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# Chapter 2 - Section 2.5 - Equations of Lines and Linear Models - 2.5 Exercises: 24

$y=-2x+1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Point-Slope Form of linear equations to find the equation of the line with the following given characteristcs: \begin{array}{l}\require{cancel} \text{through } (4,-7) \text{ having slope } -2 .\end{array} Use the properties of equality to express the equation in the slope-intercept form. $\bf{\text{Solution Details:}}$ Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions, \begin{array}{l}\require{cancel} y_1=-7 ,\\x_1=4 ,\\m=-2 ,\end{array} is \begin{array}{l}\require{cancel} y-(-7)=-2(x-4) \\\\ y+7=-2(x-4) .\end{array} Using the properties of equality, in the form $y=mx+b$ or the Slope-Intercept Form, the equation above is equivalent to \begin{array}{l}\require{cancel} y+7=-2(x)-2(-4) \\\\ y+7=-2x+8 \\\\ y=-2x+8-7 \\\\ y=-2x+1 .\end{array}

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# Human capital flight and output growth nexus: evidence from Nigeria

Oluyemi Theophilus Adeosun (Department of Economics, University of Lagos, Lagos, Nigeria)
Oluwaseyi Omowunmi Popogbe (Department of Economics, Crawford University, Ogun State, Nigeria)

ISSN: 2631-3561

Article publication date: 24 May 2021

Issue publication date: 13 July 2021

1770

## Abstract

### Purpose

Human capital flight from developing countries to developed nations has been rising and giving concerns to governments and scholars alike. This paper aims to explore the impact migration from Nigeria has on economic output growth by focusing on the migration rate, remittances, population growth and secondary school enrolment. This has not received adequate attention in the literature, as many papers have primarily focused on the impact of remittances on economic growth.

### Design/methodology/approach

Leveraging on the macro-level approach to migration, remittances and the economy, this research considers the nexus among the human capital flight and output growth variables by using the autoregressive distributed lag (ARDL) method of analysis for time series data between 1986 and 2018.

### Findings

The net migration rate from Nigeria was found from the empirical analysis to be more disadvantageous for the economy, given its negative relationship with economic growth despite the large volume of foreign incomes (remittances). It also shows that secondary school enrolment positively and significantly impacted the Nigerian growth rate in the long run.

### Originality/value

This research has widened the use of variables by combining net migration rate, remittances from abroad, population growth rate and secondary school enrolment to obtain a more robust outcome with implications for research and practice.

## Citation

Adeosun, O.T. and Popogbe, O.O. (2021), "Human capital flight and output growth nexus: evidence from Nigeria", Review of Economics and Political Science, Vol. 6 No. 3, pp. 206-222. https://doi.org/10.1108/REPS-07-2020-0088

## Publisher

:

Emerald Publishing Limited

## 1. Introduction

Human capital flight portrays a significant increase in the amount of highly proficient people leaving a geographic region which in most cases is their country of origin to an entirely different location. Globalization has to a large extent aided this movement to advanced countries of the world. The impact of increased migration on human capital development cannot be overemphasized. While the home countries (oftentimes developing countries) may become deficient in skilled labor, the host countries benefit more through the addition of skilled labor to their labor market. As a result, human capital development keeps getting weak for developing countries. Indeed, concerned stakeholders have been worried over the incessant rise in emigration as it results in loss to the country’s resources and further worsens the state of welfare of the citizens. Thus, although the net advantages of human capital flight to the countries being migrated to oftentimes are considered “brain gain” the net worth of the act is considered in some cases as a “brain drain” to the countries of origin. Aravossitas and Sugiman (2019).

The migration of people from their country of origin to other countries has been explored by people for various reasons. Human capital flight over the years has made the macroeconomic environment of an economy deplete, having a negative influence on transparency and accountability. It also makes the necessary resources to develop a nation scarce at the time when a nation wants to develop, limiting the output growth of the economy. On another hand, Africans in the diaspora have continued to contribute massively to the foreign currency income of Africa. In fact, it is observed that households that have internal and international migrants tend to be better educated and richer compared to households without migrants (Foods and Agriculture Organisation, 2017). However, human capital flight is even more detrimental to the growth and development of African economies. This is because the region is capital-scarce continuous migration of highly skilled personnel may mean financial loss for the region. As a result, the study of human capital flight in Africa deserves critical attention.

Continuous migration of skilled labor out of Nigeria is especially worrisome. This is because unemployment, rising poverty, inequality among other socio-economic challenges characterize the Nigerian economy. In fact, Nigerians have been recognized as one of the most mobile populations in Africa with Nigerian citizens found in almost all continents (Adeagbo and Ayandibu, 2014). Notably, a large proportion of migrants relocate to high-income countries. While it is expected that the policymakers and other stakeholders will rise to the occasion to formulate and execute policies that will improve the economy and cut down the rate of migration out of the country, the reverse is the case. The net emigration rate in Nigeria has maintained a negative figure over the past 30 years implying that the emigration rate is more than the immigration rate. More worrisome is the fact that the negative value has continued to increase over the years. As of the year 2018, the net emigration rate was −0.3 as against −0.2 in 1990 (World Bank, 2019). This reveals the desperation in Nigerians to leave their country. A major argument for migration is remittances from abroad. World Bank (2016) further revealed that Nigeria is the top remittance-receiving country in Africa and fifth in the world. However, the direct impact of migration on economic growth is an area not very much studied in the literature.

Given the assertion above, our paper seeks to extend and augment two strands of human capital flight economic literature. First, are those who argue that human capital flight is instrumental to shaping the structure of an economy in terms of remittances or income from abroad (Bredtmann et al., 2019; Ubi and Ebi, 2017). Second, are those who argue that human capital flight hampers economic growth in that value is rather added to another man’s land rather than the homeland (Aravossitas and Sugiman, 2019; Musibau et al., 2019). Which of these two positions is then closer to the reality for Nigeria?

Therefore, the purpose of this study is to examine the human capital flight and output growth nexus in Nigeria using the Autoregressive Distributed Lag (ARDL) model. This is to enable us to study the relationships among emigration, remittances, education outcomes and output growth in the Nigerian context. From the understanding reached through our findings, this research is among the scanty papers that have applied the ARDL approach in examining this relationship using the variables under study. Furthermore, this paper would take a distinctive approach from the overly stretched perspective that is pervasive in the existing literature on the determinants of human capital flight. This approach is very important as it takes a broader approach in analyzing the relationship between human capital flight and output growth through the inclusion of the emigration rate in the model.

The remainder of this paper proceeds as follows: Section 2 presents the theoretical and empirical review. Section 3 discusses the methodology used while the result discussions are presented in Section 4. Section 5 provides the conclusion and recommendations from the study.

## 2. Literature review

Large empirical studies have been carried out to examine migrants’ decisions and the impact on home and host economies. Beine et al. (2001) focused on the effect migration potentials have on human capital formation and growth using cross-sectional data 37 of developing economy. They assumed the skill set and educational attainment of the agents to be diverse in the setting of doubt as to the migrations in the future. They also distinguished between the two effects of growth: an ex-ante “Brain Effect” (the migration potentials, encourages educational sector investment owing to increased remittance from abroad) and an ex-post “Drain Effect” (as a result of flows in actual migration). According to them, the case for a Beneficial Brain Drain (BBD) arises from the dominance of the initial effect, that is, in situations where the average rate of human capital is more in an economy prone to migration in lieu of an economy, which is not migration prone. Their examination opines that educational subsidies are less relevant with the increased probability of the educated citizens departing the country. Ndulu (2004) corroborated the assertion made by Beine et al. (2001) by opening that developing countries lack the capacity to retain educated and skilled citizens. Again, although Ndulu (2010) recommended that African countries should possess the ability to secure skilled workforce and also adopt repatriation technique in bringing back to home countries educated and skilled migrants, Ndulu (2004) observed that the cost of repatriation to African countries is often huge, thus, the “moderate success” of repatriation programs.

Joshua et al. (2014), Egbefo (2014) and Tabassum et al. (2017) opined that leadership failure to a large extent is the cause of brain drain from African countries. This again was corroborated by the findings from the study carried out by Omonijo et al. (2011). The outcome from the study showed a correlation between deficient leadership of the country and brain drain. Furthermore, it revealed students had left their countries of origin after their studies in a bid to familiarize themselves with advanced societies. Along with similar research thought, Ajide and Alimi (2018) observed that political instability was a leading cause of human capital flight and also influenced the level of remittances to African countries. The authors, thus, recommended the need for African political leaders to provide a stable environment, which is conducive for growth to take place which will also reduce human capital flight. Faggian et al. (2017), however, opined that the role of innovation in the development of the local economy is colossal to reduce the likelihood of migration. Indeed, the Endogenous growth model of the 1980s placed much emphasis on the role of innovation.

Other push factors have also been identified in the literature. Yamin and Luna (2016) opined that push factors such as infrastructure, lack of job opportunity, unavailable higher education facilities among other factors “push” migrants out of their home country. However, the study by Popogbe and Adeosun (2020) revealed that increased population growth rate and poor life expectancy increases the likelihood of migrating out of Nigeria. Indeed, Adeosun and Popogbe (2020) affirmed that the increasing population has always been to the disadvantage of the Nigerian economy. This is because although the population has spiraled over the years, human development utilization is very poor. This is shown in the high rate of unemployment and level of education. The study by Tabassum et al. (2017) again affirmed that in Pakistan, a high rate of unemployment led to labor migration which negatively impacted the economy.

While developing countries are characterized by factors that “push” migrants out of the countries, advanced countries are characterized by factors that “pull” migrants into them. According to Yamin and Luna (2016), some of these pull factors are the provision of financial benefits and better career or professional developments. Foo (2011) again adopted the survey approach and descriptive technique to discuss some pull factors with a special focus on the Malaysian economy. According to the study, some of these factors are wage differentials and better quality of life for the family. This to an extent supports the altruism theory that migrants are often concerned with the welfare of their families.

Literature has also revealed that the act of migration is not without its own costs and benefits. The costs and benefits are experienced in varying degrees by both the home and host countries. Mago (2018) examined if the benefits of migration are realized by Ethiopian migrants with respect to their livelihood. Using primary data and descriptive analysis, interesting findings were gotten from the migrants based largely in South Africa. A large number of respondents opined that migration had reduced unemployment; enhanced migrants’ standard of living and increased the likelihood of sending remittances back to home countries. Findings also show that similar to previous studies, a large part of remittances was spent on consumption purposes; however, some other recipients also invested remittances in business-oriented activities. The study further recommends implementing a framework that will enhance the inflow of remittances into Ethiopia. Furthermore, Aravossitas and Sugiman (2019) examined the impact of the “brain drain” from Greece on the Canadian economy. Using descriptive statistics, the study revealed that the migration of Greeks was actually “brain gain” for Canada in the following respect: educational, socio-political and economic advancement to Canada. Regrettably, the benefits migrants enjoy may be a leading factor in the increase in the number of irregular migrants (Ambrosini, 2016; Erdal and Oeppen, 2017).

The negative impact of migration on the home country was established by Akanbi (2017) and Vecchione (2018). Focusing on 19 sub-Saharan countries between 1990 and 2013, Akanbi (2017) examined the impact of migration on both economic growth and human development in the region. On the other hand, Vecchione (2018) focused on the Italian economy and found that high skilled migration drastically reduced human capital accumulation in Italy The findings showed that migration negatively impacted human capital development. These findings imply that the problem of human development may be a cause and effect of human capital flight as revealed by Tabassum et al. (2017), Adeosun and Popogbe (2020); and Popogbe and Adeosun (2020). The study by Docquier and Rapoport (2012) further revealed that uncontrolled high-skilled migration led to a shortage of health workers in Sub-Saharan Africa in 2010, which, in turn, led to worsened health status. Kim and Lee (2016), however, provided a different perspective on the effect of human capital flight on the home economy. Applying the static fixed-effects model and comparing with results derived in the dynamic panel model with system generalized methods of moments estimators, the study found a negative effect of high-skilled migration and foreign direct investment in the latter estimation technique used. However, Kim and Lee (2016) revealed that by combining other related variables, there was a positive relationship between high-skilled migration and the growth rate of source countries. It can, therefore, be deduced that while migration alone may negatively impact economic growth, the interaction of migration with other variables can produce positive impacts on the home economy.

The impact of remittances on developing countries’ economies has also been widely examined in the literature. Examining the long-run relationship between migrants’ remittances and the Nigerian economic growth between 2000 and 2010, Afaha (2013) used the cointegration and error correction mechanism techniques. Findings from the study show that the real GDP growth was significantly in line with the growth in remittances. It was also observed that remittances from abroad subsidized household livelihoods and improved their welfare. The findings by Afaha (2013) were also similar to that of Azizi (2018) and Adeagbo and Ayandibu (2014). However, Azizi (2018) opined that if remittances are done on the basis of altruism, the resulting effect may be consumption smoothing rather than investment purpose which would have strengthened the business cycle in the home country while Adeagbo and Ayandibu (2014) recommended the need for a policy framework to efficiently use remittances from abroad for the benefits of the larger economy.

On the contrary, using Pedroni’s cointegration test, Lim and Simmons (2015) observed that there was no form of a long-run relationship between remittances and economic growth in the Caribbean but a long-run relationship existed between remittances and consumption. In a similar vein, Anetor (2019) found a significant negative relationship between remittances and economic growth in both the short and long run in Nigeria. This further proves that remittances are oftentimes spent on consumption rather than investment purposes as revealed by Mago (2018). Contrarily, Meyer and Shera (2017) found a positive impact of remittances on economic growth with the impact increasing at higher levels of remittance compared to the Gross Domestic Product in a panel study conducted in six developing countries. Similar to findings by Tabassum et al. (2017) and Mago (2018), Asad et al. (2016) confirmed a long-run relationship between workers’ remittances and economic growth and a uni-directional causality from workers’ remittances to economic growth. Furthermore, the study found a uni-directional causality from unemployment to labor migration. Interestingly, the level of remittances to home countries may not be influenced by the level of migrants’ education (Bredtmann, et al., 2019).

Comparing the sources of revenue in Africa, Masiyiwa (2016) opined that if oil revenue was stripped out, diaspora remittances would be above the revenues derived from the exportation of all available forms of minerals and the cash crops from agriculture such as tobacco, cotton, coffee, etc. This contribution was estimated to be over 20% of their net income seeing that on average, they repatriate to their countries of origin an estimated $62Bn annually from the annual$310Bn net income earned yearly from their jobs abroad. More practically, Meyer and Shera (2017) revealed that in recent times, about 27% of developing nations’ GDP is accounted as remittances. Sadly, remittance inflows have been seen as being used for consumption purposes rather than productivity spending (Asad et al., 2016; Lim and Simmons, 2015).

From the foregoing, the review of empirical literature has indicated that there are controversial findings on the relationship between human capital flight and economic growth, thus the need for further studies. Again, Nigeria is one of the many countries experiencing a high rate of human capital flight and understanding the impact of this on output growth, in the long run, is a welcome development. Furthermore, the reviews have shown that many studies carried out in Nigeria either examined the factors that contributed to migration (Ndulu, 2010; Joshua et al., 2014; Egbefo, 2014; Tabassum et al., 2017; Ajide and Alimi, 2018; Popogbe and Adeosun, 2020) or examined the impact of remittances on the home economies (Anetor, 2019; Mago, 2018; Azizi, 2018). On another hand, while the studies by Henry (2013) and Okonkwo et al. (2020) on the impact of capital flight on economic growth in Nigeria have a semblance of our current study; however, it is important to note that human capital flight and capital flight are two distinct concepts. While capital flight focuses on capital and investment outflows, human capital flight focuses on the migration of humans from one country to another. Thus, less attention has been given to empirically examine the impact of migration on the economic growth of the home countries. The study, therefore, seeks to examine this relationship, as well as the relationship of other control variables such as remittances, education and population growth rate with economic growth.

## 3. Theoretical framework and methodology

### 3.1 Theoretical framework

#### 3.1.1 Macro-Level approach to migration, remittances and the economy.

Remittances are framed in terms of global flows and the national impact of migrants’ actions and funds on the home economy. The macro-level approach also provides a framework to understand the push-pull factors that draw surplus labor from sending countries (Cohen, 2005). Within this theoretical approach, Cohen opines that loss of workers diminishes the welfare and bargaining power of the sending nation and their populations. Again, there is difficulty in replacing lost workers because of rigidity in transferring skills.

A key impact of migration on economic development is from the perspective of remittances sent by migrants to family members back in their home country. Remittances also have the potential to secure the foreign capital of a country which makes savings and household maintenance possible (Cohen, 2005). However, if the “substitutability” between migrants and natives is low, migration may have a negative impact on output and productivity. Therefore, the skill composition of labor in migrants’ sending economy is critical in determining income and productivity. This is influenced by advancement in human capital made possible as a result of access to education. This will improve the skills of migrants and make them more competitive in host countries (Katseli et al., 2009). Again, remittances have been seen as an important factor in consumption smoothing and enhancing the productivity of migrants’ families back in-home country (Adeagbo and Ayandibu, 2014). Remittances, thus, have the ability to indirectly foster savings, ease foreign exchange and positively change national economics (Cohen, 2005; Katseli et al., 2009).

Cohen also opined that geography, regional and local history can impact the flow of remittances to the home nation. Geographic location has barred the inflow of remittances from certain countries in the world; this is due to fear of terrorism financing which has led to tight monetary control (Wagle and Devkota, 2018). Historically, events in time affect the use of remittance in the destination region and the amount of inflow from the source region. The impact of these remittances over time has a positive effect on the source region. Regionally, Cohen opined that migrant remittances increase inequality in the migration region, as those with remittances are better off than others; this is at an early stage of migration (Adida and Girod, 2011). As the cost of migration becomes affordable by many, inequality begins to decrease as many now have remittances from abroad.

Migration has the capacity to aid development in both host and home countries if migration is well explored and strengthened (Katseli et al., 2009). Indeed, a moderate rise in migration has the capacity to enhance productivity and improve the home country. On the other hand, migration can also lead to depopulation and or large departure of labor with specific levels of skills which may have an adverse effect on the human capital of the home country. Therefore, these interactions affect the economic development of an economy.

### 3.2 Methodology

#### 3.2.1 Data source.

The empirical model for this study hinges on Cohen’s macro-level approach to migration and remittances and model specification is done in line with previous studies. The dependent variable is the real GDP annual growth rate and it is the proxy for economic growth; net migration rate proxy for human capital flight (Docquier and Rapoport, 2012). Other control variables to be examined are remittances from abroad, population growth rate and secondary school enrolment (see previous studies by Kim and Lee (2016), Meyer and Shera (2017)). Data sources are the World Bank and the United Nations Educational, Scientific and Cultural Organisation (UNESCO) data file from 1986 to 2018. E-views 11 statistical software was used in carrying out analysis.

#### 3.2.2 Model specification.

To determine the responsiveness of Nigerian economic growth to human capital flight, we specify the following functional relationship equation:

(1) RGDPGRt=β0+β1NMRt+β2REMITt+β3PGRt++β4SSEt+μt

Where:

RGDPGRt = Real GDP annual growth rate in time t;

NMRt = Net migration rate in time t;

REMITt = Workers’ remittances in time t;

PGRt = Population growth rate in time t;

SSEt= Secondary school enrolment in time t;

β0= Constant; β1-β4= Coefficients; and μt= Error term.

#### 3.2.3 Estimation technique.

The descriptive analysis was used to provide a trend of variables estimated in the study. Also, summary statistics were carried out to further explain the peculiarities of these variables. The Autoregressive Distributed Lag (ARDL) modeling approach developed by Pesaran and Shin (1999) has been adopted for the empirical analysis in this study. The reason for the adoption of the ARDL method of analysis is due to its flexibility in using variables that are integrated of order I(0) and I(1), unlike other cointegration techniques which may not accept such mixed stationarities. It is also advantageous in examining long-run relationships and also estimating the long-run parameters (Naiya and Manap, 2013). Therefore, by a further specification of the functional form of equation (1) above, an ARDL is specified in the form:

(2) ΔRGDPGRt=β0+β1RGDPGRt-1+β2NMRt-1+β3logREMITt-1+β4PGRt-1+β5SSEt-1+i=1ma1ΔRGDPGRt-1+i=1ma2ΔNMRt-1+i=1ma3ΔlogREMITt-1+i=1ma4ΔPGRt-1+i=1ma5ΔSSEt-1+εt

Where:

log = natural log of workers’ remittances;

Δ= first difference operator; and

a1-a5= short-run dynamic parameters of the regressors.

The null hypothesis to be tested is that there is no cointegration or long-run relationships Ho:a1=a2=a3=a4=a5=0 against the alternate hypothesis: HA:a1a2a3a4a50 as proposed by Pesaran et al. (2001).

The error correction mechanism of the short-run relationship is as indicated:

(3) ΔRGDPGRt=β0+i=1ma1ΔRGDPGRt-1+i=1ma2ΔNMRt-1+i=1ma3ΔlogREMITt-1+i=1ma4ΔPGRt-1+i=1ma5ΔSSEt-1+λ1ECMt-1+εt

Where a negative (−) λ1 shows that short-run disequilibrium as a result of shocks to all the variables used will converge back to long-run equilibrium.

## 4. Empirical results and discussions

### 4.1 Trend of estimated variables

Figure 1 provides a trend analysis of the variables measured in this study. With the exception of the net emigration rate and population growth rate, the other variables show notable differences in values over the years. The real GDP rate has fluctuated with a peak growth experienced in the year 2002 at a rate of 15% increase compared to the previous year. Notably, the government administration of Nigeria in the early 2000s created a platform for “economic recovery and growth” (Dada et al., 2017). Regrettably, the economy has been on a downward slide, as then with the economy witnessing a negative real GDP growth rate in 2016. This was due to a fall in global oil prices coupled with a contraction in non-oil revenue in Nigeria (Ohuocha and Laessing, 2017). Although the real GDP increased by 2% in 2018, the trend shows that this is still not a desirable increase as a greater increase had been recorded in previous years.

The net emigration rate shows the difference between the emigration and immigration rates. The values have remained negative since 1986 implying that emigration has always been more than migration into Nigeria. This is not surprising as the economic, political, socio-cultural conditions in Nigeria are discouraging (Ajide and Alimi, 2018; Egbefo, 2014; Tabassum et al., 2017). These challenges hinder the productivity of high skilled labor, thus the constant migration out of the economy.

The growth in remittances also shows an interesting trend. From as little as $4m in 1986, remittances inflow increased to$1,391m in the year 2000 and a whopping $24,311m in 2018. Although there was a slight decrease in remittances periodically, the decrease was not as much as the decrease seen in the growth of real GDP. Nigeria was among the top African countries with the highest inflow of remittances in 2018 and the trend also shows that the highest value of remittances to Nigeria was received the same year. Interestingly, the reported figure of remittances has been revealed to be lower than the actual estimates (Nevin and Omosomi, 2019). The secondary school enrolment reveals a sustainable increase over the years, however, with periodic decrease. The peak enrolment was experienced in 2013 with a ratio of 56% to overall enrolment and a decrease of 24% in 1999. The trend shows that since 2003, about half (and in some cases, more than half) of yearly enrolment was into secondary school. The reason for this is not far-fetched. The Nigerian government offers free education for students up to the Secondary School level (Evans-Obinna and Ndieze, 2017). Again, there is scanty information to represent tertiary education, thus the adoption of the secondary school enrolment, being the least level accepted for occupying public offices in Nigeria. It is, however, expected that the majority of secondary school graduates will proceed to tertiary education. Finally, there has been a consistent increase in the Nigerian population since 1986. Yearly, the population has increased by about 4 million (implying a 3% increase yearly). Okpala (1990) rightly predicted that the Nigerian population is expected to double in 22 years (by 2017) should the yearly growth rate of 3%–4% be maintained. Indeed, by 2017, the Nigerian population stood at 191 million from 91 million in 1985. The continuous increase has been attributed to religion, illiteracy, male-child preference, etc (Theodore, 2006). ### 4.2 Summary statistics and correlation matrix The descriptive statistics as shown in Table 1 reveals the summary statistics of the variables used in this study. On average, the real GDP growth rate of the Nigerian economy between 1986 and 2018 stood at about 4%, −0.3 per 1,000 population for net migration rate,$87m for remittances, about 3% mean population growth rate value and 90% gross secondary school enrolment mean value. The maximum real GDP growth rate was 15% while the minimum was −2%. There exists a large gap between the minimum and maximum value of workers’ remittances of about \$24bn between 1986 and 2018. This shows that there has been a large volume of remittances from abroad into the Nigerian economy over the years.

Studies have found that a large part of the remittances are spent on consumption while it is also reported that the actual remittances into the economy are greater than the recorded figures (Lim and Simmons, 2015; Mago, 2018; Nevin and Omosomi, 2019). It behooves the government and other policymakers to efficiently track remittance inflow and optimize same for the economic development of the economy. Both minimum and maximum values for net migration rate show negative values implying that the emigration rate has always been higher than the immigration rate in Nigeria. This has a negative impact on human capital development and should be checked.

The skewness, kurtosis and Jacque bera results show that the sample size of each variable is normally distributed. Although the results obtained for NMR shows a slight deviation from the accepted range for kurtosis, however, this is not a sufficient reason to discard the variable as further tests in the study showed appropriate model specification.

The correlation matrix in Table 2 shows that none of the variables are correlated. There exists a negative correlation between net emigration rate and real GDP growth rate. However, a positive correlation exists between real GDP growth rate and remittances, real GDP growth rate and population growth rate and also real GDP growth rate and secondary school enrolment. These are preliminary analyzes and the ARDL estimation will further prove these results.

### 4.3 Unit root test

Unit root tests are important to test the stationarity of time series data. This is necessary to avoid “spurious” regression results which will make accurate forecast impossible (Gujarati, 2003). The time-series properties of the data adopted for this study were, therefore, tested using the Augmented Dickey-Fuller (ADF) and Phillip-Perron (PP) tests. This is presented in Table 3.

Table 3 shows the ADF and PP unit root tests outcome. The Akaike Info Criterion (AIC) automatic selection and max lag of 4 were set for the ADF test while the Bartlett Kernel estimation method and Newey-West Bandwidth were adopted in calculating the Phillips-Perron test. The result reveals a mixture of stationarity among the variables of orders I(0) and I(1).

### 4.4 Autoregressive distributed lag estimation

As the variables are integrated of orders I(0) and I(1), the ARDL bounds test for the establishment of a long-run relationship was carried out and the result is illustrated in Table 4.

The result of the bounds test in Table 4 shows that the estimated F-Stat is 10.7 and this is above the upper critical bound at the different levels of significance. This establishes the existence of long-run cointegrating among the variables. We can, thus, proceed to estimate the ARDL estimation results.

Table 5 shows the ARDL estimation of short-run coefficients. Specifically, the net migration rate (one period lagged value) negatively impacted real GDP. This implies that while the net migration rate may not impact real GDP in the current period, it impacted real GDP in the previous period. The same result applies to the remittances inflow. While remittances did not impact real GDP in the current period, they impacted real GDP negatively in the previous period. The population growth rate also showed a negative relationship with economic growth. Thus, an increase in population does not necessarily translate to better economic growth. This corroborates the findings by Adeosun and Popogbe (2020). The error correction term is −1.7, which is statistically significant at 1%, suggests a 172% annual adjustment toward long-run equilibrium. This high value, however, depicts that the speed of adjustment fluctuates forward around the long-run value before settling to equilibrium. Therefore, disequilibrium in economic growth as a result of shocks from previous periods will converge back to long-run equilibrium.

The long-run estimates, as shown in Table 6, reveals that a unit increase in the net migration rate will reduce the real GDP growth rate by 59 units in the long run. Continuous rise in migration rate will reduce the manpower needed for productivity in the home countries. This, in the long run, will drastically reduce economic growth. Economic growth is a prerequisite for economic development; the implication of low economic growth will, thus, mean reduced welfare benefits for citizens. Worker remittances also negatively impacted the real GDP growth rate at a 1% level of significance. This negative relationship was also established in the short run. This finding is in line with Anetor (2019), although contrary to findings by Afaha (2013) and Meyer and Shera (2017). The negative relationship between remittances and economic growth simply implies that a large inflow of remittances does not necessarily lead to economic growth. This can be as a result of remittances spent on consumption purposes and not revenue-yielding investments. This has been corroborated in the literature (Adeagbo and Ayandibu, 2014; Asad et al., 2016; Lim and Simmons, 2015). Our findings do not, therefore, conform to the proposition of Cohen (2005).

Population growth rate negatively impacted real GDP growth rate, but this relationship is not significant while secondary school enrolment positively influenced growth rate and that significantly. According to Beine et al. (2001), educational attainment may increase due to increased remittances from abroad induced by migration from the home country. In fact, a unit increase in secondary school enrolment increased the real GDP growth rate by 28%. This positive relationship is also empirically found in Kim and Lee (2016). Asides, higher secondary school enrolment indirectly implies more secondary school graduates who can acquire skills needed to be productive in the economy.

### 4.5 Diagnostic and stability analysis

As shown in Table 7, the Breusch-Godfrey Serial Correlation LM test was carried out for serial correlation; Ramsey Reset test for model specification; heteroskedasticity test; and the Jacque-Bera test to test the normality of the model. The results show that the null hypothesis of the diagnostic is to be accepted against the alternate. The diagnostic tests show that the model is not auto-correlated, the model is well specified, the heteroscedasticity problem does not exist and the regression model is normally distributed. The CUSUM and CUSUM of squares are represented in Figures 2(a, b), respectively, and show that the model is relatively stable.

## 5. Conclusion and recommendations

The aim of this research is to analyze the nexus among the human capital flight and economic growth variables within Nigeria. In a bid to accomplish this objective, the real GDP annual growth rate (RGDPGR) was used as a proxy for economic growth, while the Net Migration Rate (NMR) was used as a proxy for human capital flight as the true exogenous variable. The control variables were Workers’ Remittances (REMIT), Population Growth Rate (PGR) and Secondary School Enrolment (SSE). Time series data of 32 years spanning from 1986 to 2018 was sourced from the World Bank and the UNESCO data file. Both Augmented Dickey-Fuller and Phillips-Perron tests were carried out to test the stationarity of the variables and results show that the variables are integrated of orders I(0) and I(1). This justified the use of the ARDL estimation technique in this study.

The Bounds cointegration test showed the existence of a long-run relationship among the variables. The ARDL regression result implied that the net migration rate in Nigeria negatively impacts on real GDP of the country significantly in both the short and long run. This has been supported by some previous studies and this finding further corroborates the disadvantage of migration on the Nigerian economy. Again, the study found out that although workers’ remittances from abroad have increased over the years; however, the relationship between remittances and the growth rate is negative. This shows that Cohen’s theory, to a large extent, does not apply to Nigeria. Migrants’ remittances back to their home country may possibly be based on the care and concern they have for their family members in the home country.

Again, some of the reviewed literature confirmed that remittances are oftentimes spent on unproductive activities that do not contribute to economic growth. This may, thus, have accounted for the negative impact remittances had on economic growth in this study. On the other hand, secondary school enrolment positively and significantly impacted the real GDP growth rate and this also further confirms the positive effect of human capital development on an economy’s growth.

Therefore, in line with our findings, we recommend that pull – factors like enabling environment and infrastructural facilities in foreign countries should also be established in Nigeria so as to retain human capital. This will also reduce the volume of remittances from abroad and cause skilled labor workers to be more productive in their home country. We also recommend that the labor law should be such that it will ensure competitive compensation and benefit for workers; and job security for both private and public holdings, among others. Better conditions of service will discourage skilled migration and improve the home economy.

Furthermore, the Nigerian Government should provide a linking framework with Nigerians in diaspora whereby they will be motivated to invest a greater proportion of their net income intangible assets such as real estate, government bonds and so on as this will stir plausible growth for the economy and better to improve the well-being of their family members in the country. The value of education is also incalculable in economic growth. It is, therefore, important to judiciously allocate resources that will aid the educational sector, especially at the secondary level. This level is a key determinant as students are taught basic skills that make them productive to an extent as young adults. Stakeholders are, therefore, advised to invest more in the educational sector because higher enrolment implies a broader human capital base in the economy and a higher likelihood for enhanced economic growth.

## 6. Limitations and scope of the study

The study focused on only available data between 1986 and 2018. Also, as a result of data paucity, wage differential and skilled emigration were omitted from the analysis. With the availability of such data, further studies can explore that peculiar dimension to the study as such will be a valuable contribution to the literature on migration. Moreover, future studies may carry out cross-country analysis to provide comparative analysis among countries where the human capital flight is on the rise.

## Figures

### Figure 1.

Trend of selected variables (1986–2018)

### Figure 2.

The CUSUM and CUSUM of squares

## Table 1.

Summary statistics

Variables
Statistics RGDPGR NMR REMIT PGR SSE
Mean 4.45 −0.29 87.27 2.58 90.52
Median 4.63 −0.29 1,301.06 2.59 89.74
Maximum 15.33 −0.17 24,311.02 2.68 102.11
Minimum −2.04 −0.81 2.42 2.49 78.66
SD 3.92 0.13 9,735.50 0.07 6.10
Skewness 0.45 −2.02 0.37 −0.05 0.28
Kurtosis 3.31 8.87 1.23 1.53 2.16
Jarque-Bera 1.23 69.72 5.06 2.97 1.40
Probability 0.54 0.00 0.80 0.23 0.50
Sum 146.76 −9.72 288.01 85.19 2,987.15
Sum sq. dev. 491.69 0.53 3.03E + 21 0.15 1,189.82
Observations 33 33 33 33 33

Source: Researchers’ computation 2020

## Table 2.

Correlation matrix

Variables RGDPGR NMR LOGREMIT PGR SSE
RGDPGR 1
NMR −0.0088 1
LOGREMIT 0.1011 −0.0612 1
PGR 0.2338 −0.6085 0.3550 1
SSE 0.2568 −0.1083 0.1742 −0.1353 1

Source: Researchers’ computation 2020

## Table 3.

The augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root test

Variable ADF t-statistics ADF @ 5% critical values Order of integration PP t-statistics PP @ 5% critical values Order of integration
RGDPGR −3.8435 −2.9571 I(0) −3.9265 −2.9571 I(0)
NMR −5.036 −2.9604 I(1) −4.6975 −2.9571 I(0)
logREMIT −6.5139 −2.9604 I(1) −6.5142 −2.9604 I(1)
PGR −3.2528 −2.9678 I(0) −1.9612 −1.9521 I(1)
SSE −3.1008 −2.9604 I(0) −3.9265 −2.9604 I(1)

Source: Researchers’ computation 2020

## Table 4.

ARDL bounds test for a cointegrating relationship

 Null hypothesis: no long-run relationship exists F-stat Value = 10.657 k = 4 Critical value bounds Significance I(0) bound I(1) bound 10% 2.20 3.09 5% 2.56 3.49 1% 3.29 4.37

Source: Researchers’ computation 2020

## Table 5.

Estimation of short-run coefficients

Variable Coefficient Std. error t-statistic Prob.
D(RGDPGR(−1)) 0.5761 0.1685 3.4190 0.0035
D(RGDPGR(−2)) 0.7721 0.1365 5.6564 0.0000
D(NMR) 0.9179 35.2848 0.0260 0.9796
D(NMR(−1)) −54.6293 9.4956 −5.7531 0.0000
D(LOGREMIT) −1.3322 1.3445 −0.9908 0.3365
D(LOGREMIT(−1)) −4.1184 1.2181 −3.3890 0.0038
D(PGR) −406.1421 70.6038 −5.7524 0.0000
D(PGR(−1)) 420.1417 68.3356 6.1482 0.0000
CointEq(−1)* −1.7298 0.2141 −8.0808 0.0000
R-squared 0.8858 Mean dependent var −0.1799
Adjusted R-squared 0.8423 S.D. dependent var 4.4936
S.E. of regression 1.7845 Akaike info criterion 4.2395
Sum squared resid 66.8722 Schwarz criterion 4.6598
Log-likelihood −54.5919 Hannan-Quinn criter 4.3739
Durbin-Watson stat 2.8354

Source: Researchers’ computation 2020

## Table 6.

ARDL estimation of long-run coefficients

Variable Coefficient Std. error t-statistic Prob.
NMR −58.9200 27.5498 −2.1387 0.0482
LOGREMIT −2.9418 0.7136 −4.1224 0.0008
PGR −28.6233 33.4676 −0.8553 0.4050
SSE 0.2789 0.0714 3.9034 0.0013
C 64.8478 79.1091 0.8197 0.4244

Source: Researchers’ computation 2020

## Table 7.

Diagnostic tests

Test T-Stat p-value
Breusch-Godfrey serial correlation LM test 2.0265 0.1688
Ramsey reset test 0.5283 0.6050
Heteroskedasticity test 0.7483 0.6977
Jacque-Bera −3.5438 0.1700

Source: Researchers’ computation 2020

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what affects the speed of sound?

$\begin{array}{lll}{v}_{\text{w}}& =& \left(\text{331 m/s}\right)\sqrt{\frac{T}{\text{273 K}}}=\left(\text{331 m/s}\right)\sqrt{\frac{\text{293 K}}{\text{273 K}}}\\ & =& \text{343 m/s}\end{array}\\$. a. the energy of thee first wave is less than the second b. energy of the, The wave function of a standing wave is y(x,t)=4.44mmsin[(32.5rad/m)x]sin[(754rad/s)t]. Factors like the temperature of the medium, the distribution of molecules/atoms across it, etc. If we know the medium and the temperature, however, we can predict the speed of sound. When a firework explodes, the light energy is perceived before the sound energy. Mathematically Modeling the Spread of COVID-19, Summary Of How \gamma affects speed of sound. The wavelength of a sound is the distance between adjacent identical parts of a wave—for example, between adjacent compressions as illustrated in Figure 2. (a) If a submarine’s sonar can measure echo times with a precision of 0.0100 s, what is the smallest difference in distances it can detect? Issac used the model to measure the distance between two crests. the trough of wave B has an amplitude of 2 cm. The speed of sound is affected by 3 properties: Elasticity and Density of the medium through which the sound waves travel, and the temperature of the medium. a. wave A; wave A b. wave A; wave B c. wave B; wave A d. wave B; wave B 2. The factors that effect the speed of sound are not random effects based on a whim but exact scientific principles that effect the speed of sound. Know Your Vitamins: What Do Water-Soluble Vitamins Do In The Body? (credit: Dominic Alves, Flickr) Not as much as the “Medium” does, but far more than anything else. He’ll always be up to talk about comics, movies, and music. How Can Cornea-Reshaping Lenses Correct Your Vision? Figure 1. You can also directly sense the frequency of a sound. The sound wave slows down and Physics If an earthquake wave having a wavelength of 13 km caused the ground to vibrate 10 times each minute, what is the speed of the wave? The exact number 1,126 feet per second is taken in some precise conditions: in dry air at 68% Fahrenheit. What is the distance to the object creating the echo? Circle Of Willis: Anatomy, Diagram And Functions. Which of these affects the pitch of a sound? While the days of using string phones are far behind us, we often yell to communicate with someone far away from us (for example, someone down the mountain or on the other side of the lake). http://www.physicsclassroom.com/class/sound/Lesson-2/The-Speed-of-Sound. Are Giant Insects Larger Than Humans Possible? which of the following does not cause chemical changes in the composition of rocks, muscle that help your lungs pull the air and push out. Two main factors affect the speed of sound: the material that makes up the medium—such as air or water—and the temperature. What is true about the two waves? By the end of this section, you will be able to: Figure 1. Earthquakes, essentially sound waves in Earth’s crust, are an interesting example of how the speed of sound depends on the rigidity of the medium. The wavelength decreases while frequency increases. How Big Is It and Does It Bite? A drum produces sound when its skin is struck, guitars when their strings are plucked, and the larynx (the voice box in humans) when it vibrates because of air flowing through it. One of the more important properties of sound is that its speed is nearly independent of frequency. The speed of sound in air is low, because air is compressible. When a firework explodes, the light energy is perceived before the sound energy. Explain why this is so. Here are the factors that effect the speed of sound: Medium has a huge effect of the speed of sound. 1.2 km/s 2.2 km/s 220 m/s 22 m/s If the amplitude in a sound wave is doubled, by what factor does, Isaac and Joe worked together to draw a model of a transverse wave. The flash of an explosion is seen well before its sound is heard, implying both that sound travels at a finite speed and that it is much slower than light. Does shouting in the direction or against the direction of wind really have any effect on sound waves? Read here. Why might Isaac have been confused by Joe's, Which of the following choices correctly describes the behavior of the sound wave as it moves from metal to air? Why Are There Stones Alongside Railway Tracks? While not negligible, this is not a strong dependence. Similarly, the speed of sound gets compounded by a factor equal to the speed of the wind when both are moving in the same direction, and subtracted when they are not. Thus, the difference in wind speeds results in the refraction of sound, which makes it easier to hear sounds emanating from a source downwind, and more difficult when the source is upwind. A. The amplitude of the wave. Sound travels faster in warmer air, so sound waves get refracted towards the surface and travel a greater distance than usual. So a small instrument creates short-wavelength sounds. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Sound will NOT travel through a vacuum. What is Quantum Entanglement: Explained in Simple Words. All Rights Reserved. 3. all play a role in determining how sound waves are propagated. What Would Happen If You Shot A Bullet On A Train? Which of these affects the speed of sound? The factors that effect the speed of sound are not random effects based on a whim but exact scientific principles that effect the speed of sound. Echoes are also used in medical imaging. One plays high-pitch sounds and the other plays low-pitch sounds. At 20 °C (68 °F), the speed of sound in air is about 343 metres per second (1,235 km/h; 1,125 ft/s; 767 mph; 667 kn), or a kilometre in 2.9 s or a mile in 4.7 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating. Sound travels more slowly than light, and it does not always travel at the same speed. This is called Fluid Dynamics. Sound waves traveling against the direction of wind get refracted away from the surface. (c) Discuss the significance of this uncertainty and whether it could cause difficulties for the bat. Objects like ships or large pieces of airplanes can be found by sonar, while smaller pieces must be found by other means. What are Glial Cells: Definition, Types, Functions of Glial Cells | Role in Psychology. Frequency b. amplitude c. wavelength d. wave speed Is it C? B. In short, the more pressure that is applied to the material or medium the denser it becomes and the greater the “inertia” becomes. Because they travel at the same speed in a given medium, low-frequency sounds must have a greater wavelength than high-frequency sounds. At the very basics lower temperatures will decrease the speed of sound while higher temperatures will increase the speed of sound, all other factors being equal. Figure 2. … B. The last sentence might be what you want? The speed of sound in a medium is determined by a combination of the medium’s rigidity (or compressibility in gases) and its density. Eventually, the sound wave is forced to change its direction and gets refracted downwards towards the ground. A sound wave travels faster in the direction of the wind and slower against it. The more rigid (or less compressible) the medium, the faster the speed of sound. The effect of pressure on the speed of sound is due to the materials inertial properties. (In practice, the bat continues to use sound as it closes in, eliminating most of any difficulties imposed by this and other effects, such as motion of the prey. Describe the effects of temperature on the speed of sound. You observe two musical instruments that you cannot identify. $v_{\text{w}}=\left(331\text{ m/s}\right)\sqrt{\frac{T}{273\text{ K}}}\\$, where the temperature (denoted as T ) is in units of kelvin. Required fields are marked *. Apart from providing a slight speed bump/boost, the wind has many more interesting ramifications on sound and its transmission, one of which is the refraction of sound.

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# Question 2Unanseredattempts leftHow does thelaser light detect the edge of a pit on CD or DVD?The width of the laser

Question 2 Unansered attempts left How does thelaser light detect the edge of a pit on CD or DVD? The width of the laser beam changes when reflected from within CD pit but does not change when reflected outside pit: Pits on the CD or DVD are painted different color from the surface outside the pits on the CD; these surfaces alter the color ofthe reflected Iaser light in different ways: Laser light is either bright or dim upon reflection due to wave interference. The " wavelength ofthe light changes when it'$reflected from pit; while it remains the same when reflected from land; ## Answers #### Similar Solved Questions 1 answer ##### The balance sheet of MacMillan Management Consulting, Inc. at December 31, 2017, reported the followingstockholders' equity... The balance sheet of MacMillan Management Consulting, Inc. at December 31, 2017, reported the followingstockholders' equity During 2018, MacMillan completed the following selected transactions: 1. Record the transactions in the general journal. ... 1 answer ##### Find each product. In each case, neither factor is a monomial. $\left(x^{2}+3 x+1\right)\left(x^{2}-2 x-1\right)$ Find each product. In each case, neither factor is a monomial. $\left(x^{2}+3 x+1\right)\left(x^{2}-2 x-1\right)$... 5 answers ##### Given that a complex number (1-V3i)" 1) Use polar form to simplify the given complex number: ii) Verify your answer in i) by using direct expansion. iii) Sketch the result obtained as a vector in the Argand plane. iv) Find the distance of the vector: Given that a complex number (1-V3i)" 1) Use polar form to simplify the given complex number: ii) Verify your answer in i) by using direct expansion. iii) Sketch the result obtained as a vector in the Argand plane. iv) Find the distance of the vector:... 1 answer ##### Are You Willing And Able To Discuss Additional Potentially Controversial Topics As Effective Interpersonal Communicators? Are You Willing And Able To Discuss Additional Potentially Controversial Topics As Effective Interpersonal Communicators?... 1 answer ##### 4. A baby was born deaf, physically retarded and with a variety of skin lesions. His... 4. A baby was born deaf, physically retarded and with a variety of skin lesions. His mother had an uneventful pregnancy, health-wise, but underwent no pre- natal testing of any kind because she is a Jehovah's Witness. The virus which caused this baby's condition is an enveloped RNA virus. 1.... 5 answers ##### Question 7 (1 point) Indicate the FALSE statement about the planar molecule shown below.This - molecule:will readily undergo addition reactions across the C-C bond marked by x and y.has nitrogen atom that has a lone pair of electrons that is not part of the T-system.has [0 p clectrons in its p systemhas 2 sp?-hybridized nitrogen atoms_ Question 7 (1 point) Indicate the FALSE statement about the planar molecule shown below. This - molecule: will readily undergo addition reactions across the C-C bond marked by x and y. has nitrogen atom that has a lone pair of electrons that is not part of the T-system. has [0 p clectrons in its p s... 5 answers ##### B-E Shok Polability Hht Gvfautts_ FailB 0E 0.D 0430,4 B-E Shok Polability Hht Gvfautts_ Fail B 0 E 0. D 043 0,4... 1 answer ##### On September 1, 2011, a company purchased a weaving machine for$239,800. The machine has an...
On September 1, 2011, a company purchased a weaving machine for $239,800. The machine has an estimated useful life of 8 years and an estimated residual value of$17,800. Additionally, it is estimated that the machine would produce 740,000 bolts of woven fabric over its useful life. The company ended...
##### A certain electronic product is 5% likely to be "dead" out of the box. The life expectancy of the...
A certain electronic product is 5% likely to be "dead" out of the box. The life expectancy of the remaining inventory follows an exponential distribution with a mean of 8 years. Define random variable X to model the life expectancy (in years) of the entire (combined) inventory. (a) Mathemati...
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please help me just fill out the three boxes with information . this sheet has to be about thw stages of labor . Basic Concept ACTIVE LEARNING TEMPLATE STUDENT NAME CONCEPT Labor and dey pcsLdobS NEVEW MODULE CHAPTER of Labor Nursing Interventions Underlying Principles Related Content WHOT WHEN? WI...
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##### Make appropriate plots or perform linear regression using these data to test them for fitting zero-,...
Make appropriate plots or perform linear regression using these data to test them for fitting zero-, first-, and second-order rate laws. Test all three even if you happen to guess the correct rate law on the lint trial. Determine the rate constant for the reaction. Using the rate law that you have d...
##### 03/14/2019 Name An L.TI system has an impulse response hn) and input xInl displayed in Figure...
03/14/2019 Name An L.TI system has an impulse response hn) and input xInl displayed in Figure 2 below. Apply the method of graphical convoluti and sketch the convolution output y[n] of the system givern 4. on to find y[n] x[n]*h[n]. ん[n] xIn] -4 3 2 2 3 n Figure 2...
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##### Find all points of Sketch the curves _ 'intersection of the curves n=1z Ain0 and A-1G Cpe_ S56 = TZ (0s0
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##### 2. Naruto's whack-a-smacker ninja-tool consists of a 3.42 kg copper ball of 9 cm diameter and...
2. Naruto's whack-a-smacker ninja-tool consists of a 3.42 kg copper ball of 9 cm diameter and a 4.1 kg steel ball of 10 cm diameter, rigidly joined by a 1.0 kg steel rod, 30 cm long. (a) Find the moment of inertia of this tool with respect to an axis that is perpendicular to the connecting rod a...
##### Write sentence that represent the negation of the following statement, All dogs are four-legged animalsIt is not the case that all doges are four-legged animalsAlI dogs are not four-legged animals.Some dogs are four-legged animals.No dogs are four-legged animals_
Write sentence that represent the negation of the following statement, All dogs are four-legged animals It is not the case that all doges are four-legged animals AlI dogs are not four-legged animals. Some dogs are four-legged animals. No dogs are four-legged animals_...
##### Source of Variation SS df MS F P-value F crit Rows 4.80 4 c f j...
Source of Variation SS df MS F P-value F crit Rows 4.80 4 c f j h Columns a b d g k i Error 15.09 12 e Total 114.07 19 In this Two Way ANOVA, the conclusion you arrive at is that mean blocks are not all the same. True False...
##### LcmpQuestion 8 (4 points) Saved Indicate the relationship between these two compounds QH QH'diastereomersenantiomersconstitutionalidentical
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##### Provide WWo differen Ways that thc aldchyde shoun helon could be prepared from alcohol and an alkyne.scpdicohorhatieB. Frovide diflerent ways that the ketone shown below could be prcpuared in ore siep from alkene and 4n alkym.kononao0Frovide diffcrent ways that the alcohol shoun below coulu be prepared orie slcp from different kctonesLndndConmereeeEen Provide IWo different Ways that the alkene shown below could be prcpared (Wo different ylides:sep fromOuerectyjPage 3 of &
Provide WWo differen Ways that thc aldchyde shoun helon could be prepared from alcohol and an alkyne. scp dicohor hatie B. Frovide diflerent ways that the ketone shown below could be prcpuared in ore siep from alkene and 4n alkym. kono nao0 Frovide diffcrent ways that the alcohol shoun below coulu b...
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##### Copy each figure and the translation vector. Draw the translation of the figure along the given vector.
Copy each figure and the translation vector. Draw the translation of the figure along the given vector....
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The resistivity of steel is 7.2 x 10-7 Î©âˆ—m. Calculate how long your wire is in meters if you measure its radius to be 1 mm, and the total resistance of the wire to be 22.9Î©. 10 m 1000 m 1 m 100 m...
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Find the length of the curve r = 1 + sin 20 0s0SIVZ /4. The length of the polar curve is (Type an exact answer; using as needed:)...
##### 1) Use a) the Midpoint Rule, b) the Trapezoidal Rule and c) Simpson's Rule with n =6 to approximate (using 5 decimals) the integral4dx Jx
1) Use a) the Midpoint Rule, b) the Trapezoidal Rule and c) Simpson's Rule with n =6 to approximate (using 5 decimals) the integral 4dx Jx...
##### Sketch the graph of y=f'(x) 13. Below you are given the graph of the function y(x)....
Sketch the graph of y=f'(x) 13. Below you are given the graph of the function y(x). Use the graph to answer the questions that follow. y- . O-...
##### Imagine you are working in a microbiology lab: You perform an experimentwhere take culture Of bacterial cells, transfer them to a new solution (Solution A), and Yent decermine then the number of living cells: You are surprised by the result: there are no livingecells Which of the following is a possible explanation for your observation?Solution A is hypotonic for your bacterium; resulting in the diffusion of water into the cellsSolution A is hypertonic for your bacterium; resulting in the diffu
Imagine you are working in a microbiology lab: You perform an experimentwhere take culture Of bacterial cells, transfer them to a new solution (Solution A), and Yent decermine then the number of living cells: You are surprised by the result: there are no livingecells Which of the following is a pos...
##### Activity (3: Anulxzing the datanemnIthat you have measured tlie position of moving cart u8 function ol time. The data collected shown in the following table: Plot the Fasition vs LIITIC Eraph for Ihe canDoes this plot represett straight line? ~int for the best fit line? What quantities do @u (hink What ane the slope and the (e SL LWo represent? (ravel. ilyou Iet moudur 4useconds? What distance do you expect the cartWlCSIPosition(m) 4u1.010.80KS 0424.017.0134,02 37,52
Activity (3: Anulxzing the data nemnI that you have measured tlie position of moving cart u8 function ol time. The data collected shown in the following table: Plot the Fasition vs LIITIC Eraph for Ihe can Does this plot represett straight line? ~int for the best fit line? What quantities do @u (hin...
##### Enter your How Be sure 810[ * many formula answer V U IH when 1water?
Enter your How Be sure 810[ * many formula answer V U IH when 1 water?...
##### From narrow range pH values. Use [H^+] = 10^-pH; **Use K_w = [H^+][OH] = 1.0 times...
From narrow range pH values. Use [H^+] = 10^-pH; **Use K_w = [H^+][OH] = 1.0 times 10^-14...
##### Are we moving towards creating a sustainable environment? What are some of the steps that will...
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##### A photographer takes a photograph of a Boeing 747 airliner (length L = 70.7 m) when...
A photographer takes a photograph of a Boeing 747 airliner (length L = 70.7 m) when it is flying directly overhead at an altitude of 9.20 km. The lens has a focal length of 4.80 m. How long is the image of the airliner on the film?...
##### Heinhts were measurcd for random samplo 15 plants grown beir otreared pantloia nwreni The Numolc those helght measurcments were 50 centimcters and und sdunpi Standard dcvidtion centimeters respectivcly Assumc that tne populat ion helghts treated plants rommally distnbuted with mczn Eced 45 centimcters" tle sarplo, can It be concluded that esdirterenhlmm Use the (,05 Icvel HanincancrPertorm TWo-cleoTnen comdlereDors DeldkCamy Your Intermedialo computotions ormuias thiecMore degtte places Jad
Heinhts were measurcd for random samplo 15 plants grown beir otreared pantloia nwreni The Numolc those helght measurcments were 50 centimcters and und sdunpi Standard dcvidtion centimeters respectivcly Assumc that tne populat ion helghts treated plants rommally distnbuted with mczn Eced 45 centimcte...
##### Acar manulacuret = ccncerned about pOOr â‚¬UStOrel *allsfacilon orie afILS dealershIps-The managerert decides 10 evaluate the sallslaction suivcys 08 lis next 40 customers Ife deakt will be lined If the number = customers who reprt tavoratily - betkeen 24 and 30. The dealcrshlp} will bc dssolved uet Ihan 24 customers report tavarably Il /s kro that 673 ol Ihe dealer' customere Icport tavorably 04 5ullstactian SUIveys [You moy find ubeful refarence the _ Luble-] Whaf Is the pronability Iul t
Acar manulacuret = ccncerned about pOOr â‚¬UStOrel *allsfacilon orie afILS dealershIps-The managerert decides 10 evaluate the sallslaction suivcys 08 lis next 40 customers Ife deakt will be lined If the number = customers who reprt tavoratily - betkeen 24 and 30. The dealcrshlp} will bc dssolved...
##### Multiple Choice: Wrile the Icttcr thai cortesonds to thk Feaf answtr on the line to thc Iell of the approprinte question. points cxch)Which reageni can complctc thc tolksIng tcactionNahNaBrNH;NoHONaWhet is Lhe moat likely product of the following rcaction?
Multiple Choice: Wrile the Icttcr thai cortesonds to thk Feaf answtr on the line to thc Iell of the approprinte question. points cxch) Which reageni can complctc thc tolksIng tcaction Nah NaBr NH; NoH ONa Whet is Lhe moat likely product of the following rcaction?...
##### Points) a.) Compute S4 (the Ath partial sum) of the following series.S =4nAnswer:b:) Estimate the error in using S4 as an approximation of the sum of the series. (i.e. use J4? f(c) dr > R4 )Answer:c) Use n = 4 and5,f(z) dr < S < S, +f(c)dzto find a better estimate of the sum:Answer;< 5Note: the answers in the last part are tested to high precision.
points) a.) Compute S4 (the Ath partial sum) of the following series. S = 4n Answer: b:) Estimate the error in using S4 as an approximation of the sum of the series. (i.e. use J4? f(c) dr > R4 ) Answer: c) Use n = 4 and 5, f(z) dr < S < S, + f(c)dz to find a better estimate of the sum: Answ...

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Archived threads in /sci/ - Science & Math - 107. page
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File: 1447685730197.jpg (897 KB, 1625x1117) Image search: [iqdb] [SauceNao] [Google]
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how to deal with rubberbanding selfesteem?

half the people i interact with are way lazier and dumber than me - if I have to work with them my confidence goes sky high.

the other half are much, much smarter than me, and talking to them makes me feel like an idiot braggart.

I literally dont know anyone who is at my level, so to speak, and as a result i dont know how smart I am. Am I an idiot with delusions of grandeur or a smart dude with shitty selfesteem? Do i need to push myself harder?
>>
for me personally, I just keep my head down and work hard and try to have fun while I am at it

I could say I am smarter than others, but everyone thinks that. And since Im not some great innovator and my life isnt astounding, I remind myself to just be humble

>most likely delusions of grandeur
>>
>>7783356
Stop caring.
>>
>>7783373

how?

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I'm having discrete math next quarter and I would like to study in advance.

Good discrete math books?
>>
Let's just go ahead and solve all of these threads at once:

>go to well regarded university's website
>navigate to math homepage
>find course listing
>click on course of choice
>read page to find the textbook they use
>>
>>7783321
Mathematical entities are indispensable to our best scientific theories, therefore we should think of them as real
>>
>>7783321
If you want to study in advance for a particular course you should probably use the book the course uses

discrete math is a usually a potpourri of random shit, although with a big chunk of combinatorics; topics covered vary a lot.

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Blood go in, peepee come out. Explain this shit /sci
>>
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>>7783291
Brehs pls, is the kidney just a meme?
>>
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>>7783291
>>
>>7783291
kek

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Genius or average dude who got lucky?
>>
>>7783286
because it can only be two polar opposites and nothing in between ;^)
>>
>>7783286
douchebag with a lot of money
>>
>>7783286
Remember that when he graduated university he also got a small loan of a million dollars from his dad.

Is a scientist with an interest in art less intellectual than a pure scientist because the former wastes time with non-science? Assuming both have the same IQ.
>>
no, just because someone doesn't devote all of their time to science and math doesn't mean anything about their intelligence. In fact, studies have shown that people who take an interest in art have a higher-than-average intelligence.
>>
>>7783294
OP stated both are equally intelligence. His question is about intellectualism. Nice reading comprehension, brainlet.
>>
>>7777777

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Are there any physical laws that are exact? How can we know if one is?

To clarify, I mean without taking into account universal constants that we only know approximately, and given the perfect situation in which the laws are (supposed to be) valid.

For example, we know Newton's 2nd law is only an approximation valid for low velocities, but if we consider relativity, can't the v^2/c^2 term in the gamma factor not possibly be v^2.0001/c^0.0001?
>>
>>7783269
>Are there any physical laws that are exact

That's not the point of physics.

But from (unprovable) symmetry: conservation of linear momentum, conservation of angular momentum, and conservation of energy are absolute.

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Is the Universe infinite? Show your work.
>>
The space that holds the matter is infinite by definition. The matter inside is finite.

>>
>>7783219
How can space exist if it's not matter?
>>
>>7783225
That's like asking, how can energy exist if it isn't matter? The point is, it is 'something', an undefinable something.

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If this IQ test is so accurate, why did I score 96 on my first try and 132 on my second?

Pic related.
>>
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> the same butthurt small IQ fgt shitposting
I told you 500 times, take the official Mensa test you retard. Solving some crappy online math test won't make you a math genius either.
>>
>>7783204

This is made by two guys from mensa, you turd.
>>
>>7783205
I said take the OFFICIAL MENSA TEST. Are you too retarded to comprehend what you read ? it's the 501th time now.

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>>
more like DUDE WEED LMAO videos
>>
>>7783145
>"no"
>>
>>7783139
DUDE WEED LMAO

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>ITT: /sci/ comes up with a way to measure the real volume (excluding inflation) of the Universe
>>
>>7783026
>the real volume (excluding inflation)

What does that mean?
>>
>>7783026
put it in a body of water
measure displaced volume.

this is middle school physics bruh
>>
>>7783037
The actual volume/size of the universe, as it was pre-inflation. I'm not talking about "it was smaller than an atom!", I'm talking about some way to measure it relatively to something that isn't affected by inflation; a constant.

After that you can determine and possibly predict the rate of inflation. When you find that inflation variable, you can also determine the exact limit of the speed of light, for an example, since what we currently have as C is scaled up as space inflated.

Why every ancient creatures were so huge??
because of oxygen?
>>
>>7782955
I recommend you Go /sci/
>>
The Blue Whale is the biggest animal ever and it's alive
>>
>>7782955
maybe
crocs are coldblooded too and can live without any food FOR A YEAR because of it

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How much confidence do you have in modern society to overcome the increasingly daunting problems of achieving sustainability with the Earth?
>>
I have every confidence in the future of humanity. The reasons are best explained in this manifesto, which I highly recommend you read.

http://www.ecomodernism.org/

Key reasons;
- increasing development leads to less environmental dependence, and therefore impact, per capita
- the world has reached 'peak child', where global fertility rate is a stable ~2.6 children per woman. Result; better education and opportunities for children resulting in rapid development.
- projected global population at end of century is easily fed by farming current farmland more efficiently (inefficiency in developing world is staggering due to poor access to modern agricultural technology)
>>
Earth is kill my friend. Focus on terraforming Mars.
>>
>>7782920
Well people have been predicting malthusian collapse for a little over 200 years, it's still not happened. So I'm pretty confident.

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Hi /sci/,
Does anyone know if an algorithm exists for reducing complex numbers.
>>
>>7782907
reducing to reach what form?
>>
>>7782915
$a\,=\,b\,q\,+\,r$ where $q$ is the greatest complex number smaller than $\lfloor \frac{a}{b} \rfloor$ and $0\,\leqslant r \,\leqslant b\,-\,1$.
>>
>>7782925
ok, what definition of inequalities in C do you choose?

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Is it possible to build something which could reach space (or almost) for under \$15,000? What would that be?
>>
Reach "space" yes, reach orbit no.
>>
>>7782887

Yeah, but it's unlikely you'll survive.
>>
>>7782913
Not planning to use it for personal travel.

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How does the most important physicist of the last 30 years not have a nobel prize?
>>
Not high enough IQ
>>
>>7782889
seriously why doesn't he have a nobel? he has more cultural significance than any other scientist alive. so he must at least be on the shortlist.
>>
He's a meme who think ayy lmaos want our resources.

How does anyone with a basic grasp of space and scale come to that conclusion?