## Abstract

We assess the impacts of Brexit on the UK economy along three dimensions: EU market access based on consideration of tariffs and non-tariff barriers, reduced numbers of EU citizens working in the UK, and reductions in FDI. Using a Computable General Equilibrium model with an integrated Melitz (Econometrica 71(6): 1695–1725, 2003) framework, we consider capital accumulation and population size feedback on tax income and demand for public services. In the worst-case scenario where all dimensions are considered simultaneously, welfare losses of approximately 1100 USD per UK citizen are predicted, exceeding the results of many other studies, which we attribute to our relatively comprehensive scenario design and application of the Melitz framework for manufacturing sectors. We find that a reduced labor force as a consequence of expected reduced immigration to the UK has the greatest welfare impact. Therefore, policy measures that increase labor participation and/or allow for continued immigration of workers could mitigate negative impacts of Brexit.

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## Notes

http://www.ilr.uni-bonn.de/em/rsrch/cgebox/cgebox_e.htm includes full documentation, including information how to download the code and additional material (i.e., training videos).

Livestock sectors are ctl, oap, rmk, and wol sectors (i.e., full details are found in the GTAP 9 database).

Food-processing sectors are cmt, omt, vol, mil, pcr, sgr, ofd, and b_t (i.e., full details are found in the GTAP 9 database).

Feed inputs comprise all crops (pdr, wht, gro, v_f, osd, c_b, pfb, ocr), as well as meats and food processing outputs (cmt, omt, vol, mil, pcr, sgr, ofd).

Agricultural inputs include all crops (pdr, wht, gro, v_f, osd, c_b, pfb, ocr) and livestock products (ctl, oap, rmk, wol).

The reader should note that the share parameters are absent in the original Melitz paper. We hence allow here a differentiation between products from different origins as in the Armington model in addition to the love of variety effect.

One could use industry specific shape parameter (

*a*_{i}) given the availability of data at sectoral level. In this study we assume that all firms entering in different industries draw their productivity from the Pareto distribution function with same characteristics (i.e., same scale and shape parameter).\(\tilde{Q}_{isr} = \mathop \sum \limits_{a} {\tilde{Q}}_{aisr}\).

The probability that the firm will operate is \(1 - G\left( {\varphi_{isr}^{*} } \right) = \frac{{N_{is} }}{{M_{is} }}.\)

*Y*corresponds to XP in the CGEBox.

## References

Aichele R, Felbermayr G (2015) Kosten und Nutzen eines Austritts des Vereinigten Königreichs aus der Europäischen Union, April, Munich. https://www.bertelsmann-stiftung.de/fileadmin/files/BSt/Publikationen/GrauePublikationen/BREXIT_DE.pdf. Accessed 25 Sep 2017

Akgul Z, Villoria NB, Hertel TW (2016) GTAP-HET: introducing firm heterogeneity into the GTAP Model. J Global Econ Anal 1(1):111–180

Alfano M, Dustmann C, Frattini T (2016) Immigration and the UK: reflections after Brexit’. In: Fasani F (ed) Refugees and economic migrants: facts, policies and challenges. CEPR Press, London

Arkolakis C, Costinot A, Donaldson D, Rodríguez-Clare A (2012) New trade models, same old gains? Am Econ Rev 102(1):94–130

Balistreri EJ, Rutherford TF (2013) Computing general equilibrium theories of monopolistic competition and heterogeneous firms. Handb Comput General Equilib Model 1B:1513–1570

Balistreri EJ, Hillberry RH, Rutherford TF (2011) Structural estimation and solution of international trade models with heterogeneous firms. J Int Econ 83(2):95–108

Bernard AB, Jensen JB, Redding SJ, Schott PK (2003) Firms in international trade. J Econ Perspect 21(3):105–130

Booth S, Howarth C, Persson M, Ruparel R, Swidlick P (2015) What if? The consequences, challenges and opportunities facing Britain outside the EU. Open Europe report 03/2015, London

Borchert I, Gootiiz B, Mattoo A (2014) Policy barriers to international trade in services: evidence from a new database. World Bank Econ Rev 28:162–188

Boulanger P, Philippidis G (2015) The end of a romance? A note on the quantitative impacts of a ‘Brexit’ from the EU. J Agric Econ 66(3):832–842

Britz W (2017) CGEBox—a flexible and modular toolkit for CGE modelling with a GUI, University of Bonn, Bonn. http://www.ilr.uni-bonn.de/em/rsrch/cgebox/cgebox_GUI.pdf. Accessed 25 Sep 2017

Britz W, Van der Mensbrugghe D (2016) Reducing unwanted consequences of aggregation in large-scale economic models—a systematic empirical evaluation with the GTAP Model. Econ Model 59:462–473

Busch B, Matthes J (2016) Brexit—the economic impact. A meta-analysis. institut der deutschen wirtschaft (IW) Report 10, köln. www.cesifo-group.info/DocDL/forum-2016-2-busch-matthes-brexit-june.pdf. Accessed 22 Nov 2016

Centre for Economic Performance (2016) BREXIT 2016: policy analysis from the Centre for Economic Performance. Centre for Economic Performance, London

CEPR (Centre for Economic Policy Research) (2013) Trade and investment, balance of competence review. Project report. Centre for Economic Policy Research, London

Dhingra S, Ottaviano G, Sampson T, Reenen JV (2016) The impact of Brexit on foreign investment in the UK. Centre for Economic Performance, London

Dhingra S, Huang H, Ottaviano G, Pessoa JP, Sampson T, Reenen JV (2017) The costs and benefits of leaving the EU: trade effects. Econ Policy 32(92):651–705

Dixit A, Stiglitz J (1977) Monopolistic competition and optimum product diversity. Am Econ Rev 67(3):297–308

Dustmann C, Frattini T (2014) The fiscal effects of immigration to the UK. Econ J 124(580):593–643

Ebell M, Hurst I, Warren J (2016) Modelling the long-run economic impact of leaving the European Union. Econ Model 59:196–209

Egger P, Francois J, Manchin M, Nelson D (2015) Non-tariff barriers, integration and the transatlantic economy. Econ Policy 30(83):539–584

Felbermayr G, Gröschl J, Steininger M (2017) Britain voted to leave the EU Brexit through the lens of new quantitative trade theory. The annual conference on global economic analysis, Purdue University, Purdue, USA

Harvey D, Hubbard C (2016) Why Brexit? Centre for Rural Economy discussion paper series 35, Newcastle. http://www.ncl.ac.uk/cre/publish/discussionpapers/pdfs/DP35hubbard.pdf. Accessed 22 Nov 2016

Hertel TW (ed) (1997) Global trade analysis: modelling and applications. Cambridge University Press, Cambridge

HM Treasury (2016a) HM Treasury analysis: the long-term economic impact of EU membership and the alternatives, London. https://www.gov.uk/government/publications/hm-treasury-analysis-the-long-term-economic-impact-of-eu-membership-and-the-alternatives. Accessed 20 Dec 2016

HM Treasury (2016b) HM Treasury analysis: the immediate economic impact of leaving the EU, London. https://www.gov.uk/government/publications/hm-treasury-analysis-the-immediate-economic-impact-of-leaving-the-eu. Accessed 20 Dec 2016

Hosoe N (2017) Impact of border barriers, returning migrants, and trade diversion in Brexit: firm exit and loss of variety. Econ Model. https://doi.org/10.1016/j.econmod.2017.09.018

House of Commons Foreign Affairs Committee (2013) The future of the European Union: UK Government policy. http://www.publications.parliament.uk/pa/cm201314/cmselect/cmfaff/87/87.pdf. Accessed 22 Nov 2016

Jafari Y, Britz W (2018) Modelling heterogeneous firms and non-tariff measures in free trade agreements using computable general equilibrium. Econ Modell. https://doi.org/10.1016/j.econmod.2018.04.004

Jafari Y, Tarr DG (2015) Estimates of ad valorem equivalents of barriers against foreign suppliers of services in eleven services sectors and 103 countries. World Econ 40(3):544–573

Keeney R, Hertel T (2005) GTAP-AGR: a framework for assessing the implications of multilateral changes in agricultural policies. GTAP technical paper 25. Center for Global Trade Analysis, Purdue

Kierzenkowski R, Pain N, Rusticelli E, Zwart S (2016) The economic consequences of Brexit: a taxing decision. OECD economic policy paper 16

Luckstead J, Devadoss S (2016) Impacts of the transatlantic trade and investment partnership on processed food trade under monopolistic competition and firm heterogeneity. Am J Agric Econ 98(5):1389–1402

Melitz MJ (2003) The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica 71(6):1695–1725

Melitz MJ, Redding S (2015) New trade models, new welfare implications. Am Econ Rev 105(3):1105–1146

Oberhofer H, Pfaffermayr M (2017) Estimating the trade and welfare effects of Brexit: a panel data structural gravity mode. CESifo working paper no. 6828, CESifo Munich

Ottaviano G, Pessoa JP, Sampson T, van Reenen J (2016) The costs and benefits of leaving the EU. Centre for economic performance technical report, Centre for economic performance, London School of Economics, London

Ottaviano G, Pessoa JP, Sampson T, Reenen JV (2017) The costs and benefits of leaving the EU. Econ Policy 32(92):651–705

Oxford Economics (2016) Assessing the economic implications of Brexit. Oxford Economics, London

Portes J, Forte G (2017) The economic impact of Brexit-induced reductions in migration. Oxf Rev Econ Policy 33(S1):S31–S44

PricewaterhouseCoopers (2016) Leaving the EU: implications for the UK economy, PricewaterhouseCoopers, London. https://www.pwc.co.uk/economic-services/assets/leaving-the-eu-implications-for-the-uk-economy.pdf. Accessed 25 Sep 2017

Roy M (2014) Services commitments in preferential trade agreements: surveying the empirical landscape. In: Sauve P, Shinghal A (eds) The preferential liberalization of trade in services: comparative regionalism. Edward Elgar Publishing, Cheltenham, pp 15–36

Samitas A, Polyzos S, Siriopoulos C (2017) Brexit and financial stability: an agent-based simulation. Econ Model. https://doi.org/10.1016/j.econmod.2017.09.019

Spearot A (2016) Unpacking the long run effects of tariff shocks: new structural implications from firm heterogeneity models. Am Econ J Microecon 8(2):128–167

Van der Mensbrugghe D (2008) The Environmental impact and sustainability applied general equilibrium (ENVISAGE) model. World Bank, Washington

## Acknowledgements

The authors would like to thank the anonymous referees for their insightful comments that greatly improved this paper.

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## Appendices

### Appendix 1: Technical appendix

### 1.1 Implementation of Melitz model into the standard GTAP model

We incorporate a module based on Melitz (2003) into the flexible and modular CGE model CGEBox (Britz 2017). The actual implementation of the Melitz model into CGEBox draws largely on the empirical method by Balistreri et al. (2011), Balistreri and Rutherford (2013) and Akgul et al. (2016) to introduce the Melitz (2003) model into an applied equilibrium model.

The Melitz framework focuses on intra-industry differentiation where each firm produces a single unique variety. However, data at the firm level are limited and applied equilibrium models work at aggregate levels. Fortunately, Melitz offers a numerical framework build around (marginal changes in) the average firm operating within a trade linkage. That average firm’s productivity comprises all necessary information on the distribution of productivity levels of firms active in that link. That vastly eases the model’s implementation by effectively eliminating any data needs at individual firm level as detailed below. Against a background of that definition of an average firm within each trade linkage, we now focus on the formulation of an empirically computable version of Melitz model and its linkages with the GTAP model.

Assume that a representative agent ‘*a*’ (private households, government, investors, intermediate inputs by the different firms) in region ‘r’ obtains utility \({\text{U}}_{\text{air}}\) from consumption of the range of differentiated varieties of product ‘i’ and considering the CES utility function as proposed by Dixit and Stiglitz (1977), the aggregate demand by each agent \(a\) for commodity \({\text{i}}\) in region \(r\) (\({\text{Q}}_{\text{air}}\)) which is equivalent to utility (\({\text{Q}}_{\text{air}} \equiv {\text{U}}_{\text{iar}}\)) can be represented as:

where \(\Omega _{isr}\) represents the set of products \(i\) sourced from region \(s\) to \(r\) and \(\omega \in \Omega _{isr}\) index the varieties in the set \(\Omega _{isr}\) In this context, \(Q_{aisr} \left( \omega \right)\) represents the demand quantity of commodity \(i\) for variety \(\omega\) in region \(r\) by agent a which is sourced from region \(s\), \(\sigma_{i}\) represents the constant elasticity of substitution for each commodity, and \(\lambda_{aisr}\) are preference weights (share parameters)^{Footnote 7} that reflect differences between origins not linked to diversity in varieties. Note that substitution elasticities might be differentiated by destination region \(r\), but are uniform across agents in each region in our implementation.

The resulting CES unit expenditure function which is the dual price index on Dixit–Stiglitz composite demand in region r (\(P_{air} )\) is given by:

where \(PA_{aisr} \left( \omega \right)\) is agent’s \(a\) (purchase) price of product \(i\) for variety \(\omega\) in region \(r\) sourced from region \(s\). Using the aggregate price index in Melitz (2003) based on the definition of the average firm and considering that varieties do not differ in their marginal utility for the first unit, one can define the price index as equivalent to the dual price defined in Eq. (2)

where \(\widetilde{PA}_{aisr}\) denotes the agent price inclusive of export, import and consumption taxes for the average firm, and \(N_{isr}\) refers to the number of firms operating on the trade link s-r. Equation 3 generates the top level Armington price for each agent, replacing the Armington price aggregator in GTAP from the agents’ domestic and import prices. Consistent with Melitz (2003), there is a one-to-one mapping among firms and varieties such that the number of firms is equal to the number of varieties on each trade linkage. In comparison to Eq. (2), which is based on the individual varieties, Eq. (3) summarizes the compositional change (i.e., change in the number of varieties), which goes along with an update of the average price. Again we assume the same substitution elasticities across agents.

The total (\(Q_{aisr} )\) and average per firm (\(\tilde{Q}_{aisr} )\) demand for the average variety by an agent to be shipped from s to r (\(\tilde{Q}_{aisr} )\) can be obtained by applying *Shephard’s Lema* on the expenditure function:

This equation replaces the equations determining the agent specific Armington demands for the domestic and imported good as well as the equations for bi-lateral import demand which are not agent specific in the GTAP standard model.

This reveals the main differences to a standard Armington composite: the share parameters vary with the number of operating firms (i.e., the number of varieties comprised in the bilateral trade bundles). As the agent demand for the average firm’s output in region *s* in each industry \(i\) in region \(r\) (\(Q_{aisr} )\) depends on the aggregate regional demand for that industry \(Q_{air}\), we need to determine this in equilibrium for each agent. In other word, we need to determine the demand for use of \(i\) as an intermediate input in each sector separately, and as final demand for household consumption, government consumption, investment, and for international transport margins. In the standard GTAP model, each agent has a specific preference function which determines the demand for each Armington commodity; the government and saving sector based CES preferences, while households use a CDE indirect demand function. The Armington demand for each agent and commodity is then decomposed into a domestic and import component in the first Armington nest. The second nest decomposes import demand by each region by origin, independent of the agent.

The implementation of the Melitz model thus simplifies the demand structure present in the standard GTAP model by aggregating the two Armington nests into a single one, however, note that the GTAP database does not yet differentiate in the SAM bi-lateral flows by agent. Therefore we use the same shares by origin to separate import demand for the different agents.

Assume that a small profit maximizing firm facing the constant elasticity of demand according to Eq. (4) for its variety and based on the assumption of the large group monopolistic competition, a firm will not consider its impact on the average price index and therefore follow the usual markup rule to translate their marginal cost of production (\(c_{is} )\) to the optimal price.

Firms in Melitz (2003) face different types of cost: sunk fixed cost of entry \(f^{ie}\), fixed cost of operating on a trade linkage \(f_{isr}\) and marginal cost \(c_{is}\). Let \(\varphi_{isr}\) indicate the firm’s specific productivity, which measures the amount of “variable composite unit” needed per unit of output \(Q_{isr}\). Accordingly, the marginal cost per unit is the amount of “composite input” required per unit \(( {\frac{1}{{\varphi_{isr} }}})\) times the unit cost of the “variable composite input” (\(c_{is} )\) in industry \(i\) of region \(s\). Therefore, a firm wishing to supply \(Q_{isr}\) units from region \(s\) to \(r\) employs (\(f_{isr}\) + \(\frac{{Q_{isr} }}{{\varphi_{isr} }}\)) units of “variable composite input.” The structure of fixed costs and variable composite input demand is discussed in detail below. Let, \(\tau_{isr}\) denote the iceberg cost of trade, which represent domestic production costs and not the international trade margins present in GTAP. Focusing on the average firm with a productivity \(\tilde{\varphi }_{isr}\) operating within a trade linkage and solving the firm’s profit maximization problem, the price charged by the average firm in region s to supply region r \(\widetilde{PF}_{isr}\) (inclusive of domestic transport margin) is:

where \(\frac{{\sigma_{ir} }}{{\sigma_{ir} - 1}}\) represents the constant markup ratio in industry \(i\), which reflects market power due to product differentiation into varieties. This newly introduced equation translates the variable per unit cost function for each sector and region into offer prices by the firms on each trade link including domestic sales. In the standard GTAP model, offer prices are not differentiated by destination and are equal to per unit cost corrected for output taxes.

The average price in Eq. (5) therefore depends on the price of variable composite input \(c_{is}\), which is a function of the price of intermediates and primary factors. Given the assumption of constant return to scale and the way technology is presented in the standard GTAP model, the unit cost function for sector \(i\) in region \(s\)\(c_{is}\) in GTAP is given by the Leontief composite of the value added bundle (CES aggregate of factors of production) and the aggregate of intermediate demand (Leontief aggregate of intermediate demands). In the CGEBox, *m_px*^{Footnote 8} is a macro defined as producer price, which constitute per unit costs corrected for production taxes. To be consistent with our Melitz formulation, the unit cost inclusive of production tax is directly introduced in the markup Eq. (5). It should be emphasized that the presence of fixed cost in the Melitz model is the source of increasing returns to scale in a monopolistically competitive industry: if firms expand production, the fixed cost can be distributed over a greater quantity of outputs such that per unit cost decreases.

While observed data on quantities traded and related prices allow identifying the necessary attributes of an average firm, additional information is needed to gain information about the marginal firm (i.e., the firm that earns zero profit). Obviously, the distance in productivity between the average and marginal firm reflects properties of the underlying distribution. We rely here on a Pareto Productivity distribution, which has analytical tractability.

Let \(M_{s}\) indicate the number of firms choosing to incur the fixed entry cost (i.e., total industry size), each individual firm receives its productivity \(\varphi\) draws from a Pareto distribution with Probability Density Function (PDF):

and Cumulative Distribution Function (CDF):

where \(b\) is the minimum productivity and \(a\) is a shape parameter. Lower values of the shape parameter imply higher productivity dispersion among firms. As discussed in Melitz (2003), \(a > \sigma_{ir} - 1\) should be applied in order to ensure a finite average productivity level in the industry.

On each bilateral trade linkage, the given fixed bilateral trade cost, variable costs and demand define jointly a certain cut off productivity level (\(\varphi_{sr}^{*}\)) at which firms will receive zero profit. A firm with the productivity equal to that threshold level (\(\varphi_{sr} = \varphi_{sr}^{*}\)) will therefore face zero profits and act as the marginal firm from region \(s\) supplying \(r\). Those firm whose productivity is above the threshold level (\(\varphi_{sr} > \varphi_{sr}^{*}\)) will receive a positive profit and will operate on the \(s - r\) link and those firm with productivity that is below the threshold level (\(\varphi_{sr} > \varphi_{sr}^{*}\)) will not operate on the \(s - r\) linkage. Focusing on the fixed operating cost \(f_{isr}\) in composite input units, the marginal firm on s-r linkage receives zero profit at:

where \(r\left( {\varphi_{isr}^{*} } \right) = p\left( {\varphi_{isr}^{*} } \right)q\left( {\varphi_{isr}^{*} } \right)\) denotes the revenue of marginal firm at the productivity equal to the cut off level (\(\varphi_{isr} = \varphi_{isr}^{*} ).\)

The zero cut off productivity level in each bilateral market \(\varphi_{isr}^{*}\) can be obtained by solving Eq. (8). However, it is numerically easier to define this condition in terms of the average rather than the marginal firm. To do this, we define the productivity and revenue of the average firm relative to that of the marginal firm. Following Melitz (2003), average productivity is defined as the CES aggregation of productivities of all firms operating on a given trade link:

If these productivities are Pareto distributed, we can write^{Footnote 9}:

Equation (10) provides the relationship between the productivities of the average and marginal firm

Using optimal firm pricing according to Eq. (5) and given the input technology, the ratio of revenues of the firms with marginal productivity \(r_{isr} \left( {\varphi^{*} } \right)\) in relation to the revenue of the firm with the average productivity \(r_{isr} \left( {\tilde{\varphi }} \right)\) is defined as:

Solving Eq. (10) for \(\frac{{\varphi^{*} }}{{\tilde{\varphi }}}\), substituting it into (11), and then solving the resulting equation for \(r_{isr} \left( {\varphi^{*} } \right)\) and replacing its value in Eq. (8), defines a relation between the bilateral fixed cost at current composite input price [the LHS of (12) below], the average firms revenue (\(\widetilde{PF}_{isr} \tilde{Q}_{isr}\)), the shape parameter of the Pareto distribution of the productivities and the substitution elasticity of demand:

Note that average firm’s sale in region *s* in each industry \(i\) to region r (\(\tilde{Q}_{isr} )\) at the equilibrium is composed of the demand for use of \(i\) by different agents.^{Footnote 10}

The optimal pricing in the markup Eq. (5) requires information on the average productivity on each bilateral trade link. In Melitz (2003), the probability that a firm will operate is \(1 - G\left( {\varphi_{isr}^{*} } \right)\), which is equal to the fraction of operating firms over total number of firms choosing to draw their productivity \(\left( {\frac{{N_{is} }}{{M_{is} }}} \right)\). Using the Pareto cumulative distribution function from Eq. (7) and inverting it we have:

Substituting Eqs. (13) into (10) results in Eq. (14) introduced into the model:

Next, the number of firms selecting to enter the market \(M_{is}\) is determined. Based on the free entry condition, the last firm that enters has expected profits over its life time, which just offset the sunk cost of entry. Industry entry of a firm requires a one-time payment of \(f^{ie}\). A firm that enters a market faces a probability of \(\delta\) to suffer a shock, which forces its exit in each future period. Therefore \(\delta M_{is }\) firms are lost in each period. Based on Melitz (2003), in a stationary equilibrium, the number of aggregate variables must remain constant over time, including industry size. This requires that the number of new entrants in every period is equal to the number of firms lost \(\delta M_{is }\). Therefore, total entry cost is equal to \(c_{is} \delta M_{is } f^{ie}\). Each firm faces the same expected share on that cost (i.e., \(c_{ir} \delta f^{ie}\) if risk neutral behavior and no time discounting is assumed). The firm’s expected share of entry costs must be equal to the flow of expected profit on the condition that firm will operate:

The probability that a firm will operate on the s-r trade linkage is given by the ratio of \(\frac{{M_{isr} }}{{N_{is} }}\).^{Footnote 11} Thus, the free entry condition ensures that the expected industry profits (i.e., the profits summed up over all potential bilateral trade links) is equal to the annualized flow of the fixed costs of entry

where zero profit condition in Eq. (12) is used to replace the fixed operating cost \(c_{is} f_{isr} .\) With the number of entered firm established in Eq. (16), we now turn to total composite input demand of the industry Y,^{Footnote 12} which consists of three components: sunk entry costs of all entrants (\(\delta M_{is } f^{ie}\)), operating fixed cost (\(\mathop \sum \limits_{s} N_{isr } f_{isr }\)) on each trade linkage, and variable costs (\(\mathop \sum \limits_{r} N_{isr } \frac{{\tau_{isr} \tilde{Q}_{isr} }}{{\tilde{\varphi }_{isr} }}\)). Therefore, composite input demand is defined as:

This equation replaces the output balance equation in the standard GTAP model which ensures that exports and domestic sales for each sector are equal to input composite demand. Table 7 summarizes the full set of Melitz equations, and shows the variables through which Melitz model is linked into the structure of the GTAP standard model.

### 1.2 Production structure for sectors in the Melitz module

This section briefly introduces the production technology for the Melitz commodities which is based on Akgul et al. (2016). The main differences to the GTAP standard model are production function nestings specific to variable and fixed costs. The production nesting for variable and fixed cost is shown in Fig. 1 where the total cost is the sum of variable and fixed costs, the latter is added up from fixed cost per firm which entered the industry and fixed cost on each trade link per firm operating on that link.

The variable cost nest uses both a value-added and an intermediate composite based on constant returns to scale (CRS) technology, and in the default case, the fixed cost nest only uses value-added. However, if the overall total cost share of value-added in a sector is small, also the fixed nests comprise a share of intermediate composite. This alternative is identified with the intermediate composite in brackets. The value added and intermediate bundles are CES composite of primary factors of production and intermediate inputs, respectively. The total value added (not shown here) is the sum of value added used in both variable and fixed cost nestings. Similarly, the total use of intermediate commodities and primary factors (not shown here) are the sum of their use in fixed and variable cost nestings

In the variable cost nests for the Melitz sectors, primary factors or intermediate inputs used are proportional to output, i.e. average output per firm on each trade link times firm operating on the link, summed up over all trade links, corrected for average productivity. On the other hand, the fixed cost nests reflect solely the number of firms which entered the industry and the trade links, and not average output per firm.

Each intermediate commodity used by a Melitz sector could be either a Melitz or Armington commodity, and the intermediate input bundle is a CES composite of these commodities, in the default configuration based on fixed input coefficients. For the Armington goods, we retain the standard GTAP model assumption of domestic and import distinction where imports are sourced at the border (not shown). There is no separate domestic and imports distinction for Melitz commodities, but only one aggregator with love-variety effects which comprises domestic sales and all bi-lateral imports.

### Appendix 2: Supplemental tables

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Jafari, Y., Britz, W. Brexit: an economy-wide impact assessment on trade, immigration, and foreign direct investment.
*Empirica* **47**, 17–52 (2020). https://doi.org/10.1007/s10663-018-9418-6

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DOI: https://doi.org/10.1007/s10663-018-9418-6