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81ECONOMIC SCIENCES
ASSESSMENT OF THE EFFECTS OF PUBLIC INVESTMENT ON GDP GROWTH: CASE OF
ARMENIA
Grigoryan K.,
Head of the Chair of Macroeconomics, Associate Professor, PhD in Economics Armenian State University of Economics ORCID ID: 0000-0001-7359-3407 Petrosyan G., PhD in Economics,
Head of Fiscal and Monetary Policies Coordination Division Ministry of Finance of the Republic of Armenia, Armenian State University of Economics Vardanyan K.,
Associate Professor, PhD in Economics, Armenian State University of Economics
Avagyan G.
Associate Professor, PhD in Economics, Armenian State University of Economics
ORCID ID: 0000-0003-3395-2473
ABSTRACT
Public capital investment (both investment in infrastructure and investment in human capital) is assumed to be one of the most important determinants of economic growth in theoretical literature. While the effects of public investment on GDP growth and other macroeconomic indicators vary across different countries. Thus, from policymaker's point of view, it is important to estimate the size, transmission mechanism and character of impact of public investment in short and long horizons, in order to be able to design relevant and effective fiscal policy. Thus, this paper analyzes the developments of public investment in Armenia, and implements estimation of the macroeconomic effects of public investment. The estimation has been done using two approaches: first, an empirical analysis has been performed using a simple OLS regression model and a structural VAR model, to show the historical effects between public investment and GDP based on information contained in actual data. Then, using a DSGE model, the effects of public investment and its transmission channels were analyzed based on the structure of Armenian economy. Both empirical analysis and estimation with a structural model showed, that public investment has significant positive impact on RA GDP and other macroeconomic variables. Based on the estimation results, the paper end with recommendations about directions of fiscal policy in Armenia.
Keywords: public investment, SVAR model, DSGE model, fiscal policy, fiscal multipliers.
1. Introduction3
Public capital investment is assumed to be one of the most important determinants of economic growth in theoretical literature. The role of public investment is well presented in exogenous growth models, where it is shown that increase of public investment has permanent effects on per capita income and temporary positive effects on the growth rates (Arrow K.J., & Kurz M., 1970). The endogenous growth models show that public capital investment can have also positive permanent effects on potential growth rate (Barro R.J., 1990). An analysis performed by G. Voss. et ell (2001) for a set of countries using a highly structured empirical Solow-Swan growth model, showed reasonable estimates of a positive conditional correlation between public investment and economic growth.
Empirical estimations of effects of public investment on GDP also show positive correlation, however, the amplitude of effects have different trends over
3 This work was supported by the Committee of Science of Ministry of Education, Science, Culture and Sport of the Republic of Armenia under Grant Maintaining and Development of Scientific and Scientific Technical
countries, with increasing the strength of effects in some countries and decreasing in others (Garry S. & Valdivia J.C.R., 2017). For EU economies both empirical analysis and estimation with a structural model (de Jong J., Ferdinandusse M., Funda J., Vetlov I., 2017) provides evidence of a generally positive output impact of an increase in the public capital stock, also suggesting presence of positive spill-overs at a longer horizon and absence of crowding out effects of public investment on private investment. Empirical analysis conducted for the 48 U.S. states, using semiparametric smooth-coefficient approach and based on set of data over the period 1978-2000 (Kalyvitis S., and Vella E. 2014), shows significant positive impact of public investment and spending on infrastructure's operations and maintenance, with strong cross-state spillover effects.
The difference of the size of impact of public investment on growth over time is ascribed to changes in
Infrastructure Program within the framework of the topic of "Opportunities to ensure economic development in the Republic of Armenia through the attraction of state borrowed funds".
the quality of institutions (Papagni E., Lepore A. et al., 2019), as the efficiency of public investment will be lower given the negative consequences of administrative bureaucracy, corruption, rent-seeking and other features of bad institutions. In developing countries there is a need to have a system of identification of infrastructure needs where public investment should be directed to, as it will improve the efficiency of capital spending and will increase the positive effects. Even debt-financed projects could have large short- and long-term positive effects on output without increasing the debt-to-GDP ratio, if clearly identified infrastructure needs are met through efficient investment (IMF 2014).
Nevertheless, most of the researchers stress that public investment have both short-term and long-term positive effects with varying coefficients. Meanwhile, from policymaker's point of view, it is important to estimate the size, transmission mechanism and tendency
Historically, Armenian government used capital spending in times of fiscal consolidation, cutting or delaying capital expenditure, when forced to implement fiscal retrenchment, as it was easier than slowing down the growth of mandated current expenditures. The low
of impact of public investment in short and long horizons, in order to be able to design relevant and effective fiscal policy. With this aim, we have used different methods to estimate the aforementioned relationships for Armenian economy.
2. The Dynamics of Public Investment in Armenia
In Armenia, public investment has been an important part of fiscal policy, being the main contributor to development of infrastructure. At the same time, public investment as a share of GDP remained relatively low in last two decades and decreased even more in recent years. The average level of central government investment during 2000-2017 is about 4.2% of GDP, as shown in Figure 1, and the highest levels were recorded in 2007-2009 years. In 2018-2020 years, the average yearly investment by central government decreased, reaching 3.0% of GDP, with the lowest level of 2.5% in 2018. The latter was the lowest value in the
share of public money dedicated to capital spending resulted lower stock of public capital compared to peer countries (IMF, 2017), and did not contribute to acceleration of GDP growth.
whole period analyzed.
CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCM
Figure 1. Public Capital Spending, % of GDP Source: Ministry of Finance of RA (MoF), Author's Calculations
Figure 2. Fiscal Stance and GDP GAP4 Source: Ministry of Finance of RA (MoF), Statistical Committee of the RA, Author's Calculations
Figure 2 shows the direction of fiscal policy and size of output gap in Armenia during 2000-2019 years. It can be seen, that capital investment has been used as an instrument of fiscal downward adjustment multiple times. In particular, significant decrease in level of capital investment can be observed in 2008, when in parallel with decrease of fiscal stance, public investment was decreased. Similar dynamics are recorded in 2010-2011 years. Interestingly, the opposite policy measure was implemented only time, in 2009, when increase of fiscal stance was partly implemented by capital investment. However, in 2015-2017 years, in response to economic slowdown and negative output gap, government increased fiscal stance using current spending, while public investment level remained at relatively low level.
The importance of public investment was officially underlined in the framework of Armenian new fiscal rules (see Hakobyan & Karapetyan, 2018), that
have been adopted in 2017 and became in force since 2018. Specifically, the fiscal rule that is being activated as soon as the government debt to GDP ratio exceeds 40%, sets a lower threshold for capital expenditures, making those to be equal or higher than the budget deficit. That means that Armenian authorities have defined by law, that capital expenditures can not be used as a tool for fiscal downward adjustments, as new debt can not be used for public consumption. Another fiscal rule, that is activated as soon as debt exceeds 50% of GDP, puts upper limit on current primary expenditures (current expenditures less interest spending). The limit is calculated based on average nominal GDP growth in recent seven years, or based on tax income of the central government budget (tax income is used as a limit for current expenditures if debt to GDP ratio exceeds 60%). The latter two rules, ensure that fiscal expansion can only be performed through increase of capital investment.
Underexecution
2018 2019 2020
■ Planned ■ Actual
Figure 3. Public Capital Investment planned and actual, % of GDP Source: Ministry of Finance of RA (MoF),
The RA Draft Law "On the State Budget of the Republic of Armenia" for 2018, 2019, 2020, Explanatory Note
4 GDP is calculated using a simple HP filter with lambda=1600, based on quarterly data of real GDP. Fiscal stance represents the inverse of cyclically adjusted primary fiscal balance.
The new fiscal rules, of course, were designed with the aim of maintaining public debt sustainability, which is also assumed to be a result of increased public investment. If debt to GDP ratio is higher than 40%, new public debt can be used only for capital investment instead of current spending, enhancing economic activity and economic growth and helping to decrease debt to GDP ratio in the future.
As Armenian government debt was higher than 40% of GDP since the adoption of the new fiscal rules, the capital spending was, accordingly, planned with increasing trend. However, due to issues in the stage of implementation, the capital expenditures as a share of GDP did not increased as planned, and in 2018-2020 years, it remained below the historical average. The under execution of capital investment equals almost 0.3% of GDP, meaning that more than 10% of total planned public investment failed to be implemented.
In order to assess and make more factual understanding of the size and direction of effects of public capital investment on the real GDP, and estimate the economic costs of deviation of fiscal policy from planned direction, we have performed both empirical analysis and estimation with a structural model.
2. Estimation of the effects of public capital investment on real GDP
For accessing the effects of the public capital investment on the real GDP, three different methods have been used. First, we estimated a simple regression model, to assess the correlation coefficient between public investment and real GDP and also check the significance of the relationship between those variables. Second, a structural VAR model was used, in order to assess the response function of real GDP to a shock in public capital expenditures aiming at revealing the transmission mechanism and length of impact. Lastly, we used a DSGE model to analyze the long-term effects of capital investment on GDP and other macroeco-
Figure 4. Data used in the model Log of Real GDP Log of Private Investment
13
14 13,8 13,6 13,4 13,2 13 12,8 12,6 12,4 12,2 12
12
11
10
Real GDP
Real GDP Seasonally Adj.
oooooooooo
nomic variables, at the same time considering secondary effects and interrelations between public and private investments.
2.1 Regression model
By estimating an econometric regression model, we aim at assessing the short-term correlation between government investment and GDP growth. In order to have a control variable, we have added the private investment in the regression equation, which allowed to estimate the effects of public capital spending on GDP without the effects of private investment. As private investment data is not being published, the time series has been obtained by subtracting the value of government investment from the gross fixed capital formation, that was taken from the national accounts. Thus, the regression model is the following.
GDPt = p0+pi* GDPt-i + p2 * Igov + p3 * Ipriv + et
GDPt is the log of real GDP at time t taken in 4-th difference, meaning that it is YoY growth in each quarter. Taking 4-th difference of logged data also makes the variable stationary. The Igov is the general government investment, which has been deflated using GDP deflator. This variable has also been made stationary by using the 4-th difference of logged data. Ipriv is the private investment data, which acts as a control variable, in the regression analysis. This variable is made stationary with the same way as the previous ones. All data series have been seasonally adjusted using the U.S. Census X12 method before performing the aforementioned transformations.
The time series used in the model include quarterly observations in the period from 2000 to 2019 and are plotted in Figure 4. The 2020 data is not included in the analysis, because of the possible distortions in economic relationships related to the economic crisis in Armenia caused by COVID-19 pandemic and Artsakh war.
Log of Government Investment 12
11 10 9 8 7 6
Private Investmei
Private Investmei Seasonally Adj.
3333333333
Gov. Investment
-----Gov. Investment
Seasonally Adj.
3333333333
Source: Statistical Committee of the RA, Authors ' calculations
Source: MoF, Authors ' calculations
Estimating equation (1) with OLS methodology, we obtain the following result:
GDPt = 002 + 051 * GDPt+1 + 0037 * Igov + 0133 * Ipriv (6.1147)*** (3.7985)*** (5.2891)*** R-squared = 0.7289, () t-Statistic, *** indicate statistical significance at the level of 1%.
9
8
The coefficient of determination (R-squared) of the regression analysis is high showing that the percentage of the sample variation in GDPt time series that is explained by independent variables, including public investment, is almost 72.9%. All the coefficients in the model are significant at the level of 1%. The correlo-gram of residuals shows no autocorrelation and partial correlation, meaning that residuals are white-noise process. The latter is also confirmed by normality test and absence of heteroskedasticity (the results of tests are presented in Annex 1).
The results of simple OLS regression shows that an increase of central government capital investment growth rate by 1 percentage points will lead to acceleration of real GDP growth by 0.037 percentage points. Taking into account the low share of government investment in GDP shown in Figure 1, this coefficient can be considered as quite high and implies that public investment has a multiplier higher than one. If we divide the coefficient 0.037 by the share of public investment in GDP, we'll obtain multiplier equal to 1.3, meaning that 1 unit of real public investment spending increases real GDP by 1.3 units.
2.2 Structural VAR model
For estimation of the Structural VAR model, we used the same data and the same way of data transformation as we did for the OLS regression estimation. The reason for that is to maintain the consistency of results between two econometric methods.
Structural VAR model requites estimation of reduced form VAR as a first step. Thus, we have estimated a reduced for VAR, then, in order to create IRF with structural shocks, we have identified the A matrix and estimated the structural VAR. For the reduced form VAR model, the equation is the following:
Yt=p0+ (¡J + ut (3)
Where Y is the vector of variables shown below, P0 represents the vector of constants, Pi is the matrix of coefficients and ut is the vector of error terms.
Y =
gov
priv
GDP
(4)
In order to estimate the impulse responses of structural shocks, economic structure should be added to the VAR, meaning that an A matrix need to be identified. The SVAR model equation with A matrix is the following:
A*Yt=ß0+^Yt-1+ut
(5)
A matrix shows the simultaneous relationship between variables. However, the identification requires introducing some constrains in matrix A, because otherwise the model cannot be estimated. There are different methods of identification (Brooks, 2008). In this work, the Cholesky method was used for identification of matrix A (Dostal, 2011). Thus, the matrix A is defined in the following way:
1 0 0T
A =
1
(6)
0
№31 a.37 lJ When using Cholesky identification method, the variables should be correctly ordered, starting from the most exogenous variable and ending with the most endogenous one. In this case, the most exogenous variable is the government investment as we assume that this is a policy variable and its size mostly depend on discretionary fiscal policy decisions. Private investment is in some extent affected by government decisions; thus, it is places as the second variable. Finally, the most endogenous variable is assumed to be the GDP, as both types of investments affect it.
Response of GCV_INVESTMENT to GCV_INVESTMENT
Response to Cholesky Cne S.D. (d.f. adjusted) Innovations ± 2 S.E. Response of GCV_INVESTMENT to PRIVATE_INVESTMENT
Response of GCV_INVESTMENT to GDP
123456789 10
Response of PRIVATE_INVESTMENT to GCV_INVESTMENT
Response of PRIVATE_INVESTMENT to PRIVATE_INVESTMENT
Response of PRIVATE_INVESTMENT to GDP
123456789 10
123456789 10
123456789 10
Response of GDP to GCV_INVESTMENT
Response of GDP to PRIVATE_INVESTMENT
Response of GDP to GDP
123456789 10
Source: Author's Calculations
Figure 5. IRF of SVAR model
The results of estimation of the SVAR model, presented in Figure 5 (detailed results of SVAr model are presented in Annex 2), show that government capital investment have positive effects on real GDP, lasting almost five quarters. After fifth quarter the noticeable change of direction of IRF is due to the pattern of the shock, plotted in top left chart of the Figure 5. Thus, we can conclude that the relationship between Government investment and real GDP is mostly positive in the whole estimated period. The amplitude of response of GDP to shock of government investment is consistent with the results obtained from estimation of OLS regression. At the same time, with SVAR impulse-responses we can see, that the effects of public investment on private investment are not straightforward. In the first period, the increase of public investment cause private investment to drop, however, the latter increases after second period. Thus, with SVAR model we cannot make clear conclusion whether there is a crowding out effects of public investment on private investment. That question, among others, will be an object of analysis using a DSGE model. 2.3 Estimation with a DSGE model The empirical estimation of the relationship between government investment and GDP is very important, however, it more comprehensive estimation can be done using a structural DSGE model, which can cover the long-term effects, taking into account relationship in production function and aggregate supply. Furthermore, the econometric models are based on historical approach, whereas the change of policy decisions are not having exactly the same results every time (Chris-tiano L, et All (2018)). To solve that limitation, and estimate the long-term effects of government investment, taking into account the secondary effects, a DSGE model have been used in this analysis. We chose the New Keynesian DSGE GIMF (Global Integrated Monetary and Fiscal model) model, which is created and developed by IMF (see Laxton et al., 2010) and is widely being used for analysis of effects of policies and shocks (eg. Clements B et al., 2009, Santoro M. 2017). We have calibrated the model to match Armenian data, and have used it in our previous researches (see Grigoryan K., Petrosyan G. et al., 2019). The main advantages of GIMF compared to other DSGE models includes the presence of multiple fiscal policy tools, including expenditure measures (public consumption, public investment, transfers) and tax measures (consumption tax, capital income tax, labor income tax), that allows to analyze the multidimensional effects of fiscal policy. To understand the effects of public investment not only on aggregate demand, but also on aggregate supply, GIMF model assumes that government investment spending has a critical function
in this economy. It augments the stock of publicly provided infrastructure capital Kf, the evolution of which is, after rescaling by technology and population, given by
AKtG_hgn =(1- SGI)Kf + G™ (7) where SGI is the depreciation rate of public capital, Glnv is public investment, g is the economic growth rate and n is the population growth rate. This kind of specification of public capital allows to estimate the productivity effects of public investment.
In addition, in the model it is assumed that Ricardian equivalence does not hold having the following features:
• Multiple distortionary taxes, including taxes on labor income, capital income, consumption and imports,
• Declining life-cycle labor productivity. The life-cycle pattern of labor productivity is declining with their age making wealth less dependent on future labor income. This feature means that workers discount the effects of future payroll tax increases as the latter are likely to occur when they are older and less productive.
• The model contains liquidity-constrained consumers (LIQ) who do not have access to financial markets to smooth consumption. This means that LIQ households are spending all the income they have, so the increase of their after-tax income goes only to consumption.
• OLG households with finite lifetimes - high subjective discount rates. They have different discount rate compared to government; thus, they are not holding the Ricardian equivalence
The coefficients characterizing the weights of the various variables in the model, in particular the data on each type of taxes, government current and capital expenditures, exports, GDP expenditure components and external trade, are presented as a percentage of GDP (without value added taxes) and calculated on the basis of actual 2010-2019 average values. Long-term government debt to GDP ratio is set at 40%, which corresponds to the new fiscal rules.
The discount coefficient (P) was set at 0.95, the planning horizon (life expectancy) of OLG households is 20 years, so the probability of each economic agent remaining alive (0) is assumed to be 0.95 over the next period. The rest of parameters of the model are based on different analysis done previously on Armenian economy (Mkrtchyan, 2008) and our expert judgement (see Table 1). Other parameters were calibrated based on the original model designed by Laxton et all (2010).
Table 1.
List of model Parameters
Parameter Value
World Technology Growth 1.015
Steady State Inflation Rate 1.04
Long Run Real Interest Rate 1.05
Average Planning Horizon in Years 20
Intertemporal Elasticity of Substitution 0.25
Labor Supply Elasticity 0.5
Share of Liquidity Constrained Agents 0.4
Dividend Share of Liq. Constrained Agents 0.125
Depreciation Rate of Private Capital 0.1
Steady State Markups
Nontradables Manufacturing 1.125
Tradables Manufacturing 1.125
Union Wage Setting 1.125
Investment Goods Production 1.075
Consumption Goods Production 1.075
Retail Sector 1.075
Nontradables Import Agents 1.05
Tradables Import Agents 1.05
Government investment, % in GDP
1,2 1,0 0,8 0,6 0,4 0,2 0,0
-0 2 0,0 °,00,00,00,00,00,°0,0 1 3 5 7 9 11 13 15
1,2 1,0 0,8 0,6 0,4 0,2 0,0
Real Private Investment % dev. from steady state 1,1
Real Consumption % dev. from steady state
0,6 0,5 0,4 0,3 0,2 0,1 0,0
1 3 5 7 9 11 13 15
1 3 5 7 9 11 13 15
Real GDP % dev. from steady state
1,4 1,2 1,2 1,0 0,8 0,6 0,4 0,2 0,0
1 3 5 7 9 11 13 15
Real Export % dev. from steady state
Real Consumption % dev. from steady state
0,4 0,3 0,3 0,2 0,2 0,1 0,1 0,0
0,6 0,5 0,4 0,3 0,2 0,1 0,0
1 3 5 7 9 11 13 15
1 3 5 7 9 11 13 15
Real Wage % dev. from steady state
Employment pp. dev. from steady state
Government Debt, % in GDP
0,6 0,5 0,4 0,3 0,2 0,1 0,0
1 3 5 7 9 11 13 15
1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0
0,2 0,0 0,1 n°,10,10,0 0,0 0,4 -0,2
1 3 5 7 9 11 13 15
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0
0|0 3 5 7 9 11 13 15
Figure 6. Results of Government Investment Shock estimated by a DSGE model Source: Authors' calculations
For estimation of the effects of government investment on the macroeconomic variables with the DSGE model we used the shock size equal to 1% of GDP. The advantage of DSGE model is that it allows to analyze not only the size and direction of the effects on GDP, but also the transmission mechanism of its impact. The results of estimation, presented in Figure 6, confirm the main result obtained by empirical analysis. That is, the increase of public capital spending has positive effects on real GDP. Moreover, the positive effect is more than the size of shock: the increase of public investment to GDP ratio by 1 percentage lead to increase of real GDP by 1.2 percent. That means that the multiplier is higher than one, which is in line with the multiplier estimated by regression model.
As we can tell by the results of the DSGE model, there are multiple channels of transmission of higher public investment to real GDP. Firstly, it simply increases the aggregate demand, and lead to more output. However, this channel is not very significant as small part of investment goods are produced domestically. Stronger channel is through production function. Higher government investment increases public capital, leading to increased productivity, and positively affecting the growth rate (in short term) and the level (in longer horizon) of potential output. The long-term effect is visible in the chart of response of GDP to increase of public investment (Figure 6, left chart in the middle row). One-time public investment shock has permanent effect on GDP, as it stays on average 0.3 percentage points higher from the initial level after the shock is ended, which can be interpreted as increase of potential output.
Higher government investment also leads to higher private investment, due to higher productivity and higher consumption. The hike of consumption can be explained by increased wages and higher employment. The latter ones are affected by higher demand for labor and increased production. Thus, the dynamics private investment as a result of public investment shock shows that there is crowding in effects of public investment on private investment. This result is intuitive and expectable for Armenian economy. The reason for that is the fact, that public investment projects are mostly financed through external debt, and does not create lack of resources in domestic economy and does not have
significant effect on interest rates. On the other hand, increase of public capital makes private sector more productive, as the demand for public infrastructure investments is still far from being exhausted.
In fiscal side, there are also positive developments. Increase of public investment, leads to higher public debt (estimation is done with a scenario, where the increase of public investment is fully financed with public debt), however, the increase of debt to GDP ratio is smaller than increase of public investment. Moreover, in the long-term debt to GDP ratio has downward trend, due to higher potential GDP.
3. Conclusions
The importance of capital investment leaves almost no doubt both in theoretical and empirical studies. Yet, the size and length of impact of public investment on output varies in different countries depending on various conditions. Thus, from the policymakers' point of view for each country separate analysis should be done, to have idea about the most expected impact of public investment on macroeconomic variables. To reach that goal, in this paper we have analyzed the dynamics of government investment and estimated their short- and long-term effects using a set of different tools. The estimations have been performed using an OLS regression, a structural VAR model, and a DSGE model.
In Armenia, public investment has been on low level relative to GDP, and further decreased during 2018-2020 years, mainly because of lack of capacity of implementation of the projects. Before introduction of new fiscal rules in 2017, capital expenditures were frequently used as an instrument for fiscal adjustments, as the government current expenditure have large mandatory part. However, both empirical analysis and estimation with a structural model showed that public investment has significant positive impact on Armenian GDP and other macroeconomic variables. The multiplier of public investment is 1.2-1.3, which is quite high and shows that increase of public investment is a right direction of fiscal policy. The SVAR model also shows, that the relationship between Government investment and real GDP is mostly positive in the whole estimated period.
In addition to empirical analysis, we used a structural general equilibrium model to assess the long term
effects of public investment, as well as to analyze the transmission channels. The DSGE model showed three important results: first, it confirms the hypotheses that public investment has positive long term effects on output, meaning that one time increase in public investment can have permanent effect on potential GDP. Second, increase of public investment have crowding in effect on private investment. This result is explained by debt-financing of capital expenditures and low level of development of infrastructure (as a result high return of increased public capital). Third, the increase of public
investment by 1% of GDP, fully financed with debt, increases government debt to GDP ratio by less than 1 percentage points.
Therefore, we can conclude, that increase of public investment will be a right direction of fiscal policy of Armenia, which will accelerate economic growth, at the same time not causing risks for fiscal sustainability. Thus, Armenian government need to increase the capacity of implementation of public investment projects and enhance their level in GDP at least close to the historical 4.0%. Moreover, the goal of the government should be reaching the pre-crisis highest level, i.e. 6.2% in GDP that was recorded in 2007.
Annex 1. Results of Residual diagnostic tests of the regression model
.10 .05 .00 ,05-.10 .15
ll
A »\ a a/\A N\ f\ WA V \/ \A A a a a A
1 V № V / vv Ti/^V VW
T
2002 2004 2006 2008 2010 2012 2014 2016 2018
.2 .1 .0 -.1 -.2 -.3
|_Residual_Actual_Fitted
Figure 1. Fitted and Actual values
Date: 05/09/21 Time: 18:09 Sample: 2000Q1 2020Q4 Included observations: 75
Q-statistic probabilities adjusted for 1 dynamic regressor
Autocorrelation
Partial Correlation
AC
PAC Q-Stat Prob*
. i . i i . i 1 -0.049 -0.049 0.1908 0.662
. i* i i* i 2 0.130 0.127 1.5184 0.468
. i* i i* i 3 0.113 0.127 2.5436 0.467
*i . i *i . i 4 -0.163 -0.173 4.7073 0.319
. i* i i* i 5 0.171 0.131 7.1078 0.213
. i . i i . i 6 -0.031 0.013 7.1885 0.304
. i . i i . i 7 -0.011 -0.018 7.1979 0.409
**i . i **i . i 8 -0.297 -0.385 14.821 0.063
. i . i i . i 9 0.013 0.072 14.837 0.096
. i . i i* i 10 -0.005 0.089 14.839 0.138
*i . i *i . i 11 -0.176 -0.149 17.643 0.090
. i . i *i . i 12 0.018 -0.170 17.673 0.126
*i . i i . i 13 -0.152 0.036 19.835 0.099
*i . i *i . i 14 -0.177 -0.146 22.802 0.064
. i . i i . i 15 0.065 -0.017 23.209 0.080
. i . i *i . i 16 -0.047 -0.085 23.429 0.103
*i . i i . i 17 -0.083 -0.040 24.119 0.116
. i . i i . i 18 0.034 -0.008 24.236 0.147
. i . i i . i 19 0.041 0.060 24.408 0.181
. i . i *i . i 20 -0.030 -0.110 24.505 0.221
. i . i i . i 21 0.061 -0.040 24.898 0.252
. i . i i . i 22 0.040 -0.043 25.076 0.293
. i . i i* i 23 0.057 0.167 25.433 0.328
i . i 24 0.091 -0.032 26.374 0.334
i* i 25 0.174 0.094 29.890 0.228
.i. i i . i 26 0.007 -0.010 29.896 0.272
*i . i 27 -0.068 -0.089 30.450 0.294
i . i 28 0.115 -0.022 32.080 0.271
*i . i 29 -0.189 -0.133 36.589 0.157
i* i 30 0.135 0.105 38.941 0.127
*i. i *i . i 31 -0.088 -0.092 39.959 0.130
*i . i i . i 32 -0.076 0.032 40.742 0.138
*Probabiliti es may not be valid for this equation specification.
3
Figure 2. Correlogram of Residuals
Date: 05/09/21 Time: 18:10 Sample: 2000Q1 2020Q4 Included observations: 75
Autocor relation Partial Correlation AC PAC Q-Stat Prob
. |*. | . |*. | 1 0.155 0.155 1.8704 0.171
. |*. | . |*. | 2 0.184 0.164 4.5395 0.103
. |*. | . | . | 3 0.076 0.028 4.9984 0.172
. |*. | . |*. | 4 0.182 0.146 7.6881 0.104
. |** | . |** | 5 0.256 0.214 13.075 0.023
. |*. | . | . | 6 0.108 0.008 14.050 0.029
. | . | . | . | 7 0.048 -0.047 14.242 0.047
. | . | . | . | 8 0.016 -0.038 14.264 0.075
. | . | . | . | 9 0.042 -0.028 14.416 0.108
. | . | .*| . | 10 -0.041 -0.120 14.562 0.149
. | . | . | . | 11 -0.035 -0.056 14.674 0.198
. | . | . | . | 12 -0.045 -0.015 14.860 0.249
.*| . | .*| . | 13 -0.101 -0.087 15.817 0.259
. | . | . | . | 14 -0.063 -0.019 16.189 0.302
.*| . | . | . | 15 -0.129 -0.052 17.792 0.274
.*| . | . | . | 16 -0.113 -0.050 19.035 0.267
.*| . | .*| . | 17 -0.156 -0.083 21.447 0.207
. | . | . | . | 18 -0.052 0.052 21.725 0.244
.*| . | .*| . | 19 -0.154 -0.077 24.173 0.190
. | . | . | . | 20 -0.064 0.019 24.603 0.217
.*| . | .*| . | 21 -0.162 -0.068 27.399 0.158
.*| . | .*| . | 22 -0.158 -0.091 30.114 0.116
. | . | . | . | 23 -0.029 0.050 30.205 0.144
.*| . | . | . | 24 -0.096 -0.031 31.257 0.147
. |*. | . |*. | 25 0.124 0.193 33.046 0.130
. | . | . |*. | 26 0.023 0.093 33.108 0.159
.*| . | .*| . | 27 -0.107 -0.142 34.482 0.152
. | . | . | . | 28 -0.055 -0.058 34.860 0.174
. |*. | . |*. | 29 0.097 0.111 36.048 0.172
. |*. | . | . | 30 0.147 0.049 38.834 0.129
. | . | . | . | 31 0.054 -0.039 39.215 0.148
.*| . | .*| . | 32 -0.086 -0.143 40.210 0.151
Figure 3. Correlogram of Residuals Squared
24
20
16
12
0
-0.12 -0.10 -0.08 -0.06
-0.04 -0.02 0.00 0.02
Figure 4. Histogram
0.04 0.06 0.08
Normality Test
Series: Residuals Sample 2001Q2 2019Q4 Observations 75
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera Probability
I.39e-19 -0.001052 0.078533 -0.114842 0.036449 -0.736045 4.214973
II.38502 0.003371
8
4
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 0.734204 Prob. F(2,69) 0.4836
Obs*R-squared 1.562837 Prob. Chi-Square(2) 0.4578
Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/09/21 Time: 18:11 Sample: 2001Q2 2019Q4 Included observations: 75
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
D4 RG DP(-1) -0.031811 0.108266 -0.293822 0.7698
D4_INV_GOV 0.002903 0.010155 0.285922 0.7758
C 0.001576 0.007168 0.219914 0.8266
D4_INV_PRIV 0.005861 0.026508 0.221086 0.8257
RESID(-1) -0.016536 0.148863 -0.111084 0.9119
RESID(-2) 0.154545 0.139523 1.107667 0.2719
R-squared 0.0 20838 Mean dependent var 1.39E-19
Adjusted R-squared -0.050116 S.D. dependent var 0.036449
S.E. of regression 0.037351 Akaike info criterion -3.660309
Sum squared resid 0.096260 Schwarz criterion -3.474910
Log likelihood 143.2616 Hannan-Quinn criter. -3.586281
F-statistic 0.293682 Durbin-Watson stat 2.040933
Prob(F-statistic) 0.914878
Figure 5. Serial Correlation - LM Test Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 1.6 17210 Prob. F(3,71) 0 .1930
Obs*R-squared 4.797157 Prob. Chi-Square(3) 0.1873
Scaled explained SS 6.910754 Prob. Chi-Square(3) 0.0748
Test Equation:
Dependent Variable: RESIDA2 Method: Least Squares Date: 05/09/21 Time: 18:12 Sample: 2001Q2 2019Q4 Included observations: 75
Variable Coefficient Std. Error t-Statistic Prob.
C 0.001725 0.000384 4.498591 0 .0000
D4 RGDP(-1) -0.005335 0.005265 -1.013323 0.3143
D4 INV GOV -0.000836 0.000613 -1.363631 0.1770
D4_INV_PRIV -0.001039 0.001581 -0.657366 0.5131
R-squared 0.063962 Mean dependent var 0.001311
Adjusted R-squared 0.024411 S.D. dependent var 0.002366
S.E. of regression 0.002337 Akaike info criterion -9.227992
Sum squared resid 0.000388 Schwarz criterion -9.104393
Log likelihood 350.0497 Hannan-Quinn criter. -9.178641
F-statistic 1.617210 Durbin-Watson stat 1.774811
Prob(F-statistic) 0.193018
Figure 6. Heteroskedasticity test Test
Annex 2. Results of diagnostic tests of the SVAR model
Vector Autoregression Estimates Date: 05/09/21 Time: 18:14 Sample (adjusted): 2002Q1 2019Q4 Included observations: 72 after adjustments Standard errors in ( ) & t-statistics in [ ]
D4 INV GOV D4 INV PRIV D4 RGDP
D4 INV GOV(-1) 0.139667 (0.13332) [ 1.04763] 0.095299 (0.05671) [ 1.68058] 0.011857 (0.01385) [ 0.85585]
D4 INV GOV(-2) 0.194442 (0.13949) [ 1.39391] 0.103114 (0.05933) [ 1.73787] 0.024276 (0.01450) [ 1.67469]
D4 INV GOV(-3) -0.120592 (0.13578) [-0.88814] -0.051065 (0.05775) [-0.88418] -0.024315 (0.01411) [-1.72323]
D4 INV GOV(-4) -0.445953 (0.13996) [-3.18623] -0.006102 (0.05953) [-0.10250] -0.021687 (0.01454) [-1.49107]
D4 INV PRIV(-1) -0.296609 (0.35763) [-0.82937] 0.378762 (0.15212) [ 2.48990] 0.071016 (0.03716) [ 1.91088]
D4 INV PRIV(-2) 0.984592 (0.36523) [ 2.69579] 0.195314 (0.15535) [ 1.25724] 0.050477 (0.03795) [ 1.32995]
D4 INV PRIV(-3) -0.104106 (0.37882) [-0.27481] 0.023926 (0.16113) [ 0.14849] -0.073842 (0.03937) [-1.87576]
D4 INV PRIV(-4) 0.254164 (0.35013) [ 0.72591] -0.361889 (0.14893) [-2.42994] -0.019760 (0.03638) [-0.54308]
D4 RGDP(-1) -1.056506 (1.39128) [-0.75938] 1.507483 (0.59178) [ 2.54736] 0.690640 (0.14458) [ 4.77694]
D4 RGDP(-2) -0.899767 (1.57639) [-0.57078] -1.056964 (0.67052) [-1.57634] -0.074190 (0.16381) [-0.45289]
D4 RGDP(-3) -1.332602 (1.59244) [-0.83683] 0.724037 (0.67734) [ 1.06893] 0.052403 (0.16548) [ 0.31667]
D4 RGDP(-4) -0.089852 (1.26005) [-0.07131] 0.609796 (0.53596) [ 1.13776] 0.037452 (0.13094) [ 0.28602]
C 0.181252 (0.08606) [ 2.10613] -0.064454 (0.03661) [-1.76078] 0.016278 (0.00894) [ 1.82016]
R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent 0.423718 0.306508 9.239622 0.395732 3.615030 -28.24963 1.145823 1.556888 0.023836 0.475204 0.603728 0.523130 1.671660 0.168325 7.490638 33.29899 -0.563861 -0.152796 0.063765 0.243752 0.719898 0.662928 0.099777 0.041123 12.63645 134.7699 -3.382498 -2.971433 0.060602 0.070832
Determinant resid covariance (dof adj.) 5.01 E-06
Determinant resid covariance 2.76E-06
Log likelihood 154.3635
Akaike information criterion -3.204541
Schwarz criterion -1.971346
Number of coefficients 39
Figure 1. Reduced form VAR estimation results
Inverse Roots of AR Characteristic Polynomial
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
• •
• •
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Figure 2. Inverse Roots of AR Characteristic Polynomial
Cor(D4_INV_GOV,D4_INV_GOV(-i))
Autocorrelationswith Approximate 2 Std.Err. Bounds Cor(D4_INV_GOV,D4_INV_PRIV(-i))
Cor(D4_INV_GOV,D4_RGDP(-i))
1 2 3 4 5 6 7 8 9 10 11 12 Cor( D4_I NV_PR IV, D4_I NV_GOV(-i))
1 2 3 4 5 6 7 8 9 10 11 12 Cor(D4_INV_PRIV,D4_INV_PRIV(-i))
1 2 3 4 5 6 7 8 9 10 11 12 Cor(D4_INV_PRIV,D4_RGDP(-i))
1 2 3 4 5 6 7 8 9 10 11 12
Cor(D4_RGDP,D4_INV_GOV(-i))
1 2 3 4 5 6 7 8 9 10 11 12
Cor(D4_RGDP,D4_INV_PRIV(-i))
1 2 3 4 5 6 7 8 9 10 11 12
Cor(D4_RGDP,D4_RGDP(-i))
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
Figure 3. Autocorrelations with Approximate 2 Std. Err. Bounds
-.2
-.2
-.2
-.4
-.4
-.4
-.2
-.2
-.2
-.4 -
-.4
-.4
-.2
-.2
-.2
-.4 -
-.4
-.4
Response of D4_INV_GOV:
Period D4_INV_GOV D4_INV_PRIV D4_RGDP
1 0.395732 0.000000 0.000000
2 0.065144 -0.068179 -0.037531
3 0.013927 0.076224 -0.079009
4 -0.041398 -0.032789 -0.058473
5 -0.193757 0.019928 -0.084886
6 -0.073646 0.034991 -0.015406
7 -0.004816 -0.044079 0.025945
8 0.042737 0.021556 0.019568
9 0.112535 -0.009909 0.047441
10 0.064995 -0.011903 0.005562
Response of D4_INV_PRIV:
Period D4_INV_GOV D4_INV_PRIV D4_RGDP
1 -0.054616 0.159218 0.000000
2 0.026053 0.090204 0.053551
3 0.047346 0.075497 0.016144
4 0.027418 0.082556 0.031596
5 0.039986 0.023363 0.046824
6 -0.010711 0.029773 0.020641
7 -0.030386 0.025187 0.031754
8 -0.023623 0.000295 0.030329
9 -0.027831 0.009939 0.023284
10 -0.000548 0.000250 0.032776
Response of D4_RGDP:
Period D4_INV_GOV D4_INV_PRIV D4_RGDP
1 0.005988 0.019833 0.035524
2 0.004949 0.025005 0.024534
3 0.012446 0.029432 0.017667
4 0.009377 0.016918 0.014244
5 -0.000790 0.014540 0.008549
6 -0.005245 0.008800 0.009671
7 -0.009181 0.002736 0.009522
8 -0.008071 0.003121 0.009321
9 -0.002025 -0.000507 0.010943
10 0.001895 -0.001118 0.008900
Cholesky Ordering: D4_INV_GOV D4_INV_PRIV D4_RGDP
Figure 4. Impulse Response to Cholesky One S.D. (d.f. adjusted) Innovations
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