Explaining corruption: How do firms respond to non-gravity trade in developing countries?

: There has been limited effort to explore whether non-gravity trade, as not driven by standard variables entering an augmented gravity model, matters for firms’ corruption. To fill this gap, this paper explores the effect of non-gravity trade on firms’ corruption in 141 developing countries during the period 2006-2017. Our results show that non-gravity trade does matter for the firms’ corruption behavior. Specifically, we find that firms’ corruption decreases by 0.09% to 0.23% following a unit increase in non-gravity trade (e.g. 19.7 million dollars’ increase in real trade), and the effect is much larger during the world financial crisis period. The result is robust to exploiting conditional heteroskedasticity for identification, constructing a Bartik-type instrument variable, applying different econometric technics, and using alternative measures of firm corruption. same, and they show that an increase of 1 percentage point in non-gravity trade reduces the level of corruption by almost 0.21 percentage points.


Introduction
The adverse effects on firm exports and trade of corruption have been widely recognized by policy makers and the World Bank (Dutt & Traca, 2010;Sequeira & Djankov, 2014;Martins et al., 2020;Qi et al., 2020) . As emphasized by Stigler (1975) (Dong and Torgler, 2013;Gokcekus and Knorich, 2006;Treisman, 2000). However, there has been limited effort to explore whether non-gravity trade, as not driven by standard variables entering an augmented gravity model, matters for firms' corruption. This paper attempts to fill this gap. We investigate the impact of non-gravity trade on firms' corruption behavior in the context of 141 developing countries during the period 2006-2017. This is also a particularly important setting given renewed interest in understanding the micro-level drivers of corruptions (Chatterjee & Ray, 2012;You & Nie, 2017).
Non-gravity trade, as suggested by Brueckner, Long & Vespignani (2020), is the exchange of goods and services that is not determined by standard variables entering a gravity equation. In the spirit of this definition, we construct our measure of non-gravity trade 1 between two countries as the residual in a gravity equation, following Head et al. (2010). For the total non-gravity trade for one (i.e. home) country, the measure comes from taking a weighted average of its residuals. The weights, in turn, are based on other (i.e. foreign) countries' trade share with the home country. Thus, the total nongravity trade of a country is calculated as a weighted average indicator. To measure the extent that enterprises are affected by non-gravity trade, we use the enterprise's trade shares as weights to derive our main interested variable, firm-level non-gravity trade, which helps to fit the firm-level corruption indicator used in the current study. We find that non-gravity trade negatively affects firm's corruption in developing countries.
In order to identify the effect of non-gravity trade on firms' corruption, one may concern about the endogeneity issue of non-gravity trade. First, non-gravity trade is plausibly seen as an exogenous shock to micro-firms, accounting for the variation of trade driven by non-fundamental components. It is mainly because the national level non-gravity trade is predicted using a gravity model, and normally individual firms only contribute little to its variations. In addition, as complementary casual identification strategies, an aggregate instrument variable (e.g. average non-gravity trade for each industry at the ISIC 2-digit level) is constructed in this paper to uncover the casual effect of non-gravity trade on firms' corruption following the logic of previous casual identification studies (Bentolila et al., 2010;Card & Krueger, 1996;Evans et al., 1992).
Furthermore, we apply estimation approach that identifies the effect by exploiting conditional heteroskedasticity, following Lewbel (2012Lewbel ( , 2019) (see also, Baum et al., 2012;Baum & Lewbel, 2019;Klein & Vella, 2010). Our instrumental approach shows that firms' corruption decreases by 0.23% at most following a unit increase in nongravity trade (e.g. 19.7 million dollars' increase in real trade), and the effect is much larger during the world financial crisis period.
This work builds on the growing literature that examines the effects of trade on corruption. It has been found that corruption is negatively associated with trade (Dong & Torgler, 2012;Dutt, 2009;Gokcekus & Knörich, 2006;Neeman et al., 2008;Treisman, 2000), and the potential mechanism is that greater openness could alter both the political-economic structure of the country and social norms. However, whether and how the non-gravity trade affects corruption remains unsolved. As the first work studying this relation, to the best of our knowledge, this work contributes a new perspective to explore the causes of corruption. In addition to augmenting the literature by looking into a non-fundamental determinant of corruption, the paper links the stream of literature to the one that studying how income affects corruption. This rationale is that non-gravity trade affects income variation (Acemoglu et al., 2001), and 'if other factors lead to vigorous economic development, corruption is likely to decrease (Treisman, 2000). It has been found that richer countries tend to have less corruption which is usually used as the proxy for governance (Cole, 2007;Glaeser et al., 2004;Husted, 1999;Paldam & Gundlach, 2008), and the underlying reason is that wealthier countries tend to have better institutions (See Treisman, 2000;Graeff & Mehlkop, 2003;Lambsdorff, 2006;Serra, 2006). However, those previous analyses focus on the effects of income, driven by fundamental factors, has on corruption. This study instead employs non-gravity trade as a non-fundamental determined indicator and examines the effect that non-gravity trade driven income variations have on firms' corruption.
This non-gravity trade variation is measured by the unforecastable component of the linear model (Jurado et al. 2015), which could be seen as one uncertainty shock to firms. Non-gravity trade displays much volatility than that of gravity trade and this stylized fact is confirmed through applying a variety of specifications of the gravity equation (Brueckner, Long & Vespignani, 2020) Thus, this work is also related to the stream of literature investigating the relationship between uncertainty and corruption which receives little attention. As documented by previous research, economic uncertainty is positively related to corruption based on empirical analysis from a large cross-country sample (Goel & Ram, 2013). In addition, political uncertainty increases corruption in different variations and time periods and the result is robust when alternate dimensions are considered (Goel & Saunoris, 2017). This work is different with them in two aspects. First, we aim at identifying whether non-fundamental factors measured by non-gravity trade matter for firms' corruption while they look at how uncertainty determined by fundamental factors affects corruption at country level. Second, the impact of non-gravity trade on corruption is found to be negative while that of economic and political uncertainty is positive, and this is because the increase of non-gravity trade stimulates economy while the other two bring more risks.
The remainder of this paper is structured as follows. Non-gravity trade is discussed in section 2. The data and methodology are presented in Section 3. Section 4 examines the effect of non-gravity trade on perceived corruption at the firm level, using different indicators and methods of estimation. Section 5 concludes.

Non-gravity trade
The interested variable in this paper is non-gravity which accounts for the variation of trade driven by non-fundamental components. We construct this indicator at the firm-level in three steps. First, non-gravity trade between home and foreign countries is estimated as the residual of a traditional gravity model ( Brueckner, Long & Vespignani, 2020;Tian et al., 2020). Second, based on the derived residuals, we compute the country level non-gravity trade as a weighted average taking trade shares as weights. Third, the firm level non-gravity trade is computed as the product of the country level non-gravity trade and the total share of trade for each firm, where the total share is the sum of the proportion of total sales that are exported directly and indirectly, and the proportion of total inputs that are of foreign origin.
Step 1: Non-gravity trade is formally defined as an unforecastable component of a linear estimation. In this paper, we apply this methodology in a gravity equation following Head et al. (2010). Non-gravity trade is constructed as the residual of a gravity equation (Brueckner, Long & Vespignani, 2020;Tian et al., 2020) The coefficients 1 to 8 are parameters to be estimated, and is an error term. Following the definition of non-gravity trade, the residual (̂) on the estimates of equation (2) is our interested variable. Thus, non-gravity trade is the variation of the log of bilateral trade/nominal GDP that cannot be explained by variables that the trade literature has found to be significant determinants of trade (Brueckner, Long & Vespignani, 2020;Tian et al., 2020).
Step 2: The second step is to calculate the non-gravity trade of country in year . It is calculated as a weighted average indictor ( − ). The weights, in turn, are based on other (i.e. foreign) countries' trade share with the home country. Thus, it is calculated as where is the share of trade between country and country . ̂ is the residual predicted based on equation (2) with Ordinary Least Square (OLS) estimation.
Step 3: The third step is to compute the firm-level non-gravity trade, which is main interested variable in this work. To be consistent with the target of this paper and the measurement of the dependent variable, we use equation (4) to calculate this indicator.
where _ indicates non-gravity trade for firm in country at time ,

Data sources
The main data source is the firm-level database provided by the World Bank Enterprise Surveys (WBES), spanning a wide range of developing countries during the period 2006-2017. In total, the stratified random sample data cover 136,887 firms in 141 countries. The firms were surveyed through face-to face interviews with manager and owners. The dataset contains detailed firm-level information on domestic sales, exports, imports, firm size and age, ownership, and legal status. The macro-level institutional quality indicators like access to finance, political stability, tax administrations and tax rates are also included. In particular, the dataset contains information on firm-level perception of corruption, which is used as the dependent variable here. The main interested variable, non-gravity trade, is estimated through applying the gravity model with the data from Rose ( 2019).

Corruption
The main firm-level corruption measure draws from firm's response to the question "in reference to that application for an import license, was an informal gift or payment expected or requested". We adopt this indicator that focus on bribes to secure import licenses as the dependent variable because it fits our study the best. To deal with the potential endogenous issue, we further calculate a Bartik-type variable to identify the causal effect following the idea of Liu et al. ( 2020).
where is the average reported corruption for firms in country i in year t, and is the average corruption for firms in industry j (denoted at the ISIC 2-digit level) worldwide. Using such a measure partially removes the idiosyncratic components of the firm-level reported corruption, and potentially alleviates the endogeneity problem.
For robustness checks, we further apply other alternative corruption measurement indicators to confirm our results.

Control variables
We control for two categories of factors that may potentially correlated with our interested variable, non-gravity trade.

Identification specification
To examine the effects of non-gravity trade on corruption, we conduct the following regression: where is the corruption reported by firm of country in year . _ indicates non-gravity trade at the firm level as calculated in section 2.
Non-gravity trade is plausibly seen as an exogenous shock to micro-firms, accounting for the variation of trade driven by non-fundamental components. It is mainly because that the national level non-gravity trade is predicted using a gravity model, and normally individual firms only contribute little to its variations. is a vector of controls including firm ownership, firm age and size, manager experience in the industry, employment, legal status, proportion of government ownership, proportion of other ownership, and a set of institutional quality controls, such as financial constraint, political instability, tax administrations and tax rates. We let and be generic representation of country fixed effects and industry fixed effects that capture all time invariant country-specific and industry-specific characteristics and permanent differences.
denotes the year fixed effects, which is modelled to remove the timevarying macroeconomic worldwide common shocks that affect the developing countries identically. is the idiosyncratic error term clustered at the country-year level.

Instrument variable approach
Even we have discussed that non-gravity trade could be potentially seen as an exogenous shock to micro-firms, and we add the control variables mentioned above to satisfy the conditional independence assumption (CIA) to uncover the casual effect (Angrist & Pischke, 2008), one may still concern about the endogeneity issue of nongravity trade. To deal with the potential endogeneity issue, we develop an aggregate instrument variable at industry-year level following the ideas of Evans et al. (1992), construct an average non-gravity trade for each industry at the ISIC 2-digit level at year . This instrument variable for micro-level firms is denoted as − − .

A complementary approach
As a complementary approach, we apply another estimation approach proposed by Lewbel (2012). This estimator exploits heteroskedasticity for identification and eliminates the concern about exclusionary restriction associated with using instrument variables. It is constructed in the following way as equation (7) shows, where ̂ is the residual derived by regressing the potential endogenous variable on all the control variables, and ̅ is the mean of non-gravity trade. As shown by (Lewbel, 2012(Lewbel, , 2018(Lewbel, , 2019, excellent candidates for the vector are the variables that may alternatively be used as instruments in a given context. Accordingly, in the context of our application, we use the mentioned instrument of non-gravity trade as and implement the two-stage estimator proposed by Lewbel (2012;. First, the residuals ̂ are retrieved by regressing non-gravity trade on all the control variables. Following Lewbel (2012), we use the Breusch-Pagan test of heteroskedasticity which satisfies the requirement to construct the instrument variable.
The new instrument variable is therefore can be created by equation (7). Second, we use ( − ̅ ) ̂ as the instrument variable to identify the causal effects of non-gravity trade on the changes in firms' corruption.  (4), and the results show that the negative relation is reinforced when this institution factor is taken into account. More such factors are put in the last column, but it turns out that they are not playing a role and the coefficient of interest barely changes. Overall, we find that firm reported corruption is significantly negatively correlated with non-gravity trade. A unit of nongravity trade increase contributes to at least 0.08% decrease in corruption. Even we have added the control variables to satisfy the conditional independence assumption (CIA) (Angrist and Pischke, 2008) in Table 2, there may be some other variables omitted, like those variables that are not observable or unmeasurable. Fixed effects models are applied to deal with this type of omitted variable problem, and the results are reported in Table 3. We first add the year fixed effects, removing the worldwide common shocks in corruption. The results show that non-gravity trade still has a significant negative association with corruption, and the effect size changes little.

Benchmark results
Next, we further add country and industry fixed effects in column (2) and (5).
Particularly, as the last column shows, the way and the extent of how non-gravity trade affects corruption remain the same when all the year, country and industry fixed effects are controlled, compared to the baseline results. With the other two combinations of fixed effects being controlled, column (3) and (4) generate the similar results. These estimations further support the finding that the firm-level perceived corruption is decreasing in non-gravity trade. The effect size is around 0.08 which is robust with the results reported in Table 2. The potential measurement error issue may lead to the downward estimation bias in the OLS regression as shown in Table 2 and Table 3.

IV regression results
As noted in the last section, the average non-gravity trade at the industry level is taken as the instrument variable to deal with endogeneity, and a two-stage least square (2SLS) estimator is further employed to tackle the issue of exclusionary restriction associated with using an IV. The corresponding results in details are presented in this subsection. We further identify the causal effect of non-gravity trade on firm perceived corruption using generalized method of moments (GMM), and the results shown in column (4) provide robust evidence of our finding. The effect size under the IV estimation is almost twice as that reported in Table 3. Potentially, the instrument variable not only deals with the endogenous issue, but also solves the measurement error problem of non-gravity trade.

Identification through heteroskedasticity as a complementary approach
The following Table 5 presents the estimation results using the Lewbel instrument variable obtained by equation (7) via the same estimation methods as shown in Table   4. The heteroskedasticity is very strong in terms of errors in the first-stage regressions, which could sufficiently satisfy the heteroskedasticity requirement for applying Lewbel estimation approach. The point estimates are statistically significant at a 1% level, and the effect size is strengthened under this method. In particular, the estimates of 2SLS and GMM model taking all the fixed effects into account (in the last two columns) are the same, and they show that an increase of 1 percentage point in non-gravity trade reduces the level of corruption by almost 0.21 percentage points.
Therefore, both the benchmark and IV regression results provide robust evidence that non-gravity trade has a significant negative impact on the perceived corruption at the firm level. This is contrary to how economic and political uncertainty impact corruption. The underlying reason could be that an increase in non-gravity trade driven by non-fundamental factors results in economic development which in turn reduces corruption, while the other two types of uncertainty put economic agents at more risks such that corruption, as a way of risk prevention, becomes more attractive. (2)

2SLS
(5)  Notes: i) Clustered standard errors in parentheses; ii) *** p<0.01, ** p<0.05, * p<0.1; iii) firm ownership, firm age, manager experience in the industry, firm size, employment, legal status, proportion of government ownership, and proportion of other ownership, financial constraint, political instability, tax administrations are all controlled at the first and second stages.

Different measurement of corruption
The effect of non-gravity trade may be sensitive to different corruption indexes.
For this reason, we make robustness checks and present the outcomes in Table 6.
Taking the other corruption indicators in the survey as the dependent variable, the estimates shown in Table 6 provide evidence that the relationship between firms' perceived corruption and non-gravity trade is not sensitive to the use of different indexes of corruption. In particular, the positive point estimate (0.208) for the last measurement also supports the argument that the increase in non-gravity trade can lead to a lower level of corruption because this proxy is contrary to the other corruption indicators as it measures the ratio of firms which believe that the court system is fair, impartial and uncorrupt. There exists one exception that the estimate is insignificant when corruption is measured by the percent of firms expected to give gifts to get a phone connection. With the popularization of telephone, obtaining telephone connection is no longer a constraint for enterprises to set up and operate. The results show that non-gravity trade affects firms' corruption through the bribery behaviors of both customs-related and non-exporting related officials in emerging countries, which is different from Gatti (2004) who finds that openness does not lead the corruption behaviors related to non-customs officials.

Table 6 Non-gravity trade on corruption (Robustness checks I)
Percent of firms expected to give gifts in meetings with tax officials -0.067***(0.018) Percent of firms expected to give gifts to secure a government contract -0.100***(0.014) Value of gift expected to secure government contract -0.008***(0.001) Percent of firms expected to give gifts to public officials -0.255***(0.024) Percent of firms expected to give gifts to get a phone connection -0.007 (0.006) Percent of firms expected to give gifts to get an electrical connection -0.033***(0.009) Percent of firms expected to give gifts to get a water connection -0.024***(0.006) Percent of firms expected to give gifts to get a construction permit -0.049***(0.010) Percent of firms expected to give gifts to get an operating license -0.066***(0.013) Percent of firms identifying corruption as a major constraint -0.212***(0.027) Percent of firms believing the court system is fair, impartial, and uncorrupted 0.208*** (0.029) Notes: i) Clustered standard errors in parentheses; ii) *** p<0.01, ** p<0.05, * p<0.1; iii) firm ownership, firm age, manager experience in the industry, firm size, employment, legal status, proportion of government ownership, and proportion of other ownership, financial constraint, political instability, tax administrations are all controlled at the first and second stages.

A Bartik-type corruption
Next, we use the Bartik-type variable generated by equation (5) to identify the causal effect of non-gravity trade on corruption, and the results are performed in Table   7. Not only is this a robustness check with a different type of corruption index, but also a way of mitigating the endogeneity problem. Following the framework of identification discussed above, we estimate the causal effect with the methods of twostage least square (2SLS) by employing the two instrument variables introduced above respectively. The outcomes show that non-gravity trade still has a significant negative impact on corruption even the effect size drops, providing robust evidence that the main result can survive with various measure of corruption.

Different time periods and adding more control variable
The effect may also be heterogeneous in different time periods, and with more variables under control. The following estimations try to tackle this issue by using the complementary approach using the Lewbel-IV. Specifically, Column (1) -(3) in Table   8 checks the robustness of negative relation between non-gravity trade and corruption over 3 durations (namely the time of period from 2006-2009, 2010-2012 and 2013-2017), verifying that the relationship does exist. The effect is much larger during the financial period 2006-2009, and a drastic fall in the effect size can be seen from this period to the last two. It may be attributed to that the firms' corruption behavior is much more sensitive to the incomes driven by non-gravity trade during hard times. Column (4) and (5) further examine the relationship by successively adding tax rate and transport as the extra control variables of institutional characteristics. It turns out that the point estimation remains the same as that in Table 5. Overall, these estimations provide robust evidence that the increased non-gravity trade can lead to a lower level of reported corruption at the firm level. Notes: i) Clustered standard errors in parentheses; ii) *** p<0.01, ** p<0.05, * p<0.1; iii) firm ownership, firm age, manager experience in the industry, firm size, employment, legal status, proportion of government ownership, and proportion of other ownership, financial constraint, political instability, tax administrations are all controlled at the first and second stages from column (1) to column (3); iv) tax rate and transport as the extra control variables are successively added in column (4) and (5).

Concluding remarks
Corruption can be explained by various socio-economic, political and institutional factors. Among these factors, fundamental ones, such as economic growth, political structure and legal system, receive much more attention than the non-fundamental ones like non-gravity trade. Although it has been argued that trade is an important determinant to corruption (Dong & Torgler, 2012;Gokcekus & Knörich, 2006;Neeman et al., 2008;Treisman, 2000), how non-gravity trade, as not driven by standard variables entering a gravity equation affects corruption remains unknown.
In this paper, we quantify the effects of firm-level non-gravity trade on perceived corruption by using a large sample country over the period 2006-2017. The results show that non-gravity trade is negatively linked to corruption and it is robust against various identification strategies and measures of corruption. The potential mechanism is that non-gravity trade of a country affects firm's income (Brueckner, Long & Vespignani, 2020;Tian et al., 2020), and the increased income level in turn deters corruption. The present study therefore mainly contributes to the literature by providing a new perspective on the determinants of corruption and identifying that the nonfundamental driven trade can deter corruption at firm level in the developing countries.