# Introduction
Owing to the numerous conflicts and wars in the world, military expenditures are in dispensable for every country to protect its national independence and boundaries. Unfortunately, these military expenditures have formed a hindrance for other sectors to develop their services which consequently affects citizens negatively. Despite the scientific progress that humanity has experienced, the cries of children dying of hunger in many countries, and continued calls for dialogue about religion and civilizations: a failure has marked the foundation of sustainable peace in the world. Examining the maps of conflicts, wars, and poverty in the Middle East symbolizes such failure. The paper aims to measure the impact of each of two variables: Gross Domestic Product (GDP) and Human Development Index (HDI) on worldwide military expenditures (ME). After consulting the data on the World Bank website, 116 countries without missing data have been selected covering the period 2008-2017 for the three variables: that is small T and large N balanced panels. Economically speaking, and given the The paper is divided into five sections, the first being the introduction. In the second, a panoramic view of all variables is presented using descriptive statistical analysis. Review of literature is devoted to the third section, and the econometric methodology and applications are dealt with in the fourth one. Finally, in the fifth section, a conclusion is made from the findings with a recommendation to continue this research that may be considered as the basis for future analysis of duration analysis or II.
# Descriptive Statistical Analysis
In a graph illustration, the researchers describe in depth the temporal evolution of the variables by focusing on the political and economic events that left their traces on the studied variable. Also, statistical calculations help to provide an insight into the extent of change over the period under review. Among these statistics, the Min, the Max, the median, the mean, the standard deviation and the Compound Annual Growth Rate (CAGR) that is a specific term for the geometric progression ratio that provides a constant rate of evolution over the period. For a time series, the CAGR, between the first and final observations is given by the formula, CAGR(1, T) = ? current situation in the world, especially the competition between countries and the search for new markets to sell the various goods and services, the GDP variable should have a positive impact on the ME variable because it cannot be carried out without financial resources. However, a high score in a country's HDI variable should reduce its military expenditures to the strict minimum. Nevertheless, a state cannot make such decision alone, especially if elsewhere the world is experiencing conflicts of all kinds. Indeed, there is a need for a global policy that aims to reduce the military spending and thereby increase spending in the areas that bring about social and economic well-being such as the availability of job opportunities, health care, schooling, housing, justice, and first and foremost law. Technically, the paper approaches the construction of a Dynamic Panel Data (DPD) model by taking ME as a dependent variable and GDP and HDI are considered as exogenous variables. The uses of DPD models were extensive in the last two decades especially after the appearance of econometric approaches which allow adequate estimates of the parameters in question. Among these, are the publications made by the remarkable works of Arellano and Bond (1991) using the GMM estimator to estimate the DPD models and considering the one-step Arellano-Bond estimator for the two-step Arellano-Bond estimator that is asymptotically consistent and efficient in the presence of heteroscedasticity. This approach involves extensive exploitation of instrumental variables in first-difference equations. Arellano-Bover (1995) used lagged differences as possible instruments for equations in levels (level GMM estimator), Blundell and Bond (1998) improved the properties of the standard first-differenced GMM estimator by using two alternative linear estimators , Arellano(2002) discussed the theory of instrumental-variables (IV) estimation developed by Sargan, Bond (2002) to refer to econometric methods for DPD models that focus on panels where a large number of individuals are observed for small time periods. The Arellano-Bond (AB) 1-step and 2-step estimators are used to estimate the DPD model considering the first differences of the two independent variables GDP and HDI, as strictly exogenous regressors. The effects between the variables are investigated respecting the orthogonality conditions that exist between lagged values of the dependent variable and the disturbances signaling that the method generates consistent estimates.
Like GDP, the military expenditures ME116 and MEW keep a similar trend with CAGR of 1.487% and 1.436% respectively. Since the corresponding medians have relatively higher values than the means, this translates into a decrease over the period 2013-2017. The global financial crisis did not negatively affect the military expenditures ME116 and MEW as it did with the variables GDP116 and GDPW. This information reveals a mad trend of humanity towards weaponry at the expense of health and education expenditures. This policy was very clear for a leading country like the United States where a drop in GDP has witnessed yet military spending has increased between 2008 and 2009 with a growth rate of(7.637 %). After 2014, the military expenditures decreased both in ME116 and in MEW. This decrease is due to the significant drop in the crude oil prices in two consecutive years 2015 and 2016. For the United States, it seems that after 2011, the MEUS variable decreased remarkably. The reason behind this decrease is the withdrawal of the American army in Iraq due to the announcement made by President Obama on October 21, 2011, that all U.S. troops and trainers would leave Iraq by the end of the year. Figure (3) illustrates both variables RMEGDP116 and RMEGDPW. These ratios peaked in 2009, one year later after the global financial crisis. Indeed, for the 116 countries, the GDP decreased at a rate of 5.47%, while the military expenditures rose by 3.83% and as a result, the ratio increased at an annual rate to 9.84%. For the world, the GDP decreased by 5.19 %, the military expenditures increased by 3.72%, and the ratio increased by 9.4%. After 2009, it seems that an almost decreasing linear trend has scored in both time series, with a break in 2015 during which the variable RMEGDP116 increased with an annual rate of (1.35 %). Over the whole period, CAGR recorded negative values of (?1.09 %) and (?1.24 %) for RMEGDP116 and RMEGDPW respectively. Finally, let's contemplate the evolution of the ratio of military expenditure of 116 countries to military expenditure of the world RME116W and the ratio of GDP of 116 countries to GDP of the world RGDP116W. Two points deserve to be mentioned: first, focusing on the period 2008-2009, we notice a decrease of (0.3 %) in RGDP116W and an increase of (0.11%) in RME116W. Second between 2014 and 2015, RME116W increased by (1.73 %) while RGDP116W decreased by (0.09%). Notes allows a comparison of three-time series: GDP associated with 116 countries chosen in this research (GDP116), GDP in the world (GDPWORLD) and the GDP of the United States of America (GDPUS)due to the importance of America's economy and its role in the international arena. The Graphs of GDP116 and GDPW almost have the same shape with a gap almost conserved overtime. Between 2008 and 2009, a small decline is observed due to the global financial crisis. The crude oil prices per barrel reached 107.95 USD in June 2014 (year high), and a sudden fall has started to finish in 53.45 USD (year close) with a yearly percent change at (?50.48 %). The price has continued its decline in 2015 to reach the price year closed at 37.04 USD with an annual percent change (?30.7 %). These figures explain well the variation in the trend of GDP variables in both 116 countries and the world. However, the GDP of the United States has not changed its growth trend. The US is the largest oil consumer worldwide, and therefore, has economic and political interests in low oil prices. The evolution of the variable GDPUS has maintained a growing trend over the period 2009-2017, except the small decrease observed between 2008 and 2009 from (bn 14718.58) to (bn 14418.74), i.e. ?2.037% .
( ( According to the United Nations Development Programme (UNDP), there are four human development classifications:
An intriguing point that needs to be well explored is the sort of data associated with the variables GDP116 and ME116 according to HDI from smallest to largest. This allowed us to divide the 116 countries into four groups: those that have LHD, MHD, HHD, and VHHD respectively. For each group, two ratios have been calculated: The first administer the share of the total GDP of the group to the GDP116, denoted ?????? ???????? , and the second is the share of the entire military expenditure of the group to the ME116, denoted by ???? ???????? . The graphs for each 10 years (2008-2017) are included in appendix one. It is clear that the ?????? ???????? and ???? ???????? variables contain 70.3% of
# Literature Review
The Arellano-Bond estimator, usually called difference GMM, is based on the a generalization for (2SLS) and instrumental-variable (IV) estimators. If the residuals are homogeneous and not correlated, then the estimator (GMM) is equated with the (2SLS) estimator in the over-identified structural equation and with (IV) estimator in the identified structural equation. While if heteroscedasticity is present in the data, then (GMM) estimator will be more accurate than the estimator (2SLS) and (IV) estimators, see Cameron & Trivedi (2005). In this context, all began seriously with Sargan (1958), and then Hansen (1982) developed the properties of the GMM estimator particularly the strong consistency and asymptotic normality of such estimators under the assumption that the observable variables are stationary and ergodic. Concerning the GMM estimator, Kholodilin, Siliverstovs, and Kooths (2008) used the GMM estimator of Arellano -Bond to estimate the fixed-effects model without spatial autoregressive lags for the annual growth rates of the real GDP for each of the 16 German Länder. Swaleheen (2011) studied the effect of corruption on the rate of economic growth using AB estimator and carried out a finding revealing a significant indirect effect on the growth rate of real per capita income. Bun and Sarafidis (2013) gave a broad overview emphasizing on GMM estimator and discuss the assumption of mean stationarity underlying the system GMM estimator. Oikarinen and Engblom (2016) analyzed the data of Finnish housing price dynamics over 1988-2012 using the Arellano-Bover/Blundell-Bond estimation technique. Kiviet, Pleus, and Poldermans (2017) used simulation to permit a reasoned choice between many different possible implementations of Arellano-Bond and Blundell-Bond generalized method of moments (GMM) estimators. An excellent recent paper for Hsiao and Qiankun (2017) considered the asymptotic properties of the GMM estimators for structural equations in a panel dynamic simultaneous equations model and showed that the consistency of the GMM estimator need N (number of individuals) much greater than T (size of time series), i.e., ?? ?? ???? ???? 0. However, the GMM estimator is still asymptotically biased as long as
?? 3 ?? ???? ???? ?? ? 0 < ?.
# Notes
Generalized Method of Moments (GMM) that is the jackknife Instrumental Variables Estimation (JIVE) proposed by Imbens, Angrist, and Krueger (1999), is asymptotically normal without an asymptotic bias. To see how the GMM estimators and particularly the Arellano-Bond estimator work, we guide researchers to Greene (2008) for a general GMM estimation of DPD models developed in several stages in the literature, Arellano (2018) for the necessary steps to reach the Arellano-Bond estimator, Mourad (2019) for a panoramic analysis of GMM estimators, and Mourad, El-Mourawed and Mourad (2019) for using the Arellano-Bond approach in estimating a DPD model that links the variables: GDP, HDI, and ME in 116 countries.
IV.
# Econometric Methodology and Applications
The study focuses on three variables: Military Expenditures chosen as a dependent variable (Y it ), Gross Domestic Product (GDP = X 1it ) and Human Development Index (HDI = X 2it ) are taken as two lagged independent variables and considered as predetermined or strictly exogenous variables. All the variables are taken in natural logarithm. In fact, for purposes of economic analysis, the great advantage of the natural logarithm is that small changes in the natural logarithm of a variable are directly interpretable as percentage changes, to a very close approximation. Furthermore, this use can be justified based on statistical and economic theories. The proposed dynamic panel data (DPD) model is considered with constant coefficients. The samples contain (NT = 116 × 10 = 1160) observations. The data are available on the website of the World Bank. The (? 0t , t = 2008, ? ,2017) reflect the time impact resulting from macroeconomic shocks and political crisis that affect the world in the same way. Finally, f i represents the country-specific effect without regard to the time, but it is specific to each country, and it depends on the degree of the conflict situations that arise among countries. Both endogenous regressors and predetermined regressors can be correlated with disturbance ? it and with the individual specific effect f i . If X 1,i,t and X 2,i,t are considered as predetermined variables then ?E?X k,i,t ? is ? ? 0, k = 1,2 for s < ??? but zero otherwise. In this case, ?X k,i,1 , ? , X k,i,s?1 , k = 1,2), are valid instruments of the equation in first difference for the time s. If the X 1,i,t and X 2,i,t are considered as strictly exogenous then they can be used as valid instruments for all equations both in level and in first difference. In fact, since the first differences of instrument variables are uncorrelated with the fixed effects, more instruments can be introduced allowing the improvement of efficiency (Oikarinen and Emblem (2016)). In the research carried out by Arellano and Bover (1995), Blundell and Bond (1998), the potential weakness of the Arellano-Bond estimator has been revealed especially if the left-hand variable follows a random walk process, in which case, the instruments associated with the level lagged variables are poor instruments for the first difference variables. Moreover, with the Arellano-Bond approach, the other variables that are presumed to be endogenous can be instrumented. The choice of the maximum values of (p i , i = 1,2,3) is chosen (p = 3) rounding up
using int ?4 ? T 100 ? 1 4 ?
? according to the Schwert (1989); the optimal orders will be made experimentally using, for example, an automatic approach such as AIC, BIC, and HQ.
Considering the differenced dynamic panel data, the country-specific effect f i and the constant term ? will be removed, hence the model (M 1 ) becomes:
Y it = ? + ?? 0t + ? ? j p 1 ?? =1 Y it?j + ? ? j p 2 j=1 X 1,i,t?j + ? ? j p 3 j=1 X 2,i,t?j + f i + ? it (M 1 )
Where the residuals are used for (t ? p + 2) and ?? t represents the time dummy variables that are limited to (10 ? (p + 1)) variables. For example, if (p = 2) then the time dummy variables will be:
d 2011 = ? 1 t = 2011 0 t ? 2011 , ? , d 2017 = ? 1 t = 2017 0 t ? 2017
Noting now that the disturbances ?? it follow a moving average process at first order MA (1). The instrumental variables approach proposed by Anderson and Hsiao (1982) does not manipulate the global information in the data which made Arellano and Bond (1991) push ahead the dynamic panel data (DPD) model using the Generalized Method of Moments (GMM) to obtain more efficient estimates of the parameters considering the lagged values of the instrumented variables as internal instrumental variables with the possibility to introduce external instrumental variables in the model. The number of parameters in the model (M 2 ) varies with p and with the size of the time series. More precisely, for p=0, 1, 2 and 3, the number will be 9,12, 15 and 18 respectively. To determine the selection of the optimal orders for the DPD model according to the Arellano-Bond Two-Step Estimator, the findings in Table (1) reveal that the AIC criterion suggests the orders (3, 3, 0) while BIC and HQ criteria both propose the orders (3,0,0). Investigating the significance of parameters for each model, the lag-3 parameter associated with the variable ?Y i,t?3 is not significant at 5% level (p -value= 0.44895). Similarly for the parameters associated with the variables In the following, with the optimal orders , the model (M 2 ) is written as: ?Y i,t = ?? t + ? ? j 2 j=1 ?Y i,t?j + ? 0 ?X 1,i,t + ?X 2,i,t?2 + ?? i,t (M 3 ) According to the moment or orthogonality conditions associated with both models in difference and in level, the identification of the instrumental variables for the endogenous variable ?Y i,t respects the following:
E ?Y i,t?(p+1) ?Y i,t?p ?Y i,t?(p+1) ?? ? 0 but E?Y i,t?(p+1) ? i,t?p ? = 0 , ?Y i,t?(p+1) ? i,t?p+1 ? = 0 and by consequence E ?Y i,t?(p+1) ?? i,t?p+1 ?? i,t?p ?? = E?Y i,t?(p+1) ?? i,t?p+1 ? = 0. This means that the variable Y i,t?(p+1) ?Y i,t?p ?Y i,t?(p+1) ?.
To render this task more comprehensive, we assume p= 2. (p 1 = 2, p 2 = 0, p 3 = 2)
For t = 4 E?Y i,1 ? i,4 ? = 0 , E?Y i,1 ? i,3 ? = 0 ? E?Y i,1 ?? i,4 ? = 0 E?Y i,2 ? i,4 ? = 0 , E?Y i,2 ? i,3 ? = 0 ? E?Y i,2 ?? i,4 ? = 0 E?Y i,3 ? i,4 ? = 0 , E?Y i,3 ? i,3 ? ? 0? 2
So, the moment conditions are given by: E(y i?? ? it ) = 0; ? s = 1, ? , t ? 2, t = 4, ? , T. Hence, there are available instruments for individual ( ) associated with the endogenous variable ?Y i,t for the first difference equation(M 2 ).
If the variables ?X 1,i,t ? and ?X 2,i,t ? are assumed to be strictly exogenous with E?X 1,i,s ? i,t ? = E?X 1,i,s ? i,t ? = 0 ?(t, s) but correlated with f i then they are valid instruments for the first-differenced equation. Indeed, we formally add the following instruments: Therefore, all these instruments should be added to each column in V i ? causing vastly overidentified restrictions. Thus, in the following, the only held instruments will be the 35 ones associated with the endogenous variable, plus 7-time dummy variables plus two instruments linked to the strict exogenous variables, so 44 instruments. The(M 3 ) model can be reformulated as:
Fort = 4: ?X 1,i,y i,t = ?? i,t ? ? + ? i,t (M 4 )
Where
?? i,t ? = ??? 11 , ? , ?? 17 , ?Y i,t?1 , ?Y i,t?2 , ?X 1,i,t , ?X 2,i,t?2 ? ? = (?? 11 , ? , ?? 17 , ? 1 , ? 2 , ? 0 , ? 2 )?
If the instrumental variables associated with the endogenous variable and the 7time dummy variables are only held then the corresponding matrix of instruments for the lagged difference will be:
V i ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Y i,09 0 0 Y i,08 0 0 11 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 0 Y i,10 Y i,09 Y i,08 12 0 ? ? ? ? ? ? ? ? 0 ? ? 0 0 0 0 0 ? Y i,15 Y i,14 Y i,13 Y i,12 Y i,11 Y i,10 Y i,09 Y i,08 ?? 17 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? × ( 3)
Where m = (2 + 1) + (3 + 1) + ? + (8 + 1) = 42 and (T ? 3) = 7.
The residual vector ? i is given by: ? i = ?? i,2017 , ? i,2016 , ? i,2015 , ? i,2004 , ? i,2013 , ? i,2012 , ? i,2011 ? ?with dimension(1 × 7). According to Arellano-Bond, the initial weighting matrix H i must be constructed; it is the result of the covariance of residuals ? it which is a moving average process with first order MA(1).
Assuming ? ? 2 = 1, the variance-covariance matrix of the error is:
?? ?? = ? ? 2 ? ? ? ? ? 2 ? 1 0 0 0 0 0 ?1 2 ? 1 0 0 0 0 0 ? 1 2 ? 1 0 0 0 0 0 ? 1 2 ? 1 0 0 0 0 0 ? 1 2 ? 1 0 0 0 0 0 ? 1 2 ? 1 0 0 0 0 0 ? 1 2 ? ? ? ? ? = ? ? 2 ?? ?? ? ?? × ??
The moment conditions:
E?? V i ? ?? ?? N i=1 ? = 0
includes computing the following estimator of parameters:
(??)
# Notes
The one-step (GMM)
d d m T-? (????) A N = ? ?? ?? ? V i ? H i V i ?? ??=?? ? ?1 ? (42 × 42) (??) ? (???? × ??) × (?? × ????) × (?? ?? ?? ?? ?? ?? ?? ??? ? ? ? ? ? ? ? ?? × ????
Indeed, the two-step Arellano-Bond estimator uses the residuals of the one-step estimator to become consistent and asymptotically efficient in the presence of heteroscedasticity.
estimator needs ?? ? ?? to save the residues ? ? it with
? ? ? 2 = ? ? ? ? ? ? T i N i=1
?1 and calculate the optimal weighting matrix W given by: And by consequence, the Arellano-Bond Two-Step Estimator will be:
The estimated DPD model is presented in table (2).
# Notes
Where:
The two-step (GMM) Note 1: The Hansen-Sargan test follows asymptotically the chi-square distribution with degrees of freedom equal to the difference between the full available instruments and the number of estimated coefficients. Note 2: RATS Software reports the Wald statistic of the null hypothesis that all the coefficients except the constant are zero. Here the null hypothesis is that all the coefficients are zero because there is no constant in the model. Note 3: If the chi-square test of the null hypothesis that all the coefficients are zero, except the time dummies, is reported then we obtain: ?????2(4) = 114.01 or ??(4, * ) = 28.50 with Significance Level 0.0000 for one-step estimator ?????2(4) = 333.20 or ??(4, * ) = 83.30with Significance Level 0.0000 for second-step estimator
The validity of the moment conditions or the instrument validity will be tested using the conventional GMM test of over identifying restrictions proposed by Sargan (1958) and Hansen (1982). Since the null hypothesis of instrument validity will be tested using the Sargan/Hansen test of over identifying restrictions, both are identifying the existence of instrument excesses: H 0 : E(Z??? i ) = 0 All the restrictions of overidentification are valid.
The idea consists of calculating the J test statistic for overidentifying restrictions. Since there are more moment conditions than variables, the specification is overidentified. Practically if the J statistic is smaller than the chi-square statistic with degrees of freedom equal to the degree of overidentification then H 0 will be accepted. Since ?? < ?? 0.05;37 2 = 52.19? the used instruments in the estimation are valid, and therefore overidentification doesn't exit.
# Notes
# DW
The results of the estimated model reveal a set of great important information. First of all, let us remember that the force of military expenditure is measured by 85?20 ? . Second the Education Index (EI) which is the average of Mean years of schooling Index and Expected Years of Schooling Indexand third, a decent standard of living characterized by a high level of Gross national income (GNI) per capita. An increase in these components will lead, without any doubt, to an improvement in the life quality of a nation, as there will be an activation of a human process of development in a climate favoring the development of individuals as well as communities to acquire a harmonious, quiet and happy life. So any increase of (1%) in the growth factor of HDI will cause, two years later, a decrease of (0.7 %) in the growth factor of military expenditures. Let's now look at the effects of time through the year dummy variables representing the years from 2011 to 2017. It seems that in both years 2011 and 2012, there was a decrease in the growth factors of military expenditures of (0.024 %) and (0.031 %) respectively. While an increase of (0.019%) and (0.034%) occurred in the years 2013 and 2016 respectively. For the other years (2014, 2015 and 2017), the impacts are not significant. Let us see the annual growth rates of military expenditure in the United States, which are the highest among all countries in the world. These growth rates altered from (7.
ln ? Y i,t Y i,t?1 ? = ln?Y i,t ? ? ln?Y i,t?1 ? = ?ln?Y i,
# Discussion and Conclusion
This research has yielded many interesting results that will help to understand the relationship between military expenditures and Gross Domestic Product (GDP) and Human Development Index (HDI) in 116 countries that cover just over 92% of global military expenditures and 89% of global GDP in the world. The countries classified as VHHD have the highest GDP and military expenditure among the 116 countries studied in this research, with ratios of 70.3% and 76.4% respectively. This means that even if a country has a high HDI score (such as the USA, for example), its military expenditures won't be limited ; but a negative impact on the growth factor of military spending has occurred with a delay of two years so that an increase of (1 %) in the growth factor ? X 2,i,t?2 X 2,i,t?3 ? leads to a decrease of (0.7%) in the growth factor ? Y i,t Y i,t?1 ?. For the positive impact of a growth factor in GDP on the growth factor in ME, the result was not surprising for us. Countries with flourishing economies tend to protect themselves from any possible conflict with other countries, and consequently, they seek to improve their military forces in the face of any enemy. The HDI and GDP of developing countries are very low, and their military expenditures are very low too. It is evident that the lack of financial resources leaves these countries far from acquiring adequate weapons. It is true that a very high HDI score reflects a very decent quality of life whose social welfare is ensured for all citizens. Every man wants to live in a country where the law is respected, and human dignity is protected. However, there is an attractive observation which sheds light on the importance of the weights of military expenditures in the countries having the VHHD scores. Indeed, in 2008, 33 countries belonged to this HDI classification. The military expenditures in these countries were about (70. 4%) of the world's military expenditures, giving an amount of (1053.4 bn USD). In 2017, the number of countries became 46 and the amount reached (1185.82 bn USD) with a CAGR of (1.32%). The big question to be addressed to these rich" countries in their quality of life and social well -being is: if one year worth of military expenditures is granted for developing countries having the LHD classification, there would be on average an amount of 1120 (bn USD) intended to improve the quality of life of these developing countries. What will be the impact on our world if all countries follow such constructive policies?
As an inspired recommendation by this research, it would be logical to track the time evolution of the state associated with HDI score and the duration it requires to move from one class to another, keeping in mind that a decreasing HDI is an exception and not a rule. For example, the Syrian Arab Republic's HDI value decreased from (0.642) in 2011 (beginning of Syrian conflict) to (0.536) in 2017 (a decrease of 16.5%) which resulted in a shift from MHD to LHD. Generally, the transition is from a less HDI state to a better one. For this reason, 13 more countries reached the VHHD level in 2017. At the end of this research, we recommend the opening of thought-provoking topics about duration analysis or duration modeling of the HDI classifications.
1![?1 ? 1.](image-2.png "1 T")
1![Impact of GDP and HDI on Military Expenditures: Survey and Evidence from Dynamic Panel Data Model Notes duration modeling of the HDI classifications.](image-3.png "Figure ( 1")
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![Impact of GDP and HDI on Military Expenditures: Survey and Evidence from Dynamic Panel Data Model 18. Roodman, D. (2009). PRACTITIONERS' CORNER-A Note on the Theme of Too Many Instruments. Oxford Bulletin of Economics and Statistics, 71(1), 135-158. 19. Sargan, J. D. (1958). The Estimation of Economic Relationships Using Instrumental Variables. Econometrica, 26, pp. 393-415 20. Sato, Y. and Söderbom, M. (2017). MM estimation of panel data models with timevarying slope coefficients. Applied Economics Letters, 1-8.](image-11.png "")
21![Schwert, G. W. (1989). Tests for Unit Roots: A Monte Carlo Investigation. Journal of Business and Economic Statistics, 7, 147-160. 22. Swaleheen, M. (2011). Economic growth with endogenous corruption: an empirical study. Public Choice, 146(1/2), 23-41.](image-12.png "Notes 21 .")
3.00 GDP116 and 76.2009:2.652017:2.192.502.002009:2.581.502017:2.11Notes0.50 1.000.002008 2009 2010 2011 2012 2013 2014 2015 2016 2017 RMEGDP116 RMEGDPWYear 2019Figure (3): Ratio of military expenditure to GDP1 593.00 94.002008: 91.672014:91.302015:92.882017:92.09ersion I V II91.00 92.00Issue88.00 89.00 90.002008:89.592015:89.27 2014:89.342017:88.75Volume XIX86.00 87.00( F )20082009 Figure (4): Comparison of RME116W and RGDP116W 2010 2011 2012 2013 2014 2015 RME116W RGDP116W20162017Frontier ResearchHDI classifications Very high human development (VHHD)Ranges 0.800-1.000of ScienceHigh human development(HHD) Medium human development(MHD) Low human development(LHD)0.700-0.799 0.550-0.699 0.350-0.549Global Journal© 2019 Global JournalsIII.
(Arellano-Bond Two-Step EstimatorVariablesAutomatic Criteria?Y 3?X 1 0?X 2 0AIC -4.047BIC -3.870HQ -4.019301-4.043-3.849-4.013302-4.051-3.840-4.017303-4.034-3.807-3.998310-3.953-3.759-3.923311-3.948-3.738-3.915312-3.960-3.733-3.924313-3.940-3.697-3.902320-3.944-3.733-3.910321-3.945-3.719-3.909322-3.949-3.705-3.910323-3.932-3.672-3.891330-3.974-3.747-3.938331-3.980-3.737-3.942332-3.988-3.728-3.947333-3.976-3.700-3.932
42 × 42) × (42 × 7) × (7 × 11) ? (11 × 11)(????) ? (???? × ??) × (?? × ????) × (42 × 42) × (42 × 7) × (7 × 1) ? (11 × 1)?= ??? 1,11 ??, ?? 1,12 ??, ?? 1,13 ??, ?? 1,14 ??, ?? 1,15 ??, ?? 1,16 ??, ?? 1,17 ?????? ?? ?? = ?= ?x 2,09 i, x 2,10 i, x 2,11 i, x 2,12 i, x 2,13 i, x 2,14 i, x 2,15 i???? 10 ???? 09 ???? 1,11 ???? 2,09 ???? ?? ?? ?? ?? ?? ????? 11 ???? 10 ???? 1,12 ???? 2,10 ???? ?? ?? ?? ?? ?? ???? ?? =? ? ? ? ??? 12 ?? ?? 13 ?? ?? 14 ?? ?? 15 ???? 11 ?? ?? 12 ?? ?? 13 ?? ?? 14 ???? 1,13 ?? ?? 1,14 ?? ?? 1,15 ?? ?? 1,16 ???? 2,11 ?? ?? 2,12 ?? ?? 2,13 ?? ?? 2,14 ???? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ????? 16 ???? 15 ???? 1,17 ???? 2,15
(One-Step EstimatorTwo-Step EstimatorVariables??????????Std Errorð?"ð?" ? ??????????????????Std Errorð?"ð?" ? ?????????Y i,t?10.3540.157332.248090.4080.05587.30594?Y i,t?2-0.0800.04262-1.88194-0.0940.01497-6.30927?X 1,i,t0.7410.084038.815360.7110.043216.45914?X 2,i,t?2-0.0590.62148-0.09456-0.7000.31515-2.21993?? 11-0.0210.01481-1.43533-0.0240.00908-2.59926?? 12-0.0260.01316-1.96728-0.0310.0073-4.22922?? 130.0200.012261.599720.0190.006992.65163?? 14-0.0070.01225-0.561860.0040.006850.61122?? 150.0080.015560.485640.0080.008660.89995?? 160.0110.019050.594290.0340.009233.67548?? 17 Hansen-Sargan and Wald tests-0.010 RSS = 12.8591 s = 0.1267 0.01135 -0.88373 DW = 2.56-0.008 RSS = 13.4664 s = 0.1297 0.00815 -1.01614 = 2.63J ? Specification(37) = 51.32J ? Specification(37) = 51.32SignificanceLevelofJ = 0.059SignificanceLevelofJ = 0.059Wald Chi2(11) = 365.35Wald Chi2(11) = 1080.66or F(11, * ) = 33.21or F(11, * ) = 98.24with Significance Level 0.0000with Significance Level 0.0000
Y i,2017 Y i,2016? =? Y i,2017 ?Y i,2016 +Y i,2016 Y i,2016? =Y i,2017 ?Y i,2016 Y i,2016+ 1 = 1+= 1 + 0.016083. This meansthat Y i,2017 = 1.016083 × Y i,2016 or ln ?Y i,2017 Y i,2016? = ln ? 1.016083×Y i,2016 Y i,2016? = ln(1.016083). Focusing onthe two-Y i,t?1 Y i,t?2? increases by 1 %then ? Y i,t?1 Y i,t? increases by(0.408 %) while it decreases by(0.094 %) ifY i,t?2 Y i,t?3increases by1 %. As a result, the LRM (Long Run Multiplier) will be (0.314%).Concerning the gross domestic product variable ?X 1,i,t , an important positiveimpact on ?Y i,t is marked. There will be an increase of 0.711 % in ? Y i,t?1 Y i,t of 1 % will take place in ? X 1,i,t X 1,i,t?1 ?. growth factor ? X 2,i,t?2 X 2,i,t?3 ? results in a decrease of (0.7 %) in the growth factor ? ? if an increase Y i,t Y i,t?1 ?. Thisindicates the increase in the values of the components of HDI: First, Life Expectancy(LE) at birth, which is now known as Life Expectancy Index (LEI) according to theUnited Nations Development Programme (UNDP) and is now calculated by ?LEI =LE ?20
Year 201974.6 80.0067.9 70.0060.0040.00 Ratios 50.0030.0020.0010.000.00Year 2012GDP116 ME11680.00 75.770.00 69.660.0050.0040.00 Ratios30.0020.0010.000.00Year 2017GDP116 ME116Notes1 Global Journal of Science Frontier Research ( F ) Volume XIX Issue ersion I V II 1673.2 60.00 Ratios 70.00 80.00 76.8 90.00 40.00 50.00 60.00 70.00 72.9 Ratios Ratios 40.00 50.00 20.00 30.00 10.00 20.00 30.00 71.4 10.00 10.00 0.00 0.00 0.00 20.00 30.00 40.00 50.00 60.00 70.00 69.1 80.00 76.5 90.00 78.1 80.00 90.00 76.2 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 Ratios 90.00Year 2008 Year Year 2009 2010 Year 2011GDP116 ME116 GDP116 ME116 GDP116 ME116 GDP116 ME11680.00 70.3 77.8 90.00 70.00 80.00 69.7 76.8 70.00 80.00 69.3 75.9 69.6 76.0 70.00 80.0070.00 60.00 60.00 60.0030.00 30.00 40.00 Ratios 50.00 Ratios 40.00 50.00 60.00 Ratios 30.00 40.00 50.00 Ratios 30.00 40.00 50.0020.00 20.00 20.00 20.0010.00 10.00 10.00 10.000.00 0.00 0.00 0.00Year 2013 Year 2014 Year 2015 Year 2016GDP116 ME116 GDP116 ME116 GDP116 ME116 GDP116 ME116© 2019 Global Journals
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1424.005 2011: 1594.508 2014:1596.686 2017:1566.338 2009:1551.864 2011:1739.177 2014:1748.820 2017:1701.030 2008:621.131 2009: 668.567 2011: 711.338 2015: 596.105
GDP116 GDPWORLD
United States
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017. 2009
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