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Fiscal Budget Decision and Gross Domestic Product

Introduction

This is a case of a developing economy where the government has a supplemental $2 billion budget meant for policies to boost per capita Gross Domestic Product (GDP) over a 15-year planning horizon.

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Two proposals have been tabled. The first aims to raise the literacy, competence, and self-sufficiency of the population by funding an increase of 6 percentage points in the percentage of the secondary school-age population that is enrolled, aiming to reach 61% at the end of fifteen years. But this is a long-term benefit for the population whereas the banking sector of the country is currently in crisis. The ratio of Private Credit by Deposit Money Banks and Other Financial Institutions to GDP has fallen steeply to 0.38 (from 0.52 in the prior period), thus imperiling the liquidity of the system and all business activity dependent on loans from local banks. As this threatens an immediate slowdown in business activity and a consequent reduction in per-capita GDP, the government has been asked to allot emergency loans to the sector. The analytical task, therefore, involves an empirical model to test which alternative is more likely, all other things equal, to raise per-capita GDP.

Data Compilation and Variable Transformation

The compiled data is shown in Table 1.

Table 1: All Required Logged and Calculated Data

X country DPC 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

First Test of Hypotheses for the Empirical Model

When historical data PCI ch is employed as the dependent variable in a model using the above logged and transformed data, the coefficients derived (Table 2 overleaf) result in the following model:

  • 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)

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

An ANOVA on the overall model. This represents a test of the:

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  • Null hypothesis H0: β2=β3=β4=β5=β6=β7=0
  • Alternative hypothesis H1: β1 ≠ 0

Table 3 (overleaf) reveals such an elevated F value that it is associated with a significance statistic p < 0.05, suggesting that beta coefficients greater than zero could have resulted by random chance alone just three or four times in a hundred derivations of empirical data. As this meets the minimum hurdle of p = 0.05, one rejects the null hypothesis and accepts the alternative that the independent variables do influence the growth of per-capita income.

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

Performing single-factor regression runs for all the independent variables, one finds that:

  • From a rather low negative value, β2 for the variable lypc90 improves from -0.915 in the multiple-regression model to -0.036. But the t test results in such a low value of -0.25 that the significance statistic comes to just p = 0.81, clearly no enough to rule out chance occurrence of a relationship between the logged value in 1990 and PCI ch.
  • The hypothesis test for this one-to-one regression also implies that log transformation of per-capita GDP in 1990 cannot per se ably predict the growth of the logged value dlypc 1990 to 2005. Table 4 (overleaf) reveals an F value for β2 so inadequate random occurrence cannot be precluded.

Table 4: Hypothesis Test 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

Taking just the variable seced (percentage of those of secondary school age enrolled as of 1990), the outcome is a coefficient that falls to 0.052 from 0.577 in the multiple-regression model. The t-test derived is so marginal (0.35) as to yield an unsatisfactory significance statistic p = 0.73, certainly nowhere near the 0.05 minimum requirement at the 95% confidence level.

The one-to-one hypothesis test (Table 5) is similarly dissatisfying. β3 bears an F value so marginal that the coefficient might have cropped up one-fourth of the time that a compilation of international macroeconomic data is processed. One must therefore accept the null hypothesis and state that the log of secondary enrolment rate in 1990 cannot, by itself, be used to predict the rise from 1990 to 2005 of the logged value dlypc.

Table 5: Hypothesis Test for Logged SECED

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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

Reducing the required confidence hurdle to 90% CL for the single-IV model employing involving credit (ratio of private credit by deposit money banks and other financial institutions to GDP in 1990), the result is that the for β7 coefficient falls from 0.390 (multivariate model) to only 0.109. Even worse, the t test calculated for this beta coefficient is so abysmally minimal (0.76) that the significance statistic is p = 0.45. This is tantamount to saying that the stated value of β7 about every other time, same as coin-toss odds, an analytical model is run. This is the same outcome one gets for the hypothesis test (Table 6): an F value for β7 of just 0.57 and p = 0.45. We are unable to reject the null hypothesis and must conclude that the ratio of private-sector credit to local GDP in 1990 has no empirical value for “predicting” the rise in logged value dlypc from 1990 to 2005.

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

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

The Allocation Problem

The base empirical model suggests that ceteris paribus, allotting $2 billion to prop up domestic lending activity impacts per-capita income more favorably.

If one first removes from consideration the credit variable and reformulate the model, and recalculate by inputting average values for the five other independent variables (except for inserting the 61% goal for seced)…

  • 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)

If the $2 billion were allocated to policy measures designed to increase secondary school enrolment rates immediately, the outcome will likely be an average improvement of 2.62% in per-capita GDP on the fifth year and 10.5% in the 15-year planning horizon. One needs to treat this finding with caution, however, since education explains only 8% of the total variance in the per-capita income growth for the typical developing market.

In turn, deciding to allocate the supplemental budget in support of private-sector credit requires replacing seced in the model with credit. Then the outcome is:

  • 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)

The latter model explains rather more (9.4%) of the total variance in per-capita GDP growth. By the end of the 15 years targeted, one has reason to believe that a 2% annual rebound in PCI ch would cumulate to 30.9%.

Diagnostics

To test the linearity assumption for Y (dlypci ), seced and credit, one first has recourse to visual inspection of plots (Figs. 1 and 2, overleaf). These do show a positive linear relationship though unadjusted R2 ≈ 9% in both cases and there is considerable dispersion around the mean of credit.

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Plotting to check the same assumption for the three other IV’s, Figures 3 to 5 (page 13), reveal that one discerns that openness (unadjusted R2 ≈ 1%) bears the weakest linear relationship. Nonetheless, the linearity assumption appears to be met for 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

The homoscedasticity assumption is essentially met by the fact that all IV’s are either interval or ratio and continuous “scales”. And as long as the use of dummy variables (normally classed nominal or categorical) is limited to the IV’s, the assumption of homoscedasticity holds.

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StudyCorgi. (2021, December 18). Fiscal Budget Decision and Gross Domestic Product. Retrieved from https://studycorgi.com/fiscal-budget-decision-and-gross-domestic-product/

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"Fiscal Budget Decision and Gross Domestic Product." StudyCorgi, 18 Dec. 2021, studycorgi.com/fiscal-budget-decision-and-gross-domestic-product/.

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