Asymmetric effects of capital flight on domestic investment in Nigeria: evidence from non-linear autoregressive distributed lag model

Economic theory prescribes that domestic investment is a decreasing function of capital flight. However, is there a possibility that reversals in capital flight might lead to a decline in investment levels in Nigeria? Put differently, is there a tendency for domestic investment to maintain a downward spiral, a ratchet effect, even in the face of lower levels of capital flight? Extant literature on capital flight in Nigeria is silent on this enquiry. This study is therefore a modest first attempt at investigating these possibilities. Employing the non-linear autoregressive distributed lag model, the study finds evidence of asymmetric impact of capital flight on investment undertaken at the national level. However, investment by subnational governments revealed the existence of symmetry, while overall, total public sector investments (by both States and Federal Governments) indicated the existence of asymmetric effects between positive and negative deviations of capital flight. The paper re-echoes the need for the strengthening of institutions and policy measures that go beyond the conventional in tackling capital flight.


Introduction
Classical economic theory underlines the pivotal role of investment in accelerating the pace of economic growth. Investment could be conceptualised as either in the direction of human capital or physical capital. It could also be viewed in terms of its source: in an autarky, aggregate investment is seen largely as emanating from only within the domestic economy, while in an open economy, it could be driven by the inflow of capital, either as foreign direct investment or as foreign portfolio investment. Thus, economic policy must ensure that the economy witnesses and benefits from large doses of investment, whether domestically driven or by way of FDI. In other words, there has to be significant positive change in the capital stock to ensure growth. Furthermore, policy must evolve ways of making investment more productive by way of enhancing the efficiency of productive factors in the aggregate input-mix, and also ensure that efforts at domestic mobilization of investment are not compromised by capital flight. But developing economies, including Nigeria, are not so blessed with positive doses of these phenomena. While domestic capacity for investments is largely constrained by structural challenges ranging from the economic, to the social, and even political, it is also made worse by the blighting effects of flight capital.
There is a recurring and frightening amount of capital exiting the Nigerian economy in recent times compared to aggregate domestic investment, leading to a reduction of potential growth. For instance, estimates of flight capital in Nigeria in 2010 exceeded $311 million, approximating 158.2% capital flight-GDP ratio. The proportion of real GDP lost to capital flight in Nigeria stood at 4.7% (Effiom and Edet 2019a,b). From 2012 to 2015, the rate of growth of Nigeria's capital flight has been decreasing, though it is still significantly huge when considered in absolute values (Englama et al. 2007). Deppler and Williamson (1987) noted that the growth rate of the domestic economy is constrained by an amount basically equivalent to the magnitude of capital flight. Capital flight reduces the investible capital available in the domestic economy (Ndikumana and Boyce 2018). This submission is corroborated by The World Bank (2015) which notes that in 1990, Nigeria's domestic investment stood at $43.8 billion, which dropped consecutively for two periods-$37.3bn in 1992periods-$37.3bn in to $20.1bn in 1995periods-$37.3bn in . However, from 2010 to 2015, there was a significant capital outflow exceeding $900bn compared to a paltry domestic investment of $134bn. Updated estimates reveal that capital flight stood at $411.0 in 2015, representing capital flight-GDP ratio of 68.8% (Ndikumana and Boyce 2018).
Several streams of research have been devoted to investigating the growth impact of capital flight in Nigeria (see for instance Umoru 2013;Onwioduokit 2000;Samson and Edeme 2012;Ajayi 1997, etc.). However, only a single study (i.e. Adetiloye 2012) focuses specifically on domestic investment impact of capital flight. Even then, that study is fundamentally flawed because the capital flight variable is clearly lacking as an explanatory variable in the empirical model. The current paper, besides adding to the already rich body of empirical studies on capital flight in Nigeria, is significant on two scores. First, the study takes a comprehensive and disaggregated view of domestic investment in Nigeria. Previous studies focused on investment at the Federal or Central Government, without a corresponding emphasis on that undertaken by subnational units. It must be noted that Nigeria's federal political structure consists of a three-tier administrative system with concurrent albeit unequal spending powers, with the central and state governments having considerable influence on domestic investment dynamics.
Second, studies on the effect of capital flight on growth or on different sectors of the economy generally assume an underlying linear relationship. These studies are premised on the assumption that the impact of capital flight on investment is symmetric, meaning that reductions in capital flight should equally lead to proportionate increases in investment levels. This might not be so given the mobility and speed in which capital travels internationally with the aid of financial innovation platforms (Lerner and Tufano 2011), coupled with the negative indirect impact capital flight might have on other macroeconomic variables directly associated with investments, such as exchange rate and inflation. Thus, this paper contributes to the capital flight literature in Nigeria by decomposing changes in capital flight into their partial sum of negative and positive changes and investigates if these variations have asymmetric impacts on investment. In contrast to the linear form of the autoregressive distributed lag (ARDL) framework, the paper employs the nonlinear ARDL (NARDL) developed by Shin et al. (2014) which permits the separate estimation of the effect of capital flight increases and capital flight decreases on domestic investment levels. A major research question is: is there a tendency for domestic investment to maintain a downward spiral or a ratchet effect, even in the face of lower levels of capital flight? Our interest in Nigeria is borne from the fact that, besides her being the largest economy in Africa, she also attracts the highest inflow of both FDI and remittances, but is regrettably equally blighted by the highest levels of capital flight on the continent (Effiom and Edet 2019a;Boyce and Ndikumana 2012).
Employing the NARDL, the study finds evidence of asymmetric impact of capital flight on aggregate investment in Nigeria. This is arguably the first attempt in the capital flight literature in Nigeria. The findings of the study have implications for policy, namely, that policy-makers might be misled to assuming that periods of decline in capital flight might necessarily translate to the availability of more financial resources for investment purposes. The reality might be that the damaging effects of capital flight on the domestic economy through its influence on macroeconomic indicators of exchange rate, interest rate and inflation might persist into periods of capital flight decline, thus frustrating the investment capacity of the government. The remainder of the paper is devoted to finding answers to this enquiry.

Theoretical linkage between domestic investment and capital flight
The underlying notion of capital flight is that it is a transfer of domestic resources, whether they are of the public or private sources. From the domestic private investment angle, capital flight leads to a reduction in savings, with banks mobilising less savings deposits. With lower levels of savings mobilisation, there is an increasing constraint on the banking sector's capacity to extend credit. This ultimately results in lower levels of domestic investment itself. As noted by Ajayi (1997), the tax base is also adversely affected by capital flight, leading to diminishing government revenue. This negatively leads to a reduction in public investment, with negative consequences on private investment. A further corollary of this negative process is that continuous reduction in public revenue due to the erosion of the tax base via capital flight may lead to an increase of seignorage by the government. This will inevitably lead to an increase in inflation tax, which may compel investors to divest in the domestic economy, so as to escape the devaluation of the real worth of their assets occasioned by the inflation tax surge. Thus, in line with the prediction of the portfolio selection theory, they may be induced to seek investment opportunities elsewhere (Collier et al. 2004).
Equally important is the fact that increased capital flight can propel uncertainty and doubts on the part of agents in the capacity of the government to finance its deficit budgets or debt. Thus, persistent fiscal deficits put pressure on the financing needs of the government. This leads to inflationary tensions, thus, increasing the tendency for the depletion of domestic assets held by the private sector. This results in a decrease in private investment, if this occurs. From a different perspective, persistent budget deficits may result in debt unsustainability. Ndiaye (2014) observes that in relation to domestic debt, debt unsustainability may lead to a risk of bankruptcy of private firms, leading ultimately to reduction in private domestic investment. On the other hand, rising and unsustainable government debt may lead to lack of confidence in government securities. Financial markets may respond poorly when government bonds are issued. A third consequence of rising debt is that investors may be forced to anticipate tax increases by the government to deal with the situation. This increases the risk of a decline in the value of domestically acquired assets and may compel private domestic agents to alter their portfolio of assets in favour of foreign denominated assets.
There is also the issue of speculative bubbles in relation to the effect of capital flight on domestic investment. With capital flight comes diminishing control over outflows of capital. However, unregulated capital flow exacerbates the volatility which results in uncertainty in the macroeconomic environment, resulting in a potential loss of private sector assets. Consequently, domestic private investors may seek for safe havens outside of the domestic environment.
Several approaches have been deployed in measuring capital flight, namely, balance of payment, residual, and bank deposit approaches. In this study, the residual approach of the World Bank (1985) is used, being the most extensively employed method of measuring capital flight because it obviates the distinction of capital flight from normal capital outflows (World Bank 1985).

Empirical literature
The capital flight literature has a rich historical antecedent, partly because the phenomenon has lived and lingered for long-not only in Nigeria, but also in sub-Sahara Africa and other developing countries. It does appear however that it is worse in the former than in other continents (Collier et al. 2001;Henry 2012). These studies show that relative to other regions, Africa has low levels of capital stock. However, African nationals have a tendency to hold a greater proportion of their investments overseas compared to nationals of other regions.
Trevelline (1999) notes several factors responsible for the birth, growth and sustenance of capital flight globally. Among these are the ready availability of efficient and safe medium of funds transfer across national boundaries; developments in information and communications technology (ICT), as well as efficiency in different modes of transportation which aid in keeping track of investments overseas. Others are the rate at which information and knowledge about global financial centres like London and New York are disseminated; the widespread and universal use of the United States dollar which obviates the need to convert local currencies to the dollar because most developing countries already hold their liquid assets in the dollar or other global convertible currencies. Tornell and Velasco (1992) also observe that the institutionalization of capitalism as the dominant economic system worldwide, as well as the evolution of welfarism to ameliorate the crushing effect of capitalism, has made private investors to seek safe havens abroad to avoid taxation by the state.
These avenues through which capital exits a country's economy, combined with unhealthy domestic macroeconomic and political conditions, result in massive and widespread distortions and loss of confidence by private capital holders. On the macro front, high and persistent inflation, cost of capital differentials, differentials in the rate of return on investment, huge budget deficits, exchange rate devaluation, poor governance, as well as domestic tax cum trade policies may significantly inspire the flight of capital from the domestic economy (Asongu and Nnanna 2020; Asongu and Odhiambo 2019; Gankou et al. 2016;Ndikumana 2016;Okoli and Akujuobi 2009;Hermes and Lensink 2000;Cuddington 1987;Lessard and Williamson 1987;Olopoenia 2000).
Other studies identify low GDP growth rates (Anetor 2019;Pastor 1990;Nyoni 2000), rising inflow of foreign aid (Aziz et al. 2014;Collier et al. 2004), as well as external debt overhang (Al-Basheer et al. 2016;Chipalkatti and Rishi 2001;Demir 2004). Non-economic or political factors including political instability, insecurity, leakages in public financial management (Forson et al. 2017;World Bank 2015;Le and Rishi 2005), for instance, may conspire with the above factors to encourage flight capital out of the domestic economy. In particular, Ndikumana (2014) submits that the existence and proliferation of safe or tax havens facilitate capital flight in sub-Saharan African countries. These mechanisms aid to conceal and transfer illicit capital procured through embezzlement, over invoicing of imports and under-invoicing of exports, corruption, tax evasion and sheer and brazen smuggling of natural resources and capital out of the domestic economy.
The revelations contained in the Panama Papers suggest that capital flight from Africa and other developing countries are far from abating; indeed, it is increasing in an overwhelming scale. As early as the 1990s studies indicated massive amounts of capital flight transferred abroad (see for instance Chang and Cumby 1991; Ajayi and Khan 2000;Hermes and Lensink 2000). With regard to Nigeria, there seems to be no precise estimate of capital flight from the country due to general methodological differences and a lack of consensus on measurement parameters in the literature. However, a study conducted by Le and Zak (2006) estimates that capital flight for Nigeria in 1987 was 31.0% of GDP, while Collier et al. (2001) reveal that as in 1999, Nigeria's capital flight was $107 billion as against $51.8 billion aggregate real GDP for the same year. Using several measures, Englama et al. (2007) estimated the capital flight for Nigeria from 1971 to 2006. With the World Bank (1985), they found a capital flight of $16.14 billion, with Morgan Trust co. measure of 1986, capital flight was $64.26 billion, while it found a capital flight of $130.80 billion when it deployed the Modified Approach. In particular, CBN (2015) reveals that the net capital flow for Nigeria was in the sum of $8.8 trillion and $1.1 trillion in 2011 and 1999, while the IMF (2015) reports a whopping $11.6 trillion held as offshore assets and $866 billion as income generated by these assets accruing to other countries. Consequently, countries steeped in capital flight loose tax revenues amounting to about $255 billion.
While studies devote attention to the investigation of the effect of capital flight on the Nigerian economy generally using GDP as proxy, there are several studies though, which investigate the sectoral impact of capital flight. For example, the impact of capital flight on the agricultural sector in Nigeria was investigated by Usman and Arene (2014). The study found an insignificant but negative impact of capital flight on the sector. Similarly, Uguru (2016), deploying regression analysis on time series data finds evidence of an inverse relationship between capital flight and tax revenues in Nigeria. More recently, Effiom et al. (2019) investigate the impact of capital flight on domestic investment in Nigeria and found that capital flight impacts negatively on domestic investment more severely in the long run than in the short run. Ubi and Bassey (2017) investigate the comparative impact of capital flight and remittances on poverty in Nigeria, and utilising the co-integration and error correction techniques on data spanning 1970-2010 found that capital flight worsens poverty in Nigeria. Furthermore, Uche and Effiom (2021), deploying the quintile ARDL methodology to investigate the effect of global economic policy uncertainties and exchange rate volatilities on capital flight in Nigeria, found the presence of hysteresis in the response of capital flight. In particular, their study discovered that global uncertainties and exchange rate volatilities are sensitive to different quantiles of capital flight distributions. The study therefore comes to the conclusion that capital flight is a systemic problem, as previous capital flight begets more capital flight. Rahmon (2017) also examined the impact of capital flight on domestic investment in Nigeria. An interesting result emanated from this study, namely "that capital flight has a statistically significant positive relationship with gross domestic investment in Nigeria contrary to a priori theoretical expectation". The rational implication of this is that as capital flight increases, domestic investment increases. This is indeed curious. However, the policy recommendation of the paper is inconsistent with the findings, when it recommends that "government should intensify its efforts to ensure speedy recovery of looted funds by corrupt public office holders from foreign accounts to inject funds into the economy for investment purposes". One would have thought that with a positive relationship found between capital flight and domestic investment, the rational policy outcome should have been an encouragement of capital flight.
Thus given this theoretical inconsistency as well as the realization that to the best of our knowledge, study is yet to be conducted to ascertain the asymmetric relationship or effects of flight capital on Nigeria's domestic investment, the present study undertakes to fill this gap. Our operationalization of domestic investment excludes private sector investment for, as argued above, much of capital flight in Nigeria is directed against public resources.

Stylised facts of capital flight and domestic investment in Nigeria
The Nigerian economy has witnessed massive outflow of capital (mostly dollar denominated) as politicians, corporate bodies and foreign investors move funds out of the country in response to insecurity, macroeconomic instability as well as exchange and interest rates differential. Table 1 and the accompanying Fig. 1 show that the magnitude of capital flight is alarming. From $3387 billion in 1980, capital flight rose abruptly to $10728 billion in 1981 and plummeted the following year, rising acutely again to $11,569.3 in 1983. It should be noted that this Table 1 Capital flight (CAPF) in Nigeria . Source: Author's Computation using data from WDI (2018), CBN Statistical Bulletin (2018) and Boyce and Ndikumana (2012). We measure capital flight deploying the residual approach, since it is the most widely used technique (Aziz et al. 2014;Al-Basheer et al. 2016). Here, capital flight is computed by relating the sources of funds with the uses of funds, the former including all net official flows (comprising of net increases in foreign debts of the public sector and the net flow of FDI) while the latter comprise additions to reserves and current account deficit. Algebraically, it is measured as: ΔEXD + NFDI − (CAD + ΔFER) period of undulating trends in capital flight coincided with pervasive economic crises in Nigeria in the 1980s. Capital flight has been steadily rising from 1998 to its peak value of $37,990.8 in 2008, when it further nosedived in 2010. Figure 2 further justifies the present effort of investigating the effects of capital flight, not just on investment spending by the central government, but also incorporating capital spending by the states. From 1981, the combined capital expenditure by the subnational units was at par with that of the Central Government. Stable trends were also noticed up till 1999 when states' investment expenditure consistently grew above that of the Federal Government. Figure 3 exhibits the fact that notwithstanding huge public sector investment, capital flight has remained a huge challenge, competing favourably with domestic investment and exceeding the latter from 2010.

Research methodology
The model The analysis provided above on the theoretical nexus between capital flight and domestic investment justifies the adoption of an eclectic model which is a synthesis of the Keynesian theory of investment and the Investment Diversion theory of capital flight. The Keynesian theory of investment states that there is need to induce investment either by way of reduction of interest rates or by increased government expenditure. The investment diversion theory on the other hand states that macroeconomic and governmental uncertainties and presence of wide range of financial instruments abroad, cause economic agents to take away scarce resources from the domestic economy, thereby reducing investible funds and constraining domestic investment. On this score, following Ndiaye (2007), Ndikumana (2013) and Asante (2000), the functional form of the model is presented as: The econometric expression of Eq. (1) assumes the linear form: The log-linear specification of Eq.
(2) is expressed as: Equation (3) is the Federal Government investment equation to be estimated. For investment by the state governments, we have the functional form presented thus: The log-linear specification of Eq. (4) is expressed as: (1) FGINV = f (CFL, RGDP, DBT).
where: FGINV = Federal Government investment as a ratio of the GDP, SGINV = State Government investment as a ratio of the GDP, TDINV = total domestic investment as a ratio of the GDP, CFL = capital flight to the GDP (residual approach estimated by World Bank 1985), RGDP = real gross domestic product in billions of dollars, DBT = total debt as a ratio of the GDP in billions of dollars, μ = stochastic error term, c , δ, ƛ = coefficients of economic relationship to be estimated.
The above models indicate that domestic investment is impacted by capital flight, real GDP and the stock of debt. From a priori, we expect domestic investment to be a decreasing function of capital flight. Equally, real gross domestic product should exhibit a positive relationship with domestic investment. The debt stock could either accelerate or decelerate the pace of investment, depending on the structure of repayment and the productivity of the debt. The study employs annual secondary time series data from 1980 to 2017, sourced from the various editions of the Central Bank of Nigeria (CBN) Statistical Bulletin, the Nigerian National of Statistics (NBS) and the World Development Indicators (2018).

Empirical methodology
There is a growing body of empirical studies that utilize the nonlinear autoregressive distributed lag model (NARDL) in analysing asymmetric effects and relationships in macroeconomic time series data. The NARDL is useful for several reasons. First, it permits the estimation of both dynamic and static impacts of the explanatory variables on the dependent variable. This is in contrast to a static model which only permits the estimation of fixed effects only. Second, like the conventional ARDL, it also affords the opportunity of evaluating the existence of a long-run relationship among variables, also called the bounds test. Finally, NARDL offers a framework which permits the evaluation of dynamic effects of both negative and positive changes in the regressors on a specific dependent variable (Adekunle and Ndukwe 2018).
Suppose we specify a simple static model that expresses the relationship between domestic investment (y) and capital flight (X) of the form: where β 1 is the capital flight elasticity of domestic investment, expected at a priori to be negatively signed. Equation (1) says that an increase (decrease) in capital flight leads to a contraction (rise) in domestic investment, whether private or public. Put LOG TDINV t = 0 + 1 LOG(CFL) + 2 LOG(RGDP) + 3 LOG(DBT) + (7) y t + t + 1 X t + t differently, within a symmetric and linear context, the response of domestic investment to periods of capital flight surge is just a reflection of what will happen during periods of downturns in capital flight. However, to investigate the impact of the two periods concurrently, the asymmetric ARDL technique is employed (Shin et al. 2011(Shin et al. , 2013. In the NARDL model, nonlinearity is introduced by the decomposition of the conventional ARDL model to capture for both the long-run and short-run asymmetries in the transmission mechanism simultaneously. According to Shin et al. (2013), the asymmetric cointegrating relationship with the NARDL framework proceeds by decomposing the exogenous variable in Eq. (1) into a partial sum process represented as: where y t is k × 1 vector of domestic investment at time t; X t is a k × 1 vector of multiple regressors specified such that X t = X 0 + X t + + X t -which is the natural logarithm of capital flight; μ t represents the error term, while β + and β − are the corresponding asymmetric long-run parameters, showing that domestic investment responds asymmetrically during volatile or unstable periods of capital flight movement. On the other hand, X t + and X t − signify the partial sum processes of negative (−) and positive (+) shocks in X t defined as: where ΔX j represents changes in the explanatory variable X t . The '+' and the superscripts represent the negative and positive processes around a zero threshold, which defines and sets boundaries for the independent variables. This means that the series of the first difference is assumed to be normally distributed with zero mean. Equation (5) is a nonlinear ARDL (p, q) framework exhibiting both long-and short-run asymmetries: Thus, the conditional error correction model for Eq. 5 with regard to the negative and positive partial sums can be expressed as: Shin et al. (2013) submit that Eq. 6 adequately corrects for the potentially feeble endogeneity of non-stationary regressors in a nonlinear ARDL model. This feature (8) guarantees that the causal relationship proceeds from capital flight to domestic investment both in the long and short run (see for example, Coers and Sanders 2013; Jaunky 2011). The relationship β t + = − θ + ⁄ρ and β t = − θ − ⁄ρ is used in calculating the long-run coefficients, while the null hypothesis of no-long-run relationship between the levels of y t , X t + , and X t -(which gives ρ = θ + = θ − = 0) will be tested with the bound testing technique of Pesaran et al. (2001). This method is valid irrespective of the time series characteristics of X t . We estimate the short-and long-run asymmetries using the conventional Wald test. The null hypothesis of no asymmetry in the long-run coefficients (β x + = β x − ) as well as in the short-run (π j + = π j − ) is investigated. This will result in a rejection of either or both.
Before implementing the NARDL framework, the study proceeds by undertaking preliminary test of the data to ascertain their underlying statistical as well as stationarity properties. While the former is accomplished by computing the data's descriptive properties, the latter is achieved by the use of the Augmented Dickey-Fuller (ADF) and Philip-Peron unit root tests as well as the bounds test for cointegration. We also test for the direction of causality between capital flight and domestic investment using the Granger causality test. Post-mortem or diagnostics tests were also conducted to ensure the validity and reliability of our NARDL estimates. Specifically, we test the assumptions of normality, linearity, serial correlation, and heteroskedasticity of the estimated model. Of crucial relevance to this study is the Wald test for asymmetry (both in the short run and long run). We test the null hypothesis that positive and negative changes in capital flight have direct opposite effects on domestic investment. The decision rule is that if the probability associated with the Wald test is greater than the conventional significance level of 0.01 or 0.05, then the null hypothesis of no asymmetry is accepted. On the other hand, if the related probability is less than the conventional significance level, then we conclude that there is evidence of asymmetric effects of capital flight on domestic investment in Nigeria. Table 2 presents the descriptive statistics of the data. It indicates that our core variables of interest, namely: capital flight, Federal Government investment, State Government investment and total domestic investment have mean values of 12,615.57, 866.20, 19,999.87, and 20,866.08, respectively, with corresponding maximum and minimum values as exhibited in the table. While standard deviation values show some significant drifting of the variables away from their mean values, their kurtosis however indicated that our policy variables are normally distributed. In particular, capital flight, and the different layers of investment as well as total domestic investment show kurtosis values approximately equal to 3. A few of the variables were leptokurtic, with kurtosis values exceeding 3. All variables are positively skewed, indicating a long right tail, with Jarque-Bera statistics revealing that the variables are relatively normally distributed.

Results and discussion
In Table 3, the results of the stationarity properties of the variables are presented. It is observed that most of the variables were non-stationary at levels, except inflation. However, upon first differencing, stationarity was achieved. We thus have a situation of a mixture of variables stationary at levels and at first difference. Next, cointegration is carried out to evaluate if there is any long run cointegrating relationship amongst the variables. The bounds test is used for this purpose, and the results are presented in Table 4. Cointegrating test results indicate that, though the variables are non-stationary at levels, there exists a long-run relationship among them. In particular, the calculated F-statistics of 23.55, 68.56, and 8.67 for the Federal Government investment, State Government investment and total domestic investment models were all greater than their upper bound critical values at the 5 percent level of significance. The Granger causality test result presented in Table 5 shows that there is a unidirectional causality running from capital flight to the different components of investments. This is in line with existing literature which shows that capital flight influences the quantum of resources earmarked for investment in developing countries (Ndikumana 2000). Table 6 presents both the short-and long-run NARDL estimated results of the optimal model (4, 3) obtained via the Akaike information criterion (AIC). Results indicate that Federal Government investment in the current period is adaptive to previous investments. In other words, current levels of investment respond positively to investments undertaken in the first, second and third lagged periods, even though it was only significant in the third lag. Capital flight for all the periods indicated negative relationship with investment. Real GDP is shown to be a significant driver of investment at the Federal level. From panel A, we particularly note that increases (positive deviations) in capital flight [(CFL)_POS(− 1))] led to a significant reduction in investment, while negative changes in capital flight [(CFL)_NEG(− 1))] also significantly decreased investment undertaken at the Federal level.

Result of Federal Government investment: capital flight model
From the long-run estimated results in panel B, a 100% increase in capital flight reduces domestic investment of the Federal Government by almost 71%,  Table 3 Unit roots test results. Source: Authors' computation * is significant at the one percent (0.01) level; ** is significant at the five percent (0.05) level Variable while a decrease of capital flight by 100% will on the average decrease domestic investment by almost 28%, all things being equal. It should be noted however that the negative effect (− 0.275) of decreasing capital flight on investment is less than the negative effects of increasing capital flight (− 0.706). The shortrun results in panel A apparently mimic that obtained in the long run. They indicate that an increase in capital flight [(CFL)_POS(− 1))] by 100% significantly reduces domestic investment by 73%. However, a reduction in capital flight [(CFL)_NEG(− 1))] still depresses domestic investment, contrary to theoretical expectation. To ascertain the long-run symmetric or asymmetric effects of capital flight on Federal Government investment, a Wald test is conducted and results reported in Table 7 along with other diagnostic tests results.
The null hypothesis of the Wald test is that there is symmetry in the positive and negative changes in capital flight on domestic investment by the Federal Government. The results indicate the presence of asymmetric effect of capital flight on domestic investment in the long run. This is because the null hypothesis of no asymmetry or symmetry in the long-run coefficients (β x + = β x − ) could not be accepted at the conventional 5% significance level. For the short run (π j + = π j − ), however, the null hypothesis of symmetric effects of capital flight must be Decision: There is co-integration accepted. The diagnostic results show that the model is correctly specified as indicated by the Ramsey RESET specification test, the residuals are normally distributed (p = 0.32), and do not suffer from autocorrelation (p = 0.23) and is homoscedastic (p = 0.51).  Table 8 presents the results of the non-linear specification of the state government investment-capital flight model. The estimated results reveal that in the short run, current levels of investments by state governments are positively and significantly influenced by previous levels of investments, while real GDP significantly drives investment at the subnational level. Consistent with theoretical postulation, results show that State-level investment is a decreasing function of positive variations of the debt stock. Specifically, an increase in the debt stock by 100% on the average results in 13.3% decreased in investment. This position was apparently controverted by the fact that the estimated parameter was non-significant, implying that investment decisions by subnational governments were not considerably influenced by the size of the existing stock of debt. Perhaps other considerations, mostly political, may have weighed in on investment decisions by states. The short-run positive variations in capital flight both at levels and in its first lag indicated an inverse and significant relationship with and impact on investment. In particular, a positive increase in capital flight by 100% is associated with about 73% decline in domestic investment. A decrease in capital flight by 100% however exerts a positive and non-significant increase in domestic investment by 65.6%. While this informally suggests symmetric effects, it must be stressed that the positive effect of capital flight on domestic investment exceeds its corresponding negative impact. Long-run estimated coefficients of capital flight indicate that a 100% increase in capital flight on the average led to 37% decrease in State Government investment, ceteris paribus, while a 100% negative deviation in capital flight led to about 15.9% increase in state-level domestic investment. Table 9 presents results of the Wald test to formally ascertain the long-run symmetric effects of capital flight on State Government investment levels in Nigeria.

Results of State Government investment: capital flight model
The result of the Wald test of symmetry shows that for both the long-and shortrun parameters, the null hypothesis of symmetry must be accepted, since the probability values exceed the 5% significance level. Put differently, an increase in capital flight induces a decline in domestic investment, while a corresponding decrease in capital flight leads to an increase in domestic investment. The relevant post-estimation tests reveal that the estimated model is well specified as represented by the Ramsey RESET specification test (p = 0.955), the residuals are normally distributed (p = 0.9815), and are not serially correlated (p = 0.666) and are homoskedastic (p = 0.696). Table 10 and its associated Table 11 are the results of the third model, which serves the purpose of robustness. It seeks to investigate if there would be any significant difference between the response of aggregate investment by both tiers of government (Federal and states) to capital flight deviations in Nigeria.

Results of total domestic investment: capital flight model
Results confirm that capital flight exerts similar effects on aggregate investments expenditure as it does when they are isolated. The short-run results (panel A) of the decomposition of the capital flight variable into both positive and negative deviations show that a 100% increase in capital flight, on the average, leads to 73.3% decrease in total domestic investment in Nigeria. A reduction in capital flight which was theoretically expected to exert a positive impact on total domestic investment, turned out with a contrary result. Specifically, it is associated with a 47.2% decline in total domestic investment, suggesting, by the rule of thumb, a short-run asymmetric impact. The non-linear long-run decompositions of the positive and negative  Table 11 presents the results of the Wald test of symmetry to determine conclusively the relationship existing between these deviations. With a probability value of less than 5%, the null hypothesis of symmetry between the effects of negative and positive deviations of capital flight on total domestic investment in Nigeria must be refuted. In effect, we conclude that there exist asymmetric effects of capital flight on public sector investment in Nigeria in both short and long run. The post-estimation tests are all satisfactory. Our findings broadly agree with empirical evidence furnished from previous studies showing that capital flight hurts economic growth of victim economies (Akinwale 2020; Anetor 2019; Ndikumana 2016). Capital flight impacts growth through its direct effect on investments. On this score, our results are in tandem with that of Ndikumana and Boyce (2018) and The World Bank (2015) who avers that capital flight in Nigeria has been a significant constraint on investment. The study's findings are at variance with Rahmon (2017). Regrettably, however, we could not find a study to either compare or contrast the findings of this paper with specific regards to the question of asymmetric effects of capital flight on investments, which was the major thrust of our inquiry.

Conclusion and recommendation
This study employs the NARDL to test the existence or otherwise of symmetry in the response of public sector investment (States and Federal Governments) to capital flight in Nigeria. Our findings indicate that over the long term, there exists asymmetric effect of capital flight on Federal Government investment in Nigeria. This means that an increase in capital flight induces a reduction in the investment capacity at the Federal level, while a corresponding reduction in capital flight does not lead to an increase in investment. Investment by subnational governments however revealed the existence of symmetry in both the short and long run, while overall, total public sector investments (by both States and Federal Governments) indicated once again the prevalence of asymmetric effects between positive and negative deviations of capital flight. For investments by the states, a surge in capital flight induced a reduction in investment, while its corresponding decline initiated a rise in investment.
Several factors could be adduced for this outcome, one of which could be that persistence of capital flight may worsen the fiscal position of the government, inducing external borrowing, with consequences on repayment of both principal and interest. Ndiaye (2014) is particularly worried with the consequences of debt unsustainability in the presence of capital flight, while Ajayi (1997) laments that external borrowing and the availability of foreign exchange actually fuel its persistence Thus, even when there is a significant reduction in capital flight, government may have to grapple with the short-to medium-term negative effects of its occurrence. In the meantime, investment must be halted or considerably slowed. Furthermore, the negative macroeconomic distortions of capital flight especially on inflation and exchange rate stability might account for this asymmetry, considering the implications of capital flight on the value of government receipts, which form the basis its investments outlay. Our findings have implications for the range of policy alternatives available to government to curb the menace of capital flight. Traditional policy tools to control capital flight and boost investment, for instance, may rest on the erroneous assumption that once capital flight is significantly curbed, domestic investment may surge almost immediately by default. But this might not be the case, with the present evidence furnished of asymmetric effects of capital flight on investment behaviour. This means that besides conventional policy tools, for example, of strengthening institutions, government must think out of the box in dealing with problems of asymmetric impacts of capital flight and investment behaviour, in both the short to the long term.
Author contributions LE conceptualised the study, wrote the introduction through to the literature review, EU handled the methodology and results section, while OAO sourced for data, and also did some parts of the analysis. All authors proofread and approved the submission of the manuscript.
Funding There is no funding whatsoever for this study.
Availability of data and materials Data for this study are sourced from the Central Bank of Nigeria Statistical Bulletin as well as the World Bank Development Indicators.