PEP DISCUSSION PAPER 2022-1E

Eggs first or chickens? A re-examination of Granger causality between increase in government
spending and GDP growth.
PARK Seung-Joon1
Japanese original, 28 Jun. 2022
English translation, 06 Jul. 2022.
machine translation with author’s correction

Draft, please do not quote

Abstract
Based on data from various countries, a strong correlation was noted between the growth rate of government
expenditure and the growth rate of nominal and real GDP, but there was some debate about the direction of
causality. In this paper, a simple theoretical simulation model was first constructed to show that scatter plots similar
to those actually observed can be drawn in either direction we assume the causality. We then tested Granger
causality between general government expenditure, nominal GDP and GDP deflators using data from 1980 to 2021
for 38 OECD countries, and found that the results differed significantly from country to country at different time
periods, with many cases suggesting a causality from growth to government expansion. However, as government
expenditure statistics such as in the SNA are produced on an accrual basis, the point in time when the amounts arerecorded may be later than when the orders are placed, which means that 'spurious causality' may be observed.
Therefore, we tried using the lead variable (a variable of later period) of public spending to test for Granger
causality, and found that the results could change. To examine this point in more detail, we used quarterly data fromthe Japanese GDP statistics (1994-2021), namely nominal GDP, government fixed capital formation andgovernment consumption. We found that in Japan since 2008 there was (practically) no causal relationship inneither direction without lead variables. However, with lead variables of government expenditure, one-way Granger
causality from public spending to nominal GDP was observed.
Figure: possible spurious causality from change in GDP to public spending

1

Kwansei Gakuin Univ., School of Policy Studies. e-mail: cce55691@kwansei.ac.jp

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PEP DISCUSSION PAPER 2022-1E

Eggs first or chickens? A re-examination of Granger causality between increase in government
spending and GDP growth.
PARK Seung-Joon
Japanese original, 28 Jun. 2022
English translation, 06 Jul. 2022.
machine translation with author’s correction
Draft, please do not quote

1. Introduction.
There is a clear correlation between the nominal/real GDP growth rates of countries and the growth rate ofgovernment expenditure (Shimakura 2018, Park & Shavetail 2020; Figure 1). Moreover, it is noteworthy in thesefigures that there are no dots significantly to the upper left or lower right of the regression line. This means that 'no
country has high GDP growth without increasing government spending, and no country has low GDP growth withincreased government spending' or 'no country increases public spending following GDP growth'. Here, Japan isamong the lowest in the world, both in terms of the growth rate of government expenditure and in real/nominal
economic growth. Therefore, the proponents of active fiscal policy (including the author) who are focused ongetting Japan out of its current recession tells us that government spending should be increased.
In contrast, Atkinson (2022) casts doubt on this interpretation of causal direction, stating that "some people saythat if you increase government spending the economy will grow, but this logic is too simplistic. Frankly, this claim
is wrong" and cites a review by Nyasha et al. (2019) (summarised in Appendix 1) as an argument supporting his
view.
Figure 1: Correlation between government spending growth and growth of nominal GDP (left) and real GDP (right)

Source: Park & Shavetail (2020), p. 173.
Note: Average annual growth rates over the last 20 years of real/nominal GDP and general government expenditure (nominal) for eachcountry. The original data are from IMF World Economic Outlook (2019),

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PEP DISCUSSION PAPER 2022-1E

The review describes existing studies that address the causality between government spending and economic
growth. According to the review, the results belong to 1 of four views: "(1) Keynesian view: the size of governmentis the cause of economic growth [6 studies]", "(2) Wagner's Law: government is inefficient and cannot promoteeconomic growth [22 studies], "(3) Bidirectional causality view: there is a bi-directional causal relationship [10studies]" and "(4) Neutrality view: there is no relationship [12 studies]". Various statistical methods are used withthe main ones being Granger Causality tests (see Section 3), and studies using other methods practically applies thesame concept of causality. On the basis of this review, Atkinson stated that it is wrong to say that the economy willgrow if government spending is increased. But it is difficult to conclude this way.
Firstly, the results of causality tests (as the review concerned concludes) vary from country to country and fromperiod to period. Although the view (2) seems at first glance reasonable on the basis of numbers, this is not
something that should be decided by majority vote.
Secondly, a review of the papers included in this review shows that the overwhelming majority are based on datafrom developing countries such as Africa, and moreover, the studies are not necessarily new (none of them deal
with sufficient data from developed countries since the global financial crisis in 2007).
Furthermore, GDP and fiscal statistics are recorded on an accrual or cash basis, which means that the amount ofgovernment expenditure is recorded long after orders have been placed, such as for public works2. Therefore, aspurious causal relationship can occur. That is, long before the statistical amount of government expenditure
increases, orders may have been placed by the government to enterprises, and when the enterprises have started
production the GDP would have been increased (Figure 2). Existing studies summarised in Nyasha et al. (2019)(Appendix 1) seems not explicitly take this issue this into account, but the authors of previous studies may need torevise their conclusions.
Figure 2: Timing issues of statistical government expenditure

Source: prepared by the author.

2 This problem was pointed out by Mukai (2010). Tanaka and Adachi (2003) found that a monthly comparison of consumer prices andthe government budget balance in 1933, when the US economy improved, showed that the rise in prices progressed about six months
faster than the rise in the budget deficit, making the argument that fiscal stimulus caused inflation untenable (ibid., p. 88, Fig. 4).
However, while the fiscal balance is expenditure-based, the effects of fiscal stimulus occur when the order placed. As soon as acompany receives an order, it places a bulk order for raw materials and construction machinery, contracts with labour and relatedcompanies and starts construction and production, which affects material prices and wages. On the other hand, the government's
spending is delayed for some months after the order, and takes place ex post and in stages" (Mukai 2010, p. 299).

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PEP DISCUSSION PAPER 2022-1E

Finally, it is disconcerting (even though there are a number of studies based on this conceptualisation) to refer tothe position that asserts a causal link from economic growth to increased government expenditure as 'Wagner's
Law', since Wagner (1958, 1883) 'pointed to a law of expansion of public sector activity (especially state activity)'
but did not point to a causal link from national income to government expenditure (-> Appendix 2).
The paper first examines the mechanism behind the appearance of the graphs shown in Figure 1 using a simple
theoretical simulation model, taking into account both causalities 'from government expenditure to GDP (G->Y)'and 'from GDP to government expenditure (Y->G)'. Next, using annual data from 1990 to 2021 for 38 current
OECD member countries, we perform Granger causality tests for the full period, pre-2007 and post-2008 (theavailable data period varies from country to country). Here, we also pay attention to how the results change when
taking into account the issue of the timing of government spending orders and the point in time when the amounts
are recorded in the statistics. Finally, a more detailed causality study is conducted based on quarterly data focusing
on Japan from 2008 onwards. Based on these findings, we conclude.
Figure 3: Graphs with the direction of causality as 'G->GDP' (left) and 'GDP->G' (right)

Source: author's calculations.
Note: The horizontal axis is government expenditure growth, the ▲ vertical axis is nominal GDP growth and the ○ vertical axis isreal commission GDP growth.

2. Simple simulation of the relationship between government expenditure and GDP
This section presents the results of simulations based on common-sense macroeconomic theory and discusses thecausal relationship between government expenditure and nominal and real GDP (see Appendix 3 for details). The
system of theoretical equations is made simple so that everyone can easily understand it, through simple one-way
calculations with no feedback. Each country develops its own GDP supply capacity (Ys, real), but GDP is actually
generated in response to aggregate demand (YD, nominal aggregate demand = consumption + private capital
investment + government expenditure). YD divided by the price index (P) is real aggregate demand. If this exceeds
the supply capacity, price inflation will occur and real growth will be hampered. Under these common-sense
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PEP DISCUSSION PAPER 2022-1E

assumptions, 20-year estimates were made for hypothetical countries (in this case 20 coutries), with varying
parameters, and the results were compared.
The left-hand diagram in Figure 3 is produced based on the causality from government expenditure to GDP (G toGDP; i.e. each country's government expenditure continues to increase at a constant growth rate independent ofGDP), while the right-hand diagram shows the results based on the causality from GDP to government expenditure(GDP to G; government expenditure is a constant percentage of nominal GDP in the previous year). The horizontal
axis is the growth rate of public spending and the vertical axis is the growth rate of national income, where '▲' isnominal GDP and '○' is real GDP. In both cases, it was found that the figures are broadly similar to Figure 1.
In practice, there may be a difference in the direction of short-term causality between periods when effective
demand is lower than supply and periods when demand has reached the ceiling of supply capacity. In the next
section, we use time-series data for several countries to apprehend causality in Granger's sense dividing the time
period.

3. The Granger causality test with data from OECD countries
Granger causality tests are useful to ascertain whether increases in government expenditure precede GDP growthor vice versa. For example, Thurman et al. (1988) used time series data to test whether 'eggs come first or chickens
come first' and published in the Journal of Agricultural Economics.
The review by Nyasha et al. (2019), presented in the Introduction (Appendix 1), includes a number of studies
using this type of methodology. Focusing on recent data from developed countries, Granger causality tests are
conducted here for 38 OECD Member States as of June 2022.
3.1. Data and analysis methods
Data are nominal GDP (Y), real GDP and general government expenditure (G) for 38 OECD member countries
from the IMF's World Economic Outlook Database (April 2022).3 The data period is 1980-2021, but varies fromcountry to country. The GDP deflator (P) is obtained by dividing nominal GDP by real GDP.
Tests of Granger causality are generally based on the following formulas for regression analysis, with the null
hypotheses 𝛽1 = 𝛽2 = ⋯ = 𝛽𝑙 = 0 , and 𝛿1 = 𝛿2 = ⋯ = 𝛿𝑙 = 0, where Δ is the symbol for the time difference ofthe respective variable, and the lowercase letter l is the number of lags of the explanatory variable
𝛥𝑦𝑡 = 𝛼0 + 𝛼1 𝛥𝑦𝑡−1 + ⋯ + 𝛼𝑙 𝛥𝑦𝑡−𝑙 + 𝛽1 𝛥𝑥𝑡−1 + ⋯ + 𝛽𝑙 𝛥𝑥𝑡−𝑙 + 𝜀𝑡

(Equation 1)

3 The General Government Gross Expenditure (GGX) in the relevant IMF database is from the IMF's Government Finance Statistics(GFS). It includes central government as well as local governments and social security funds, etc., but does not include government
enterprises (IMF 2014, p. 18). It also includes social security-related transfer payments, unlike government expenditure in the GDP
statistics (IMF GFS database). The author's intention was to use government expenditure (government consumption and public fixed
capital formation only), which is included in the definition formula for expenditure-side GDP, but statistics matching it were difficult
to obtain in the database which includes many countries, so this was used instead.

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PEP DISCUSSION PAPER 2022-1E

𝛥𝑥𝑡 = 𝛾0 + 𝛾1 𝛥𝑥𝑡−1 + ⋯ + 𝛾𝑙 𝛥𝑥𝑡−𝑙 + 𝛿1 𝛥𝑦𝑡−1 + ⋯ + 𝛿𝑙 𝛥𝑦𝑡−𝑙 + 𝜇𝑡

(Equation 2)

In Equation 1, if the coefficients 𝛽1 = 𝛽2 = ⋯ = 𝛽𝑙 are all zero, we can say that the past values of Δx do notaffect Δyt (not causal in the Granger sense), and in Equation 2 if 𝛿1 = 𝛿2 = ⋯ = 𝛿𝑙 are all zero, we can say that thepast values of Δy do not affect Δxt (not causal in the Granger sense). This is confirmed by the F-test (Wald’s test).
Depending on the results of the test, not only one-way causality but also two-way causality may be confirmed, or
there may be cases where no causality is found between each other (independent or neutral).
The reason for taking time-differences for each variable is that in many cases, the level values of time series data
have a unit root (and therefore are not stationary) and should not be used in regression analysis, but by taking timedifferences they become stationary (Enders 2019, p. 190). First, the unit root test for each variable is performed in
the next section.
3.2. Unit root test
For the GDP deflator (P), general government expenditure (G) and nominal GDP (Y) for 38 countries, we first
perform a unit root test using the ADF test method to check for stationarity of the variables (Enders 2019, p. 209).
Here, we use a formulation that includes a drift (constant term) and a linear trend, as these variables are considered
to have an increasing trend along time (equation 3).
𝛥𝑦𝑡 = 𝛼0 + 𝛾𝑦𝑡−1 + 𝛼2 𝑡 + 𝛽1 𝛥𝑦𝑡−1 + ⋯ + 𝛽𝑘 𝛥𝑦𝑡−𝑘 + 𝜀𝑡

(Equation 3)

Here, if the null hypothesis of γ = 0 can be rejected, there is no unit root. Table 1 shows the results. 4[Table 1 at the end of this report corresponds here].

We find that most of the level variables cannot reject the existence of a unit root; taking the first-order difference(Δ) eliminates the unit root of most cases, but some still have a unit root; taking the second-order difference (2Δ)
eliminates the unit root of most cases, but a few still have a unit root. In this paper, Granger causality tests are only
performed on variables with first-order differences. For this reason, we gave the sign of I(0) for differenced
variables which is already stationary, the sign I(1) which becomes stationary after a further first-order difference,and the sign I(2) which becomes stationary only after a difference of two or more orders. 5
3.3. Conducting the Granger causality test
For each of the 38 countries, pairs of GDP deflators (P), general government expenditure (G) and nominal GDP

4 The calculations were performed using EViews (ver. 12), which was programmed to calculate all three variables for all countries atonce. The number of lag variables to be included in the estimation equation for each variable was automatically selected based on the
Akaike Information Criterion (AIC).
5 Unit root tests were only performed up to second-order differences, and those here that may need to take more than third-storey
differences are also denoted as I(2) for convenience.

6

PEP DISCUSSION PAPER 2022-1E(Y) were selected and fitted to Equations 1 and 2 to perform Granger causality tests. For each country, six types ofGranger causality were tested, with the direction of causality as 'influencing variable -> influenced variable': 'ΔP>ΔG', 'ΔG->ΔP', 'ΔY->ΔG', 'ΔG->ΔY', 'ΔY->ΔP' and 'ΔP->ΔY'. In doing so, due to the limited number of time series
data periods available, all lags of variables included in the equations were limited to two periods in order to ensuresufficient estimation periods. 6
Estimates for the entire period available (1980-2021 at most) are presented in Table 2, broken down before andafter the global financial crisis, Table 3 using data from before 2007 and Table 4 using data from 2008 onwards.
The values shown in the tables are p-values for the F-test. In these studies, the following points should be noted.

[Tables 2, 3 and 4 at the end of this report correspond here].
First, when two of the three variables, ΔP, ΔG and ΔY, were selected and paired, and when both were I(0)variables with no unit root, the results of the F test of Granger causality were used as is, with a significance level of
5%. The sign and significance of the coefficients were checked and when there was one significant variable, its sign(+ or -) was attached in front of the value. When there were two significant variables and the signs were identical,
the sign was shown (+ or -), and when they were different, the signs of the coefficients of the lag variables in thefirst and second period were checked in turn, and the sign (+ -) or (- +) was attached. Those for which no
significant variables were found were marked with an '○' sign for caution, but the results of the F-test were used asthey were.
Second, if one of the above pairs of two variables is an I(0) variable and the other is an I(1) variable, the F-test is
not available, but the significance of the coefficients can be checked using a t-test (Enders 2019, p. 294). In thiscase, the '*' sign is prefixed to the value in the table. Regardless of the result of the F-test, the coefficient of lag ofthe paired partner variable (β1 and β2 in Equation 1) is determined by the t-test at a significance level of 5 %. As in
the preceding paragraph, the signs and coefficients are checked and marked with a symbol.
Furthermore, when both in the couple of the variables are I(1), or when at least one of the variables is an I(2) or
higher (a variable for which the unit root remains even if the second-order difference is taken), it was decided to
exclude from consideration as causality testing is difficult and the cell was painted black.
According to Table 2, which summarises the results using data from the entire period, the cases of causality 'ΔP>ΔG' were in four of the 28 countries available for consideration, 'ΔG->ΔP' in three of the 28 countries, 'ΔY->ΔG'
in 15 of the 28 countries, 'ΔG->ΔY' in 6 of 32 countries for 'ΔY->ΔP', 11 of 32 countries for 'ΔP->ΔY' and 6 of 32
countries for 'ΔP->ΔY'. Thus, if we focus on the causal relationship between nominal GDP and government
expenditure, more results show causality from the former to the latter than vice versa.
Table 3, which summarises the results using pre-2007 data, shows that the 'ΔP->ΔG' causality was confirmed in
2 of the 27 countries available for consideration, 'ΔG->ΔP' in 4 of the 27 countries, 'ΔY->ΔG' in 12 of the 28

6 The calculations were made using EViews (ver. 12), which was programmed to perform Granger Causality tests for all three pairs of

all target countries, including two periods of lag, automatically. Note that EViews has a simple Granger Causality view command andthis programme produces the same results.

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PEP DISCUSSION PAPER 2022-1E

countries, 'ΔG->ΔY' in 2 of the 28 countries, 'ΔY->ΔP' is 10 out of 31 countries and 'ΔP->ΔY' is 4 out of 31
countries. If we focus on the causal relationship between nominal GDP and government expenditure, more results
show causality from the former to the latter than vice versa.
Figure 4, which summarises the results using data from 2008 onwards, shows that the causality of 'ΔP->ΔG' wasconfirmed in 3 of the 28 countries available for consideration, 'ΔG->ΔP' in two of the 28 countries, 'ΔY->ΔG' inthree of the 28 countries, 'ΔG->ΔY' in one of the 28 countries, 'ΔY -> ΔP' is five out of 32 countries and 'ΔP -> ΔY'
is six out of 32 countries. Overall, the short sample period may have made it difficult to obtain statisticallysignificant results. Again, if we focus on the causal relationship between nominal GDP and government expenditure,
more results show causality from the former to the latter (three countries) than vice versa (one country).
The above results appear to correspond with the review's finding of Nyasha et al. (2019) that GDP is most often
the determinant of government expenditure, irrespective of the periods. However, this may be due to the issue ofthe timing of statistical government expenditure (Figure 2), as discussed in the Introduction. This issue is examinedin more detail in the next section.
3.4. Analysis with “lead” on general government expenditure
In the previous section, more cases showed Granger’s causality 'ΔY->ΔG' than cases of 'ΔG->ΔY' for any of theperiods taken. However, this does not necessarily mean that 'ΔY->ΔG' is the predominant direction of causality. The
discussion here pays attention to the issue of the timing at which general government expenditure (in particular of
public construction projects) is recorded in the statistics.
In the IMF-GFS, the timing is the same as in the national accounts (SNA) and is recorded on an accrual basis(IMF 2014, p. 352, A7.6). In the SNA, fixed assets are recorded when ownership is transferred to the user, not at
the point of production or order. In the case of construction projects, for example, if payments are made in stages as
progress is made, this is considered a partial purchase (European Communities et al. 2009, p. 201). Therefore, there
must be a considerable time lag between when the government places an order for public works with a contractor
and when the phased payments and deliveries are actually made and recorded in the statistics.
This means that, for example, public works projects that are recorded as government expenditure in amount inyear t+1 may have been planned by the government and been placed the orders with contractors in period t or t-1.
At that point, firms would have started work, so personnel would have been employed and materials etc. would
have been purchased, and the impact on nominal/real GDP and prices would have occurred (an increase in Yt and anincrease in Pt). An spurious causal relationship from Yt to Gt+1 may occur if the amount of government expenditure(Gt+1) is recorded in year t+1 (Figure 2).
If this reasoning is correct, then even if the results of the causality tests conducted so far show that the directionof causality of "ΔY->ΔG" or "ΔP->ΔG" is dominant, this is merely a manifestation of the statistical timing problem
of government expenditure. In this case, using values for general government expenditure at a later point in time(lead variables) may improve the results of the Granger causality test, as it would capture the effects occurring at
the time of ordering government expenditure.
To check this point, we have therefore used the lead variables (Gt+1 and Gt+2) for general government expenditure
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PEP DISCUSSION PAPER 2022-1E

Gt, taking the value at the relevant time (Gt) and the lead (k) for years 1 and 2, to see whether the results improve,based on Equations 4 and 5 below.

𝛥𝑃𝑡 = 𝛼0 + 𝛼1 𝛥𝑃𝑡−1 + 𝛼2 𝛥𝑃𝑡−2 + 𝛽1 𝛥𝐺𝑡+𝑘−1 + 𝛽2 𝛥𝐺𝑡+𝑘−2 + 𝜀𝑡

(Equation 4)

𝛥𝑌𝑡 = 𝛾0 + 𝛾1 𝛥𝑌𝑡−1 + 𝛾2 𝛥𝑌𝑡−2 + 𝛿2 𝛥𝐺𝑡+𝑘−1 + 𝛿2 𝛥𝐺𝑡+𝑘−2 + 𝜇𝑡

(Equation 5)

In these tables, the numbers in brackets around the symbols G(0), G(1) and G(2) are the number of lead periods.
The columns denoted by 'G(0)->P', 'G(1)->P' and 'G(2)->P' confirm the impact (ΔP->ΔY) from government
expenditure G to prices P (the number in brackets is the number of periods of lead). The columns denoted by 'G(0)>Y', 'G(1)->Y' and 'G(2)->Y' confirm the impact (ΔG->ΔY) from government expenditure G (number of lead
periods in brackets) to nominal GDP Y (both calculations are based on first-order difference variables, but the Δ
symbol is not marked in the table due to space constraints. In both cases, the calculations are based on first-orderdifference variables.)[Tables 5, 6 and 7 at the end of this report correspond here].

First, Table 5 (data for the entire period) confirms the improvement in the results. Here, 'improvement' is definedas the sign being correctly positive and the p-value of the t-test being smaller than 5%, compared to the case where
the lead (k) is 0. Note that in this table, a three-character country code was used for the country name. The country
name code is marked with a symbol such as '0_*', '*_!’ next to the country code. The symbol is '0' if the time series
variables used in the analysis are I(0) variables, the symbol is '*' if they are a combination of I(1) and I(0) variables,
and the symbol is '!' if both variables are I(0) or any is I(2). For example in "0_*", the first symbol relates to "ΔG>ΔP" and the second to "ΔG->ΔY". Cases with “!" symbols are not included in the study here (cells are blackedout).
The figures in the table show the p-values of the t-tests for the coefficients β1 and β2 or δ1 and δ2 for the variables
Gt+k-1 and Gt+k-2 in equation 4 and equation 5 respectively. The sign in front of it is the sign of the coefficient, andthe symbol '#' in front of it further indicates that the coefficient is significant at the 5% significance level (the cell isalso brightened).
In the 'ΔG->ΔP' test, it can be seen that when taking a one-period lead, the results improve in five (1+4) of the 28(14+14) countries. In addition, when taking a two-period lead, the results improved in 8 of the 28 countries. In
these cases, therefore, it is possible that an increase in prices may have occurred between the time the order wasplaced and the time it was recorded in the statistics, i.e. an 'spurious causality' may have occurred.
In the 'ΔG->ΔY' test, it can be seen that when taking a one-period lead, the result improves in seven (3+4) of the
28 (13+15) countries. In addition, when taking a two-period lead, the results improve in 12 (5+7) of the 28 (13+15)
countries. In other words, an 'spurious causal effect' may have occurred in these cases as well.
9PEP DISCUSSION PAPER 2022-1E

The interpretation is similar for Table 6 (pre-2007 data) and Table 7 (post-2008 data). In Table 6, the 'ΔG -> ΔP'
test shows that when taking a one-period lead, the results improve in four (3+1) of the 27 (13+14) countries. In
addition, when taking a two-period lead, the results improved in seven of the 27 countries (2+5). In the ‘ΔG->ΔY’
test, the results show that when a one-period lead is taken, the results improve in one country (1+0) out of 28(13+15). In addition, when taking a two-period lead, results improve in 12 (7+5) out of 28 (13+15) countries. In
these cases, 'spurious causality' may have occurred.
In Table 7, the 'ΔG->ΔP' test shows that when taking a one-period lead, the results improve in three (1+2) of the
28 countries (14+14). In addition, when taking a two-period lead, the results improved in two of the 28 countries.
In the ΔG->ΔY test, it can be seen that when taking a one-period lead, the result improves in two (1+1) of the 28(13+15) countries. In addition, when taking a two-period lead, results improve in six (7+5) out of 28 (13+15)
countries. It is possible that 'spurious causality' also occurred in these cases.
Thus, in many cases, taking the lead improved the results. It suggests that government expenditure that appears
as a monetary amount at time t was ordered at an earlier point in time and that an economic effect had occurred.
Studies using government expenditure will need to bear this in mind.
Of course, nothing definitive can be said here, as it is clear that if there is causality from GDP to G, taking G's
lead would reverse causality. This section will not go into further detail on the results for each country. A moredetailed examination will be made only in the case of Japan in the next section.

4. Analysis using Japanese quarterly data
In this section, we use Japanese quarterly data to examine Granger causality and timing issues for government
expenditure variables in more detail. The data used here are the Japanese GDP statistics (seasonally adjusted) for
109 periods from the first quarter of 1994 to the first quarter of 2021. As variables, we use GDP (GDPn in nominal
terms and GDPr in real terms), aggregate demand excluding inventory investment (nominal Yn and real Yr), GDPdeflator (P), government consumption expenditure (GC) and public fixed capital formation (GI) (here, unlike the
IMF data treated in Section 3, government transfers such as social security benefits expenditure is not included in
the considerations7). The reason why we consider not only GDP but also aggregate demand excluding inventory
investment is that even when aggregate demand declines, GDP records unsold goods as output in the form of
inventory investment, therefore GDP is considered insensitive to changes in aggregate demand.
4.1. The ADF test
First, the results of the ADF test for these variables (for all periods) are shown in Table 8. In the tests, the drift(constant term) and trend were included and the number of lag variables in the ADF test was automatically selected

7 The interest of this paper is Granger causality between the variables included in the idintity of expenditure-side GDP, Y=C+I+G+NX,

where G should be the government expenditure comprising GDP; G includes GC and GI but not transfer payments (which contributes
aggregate demand through consumption). The IMF data in Section 3 on general government gross expenditure, including transfer
payments, were used as is because it was not possible to obtain data on government consumption and government fixed capitalformation alone from this database.

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PEP DISCUSSION PAPER 2022-1E

based on the AIC. According to the results, GDPn, GDPr, Yn, Yr, P and GI are I(1) variables, while GC is an I(2)variable. Therefore, when testing for Granger causality, first-order differenced variables are used.

[Table 8 at the end of this paper corresponds here].
4.2. Granger causality
Table 9 shows the results of the Granger causality test. In the upper panel, ‘smpl’ refers to the sample period,
which is the whole period, pre-2007 and post-2008; ‘lead’ is the lead period (one or two years) for public fixed
capital formation (ΔGI) or government consumption (ΔGC) (the sample period used for the test was restricted,
taking into account the two-year lag and lead, and the impact of the October 2019 consumption tax increase).
Furthermore, Y represents nominal or real gross output, with the following distinction. If we focus on the left
column, ΔGDPn is the case using the difference of nominal GDP, while ΔYn is the case using the difference of
nominal aggregate demand (excluding inventory investment). ΔGDPr is the case using the difference of real GDP
and ΔYr is the case using the difference of real aggregate demand (excluding inventory investment). ΔP is thedifference of the GDP deflator.

[Table 9 at the end of this report corresponds here.]

Explanatory variables included were of two years (eight periods). Results are determined by the F-test at asignificance level of 10%, with significant results turning cells white. However, in analyses including the variable
GC, which is an I(1) variable, null hypothesis of no Granger causality is rejected if the coefficient is t-tested at asignificance level of 5% after checking the sign and p-values, even if the F value is slightly above 0.1.
First, the impact of ΔGI on GDP deflator (ΔP) was checked (GI->P), and the results for the period before 2007
improved when a one-year lead was taken, but not for the period after 2008. For the impact of ΔGC on ΔP (GC>P), the results for the whole period and for the pre-2007 period improved when taking a one- or two-year lead, but
not when taking a lead from 2008 onwards. This suggests that before 2007, government consumption had an
immediate impact on prices, but that this impact has disappeared since 2008.
Next, we look at the relationship between government expenditure and GDP, first using nominal GDP as it is(ΔGDPn). Looking at the 'GI->Y' column, ΔGI affects ΔY only for data from 2008 onwards, with a two-year lead;
ΔGC affects ΔY for data from the whole period, with a one- or two-year lead. 8
Next, we examine the results when using aggregate demand excluding inventory investment (ΔYn). Looking at
the 'GI->Y' column, ΔGI affects ΔY when it has a two-year lead for data before 2007 and when it has a one- or twoyear lead for data after 2008. Looking at the 'GC->Y' column, ΔGC affects ΔY when one or two years of leads aretaken for any period.
The results so far suggest that government capital formation and consumption have had the effect of boosting (or8 With regard to the 'GC->Y' relationship, it was observed in some cases where ΔGDPn affected ΔGI and ΔGC leading two periods inthe pre-2007 data, but the reasons for this are not clear.

11

PEP DISCUSSION PAPER 2022-1E

reduced public spending had the effect of depressing) nominal aggregate demand in the Japanese economy since
the collapse of Lehman Brothers.
The results improved when a lead of two years was taken for ΔGC for the case where data from the whole
period was used.
Looking at the real ΔYr as the explained variable, for the relationship between ΔGI and ΔY, the results improved
when taking a two-year lead on ΔGI for data from 2008 onwards; for the relationship between ΔGC and ΔY, when
taking a one- or two-year lead on ΔGC for data from all time periods. In the case of pre-2007 data, results improved
when taking a two-year lead on ΔGC.
These results suggest that government spending has actually had the effect of boosting nominal and real
aggregate demand and GDP in Japan in recent years.
To examine this point in more detail, we focus on the estimated Granger causality for ΔYn and ΔGI, and ΔYn and
ΔGC, based on data from 2008 onwards. Table 10 confirms the coefficients of the lag variable for ΔY (for the last
two years, eight periods) to confirm the causality of 'ΔYn->ΔGI'.

[ Table 10 at the end of this report corresponds here].

The '$' marks on the right-hand side of the table indicate the point in time of explained variable for which thelead was taken (K, 0 years = same point in time, 1 year = 4 periods ahead, 2 years = 8 periods ahead). It is assumed
that the orders were placed at some point before the amounts were recorded in the statistics (to be seen in
conjunction with Figure 2). The table clearly shows that past ΔY has no effect on either ΔGI or ΔGC (eachcoefficient is ±0.0 (one is +0.1) at every instance, and the t-test is not significant at the 5% significance level). This
result is also true when ΔGDPn is used as an explanatory variable. Therefore, it can be said that in recent years,
government expenditure has not increased (or decreased) in response to a preceding increase (or decrease) inaggregate demand or GDP, but has been independently and exogenously determined. This finding means that evenif we use lead values of public spendings we will not produce spurious causality toward growth.
Table 11 confirms the Granger causality; ΔGI to ΔYn and ΔGC to ΔYn. None of the lagged explanatory variables
ΔGI or ΔGC has significant effect on ΔYn in period t, the time represented by the symbol '$'. This means thatgovernment expenditure does not affect aggregate demand after it is recorded in the statistics.
However, when lead variables are used, ΔGI is statistically significant for the same period and for those taking
the lead of one and two quaters. This can be interpreted that orders for public works and other projects that affectΔYn in period t have been placed in or before period t and recorded after period t in terms of value, as shown in
Figure 2.
In the case of government consumption ΔGC, it could be that the ΔGC recorded at time t affected the ΔYn at thesame time, or that orders affecting the amount of ΔGC at time t were placed shortly before that. The ΔGC with alead of exactly one year (four periods) is also significant. This may be due to the impact of the implementation of
government expenditure items that are paid exactly one year later on ΔYn at period t.
The results of this section reveal that the direction of Granger causality is unambiguously from government
12

PEP DISCUSSION PAPER 2022-1E

expenditure to aggregate demand in the Japanese economy since 2008.
5. conclusion.
Based on data from various countries, a strong correlation was noted between the growth rate of government
expenditure and the growth rate of nominal and real GDP, but there was some debate about the direction of
causality. In this paper, a simple theoretical simulation model was first constructed to show that scatter plots similar
to those actually observed can be drawn in either direction we assume the causality. We then tested Granger
causality between general government expenditure, nominal GDP and GDP deflators using data from 1980 to 2021
for 38 OECD countries, and found that the results differed significantly from country to country at different time
periods, with many cases suggesting a causality from growth to government expansion. However, as government
expenditure statistics such as in the SNA are produced on an accrual basis, the point in time when the amounts arerecorded may be later than when the orders are placed, which means that 'spurious causality' may be observed.
Therefore, we tried using the lead variable (a variable of later period) of public spending to test for Granger
causality, and found that the results could change. To examine this point in more detail, we used quarterly data fromthe Japanese GDP statistics (1994-2021), namely nominal GDP, government fixed capital formation andgovernment consumption. We found that in Japan since 2008 there was (practically) no causal relationship inneither direction without lead variables. However, with lead variables of government expenditure, one-way Granger
causality from government spending to nominal GDP was observed.

13

PEP DISCUSSION PAPER 2022-1E

Table 1: Unit root tests (ADF test, drift and linear trend) for data from 38 OECD countries
level

First order difference

Second order difference

P

G

Y

ΔP

ΔG

ΔY

Δ2 P

Δ2 G

Δ2 Y

Australia

0.258

1.000

0.985

[I(0)] 0.014[I(0)] 0.070[I(0)] 0.000

0.000

0.022

0.027

Austria

0.731

0.461

0.980

[I(0)] 0.018[I(0)] 0.000[I(0)] 0.001

0.000

0.001

0.001

Belgium

0.227

0.998

0.195

[I(0)] 0.002[I(0)] 0.015[I(0)] 0.009

0.026

0.036

0.026

Canada

0.169

1.000

0.856

[I(0)] 0.007[I(1)] 0.957[I(0)] 0.000

0.001

0.000

0.081

Chile

1.000

1.000

1.000

[I(0)] 0.042[I(2)] 1.000[I(0)] 0.004

0.053

1.000

0.012

Columbia

0.030

1.000

1.000

[I(0)] 0.042[I(1)] 0.666[I(0)] 0.040

0.476

0.072

0.032

Costa Rica

0.415

0.986

0.145

[I(1)] 0.673[I(0)] 0.002[I(0)] 0.891

0.000

0.883

0.956

Czech Rep.

0.210

0.525

0.024

[I(1)] 0.993[I(0)] 0.043[I(0)] 0.052

0.033

0.000

0.017

Denmark

0.225

0.901

0.830

[I(1)] 0.362[I(0)] 0.013[I(0)] 0.000

0.000

0.041

0.002

Estonia

0.017

0.674

0.611

[I(0)] 0.013[I(1)] 0.287[I(0)] 0.006

0.023

0.020

0.006

Finland

0.162

0.810

0.159

[I(0)] 0.031[I(0)] 0.055[I(0)] 0.001

0.000

0.000

0.000

France.

0.307

0.478

0.062

[I(1)] 0.195[I(1)] 0.186[I(0)] 0.000

0.000

0.000

0.050

Germany

0.522

1.000

0.678

[I(0)] 0.031[I(0)] 0.004[I(0)] 0.000

0.234

0.000

0.000

Greece

0.611

0.576

0.541

[I(1)] 0.437[I(1)] 0.139[I(1)] 0.288

0.000

0.000

0.000

Hungary

0.528

0.962

0.905

[I(1)] 0.183[I(1)] 0.305[I(0)] 0.034

0.001

0.000

0.106

Iceland

0.785

0.890

0.998

[I(0)] 0.062[I(0)] 0.000[I(0)] 0.010

0.000

0.000

0.037

Ireland

0.788

0.405

0.904

[I(0)] 0.005[I(0)] 0.000[I(2)] 0.158

0.000

0.000

0.216

Israel

0.363

0.999

0.853

[I(0)] 0.045[I(1)] 0.108[I(1)] 0.211

0.000

0.001

0.000

Italy

0.935

0.208

1.000

[I(0)] 0.002[I(2)] 0.829[I(0)] 0.068

0.001

0.895

0.000

Japan

0.001

0.696

0.722

[I(1)] 0.915[I(1)] 0.437[I(0)] 0.047

0.003

0.000

0.000

Latvia

0.189

0.231

0.055

[I(0)] 0.013[I(1)] 0.240[I(0)] 0.005

0.000

0.017

0.001

Lithuania

0.066

0.202

0.747

[I(0)] 0.053[I(1)] 0.316[I(0)] 0.013

0.006

0.004

0.001

Luxembourg

0.869

1.000

0.757

[I(0)] 0.000[I(1)] 0.846[I(0)] 0.000

0.004

0.027

0.005

Mexico

0.815

0.694

0.886

[I(0)] 0.090[I(0)] 0.000[I(1)] 0.190

0.000

0.000

0.007

Netherlands

0.222

0.342

0.661

[I(0)] 0.100[I(0)] 0.025[I(0)] 0.000

0.000

0.000

0.000

New Zealand

0.369

0.999

1.000

[I(1)] 0.694[I(0)] 0.055[I(0)] 0.002

0.002

0.104

0.054

Norway

0.622

1.000

0.822

[I(0)] 0.001[I(1)] 0.735[I(0)] 0.000

0.000

0.079

0.015

Poland

0.091

0.993

0.491

[I(1)] 0.137[I(2)] 0.988[I(1)] 0.788

0.000

0.984

0.016

Portugal

0.920

0.704

0.606

[I(0)] 0.009[I(1)] 0.186[I(2)] 0.602

0.000

0.000

0.549

Slovakia

0.846

0.114

0.741

[I(1)] 0.186[I(0)] 0.011[I(0)] 0.012

0.041

0.031

0.006

Slovenia

0.779

0.494

0.785

[I(1)] 0.155[I(0)] 0.000[I(0)] 0.017

0.002

0.000

0.001

S. Korea.

0.580

0.999

0.037

[I(0)] 0.003[I(1)] 0.179[I(0)] 0.022

0.003

0.000

0.044

Spain

0.405

0.004

0.903

[I(1)] 0.355[I(0)] 0.003[I(0)] 0.001

0.001

0.190

0.021

Sweden

0.212

0.943

0.987

[I(1)] 0.137[I(1)] 0.592[I(0)] 0.000

0.019

0.048

0.002

Switzerland

0.587

0.170

0.441

[I(1)] 0.705[I(0)] 0.001[I(0)] 0.000

0.000

0.000

0.000

Turkey

1.000

1.000

0.977

[I(2)] 1.000[I(2)] 1.000[I(2)] 1.000

1.000

0.573

1.000

United Kingdom
United States ofAmerica

0.458

1.000

0.172

[I(1)] 0.324[I(0)] 0.011[I(0)] 0.010

0.000

0.530

0.000

0.832

0.975

0.963

[I(1)] 0.762[I(2)] 0.992[I(0)] 0.000

0.000

0.377

0.004

Source: author's calculations.
Note: The numbers in the cells are the p-values of the ADF test results for the null hypothesis of γ = 0. Those that can be rejected at asignificance level of 10% are represented by white cells. Only the first-order lag variables used in the analysis of this paper are marked
with the symbols I(0), I(1) and I(2).

14PEP DISCUSSION PAPER 2022-1E

Table 2: Granger causality test for data from 38 OECD countries (entire period)

Australia
Austria
Belgium
CanadaChile
Columbia
Costa Rica
Czech Rep.
Denmark
Estonia
FinlandFrance.
Germany
GreeceHungary
Iceland
IrelandIsraelItaly
Japan
LatviaLithuania
Luxembourg
MexicoNetherlands
New Zealand
NorwayPolandPortugal
Slovakia
Slovenia
S. Korea.
Spain
SwedenSwitzerland
TurkeyUnited Kingdom
United States ofAmerica
SIgnificant results

Use data as long-term as possible
ΔP -> ΔGΔG -> ΔP
0.4801
0.05630.12080.80850.59690.9852* 0.8664* (+) 0.0000! (+) 0.1184! (+) 0.0679* 0.0822* 0.4970* 0.3148* (-) 0.0084* 0.6763* 0.2867* 0.6404* 0.9381*(+-)0.0037* 0.3308
0.50330.2843! 0.5488! 0.4092
0.11190.3884! 0.7189! 0.4652! 0.3876! 0.6543
0.73710.21700.15250.9491* 0.2995* 0.9529! 0.5096! 0.5035! (+) 0.0217! 0.8903* 0.4402* 0.9278* 0.5755* 0.9448* 0.3028* 0.7803
0.80200.9751(+) 0.0043
0.6068* 0.4031* 0.3420* (+) 0.0066* 0.2426! 0.4966! 0.1400* 0.0650* 0.1991* 0.9584* 0.2747* 0.6203* 0.9508* 0.3413* 0.4190* 0.2230* (-) 0.0530! (+) 0.0544! 0.9792* 0.0040* 0.3037! (+-) 0.0082! (-+)0.0025* 0.8904* 0.6193

ΔY -> ΔG
0.1388(+) 0.0282(+) 0.0011* 0.2583! 0.5965* (+) 0.0000! (+) 0.0001(+) 0.0344
0.1018*(+-)0.0001(+) 0.0417* 0.0743
0.2627! 0.0006* (+) 0.0194(+) 0.0002! 0.3277! (+) 0.0068! 0.2337* 0.1587* (+) 0.1103* 0.1600* 0.1487* 0.7125(+) 0.0001(+) 0.0009* (+) 0.0002! 0.2521! (-) 0.0055
0.33820.0595* 0.1449(+) 0.0001* (+) 0.0299(+) 0.0003! (+) 0.0006
0.0591

ΔG -> ΔY(-+) 0.0041
0.8546
0.7313* (+) 0.0002! (+) 0.0000*(-) 0.0000! (-+) 0.0000
0.24840.4837*(+) 0.0206(-) 0.0318* 0.8667
0.5017! (-) 0.0406* 0.5977
0.1489! 0.6594! 0.2733! 0.5890* 0.5475* 0.8234* 0.6667* 0.5965* 0.9335
0.29330.1368* 0.0174! 0.6836! 0.5344
0.64050.8195* 0.8466
0.2610* 0.5548
0.6664! (-) 0.0058
0.2904

ΔY -> ΔP
0.21030.7146
0.0557(-+) 0.0001(-+) 0.0026(-+) 0.0006! 0.2231* 0.2673* 0.1202
0.5800(+-) 0.0168* (+) 0.0452
0.6880! 0.2311* (+) 0.1808
0.1811! 0.2597
0.1291(+) 0.0094*(+) 0.0016
0.48480.90190.4391* (-) 0.1101(+) 0.0070* 0.8451
0.7104! 0.8453! 0.5937* 0.3754* 0.1648
0.3228* 0.4959* 0.9707* 0.9297! (+) 0.0642* 0.3493

ΔP -> ΔY
0.08960.73520.3815(-)0.0255(+-) 0.0000
0.2793! 0.0291* 0.6277* 0.3493○ 0.0466
0.2383* 0.4001
0.4849! 0.9933* (+) 0.0516
0.2028! (-) 0.0170
0.57700.1616* 0.8747
0.34150.75740.6419* (+) 0.0437
0.7236* (-) 0.0797
0.8312! 0.5386! 0.1784* 0.2535* 0.9976
0.1319* 0.2520* 0.2439* 0.2864! 0.1837* 0.4468! 0.3038! 0.4586! (+) 0.0057! 0.1200* (-) 0.0022* (-) 0.0112

4/28

3/28

15/28

6/28

11/32

6/32

Source: author's calculations.
Note: The value in each cell is the p-value of the F-test, with cells with p>0.1 coloured white. For each country 1980-2020, themaximum available period of data was used for the paired variables to be included in the analysis, excluding missing before and after
available data. Estimated periods may therefore differ between countries and pairs of variables.

15

PEP DISCUSSION PAPER 2022-1E

Table 3: Granger causality test for data from 38 OECD countries (pre-2007 data)

Australia
Austria
Belgium
CanadaChile
Columbia
Costa Rica
Czech Rep.
Denmark
Estonia
FinlandFrance.
Germany
GreeceHungary
Iceland
IrelandIsraelItaly
Japan
LatviaLithuania
Luxembourg
MexicoNetherlands
New Zealand
NorwayPolandPortugal
Slovakia
Slovenia
S. Korea.
Spain
SwedenSwitzerland
TurkeyUnited Kingdom
United States ofAmerica
Significant results

Using pre-2007 data.
ΔP -> ΔGΔG -> ΔP
0.3007(+) 0.0018(+) 0.0072
0.51400.48040.3712* 0.5778* 0.3779! (+) 0.0139! 0.3617* 0.1717* 0.7421* 0.3844* 0.3344* 0.9222* 0.3530* 0.7498* 0.8703* 0.4745* 0.4480
0.75500.1791! 0.8212! 0.3423
0.21720.8930! 0.6022! 0.1482! 0.8433! 0.6067
0.3596
0.99120.6079(+-) 0.0597! 0.4997! 0.6659! (+) 0.0063! 0.9474* 0.4336* 0.6579* 0.1511* 0.1692* 0.3696* 0.8510
0.25170.7126(+) 0.0081
0.3244* 0.7953* 0.3505* 0.0387* 0.2467! 0.9726! 0.7869* 0.8091* 0.7862* 0.0816* 0.4684* 0.5677* 0.5985* 0.9961* 0.9533* 0.2634* (+) 0.1200! 0.1317! 0.8639* 0.0155* 0.3771* 0.8891*(+-)0.0360
-

2/25

4/25

ΔY -> ΔG
○ 0.0379
0.8396(+) 0.1311* (+) 0.0205! (+) 0.0000* (+) 0.0002! 0.1447
0.83110.1585* (+) 0.0017
0.5938* (+) 0.0040
0.3847! (+) 0.0014* 0.3100(+) 0.0068! 0.0128! 0.3753*** 0.0066* 0.1559* (+) 0.0109* 0.2360* 0.5964○ 0.0115(+) 0.0008* (+) 0.0011! 0.5536! 0.3481
0.55270.5160* 0.3092(+) 0.0027* 0.4904(+) 0.0030
0.1274

ΔG -> ΔY
0.18540.36580.3486* 0.2977! 0.6601* 0.3222! 0.3920
0.9016
0.8835* 0.5646
0.4266* 0.6488
0.4750! 0.2079* 0.4513
0.5960! 0.0741! 0.5036* (+) 0.0830* 0.9063* 0.5407* 0.7704* (+) 0.0433
0.20460.7336* 0.1765! 0.9527! 0.4021
0.6672
0.6355* 0.3923
0.7585* 0.2601
0.82640.5637

ΔY -> ΔP
0.3797
0.94650.04590.69820.4154(-+) 0.0215! (+) 0.0830* 0.4227* 0.8365(+) 0.0105(+-) 0.0017* 0.0523
0.2080! 0.3555* 0.7698
0.9674! (+) 0.0605
0.1301* (+) 0.0001
0.0001(+) 0.0447
0.4712* 0.9929○ 0.0084* 0.6441
0.6044! 0.2285! 0.4074* 0.8306* 0.3154(+-) 0.0477* 0.4526* 0.6035* (+) 0.0102* 0.4755

ΔP -> ΔY
0.42400.74290.09630.29340.48350.1505! 0.1872* 0.1124* 0.7639
0.1856(-) 0.0038* 0.3586
0.3554! 0.6584* 0.1728
0.0259! (-) 0.0523
0.5595* 0.2007
0.0787(-) 0.0683
0.1101* 0.5136
0.0859* 0.3990
0.1185! 0.1732! 0.3013* 0.1700* 0.0197
0.8117* 0.1522* (-) 0.0134* 0.6361* 0.1062--*** 0.0105* 0.6713

9/27

4/27

12/25

2/25

Source: author's calculations.
Note: The value in each cell is the p-value of the F-test, with cells with p>0.1 coloured white. For each country 1980-2007, themaximum available period of data was used for the paired variables to be included in the analysis, excluding missing before and after
available data. Estimated periods may therefore differ between countries and pairs of variables.

16

PEP DISCUSSION PAPER 2022-1E

Table 4: Granger causality test for data from 38 OECD countries (data from 2008 onwards)

Australia
Austria
Belgium
CanadaChile
Columbia
Costa Rica
Czech Rep.
Denmark
Estonia
FinlandFrance.
Germany
GreeceHungary
Iceland
IrelandIsraelItaly
Japan
LatviaLithuania
Luxembourg
MexicoNetherlands
New Zealand
NorwayPolandPortugal
Slovakia
Slovenia
S. Korea.
Spain
SwedenSwitzerland
TurkeyUnited Kingdom
United States ofAmerica
Significant results

Using data from 2008 onwards
ΔP -> ΔGΔG -> ΔP
0.82170.31550.95790.63830.4586
0.3699* 0.8896* (+) 0.0059! 0.4751! (+) 0.0578* 0.3894* 0.6336* 0.7153* (-) 0.0623* 0.6366* 0.7048* 0.4925* 0.8559*(+-) 0.0181* 0.3239
0.42080.2248! 0.2852! 0.6808(+) 0.0666
0.4504! 0.6366! (+) 0.0576! 0.7079! 0.9224
0.74740.71360.47290.8206* 0.5344* 0.7550! 0.5930! 0.6322! 0.8699! 0.4142* 0.5815* 0.9894* 0.5453* 0.9839* 0.4473* 0.93650.75020.6728(+) 0.0218
0.8874* 0.4151* 0.3737* 0.8207* 0.8163! 0.4313! ○ 0.0484* 0.2136* 0.1310* 0.1099* 0.4216* 0.5486* 0.9984* 0.1693* 0.3313* 0.1526* 0.3059! 0.4624! 0.2840* 0.0245* 0.4846! (+) 0.0134! (-) 0.0108* 0.6038* 0.9988

ΔY -> ΔG
0.6026
0.0760(+) 0.1132* 0.7258! 0.9847* 0.4881! 0.5357
0.16190.4376* (+) 0.0202
0.3160* 0.4839(+) 0.0464! 0.1656* 0.2522
0.1578! 0.8246! 0.2295! 0.4127* 0.9958* 0.2952* 0.4752* 0.1329* 0.4975(+) 0.0017
0.1637* 0.4704! 0.3789! 0.1828
0.55680.2418* 0.0701
0.0693* (+) 0.1273
0.1434! (+) 0.0064
0.2608

ΔG -> ΔY(-) 0.1089
0.56160.1404* 0.1822! (+) 0.0179* (-) 0.0074! (-) 0.0023
0.26660.3748* (+) 0.1025
0.1831* 0.9343
0.6526! 0.0373* 0.7412
0.7701! 0.8426! 0.5306! 0.6302* 0.2836* 0.4410* 0.6170* 0.5950* 0.2931
0.67880.1936* 0.5021! 0.5671! 0.7522
0.47140.8840* 0.4057
0.4902* 0.4963
0.7078! (-) 0.0274
0.1486

ΔY -> ΔP
0.21490.89290.5299(-) 0.0227
0.1116(-) 0.0164! 0.5804* 0.1013* 0.2697
0.14440.1813* 0.5876
0.1586! (+) 0.0144* 0.3694
0.8868! 0.4808* 0.3233(+) 0.0180* 0.1061
0.96220.92180.7483* 0.1940
0.3306* 0.7411
0.3209! 0.1532! 0.5456* 0.4986* 0.1384
0.6812* 0.0877* 0.7852* (-) 0.0450! 0.1019* 0.6577

ΔP -> ΔY
0.19220.74350.81070.5514(+) 0.0009
0.8015! 0.5559* 0.6795* (-) 0.0591(-) 0.0034
0.1529* 0.5730
0.8733! 0.1508* 0.2424
0.4405! 0.1774* 0.8012
0.9955* 0.6354
0.26500.35990.1053* 0.6140
0.9436* 0.1990
0.7286! 0.5156! 0.4907* 0.2628* 0.5992(+) 0.0251* 0.7189* 0.8814* (+) 0.0686! 0.0960* 0.2628! 0.2153! 0.7625! (+) 0.0025! (-) 0.1012* (-) 0.0265* (-) 0.0487

3/29

2/29

3/28

1/28

5/29

6/29

Source: author's calculations.
Note: The value in each cell is the p-value of the F-test, with cells with p>0.1 coloured white. For each country 2008-2020, themaximum available period of data was used for the paired variables to be included in the analysis, excluding missing before and after
available data. Estimated periods may therefore differ between countries and pairs of variables.

17

PEP DISCUSSION PAPER 2022-1E

Table 5: Improved results with lead variables for government expenditure (data for entire period)
AUS 0,0
AUT 0,0
BEL 0,0CAN *,*
CHL ! ,!
COL *,*

G(0)->PG(1)->PG(2)->P

G(0)->YG(1)->YG(2)->Y(-) 0.188(+) 0.270(+) 0.335# (-) 0.003(+) 0.131# (+) 0.027# (+) 0.019(+) 0.736(+) 0.498# (+) 0.007(+) 0.171(+) 0.239(-) 0.762(+) 0.334# (+) 0.014(-) 0.592(-) 0.449(+) 0.730(-) 0.520(+) 0.611(+) 0.065(-) 0.719(-) 0.312(-) 0.911(-) 0.870(+) 0.651(+) 0.649(-) 0.635(-) 0.588# (+) 0.006(+) 0.945(-) 0.874(+) 0.730(-) 0.579(-) 0.796(-) 0.292# (+) 0.000(-) 0.338(-) 0.999# (+) 0.000# (-) 0.001(+) 0.258(-) 0.817(+) 0.158(+) 0.495(-) 0.163(+) 0.102(+) 0.803(+) 0.086# (+) 0.039(+) 0.870# (+) 0.000(-) 0.232(+) 0.814(-) 0.774(-) 0.772(+) 0.505(-) 0.161# (+) 0.017(+) 0.304(+) 0.739(+) 0.633(+) 0.709(+) 0.524(+) 0.065(+) 0.423(-) 0.258(-) 0.977(+) 0.656# (-) 0.000(+) 0.179(+) 0.056# (-) 0.002(+) 0.271(-) 0.686# (-) 0.000(-) 0.949(-) 0.051(+) 0.331# (-) 0.015(+) 0.552# (+) 0.004# (-) 0.000(-) 0.244

CZE *,0(+) 0.179(+) 0.209(+) 0.586(-) 0.469(+) 0.550(+) 0.121(-) 0.441(+) 0.240(+) 0.407(-) 0.118(+) 0.850(+) 0.538

DNK *,0(-) 0.929(+) 0.293(+) 0.504(-) 0.242# (-) 0.024(-) 0.256(+) 0.726(+) 0.964(+) 0.423(-) 0.793(-) 0.294(-) 0.052(+) 0.161(-) 0.780# (+) 0.023# (+) 0.006(+) 0.864# (+) 0.000(-) 0.927(-) 0.655(+) 0.959(-) 0.787(+) 0.756(+) 0.294

CRI *,!

EST *,*
FIN 0,0
FRA ! , *DEU 0,0
GRC ! ,!
HUN ! ,*
ISL 0,0
IRL 0,!
ISR *,!
ITA ! ,!
improvement(-) 0.151(+) 0.132(+) 0.271# (-) 0.021(-) 0.234# (+) 0.013(+) 0.189(-) 0.130(+) 0.890(+) 0.958(-) 0.140# (-) 0.001(+) 0.917# (+) 0.043(+) 0.055(+) 0.931# (-) 0.001# (+) 0.012(-) 0.202(+) 0.962(+) 0.945(+) 0.684(+) 0.489(-) 0.462(+) 0.174(+) 0.119(+) 0.113(+) 0.346(-) 0.451(+) 0.282(+) 0.820(+) 0.736(+) 0.055(+) 0.454(-) 0.926(+) 0.314(+) 0.220# (+) 0.016(+) 0.468(+) 0.706(-) 0.427# (+) 0.000(-) 0.579(-) 0.218# (+) 0.028# (-) 0.026(-) 0.060# (+) 0.005(-) 0.844(+) 0.053(+) 0.159(-) 0.338# (+) 0.001# (+) 0.027(+) 0.364(-) 0.196(+) 0.105(-) 0.652(-) 0.830# (+) 0.001(+) 0.096# (+) 0.006(-) 0.142(-) 0.053# (+) 0.013# (+) 0.001(+) 0.346(+) 0.072# (+) 0.019(-) 0.789# (-) 0.012# (+) 0.000(-) 0.865(-) 0.306(-) 0.095(-) 0.651(+) 0.938(-) 0.246(-) 0.761(-) 0.802(-) 0.108(-) 0.387(-) 0.818(-) 0.794(+) 0.930(+) 0.057(-) 0.148(+) 0.669(+) 0.106(+) 0.100(+) 0.806(-) 0.790# (+) 0.036(-) 0.116(-) 0.210(+) 0.091(+) 0.556# (+) 0.027(+) 0.111(+) 0.889(+) 0.817# (+) 0.005(+) 0.419(+) 0.880
1/14
cases

(+) 0.137
4/14
cases

(+) 0.409(+) 0.567
3/13
cases

(-) 0.535
5/13
cases

base

base

JPN ! ,*
LVA *,*LTU *,*LUX *,*
MEX 0,*
NLD 0,0G(0)->PG(1)->PG(2)->P

G(0)->YG(1)->Y(-) 0.721(+) 0.515# (+) 0.011(+) 0.625(-) 0.504

G(2)->Y(+) 0.573(+) 0.913(-) 0.931(+) 0.068(+) 0.281(-) 0.929(-) 0.738(+) 0.909# (+) 0.000(+) 0.878(-) 0.582# (+) 0.000# (+) 0.033(+) 0.766(-) 0.271# (+) 0.000(-) 0.977(-) 0.297# (+) 0.000(-) 0.986# (+) 0.001(+) 0.179(-) 0.477# (+) 0.004# (+) 0.008(+) 0.740(+) 0.665# (+) 0.002(-) 0.634(-) 0.468# (+) 0.023(+) 0.791(-) 0.695(-) 0.235(-) 0.484(-) 0.145(-) 0.476(+) 0.654(+) 0.481(+) 0.472(+) 0.335(+) 0.273(-) 0.413(-) 0.844(+) 0.115(+) 0.649(+) 0.805(+) 0.149(+) 0.215(+) 0.919(-) 0.702(+) 0.119(+) 0.763(-) 0.100# (+) 0.003(-) 0.421# (+) 0.023# (+) 0.004(-) 0.364(-) 0.951# (+) 0.042(+) 0.556(-) 0.478# (+) 0.026(-) 0.237(-) 0.356(+) 0.625(+) 0.240# (+) 0.032(-) 0.525(-) 0.120# (+) 0.019(+) 0.739(+) 0.952(-) 0.379# (+) 0.031(-) 0.775(-) 0.122(+) 0.161

NOR *,*(+) 0.388(-) 0.867(+) 0.064(+) 0.069(-) 0.584# (+) 0.011(+) 0.998(-) 0.740(-) 0.150(-) 0.681(+) 0.763(-) 0.178

POL ! ,!

(+) 0.364(+) 0.120(+) 0.902(+) 0.393# (+) 0.003(+) 0.439(+) 0.368(+) 0.972(+) 0.265(-) 0.789(+) 0.471(+) 0.059

NZL *,0

PRT *,!
SVK *,0
SVN *,0
KOR *,*ESP *,0
SWE ! ,*CHE *,0
TUR ! ,!
GBR *,0
USA ! ,!
improvement(-) 0.124(+) 0.287(+) 0.126(+) 0.323(+) 0.906(+) 0.862(-) 0.498(-) 0.108(+) 0.579(-) 0.504(+) 0.930(+) 0.068(-) 0.146(-) 0.710(+) 0.806(-) 0.426(-) 0.960(+) 0.277(-) 0.427(-) 0.171(-) 0.718(-) 0.590(-) 0.611(+) 0.967(-) 0.756(+) 0.226(+) 0.689(+) 0.629(-) 0.607(+) 0.772(-) 0.876(-) 0.755(+) 0.051(-) 0.862(-) 0.522(+) 0.477(-) 0.220(+) 0.766(-) 0.652(+) 0.646(-) 0.609(+) 0.114(-) 0.647(-) 0.596(+) 0.372(-) 0.730(+) 0.320(-) 0.817# (+) 0.002(+) 0.644(-) 0.619(+) 0.094(-) 0.537# (-) 0.047# (-) 0.018(-) 0.910(-) 0.267(-) 0.212(-) 0.349(-) 0.143(-) 0.854(+) 0.102(+) 0.055(+) 0.358(+) 0.115# (+) 0.039(+) 0.505(+) 0.987(-) 0.331(+) 0.913(-) 0.332(-) 0.719(-) 0.951(-) 0.504(+) 0.091(-) 0.425(-) 0.541(+) 0.141(-) 0.126(+) 0.976(-) 0.621(-) 0.749(-) 0.355(-) 0.948# (-) 0.003# (+) 0.001(+) 0.464# (-) 0.013(+) 0.073# (+) 0.002# (+) 0.002(-) 0.595# (+) 0.030(+) 0.093(+) 0.698(+) 0.090(+) 0.360(+) 0.497(+) 0.287(-) 0.120(+) 0.948(+) 0.621(-) 0.425(-) 0.854(-) 0.953(+) 0.293(-) 0.264(-) 0.395(-) 0.456(-) 0.890# (+) 0.025(+) 0.281(-) 0.075# (+) 0.024(+) 0.223(-) 0.952
4/14
cases

(-) 0.293
4/14
cases

(-) 0.050(+) 0.397
4/15
cases

# (-) 0.016
7/15
cases

base

base

Source: author's calculations.
Note: The figures in the table are the p-values of the t-tests; white colour in the cells (with # sign) indicates significance at the 5% levelof significance. (+) or (-) indicates the sign of the coefficient on the counterpart lag variable (top row: first period lag, bottom row:second period lag). The bottom row is the number of countries where the sign or significance of the coefficient has improved. Cells
that are not used in the study are in dark grey.

18

PEP DISCUSSION PAPER 2022-1E

Table 6: Improved results with lead variables for government expenditure (pre-2007)
AUS 0,0
AUT 0,0
BEL 0,0CAN *,*
CHL ! ,!
COL *,*CRI *,!
CZE *,0G(0)->PG(1)->PG(2)->P

G(0)->YG(1)->YG(2)->Y#(+) 0.043(-) 0.994(+) 0.114(+) 0.140(+) 0.531#(+) 0.045#(+) 0.012#(+) 0.044(-) 0.960(+) 0.420(+) 0.057(+) 0.562(-) 0.939(+) 0.589#(+) 0.007(-) 0.225(+) 0.717(+) 0.947(-) 0.376(+) 0.461(+) 0.118(+) 0.889(-) 0.239(+) 0.387(+) 0.356(+) 0.282(+) 0.658(+) 0.732(-) 0.983#(+) 0.005(+) 0.193(+) 0.380(+) 0.381(+) 0.155(-) 0.868(+) 0.436(+) 0.671#(+) 0.017(+) 0.070(-) 0.124(+) 0.320#(+) 0.003(+) 0.313(-) 0.846(+) 0.206(+) 0.322(-) 0.123(-) 0.070(+) 0.382(-) 0.496(+) 0.066(-) 0.755(-) 0.320#(+) 0.023(-) 0.173(+) 0.463(-) 0.101(-) 0.552(-) 0.999(-) 0.052(+) 0.491(+) 0.455(-) 0.138(+) 0.341(+) 0.107(+) 0.471(-) 0.585(+) 0.875(+) 0.124(-) 0.315(+) 0.128(+) 0.169(+) 0.357(+) 0.118(-) 0.982(+) 0.540(+) 0.823(-) 0.580(+) 0.278(+) 0.129(+) 0.058(+) 0.238(+) 0.541(+) 0.925(+) 0.638(+) 0.927(-) 0.862(+) 0.671(-) 0.662(-) 0.868(-) 0.256(+) 0.459(-) 0.766(+) 0.943(+) 0.838(-) 0.552

DNK *,0(-) 0.977(+) 0.288(-) 0.639(-) 0.704(+) 0.943#(-) 0.048(-) 0.616(-) 0.739(+) 0.297(+) 0.692(-) 0.765(+) 0.689

EST *,*(+) 0.494#(+) 0.018(+) 0.455(+) 0.382(+) 0.345#(+) 0.010(+) 0.476(+) 0.809(+) 0.065(+) 0.713(+) 0.201(+) 0.985(-) 0.125(+) 0.756(+) 0.569(-) 0.323(-) 0.169(+) 0.121(+) 0.129(-) 0.285(-) 0.798(+) 0.302(-) 0.734#(-) 0.038(+) 0.164#(+) 0.020(+) 0.476(-) 0.359(-) 0.905#(+) 0.042(-) 0.342(+) 0.985(+) 0.056(+) 0.656(-) 0.475(-) 0.420(-) 0.764(+) 0.265(+) 0.803(-) 0.255(+) 0.775(+) 0.137(-) 0.659(+) 0.700(+) 0.287(-) 0.356(-) 0.653(+) 0.313(-) 0.075(+) 0.506(-) 0.653(-) 0.082#(+) 0.002#(+) 0.022(-) 0.490(-) 0.061(+) 0.594(-) 0.758(-) 0.631#(+) 0.000(-) 0.350(-) 0.427(+) 0.829(-) 0.252(+) 0.144(+) 0.220

FIN 0,0
FRA ! , *DEU 0,0
GRC ! ,!
HUN ! ,*(+) 0.788(-) 0.134(-) 0.764(+) 0.816(-) 0.536#(+) 0.035

ISL 0,0(-) 0.897#(+) 0.046#(-) 0.011(-) 0.691#(+) 0.000(+) 0.370(+) 0.996(-) 0.365#(+) 0.003(-) 0.315(+) 0.108#(+) 0.000

IRL 0,!

#(+) 0.025(-) 0.869(+) 0.529(-) 0.323(+) 0.850(+) 0.122#(-) 0.037(+) 0.431(-) 0.895(-) 0.076(-) 0.164(-) 0.400#(+) 0.025(-) 0.869(+) 0.529(-) 0.323(+) 0.850(+) 0.122#(-) 0.037(+) 0.431(-) 0.895(-) 0.076(-) 0.164(-) 0.400(+) 0.676(+) 0.250(+) 0.576(+) 0.382(+) 0.355(+) 0.450(+) 0.574(+) 0.741(+) 0.311(-) 0.278(+) 0.961(+) 0.552

base

3/13
cases

2/13
cases

base

1/13
cases

7/13
cases

ISR *,!
ITA ! ,!
improvement

JPN ! ,*
LVA *,*

G(0)->PG(1)->PG(2)->P

G(0)->YG(1)->Y(-) 0.761(+) 0.741#(+) 0.008(+) 0.606(-) 0.458

G(2)->Y(+) 0.361(-) 0.927(-) 0.963(+) 0.065#(+) 0.035(-) 0.336(+) 0.675(-) 0.223(-) 0.431(+) 0.169#(-) 0.012(+) 0.815(+) 0.243(-) 0.416(-) 0.573#(+) 0.005(+) 0.925(+) 0.727(+) 0.097

LTU *,*(+) 0.146(+) 0.116(+) 0.253(-) 0.331(+) 0.068#(+) 0.007(+) 0.515(+) 0.293(+) 0.487(+) 0.574(+) 0.975#(+) 0.030

LUX *,*(+) 0.925(+) 0.706(-) 0.398(-) 0.770(-) 0.902(-) 0.156(+) 0.622(+) 0.602(+) 0.487(+) 0.496(+) 0.768(+) 0.960(+) 0.516(+) 0.550(+) 0.980#(+) 0.033(+) 0.154(-) 0.799(-) 0.543(+) 0.792(+) 0.535(-) 0.500#(+) 0.023(+) 0.094

MEX 0,*
NLD 0,0(-) 0.677(+) 0.125#(+) 0.003(-) 0.118(-) 0.362#(+) 0.022(+) 0.254(-) 0.812#(+) 0.010(+) 0.896#(-) 0.049(+) 0.508(+) 0.446(+) 0.480(+) 0.881(+) 0.470(+) 0.474#(+) 0.013(+) 0.754(+) 0.804(+) 0.576(-) 0.681(+) 0.897(-) 0.729

NOR *,*(+) 0.901(+) 0.225#(+) 0.022(+) 0.599(+) 0.369#(+) 0.000(+) 0.187(+) 0.879(+) 0.878(+) 0.232(+) 0.368(+) 0.371

POL ! ,!

(-) 0.679(+) 0.575(+) 0.431(+) 0.856(+) 0.404(+) 0.073(+) 0.620(-) 0.830(+) 0.810(+) 0.788(+) 0.586(+) 0.716

PRT *,!

(-) 0.585(+) 0.231(+) 0.356(-) 0.339(+) 0.061(+) 0.102(+) 0.544(-) 0.254(+) 0.590(-) 0.466(-) 0.121(+) 0.324(-) 0.452(+) 0.785(-) 0.297(+) 0.467(+) 0.733(-) 0.212(-) 0.233(-) 0.844(+) 0.912(-) 0.962(+) 0.485(-) 0.947(-) 0.340#(+) 0.001(+) 0.605(-) 0.404(+) 0.268(+) 0.102(-) 0.931(-) 0.349#(+) 0.001(+) 0.597(-) 0.761(+) 0.249(+) 0.369

NZL *,0

SVK *,0
SVN *,0
KOR *,*ESP *,0(-) 0.980(+) 0.551(-) 0.979(+) 0.255(+) 0.513(-) 0.769(+) 0.983(+) 0.556(-) 0.644(+) 0.141(+) 0.632#(+) 0.042(+) 0.152(-) 0.379(-) 0.468(-) 0.719#(+) 0.034(-) 0.228(+) 0.949#(+) 0.050(+) 0.887(-) 0.595(-) 0.177

SWE ! ,*(-) 0.602(+) 0.093#(+) 0.044(-) 0.927(+) 0.381(+) 0.288(+) 0.916(-) 0.273(+) 0.647(-) 0.214(-) 0.177(-) 0.712

CHE *,0(+) 0.527(-) 0.979#(+) 0.032(+) 0.774(-) 0.306(-) 0.946(-) 0.265(+) 0.408(+) 0.782(-) 0.577(-) 0.966(-) 0.303(+) 0.527(-) 0.979#(+) 0.032(+) 0.774(-) 0.306(-) 0.946(-) 0.265(+) 0.408(+) 0.782(-) 0.577(-) 0.966(-) 0.303#(+) 0.014(+) 0.835(-) 0.975(+) 0.489(+) 0.546(+) 0.815#(-) 0.017(+) 0.720(+) 0.590(+) 0.893(+) 0.712(+) 0.416#(+) 0.014(+) 0.835(-) 0.975(+) 0.489(+) 0.546(+) 0.815#(-) 0.017(+) 0.720(+) 0.590(+) 0.893(+) 0.712(+) 0.416

base

1/14
cases

5/14
cases

base

0/15
cases

5/15
cases

TUR ! ,!
GBR *,0
USA ! ,!
improve
ment

Source: author's calculations.
Note: The figures in the table are the p-values of the t-tests, with white (with # sign) in the cells indicating significance at the 5% levelof significance. (+) or (-) indicates the sign of the coefficient on the paired partner lag variable (top row: first period lag, bottom row:second period lag). The bottom row is the number of countries where the sign or significance of the coefficient has improved. Cells
that are not used in the study are in dark grey.

19

PEP DISCUSSION PAPER 2022-1E

Table 7: Improved results with lead variables for government expenditure (since 2008)
G(0)>P

G(1)->PG(2)->P

G(0)->YG(1)->YG(2)->Y(-) 0.474(+) 0.418(+) 0.879

#(-)
0.049

(+) 0.260(+) 0.425(+) 0.142(+) 0.642(+) 0.269(+) 0.135(+) 0.642(+) 0.592(-) 0.414(+) 0.349(-) 0.872(-) 0.770(-) 0.078(+) 0.597(+) 0.615(-) 0.305(+) 0.383(-) 0.308(-) 0.288(-) 0.317(+) 0.766(+) 0.718(+) 0.448(-) 0.969(-) 0.660(+) 0.391(-) 0.179(-) 0.714(-) 0.835(-) 0.073(-) 0.659(-) 0.228

CAN *,*#(+) 0.003(-) 0.570(+) 0.756(+) 0.073#(-) 0.032(+) 0.334(+) 0.617(+) 0.603(-) 0.544(-) 0.502(+) 0.682(-) 0.295

CHL ! ,!

#(+) 0.035#(+) 0.021(-) 0.733#(+) 0.010(-) 0.209(-) 0.791(+) 0.314(+) 0.197(+) 0.294(-) 0.949(+) 0.317(-) 0.846

AUS 0,0
AUT 0,0
BEL 0,0

COL *,*(-) 0.985(+) 0.699(+) 0.654(+) 0.588(+) 0.250(+) 0.596(+) 0.907(+) 0.478(+) 0.164(+) 0.948(-) 0.866#(-) 0.006
#(-)
0.002

(+) 0.301

CRI *,!

(-) 0.380
#(-)
0.024

(-) 0.238(-) 0.373(-) 0.181(+) 0.874(+) 0.780(-) 0.464
#(-)
0.004

(-) 0.248

CZE *,0(+) 0.584#(+) 0.040(+) 0.639(-) 0.479(+) 0.400(+) 0.109(+) 0.519(+) 0.676(+) 0.125(-) 0.144(-) 0.926(+) 0.557(+) 0.824(+) 0.476(+) 0.144(-) 0.203(-) 0.130(-) 0.730(+) 0.606(+) 0.642(+) 0.641(-) 0.447(-) 0.263(-) 0.222

DNK *,0
EST *,*(+) 0.157#(-) 0.029(+) 0.322#(+) 0.043(-) 0.795#(+) 0.006(+) 0.870(+) 0.264(-) 0.374(-) 0.813(+) 0.907(+) 0.452

FIN 0,0(+) 0.510(+) 0.283(-) 0.935(-) 0.911(+) 0.782(+) 0.216(+) 0.241(+) 0.972(+) 0.353(-) 0.228(-) 0.272(-) 0.167

FRA ! , *(+) 0.585#(+) 0.043(+) 0.236(-) 0.724#(-) 0.021(+) 0.156(-) 0.461(+) 0.234(-) 0.905(+) 0.832(-) 0.998(-) 0.369

DEU 0,0(+) 0.234(+) 0.863(+) 0.071(-) 0.933(-) 0.067(-) 0.760(-) 0.840(-) 0.263(-) 0.720(+) 0.438(+) 0.266(+) 0.466

GRC ! ,!
HUN ! ,*
ISL 0,0
IRL 0,!
ISR *,!
ITA ! ,!
improvement#(+) 0.049(+) 0.339(-) 0.769(+) 0.112(-) 0.167#(+) 0.014(+) 0.839(+) 0.553#(+) 0.034(-) 0.184(+) 0.706(+) 0.633(-) 0.997#(+) 0.024(+) 0.213(-) 0.496#(+) 0.014(+) 0.207(+) 0.697(-) 0.479(+) 0.068(-) 0.628(+) 0.738#(+) 0.024(+) 0.456(+) 0.183(-) 0.423(-) 0.528(+) 0.192#(+) 0.003(+) 0.593(+) 0.419(+) 0.623(+) 0.863(-) 0.227#(+) 0.000(-) 0.616(-) 0.474(-) 0.271(-) 0.734(-) 0.969(-) 0.564(-) 0.618(-) 0.628(-) 0.267(-) 0.597(-) 0.854(-) 0.811(-) 0.577(-) 0.506(-) 0.615(+) 0.350(+) 0.521(+) 0.860(-) 0.764(-) 0.604(-) 0.573(-) 0.498(+) 0.439(+) 0.473(-) 0.831(+) 0.107(+) 0.497(-) 0.390(-) 0.457#(+) 0.026(+) 0.413(-) 0.528(+) 0.136(+) 0.511(-) 0.675(-) 0.317

base

1/14
cases

0/14
cases

base

1/13
cases

3/13
cases

G(0)>P
JPN ! ,*
LVA *,*LTU *,*LUX *,*
MEX 0,*
NLD 0,0G(1)->PG(2)->P

G(0)->YG(1)->YG(2)->Y(-) 0.199(+) 0.961(-) 0.885(+) 0.125(-) 0.066(-) 0.117(-) 0.845(-) 0.249(+) 0.793(+) 0.771(+) 0.251#(-) 0.006(-) 0.887#(+) 0.004(-) 0.191(-) 0.529#(+) 0.004(+) 0.339(+) 0.957(-) 0.358#(+) 0.006(-) 0.430(-) 0.242#(+) 0.005(+) 0.128(+) 0.912(+) 0.057(+) 0.705(-) 0.499(+) 0.162(+) 0.879(+) 0.718(+) 0.073(-) 0.513(-) 0.568(+) 0.182(+) 0.783(-) 0.999(-) 0.601(-) 0.328(-) 0.343(+) 0.706(-) 0.168(+) 0.927(-) 0.976(+) 0.712(+) 0.998(-) 0.758(-) 0.391(+) 0.468(+) 0.587(-) 0.163(-) 0.769(+) 0.185(-) 0.614(-) 0.561(+) 0.258(-) 0.198(-) 0.054(+) 0.067(-) 0.910(+) 0.092(+) 0.255(-) 0.926(+) 0.855#(+) 0.015(-) 0.752(-) 0.394(+) 0.351(-) 0.600(-) 0.693(-) 0.268(+) 0.180#(+) 0.038(-) 0.703(-) 0.282(+) 0.119(-) 0.738(-) 0.795(+) 0.972#(+) 0.043(-) 0.398(-) 0.185(+) 0.430(+) 0.539(+) 0.903(+) 0.351(+) 0.262(-) 0.950(+) 0.219(-) 0.792#(-) 0.035(-) 0.224(-) 0.427(-) 0.061(-) 0.248(+) 0.160(+) 0.295(-) 0.225(+) 0.302#(+) 0.020(-) 0.769(+) 0.248(+) 0.564(+) 0.081(-) 0.838(+) 0.581#(+) 0.040(-) 0.251(+) 0.416(+) 0.244(+) 0.622(-) 0.866(-) 0.872(-) 0.107(-) 0.383(+) 0.541(-) 0.547(-) 0.933(+) 0.393

SVK *,0(-) 0.203(-) 0.932(+) 0.106(-) 0.334(+) 0.853(+) 0.345(+) 0.999(-) 0.170(+) 0.665(-) 0.489(-) 0.456(+) 0.983

SVN *,0(+) 0.968(+) 0.241(+) 0.941(+) 0.864(-) 0.618(-) 0.998(+) 0.789

NZL *,0NOR *,*
POL ! ,!
PRT *,!

KOR *,*ESP *,0
SWE ! ,*(-) 0.987(+) 0.941(+) 0.168(-) 0.735(-) 0.502(-) 0.151(-) 0.694(-) 0.413(-) 0.227(-) 0.344(+) 0.183(-) 0.921(-) 0.475(+) 0.629(-) 0.611(-) 0.515(-) 0.588(+) 0.388(+) 0.827(+) 0.089(-) 0.722(-) 0.294(+) 0.236(-) 0.207(+) 0.470(+) 0.720(-) 0.340(-) 0.477(-) 0.556(+) 0.152(+) 0.787(+) 0.329(+) 0.265(+) 0.098#(+) 0.042(+) 0.809(+) 0.214(+) 0.793(+) 0.949(+) 0.272#(+) 0.050

CHE *,0(-) 0.529(+) 0.665(+) 0.465(-) 0.580(+) 0.535(+) 0.390(-) 0.762(+) 0.232(+) 0.271#(+) 0.003(+) 0.440(-) 0.642
#(-)
0.040

(-) 0.578

TUR ! ,!

(-) 0.303
#(-)
0.005

(+) 0.229#(+) 0.018(+) 0.172(-) 0.406#(+) 0.046(+) 0.194(+) 0.805(+) 0.267(-) 0.965(+) 0.204(+) 0.137(-) 0.109(-) 0.572(-) 0.644(-) 0.994(+) 0.768(+) 0.374(-) 0.385#(-) 0.036(-) 0.391(-) 0.567(+) 0.799(+) 0.083(-) 0.154(+) 0.081(+) 0.496(-) 0.758(-) 0.498(+) 0.226
#(-)
0.045

(+) 0.497(-) 0.057

base

2/14
cases

2/14
cases

base

1/15
cases

3/15
cases

GBR *,0
USA ! ,!
improve
ment

Source: author's calculations.
Note: The figures in the table are the p-values of the t-tests; white colour in the cells (with # sign) indicates significance at the 5% levelof significance. (+) or (-) indicates the sign of the coefficient on the paired partner lag variable (top row: first period lag, bottom row:second period lag). The bottom row is the number of countries where the sign or significance of the coefficient has improved. Cells
that are not used in the study are in dark grey.

20

PEP DISCUSSION PAPER 2022-1E

Table 8: Results of the ADF test
level

lags

1st diff.

lags

GDPn

0.517000.00000GDPr0.099000.00000Yn.

0.721210.00000Yr.

0.047800.00000p

0.999400.00000GC

0.6263

6

0.10555

2nd diff.

lags

0.00004

GI
0.990490.00158
Source: author's calculations.
Note: ADF tests using the whole period data including the drifts and trends in the equation, the number of lag variables for the ADF
test is automatically selected based on the AIC.

21

PEP DISCUSSION PAPER 2022-1E

Table 9: Results of Granger causality tests using Japanese quarterly data (first-order differences)smpl
ΔP

1996Q1 2017Q2

1996Q1 2007Q4

2008Q1 2017Q2
smpl
ΔGDPn

1996Q1 2017Q2

1996Q1 2007Q4

2008Q1 2017Q2
smpl
ΔYn

1996Q1 2017Q2

1996Q1 2007Q4

2008Q1 2017Q2
smpl
ΔGDPr

1996Q1 2017Q2

1996Q1 2007Q4

2008Q1 2017Q2
smpl
ΔYr

1996Q1 2017Q2

1996Q1 2007Q4

2008Q1 2017Q2

lead
0
1
2
0
1
2
0
1
2
lead
0
1
2
0
1
2
0
1
2
lead
0
1
2
0
1
2
0
1
2
lead
0
1
2
0
1
2
0
1
2
lead
0
1
2
0
1
2
0
1
2

GI->P
0.463
0.569
0.148
0.159
0.089
0.125
0.850
0.587
0.365
GI->Y
0.662
0.357
0.387
0.366
0.287
0.198
0.413
0.165
0.078
GI->Y
0.779
0.276
0.324
0.504
0.359
0.093
0.718
0.084
0.071
GI->Y
0.900
0.503
0.585
0.692
0.512
0.436
0.766
0.046
0.011
GI->Y
0.990
0.754
0.630
0.702
0.491
0.329
0.988
0.155
0.064

P->GI
0.180
0.824
0.544
0.094
0.132
0.560
0.266
0.986
0.917
Y->GI
0.508
0.754
0.522
0.044
0.272
0.074
0.184
0.729
0.936
Y->GI
0.387
0.644
0.495
0.063
0.155
0.042
0.161
0.521
0.853
Y->GI
0.503
0.793
0.665
0.097
0.322
0.120
0.049
0.490
0.818
Y->GI
0.437
0.738
0.637
0.126
0.114
0.054
0.128
0.342
0.799

GC->P
0.184
0.057
0.073
0.595
0.021
0.037
0.152
0.864
0.737
GC->Y
0.602
0.045
0.008
0.465
0.250
0.308
0.832
0.145
0.100
GC->Y
0.246
0.003
0.001
0.425
0.038
0.061
0.458
0.074
0.070
GC->Y
0.353
0.289
0.076
0.649
0.743
0.228
0.668
0.314
0.374
GC->Y
0.105
0.091
0.030
0.472
0.347
0.094
0.224
0.253
0.286

P->GC
0.571
0.535
0.248
0.674
0.602
0.007
0.598
0.827
0.913
Y->GC
0.268
0.880
0.377
0.349
0.824
0.007
0.509
0.598
0.960
Y->GC
0.041
0.916
0.679
0.076
0.887
(+)0.116
0.422
0.665
0.829
Y->GC
0.235
0.871
0.650
0.322
0.284
0.045
0.827
0.920
0.955
Y->GC
0.162
0.761
0.641
0.282
0.283
0.160
0.864
0.873
0.832

Source: author's calculations.
Note: Values in the table are F values for the F test, judged at a significance level of 10%. Results of tests involving the I(1) variable
ΔGC were confirmed based on t-values for the coefficients.

22

PEP DISCUSSION PAPER 2022-1E

Table 10: Effect of nominal aggregate demand (ΔYn) on public fixed capital formation and government
consumption (ΔGI, ΔGC)
Lags and leads

-8

-7

-6

-5

-4

-3

-2

-1

0 (=t)

ΔY -> ΔGI (K=0)

+0.0

-0.0

+0.0

+0.0

-0.0

-0.0

+0.0

-0.0

$

ΔY -> ΔGI (K=1)

+0.0

-0.0

+0.0

-0.0

+0.0

+0.0

+0.0

-0.0

ΔY -> ΔGI (K=2)

+0.0

+0.0

-0.0

-0.0

+0.0

-0.0

-0.0

-0.0

ΔY -> ΔGC (K=0)

-0.0

+0.0

-0.0

-0.0

+0.1

-0.0

+0.0

-0.0

ΔY-> ΔGC(K=1)

-0.0

+0.0

+0.0

-0.0

-0.0

+0.0

-0.0

+0.0

ΔY -> ΔGC (K=2)

+0.0

-0.0

+0.0

-0.0

-0.0

+0.0

+0.1

-0.0

1

2

3

4

5

6

7

8

$
$
$
$
$

Source: author's calculations.
Note: Values are coefficient values. Grey cells mean that the coefficient is not significant at the 5% significance level.

Figure 11: Effect of public fixed capital formation (ΔGI) and government consumption (ΔGC) on nominal aggregate
demand (ΔYn)
Lags and
leads

-8

-7

-6

-5

-4

-3

-2

-1

ΔYn
ΔGI (K=0)

+1.6

+0.0

+1.8

+0.1

+1.6

+1.7

-1.0

-3.2

+1.7

-0.2

+1.8

-1.7

ΔGI (K=2)
ΔYn

ΔGC (K=1)

1

2

3

+5.1*

-6.4*

+4.2*

-1.8

+4.4*

-5.4*

+3.4*

-2.0

+3.7*

-0.3

+0.4

-3.7

+3.4*

-0.3

+0.2

-2.3

4

5

6

7

-0.6

-0.6

+1.5

+1.4

+4.2*

+0.8

-0.8

+1.0

$

ΔGI (K=1)

ΔGC (K=0)0 (=t)

$
+2.3

-2.0

-1.1

+0.2

-2.2

+3.1

+0.7

-1.5

-1.9

+2.2

+2.9

+1.3

ΔGC (K=2)

Source: author's calculations.
Note: Values are for coefficients of explanatory variables. Grey cells mean that the coefficient is not significant at the 5% significancelevel.

23

PEP DISCUSSION PAPER 2022-1E

Appendix 1: List of existing studies examining the causality between government expenditure and GDP (1/4, continued)
Y -> G Author.

1

Bohl (1996).

2

Ansari et al. (1997).

3

obtaining Country/region

Method.

data periodvariable

G7 nations

Causality Test＊

Ghana, Kenya, South
Africa.

Granger causality test, Holmes- IFS, annual, Ghana 1963-88, Kenya Real per capita government expenditure
Hutton test
1964-89, South Africa 1957-90.
and national income

Abizadeh et al. (1988).

＊

4

Islam (2001).

＊

United States of America Regression analysis (not a US authorities, annual, 1950-1984.
causality test)
United States of America Error correction model (ECM) US authorities, annual, 1929-1996. Nominal gross government expenditure
GNP ratio, real GNP per capita

5

Tang (2001).

＊

6

Al-Faris (2002).

＊

7

Abu-Bader et al. (2003).

＊

8

Dritsakis (2004).

9

Loizides et al. (2005).

＊

10

Akoitoby et al. (2006).

＊

11

Sideris (2007).

＊Malaysia

Cointegration
tests.
Gulf Cooperation Council Cointegration
countries
tests.

andGranger IFS, annual, 1960-1998.

andGranger 1970-1997

Considerations about thetime of government’s
order placing
None.

None.

Real per capita GDP, real per capita
government expenditure
Real per capita GDP, government
expenditure as % of GDP, current
expenditurepercapita,capitalexpenditure per capita
Nominal gross government expenditure
as % of GDP, military expenditure as %of GDP

None.

Error correction model (ECM) National statistics, annual, longest Real GDP per capita, real government
1948-1995
expenditure, government expenditure
as % of GDP, etc.
Developing countries 51 Causality Test
GFS&IFS, annual, 1970-2002.
Real GDP, real government expenditurecountries
each
GreeceGranger Causality Test
Existing literature, annual, 1832- Real GDP, real government expenditure,
1938.
population

None.

Egypt, Israel and Syria.

Cointegration test,
decomposition

Greece, Turkey.

Causality Testvariance IFS, WDI, US-ACDA, annual

Greece, UK, Ireland.

None.

None.

None.
None.

Source: prepared by the author with reference to the respective tables contained in Nyasha et al. (2019). Those of them for which a paper was available are denoted by an '*' symbol.
Abbreviations: ADI: African Development Indicators; ADB: Asian Development Bank; EO: Economic Outlook (OECD); GFS: Government Financial Statistics (IMF); IFS: International
Financial Statistics, IFY: International Financial Yearbook, NA: National Accounts, PWT6.2: Penn World Table 6.2, WBDI: World Bank Development Indicators, WDI: World Development
Indicator, ACDA: Arms Control and Disarmament Agency.

24

PEP DISCUSSION PAPER 2022-1E

Appendix 1: List of existing studies examining the causality between government expenditure and GDP (2/4, continued)
Y -> G Author.

obtaining Country/region

Method.

data period

Chinese provinces

Granger Causality Test

Chinese authorities (1952-1989) Real GDP, real GDP per capita, realand existing literature (1990-2003). government expenditure

None.

Home authorities, annual, 1951- Real GNP, real government expenditure,2005.
population
Home authorities, annual, 1970- Real GDP, real government expenditure
2004.

None.

EO, GFS & AMECO, longest Nominal GDP per capita, nominal gross
1970-2006.
government expenditure

None.

12

Narayan et al. (2008).

13

Mohammadi et al. (2008).

＊

TurkeyARDL Bounds Test

14

Samudram et al. (2009).

＊

Malaysia

ARDL Bounds Test

15

Tang (2009).

Malaysia

16

Taban (2010).

TurkeyCointegration Bounds test andothers.
Bounds test and others.

17

Lamartina et al. (2011).

OECD 23 countries

panel data analysis

18

Kumar et al. (2012).

New Zealand

ARDL Bounds test and others. IFS, annual, 1960-2007.

19

Srinivasan (2013).

India

20

Akinlo (2013)

21

Biyase et al. (2015).

＊

Africa 30 countries

Cointegration
andcorrection models
Multivariate
time
analysis.
panel data analysis

22

Thabane et al. (2016).

＊

Lesotho

ARDL Bounds Test＊＊

Nigeria

variable

Considerations about the timeof government’s order placing

None.

Real government expenditure, real GDP
and GNP, government expenditure-GDP
ratio or GNP ratio (both growth rates)

None.

error- Home authorities, annual, 1973- Real GDP, real gross central government
2012.
expenditureseriesNone.

ADI, annual, 1990-2005.

WBDI, annual, 1980-2012.

25

Government expenditure as % of GDP,economic growth (nominal or real
unknown)
Real
GDP,
gross
government
expenditure (nominal?)

None.

None.

PEP DISCUSSION PAPER 2022-1E

Appendix 1: List of existing studies examining the causality between government expenditure and GDP (3/4, continued)
G to Y Author.

obtaining Country/region

Method.

data period

GDP variables
andexpenditure variables

government Considerations about thetime of government’s orderplacingNone.

1Ghali(1988).

＊

OECD countries

Vector error correction model IFS , Quarterly, 1970:1-1994:3.
(VECM)

2

Loizides et al. (2005).

＊

Greece, UK, Ireland.

3

Dogan et al. (2006).

Error correction model (ECM) National statistics, annual, longest Real GDP per capita, real government
1948-1995
expenditure, government expenditure
as % of GDP, etc.
Granger Causality Test

4

Blankenau et al. (2007).

5

Chandran et al. (2011).

＊

Malaysia

6

Ebaidalla (2013).

＊

Sudan

Author.

Philippines, Indonesia,
Malaysia, Singapore,
Thailand.

*Developed andEndogenous growth models, WDI, annual, 1960-2000.
Undecided developing countries (83 and their panel data analysis.
manuscript countries)

obtaining Country/region

Real per capita GDP growth, real Consideration? Adopt a
five-year average
education expenditure as % of GDP, real
government expenditure as % of GDP,
etc.
Autoregressive distributed lag ADB, 1970-2006.
Real GDP, real gross governmentNone.
method (ARDL)
expenditure, real education expenditure,etc.
Granger causality test, error Home authorities, annual, 1970- Real GDP, real gross government
None.
correction model.
2008.
expenditure
Method.

data periodvariable

Considerations at the timeof placing a government
orderHome authorities, annual, 1950- GDP per capita, government expenditure
None.
1981.
per capita (nominal and real)
IFY, annual, 1959-1993.

Real GDP, government spending, money
supplyNone.

variance IFS, WDI, US-ACDA, annual

Nominal gross government expenditure
as % of GDP, military expenditure as %of GDP

None.

Home authorities, annual, 1970- Real GDP, real government expenditure
2004.

None.

Y↔G.
1

Singh et al. (1984).

2

Cheng et al. (1997).

3

Abu-Bader et al. (2003).

4

Ahmad et al. (2005).

5

Samurdram et al. (2009).

6

Tang (2009).

None.

＊

＊

＊

India

Granger Causality Test

Korea

Vector autoregression (VAR)

Egypt, Israel and Syria.

Cointegration test,
decomposition

D-8 Member States

Granger Causality Test

Malaysia

ARDL Bounds Test

Malaysia

Cointegration Bounds test andothers.

26

PEP DISCUSSION PAPER 2022-1E

Appendix 1: List of existing studies examining the causality between government expenditure and GDP (4/4, continued)
Author.

obtaining Country/region

Method.

data periodY↔G.
7

Wu et al. (2010).

8

Taban (2010).

9

Abu-Eideh (2015).

＊

182 countries worldwide Panel Granger Causality Test

TurkeyBounds test and others.

Palestine

Granger Causality TestPWT 6.2, annual, 1950-2004.

Author.

obtaining Country/region

Method.

data period

1Singh et al. (1984).

＊

India

2

Afxentiou et al. (1296).

＊

EnlargementofEuropean Union

3

Ansari et al. (1997).

＊

4

Bagdigen et al. (2003).

5

Ahmad et al. (2005).

6

Dogan et al. (2006).

Indonesia,
Philippines,
Thailand.

7

Frimpong et al. (2009).

8

Verma and Arora (2010).

Gambia, Ghana, Nigeria. Cointegration and Granger
Tests
India
Error correction model (ECM) IFS-GFS, 1950/51-2008/09.

9
10

Taban (2010).
Afzal et al. (2010).

11

Rauf et al. (2012).

12

Ray et al. (2012).
Huang (2006).

Considerations about thetime of government’s
order placing
Real GDP, real GFDP per capita, realNone.
government expenditure, government
expenditure-GDP ratio

Considerations at thetime of placing agovernment orderHome authorities, annual, 1950- GDP per capita, government expenditure
None.
1981.
per capita (nominal and real)

Y: G

13

variable

Granger Causality Test

Government final consumption, transfers
and subsidies, GDP (per capita, nominal orreal not known)
Ghana, Kenya, South Granger causality test, Holmes- IFS, Ghana 1963-88, Kenya 1964- Real per capita government expenditure
Africa.
Hutton test
89, South Africa 1957-90.
and national income
TurkeyCointegration and Granger
Tests
D-8 Member States
Granger Causality Test＊

OECD-NA, annual, 1961-1991.

None.

Real government expenditure, real GDP,
population

None.

UECM IFS and Taiwanese authorities, Real GDP, real government expenditure,
1979-2002.
population

None.

Bounds test and others.

Pakistan.
Pakistan.

Granger & Sims Test
Autoregressive distributed lag
method (ARDL)
Causality Test

China, Taiwan.

None.

Malaysia, Granger Causality Test
Singapore,

TurkeyIndia＊

the Causality Testvariable

Bounds test
estimation.

for

27

PEP DISCUSSION PAPER 2022-1E

Appendix 2: About Wagner's Law
In Nyasha et al. (2019), Wagner (1958, 1883) was referred to, so we sought in this article thereferences to fiscal expansion, and found it only in the following paragraph. It states that tax
revenues are also described as a constraint on the expansion of the state, but basically it is argued
that the desire of progressive people for greater government overcomes their financial difficulties.
This has nothing to do with a causal direction from increased national income to higher government
expenditure.
“The ‘law of increasing expansion of public, and particularly state, activities’ becomes for the
fiscal economy the law of the increasing expansion of fiscal requirements. Both the State’s
requirements grow and, often even more so, those of local authorities, when administration isdecentralized and local government well organized. Recently there has been a marked increase inGermany in the fiscal requirements of municipalities, especially urban ones. That law is the result of
empirical observation in progressive countries, at least in our Western European civilization; its
explanation, justification and cause is the pressure for social progress and the resulting changes in
the relative spheres of private and public economy, especially compulsory public economy. Financial
stringency may hamper the expansion of state activities, causing their extent to be conditioned byrevenue rather than the other way round, as is more usual. But in the long run the desire fordevelopment of a progressive people will always overcome these financial difficulties." Wagner(1958, 1883), p. 8 [underlined by the author]

Appendix 3: On a simple simulation of the relationship between government expenditure and GDP
This section describes the design, set values and results of a simple simulation of the relationshipbetween government expenditure and GDP.
A3.1. system of equations
Real gross domestic product is determined by both supply-side GDP (supply capacity) anddemand-side GDP (effective demand) equations. It considers that the production of real GDP isrealised as minimum of supply side or the demand side. In this case, government expenditure Gt as apolicy variable plays an important role. Taxes are not taken into account (we assume that taxes are
implicitly deducted before consumption and private investment are determined). It also does not
explicitly take into account the fiscal balance (it considers that the fiscal deficit is compensated by
the issuing of money by the government, which, if excessive, will cause nominal GDP to exceed the
supply capacity and prices to rise).
- Supply-side real GDP (supply capacity)
YSt =YS0 × (1+r)twhere YSt is the supply capacity, YS0 is the initial value and r is the growth rate of supply capacity. In
this model, the supply capacity is assumed to be exogenously determined and varies from country tocountry. Critics who deny the effects of government spending and argue that 'productivity should be
increased' are, in this interpretation of the model, saying that r should be increased.
- Nominal GDP (effective demand)
Yt =Ct +It +Gt
where Yt is nominal GDP (effective demand), Ct is consumption, It is private capital investment and
Gt is government expenditure.
- Nominal consumption
Ct =c×Yt-1
28

PEP DISCUSSION PAPER 2022-1E

Where consumption (Ct) shall be determined by the consumption propensity c and GDP in theprevious period (Yt-1).
- Nominal private-sector capital investment
It =h × Yt-1 × Pt-1 +εtwhere private capital investment (It) is assumed to be determined by the investment propensity h,
GDP in the previous period (Yt-1) and prices (Pt-1). In other words, if the economy expands in theprevious period, capital investment will increase proportionally. εt is a disturbance term representingchanges in investment due to economic shocks.
- Nominal government expenditure
Gt=G0 × (1+g)twhere Gt is government expenditure, G0 is the initial value and g is the growth rate of government
expenditure (0 ≤ g < 1). g varies from country to country.
- Price index
Pt =Pt-1 ×max(1, Yt /(Pt-1 ×YSt ))In terms of nominal GDP based on prices in the previous period, prices are assumed to riseaccordingly when there is excess demand (Yt >(Pt-1 ×YSt)) and prices remain as in the previous period
when there is excess supply (Yt <(Pt-1×YSt)). In other words, deflation is not assumed.
- Real GDPR
Yt =Yt ÷Pt
Actual GDP (RYt) is nominal GDP (Yt) divided by the price index. Rising prices cause the real valueof consumption, capital investment and government expenditure to shrink in the same way.
A3.2 Simulation when the direction of causality is 'G->GDP'.
In this setting, the growth rate (r) of each country's supply capacity (YSt) and the growth rate (g) ofgovernment expenditure (Gt), an item of effective demand, are exogenously determined first, andreal and nominal GDP are consequently determined. In other words, government expenditure Gt isassumed here to grow at an initially determined rate of growth, unaffected by the resulting nominal
and real GDP (Yt, RYt). This assumes that the direction of causality is 'G -> GDP'. This is areasonable approach considering that government expenditure is exogenous: by setting four levels ofr (0%, 0.5%, 1% and 1.5%) and assuming five levels of government expenditure growth g (0%, 1%,
2%, 3% and 4%), 4 x 5 = 20 countries are assumed (country number is i). However, a random
number is added to g so that calculations are made with more diverse growth rates (Figure A3-1).
Table A3-1: Set government expenditure growth (g) and supply capacity growth (r) for 20 countries
I
R
g

1
0
0

2
0
1

3
0
2

4
0
3

5
0
4

6
.5
0

7
.5
1

8
.5
2

9
.5
3

10
.5
4

11
1
0

12
1
1

13
1
2

14
1
3

15
1
4

16
1.5
0

17
1.5
1

18
1.5
2

19
1.5
3

20
1.5
4

Source: author's settings. However, a uniform random number between minus 0.5 and plus 0.5 is added to g.

For each country, the initial values for each GDP item are set as c0 =6, I0 =2, G0 =2, YD0 =YS0 =Y0=10. The consumption propensity is set to c = 0.6 and the investment propensity to h = 0.2. The
growth rate of supply capacity is set to r and the growth rate of government expenditure is set to g,which varies from country to country. Furthermore, for capital investment It, in addition to the part
determined by multiplying the previous year's Yt-1 by the investment propensity of 0.2, a uniform
random number that takes a range from minus 0.4 to plus 0.6 is added. For each of these, a 20-year
29

PEP DISCUSSION PAPER 2022-1E

simulation was performed from t = 1 to 20.
Shown in Figure A2 is a scatterplot for the 20-year average. The first thing that can be read fromthe '▲' scatterplot is the (naturally) strong correlation between the growth rate of government
expenditure and nominal GDP (the coefficient in the regression equation is about 0.79). The verticalscatter is due to changes in capital investment (not shown here, but if no random numbers wereadded to capital investment, the ▲ points would line up in a straight line). The '○' scatter plot shows
the relationship between the growth rate of government expenditure and the growth rate of real GDP.
This one shows a positive correlation, but the fit is much worse than in the case of nominal GDP.
The vertical divergence between the '▲' and '○' figures is the difference between nominal and real
GDP growth for the same rate of government expenditure growth. It can be seen that when thegrowth of supply capacity (YS) is low and nominal government expenditure is increased excessively,
real GDP is suppressed because prices rise, even if nominal GDP grows. The regression equations
for growth of real GDP and government expenditure also show that the coefficient of determination
is much lower than for nominal GDP.
Figure A3-1 shows a similar trend to Figure 1 and is considered to capture some of themechanisms that led to the relationships shown in Figure 1 in the main text. In the next section, thereverse causal relationship is considered.
Figure A3-1: Graph with the direction of causality as 'G -> GDP'

Source: author's calculations.
Note: The horizontal axis is government expenditure growth, the ▲ vertical axis is nominal GDP growth and the ○vertical axis is real GDP growth.

A2.3. when the direction of causality is 'GDP -> G'In this setting, government expenditure shall be determined passively on the basis of nominal
GDP in the previous period, as a fixed percentage of this. This has a certain validity given the actual
budgetary decision-making mechanism. This means that the direction of causality is assumed to be‘nominal GDP -> G’.
For the growth rate of supply capacity r, as in the previous section, four levels are set: 0%, 0.5%,
1% and 1.5%. For the growth rate of government expenditure, no prior assumptions are made and
Gt=0.2×Yt-1 is assumed passively. Again, 20 countries are assumed (country number i). For all
countries, the initial values for each GDP item are set as C0 =6, I0 =2, G0 =2, YD0 =YS0 =Y0 =10. The
consumption and investment propensities are set to c = 0.6 and h = 0.2 respectively. For capital
investment It, in addition to the part determined by multiplying the previous year's Yt-1 by theinvestment propensity of 0.2, a uniform random number that ranges from minus 0.8 to plus 1.2 isadded to account for shocks due to economic fluctuations. In this case, capital investment is thedriving force behind economic growth and, as a result of chance, there will be large differences innominal and real GDP and government expenditure depending on the different rates of growth ofcapital investment.
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The results of a 20-year simulation for each of these, from t = 1 to 20, are shown in Figure A3-2.
For this one, a similar relationship can be drawn for the government expenditure growth rate andnominal and real GDP as in Figure 1 in the main text. In this case, private capital investment drives
GDP growth and government expenditure growth, with the country with the largest growth rate
(4.50% per annum) having a Y growth rate of 3.59%, G growth rate of 3.34% and RY growth rate of
1.73% and P growth rate of 1.83%. If the growth rate of private investment is large for all countries,
the distribution of the graph is broad both vertically and horizontally; conversely, if the growth rateof private investment is small for all countries, the distribution of the graph is narrow both verticallyand horizontally (for reference, see Figure A3-3).
Figure A3-2: Graph with the direction of causality 'GDP -> G'

Source: author's calculations.
Note: The horizontal axis is government expenditure growth, for the ▲ vertical axis is nominal GDP growth and the○ vertical axis is real GDP growth. A uniform random number taking a range of -0.8 to 1.2 is added to the formula forprivate capital investment. The country with the largest capital investment growth rate was 4.50% per annum, with Y
growth at 3.59% and G growth at 3.34%. The growth rate of RY and P was 1.73% and 1.83%, respectively.

Figure A3-3: Graph with the direction of causality 'GDP->G' (when capital investment growth issmall)

Source: author's calculations.
Note: The horizontal axis is government expenditure growth, for the ▲ vertical axis is nominal GDP growth and the○ vertical axis is real GDP growth. A uniform random number taking a range of -0.4 to 0.6 is added to the formula forprivate capital investment. The country with the largest capital investment growth rate is 2.55% per annum, at which
Y growth is 2.17%, G growth is 2.07%, RY growth is 1.58% and P growth is 0.58%.

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