 does not, by itself, predict the rise from 1990 to 2005 embodied by the logged value dlypc.

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Table 4: Hypothesis Test Result for β2

ANOVAb
Model Sum of Squares df Mean Square F Sig.
1 Regression .005 1 .005 .062 .805a
Residual 4.096 48 .085
Total 4.101 49
a. Predictors: (Constant), Ln PCI 1990
b. Dependent Variable: PCI ch 1990 to 2005

Item 2iii

Performing the same single-IV test with the variable seced (the proportion of the secondary school age population enrolled in 1990), one finds that the value for β3 drops from 0.577 in the multiple-regression model to 0.052. The t test associated with this beta coefficient is so low (0.35) that the significance statistic p = 0.73 also fails the minimum hurdle of a 95% confidence level. The outcome for the single-IV hypothesis test (Table 5 below) is also just as dismal. The F value for β3 is so low that this result could have been obtained roughly once in four times a random selection of nations is compiled. This means that once again, we cannot reject the null hypothesis. The log transformation of secondary enrolment rate as of 1990 does not, by itself, predict the rise from 1990 to 2005 embodied by the logged value dlypc.

Table 5: Hypothesis Test for Logged SECED

ANOVAb
Sum of Squares df Mean Square F Sig.
Regression 0.010 1 0.010 0.122 0.728
Residual 3.830 46 0.083
Total 3.840 47

a. Predictors: (Constant), Ln Secondary enrolment 1990

b. Dependent Variable: PCI ch 1990 to 2005

Item 2iv

Performing the same single-IV test with the variable credit (ratio of private credit by deposit money banks and other financial institutions to GDP in 1990) and on a less stringent 90% confidence level, one finds that the value for β7 drops from 0.390 in the multiple-regression model to just 0.109. The t test associated with this beta coefficient is so low (0.76) that the significance statistic p = 0.45 is virtually the same as even odds, the classic case of the random-outcome coin toss. The outcome for the single-IV hypothesis test (Table 6 below) is also just as dismal. The F value for β7 is so low that this result could have been obtained virtually every other time a random selection of nations is compiled. Once again, we cannot reject the null hypothesis. The ratio of private-sector credit to local GDP as of 1990 does not, by itself, reliably predict the rise from 1990 to 2005 embodied by the logged value dlypc.

Table 6: Hypothesis Test for Ratio of Private-Sector Credit to GDP as of 1990

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ANOVAb
Sum of Squares df Mean Square F Sig.
Regression 0.049 1 0.049 0.570 0.454
Residual 4.052 47 0.086
Total 4.101 48

a. Predictors: (Constant), Ratio private credit to GDP 1990

b. Dependent Variable: PCI ch 1990 to 2005

Item 3: Implications for Allocation of $2 Billion According to the Base Empirical Model

All other macroeconomic and political factors held constant, allocating the new money to supporting private loan activity has more immediate, far-reaching and significant impact on per-capita incomes.

Since the “stimulus funding” of $2 billion can go one way or the other, we first of all set aside the credit variable, re-specify the empirical model as shown below, recompute and input average values for the five known macroeconomic variables…

dlypci = β1 + β2lypc90i + β3lsecedi + β4govgdpi + β5openi + β6infli + β7crediti + ui

dlypci = 1.01 – 0.515 (lypc90) + 0.408 (lseced) + 0.222 (govgdp)+ 0.044 (open)+ 0.394 (infl)

dlypci = 1.01 – 0.515 (8.49) + 0.408 (0.61) + 0.222 (16.14)+ 0.044 (47.93)+ 0.394 (0.1)

Note that the value for SECED has been inputted as the goal of 61% of the applicable secondary-age population.

Assuming that the new funding goes to classrooms and salaries for new teachers and that the capacity to accommodate a 6 percentage point increase in secondary school enrolment is in place right when the regular school term opens in year 1, the result would be a mean rise of 2.62% in per-capita GDP every five years. Over a 15-year time span, a developing nation that made the special, one-time investment in public education might therefore expect a cumulative 10.5 percent gain in population-adjusted income. However, this model explains just 8% of the variance in the expansion of per-capita income over a 15-year span.

Allocating the money to prevent the collapse of private-sector credit means re-specifying the model by replacing seced with credit. The recalculated model is as follows:

dlypci = 0.925 – 0.40 (lypc90) + 0.235 (govgdp)+ 0.12 (open)+ 0.39 (infl) +.33 (crediti)

dlypci = 0.925 – 0.40 (0.849) + 0.235 (16.14)+ 0.12 (47.93)+ 0.39 (0.1) +.33 (0.405)

In point of explaining a marginally higher proportion of total variance (9.4 %), the diversion of funds to sustaining private credit activity looks better. All other things equal, it is likely that a fresh infusion of $2 billion in private-sector credit will raise the available stock of loans and investments, spur jobs creation and generate demand for both capital and consumption goods. Hence, it is possible to foresee annual gains in per-capita GDP in the order of 2% and, for the 15-year period targeted, around 30.9%.

The Diagnostic Tests

The test of the linearity assumption between Y (dlypci ) the two main IVs is best visualized by plotting (Figures 1 and 2 overleaf). A positive linear relationship exists though it is rather weak in both cases (unadjusted R2 ≈ 9%) and the spread around the mean of credit is wide.

Proceeding to the three other independent variables (Figures 3 to 5 below), one discerns that the linear relationship is weakest for openness (unadjusted R2 ≈ 1%). Nonetheless, one may assert that the linearity assumption is satisfied for all βi.

A Plot of the Linear Relationship between Seced and 15-Year Change in Per-Capita GDP
Figure 1: A Plot of the Linear Relationship between Seced and 15-Year Change in Per-Capita GDP.
Linear Relationship between Private Credit Ratio to GDP and 15-Year Change in Per-Capita GDP
Figure 2: Linear Relationship between Private Credit Ratio to GDP and 15-Year Change in Per-Capita GDP.

Plot of the Linear Relationship: Government Share of Real GDP Per Capita in 1990 and 15-Year Change in Per-Capita GDP
Figure 3: Plot of the Linear Relationship: Government Share of Real GDP Per Capita in 1990 and 15-Year Change in Per-Capita GDP.

Plot of the Linear Relationship: Openness in 1990 and 15-Year Change in Per-Capita GDP
Figure 4: Plot of the Linear Relationship: Openness in 1990 and 15-Year Change in Per-Capita GDP.

Plot of the Linear Relationship: Five-Year Inflation 1985 to 1990 and 15-Year Change in Per-Capita GDP
Figure 5: Plot of the Linear Relationship: Five-Year Inflation 1985 to 1990 and 15-Year Change in Per-Capita GDP.

On a basic level, the homoscedasticity assumption is satisfied by the fact that all the variables are continuous, either interval or ratio. This holds even when dummy variables are employed (see section 5 below) so long as these are done for the independent variables.

Besides simple visualization with boxplots, the classic method for testing homoscedasticity rests Levene’s statistic for the test of homogeneity of variances. For convenience, the dependent and key independent variables are categorized into quartiles (see Table 7 below). Table 8 then shows that:

  • For the dependent variable, variance is narrow in the middle of the distribution but is wider at both upper and lower extremes of the distribution.

Table 7: The Quartiles

Statistics
PCI ch 1990 to 2005 Ln Secondary enrolment 1990 Ratio private credit to GDP 1990
N Valid 50 48 49
Missing 0 2 1
Variance .084 1.632 .138
Percentiles 25 .16775 1.19475 .1320
50 .29550 2.44250 .2750
75 .41900 3.38275 .6540

Table 8

TEST FOR EQUALITY OF VARIANCES
dlypc lseced credit
Quartile 1 0.072 0.412 0.002
Quartile 2 0.002 0.168 0.002
Quartile 3 0.001 0.089 0.011
Quartile 4 0.044 0.096 0.107
  • For the logged secondary school enrolment rate, variance is lowest in the second quartile and greatest for those nations with the least propensity for schooling in the secondary-school-age population.
  • And for credit, variance is low in the lower half of the distribution but five times higher in the fourth quartile.

Hence, the original model does not meet the test for homoscedasticity of variances. Since this distorts the significance tests and affects external validity, it becomes very difficult to generalize from the original model.

Turning to the assumption of normality of distribution for the residuals, one finds that subjecting the relationship between DV and the seced IV with the one-sample Kolmogorov-Smirnov Test (see Table 9 below) for small to medium samples (in this case, n = 50) that: a) There are numerous cases of the Lilliefors Significance Correction when the change in per-capita GDP from 1990 to 2005 is constant at certain values od the DV; and, b) testing the limit of the theoretical cumulative normal distribution against the obtained distribution of residuals yields significance statistics p < 0.001 or lower. Hence, the assumption of normality for the residual distributions cannot be met.

Table 9

Tests of Normalityb,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,aa,ab,ac,ad,ae,af,ag,ah
Ln Secondary enrolment 1990 Kolmogorov-Smirnova Shapiro-Wilk
Sig. Statistic df Sig.
PCI ch 1990 to 2005 -0.511 0.260 2 0.000
0 0.239 3 0.000 0.975 3 0.697
1.065 0.260 2 0.000
1.099 0.260 2 0.000
1.386 0.260 2 0.000
1.649 0.260 2 0.000
2.398 0.260 2 0.000
a. Lilliefors Significance Correction

Relating dlypc to credit generates 100% Lilliefors Significance Correction exception warnings. The assumption of normality cannot even be evaluated.

Re-estimation with Dummy Variables

Given the calculated residuals for the regression, the 3X SE hurdle comes to 8.991. The probability plot (Figure 6 overleaf) shows, however, that there is no need to undertake the outlier-adjusted model specification.

Table 10

Residuals Statisticsa for the First Model Run
Minimum Maximum Mean Std. Deviation N
Predicted Value -.21449 .60917 .29460 .149249 48
Residual -.576514 .782357 .000000 .243776 48
Std. Predicted Value -3.411 2.108 .000 1.000 48
Std. Residual -2.209 2.997 .000 .934 48
a. Dependent Variable: PCI ch 1990 to 2005
Normal P-P Plot of Regression Standardized Residual
Figure 6: Normal P-P Plot of Regression Standardized Residual.

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