Nicolae Stef
email: nicolae.stef@yahoo.fr

Bankruptcy and the difficulty of firing

Keywords: Bankruptcy, Layoff, Labor JEL Classification G33 G38 J63 K31

Firms may use layoffs as an ex ante mechanism to avoid filing for bankruptcy.

However, the national labor law may impose some restrictions that delay or hamper the firing decision of the employer. This study proposes a different legal pathway for policymakers whose goal is to reduce the use of bankruptcy without acting on the design of the bankruptcy law. Using a sample of 33 countries from 2007 to 2015, we show that the total amount of firing restrictions leads to more bankruptcies. The employer's legal obligation to notify a third party prior the dismissal of one employee tends to increase the number of bankruptcies. It is very likely that the employer's rescue strategy endures an intense ex post monitoring of the employment contracts and/or a strong legal opposition to the layoff decision from such third party. In addition, labor codes that apply priority rules in case of reemployment can increase the use of bankruptcy.

Introduction

One of the most important legal provision of the new French labor law adopted on August 9 2016 is the possibility of employees' dismissal on the basis of firm's economic performance. Thus, a French company faced with a decline in sales can more easily dismiss some of its employees in order to protect its own existence. Such reform made the subject of a long debate in the French society in which numerous labor unions have tried to oppose to its adoption. The main argument of French policymakers was that the new labor reform will increase the competitiveness of French companies on the European market. Nevertheless, heavier regulations of labor markets are associated with lower labor force participation and higher level of unemployment among the young population [START_REF] Botero | The regulation of labor[END_REF]. Similar negative effects of such laws was also confirmed by Djankov and Ramalho (2008). Developing countries with rigid employment laws seem to be characterized by developed grey economies and higher unemployment.

Rigid labor codes also affect the input decisions of firms. According to [START_REF] Lafontaine | Do labor market rigidities have microeconomic effects? Evidence from within the firm[END_REF], labor regulations that hinder firms to adjust the labor input as a response to the fluctuations of the demand can impede the growth of firms. However, such regulations increase workers' employment tenure by protecting them against job loss when firms experience negative shocks. Not surprisingly, pro-worker governments will always encourage the adoption of amendments that strengthen the bargaining power of employees. [START_REF] Besley | Can labor regulation hinder economic performance? Evidence from India[END_REF] analyzed the consequences of such pro-worker political orientation in the case of India. Their study confirms that pro-worker labor market regulations diminished the level of investment, employment and productivity of the manufacturing sector. According to [START_REF] Klapper | Entry regulation as a barrier to entrepreneurship[END_REF], labor regulations that protect more the employees can impede the growth of new firms. Higher costs of compliance with labor regulations may inhibit firms' entry.

As opposed to pro-worker laws, less rigid labor regulations tend to harm less the national economy. Di [START_REF] Di Tella | The consequences of labor market flexibility: Panel evidence based on survey data[END_REF] examined the main consequences of such laws in 21 countries from 1984 to 1990. After controlling for time and country fixed effects, their study shows that a higher degree of flexibility of firms to adjust labor to economic realities significantly increases the employment rate and the labor force participation rate. Hence, a certain support in favor of less rigid labor laws seems to be justified by the labor literature. However, adopting a labor law that diminishes the difficulty of firing does not affect only the economic environment but also the amount of work of bankruptcy institutions.

In this paper, we want to examine another financial perspective that may shed light on the ongoing debate between rigid labor laws and flexible labor laws. Consequently, our research assesses how legal restrictions of firing and the amount of such restrictions influence the national number of bankruptcies. Rational agents should try to prevent firm's default and use different economic strategies in order to favor the firm's survival. In this context, a higher difficulty of firing should increase the pressure put on bankruptcy courts by increasing the number of bankruptcies.

In order to analyze such financial consequences of firing regulations, we constructed a sample of 33 countries from 2007 to 2015. Moreover, this study uses 4 firing restrictions provided by the World Bank such as: (1) the employer's obligation to notify a third party, e.g. a government agency, in case of the dismissal of one redundant worker, (2) the employer's obligation to consult a third party prior a collective dismissal, (3) the approval of a third party that is required for a collective dismissal and (4) the employer's obligation to apply priority rules in case of reemployment. Our estimations confirm that the presence of restrictions ( 1) and ( 4) encourages the use of bankruptcy. Furthermore, an important amount of firing restrictions also increases the use of bankruptcy in the economy. The way the layoff process is regulated by the law seems to directly affect the number of bankruptcy procedures opened in court. The estimations confirm that rigid laws that protect employees against firing are associated with a higher bankruptcy usage in the economy.

Although some studies treated the determinants of firms' exit rate such as [START_REF] Flynn | The determinants of exit in an open economy[END_REF][START_REF] Doi | The determinants of firm exit in Japanese manufacturing industries[END_REF] or [START_REF] Disney | Entry, exit and establishment survival in UK manufacturing[END_REF], firm's bankruptcy and firm's exit do not stand on a common ground.

First, the firm will not automatically exit the market when the bankruptcy petition is approved by the court. Bankruptcy procedures are lengthy. According to [START_REF] Blazy | Building legal indexes to explain recovery rates: An analysis of the French and English bankruptcy codes[END_REF], the average duration of a voluntary liquidation procedure in England is 35 months. In Netherlands, creditors have to wait on average 2 years to fully liquidate the debtor's assets [START_REF] Couwenberg | Costs and recovery rates in the Dutch liquidation-based bankruptcy system[END_REF]. Second, the bankrupt firm will definitively exit the market when the judge will impose its removal from the national register. The deregistration dictated by the court is equivalent to the legal exit of the firm. However, a bankruptcy procedure does not always lead to such outcome. A firm can settle the creditors' claims soon after the court approved the bankruptcy petition by partially liquidating its assets. Some national bankruptcy procedures are also designed to help the debtor regain her financial health such as the Chapter 11 of the U.S. bankruptcy system or the Redressement judiciaire procedure of the French bankruptcy system. Stef (2017) identified 90 countries that have such reorganization procedures that may allow the survival of the debtor under the guidance of a reorganization plan voted by claimants and approved by the court.

Our research is of primary interest for public authorities confronted with a large number of bankruptcies. One legal alternative to diminish the national use of bankruptcy was suggested by [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF]. Legal systems are able to reduce the number of bankruptcies if they have a higher judicial efficiency and grant creditors an important amount of legal rights. Such alternative would be feasible for a country with efficient institutions. However, it may be difficult for a country to raise the judicial efficiency in the short term. Some legal systems are not used to provide a higher protection to creditors such as national systems of French legal origin. This study aims to propose a different legal pathway for policymakers whose goal is to reduce the use of bankruptcy without acting on the design of the bankruptcy law. As the study shows, countries with labor codes that hamper the employer's layoff decision are more prone to have a higher number of bankruptcies. By reducing the legal restrictions that slow down the layoff process policymakers can diminish the use of bankruptcy in the economy.

The study is organized as follows. Section 2 presents the main determinants of corporate bankruptcy filing rates identified in the literature and the relationship between labor codes and insolvency risk. In section 3, we present our sample of 33 countries and describe the variables used to assess the impact of the firing regulations on the number of bankruptcies. Section 4 presents our econometric methodology and the results of our estimations. The last section concludes.

What drives the use of bankruptcy?

Determinants of corporate bankruptcy filing rates

The fall and the rise of corporate bankruptcy filings are subject to different legal and economic factors. Adopting a new bankruptcy reform may be intended to modernize the national bankruptcy system in order to better serve the interest of claimants and debtors. [START_REF] Boyes | Some effects of the bankruptcy reform act of 1978[END_REF] showed that the implementation of the 1978 Bankruptcy Reform Act of United States increased on average by 16.6% the number of bankruptcies per month in the first two years after the adoption of the new law. However, a bankruptcy reform does not always lead to an increase of bankruptcies soon after its adoption. In 1986, a new insolvency act was adopted by the United Kingdom. As argued by [START_REF] Liu | Corporate failure rates and the impact of the 1986 insolvency act: An econometric analysis[END_REF], the new law aimed to facilitate the reorganization of distressed companies and protect creditors from different malpractice. A reduction of the number of bankruptcies was recorded in the first three years following its adoption. In that period, more than 1100 companies were on average discouraged to file for bankruptcy [START_REF] Liu | Corporate failure rates and the impact of the 1986 insolvency act: An econometric analysis[END_REF]. In 1997, Belgium adopted a new bankruptcy law whose main purpose was to encourage the debtor's reorganization. According to [START_REF] Dewaelheyns | Legal reform and aggregate small and micro business bankruptcy rates: evidence from the 1997 Belgian bankruptcy code[END_REF], the Belgium reform managed to diminish the use of bankruptcy by small companies in the manufacturing and trade industries.

The variance of bankruptcy filings is also sensitive to currency fluctuations. [START_REF] Jacobsen | What influences the number of bankruptcies?[END_REF] analyzed the impact of such macroeconomic factors on the number of Norwegian bankruptcies during 1991 and 2004. Their study shows that the appreciation of the local currency and the high growth of wages lead to an increase of the number of bankruptcies in 2002.

Nevertheless, when the local currency started to depreciate and the wages to record a moderate growth in 2003, the number of bankruptcies started to decline. Another determinant of bankruptcy use is the net interest payments. [START_REF] Cuthbertson | The determinants of compulsory liquidations in the UK[END_REF] showed that an increase of net interest rate had a short-run positive impact on the number of British compulsory liquidations. In the long-run, firms can adapt more easily to high interest rates allowing them to avoid bankruptcy.

Fiscal policy also seems to play a role in the variance of bankruptcies. [START_REF] Buehler | The geographic determinants of bankruptcy: Evidence from Switzerland[END_REF] examined the determinants of bankruptcies in Switzerland. Bankruptcy rates are lower in Swiss regions where corporate taxes and unemployment rates are lower and local authorities finance high public investment projects. In addition, central municipalities of agglomerations tend to be characterized by lower bankruptcy rates. Furthermore, a drop in the regional property prices can increase the regional level of forced insolvencies in New Zealand [START_REF] Fabling | Insolvency and economic development: regional variation and adjustment[END_REF].

Hence, a decrease of the collateral value may increase the creditors' incentives to force a debtor file for bankruptcy given that the loan repayment risk is higher.

Undoubtedly, the number of bankruptcies is directly influenced by the content of the bankruptcy law. The rights granted to claimants provide a certain degree of protection that may encourage or discourage the use of bankruptcy. [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF] examined how creditor's legal rights and the judicial efficiency of public institutions affect the bankruptcy filings of 35 countries from 1990 to 1999. Bankruptcy systems that do not impose an automatic stay on debtor's assets have less bankruptcies. Moreover, bankruptcy filings increase if a judgment during a reorganization procedure is rendered in less than 90 days. A greater judicial efficiency encourages the bankruptcy use. A bankruptcy system of high judicial efficiency that provides a higher degree of protection to creditors is associated with less bankruptcies. Stef (2017) extended their research by assessing the use of the liquidation procedure (31 countries) and the use of the reorganization procedure (23 countries) from 2005 to 2012. A legal interference in terms of use exists between the two bankruptcy procedures. Such interference supposes that the approval mechanism of reorganization has an impact on the use of liquidation. National bankruptcy laws that approve more easily the debtor's reorganization favor more filings of reorganization to the detriment of the liquidation procedure. The most significant legal provision that confirms the legal interference is the cram-down right of the court, i.e. judge can overcome the creditors' rejection and impose the reorganization procedure. This legal provision decreases the use of liquidation having a positive influence on the reorganization use.

Layoffs and bankruptcy

Firms that want to prevent filing for bankruptcy will engage in different ex ante strategies such as finding cheaper suppliers, renegotiating credit contracts, expanding on other markets, diminishing cost production, improving labor productivity, abandon unprofitable projects etc.

Layoffs are also an ex ante mechanism that can prevent bankruptcy or at least delay the bankruptcy filing. When the expected costs of defending against a worker's unlawful termination lawsuit are higher, firms tend to replace firings policy, i.e. situation where few employees are displaced, with layoff policy characterized by a large number of displacements [START_REF] Oyer | Layoffs and Litigation[END_REF].

According to [START_REF] Pfann | Downsizing and heterogeneous firing costs[END_REF], a firm may have strong incentives to delay the firing decision when the firing costs are higher. Hence, the firm's insolvency risk may increase when firings are delayed.

Nevertheless, employees' interest are not protected only by the law but also by the unions. The unionization process seeks to raise the wages and to protect the employment of the current employees. However, [START_REF] Freeman | Do unions make enterprises insolvent?[END_REF] confirm that unions have on average a rational behavior that does not drive firms out of business. Although unions are able to increase workers' compensations and slow down the economic growth of union firms, they are fully aware of the social necessity of the firm's survival. In addition, the influence of unions on the insolvency risk mainly depends on the size of the unions. Large size unions favor firm's termination whereas low and medium size unions are associated with a lower likelihood of firm's insolvency [START_REF] Freeman | Do unions make enterprises insolvent?[END_REF].

The main dilemma of the employment protection is to diminish the layoff likelihood of individuals without harming the existence of the firm [START_REF] Gautié | Faut-il taxer plutôt que réglementer les licenciements?[END_REF]. Such goal may be achieved by adopting fiscal instruments that can empower firms to use more rationally the firing policy. [START_REF] Blanchard | Protection de l'emploi et procédures de licenciement[END_REF] propose the taxation of layoff and the severance pay as instruments that can reduce the social cost of firings. The use of a tax on layoff should improve the layoff decision making process of firms. As noticed by [START_REF] Gautié | Faut-il taxer plutôt que réglementer les licenciements?[END_REF], such tax may also increase the financial burden of insolvent firms that are trying to recover their financial health. Nevertheless, a layoff tax paid by bankrupt firms can hinder the settlement procedure of debt if such tax is higher than the bankruptcy costs of the legal procedure.

In addition to the protection provided by the labor code, employees also benefit from certain rights granted in case the firm files for bankruptcy. The protection granted by the bankruptcy law to employees is mainly represented by a high position in the absolute priority rule that defines the payment order of the creditors' claim. For instance, employees are paid first before the secured claimants, the state and the other unsecured creditors in France. [START_REF] Seror | Analyzing the Inadequacies of Employee Protections in Bankruptcy Southern California Interdisciplinary[END_REF] sustains that employees should be protected in such scenario for two main reasons. First, employees have only one income source that is the bankrupt debtor. Unlike the debtor's suppliers that may bear the loss of a certain unpaid claim, employees have limited diversified income sources. Second, debtor will need employees if the firm is allowed to operate as a going concern under a reorganization procedure. The fully replacement of employees during such procedure may be costly. Hence, a bankrupt debtor may have an interest to keep his employees.

In this article, we will focus on a new legal determinant of the bankruptcy use that is related to the national labor law. This legal determinant deals with the legal difficulty of firing. If the labor code imposes numerous obligations on the employer prior a layoff decision, it may be possible that his strategy of saving the firm through firings will not be so successful. Hence, countries that slow down the layoff process through the legal system should have a higher degree of bankruptcy use.

Nevertheless, [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF] also analyzed how the protection degree of employees granted by the labor law determines the bankruptcy use. National laws that provide a higher degree of job security and better conditions of employment are associated with a lower number of bankruptcies. Such restrictive labor laws deter the entry of new firms therefore diminishing the bankruptcy use. Compared to their study, our analysis is focused solely on the difficulty of an employer to fire his employees and not on the job security or employment conditions. From our perspective, less severe regulations applied on the layoff process can be used as an ex ante mechanism to sustain the debtor's survival on the market.

Data and variables

Our sample contains data about the use of bankruptcy in 33 countries from 2007 to 2015.

We measure the annual use of bankruptcy through the number of bankruptcy filings (Bankruptcy).

The data was gathered directly from bankruptcy institutions and national institutes of statistics.

Appendix B details the data sources per country. In order to assess the difficulty of firing, we use 4 legal provisions provided by the World Bank. Hence, Q2 is a dummy variable equal to 1 if the employer must notify a third party such as a public institution to terminate the employment contract of one redundant worker and 0 otherwise. Q4 equals 1 if the employer of the firm must notify or consult a third party prior a collective dismissal and 0 otherwise. Q6 identifies countries where the employer requires the approval from a third party to initiate a collective dismissal. Q8 identifies labor laws that apply priority rules in case of reemployment. Furthermore, we constructed an aggregate index that captures the amount of firing restrictions. FRI is the sum between Q2, Q4, Q6 and Q8.

We use these legal provisions for three main reasons. First, the aspects allow to measure the amount of restrictions that an employer face prior a dismissal decision. The presence of such restrictions in the national labor law delays the employer's firing strategy of saving his distressed firm. Second, the 4 variables are time-variant variables. 8 out of the 33 countries of our sample modified their legal restrictions of layoff. Compared to [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF], this time-variance of our variables will allow to integrate fixed effects in our econometric estimations.

Third, the data is driven from the Doing Business Project of the World Bank which is based on certain assumptions about the worker and the employer. Thus, the worker is assumed to be a 42-year-old nonexecutive male employee that has been working for the firm for 20 years belonging to the national majority religion and race. The employer is a limited liability domestic firm from the manufacturing sector. However, the four legal provisions that we use are independent of the assumptions made for the worker and employer. 2 The following table presents the descriptive statistics of our variables. A higher degree of bankruptcy use is encountered mainly in France, Germany, U.K. and U.S., all having an annual average value of Bankruptcy superior to 20 000 opened bankruptcy procedures. Not surprisingly, France records the highest average number of bankruptcies in our sample. 59 613 bankruptcy procedures are on average opened every year in France, a country whose legal system is recognized for its debtor-friendliness orientation. Conversely, United Kingdom with its creditor-friendly bankruptcy environment has on average nearly 3 times fewer bankruptcies than France. Moreover, Eastern European countries have on average a low number of bankruptcies, e.g. Bulgaria, Estonia, Latvia, Lithuania, Slovakia or Poland. Such countries have very young bankruptcy systems compared to the Western European countries. As suggested by [START_REF] Blazy | How do bankruptcy systems perform in Eastern Europe?[END_REF], Eastern European bankruptcy users may have a poor knowledge about the bankruptcy procedures which may lead to fewer bankruptcies. On the same note, bankruptcy procedures are also rarely used in South America, e.g. Chile, Brazil, and in Southern Asia, e.g. Korea, Singapore.

{Table 1}

Table 1 shows the average values of the firing restriction variables. In 13 countries of our sample, the employer is obliged by the law to notify a third party prior the layoff of one employee (Q2). In half of the sample, the labor law obliges the employer to consult a public institution if he intends to engage in a collective dismissal (Q4). However, the employer cannot dismiss more employees without the approval of the law in 18 countries (Q6). Priority rules in case of reemployment of former employees must be applied in about 32% of the labor laws (Q8). The most restrictive firing environments are in Finland and Portugal for which FRI is equal to 4. However, 10 countries have no legal restrictions on the layoff process, i.e. FRI equals 0. Hence, it is much harder to layoff an individual in Portugal than in U.K. and United States (U.S.). These preliminary statistics confirm that the firing regulations are not homogenous. In the following section, we will estimate the influence of such regulations on the bankruptcy use.

2 According to the answers provided by the World Bank.

Estimations

We will assess the propensity to file for bankruptcy using Bankruptcy. One main econometric issue in estimating the determinants of the bankruptcy use is that the bankruptcy procedure can be the result of a converted bankruptcy procedure. For instance, failing to comply with the payment schedule of the reorganization plan can determine the judge to convert the reorganization procedure into a liquidation procedure. In certain countries as France and Belgium, the bankruptcy law allows companies that initially filed for liquidation to be rescued through a reorganization procedure if such procedure is viable from an economic point of view. In addition, a firm that filed for bankruptcy for reasons of payment default can provoke their main suppliers or partners to go bankrupt if their survival is entirely dependent on the payments made by the first firm. In the light of these arguments, we will introduce the 1-year lagged value of Bankruptcy in the following econometric model:

Bankruptcy i,t = α i + β t + Firing i,t-1 + Bankruptcy i,t-1 + Z i,t-1 + μ i,t (1)
where i is the index of countries ranging from 1 to 33, t is the year index ranging from 2007 to 2015, α i is the unobserved country effect, β t is the unobserved time effect, Firing i,t-1 is a variable lagged by one year with Firing ϵ { FRI, Q2, Q4, Q6, Q8 }, Z i,t-1 is a set of control variables lagged by 1 year and μ i,t is the error term. We measure the difficulty of firing using the lagged values of the time-variant aggregate index FRI and the legal aspects counted by Q2, Q4, Q6 and Q8. Such lagged values are justified by the fact that a layoff decision aimed to prevent bankruptcy filing requires a certain time period in order to produce its effects. If the layoff is used as an ex ante mechanism of bankruptcy prevention, the firing decision will not be generally taken one day before submitting a bankruptcy petition.

In addition, we use a similar set of control variables as [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF]. Our estimations control for the judicial efficiency of public institutions (Rule of Law), for the amount of rights granted to claimants by the collateral and bankruptcy laws (LRI), for the economic development of the country (Logarithm of the gross domestic product per capita (GDP per capita)), for the national economy's recession (Growth Rate of the national GDP) and the financial cost of debt (long term interest rate measured as a 10-year benchmark government bond yields (LTIR)). We use GDP per capita as a control variable given that large national economies should be associated with more bankruptcies compared to middle and low-income countries. Moreover, we expect that high cost of debt financing (LTIR) encourages firms to open a bankruptcy procedure whereas countries with growing economies (Growth Rate) should have less bankruptcies. [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF] argued that bankruptcy systems with high judicial efficiency that grant more rights to creditors are associated with less use of bankruptcy. Hence, we include the interaction term between Rule of Law and LRI (Rule of Law t-1 * LRI t-1 ). Appendix A provides a detailed description of our variables.

{Table 2}

Table 2 presents the results of our estimations. In the first column, the 1-year lagged variable FRI has no significant impact on Bankruptcy. In the second column of table 2, we introduced all the firing restrictions but none of them has a significant coefficient with the exception of Q2. In addition, lagged Q2 has also a positive and significant coefficient in the third column of table 2. If the employer has to notify a third party to terminate the employment contract of one employee, such third party can delay the layoff decision by requesting additional documents that should prove that the layoff background complies with all the national labor law regulations.

Moreover, the notification can be followed by a monitoring activity from regional or national department of labor rights that can be entitled by the law to check all the current employment contracts. According to [START_REF] Hogan | Enforcement of implicit employment contracts through unionization[END_REF], labor unions monitor how the contract clauses are respected by the employer and they provide valuable information to the workers about their legal rights settled by the contract. Such ex post pressure on the employer's activity may affect his financial strategy of saving the firm.

The signs of the estimated coefficients of our control variables follow a logic path although some of them are not statistically significant such as the coefficients of GDP per capita and LTIR.

Contrary to the study of [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF], national systems with efficient public institutions that grant creditors an important amount of legal rights have no significant influence on the use of bankruptcy. In the table 2, the interaction term between Rule of Law and LRI has a non significant coefficient. One possible explanation for this result is the use of country fixed-effects that were not employed by [START_REF] Claessens | Bankruptcy around the world: Explanations of its relative use[END_REF] due to the fact that their legal variables were time-invariant variables. Furthermore, the bankruptcy use increases in countries that underwent an increase of the number of bankruptcies in the previous year (Bankruptcy t-1 ).

Nevertheless, economy's growth helps companies survive longer (Growth Rate t-1 ).

We test the robustness of our results using the 2-years lagged values of our firing restriction variables on the amount of bankruptcies. We apply the same econometric approach and we use the same control variables. Table 3 presents the results of our estimations. We can notice that the layoff restrictions have a stronger power when they are lagged by 2-years. In column (1), the amount of firing regulations existing in the labor law 2 years prior the bankruptcy filing (FRI t-2 ) has a positive and significant impact on Bankruptcy. The total amount of firing restrictions 2-years prior the bankruptcy filing process seems to favor more bankruptcies. If such process is subject to multiple legal provisions, the employer's strategy of saving the firm through layoff may not be so successful. Hence, firm's bankruptcy will be a very probable outcome. In column (2), Q2 t-2 , Q4 t-2 and Q8 t-2 have a significant influence on Bankruptcy. However, only the coefficients of Q2 t-2 and Q8 t-2 kept their significance in regressions of columns ( 3) and ( 6) where they are separately treated.

The presence of a legal obligation to notify a third party in case of firing one employee (Q2 t-2 ) in the previous 2 years encourages significantly the use of bankruptcy in the economy. Surprisingly, the existence of a legal provision that imposed the application of priority rules for reemployments 2 years before (Q8 t-2 ) is a significant growth source of bankruptcy. The application of priority rules supposes that individuals that had worked for a given employer have a reemployment priority over the other candidates if the working position is again available. If the employer is obliged by the law to rehire an individual that was previously fired due to his low degree of efficiency and/or competence, such reemployment may lead to the employer's bankruptcy ceteris paribus. By restraining the hiring decision, the law may diminish the success likelihood of the employer's economic strategy in the long-term.

{Table 3}

Our econometric approach shows that the ex ante difficulty of firing can increase the degree of bankruptcy. However, this approach has two major caveats. First, the labor regulations that we considered are not exhaustive. Other firing restrictions are provided by the World Bank such as the approval from a third party for the layoff of one worker, the application of priority rules to redundancy dismissals or the obligation of retraining a worker prior his dismissal. Nevertheless, such regulations are time-invariant aspects which hamper the use of a fixed-effect regression.

Second, the estimations do not control for the regional tendency of using the bankruptcy procedure.

Although Bankruptcy measures the national number of bankruptcies, the distribution of bankruptcies is not homogeneous among the regions and/or counties of the country. A most suitable approach would be to identify such distribution and to integrate the regions instead of the countries in the estimations.

Conclusion

National labor law may impose some restrictions that delay or hamper the firing decision of the employer. As opposed to flexible laws, such rigid labor laws can be in contradiction to firms' objectives to use layoffs as an ex ante mechanism to avoid bankruptcy. Labor regulations that delay the layoff decision may incite owners and/or managers to find other rescue strategies. If no other solution cannot hamper the payment default of debts, firms may be forced to file for bankruptcy.

After controlling for the economic and legal environment, time effects and country fixed-effects, our study shows that the amount of firing restrictions 2-years prior the bankruptcy triggering leads to more bankruptcies. Rigid laws with a slow down layoff process are associated with a high level of bankruptcy use. Although employees' interests benefit from such laws, it seems that the failure risk of firms tends to be higher when rescue layoff strategies cannot be so easily implemented by the firms.

Moreover, two firing regulations play a significant role as determinants of bankruptcy use.

Firstly, the employer's legal obligation to notify a third party prior the dismissal of one employee increases the use of bankruptcy. It is very likely that a third party such as a public institution or a labor union act as a legal guardian for the dismissed employee. The employer may endure an intense ex post monitoring of the employment contracts and/or a strong legal opposition to the layoff decision from such third party. Secondly, labor codes that apply priority rules in case of reemployment can determine the firm's bankruptcy by harming ex post its financial health. It is very likely that the priority rules applied in case of reemployment of unskilled individuals can worsen the financial health of the firm which eventually can force the firm to file for bankruptcy.

Hence, a legal alternative that could help diminish the growth of bankruptcies without modifying the content of the bankruptcy law could consist in acting on the content of the labor law. However, certain policymakers would want to protect employment at the expense of some bankruptcies in the economy. The trade-off between diminishing the bankruptcy risk and protecting the employees can be the subject of further research.

Table 1 .

 1 Descriptive statistics Average values are provided for each country of the first column. A detailed description of the variables is provided by Appendix A.

	Country	Bankruptcy	Q2	Q4	Q6	Q8	FRI
	Australia	14235.63	0	0	0.63	0	0.44
	Austria	6098.50	1	1	0	1	3
	Belgium	9929.63	0	0	0	0	0
	Brazil	2044.50	0	0	0	0	0
	Bulgaria	552.75	0	0	0	0	0
	Canada	4391.38	0	0	0	0	0
	Chile	145.63	1	1	0	0	2
	Czech Republic	5365.00	0	0	0	0	0
	Denmark	4774.63	0	0	0	0	0
	Estonia	490.25	0.38	0.38	1	0.56	2.67
	Finland	2878.75	0.88	0.88	1	1	4
	France	59613.00	0	1	1	1	3
	Germany	28951.50	1	1	1	0	3
	Hungary	15959.88	0	0	0	0	0
	Ireland	1188.88	0.75	1	0	0	1.89
	Italy	11076.75	0.38	1	1	1	3.22
	Japan	12997.75	0	0	1	0	1
	Korea	1628.25	1	1	0	1	3
	Latvia	1346.88	0.63	0.63	1	0	2.56
	Lithuania	771.38	0	0	1	0	1
	Netherlands	7052.88	1	1	1	0	3
	New Zealand	1871.50	0	0	1	0	1
	Norway	4183.25	0	0	1	1	2
	Poland	688.75	0	0	0.88	1	2
	Portugal	6787.50	1	1	1	1	4
	Singapore	185.00	0	0	0	0	0
	Slovakia	1197.13	1	1	1	0	3
	Slovenia	766.63	0	0	0.88	0.89	1.89
	South Africa	3958.63	1	1	1	0	3
	Spain	5475.50	1	1	0	0	2
	Sweden	7035.13	0	1	1	1	3
	U.K.	20718.25	0	0	0	0	0
	U.S.	42132.88	0	0	0	0	0
	Average	9090.54	0.38	0.46	0.53	0.32	1.69
	Notes:

Table 2 . Regressions of the number of bankruptcies and the firing regulations lagged by 1-year

 2 Fixed effects and time effects are included in each regression. The dependent variable is the logarithm of Bankruptcy. A detailed description of the other variables is provided in Table1. p-values are reported in brackets. * indicates a significant coefficient at 10%. ** at 5% and *** at 1%.

	Independent Variables	(1)	(2)	(3)	(4)	(5)	(6)
	FRI t-1	0.034
		(0.137)
	Q2 t-1		0.215**	0.117*
			(0.013)	(0.064)
	Q4 t-1		-0.165		0.046
			(0.243)		(0.527)
	Q6 t-1		0.044			0.048
			(0.510)			(0.473)
	Q8 t-1		-0.009				0.026
			(0.952)				(0.829)
	Bankruptcies t-1	0.664***	0.663***	0.665***	0.665***	0.664***	0.665***
		(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	Rule of Law t-1	0.678**	0.705**	0.650**	0.647**	0.692**	0.654**
		(0.018)	(0.034)	(0.025)	(0.024)	(0.030)	(0.022)
	LRI t-1	0.128**	0.129**	0.123**	0.123**	0.128**	0.124**
		(0.032)	(0.046)	(0.041)	(0.037)	(0.041)	(0.033)
	Rule of Law t-1 * LRI t-1	-0.067	-0.069	-0.062	-0.064	-0.070	-0.065
		(0.108)	(0.146)	(0.141)	(0.130)	(0.128)	(0.117)
	Logarithm (GDP per capita) t-1 -0.063	-0.071	-0.035	-0.039	-0.076	-0.044
		(0.892)	(0.881)	(0.938)	(0.931)	(0.877)	(0.924)
	Growth Rate t-1	-0.012**	-0.013***	-0.013***	-0.012**	-0.012***	-0.012***
		(0.011)	(0.009)	(0.008)	(0.011)	(0.009)	(0.016)
	LTIR t-1	-0.005	-0.006	-0.007	-0.004	-0.003	-0.003
		(0.718)	(0.673)	(0.632)	(0.776)	(0.847)	(0.819)
	Intercept	1.732	1.795	1.644	1.693	1.826	1.718
		(0.422)	(0.407)	(0.434)	(0.430)	(0.416)	(0.428)
	Observations	297	297	297	297	297	297
	Time effects	Yes	Yes	Yes	Yes	Yes	Yes
	Fixed effects	Yes	Yes	Yes	Yes	Yes	Yes
	R²	0.622	0.625	0.624	0.621	0.621	0.621
	Notes:

Table 3 . Regressions of the number of bankruptcies and the firing regulations lagged by 2-years

 3 Fixed effects and time effects are included in each regression. The dependent variable is the logarithm of Bankruptcy. A detailed description of the other variables is provided in Table1. p-values are reported in brackets. * indicates a significant coefficient at 10%. ** at 5% and *** at 1%.

	Independent Variables	(1)	(2)	(3)	(4)	(5)	(6)
	FRI t-2	0.031**
		(0.014)
	Q2 t-2		0.263***	0.104**
			(0.000)	(0.016)
	Q4 t-2		-0.264***		0.055
			(0.004)		(0.122)
	Q6 t-2		0.032			0.033
			(0.717)			(0.699)
	Q8 t-2		0.071*				0.075**
			(0.066)				(0.028)
	Bankruptcies t-1	0.571***	0.566***	0.570***	0.573***	0.572***	0.573***
		(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	Rule of Law t-1	0.466	0.515	0.441	0.428	0.465	0.440
		(0.162)	(0.206)	(0.183)	(0.198)	(0.239)	(0.183)
	LRI t-1	0.098	0.103	0.094	0.093	0.098	0.096
		(0.150)	(0.186)	(0.170)	(0.171)	(0.196)	(0.151)
	Rule of Law t-1 * LRI t-1	-0.039	-0.043	-0.034	-0.034	-0.040	-0.036
		(0.417)	(0.475)	(0.481)	(0.474)	(0.482)	(0.448)
	Logarithm (GDP per capita) t-1 0.015	-0.000	0.033	0.033	0.008	0.032
		(0.975)	(0.997)	(0.948)	(0.946)	(0.987)	(0.949)
	Growth Rate t-1	-0.015***	-0.015***	-0.015***	-0.015***	-0.015***	-0.015***
		(0.004)	(0.002)	(0.003)	(0.004)	(0.004)	(0.004)
	LTIR t-1	-0.008	-0.008	-0.009	-0.008	-0.007	-0.007
		(0.574)	(0.595)	(0.548)	(0.594)	(0.635)	(0.598)
	Intercept	2.369	2.438	2.327	2.346	2.442	2.329
		(0.290)	(0.302)	(0.298)	(0.295)	(0.294)	(0.301)
	Observations	264	264	264	264	264	264
	Time effects	Yes	Yes	Yes	Yes	Yes	Yes
	Fixed effects	Yes	Yes	Yes	Yes	Yes	Yes
	R²	0.507	0.510	0.508	0.507	0.506	0.507
	Notes:

Acknowledgements

We are grateful to Anna Reva, Nadine Levratto and the World Bank for their invaluable research assistance.

Appendix A Table 4. Definition of variables Variable Definition

Bankruptcy

Annual number of bankruptcy procedures opened in court.

Q2

Dummy variable equals 1 if the employer must notify a third party to terminate one redundant worker, 0 otherwise. Source: World Bank.

Q4

Dummy variable equals 1 if the employer must notify or consult a third party prior a collective dismissal, 0 otherwise. Source: World Bank.

Q6

Dummy variable equals 1 if the employer requires approval from a third party to initiate a collective dismissal, 0 otherwise. Source: World Bank.

Q8

Dummy variable equal 1 if priority rules must be applied for reemployment, 0 otherwise. Source: World Bank.

FRI

Firing restrictions index equal to the sum between Q2, Q4, Q6 and Q8.

Rule of Law

An annual index that aggregates indicators that deals with the quality of contract enforcement, property rights, the police and the courts and the likelihood of crime and violence. The index ranges from -2.5 to 2.5.

Source: World Bank. Worldwide Governance Indicators.

LRI

Legal rights index measures the degree to which collateral and bankruptcy laws protect the rights of borrowers and lenders and thus facilitate lending. The index ranges from 0 to 10. Source: World Bank. The Swedish Agency for Growth Policy Analysis U.K.

GDP per capita

The Insolvency Service U.S.

American Bankruptcy Institute


Keywords: JEL classification: C68, D72, D78, F13, H32, P16 Lobbying, Public Policies, Computable General Equilibrium Model Classification JEL: C68, D72, D78, F13, H32, P16 Lobbying, Politiques Publiques, Modèle d'Equilibre General Calculable

This paper aims at making explicit the micro foundations of the government's preference function in an influence-driven political economy model. It also addresses the behavior functions of domestic and foreign firms in their attempts to gain policy favors. These favors are granted by means of subsidies. In our model, the government simultaneously chooses three interdependent policy instruments under the political influence of domestic and foreign firms. Thus, we create a political market characterized by utility-maximizing and profit-maximizing behaviors of its actors, which takes place in a computable general equilibrium model. Endowed with these features, this model fills a gap in the literature. However, our results demonstrate that the model is only valid under a reasonable set of constraints on its parameters. Finally, this paper formally shows the key role of the subsidy elasticity of political cost in limiting the distortions created by the influence of interest groups.

1-Introduction

Since the seminal work of [START_REF] Bentley | The process of government; a study of social pressures[END_REF], numerous contributions have emphasized the role of interest groups in the political process and/or the calculus of consent made by politicians attempting to be elected. Amongst them, Downs 'contribution (1957) is a striking example of the way to include economic reasoning in the political sphere. Downs was a pioneer in using a rational choice approach in the political-economic field. In this early analysis, the interest group only consists of the voters. His model assumes selfish and maximizing behavior from the politicians who are aiming to be elected, and maximizing behavior from the voters who vote for the political program that will bring them higher utility. This, however, ignores the fact that politicians can have strong beliefs and ideologies whilst being benevolent towards the population. More recent studies, of which the most famous is [START_REF] Grossman | Protection for Sale[END_REF] research, include these features. Empirical analysis has emerged to empirically validate this concept. The literature survey (Section 2) will give more details on this point and will discuss the alternative models available (election-oriented and influence-oriented) to represent the influence of interest groups on the policy making process.

When considering international trade, some facts are hard to explain with traditional economic models. Indeed, there is a widespread consensus amongst economist about the free trade superiority over protectionism on world economic efficiency. However, very few countries in the world apply full liberalization of their foreign trade in practice. A likely explanation could be that trade opening come with income redistribution within stakeholders. Interest groups can then claim for a particular modality of opening that either improves their economic advantage or that reduce their costs if the trade opening gives rise to harmful consequences. The result is that the equilibrium in trade opening is not Pareto-optimal and, hence, differs from free trade. Existing models of political economy manage to include some elements of this nature to explain economic decisions but they suffer from different shortages (Section 2). The economic environment is often complex and fast changing, so partial equilibrium models can lead to mistaken predictions. In order to take these factors concerning complexity into account and to consider the behavior of economic agents within a changing environment, Computable General Equilibrium Models (CGEM) are useful. They allow several public policies, commitments to agreements, and the behavior of economic agents to be combined; the cross effects can also be taken into consideration. For instance, in the case of a negotiated trade opening, a government could intend to pursue policies of import substitution. This implies at least two initial shifts in the economic environment. Firstly, it implies a decrease in tariffs, which are often constrained in their targets and in the intensity of the framework of the talks. Secondly, there often exists a policy of sectorial support needed to meet the requirements of the economic policy pursued. In a standard economic model, these two features are determined exogenously. For the decrease in tariffs, the terms of the agreement might be so precise that it is easy for the modeler to input the data into the model. For the policy of import substitution, the modeler will likely run a set of simulations to predict the different effects of different measures. In contrast, in a political economy model, the modeler tries to determine these features endogenously. In this view, it is assumed that economic agents have economic interests at stake about the structure of the trade opening and the economic policy. For the decrease in tariffs, if the terms of the agreement are too precise, the modeler has no choice but to set it exogenously. As far as domestic economic policy is concerned, it is more delicate for the partner of the agreement or for the WTO to impose a particular policy response to accompany the trade opening. An endogenous formalization for that policy seems more practicable. Therefore, shifts in the economy will impact upon the reactions of economic agents and upon the government that will shape the policy response.

By acknowledging that the situation above matches reality, we can address a gap in the literature by developing a political economy model in general equilibrium, which is influence-oriented and based on interdependent subsidies allocated by the government (Section 3). Indeed, the purpose of this paper is to introduce political consideration in a CGEM that could both guide and explain trade policies . The underlying research question is: what key parameters have to be considered to limit the distortions created by the political economy forces? We find that a key role is played by the subsidy elasticity of political cost in limiting the distortions created by the influence of interest groups. This result, in line with common sense, is formally demonstrated at the end of Section 3.

As far as the methodological approach is concerned, we mainly keep standard equations for the macroeconomic part of the CGEM. The notable exception is the labor market equilibrium condition that includes labor for lobbying that would be otherwise dedicated to production. For the microeconomic part of the model, the behavior of government and two kinds of interest groups (domestic producers and foreign producers) are formalized using maximization programs. In this model, the government taxes domestic consumption and uses the tax revenue to provide production, export and import subsidies to firms. Hence, the government balances the interests of the firms, who share part of the rents generated by the subsidies with policymakers, and the consumers who pay for those subsidies through higher prices. Interest groups can become applicants for indirect protection, commercial advantage, or accessibility to domestic markets.

While the granting of an economic advantage by means of tariffs is internationally visible by the WTO or by trade partners, subsidies are more discrete and are deemed to be a more efficient tool to resolve national economic issues. This policy tool is more direct for national purposes and more indirect in terms of foreign trade when compared to using tariffs. Even though decreases in subsidies are also negotiated in WTO rounds, the WTO recognizes that it can be sensitive, in terms of fairer trade, to ask its members to stop subsidies because the latter are required to address a number of concerns. The limitation of the constraints in that field is a question of the viability of the system of world trade governance; international organizations are sometimes accused of interference in, and disrespect of, national sovereignties1 . Indeed, subsidies can be used to pursue social objectives, to promote national security including food security, to build infrastructures, to foster research, to alleviate regional imbalances, to tackle rural depopulation, and to maintain cultural diversity. This does not constitute an exhaustive list of undeniable needs to address market failures. Meanwhile, these possibilities give space for lobbyists to vie for the advantages conferred on the sectors picked to implement chosen public policies.

All of these implementations do not necessarily involve subsidies. This is why our formalization bellow considers the other forms of government interventions through the notion of subsidyequivalent. This notion takes its inspiration from the "producer subsidy equivalent" [START_REF] Josling | Agricultural Protection: Domestic Policy and International Trade : Conference, Food and Agriculture Organization of the United Nations[END_REF] notoriously used by OECD (Organization for Economic Co-operation and Development), which has created its own indicator of this kind for the agricultural sector. The OECD defines this as an indicator used to quantify the domestic support for agricultural producers; it arises from policy measures, regardless of their nature, objectives or impacts. Our notion of subsidy-equivalent is the same for all the sectors and for all types of subsidies. The section that develops the model (Section 3) ends with an examination of the conditions in which to use the model.

In the discussion (Section 4), we draw parallels with the models built in the literature, discussing the value of the parameters and their underlying principles. We also give several insights for alternative features within the model.

Finally, we conclude (Section 5) by drawing some shortcomings and by proposing some possible applied uses of the model that we have presented.

2-Literature

Political economy stress that economic policies are formulated in response to the demands of interest groups. The supply side, namely (i) policy makers and (ii) the institutional settings in which policies take place [START_REF] Rodrik | Political economy of trade policy[END_REF], propose policy outcomes in order to obtain favors from the interest groups organized in lobbies. The objects of the economic analyses are several periods within the political cycle. Two approaches and corresponding modeling dominate the literature. The first approach assumes that the time of the election has passed and the lobbies are trying to exercise their influence on the incumbents in charge of policy making or policy voting (Findlay and Welitz, 1982;[START_REF] Grossman | Protection for Sale[END_REF][START_REF] Stoyanov | Trade policy of a free trade agreement in the presence of foreign lobbying[END_REF]. This is known as the influence-driven approach. The second approach assumes that the time of the election is coming and the lobbies are making contributions to increase the likelihood of the election of the candidate that better represents their interests [START_REF] Hillman | Domestic Politics, Foreign Interests, and International Trade Policy[END_REF][START_REF] Magee | Black Hole Tariffs and Endogenous Policy Theory: Political Economy in General Equilibrium[END_REF][START_REF] Das | Foreign lobbying and the political economy of protection[END_REF]. We call this the election-driven approach. Both approaches create competitive situations among the pressure groups. In this brief survey of literature, we will assert why we adopt the first approach in our paper. It could be argued that the political regime is a crucial parameter to be taken into consideration in the analyses. In this paper, we will focus solely on the case of representative democracies2 . Findlay and Welitz (1982) initiate the approach where a tariff level is endogenously determined by a function that reflects the competition between two lobbies for influence on trade policy. In this general equilibrium model, one lobby advocates free trade whereas the other argues for protection. Each lobby engages its resources in the lobbying process in terms of the labor factor in order to obtain favorable tariffs. The other production factors are sector specific. A Cournot-Nash equilibrium determines the equilibrium tariffs. In this model, the political decision process is a black box, since we just know that the policy maker changes the tariffs when he or she receives inputs. Our model will address this shortcoming by focusing on the government incentive to shift tariffs as we will propose a microfoundation for this.

In their famous model known as the GH model, [START_REF] Grossman | Protection for Sale[END_REF] already address this shortcoming by adding a preference function for the government. This has two weighted components, namely (i) the contributions received from the lobbies and (ii) the aggregate welfare of the population. An interesting point is that the aggregate welfare equally contains the welfare of the individual members of lobbies as consumers so that protection can simultaneously increase the interests of the lobbies as a whole and decrease the utility of some of its individual members. The theoretical framework remains sector specific; the mobile labor factor constitutes the complementary input for specific factors in each sector within the production function. The model is developed with the lobbies struggling to maximize the aggregated utility of their members. The government then chooses the vector of policies that maximizes its preference function. Our paper equally proposes a preference function for the government but its components are very different. In the GH model, there is one instrument, namely, the contributions used by a homogeneous kind of lobbies to influence the government in choosing the level of a single public policy, the level of tariffs. In our model, the domestic firms shift some labor resources from the production process to influence the government, foreign firms lobbying is introduced, three interdependent policy instruments are available for the government, and all the sectors are organized to lobby. In addition, the consumervoter component of the preference function for the government introduces a new interesting concept. It takes into account the shortsighted view of the consumer-voter on the cause of the shift of their wellbeing and the government takes this feature into consideration rather than directly using the welfare level of the consumer-voter given by a perfect information hypothesis.

In these previous models, one factor is mobile and the others are sector specific. In this case, the tariffs on the goods in a sector increase the relative revenue drawn from the sector specific factors due to the increase in scarcity relative to the mobile factor. On the contrary, the mobile factor moves toward the protected sector; the revenues from the other sector specific factors fall, due to a rise in the relative abundance of these specific factors. This forms a stimulating point for competition between lobbies; inertia, instead of being neutral, is in fact harmful.

In an earlier work, [START_REF] Becker | A Theory of Competition Among Pressure Groups for Political Influence[END_REF] had already accounted for the losses incurred by the community as a whole as a result of political decision making, specifically subsidies. This political decision is made in favor of a particular interest group. Indeed, Becker considers two kinds of lobbies. One pays taxes to finance the subsidies perceived by the other. This feature seems very useful in the context of general equilibrium modeling. It leads us to adopt it in our model. In addition, Becker shows that it is easier for small interest groups to obtain political favor because, the larger the interest group, the more free-riding [START_REF] Olson | The Logic of Collective Action[END_REF] problems occur. Furthermore, subsidies for small groups have a very slight impact on the taxation of the larger community.

The GH model was extended notably by [START_REF] Stoyanov | Trade policy of a free trade agreement in the presence of foreign lobbying[END_REF] to include lobbying by foreign interest groups. In his article, which is both theoretical and empirical (including data for Canada), Stoyanov additionally stresses whether or not foreign lobbyists should be distinguished by the criteria of the Free Trade Agreement partners. The former foreign lobbyists fight for more protection in their sector in the domestic country since they benefit from the trade agreement. The latter foreign lobbyists from the rest of the world lobby for a decrease in protection, thus complying, in this particular case, with the mainstream of the literature including foreign lobbying. This view was previously argued by [START_REF] Gawande | Foreign Lobbies and U.S. Trade Policy[END_REF] for the United States. They have equally used an extended Grossman and Helpman model to test this view econometrically. [START_REF] Hillman | Domestic Politics, Foreign Interests, and International Trade Policy[END_REF] research constitutes a seminal work in including foreign lobbies in the models of trade policy determination. In this model, the domestic industries are import-competing. Two candidates, one of whom is rather protectionist and the other is rather liberal, compete for political power. The lobbies try to favor the candidate who better represents their interests by means of contributions aimed at winning over voters. The underlying assumption is a positive link between the money that a candidate can spend on his or her political campaign and the number of votes he or she will gain. This forms the second major type of political economy model in the literature.

In a related work, [START_REF] Magee | Black Hole Tariffs and Endogenous Policy Theory: Political Economy in General Equilibrium[END_REF] implement a general equilibrium model in the Heckscher-Ohlin-Samuelson framework with two sectors, two factors, two parties, and two lobbies. They develop a model with numerous relationships in the economy, including the maximization behavior of voters, lobbies, and political parties. The two lobbies represent labor and capital; they are respectively for and against protection. The higher their political contributions, the more likely the election of their favored political party, but the cost of lobbying becomes higher. The equilibrium tariffs are the outcomes of the Nash game between the two competing lobbies. In our paper, the development of our general equilibrium model is deeply different from the structure of Magee, Brock and Young. Actually, we chose another conception of the influence which is presented at the beginning of this section. We are going to justify this choice thereafter.

A separate, more empirical, strand of the literature assesses the validity of political-economy models or the existence of an influence of lobbyists on political outcomes. [START_REF] Gawande | Is Protection for Sale? Evidence on the Grossman-Helpman Theory of Endogenous Protection[END_REF] tested the GH model econometrically using cross sectional non-trade barrier data for the US in 1983. They established that the GH model is reliable for both its predictions on the protection and the lobbying side. For the same period in the US, [START_REF] Goldberg | Protection for Sale: An Empirical Investigation[END_REF] showed that the GH model is overall consistent with their data. Besides this, they underlined the very strong weight attached by the government to social welfare in comparison with the weight attached to the contributions from the lobbies. Econometrically, they found the former to be about 49 times higher than the latter. [START_REF] Eicher | Protection for Sale: An Empirical Investigation: Comment[END_REF], using a very close database, proved that the GH model and the Findlay and Wellisz model (1982) both perform well in an empirical sense. They also found that the GH model holds more explanatory power than the model of Findlay and Wellisz.

More broadly, [START_REF] Baldwin | Is Trade Policy for Sale? Congressional Voting on Recent Trade Bills[END_REF] studied the votes for three important trade policies in the US Congress in 1993 and 1994. They estimated an econometric model wherein the votes are explained by the characteristics of consistency, the labor contributions, and the business contributions. The two latter groups form the lobbies in competition. Thus, they showed that contributions matter in the outcomes of the votes in the US Congress. In addition, [START_REF] Grossman | Protection for Sale[END_REF] highlight the fact that three quarters of the PACs (Political Action Committees) contributions were given to incumbents in Congress in 1988 and 62% were given in the first 18 months of the election cycle. They drew the figures on PACs contribution from [START_REF] Magleby | The Money Chase: Congressional Campaign Finance Reform[END_REF]. Hence, on the one hand, the empirical literature shows that contributions are effective and, on the other hand, it shows that these contributions are made to influence the incumbent of political power rather than to influence the outcome of an election. The model proposed in this paper will take these observations into account and will adopt the political-economy influence functional form.

3-Model

This paper considers a two-country world with a domestic and a foreign economy. Most standard equations of the model are inspired by [START_REF] Decaluwé | La politique économique du développement et les modèles d'équilibre général calculable: une introduction à l'application de l'analyse mésoéconomique aux pays en développement [Development economic policy and the computable general equilibrium models: an introduction to applied mesoeconomic analysis to developing countries[END_REF]; the model is then rearranged to include political-economy features (see the appendix for the full model). The m sectors of the domestic economy (i = 1 to m) produce m single goods (XS i ) with labor (LDprod i ) and a sector-specific capital factor (K i ) under a production system with Cobb-Douglas and Leontief functions such as:

/ (1)
where VA i is the Value Added in the sector i and v i is the Leontief's technical coefficient.

A i . .

(

) 2
where A i is the scale parameter for sector i and is the parameter of the contribution of the labor factor in the Value Added. Capital and labor are assumed to be immobile across national borders but labor is mobile across domestic sectors.

In this model, we include a political market based on the behavior of maximization by its actors.

We consider lobbies organized by sectors that try to obtain government favors in the form of subsidies. We assumed two elements of strategy from two kinds of different players. Firstly, if a government is closely monitored by other members of the World Trade Organization, it will find a discrete way to ensure that influential sectors obtain the equivalent of the amount provided with a subsidy. For instance, it will provide this as public goods, facilities or infrastructures that mainly serve the desired sector. Secondly, we assume that firms think in terms of relative competitive advantage and estimate to be more efficient in influencing policymakers on their behalf rather than trying to influence policymakers to lower the advantage granted to their competitors. The rationale for this assumption is an information asymmetry that affects the efficiency of the lobbying. The interest group has better information on the relation that it maintains with policymakers rather than the relationship between its competitors and the policymaker. In addition, the advantage obtained on its behalf is, de facto, multilateral and not competitor-specific.

Let F be the degree of (real or purported) political favor granted to the lobby of the sector i and let y be the set that characterizes the nature of the subsidy that one is analyzing; production, import and export subsidies, respectively, y = , , :

(

where S y is the rate of subsidy granted to the sector i. Thus ε Fy is the y-type subsidy elasticity of political favor granted to sector i. If F y (S y ) is a convex and growing function then ε Fy > 1.

For each unit of political effort granted, lobby in sector i provides the government with X 1 units of labor ( ) as a counterpart to obtain its production subsidies so that these units of labor are diverted from the production process such that:

. ( 4
)
In other words, is the total amount of labor used in the lobbying process for getting the production subsidy. At this preliminary step, by considering only the lobbying for one kind of subsidy, we then have:

(5) where is the total labor demand of the sector i and is the labor demand for the production process. We assume full employment where LS is the total labor supply in such a way that:

(6)

The government sources of satisfaction are then:

X 1i . = X 1i . ( 7
)
Subsidies are funded with an increase in the rate of Value Added Tax on the overall consumption of goods so that this creates a political cost, PC y , for the government to grant subsidies:

PC y (8)
where P y is the subsidy elasticity of political cost in sector i. If PC y (S y ) is a convex and growing function then P y > 1. This cost is weighted by the effect that the subsidy will have on the relative variation of the wellbeing of the consumers. The better the level of wellbeing in the situation before the introduction of the subsidy (wb 1 ) related to the level of wellbeing after the introduction of subsidy (wb 2 ), the higher the increase in the political cost. The final political cost to grant a production subsidy (FC pi ) equally depends on the government's own objectives measured by X 2 . In other words, X 2 is a measure of how much the government cares about the impact of the production subsidies on the wellbeing of the consumers.

FC pi

.

. X 2i

(9)

With a simple mathematical development we obtain:

1 (10)
In our paper, the level reached by the wellbeing function depends on the level of consumption within the population. A more elaborate wellbeing function could also be used.

∏ ∏ ∏ with ∑ ζ =1 ( 11
)
where C i1 and C i2 are respectively the quantities of goods from sector i purchased by consumers before and after the introduction of the subsidy and its VAT (Value Added Tax) counterpart.

Technically, we hold constant the revenue of the government (YG) which is the sum of the different taxes collected in the economy minus the amount of subsidies granted. The adjustment variable is the amount of VAT (TI i ) collected on the value of non-exported production and imports (M i ), that is to say the domestic consumption.

.

. . 1 . . ( 12
)
where tx i is the rate of the VAT on products, p i is the price to producer and pm i is the all-tax included price of the imported good. The implementation inspired by [START_REF] Viroleau | Evolution of Gender Inequalities in Wages in Senegal Following the Economic Partnership Agreements[END_REF] consists of using an endogenous variable τ, the homogeneous rate of increase in the VAT to modify the exogenous initial rate of the VAT (txx i ) up to the required level.

.

This formalization captures the general equilibrium effects of the subsidies on the economy since if subsidies have positive or negative spillovers on other components of the revenue of the government, these spillovers are taken into account in the calculus of the amount of VAT required to meet the status-quo level of the revenue for the government.

We then assume that voter-consumers know the amount of each subsidies granted by the government by means of the transparency in the democratic process. In addition, we assume that voter consumers attribute the shift in their wellbeing to the subsidies granted to interest groups in a non-proportional fashion. This view matches with the feeling of the population against a particular kind of subsidy and it determines the value of P y . So there is a dichotomy between (i) the real and intricate macroeconomic effects on consumer wellbeing due to a specific subsidy granted to interest groups and (ii) the voter-consumer feeling of these effects. The latter is important for the policy maker because the voters base their assessment of the government action on it. This mechanism describing the consumers view is an important point of the reasoning of the model because it introduces interdependence between coveted subsides. In fact, the more a competitor asks for subsidies in any type, the harder it becomes to obtain new subsidies because the consumer prices rise and impact the consumer-voter wellbeing.

The level of production subsidies (S pi ) granted by the government comes from its maximization program. With ( 7) and ( 9), government welfare function (WG) is defined as:

WG = ∑ . . . (14)
Using logarithms and rearranging the terms, the first order condition of optimization leads to:

S pi = . . . (15)
The mathematical conditions in which this formulation is consistent with reality are shown below.

Let us now make explicit export subsidies (S xi ) for sector i. All parameters are likely to change but the previous reasoning applies and leads to:

S xi = . . . (16)
Where lobby i has to provide the government with ( . X 3i ) units of labor ( ) and where X 4 is a measure of how much the government cares about the wellbeing of the consumers following the implementation of export subsidies (S xi ).

We then introduce foreign lobbies whose efforts are aimed at obtaining import subsidies (S mi ). As this study assumes that the latter do not employ domestic labor in their production processes, the price to pay for gaining political favor is not a labor diversion. It is rather a monetary contribution (CF) to the government. Following the same reasoning:

S mi = . . . (17)
Where lobby i has to provide the government with ( . X 5i ) units of monetary contribution (CF)

and where X 6 is a measure of how much the government cares about the wellbeing of the consumers following the implementation of import subsidies (S mi ).

The second order conditions are subject to the signs of the minor determinants of the Hessian matrix (HM1). Since crossed-derivatives are equal to zero, one can simplify the matrix:

HM1 0 0 0 0 0 0 (18)
If one wants the government optimization program to lead to a maximization of its welfare, the minor determinant of order 1 ( ) has to be negative, the minor determinant of order 2 ( . ) has to be positive and determinant HM1 has to be negative.

The first condition, 0 leads to:

> . . . (19)
With ( 14), we notice that ( . has to exceed ( . . ) otherwise it would mean that the government get a negative welfare contribution on a particular type of subvention granted. Therefore, in (19) the right hand side term is upper than 1. We draw from that the necessary condition > .

Let Δ pi be the difference (P ε that satisfies 0, then:

. > . . (20)
The left hand side term increases when Δ pi increases. For the right hand side term, two situations are conceivable depending on the value of S pi .

Firstly, if S pi is upper than 1, then the right hand side term decreases when Δ pi increases. In that configuration, given the positive sign of Δ pi , the hardest conditions to satisfy (20) are when Δ pi tends toward zero. In that case, we obtain:

1 > . ⟺ X . > X (21)
Therefore, this leads to a contradiction with the assumption made above. So, we demonstrate that a sufficient condition can be deduced for values of Δ pi beginning from 1:

ε > . . . . (22)
Hence, if S pi is upper than 1, a sufficient condition is ( 22) and that P ≥ ε 1.

Secondly, if S pi is lower than 1, then the right hand side term in (20) increases when Δ pi increases. In that configuration, given the positive sign of Δ pi , the hardest conditions to satisfy (21) are when Δ pi tends toward infinite. In that case, we obtain:

lim → ε Δ . ε Δ 1 . S 0 (23)
Therefore, this leads to a contradiction because as considering (20), it means that a ratio of positive economic terms should be lower than 0. So, we demonstrate that a sufficient condition can be deduced for value of Δ pi beginning from 1 and not too large. Thus, the higher Δ pi , the harder to satisfy the conditions in (20).

As and are analogous in their formulation, similar conditions are required to obtain a negative sign for in order for the minor determinant of order 2 ( .

) to be positive.

The third required condition to define the optimum of WG as a maximum is to obtain a negative sign for determinant HM1 . .

. By considering the two previous conditions as satisfied, this means to obtain a negative sign for . As already mentioned above, analogies in the formalization of the derivatives of degree 2 for the different kinds of subsidies allow us to use the previous results.

To sum up, if we consider the most polyvalent conditions (valid for both S y lower and greater than 1), a sufficient set of constraints required is called A such as:

A ε Δ . ε Δ ε ε . Δ . 1 2 and ε L ε 1 where L is a large number ε Δ . ε Δ ε ε . Δ . 1 2 and ε L ε 1 where L is a large number ε Δ . ε Δ ε ε . Δ . 1 2
and ε L ε 1 where L is a large number Under this set of constraints, the Hessian Matrix is negative definite. Thus, WG is a concave function and its optimization program is a maximization program. We note that the set of constraints for a local maximum is simpler, namely P > ε .

Thus there are restrictions on the parameters when using the model. Likewise, the maximization program of the other stakeholders could introduce additional restrictions. We are going to demonstrate that a configuration exists that is compatible with all the required restrictions.

The level of contributions brought by the foreign lobbyists (CF i ) is determined in order to maximize their profits (π Fi ):

π Fi pwm i . M i S mi . pwm i .M i -Cr i . M i -CF i (24)
where pwm i is the international price of the goods produced by sector i, M i is the quantity of goods i sold in the domestic market by foreign firms, and Cr i is the production cost of goods i for foreign firms.

The first order conditions lead to:

CF i = . . (25)
And the second order conditions imply:

0 ⟺ . . P ε . CF 0 ( 26
)
In the developed form in (26) all economic variables are positive. Considering the negative sign before the equation, the term is positive if P ε is positive ; this results in the following condition:

ε (27)
This condition does not bring unexpected additional constraints to our restriction bundle.

By replacing the value of CF i find with ( 25) in ( 17) we obtain the equilibrium value of S mi :

S mi = . . . . . (28)
The equilibrium value of CFi is then obtained with ( 17) or ( 25):

CF i = . . . . ( 29
)
The point of splitting labor into three categories, namely productive labor, labor used to lobby for obtaining production subsidies, and export subsidies, is a more complex issue. The domestic producers will make their choices by means of their profit (π i ) maximization: πi . Spi.

.

Sxi.

i .

-ri . Ki -w.( .

) (30
where p i is the sales price of production, pe i is the sales price of exportations (EX i ), r i is the remuneration of capital, w is the remuneration of the labor factor, and pc i is the composite price of the intermediate consumption (CI i ).

We have to bear in mind that this optimization is done under the constraint of a finite quantity of labor (LS) available in the economy. This implies constraints for each sector i:

(31)

But firstly, let's study the conditions under which the profit function of domestic producer is concave.

The first order conditions of optimization for π i without including, by now, the constraint in (31) lead to:

. .

. 1 . ( 32
)
For the diverted labors we obtain ( 33) and ( 34):

. . . . ε (33) . . . . ε (34)
The second order conditions are subject to the signs of the minor determinants of the Hessian matrix (HM2). Since some derivatives are equal to zero, one can simplify the matrix:

HM2 0 0 0 0 (35)
If one wants the optimization program to lead to a maximization, the minor determinant of order 1 ( ) has to be negative, the minor determinant of order 2 ( .

. ) has to be positive, and determinant HM2 has to be negative.

The first condition, 0 leads to:

. . .

< 0 (36)

This inequality is always satisfied since we have a negative sign before a ratio of positive economic values.

If one wants the minor determinant of order 2 to be positive then it leads to:

ε 1 S . ε 1 > . ( 37
)
Since 0 1 , a sufficient condition to satisfy (37) is ε 2.

The third condition to satisfy is subject to the sign of the determinant of the Hessian matrix (HM2):

Det HM2 (38)

If one wants the domestic firm's optimization program to lead to a maximization of the profit, determinant HM2 has to be negative. By considering that ( 37) is satisfied, this means a negative value for:

. . . ( 39
)
Since a ratio of two positive economic variables results necessarily in a positive sign, the only first term is to consider determining the sign in (39). The denominator of the first term is always positive.

In that case, it becomes obvious that the sign of is strictly negative when εFxi + 1.

Thus, the second order conditions for the maximization program of the domestic producers implies new restrictive constraints on parameters. It remains, however, compatible with the constraints required by the maximization program of other stakeholders.

To sum up, the use of this model is subject to the following set of constraints (A') on the parameters:

A' ε Δ . ε Δ ε ε . Δ . 1 2 and ε L ε 2 where L is a large number ε Δ . ε Δ ε ε . Δ . 1 2 and ε L ε 1 where L is a large number ε Δ . ε Δ ε ε . Δ . 1 2
and ε L ε 1 where L is a large number

We demonstrate that under these conditions, the domestic producers profit is concave since the Hessian Matrix is negative definite. If we add a linear constraint such that (31) to the domestic producers program, it does not modify the concavity of the function. So it is to say, the Lagrangian (L ) is concave.

L i . ( 40
)
Taking into consideration constraint (31) strengthens the interdependence between the different nature of labor and the different kinds of subsidies. Indeed, the first order conditions of optimization for L i lead to:

. .

. 1 . ε . ε . . ε . . ε . 1 . . . ε . LD (41)
For the diverted labors we obtain ( 42) and ( 43):

. . . ε F i . . ε F i . . ε F i . 1 . . . ε F i . LD i (42) . . . ε F i . . ε F i . . ε F i . 1 . . . ε F i . LD i (43)
All kinds of labor have the same denominator. We can make analytical predictions thanks to the numerators reasoning in relative terms. For the diverted labors, when P y , the subsidy elasticity of political cost in sector i for one kind of subsidy grows, it increases the quantity of labor diverted in order to obtain the other kind of subsidies. The inverse shift is noticed for ε Fy, the subsidy elasticity of political favor granted to sector i. As expected, the greater a subsidy, the more labor diverted to obtain it. The relative share of the labor used in the production process equally finds a logical explanation. The higher , the parameter of the contribution of the labor factor in the Value Added, the higher the share of labor dedicated to the production process. In addition, this share rises when the diverted quantities of labor are deterred by high P y and low ε Fy. Finally, we underline that the height of the production subsidy has a positive effect on the relative quantity of labor used in the production process. Indeed, it gives an incentive to produce more since it relates to an increase in the price of the product. This illustrates the tradeoff for the producer to choose between a high subsidy on a small production and a low subsidy on a bigger production.

Thus, our results show the importance of the elasticities P y and ε Fy in determining the diverted quantities of resources. As far as P y is concerned, an important role is given to the voter-consumers who can deter the diversion of resources by refusing that sectors receive high subsidies. This implies high values for P y in the model that create an increasing political cost to grant subsidies. On the other hand, if the government assesses their political efforts to grant subsidies as a worthy action that deserves a growing counterpart from lobbies (high ε Fy ), it receives a large amount of resources which are diverted from the production process.

These results are drawn from an analytical analysis but the great interest of developing a CGEM of this kind will be to work with a real economy and to obtain numerical results. In that case, the equilibrium of the model will then be found in the framework of the CGEM, which will adjust the vector of relative prices in such a way that all the markets are supposed to clear.

4-Discussion

The model displayed leads to competition among interest groups. However, this is different from the situation in Findlay and Welitz (1982), in which lobbies struggle with the same object, notably the height of the tariff barriers. In our model, there is indirect competition amongst lobbies, since each subsidy granted by the government has a VAT counterpart similar to [START_REF] Becker | A Theory of Competition Among Pressure Groups for Political Influence[END_REF]. However, Becker does not specify the nature of the taxes. Therefore, it becomes harder and harder to obtain a subsidy while consumer prices are climbing with each government grant. We need to remember here that the loss of wellbeing, based on a decrease in consumption, acts as a brake on the function that determines the amount of subsidies received by sectors. In this way, and for the wellbeing functional form to be retained, the price elasticities of consumption for the different goods available in the economy play an important role in this model.

The links between sectors depend on the configuration of the sectorial input-output parts of the Social Accounting Matrix (SAM). To recap, a CGEM is composed of equations describing the links between the variables of the model and a SAM that represents all the flows of transactions in an economy and constitutes its baseline state. Hence, a part of the SAM is dedicated to the sectorial inputs-outputs. This means that some sectors can benefit from the good health of other sectors and vice versa due to upstream and downstream links between sectors. This could result in cross-sectoral contributions in order to influence the government to help another sector that creates economics spinoffs for the contributors. To simplify the model, it is more convenient to assume that the sectors only make contributions to influence the government for their own direct benefits. Rationales for that include (i) the fact that cross-contributions could be considered as less efficient in terms of returns on investments and (ii) a risk-inversion effect could appear since very indirect economic mechanisms generate uncertainty in the returns on investments. Finally, even though the crosssectorial contributions are not applied in the model, the cross-sectorial effects of the political economy behaviors are expected in this model. This is a strength of the CGEM.

Another important point is the results we obtain for the government preference function. From ( 14) and comments that followed, we have implicitly augmented this function. Let us make the final form explicit:

WG = ∑ ∑ . . . (44)
Our specification of government preference is consistent with [START_REF] Grossman | Protection for Sale[END_REF] since the government is enabled to care about the wellbeing of civil society. This feature is important in view of [START_REF] Goldberg | Protection for Sale: An Empirical Investigation[END_REF] results exposed above. The weight of this benevolence is measured by the parameter in our model. In an extreme view of the political process, could equal 0. In that case, the government must conduct a transactional relationship with civil society and has to regard its political mandate as ephemeral. Conversely, a high value for is compatible with a lasting relationship. It characterizes governments with a real willingness to be reelected and/or with a strong ideology. Besides, is the weight of the price to pay to obtain political favors. This matches with the appetence of the government's members in taking advantage of the situation or in being convinced of the difficulties.

The model allows for the possibility of differentiating between the assessment of the government, not only by sectors, but equally by the nature of the interest group and by its type of demand. For instance, it could be easier for the domestic agricultural sector or the domestic textile industry to gain political favor; it might be easier for them to obtain such favors in the form of production subsidies. This part constitutes the object of the setting of the different elasticities in the model.

In this development of the model, to take into account the concerns of the society, the government objective function was indirectly based on consumption. However, different specifications are compatible with the model. One can for example cite other means to measure wellbeing, like the quantity of net job creations when a subsidy sustains a sector, or the willingness of the government to be accountable for their campaign pledges. The latter is past-oriented, therefore it could be more relevant and up-to-date to include, in this second part of the government preference function, indicators linked with the political agenda. Thereby, it captures the subjects on which people, politics, and the media are focusing. A weighted combination of economic indicators could then be thought to match as much as possible to the political agenda. If the government were caring to such a point that it was willing to sacrifice a part of its popularity, the second part of the government preference function could then include indicators of purely economic objectives. This would allow for the evaluation of the effects of unpopular but benevolent policy measures.

We have found that it was more realistic to work with subsidies for the reasons evoked in part 1, but it is possible to slightly rearrange the model in order to work with tariff barriers (tm i ). In that case, the rearrangement is simpler for sectors asking for protection. In the general case described by equation (3), S i should then be replaced with tm i and a new parameter of elasticity should replace . The steps should be repeated for the equations that follow. For sectors asking for free trade, which could be the case if the sector exports a lot and fears trade retaliations, it is not that direct. In our model, such a sector could have prioritized the attempt to obtain export subsidies if their costs were sufficiently lower than the production subsidies3 . It does that thanks to the allocation of the workforce between the different categories of labor and, particularly here, by allocating more resources in the labor diverted from the production process in order to lobby for export subsidies. If we talk about lowering tariffs, the cost part of the government preference function might be inefficient to act as a brake in the marginal actions of the sectors. Indeed, the loss of government revenue due to the lowering of tariffs will be financed by an increase in VAT. However, this will not necessarily create a loss of wellbeing for consumers, since imported goods meanwhile become cheaper. In this way, the behavior of the model depends more greatly on the relative weight of wellbeing elasticities to goods in the sectors. To ensure that all the demands for lower tariffs barriers do not systematically lead the tariffs concerned to zero, the cost part of WG would have to be rearranged. Different suggestions to modify this part have been discussed above.

5-Conclusion

In this paper, we have proposed a model of political economy based on the rational choices of the different stakeholders. From their assumed expectations in terms of subsidies for foreign and domestic firms and in terms of counterparts for the political effort granted by the government, we have brought a micro-foundation to the functional functions of the political market. Nevertheless, a set of constraints, named as A' above, has to be complied with in order to adopt the model.

It stems from the above that two elasticities are key parameters that influence the quantities of resources diverted and thereby the level of distortions. On the one hand, P y , the subsidy elasticity of political cost in sector i acts as a break for the subvention S y in favor of the sector i. Its level is related to increasing discontent and frustration among the population when subsidies are growing. On the other hand, ε Fy, the subsidy elasticity of political favor granted to sector i stimulates resources diversion since it determines the height of the counterpart that lobbies have to provide when receiving a subsidy; this counterpart being an incentive to grant subsidies as a source of satisfaction for the government.

If one wishes to struggle against distortion, a first recommendation can then be a much greater awareness on the part of the population about the bad effects of distortion on the state of the economy. A second recommendation can be to place importance on the personality of the candidates to elections, not only on their campaign program. However, the point is delicate since decision makers are not necessarily designated by votes.

There are some caveats in the model proposed. A first shortcoming of the model might be the role given to the consumers. They are passive in the model in the sense that they do not actively try to influence the government. This should, however, be put into perspective since they do indirectly influence the government through the benevolence and the sense of duty of the latter. This choice of modeling comes from the acknowledgement that consumers are not often organized in a unique and powerful lobby. They are more prone to divergent claims that divide their political power. However, in some countries, consumers as workers have a common claim, namely to defend their purchasing power. Unions can then be considered as their interest groups. Another point that explains the role of the consumers is the fact that we have chosen an influence-driven model. It leaves less space for consumers to actively move against the government because, in this kind of model, we consider the election as being over. Actions for influencing are then undertaken toward the incumbents.

A second shortcoming of the model lies in the restriction bundle. The results of the model are supposed to be unsecured if the difference between P y and ε Fy is a large number. We were not able to determine exactly from which number the difference is considered to be a large number. However, the modeler can lessen the inconvenience by including an automatic check of the condition A' in its program code.

In this model, we have sought to orientate the model toward trade policy features. The reason for this is the prominence gained by international trade during the last few decades. According to the WTO (2015), the growth in the volume of world trade has been approximately 5% annually during the period 1990-2014, whereas the real GDP growth for the world has been approximately 2.5% a year in the same period. However, recent data on the sub-period 2012-2014 has shown a slowdown in this differential, since the average annual growth has been slightly below 2.5% for both the volume of world trade and the real GDP. We should here stress the flexibility of the model since it accepts different features. It can be augmented particularly concerning the subsidies of different kinds. In such a way, the model can be rebalanced toward more nationally specific concerns. For each kind of subsidy added, the modeler has to think about creating a new category of diverted labor.

Numerous uses of the model are possible. To give an example in the context of foreign trade, it can be used to see the impacts of a trade agreement on the equilibrium of the economy. One could think that the protection lost in the framework of the agreement could be offset against public policies in favor of the sectors that underwent the losses. The model is able to check such an assumption.

In a normative purpose, if the selected goal is to maximize the population's wellbeing, the model can show if the current configuration of political power among interest groups allows a target level of wellbeing in the economy. Therefore, it can help to decide if lobbying should be fought, supported, or if it is not worth using resources to intervene in cases of the non-significant impact of influence.

X 5i

parameter that indicates the height of compensation to supply in return for political effort on import subsidies K i capital LDprod i labor demand for production process Influence LD spi labor demand in order to influence on the level of production subsidies LD sxi labor demand in order to influence on the level of export subsidies CF i contributions in order to influence on the level of import subsidies Sp i rate of production subsidy granted to the sector i Sx i rate of export subsidy granted to the sector i Sm i rate of import subsidy granted to the sector i Wb t

Wellbeing of the households Δwb Change in wellbeing between before (t=1) and after (t=2) the introduction of subsidies

[START_REF] Stiglitz | Globalization and Its Discontents[END_REF] explains that the IMF misled different countries during their period of crisis because the International Organization absolutely wanted them to adopt the rules of the Washington Consensus.

For an analysis of a regime under direct democracy, see the leading approach ofMayer (1984).

For the same price, a given rate of production subsidies always dominates the same given rate of exports subsidies, since the former procures its effects not only on the value of exports but also on the value of domestic sales.

Appendix : Computable General Equilibrium Model of Influence on

parameter that measures of how much the government cares about the impact of the production subsidies on the wellbeing of the consumers X 4i

parameter that measures of how much the government cares about the impact of the export subsidies on the wellbeing of the consumers X 6i

parameter that measures of how much the government cares about the impact of the import subsidies on the wellbeing of the consumers variable that indicates the height of compensation to supply in return for political effort on production subsidies X 3i variable that indicates the height of compensation to supply in return for political effort on export subsidies

III-Variables