# The Redistribution of Trade Gains When Income Inequality Matters

## Abstract

**:**

## 1. Introduction

#### 1.1. Redistribution and Income Inequality

#### 1.2. Related Literature

## 2. Theoretical Framework

#### 2.1. Model

- Firms draw their productivity and decide whether to enter the domestic market and, additionally, whether to export varieties abroad. In the case of production, firms post vacancies at no cost.
- Individuals apply for the jobs, and each firm randomly hires some workers from the pool of applicants.
- The firms’ employees form a monopoly trade union at the firm level, which sets the wage on behalf of their members.
- Given the wage set by the union, the firm can readjust the employment decision of Stage 2, i.e., its right-to-manage privilege.

#### 2.2. Partial Equilibrium

#### 2.2.1. Employment and Prices (Stage 4)

#### 2.2.2. Wages and Applications (Stage 3 and 2)

#### 2.2.3. Production and Export Decision (Stage 1)

#### 2.3. General Equilibrium

#### 2.3.1. The Representative Firm

#### 2.3.2. Free Entry

#### 2.3.3. Labor Market

#### 2.3.4. Goods Market

## 3. The Government

#### 3.1. Objective Function

#### 3.2. Income and Income Inequality

#### 3.3. Optimization Problem

## 4. Numerical Solution

#### 4.1. Calibration

Parameter | Value | Interpretation | Source |
---|---|---|---|

${\tau}_{0}$, ${\tau}_{1}$ | 1.6, 1.3 | Iceberg trade costs | [33] |

σ | 3.8 | Elasticity of substitution | [32] |

k | 5.2 | Shape parameter Pareto | [34] |

f | 1.77 | Fixed costs | [32] |

${f}_{e}$ | 39.57 | Entry costs | [32] |

δ | 0.025 | Firms’ death probability | [33] |

ω | 0.8 | Weight of workers’ abilities | [35] |

α | 0.25 | Quality requirement | |

γ | 0.2 | Inequality aversion | [36] |

#### 4.2. UB Financed by a Wage Tax

**Figure 1.**UB (unemployment benefits) financed by a wage tax. (

**a**) income; (

**b**) Gini coefficient; (

**c**) welfare.

**Result 1.**Suppose that the government finances UB by a wage tax. Then, (i) income per capita decreases, (ii) the Gini coefficient decreases and (iii) the welfare path is hump-shaped with the maximum at $s={s}_{{t}_{w}}^{*}$.

#### 4.3. UB Financed by a Payroll Tax

**Result 2.**Suppose that the government finances UB by a payroll tax. Then, (i) income per capita decreases, (ii) the Gini coefficient decreases and (iii) welfare declines. Optimization yields the corner solution $s={s}_{{t}_{pw}}^{*}=0$.

#### 4.4. UB Financed by a Profit Tax

**Result 3.**Suppose that the government finances UB by a profit tax. Then, (i) income per capita decreases, (ii) income inequality decreases and (iii) welfare declines. Optimization yields the corner solution $s={s}_{{t}_{\pi}}^{*}=0$.

**Result 4.**The government’s optimal redistribution policy is to finance UB by a wage tax and to set $s={s}_{{t}_{w}}^{*}$.

## 5. Summary

## Acknowledgments

## Conflicts of Interest

## A. Appendix

#### A.1. Derivation of the Export Cutoff Productivity

#### A.2. Derivation of the Revenue of the Representative Firm

#### A.3. Derivation of the Lorenz Curve

#### A.3.1. First Segment

#### A.3.2. Second Segment

#### A.3.3. Third Segment

#### A.3.4. Fourth Segment

#### A.4. Robustness Checks

#### A.4.1. Main Specification

#### A.4.2. Optimal Redistribution for Different Trade Costs

#### A.4.3. Optimal Redistribution for Different Inequality Aversions

^{1.}The work by [2] shows, for instance, that low productive firms are harmed by trade liberalization. More specifically, they use data of French firms and find that trade liberalization leads to a substantial market exit of low productive firms. In addition, there is new evidence, provided, e.g., by [3,4], that the effects of trade liberalization are ability specific, favoring (harming) high-ability (low-ability) workers in terms of employment and wages.^{2.}As pointed out by [10], bargaining agreements are still an important determinant for wage setting, in particular in European countries. For instance, the union coverage rate in Europe is about 66%.^{3.}Worker heterogeneity is also introduced by [13,14], who set up a free trade model with search and matching frictions. In contrast to our model, however, they assume that abilities are match-specific and independently distributed. Consequently, a worker’s ability for a given match does not convey any information about his or her ability for other (future) matches.^{4.}While the cited studies introduce (firm and/or worker) heterogeneity in their models, which is also done in our paper, there is a strand of literature that investigates the redistribution of trade gains without sources of heterogeneity. For instance, [19] find that commodity taxes compensate the losers and recover the trade gains in the case of perfect competitive labor markets. The work in [20] argues, however, that this result does not hold if labor market imperfections are considered. Assuming a binding minimum wage, and hence the existence of involuntary unemployment, they find that the compensation of the losers fully negates the gains from trade.^{5.}The specification of the CES aggregator rules out external scale effects; a well-understood mechanism through which free trade influences aggregate output. This assumption is made because we want to focus as clearly as possible on the effects of trade unions, as well as firm and worker heterogeneity for the implications of different redistribution schemes (see [22] for a similar line of reasoning).^{6.}In Section 2.2.2, we analytically show that $\partial b/\partial a>0$ holds. Intuitively, high-ability workers are able to work in high productive firms, which pay higher wages. This raises their expected wage rates and, thus, their reservation wages.^{7.}Equation (11) fits two empirical regularities regarding the design of the UB in most countries (see [24] for evidence). First, UB are related to the individuals’ average income. Second, individuals pay tax on UB, either since their calculation is based on net average income or since the payment itself (based on gross earnings) is taxable.^{9.}The ad hoc specification of ${\overline{w}}_{j}$ is needed because we have to deal with the simultaneity between the application process and the expected wage rate. On the one hand, a worker applies for a job if the wage offer is no less than the reservation wage (depending on the outside wage). On the other hand, the expected wage rate depends on the number and characteristics of jobs for which the worker applies. Thus, the decision to apply is determined jointly with the expected wage rate.^{10.}Notably, we assume that vacancy posting is costless to avoid further sources of labor market frictions.^{11.}Because the structure of the game is common knowledge, both firms and workers perfectly foresee the wage-employment outcome of Stages 3 and 4, and ${h}^{0}=h$ holds. This implies that the threat to readjust employment in Stage 4 is credible. Neither the worker/union nor the firm have an incentive to deviate from the anticipated wage-employment combination. Note further that the pool of applicants at Stage 2 is characterized by a mass of workers (with $a\in [{a}_{l},{a}_{z}]$). This implies that $\overline{a}$ cannot be changed by adjusting the employment decision at Stage 4 as long as the firm randomly chooses workers from the application pool (which we assume in our model).^{12.}The difference between the two averages ${\tilde{\varphi}}_{t}$ and $\tilde{\varphi}$ can be explained by the interplay between the lost-in-transit effect (i.e., goods vanish en route because of iceberg transport costs) and the export-selection effect (i.e., exporting firms are the most productive in the economy). Compared to the domestic level $\tilde{\varphi}$, the former shrinks total average productivity ${\tilde{\varphi}}_{t}$, while the latter increases it.^{13.}“Active” means that these workers have a positive employment probability. Nevertheless, active workers can also be unemployed.^{14.}As also stated by [16], the functional form of the welfare function given by Equation (35) was introduced by [29]. As shown by [30], it fits quite well with the empirical evidence on individuals’ inequality aversion. Hence, we use a welfare specification that is relatively simple (and therefore highly tractable), is established in the literature and seems not to be at odds with empirical findings.^{15.}In a similar study, [31] also investigates the impact of different redistribution schemes on welfare. This study, however, sticks to the assumptions that only exporting firms have to pay a profit tax and that budget is ex ante neutral, i.e., repercussion effects of policy instruments on the budget constraint are ruled out.^{16.}This result is heavily driven by our modeling approach regarding UB (see Equation (11)). If, for instance, UB are based on gross expected income, the neutrality result between w and ${t}_{w}$ vanishes. We argue, however, that a tax collection on UB is the empirically-relevant case. In addition, simulations suggest that setting ${t}_{w}=0$ in Equation (11) will only lead to a quantitatively low effect of ${t}_{w}$ on w, in particular for low values of the wage tax rate. These simulations are available upon request.^{17.}Note further that we allow only values of s for which Laffer efficiency holds, i.e., an increase in tax rates must not imply a decline in tax revenues.^{18.}The reduction in $\widehat{w}$ passes through to wage setting at the firm level because of the implied decrease in the outside wage (see Equation (12)). Thus, unions set c.p. a lower wage rate. If w decreases, the number of workers employed by active firms rises, but there is also the decline in goods demand because of the payroll tax mentioned above, which reduces h. In the equilibrium, these two effects exactly offset each other, and employment per firm remains constant.

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De Pinto, M. The Redistribution of Trade Gains When Income Inequality Matters. *Economies* **2015**, *3*, 186-215.
https://doi.org/10.3390/economies3040186

**AMA Style**

De Pinto M. The Redistribution of Trade Gains When Income Inequality Matters. *Economies*. 2015; 3(4):186-215.
https://doi.org/10.3390/economies3040186

**Chicago/Turabian Style**

De Pinto, Marco. 2015. "The Redistribution of Trade Gains When Income Inequality Matters" *Economies* 3, no. 4: 186-215.
https://doi.org/10.3390/economies3040186