\begin{document} \title{Services Elasticities\vspace{0.5in}% } \author{Samantha Schreiber\thanks{U.S. International Trade Commission.\newline Contact emails: samantha.schreiber@usitc.gov}} \date{\vspace{1.5in}% \today} \thispagestyle{empty} { % set font to helvetica (arial) to make it 508-compliant \fontfamily{phv}\selectfont \begin{center} {\Large \textbf{ESTIMATING ELASTICITIES FOR TRADABLE}} \\ \vspace{0.25in} {\Large \textbf{SERVICES IN POLICY SIMULATIONS}}\\ \vspace{0.75in} {\Large Saad Ahmad and Samantha Schreiber}\\ \vspace{0.75in} {\large ECONOMICS WORKING PAPER SERIES}\\ Working Paper 2024--09--B \\ \vspace{0.5in} U.S. INTERNATIONAL TRADE COMMISSION \\ 500 E Street SW \\ Washington, DC 20436 \\ \vspace{0.25in} September 2024 \end{center} \vfill \noindent The authors thank David Riker, Peter Herman, and seminar participants at the 27th Annual Conference on Global Economic Analysis for helpful comments and suggestions on an earlier draft. Office of Economics working papers are the result of ongoing professional research of USITC Staff and are solely meant to represent the opinions and professional research of individual authors. These papers are not meant to represent in any way the views of the U.S. International Trade Commission or any of its individual Commissioners. \newpage \thispagestyle{empty} % remove headers, footers, and page numbers from cover page \begin{flushleft} Estimating Elasticities for Tradable Services in Policy Simulations\\ Saad Ahmad and Samantha Schreiber \\ Economics Working Paper 2024--09--B \\ September 2024\\~\\ \end{flushleft} \vfill \begin{abstract} \noindent We provide new estimates of the Armington elasticities of substitution for several services sectors. Our approach relies on methods that utilize the theoretical relationship between the elasticity and profit margins in a monopolistic competition framework as described in Gervais and Jensen (2019) and Ahmad and Riker (2019). We find that the median elasticity of substitution is 5.65 at the NAICS 3-digit level and 5.42 at the more aggregated GTAP sector level. Finally, we illustrate the importance that these services trade elasticities can have on model outcomes in GTAP by simulating a hypothetical and stylized agreement that liberalizes services trade between the US and the UK. \end{abstract} \vfill \begin{flushleft} Saad Ahmad\\ Research Division, Office of Economics\\ \href{mailto:saad.ahmad@usitc.gov}{saad.ahmad@usitc.gov}\\ \vspace{0.25in} Samantha Schreiber\\ Research Division, Office of Economics\\ \href{mailto:samantha.schreiber@usitc.gov}{samantha.schreiber@usitc.gov}\\ \vspace{0.75in} \end{flushleft} } % end of helvetica (arial) font \clearpage \newpage \doublespacing \setcounter{page}{1} \section{Introduction} The elasticity of substitution, or the trade elasticity, is often a key parameter in Armington trade models as it captures how consumers shift between domestic and imported varieties of a product after a change in relative prices that may arise as a result of policy actions such as an increase in tariffs. The chosen value for the elasticity of substitution can significantly impact the estimated welfare gains or losses arising from changes in trade policy in CGE simulations \cite{mcdaniel}. Given its importance, recent works have made considerable progress in providing analysts and researchers with updated estimates on the elasticities of substitution for traded goods \cite{fontagne}. However, less information is currently available on the elasticities of substitution for the services sectors. Several factors have made it difficult to pin down empirically-grounded estimates of elasticities of substitution for the services sectors including: common methods used to estimate elasticities of substitution for traded goods requires data inputs that are not available with traded services; trade data for disaggregated services is often absent for most countries; and some services are not traded across borders. From a policy perspective though, the lack of reliable estimates on trade elasticities for services sectors is especially disconcerting as recent trade agreements have focused more on non-tariff measures that affect the ability of firms to trade services across borders.\footnote{For example, the U.S. and partners have started negotiations on the Indo-Pacific Economic Framework for Prosperity (IPEF) which includes a range of non-tariff measures such as cross-border data flows and data localization standards, clean energy standards, and anti-money laundering and anti-bribery standards.} This paper contributes to the literature by providing new estimates on the elasticities of substitution for several disaggregated U.S. services sectors. Our estimation approach relies on the theoretical relationship that exists between the elasticity and profit margins in a monopolistic competition model of trade as illustrated in Gervais and Jensen (2019) and Ahmad and Riker (2019). First, we estimate elasticities at the NAICS 3-digit level using industry output and gross operating surplus data from the U.S. Bureau of Economic Analysis (BEA). We then concord the 3-digit NAICS codes to GTAP sectors and re-estimate services elasticities at the GTAP sector level. The median elasticity of substitution is 5.65 at the NAICS 3-digit level and 5.42 at the more aggregated GTAP sector level. For the core tradable services sectors that are often targeted in FTAs, the mean elasticity is 5.01, similar to other average services estimates in the literature. Finally, to illustrate the impact that the services elasticities can have on model outcomes, we simulate the implementation of a hypothetical and stylized US-UK agreement that liberalizes services trade using the GTAP modeling framework. \section{Literature Review} Only a small number of studies have directly estimated trade elasticities for services sectors. Most of these studies rely on the monopolistic competition model of trade which postulates that a firm's revenues and profits are linked with the elasticity of substitution in its sector. Section 3 provides a brief overview of this mark-up approach for estimating trade elasticities. Using the mark-up approach on firm-level data from Statistics Finland and the UK Office of National Statistics, Rouzet et al.\@ (2017) calculate their elasticities as the median ratio of sales to operating profits among all firms in a given sector. The median estimate from Rouzet et al.\@ (2017) is 2.30, ranging from 1.6 (banking) to 5.4 (distribution services). They note that the estimates are lower than what is usually found for estimates of $\sigma$ for goods sectors, likely because of the higher aggregation level and the lower substitutability of services compared to goods. Christen et al.\@ (2019) use Austrian firm-level financial data from the Bureau van Dijk AMADEUS database. Compared to the other studies, they have the most number of disaggregated services sector after our paper and Gervais and Jensen (2019). The median estimate for these sectors is 3.55 and estimates range from 1.33 (real estate activities) to 4.36 (computer and IT). Blank et al.\@ (2022) rely on the Deutsche Bundesbank for balance sheet information to estimate the elasticity of substitution with the mark-up method. Rather than taking the median ratio across all firms as their estimate, as in Rouzet et al.\@ (2017), Blank et al.\@ (2022) instead add up all firms' sales and divide it by the sum of operating profits in each services sector. This matches the approach taken in this paper since we are restricted to industry-level data from the BEA. The median services elasticity in Blank et al.\@ (2022) is 4.86, ranging from 3.27 (other services, including financial services and insurance) to 6.00 (construction). Gervais and Jensen (2019) rely on the mark-up method to estimate elasticities with U.S. data for both manufacturing and services sectors. Utilizing data from the U.S. Bureau of Economic Analysis, they estimate the trade elasticities with industry data on profit margins for firms operating in the United States. They find that the elasticity for manufacturing industries using this approach is in line with other estimates provided in the literature. For services scectors, they report a median elasticity estimate of 5.98, with a much larger range seen in services sectors than found in manufacturing sectors. Our paper extends their work by using more recent BEA data (2013-2022) for our estimates and by concording the NAICS data to GTAP sectors to get the trade elasticity estimates for our GTAP simulations. In contrast to these above studies, Nakano and Nishimura (2024) estimate their elasticities for services sectors using variation in exchange rates rather than firm-level markups. Nakano and Nishimura (2024) estimates are among the lowest in the studies compared, centering around 1, with some sectors' elasticities less than one. \section{Methodology and Data} Following Gervais and Jensen (2019) and Ahmad and Riker (2019), our estimates of the elasticity of substitution for the services sectors are based on the relationship that exist between the elasticity of substitution and profit margins in a monopolistic competition model of trade. In the model, consumers are assumed to have constant elasticity of substitution (CES) preferences with an elasticity parameter $\sigma_s$ that describes the level of substitutability, or tradability, across the different varieties of the service offered by firms (domestic and foreign) in a given sector.\footnote{The elasticity of substitution parameter should be a positive number greater than one in a model with CES demand.} Services industries $s$ are segmented and behave under a monopolistic competition framework where there are a continuum of homogeneous firms, each producing a unique variety of the service provided. Each firm has a constant marginal cost and sell their service at a marked up price above their marginal cost. Given these assumptions, it is easy to show that each firm's profits $\pi_i$ will be determined by the following rule: \begin{equation} \pi_{i} = \Big(\frac{R_{i}}{\sigma_s}\Big)-F_{i} \end{equation} \noindent where $R_i$ are the revenues generated by the firm and $F_i$ are the firm's fixed costs. Rearranging terms and aggregating by all firms in a sector, the elasticity of substitution is given as: \begin{equation} \sigma_{s} = \frac{Revenues_s}{Gross\_Operating\_Profits_{s}} \end{equation} Here we define $Gross\_Operating\_Profits_s$ in sector $s$ as $\pi_s+F_s$. Following Gervais and Jensen (2019), we estimate the elasticity of substitution for each services industry using data on industry output and gross operating surplus from the Bureau of Economic Analysis (BEA) input-output tables.\footnote{The BEA data series used was "Composition of Gross Output by Industry".} This data is organized at the NAICS 3-digit level and includes roughly 40 services sectors. We use annual industry data from the BEA for the time period 2003-2022. Due to data constraints, we will focus on industry-level data from the BEA rather than firm-level data to estimate trade elasticities for the U.S. services sectors. An advantage of the industry-level data is that it allows us to estimate trade elasticities at the NAICS 3-digit level, resulting in much more disaggregate estimates than what is commonly found in the literature. These NAICS sectors can also be concorded to the GTAP sectors, enabling us to directly estimate the services trade elasticities for our policy simulation in Section \ref{sec:sim}. For each services NAICS sector, the elasticities of substitution were calculated by dividing its industry output with its gross operating surplus on an annual basis. Our preferred measure of the elasticity for a NAICS sector was the median of the yearly estimates over the ten year periods (2003 to 2012 and 2013 to 2022).\footnote{A median was chosen to not be overly affected by outlier observations, as was the case during the height of the COVID-19 pandemic.} A similar approach was taken to estimate the elasticities by GTAP sector once a concordance between the services NAICS codes and GTAP codes had been established.\footnote{See appendix table \ref{tab:concordance} for NAICS-GTAP services concordance.} A custom concordance was constructed by first assigning GTAP codes to ISIC codes using the GTAP-ISIC concordance from the GTAP website.\footnote{The GTAP-ISIC concordance can be found here: \url{https://www.gtap.agecon.purdue.edu/databases/contribute/concordinfo.asp}} Then, ISIC codes were concorded to NAICS 6-digit codes using a custom ISIC-NAICS concordance. Finally, the 6-digit NAICS codes were aggregated up to the 3-digit level and GTAP elasticities estimated.\footnote{Using this method, there are some instances where a 6-digit NAICS component must be reallocated to a different 3-digit NAICS category. For example, NAICS 525 (Funds, Trusts and Other Financial Vehicles) is concorded to GTAP sector OFI (Other Financial Intermediation). However, a component of NAICS 525, NAICS 525110 (Pension Funds), should be reallocated to GTAP sector INS (Insurance). In the elasticity estimates provided in this paper, 6-digit NAICS components were not reallocated to different 3-digit NAICS groupings; the 3-digit NAICS code was mapped to the GTAP sector for which a majority of the 6-digit components were mapped. In future versions of this paper, the 6-digit NAICS components will be reallocated.} \section{Elasticity Estimates} Table \ref{tab:bynaicsgroup} summarizes estimates by broad 2-digit NAICS grouping and illustrates that there is significant heterogeneity by sector. Most of the individual estimates in Table 1 are comparable to what was reported in Gervais and Jensen (2019). We find that the core services sectors that are commonly targeted in FTAs such as wholesale and retail trade, information, finance and insurance, and professional services, have estimates in the middle of the distribution. We note that real estate has the lowest estimated elasticity of 1.98, indicating that foreign firms face significant barriers to entry in this sector. At the other end, services that are traded through the movement of people across borders such as education and health care have higher elasticity estimates of 13.78.\footnote{Since these sectors are also not typically targeted by FTA provisions, we will be excluding them from the GTAP simulations in Section 5.} Lastly, the elasticities of substitution at the more disaggregated NAICS 3-digit sector level are reported in appendix tables \ref{tab:bynaics}. Again, we find considerable heterogeneity across sectors with the median elasticity of substitution at the 3-digit NAICS level estimated at 5.65 and a standard deviation of 5.60. Given the diversity and size of the U.S. service sectors, this is not a surprising result. \begin{table}[htbp] \centering \begin{threeparttable} \caption{Summary of Elasticity Estimates by NAICS Group} \begin{tabular}{p{1.1cm} p{5cm} r r r } \toprule NAICS & Description & Mean $\sigma$ & Median $\sigma$ & Std. Dev. \\ \midrule 23 & Construction & 5.42 & 5.42 & -\\ 42 & Wholesale trade & 4.79 & 4.79 & - \\ 44-45 & Retail trade & 7.49 & 6.00 & 3.85 \\ 48-49 & Transportation & 6.50 & 5.22 & 5.08 \\ 51 & Information & 3.04 & 3.06 & 0.21 \\ 52 & Finance and insurance & 8.27 & 5.45 & 7.72 \\ 53 & Real estate and leasing & 1.98 & 1.98 & 0.42 \\ 54 & Professional services & 5.08 & 5.08 & - \\ 55 & Management of companies & 15.87 & 15.87 & - \\ 56 & Administrative services & 6.61 & 6.88 & 0.74 \\ 61-62 & Education and health care & 13.78 & 10.71 & 7.90 \\ 71-72 & Recreation and food service & 6.31 & 6.29 & 2.83 \\ 81 & Other personal services & 7.11 & 7.11 & - \\ \bottomrule \end{tabular}\label{tab:bynaicsgroup} \multicolumn{3}{l}{{\footnotesize Note: The summary statistics reported in this table are calculated across all three-digit NAICS codes within each NAICS group. The mean $\sigma$ is the mean elasticity estimate across the three-digit NAICS codes within the group. For NAICS groups with only one three-digit code, there is no standard deviation.}} \end{threeparttable} \end{table} A feature of the BEA data is that we can compare the elasticity estimates over the most recent 10 years, with elasticity estimates from the 10 year period prior. To facilitate these comparisons and examine if services tradability has changed over time, Table \ref{tab:bynaics} provides elasticity estimates using data from the latest ten years (2013--2022) with the prior ten years (2003-2012). The industries with the largest decreases in trade elasticity estimates are air transportation (NAICS 481), nursing and residential care facilities (NAICS 623) and general merchandise stores (NAICS 452). Industries with the largest increases in elasticity estimates are warehousing and storage (NAICS 493), social assistance (NAICS 624), and securities, commodity contracts, and investments (NAICS 523). However, for most sectors, the elasticities appear to be relatively stable over time. Estimated elasticities for GTAP services sectors are shown in table \ref{tab:bygtap}, and we continue to find significant heterogeneity across the different GTAP sectors. The median elasticity of substitution at the GTAP sector level is 5.42 and the standard deviation is 3.84. Note that in the standard GTAP model, the elasticity of substitution are assumed to be 3.8 for all services sectors. However, as seen in \ref{tab:bygtap}, the estimated elasticities for services sectors can vary considerably from the default GTAP values when estimated. In the next section, the impact of the new services trade elasticities on model outcomes is illustrated by simulating the implementation of a hypothetical and stylized US-UK free trade agreement using the GTAP model. Table \ref{tab:litreview} compares our elasticity estimates at the NAICS 3-digit level and GTAP sector level with the studies described in section 2. We see that our median estimates are of a similar magnitude to the estimates found in Gervais and Jensen (2019) and Blank et al. (2022). Other studies such as Rouzet et al. (2017) and Nakano and Nishimura (2024), however, have smaller median estimates. The more disaggregated services in our sample (40 NAICS sectors) as well as estimating it at the industry level, rather than at the firm level, could have contributed to our estimates being slightly higher than these studies. \begin{table}[htbp] \centering \begin{threeparttable} \caption{Comparison of Services Trade Elasticity Estimates in the Literature} \begin{tabular}{>{\raggedright\arraybackslash}p{2.3cm} >{\raggedright\arraybackslash}p{3.9cm} >{\raggedright\arraybackslash} p{1.7cm} >{\raggedright\arraybackslash} p{2.3cm} >{\raggedleft\arraybackslash} p{1.85cm} >{\raggedleft\arraybackslash} p{1.7cm}} \toprule Paper & Data & Countries & Sector classification & No. of sectors & Median estimate\\ \midrule Rouzet et al. (2017) & UK Annual Business Survey and Finnish Financial Statements Panel & UK and Finland & OECD STRI & 15 & 2.30 \\ \\ Gervais and Jensen (2019) & U.S. Bureau of Economic Analysis Input-Output Tables & United States & 3-digit NAICS & 40* & 5.98 \\ \\ Christen et al. (2019) & Balance sheet data from the Bureau van Dijk AMADEUS database & Austria & 2-digit NACE & 22 & 3.55 \\ \\ Blank et al. (2022) & Transaction and firm-level information from Deutsche Bundesbank for German firms & Germany & Author grouping & 5 & 4.86 \\ \\ Nakano and Nishimura (2024) & Japan Trade Statistics & Japan & WTO & 8 & 1.04\\ \\ Ahmad and Schreiber (2024) & U.S. Bureau of Economic Analysis Input-Output Tables & United States & 3-digit NAICS & 40 & 5.65 \\ & & & GTAP & 15 & 5.42\\ \bottomrule \end{tabular}\label{tab:litreview} \multicolumn{3}{l}{{\footnotesize Note: All of the studies included in this table use the mark-up method to estimate the elasticity of substitution parameters, except for Nakano and Nishimura (2024) who use variation in exchange rates. \\ * Gervais and Jensen (2019) only reports summary statistics, they do not report the full set of elasticity estimates. They use the same BEA data as this paper and the number of services sectors is roughly 40.}} \end{threeparttable} \end{table} \section{US-UK Services FTA Simulation}\label{sec:sim} Modern trade agreements have increasingly focused on non-tariff measures that affect the ability of firms to trade services across borders, making it even more important to have precise estimates of services elasticities when running policy simulations to determine the overall effects of an agreement. This section illustrates the importance of the elasticity of substitution of services sectors in GTAP by simulating a hypothetical services FTA between the United States and United Kingdom. Using GTAP Model 7 and GTAP database version 11 (2017), the policy experiment assumes a reduction in trade barriers in services sectors between the U.S. and the UK as a result of the trade agreement. The simulation is run twice, once with the default GTAP elasticities in place and again with the new markup-method elasticity estimates, and outcomes are compared across simulations. Table \ref{tab:ntms} lists the reduction in trade barriers, as ad valorem equivalent (AVE), for the core GTAP services sectors as a result of a U.S.-UK agreement on services trade liberalization.\footnote{In practice, services provisions in trade agreements are likely to affect both a firm's fixed costs as well as its variable costs. However, we follow the standard GTAP modeling assumptions here and treat the removal of trade barriers as a reduction in AVEs in the policy simulation.} The AVEs are based on estimates from a structural gravity model used in the U.S. International Trade Commission's 2021 report on the Economic Impact of Trade Agreements Implemented under Trade Authorities Procedures \cite{usitc}. The estimates from the gravity model in that study were designed to capture the incremental impact of a trade agreement with services provisions on cross-border trade in services at the GTAP sector level. The analysis measures an average effect of all trade agreements (U.S. and non-U.S.) with services provisions, assuming that countries have the same average effect on barriers to services trade. The core tradable services sectors were restricted to the following GTAP sectors: information and communication (ins), construction (cns), insurance (ins), other business services (obs), other financial intermediation (ofi), and wholesale and retail trade (trd). These core services sectors were considered to be the most tradable and the most impacted by FTA provisions. Other GTAP services sectors that are not typically a focus of FTAs such as travel, air transport, health and education services, and other governmental service were not impacted by the policy shocks. \begin{table}[htbp] \centering \begin{threeparttable} \caption{Gravity Estimates of the Average Impact of an FTA with Services Provisions on Trade Barriers} \begin{tabular}{p{1.4cm} p{6.5cm} >{\raggedleft\arraybackslash} p{2cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm} } \toprule GTAP Sector & Description & AVE & Default EOS & \cellcolor{green!40}New EOS \\ \midrule cmn & Information and Communication & -18.37 & 3.80 & \cellcolor{green!20}2.92 \\ ins & Insurance & -3.94 & 3.80 & \cellcolor{green!20}4.13 \\ obs & Other Business Services & -11.69 & 3.80 & \cellcolor{green!20}4.13 \\ ofi & Other Financial Intermediation & -9.63 & 3.80 & \cellcolor{green!20}5.30 \\ trd & Wholesale and Retail Trade & -5.98 & 3.80 & \cellcolor{green!20}5.19 \\ \bottomrule \end{tabular}\label{tab:ntms} \multicolumn{2}{l}{{\footnotesize Note: These AVE gravity estimates are from the U.S. International Trade Commission's 2021 report on the Economic Impact of Trade Agreements Implemented under Trade Authorities Procedures. (USITC, 2021)}} \end{threeparttable} \end{table} The 2021 ITC report had found a statistically significant reduction in trade barriers for most of the core GTAP services sectors, including cmn, ins, obs, ofi, and trd. Only the construction sector was not found to have a statistically significant effect of agreements on trade, likely because a commercial presence abroad is typically needed to provide these services in foreign markets and the data on cross-border services trade do not include such sales. The AVE estimates in table \ref{tab:ntms} illustrate that the effect of a trade agreement is likely to be heterogeneous by service sector. The information and communication sector faced a much larger barrier to cross-border trade, and thus benefits more from an FTA compared to the insurance sector and the retail trade sector. The policy simulations were conducted using the GTAP database version 11 (2017) and GTAP model 7 with 65 sectors, 12 aggregated regions, and 5 factors of production. We rely on the standard GTAP model that assumes firms operate under perfect competition.\footnote{A future extension to this paper would be to use a monopolistic competition CGE model instead so that the underlying assumptions in the parameter estimation match the assumptions in the simulation model. The estimated price-cost margins from the markup method could be used in the CGE model so that data sources are consistent.} The AVE estimates described above were inserted into GTAP as a shock to AMS, the import-augmenting technology change variable. AMS reduces the effective price of services imports, capturing efficiency-enhancing measures from the U.S.-UK services FTA, such as reduced regulations on e-commerce and digital transactions. The elasticity of substitution parameters for services sectors were changed to a non-nested structure to be comparable to the new markup estimates. The simulations were run first with the default elasticities, and again with the markup elasticities. No changes were made to goods sectors, only the core services sectors with statistically significant AVE estimates were shocked. Comparing elasticity estimates listed in table \ref{tab:ntms}, the new elasticities increased for all sectors except for cmn where the new markup elasticity is lower than the default GTAP elasticity. Because of this, we expect to see larger changes in US-UK trade with the new markup elasticities for all sectors except cmn, where we expect to see a smaller change in exports. Sectors ofi and trd see the largest increase in the elasticity of substitution, so we should see the most effect from liberalization in these two sectors. To better understand the simulation results, we first run a one-way liberalization where the UK is the liberalizing country. Economic effects at the sector level and macro level are shown in tables \ref{tab:onewaytrade} and \ref{tab:onewaymacro}. Unsurprisingly, the effect of a services liberalization on U.S. exports to liberalizing UK become larger with the new elasticity estimates for all sectors except cmn, with ofi and trd experiencing the largest increase. On the macro side, the new elasticity estimates lead to larger positive welfare effects for the U.S. who benefits from a liberalization with their trading partner and smaller welfare effects for the UK, due to a bigger terms of trade effect. \begin{table}[htbp] \centering \begin{threeparttable} \caption{One-Way Services Liberalization: Change in US and UK Exports} \begin{tabular}{p{1.4cm} p{6.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}} \toprule & & \multicolumn{2}{c}{\textbf{Default EOS}} & \multicolumn{2}{c}{\cellcolor{green!40}\textbf{New EOS}} \\ GTAP Sector & Description & US \rightarrow UK & UK \rightarrow US & \cellcolor{green!40}US \rightarrow UK & \cellcolor{green!40}UK \rightarrow US \\ \midrule cmn & Information and Communication & 49.77 & 1.09 & \cellcolor{green!20}33.71 & \cellcolor{green!20}1.01 \\ ins & Insurance & 9.93 & 1.08 & \cellcolor{green!20}10.88 & \cellcolor{green!20}1.42 \\ obs & Other Business Services & 31.09 & 0.91 & \cellcolor{green!20}42.40 & \cellcolor{green!20}1.44 \\ ofi & Other Financial Intermediation & 24.88 & 1.08 & \cellcolor{green!20}38.14 & \cellcolor{green!20}1.84 \\ trd & Wholesale and Retail Trade & 15.84 & 0.89 & \cellcolor{green!20}23.51 & \cellcolor{green!20}1.53 \\ \bottomrule \end{tabular}\label{tab:onewaytrade} \end{threeparttable} \end{table} \begin{table}[htbp] \centering \begin{threeparttable} \caption{One-Way Services Liberalization: Macro Effects} \begin{tabular}{p{4cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}} \toprule & \multicolumn{2}{c}{\textbf{Default EOS}} & \multicolumn{2}{c}{\cellcolor{green!40}\textbf{New EOS}} \\ Variable & US & UK & \cellcolor{green!40}US & \cellcolor{green!40}UK \\ \midrule QGDP (\% change) & 0.0007 & 0.0771 & \cellcolor{green!20}0.0008 & \cellcolor{green!20}0.0738 \\ PGDP (\% change) & 0.0528 & -0.2248 & \cellcolor{green!20} 0.0648 & \cellcolor{green!20}-0.2770 \\ EV (\$ mil) & 1,586.93 & 840.41 & \cellcolor{green!20}1,931.58 & \cellcolor{green!20}448.11 \\ \bottomrule \end{tabular}\label{tab:onewaymacro} \end{threeparttable} \end{table} Next, the two-way services liberalization is shown in tables \ref{tab:twowaytrade} and \ref{tab:twowaymacro}. Comparing results across default and new EOS columns, we continue to see the same trend that sectors with bigger elasticities have larger percent changes in trade flows and sectors with smaller elasticities have smaller changes in trade flows. Because there are two policy changes--a reduction in barriers to services trade at the UK border and at the U.S. border--it is difficult to isolate the impacts on macro variables such as GDP and equivalent variation. The impact of heterogeneous elasticities on macro outcomes depends on the size of trade flows subject to the change in elasticity and the ability to shift production factors. We see only small changes in table \ref{tab:twowaymacro} across the simulations with default and new services elasticities. \begin{table}[htbp] \centering \begin{threeparttable} \caption{Two-Way Services Liberalization: Change in US and UK Exports} \begin{tabular}{p{1.4cm} p{6.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}} \toprule & & \multicolumn{2}{c}{\textbf{Default EOS}} & \multicolumn{2}{c}{\cellcolor{green!40}\textbf{New EOS}} \\ GTAP Sector & Description & US \rightarrow UK & UK \rightarrow US & \cellcolor{green!40}US \rightarrow UK & \cellcolor{green!40}UK \rightarrow US \\ \midrule cmn & Information and Communication & 51.63 & 50.69 & \cellcolor{green!20}35.39 & \cellcolor{green!20}34.62 \\ ins & Insurance & 11.69 & 10.30 & \cellcolor{green!20}13.04 & \cellcolor{green!20}11.53 \\ obs & Other Business Services & 32.73 & 31.69 & \cellcolor{green!20}44.71 & \cellcolor{green!20}43.41 \\ ofi & Other Financial Intermediation & 26.47 & 26.07 & \cellcolor{green!20}40.68 & \cellcolor{green!20}40.17 \\ trd & Wholesale and Retail Trade & 17.46 & 16.00 & \cellcolor{green!20}26.02 & \cellcolor{green!20}24.06 \\ \bottomrule \end{tabular}\label{tab:twowaytrade} \end{threeparttable} \end{table} \begin{table}[htbp] \centering \begin{threeparttable} \caption{Two-Way Services Liberalization: Macro Effects} \begin{tabular}{p{4cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}} \toprule & \multicolumn{2}{c}{\textbf{Default EOS}} & \multicolumn{2}{c}{\cellcolor{green!40}\textbf{New EOS}} \\ Variable & US & UK & \cellcolor{green!40}US & \cellcolor{green!40}UK \\ \midrule QGDP (\% change) & 0.0112 & 0.1010 & \cellcolor{green!20}0.0112 & \cellcolor{green!20}0.1017 \\ PGDP (\% change) & -0.0023 & 0.1868 & \cellcolor{green!20} -0.0034 & \cellcolor{green!20}0.1853 \\ EV (\$ mil) & 2,338.57 & 3,940.34 & \cellcolor{green!20}2,299.49 & \cellcolor{green!20}3,946.85 \\ \bottomrule \end{tabular}\label{tab:twowaymacro} \end{threeparttable} \end{table} \subsubsection*{Sensitivity analysis using elasticity confidence intervals} As described earlier, we used the median of the yearly elasticity estimates from 2013--22 as the markup elasticities reported in table \ref{tab:bynaics} and \ref{tab:bygtap}. In this case, it is natural to question whether there is significant variation in the elasticity estimates across years that a median estimate may not capture. To test whether yearly variation in markups would have an impact on our simulation results, we run the one-way liberalization simulation again with a 95\% confidence interval on the elasticity of substitution estimates instead of using the median estimate.\footnote{We assume that the elasticities are not correlated, so the confidence intervals are calculated separately.} The confidence interval is calculated using the standard deviation across the yearly elasticity estimates for each sector. Table \ref{tab:confint} reports median, mean, standard deviation, and 95\% confidence interval values for the core services sectors. The 95\% confidence intervals reported in the table are narrow, indicating little variation over time. Simulation results with the low and high ends of the 95\% confidence intervals are graphed in figure \ref{fig:ciresults}. \section{Conclusion} This paper presents a set of elasticity of substitution estimates at both the NAICS 3-digit level and GTAP sector level, estimated using the markup method arising from a monopolistic competition model of trade. The median estimate is 5.65 at the NAICS 3-digit level and 5.42 at the more aggregated GTAP sector level. The estimates show considerable heterogeneity across sectors, differing from the standard GTAP assumption of services sectors having the same value. In a hypothetical simulation of a new U.S.-UK services agreement, we show that trade elasticities for services sectors can significantly impact trade flows and macroeconomic outcomes. Future extensions to this paper include estimating the elasticity of substitution for services sectors in other economies, including the EU, to compare tradability across countries. Additionally, a CGE model with a monopolistic competition framework could be used in place of this perfect competition model to better align with the assumptions used to estimate the trade elasticity. A CGE model with increasing returns to scale would also be able to account for the effects of trade provisions on the fixed costs of supplying services across borders. \begin{table}[htbp] \centering \begin{threeparttable} \caption{Elasticity Confidence Intervals} \begin{tabular}{p{2cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{1.5cm}>{\raggedleft\arraybackslash} p{2cm}>{\raggedleft\arraybackslash} p{2cm}} \toprule GTAP & Median & Mean & SD & CI: low & CI: high \\ \midrule CMN & 2.91& 2.94& 0.04& 2.85& 3.04 \\ INS & 4.13& 4.31& 0.20& 3.85& 4.78 \\ OBS & 4.83& 4.87& 0.08& 4.69& 5.05 \\ OFI & 5.30& 5.28& 0.07& 5.12& 5.43 \\ TRD & 5.19& 5.18& 0.11& 4.93& 5.43 \\ \bottomrule \end{tabular}\label{tab:confint} \end{threeparttable} \end{table} \begin{figure}[htbp] \centering \caption{Change in U.S. exports to UK, 95\% confidence interval} \includegraphics[scale=1.25]{Confidence intervals.png} \caption*{\footnotesize}\label{fig:ciresults} \end{figure} %Alt text: This graph shows simulations results of the change in U.S. exports to the UK after a UK liberalization. Each services sector has three bars, one generated using the low end of the 95% confidence interval, one generated using the mean estimate, and one generated using the high-end estimate. \pagebreak \newpage \bibliographystyle{dcu} \bibliography{biblio} \begin{table}[htbp] \centering \begin{threeparttable} \caption{NAICS Elasticity Estimates} \begin{tabular}{p{1.1cm} p{9cm} r r } NAICS & Description & EOS (2003--12) & EOS (2013--22) \\ \toprule 230 & Construction & 5.730 & 5.418 \\ 420 & Wholesale trade & 4.921 & 4.787 \\ 441 & Motor vehicle and parts dealers & 7.056 & 5.208 \\ 445 & Food and beverage stores & 6.208 & 6.793 \\ 452 & General merchandise stores & 15.267 & 13.123 \\ 4A0 & Other retail & 5.796 & 4.827 \\ 481 & Air transportation & 9.630 & 5.534 \\ 482 & Rail transportation & 4.555 & 3.662 \\ 483 & Water transportation & 6.036 & 7.264 \\ 484 & Truck transportation & 6.129 & 4.904 \\ 485 & Transit and ground passenger transportation & 3.418 & 3.625 \\ 486 & Pipeline transportation & 3.777 & 1.892 \\ 487 & Other transportation and support activities & 6.352 & 6.822 \\ 493 & Warehousing and storage & 6.737 & 18.288 \\ 511 & Publishing industries, except internet & 3.097 & 2.931 \\ 512 & Motion picture and sound recording industries & 2.875 & 3.180 \\ 513 & Broadcasting and telecommunications & 3.183 & 2.800 \\ 514 & Data processing and other information services & 2.694 & 3.261 \\ 521 & Federal Reserve banks, credit intermediation & 3.429 & 2.631 \\ 523 & Securities, commodity contracts, and investments & 14.795 & 19.569 \\ 524 & Insurance carriers and related activities & 4.165 & 4.128 \\ 525 & Funds, trusts, and other financial vehicles & 5.582 & 6.761 \\ 531 & Real estate & 1.669 & 1.684 \\ 532 & Rental services and lessors of intangible assets & 2.271 & 2.272 \\ 541 & Professional, scientific, and technical services & 4.759 & 5.083 \\ 550 & Management of companies and enterprises & 14.669 & 15.865 \\ 560 & Administrative and waste management services & 5.986 & 6.879 \\ 561 & Administrative and support services & 6.017 & 7.178 \\ 562 & Waste management and remediation services & 5.274 & 5.772 \\ 610 & Educational services & 8.269 & 8.150 \\ 620 & Health care and social assistance & 9.802 & 9.689 \\ 621 & Ambulatory health care services & 7.137 & 6.872 \\ 622 & Hospitals & 13.094 & 11.731 \\ 623 & Nursing and residential care facilities & 32.650 & 27.414 \\ 624 & Social assistance & 10.266 & 18.839 \\ 711 & Performing arts and related activities & 3.747 & 3.279 \\ 713 & Amusements, gambling, and recreation industries & 7.480 & 7.916 \\ 721 & Accommodation & 5.200 & 4.661 \\ 722 & Food services and drinking places & 9.006 & 9.388 \\ 810 & Other services, except government & 6.666 & 7.106 \\ \bottomrule \end{tabular}\label{tab:bynaics} \end{threeparttable} \end{table} \begin{table}[htbp] \centering \begin{threeparttable} \caption{GTAP Elasticity Estimates} \begin{tabular}{p{1.1cm} p{9cm} r r} GTAP & Description & EOS (2003--12) & EOS (2013--22) \\ \midrule afs & Accommodation, food and service activities & 7.756 & 7.371 \\ atp & Air transport & 9.630 & 5.534 \\ cmn* & Information and communication & 3.096 & 2.914 \\ cns* & Construction & 5.730 & 5.418 \\ edu & Education & 8.269 & 8.150 \\ hht & Human health and social work & 9.802 & 9.691 \\ ins* & Insurance (formerly isr) & 4.165 & 4.128 \\ obs* & Other business services nec & 4.450 & 4.827 \\ ofi* & Other financial intermediation & 6.343 & 5.299 \\ otp & Land transport and transport via pipelines & 5.353 & 4.696 \\ ros & Recreation and other services & 5.862 & 5.843 \\ rsa & Real estate activities & 1.669 & 1.684 \\ trd* & Wholesale and retail trade; repair of motor vehicles & 5.752 & 5.194 \\ whs & Warehousing and support activities & 6.737 & 18.28 \\ wtp & Water transport & 6.036 & 7.264 \\ \bottomrule \end{tabular}\label{tab:bygtap} \multicolumn{2}{l}{{\footnotesize *Core tradable service.}} \end{threeparttable} \end{table} \begin{table}[htbp] \centering \begin{threeparttable} \caption{GTAP-NAICS Services Concordance} \begin{tabular}{p{1.1cm} p{9cm} p{4cm}} GTAP & Description & NAICS \\ \midrule afs & Accommodation, food and service activities & 721, 722 \\ atp & Air transport & 481\\ cmn* & Information and communication & 51\\ cns* & Construction & 23\\ edu & Education & 61\\ hht & Human health and social work & 621, 622, 623, 624\\ ins* & Insurance & 524\\ obs* & Other business services & 532, 533, 541, 561\\ ofi* & Other financial intermediation & 521, 522, 523, 525, 55\\ otp & Land transport and transport via pipelines & 482, 484, 485, 486, 487\\ ros & Recreation and other services & 711, 713, 81\\ rsa & Real estate activities & 531\\ trd* & Wholesale and retail trade & 42, 44, 45\\ whs & Warehousing and support activities & 493\\ wtp & Water transport & 483\\ \bottomrule \end{tabular}\label{tab:concordance} \multicolumn{2}{l}{{\footnotesize *Core tradable service.}} \end{threeparttable} \end{table} \end{document}