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This subsection provides a detailed account of the relationship between the export pro- ductivity cutoffs and corporate tax rates. I find that the conditional probability of exporting κ is negatively related to the depreciation rate (in the source country), but the relationship with the statutory corporate tax rate is ambiguous. The first part of the result is not surpris- ing as increasing δ decreases the cost of fji which incentives more firms to enter the export

markets, all else equal. However, the direction of change for modification in τ is ambigu- ous as it depends on the level of δ . These properties can possibly explain why Bernini and Treibich (2013) and Federici and Parisi (2014) find opposite signs for the correlation between the proportion of exporting firms and corporate tax rates.

The effects of changes in δ, τ on the probability of exporting (κx_{) are expressed in terms}

of the elasticities of ϕ∗. Let Zjs be the productivity distribution in country j sector s, then:

ϒjs(x) = zjs(x)x 1_{− Z}js(x) (1.4.10) ∂ κx_jis ∂ y y = κ x jis  ϒ(ϕ∗_{j js})ξϕ∗_{j js},y− ϒ(ϕ∗jis)ξϕ∗_jis,y  for y = τ, δ (1.4.11)

• If Zjs∼ Pareto(kjs, ϕmin) then ϒ(ϕ) = kjsfor any ϕ in the support of Zjs.

• If Zjs∼ logN (mjs, vjs) then ϒ(ϕ) is an increasing function.

The above shows once again that distributional assumptions about productivity are important for the comparative statics of the model. Under the Pareto assumption, the function ϒ is constant implying that the change in κ is determine by the unweighted difference of the elasticities across firms that produce for the domestic and export market. In contrast, in the lognormal case the function ϒ is increasing on its argument implying that a higher weight is given to the elasticity of the export cutoff over the domestic one.

A graphical representation is helpful to see the relation between tax rates and the prob- ability of export. Figure 1.3 (below) presents a heat map for the probability of export κji1

as a function of τj and δj1. These values come from solving the equilibrium for countries

whose parameters are equal to those of the almost symmetric scenario, with τj, δj1 varying

to generate the surface of the plot. The left graphs of the panel show that increasing the depreciation allowance rate (δ1 j) results in a decrease in the propensity to export by firms

in country “j", but the relationship between the statutory tax rate (τj) and the probability of

export is ambiguous. In the graphs we observe that increasing τj results in an increase in the

probability of exporting but only when the value of δj1is below a certain threshold. On the

other hand, if δj1is above such threshold, the probability of export decreases with the statu-

tory corporate tax rate. The reason behind the ambiguous effect goes back to the movement of the ZPC condition in closed economy, which was positive for δ> 0 but negative for δ < 0. In the open economy the new ZPC condition also contains the term ϕ∗_ji which is determine by ratio of user costs across countries; thereby, the threshold value for δ at which the relation between τ and productivity cutoffs change is different than zero.

The relation shown in Figure 1.3 bridges two conflicting empirical findings regarding cor- porate tax effects on export dynamics. First, Bernini and Treibich (2013) find that corporate tax rates are negatively correlated with the probability that firms will engage in export activ- ities. Their results are obtained by exploiting an exogenous variation in the statutory tax rate

Figure 1.3: Heat Map for the probability of exporting obtained by simultaneously varying the values of the depreciation allowance rate of sector 1 and the statutory tax rate at Home. 0.1 0.2 0.3 0.4 0 0.5 1 1.5

Sector 1, Home, under Pareto

Statutory Tax Rate Home

δ1 Ho m e 0.1 0.2 0.3 0.4 0 0.5 1 1.5

Sector 1, Foreign, under Pareto

Statutory Tax Rate Home

δ1 Ho m e 0.1 0.2 0.3 0.4 0 0.5 1 1.5

Sector 1, Home, under Log-Normal

Statutory Tax Rate Home

δ1 Ho m e 0.1 0.2 0.3 0.4 0 0.5 1 1.5

Sector 1, Foreign, under Log-Normal

Statutory Tax Rate Home

δ1

Ho

m

e

charged to small-medium firms in France, which was reduced from 33.33% to 15% for the years 2001 to 2003, and compare the export outcomes of such firms relative to large firms as their statutory tax rate was unchanged. As we have seen in Figure 1.3, my model predicts such relationship but only when the depreciation allowance rate is above a threshold. On the other hand, Federici and Parisi (2014) use data from Italian firms, for the years 2004 to 2006, to show that export propensity is positively associated with corporate taxation, which in their study is a measure of firms’ specific effective tax rate. In my model, this would translate to a negative relationship between the sector depreciation allowance rate and the probability of

exporting, which is what we observe in Figure 1.3.16

Adding corporate taxation to a multi-sector Melitz model can also solve the critique of Segerstrom and Sugita (2014) who find that such model is inconsistent with the data. In the data, sector productivity increases more strongly in liberalized sectors than in non-liberalized sectors; however, the multi-sector Melitz model generates the opposite relationship under fairly general conditions. Using equation 1.4.7, we can observe that the effects of a unilateral decrease in trade costs (θ ) can be directly offset via corporate tax changes in either country. Hence, the critique of Segerstrom and Sugita (2014) regarding the implication of a multi- sector Melitz model can be attenuated.

While the question of interest was on the relationship between exports and the corporate tax rates I also show that the model is consistent with other standard results. Using equation 1.4.6, we see that liberalization (reduction of θ ) reduces the productivity cutoff to serve coun- try i via exports. The same equation also provides a relationship between market competition and the export productivity required to “carve" a space in such market. For example, if there are many firms operating in country i and/or the productivity of such firms is high ( ˜ϕtot,i),

then the required export productivity cutoff will be higher relative to other less competitive markets.