The Treasury Macroeconometric Model of Australia: Modelling approach

Bullen, Jared et al. Working Paper The Treasury Macroeconometric Model of Australia: Modelling approach Treasury Working Paper, No. 2021-09 Provided in Cooperation with: The Treasury, The Australian Government Suggested Citation: Bullen, Jared et al. (2021) : The Treasury Macroeconometric Model of Australia: Modelling approach, Treasury Working Paper, No. 2021-09, The Australian Government, The Treasury, Canberra This Version is available at: https://hdl.handle.net/10419/251333 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/au/legalcode The Treasury Macroeconometric Model of Australia: Modelling Approach Jared Bullen, Benjamin Conigrave, Adam Elderfield, Cecilia Karmel, Larissa Lucas, Chris Murphy, Heather Ruberl, Nicholas Stoney and Hui Yao1 Treasury Paper2 2021-09 Date created: September 2021 Date modified: September 2021 1 Macroeconomic Conditions Division, The Treasury, Langton Crescent, Parkes ACT 2600, Australia. Correspondence: Nicholas Stoney ([email protected]) and Jared Bullen ([email protected]ov.au). 2 The views expressed in this paper are those of the authors and do not necessarily reflect those of The Australian Treasury or the Australian Government. © Commonwealth of Australia 2021 This publication is available for your use under a Creative Commons BY Attribution 3.0 Australia licence, with the exception of the Commonwealth Coat of Arms, the Treasury logo, photographs, images, signatures and where otherwise stated. The full licence terms are available from http://creativecommons.org/licenses/by/3.0/au/legalcode. Use of Treasury material under a Creative Commons BY Attribution 3.0 Australia licence requires you to attribute the work (but not in any way that suggests that the Treasury endorses you or your use of the work). 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Other uses Enquiries regarding this licence and any other use of this document are welcome at: Manager Media Unit The Treasury Langton Crescent Parkes ACT 2600 Email: [email protected]ov.au iii The Treasury Macroeconometric Model of Australia: Modelling Approach. Jared Bullen, Benjamin Conigrave, Adam Elderfield, Cecilia Karmel, Larissa Lucas, Chris Murphy, Heather Ruberl, Nicholas Stoney and Hui Yao 2021-09 3 September 2021 Abstract Economy-wide models are an important tool used by fiscal authorities and central banks to support the provision of sound assessment of the economic outlook. The Treasury Macroeconometric Model of Australia (“EMMA”) is a framework to support macroeconomic forecasting, and counterfactual policy and scenario analysis at the Treasury. It has been developed, tested and used within Treasury since 2018. EMMA plays a central role in preparing the economic estimates which underpin Australian Government fiscal projections and scenario analysis which is used to assess the risks about those estimates. Macroeconomic forecasts and the scenario analysis from the model are also used to inform Treasury’s advice across a broad spectrum of policy areas to assist with both policy formulation and policy costing. The model is also used to develop capability in applied small open economy macroeconomics. The focus of this paper is to outline the model’s structure and describe its place within the macroeconomic modelling literature. Further details on the model’s equations, empirical properties and dynamics will be published over time. A macroeconomic model is never finished. The model will continue to be developed to ensure that it remains a fit for purpose tool to analyse the evolving economic and policy environment. This paper outlines the first version of the model. JEL Classification Numbers: C32, C53, E10, E17, E27, E37, E47 Keywords: Australian economy, macroeconomic model. Nick Stoney Macroeconomic Division Macroeconometric Modelling Unit The Treasury Langton Crescent Parkes ACT 2600 Jared Bullen Macroeconomic Division Macroeconometric Modelling Unit The Treasury Langton Crescent Parkes ACT 2600 iv Acknowledgements The Treasury Macroeconometric Model of Australia has been developed in Treasury by Jared Bullen, Benjamin Conigrave, Adam Elderfield, Cecilia Karmel, Larissa Lucas, Heather Ruberl, Nicholas Stoney and Hui Yao. The development of the model was guided by macroeconomic modelling consultants Professor Mardi Dungey and Chris Murphy in advisory roles. Professor Mardi Dungey was engaged as a macroeconomic modelling consultant from the start of the project. Mardi sadly passed away in January 2019. Mardi has worked closely with Treasury over many years and was a friend and a mentor to many within the Department. Mardi always showed great enthusiasm and intellectual rigour to problems, mentored and supported staff, and promoted top research, especially in empirical economics and finance. Mardi provided econometric training and used her expertise to assist in the development of the econometric framework of the model, including on the specification of key equations in the model. Chris Murphy was also engaged as a macroeconomic modelling consultant for the project. Drawing on his extensive experience in macroeconomic modelling, Chris has made a major contribution to the development of the model in an advisory role, in particular in the development of the business and financial sectors of the model. He has also had the leading role in writing this paper. We thank Professor Adrian Pagan and Professor Warwick McKibbin for their expert guidance through discussions during the model’s early development. We also thank the macroeconomic modelling team at the Reserve Bank of Australia, and in particular, Daniel Rees, for sharing an early version of their macroeconometric model, MARTIN, and their experiences in building that model. We would particularly like to thank Nigel Ray, Meghan Quinn and Angelia Grant for their support and guidance in the design of the model, along with the Macroeconometric Model Steering Committee (Nigel Ray, Meghan Quinn, Angelia Grant, Michael Kouparitsas, Jacqui Jones, Alex Heath and Daniel Rees) that oversaw the project to build the model. We also thank Treasury’s Expert Panel on Macroeconomic Modelling (Professor Heather Anderson, Dr Alex Heath, Dr Wendy Edelberg, Professor Warwick McKibbin, Professor James Morley, Professor Bruce Preston, Professor Kalvinder Shields, Dr Stephen Murchison, Dr Tim Robinson, Dr John McDermott and Associate Professor Chung Tran) for their guidance and continued and patient engagement with the project. And, we thank Peter Downes for his advice and assistance during the model’s early development. The macroeconometric model continues to be used and developed by the macroeconometric modelling unit in Treasury comprising Jared Bullen, Adam Elderfield, Hui Yao, Adam Hamilton, Duncan White and Jessica Xu. The views expressed in this paper are those of the authors and do not necessarily reflect those of The Australian Treasury or the Australian Government. Any errors are our own. 1 CONTENTS ABSTRACT ................................................................................................................................... III ACKNOWLEDGEMENTS ............................................................................................................. IV 1. INTRODUCTION ...................................................................................................................... 2 Role of the macroeconometric model ..................................................................................................... 2 History of macroeconometric models in Treasury ................................................................................... 4 Outline of the paper ................................................................................................................................. 4 2. GENERAL DESIGN ................................................................................................................. 6 Type of Model ......................................................................................................................................... 6 Economic Theory .................................................................................................................................... 8 Agent Expectations ................................................................................................................................. 9 Dynamics ................................................................................................................................................ 9 Estimation ............................................................................................................................................. 11 3. APPROACH TO HOUSEHOLDS .......................................................................................... 12 Labour supply ........................................................................................................................................ 12 Aggregate consumption ........................................................................................................................ 12 Consumer demand ................................................................................................................................ 16 4. APPROACH TO BUSINESSES ............................................................................................. 17 Production and trade technology .......................................................................................................... 17 Convergence to equilibrium .................................................................................................................. 20 Business Investment ............................................................................................................................. 22 Housing Investment .............................................................................................................................. 24 Sticky vs flexible prices ......................................................................................................................... 25 Price of local sales ................................................................................................................................ 26 Hours worked ........................................................................................................................................ 28 Import demand and export supply ......................................................................................................... 29 Inventory investment ............................................................................................................................. 30 5. APPROACH TO FOREIGN SECTOR ................................................................................... 31 6. APPROACH TO GOVERNMENT .......................................................................................... 32 Government budget .............................................................................................................................. 32 Monetary policy ..................................................................................................................................... 34 7. APPROACH TO MARKETS .................................................................................................. 36 Product markets .................................................................................................................................... 36 Labour market ....................................................................................................................................... 37 Financial markets .................................................................................................................................. 38 Flow of funds ......................................................................................................................................... 39 8. STEADY STATE .................................................................................................................... 41 Steady state growth .............................................................................................................................. 41 Steady state structure ........................................................................................................................... 43 9. CONCLUSION........................................................................................................................ 46 APPENDIX A: KEY EQUATIONS ............................................................................................... 50 APPENDIX B: DERIVATION OF BUSINESS INVESTMENT EQUATION ................................ 55 Theory equation .................................................................................................................................... 55 Final equation ........................................................................................................................................ 58 APPENDIX C: PRODUCTIVITY .................................................................................................. 60 APPENDIX D: BUSINESS SECTOR EQUILIBRIUM EQUATIONS ........................................... 64 The Treasury Macroeconometric Model of Australia - Modelling approach 2 1. Introduction The Treasury Macroeconometric Model of Australia (“EMMA”) is a framework to support macroeconomic forecasting, and counterfactual policy and economic scenario analysis at the Treasury. EMMA plays a central role in preparing the economic estimates which underpin Australian Government fiscal projections. Macroeconomic forecasts and scenario analysis from the model are also used to inform and complement Treasury’s advice across a broad spectrum of policy formulation and costings. The model is also used to develop capability in applied small open economy macroeconomics. EMMA is part of a suite of models developed, maintained and used by the Treasury for assessing the economic outlook and analysing the effects of policy. In addition to EMMA, the Treasury has developed two macroeconomic models used specifically for counterfactual policy analysis — an overlapping generations model (“OLGA”) used primarily for fiscal policy analysis and the Treasury Industry Model (“TIM”) used for analysis that requires significant industry-level detail (see Box 1). These models have different advantages, but they have been designed to complement each other. At the Treasury, insights from different models and non-modelling approaches are combined to produce economic forecasts and assessments of the effects of specific policies. Role of the macroeconometric model The fiscal aggregates in the Budget are underpinned by forecasts of economic activity over the forward estimates and projections over the medium term. In the forecasts for the Budget year and subsequent two financial years, greater emphasis is placed on detailed sectoral forecasts of the expenditure components of economic activity. Over this period, EMMA complements these detailed sectoral forecasts by aiding analysis of inter-connections between sectors of the economy. The Treasury Macroeconometric Model of Australia - Modelling approach 3 Chart 1: Closure of the output gap in the 2020-21 Budget Source: Treasury. Beyond these detailed forecast years, estimates are constructed based on expectations for the level of potential output and modelling of the path by which output converges back to this potential level (Chart 1). Potential GDP is estimated within the macroeconometric model using exogenous inputs based on an analysis of trends for population, productivity, and participation. As spare capacity in the economy is absorbed over time (that is, the output gap closes), real GDP converges towards its potential level and the unemployment rate converges towards the estimate of the non-accelerating inflation rate of unemployment (NAIRU). On the nominal side, key non-rural commodity export prices are projected based on cost-curve analysis. Domestic prices return over time to the mid-point of the Reserve Bank of Australia’s (RBA) inflation target band. Over this period, EMMA plays a central role in informing the path that output takes to return to its potential level and domestic price inflation takes to return to the mid-point of the RBA’s inflation target band. The model is also used for sensitivity and scenario analysis, for example, scenarios modelled each year in the Budget Papers. This analysis typically involves changing one or more of the exogenous variables in the model such as mining commodity prices, trend productivity or global growth. The model is also used for evaluating alternative macroeconomic policies. EMMA incorporates a range of adjustment costs and frictions, which makes it well suited to analysing the short-run dynamic response of the economy to a shock or adjustment to policy settings. The model is therefore used to help to assess the short-run implications of fiscal policy. These dual functions require striking a balance between the data consistency central to forecasting and the theory consistency important for projections and scenario analysis. In addition, the macro focus means that more attention needs to be paid to macro interactions than to industry, household or regional disaggregation. 440 460 480 500 520 540 560 440 460 480 500 520 540 560 Jun-18 Jun-19 Jun-20 Jun-21 Jun-22 Jun-23 Jun-24 $billion$billion 2020-21 Budget -Potential output 2020-21 Budget -Forecasts Forecasts The Treasury Macroeconometric Model of Australia - Modelling approach 4 History of macroeconometric models in Treasury Treasury has a long history in developing and maintaining macroeconomic models of the Australian economy (Pagan, 2019).3 Treasury has maintained a macroeconometric model since the 1970s. The first Treasury model, constructed in 1970, in conjunction with the Commonwealth Bureau of Census and Statistics (the forerunner of the Australian Bureau of Statistics), was the National Income Forecasting (NIF) model presented in Higgins (1970). The NIF model went through a considerable evolution, up to NIF-10, before a revamp as NIF-88; see Higgins and Fitzgerald (1973), Treasury (1981, 1984), and Simes and Horn (1988). NIF-88 was a medium-sized model, with 97 behavioural equations. In 1991, the Treasury Macroeconomic Model (TRYM) replaced the NIF model (see Taplin et al., 1993). TRYM was smaller model (25 estimated behavioural equations), with more emphasis placed on the theoretical basis for equations and their steady-state properties. Most equations were specified in an error correction model format which made a clear distinction between shortand long-run properties (Hawkins, 2005). TRYM was used as a compliment to the National Accounts Forecasting Framework (NAFF), a spreadsheet system that built up forecasts of GDP from the components of the expenditure measure of GDP.4 By the late 2000s, the model required redevelopment and gradually fell out use in the department. The 2017 modelling review (Murphy, 2017) endorsed the recommendation of previous forecasting reviews that an economy-wide forecasting model should be developed and embedded in the wider forecasting process, and “that the new model be a macro-econometric model, combining strong short-term empirics with well-defined long-run properties.” In response, the Treasury has built and tested EMMA alongside existing forecasting frameworks over a period of almost two years, principally 2018 and 2019, engaging regularly with their Expert Panel on Macroeconomic Modelling, the RBA, Professor Mardi Dungey and Chris Murphy. The model has been influenced by other models of the Australian economy, principally the model described in Murphy (2020), TRYM, and MARTIN, the RBA forecasting model (Ballantyne et. al. 2020) and also FRB/US, the US Federal Reserve forecasting model (Laforte, 2018). Beyond these general influences, the details of EMMA have been shaped by Treasury’s in-house research and Treasury’s own specific requirements for economic forecasting and scenario analysis. Outline of the paper This paper explains the general nature of EMMA by referring to just 20 key equations. The focus of this paper is to outline the model’s structure and describe its place within the macroeconomic modelling literature. Further details on the model’s equations, empirical properties and dynamics will be published over time. The paper begins by discussing the general design of EMMA. This includes the choice of type of macro model and the approaches to economic theory, expectations, dynamics and estimation. It then considers the behaviour of each category of economic agent. Household, business, foreign and 3 Pagan (2019) describes the history of major macroeconometric models in Australia, with a particular focus on models constructed in Treasury and the Reserve Bank of Australia. 4 Forecasts for the expenditure measures of GDP draw upon structural econometrically estimated single equations, leading indicators, business liaison insights and expert judgement. National account identities are preserved within the spreadsheet, and consistency between forecast elements is achieved by iteration between sector specialists. The Treasury Macroeconometric Model of Australia - Modelling approach 11 Estimation The emphasis on data consistency for forecasting is also seen in the approach taken to estimation. The behavioural equations in the model are estimated using quarterly data extending as far back as 1980. However, for some equations shorter estimation periods are used to avoid suspected structural changes in the 1980s or 1990s. The behavioural equations are estimated using single equation regressions estimated through maximum likelihood. This approach places more weight on the data than imposing values on behavioural parameters or using Bayesian estimation with informative priors. Data consistency is a reason that single equation estimation is used in preference to systems estimation. However, single equation estimation risks over-specifying model dynamics, for instance with correlations between macroeconomic variables captured both in the single equation and through the model’s dynamic solution. To reduce this risk, as discussed above, parsimony in the inclusion of dynamic terms has been prioritised over maximising model fit in the single equation estimation. An alternative approach to address this issue is system estimation. The much larger number of parameters being estimated at the same time under systems estimation means more reliance needs to be placed on imposed values or Bayesian estimation. Fukač and Pagan (2010) show how Bayesian full information, a popular estimator of DSGE models, can lead researchers to unknowingly adopt parameter values that lie outside of confidence intervals that would be generated if Bayesian priors were not used. The Treasury Macroeconometric Model of Australia - Modelling approach 12 3. Approach to households As noted above, household decisions about labour supply, aggregate consumption and consumer demand are modelled independently. The approach to these household decisions is discussed in turn. Labour supply EMMA models labour input in total hours worked. Thus, labour input can vary both at the extensive margin (heads) and the intensive margin (average hours worked). In modelling labour supply, the labour force participation rate equation is formulated on a heads basis. There is no supply equation for average hours worked. Rather, average hours are assumed to be determined by demand on an industry-by-industry basis, as discussed under the approach to businesses. The modelling of the labour force participation rate begins with a trend labour force participation rate. This trend rate is determined outside of the model by aggregating trend participation rates for different cohorts. The methodology for modelling the trend labour force participation rate is outlined in Gustafsson (2021). EMMA then models, at the aggregate level, cyclical variations in the participation rate around this trend, based on cyclical variations in employment reflecting an encouraged worker effect. Equation 1: Labour force participation rate (cyclical component) ∆log(𝜌𝜌𝑡𝑡)=𝛽𝛽1[log(𝜌𝜌𝑡𝑡−1)−log(𝜌𝜌𝑡𝑡−1 ∗)] +𝛽𝛽2�log �𝑁𝑁𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡�−log �𝑁𝑁𝑡𝑡∗ 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡∗�� +𝛽𝛽3∆log �𝑁𝑁𝑡𝑡−1 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡−1� (1) Where: 𝜌𝜌𝑡𝑡 is the participation rate, 𝑁𝑁𝑡𝑡 is heads employment and 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡 is population. Thus, under this approach, the participation rate is affected by demographics, social changes captured within the trend labour force participation rate model, and the encouraged worker effect. During the projection period it is not affected by real after-tax wages, so EMMA is not designed for assessing how a change in the tax burden on labour may influence labour supply. Aggregate consumption Household consumption (𝐶𝐶) is modelled using a modern, empirical version of the Ando-Modigliani (A-M) consumption equation adapted from Aron et al. (2012). The framework is relatively undemanding in the sophistication required of households (Aron et al. (2012)). That is, households are assumed to have only a basic understanding of a life-cycle budget constraint, in contrast to the assumed ‘well-informed households’ of alternative models of household consumption – see below. The A-M consumption function fits the data reasonably well, allows a role for counter-cyclical fiscal policy and has desirable long-run properties, in particular it is consistent with long run balanced growth in the model, which are important for EMMA’s forecasting and policy analysis purposes. In the model, household decision-making is inconsistent with Ricardian equivalence as households are assumed to have static expectations. Hence, the model displays standard short-run Keynesian The Treasury Macroeconometric Model of Australia - Modelling approach 13 properties in response to a debt-financed tax cut; that is, household consumption and in turn aggregate demand are stimulated by a tax cut. EMMA models equilibrium consumption as a linear homogenous function of current non-property income (𝑌𝑌𝑁𝑁𝑁𝑁), housing wealth8 (𝑉𝑉𝑉𝑉𝐻𝐻) and non-housing wealth (𝑉𝑉𝑉𝑉𝑁𝑁𝐻𝐻) (equation 2a). Under this approach, non-property income influences consumption directly, while property income appears in capitalised form as wealth, which is valued at replacement cost. This is a departure from Aron et al. (2012), where equilibrium consumption is linear homogeneous in current and permanent non-property income and wealth. The inclusion of permanent non-property income may be considered in future model development work. The EMMA consumption equation includes some refinements that are also from Aron et al. (2012). Equilibrium consumption depends negatively on the real cash interest rate. Further, actual consumption adjusts to equilibrium consumption in an error correction model (ECM). Finally, income uncertainty, as measured by the increase in the unemployment rate, has a transitory, negative effect (equation 2). Equation 2: Household consumption ∆log (𝐶𝐶𝑡𝑡) = 𝛽𝛽6[log (𝐶𝐶𝑡𝑡−1)−log (𝐶𝐶𝑡𝑡−1 ∗)]+𝛽𝛽7∆log (𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁) + (1−𝛽𝛽7)∆log (𝑌𝑌𝑡𝑡∗) + 𝛽𝛽8∆𝑈𝑈𝑡𝑡 (2) Equilibrium household consumption log (𝐶𝐶𝑡𝑡∗) = 𝛽𝛽1+𝛽𝛽2𝑑𝑑𝑑𝑑𝑑𝑑_𝑐𝑐𝑡𝑡+log (𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁) + 𝛽𝛽3�𝑉𝑉𝑉𝑉𝑡𝑡−1 𝐻𝐻 𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁 �+𝛽𝛽4�𝑉𝑉𝑉𝑉𝑡𝑡−1 𝑁𝑁𝐻𝐻 𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁 �+𝛽𝛽5𝑅𝑅𝑡𝑡 (2a) Where: 𝐶𝐶 is real consumption, 𝑌𝑌𝑁𝑁𝑁𝑁 is real non-property income, ∆𝑌𝑌∗ is potential output growth, ∆𝑈𝑈 is the change in the unemployment rate, 𝑑𝑑𝑑𝑑𝑑𝑑_𝑐𝑐𝑡𝑡 is a dummy that has a value of one until 2007 Q2 and zero afterwards, 𝑉𝑉𝑉𝑉𝐻𝐻 is real housing wealth, 𝑉𝑉𝑉𝑉𝑁𝑁𝐻𝐻is real non-housing wealth and 𝑅𝑅 is the real cash rate, calculated as the nominal cash rate deflated using the change in through-the-year trimmed mean inflation. A feature of the Ando-Modigliani consumption function is that households implicitly target a ratio of net wealth-to-income in the long run for given rates of return on assets and the steady-state growth rate of after-tax labour income. The long-run target ratio of net wealth-to-income is shown below in a stylised way, abstracting from differences in rates of return on assets, differences in propensities to consume out of different categories of wealth and from returns on the fixed factors of production. 𝜛𝜛=1−𝜔𝜔 𝜙𝜙−(𝑟𝑟−𝑔𝑔) (𝑉𝑉 𝑁𝑁𝑁𝑁−𝑇𝑇𝑁𝑁) Where: 𝜛𝜛 is private wealth, 𝜔𝜔 is the marginal propensity to consume out of income, 𝜙𝜙 is the marginal propensity to consume out of wealth, 𝑟𝑟 is the rate of return on assets, 𝑔𝑔 is the growth rate of the economy, 𝑉𝑉 is the nominal wage, 𝑁𝑁𝑁𝑁 is total hours worked and 𝑇𝑇𝑁𝑁 is labour income tax. The target implicitly reflects the household’s consumption, saving and leisure preferences over the estimation sample period. Under two conditions (𝜙𝜙 > 𝑟𝑟−𝑔𝑔; 0 < 𝜔𝜔 < 1), consumption is a positive proportion of income, where the proportion lies between zero and unity. Under these conditions, in the long run, household consumption is proportional to after-tax labour income. Hence, in the long run, consumption and GDP grow at the same rate and there can be balanced growth in 8 Housing wealth includes structures and land. Modelling the value of the stock of housing land is complex and is the subject of ongoing research. The Treasury Macroeconometric Model of Australia - Modelling approach 14 GDP and consumption. In the long-run, household wealth is also proportional to after-tax labour income. 𝐶𝐶=𝜙𝜙−𝜔𝜔(𝑟𝑟−𝑔𝑔) 𝜙𝜙−(𝑟𝑟−𝑔𝑔) (𝑉𝑉 𝑁𝑁𝑁𝑁−𝑇𝑇𝑁𝑁) Box 2. Long run properties of Ando-Modigliani consumption equation Some of the stylised long run implications of the A-M consumption equation can be seen by combining the consumption equation with the long run household income constraint, abstracting from differences in rates of return on assets, differences in propensities to consume out of categories of wealth and from returns on fixed factors of production. The long run household income constraint is obtained by using the long run national income and government budget constraints to eliminate government spending, 𝐺𝐺. 𝐶𝐶+𝐺𝐺−𝑇𝑇𝐶𝐶=𝑉𝑉 𝑁𝑁𝑁𝑁+𝑇𝑇𝐾𝐾+(𝑟𝑟−𝑔𝑔) (𝜛𝜛+𝐵𝐵) (National Income Constraint) 𝐺𝐺+(𝑟𝑟−𝑔𝑔) 𝐵𝐵=𝑇𝑇𝐾𝐾+𝑇𝑇𝐶𝐶+𝑇𝑇𝑁𝑁 (Government Budget Constraint) Where: 𝑟𝑟 is the rate of return on assets, 𝑔𝑔 is the growth rate of the economy, 𝑉𝑉 is the nominal wage, 𝑁𝑁𝑁𝑁 is total hours worked, 𝑇𝑇𝑁𝑁 is labour income tax, 𝑇𝑇𝐾𝐾 is tax on capital, 𝑇𝑇𝐶𝐶 is tax on consumption, 𝜛𝜛 is private wealth, and B is government net debt. The long run household income constraint shows that, in the steady state, household consumption is funded from after-tax labour income plus asset income net of sustainable saving. 𝐶𝐶=𝑉𝑉 𝑁𝑁𝑁𝑁−𝑇𝑇𝑁𝑁+𝑟𝑟 (𝜛𝜛+𝐵𝐵)−𝑔𝑔 𝜛𝜛 (Household Income Constraint)) The household income constraint can be used to eliminate private wealth, 𝜛𝜛, from the A-M consumption function to obtain the following reduced form equation for household consumption in the steady state. 𝐶𝐶=𝜙𝜙−𝜔𝜔(𝑟𝑟−𝑔𝑔) 𝜙𝜙−(𝑟𝑟−𝑔𝑔) (𝑉𝑉 𝑁𝑁𝑁𝑁−𝑇𝑇𝑁𝑁) Where: 𝜔𝜔 is the marginal propensity to consume out of current income, 𝜙𝜙 is the marginal propensity to consume out of wealth. The associated reduced form equation for private wealth, 𝜛𝜛, is as follows. 𝜛𝜛=1−𝜔𝜔 𝜙𝜙−(𝑟𝑟−𝑔𝑔) (𝑉𝑉 𝑁𝑁𝑁𝑁−𝑇𝑇𝑁𝑁) Some other Australian macroeconometric models follow a broadly similar approach to modelling household consumption. Specifically, in the RBA’s MARTIN model (Ballantyne et al., 2020), in the model of Murphy (2020) and in EMMA, equilibrium household consumption is linear homogeneous in current income and household wealth. The common use of current income in modelling consumption means that a debt-financed tax cut stimulates household consumption and aggregate demand in the short run in all three models. At the same time, there are some more subtle differences between the consumption equations of the three models. The Treasury Macroeconometric Model of Australia - Modelling approach 15 In MARTIN, current income refers to all of household income, whereas in EMMA it includes only the non-property component. EMMA follows Aron et al. (2012) who show that the influence of the property component of income on consumption can be captured indirectly through the inclusion of wealth. The two consumption equations also use different functional forms. In Murphy (2020), the long-run target for wealth refers to national wealth, whereas household wealth is used in EMMA. Empirical testing is unlikely to be very useful in deciding between these subtly different long-run targets, leaving conceptual appeal as the more likely deciding factor. On the one hand, Murphy (2020) shows that his national wealth target has the appealing property of being consistent with long run fiscal neutrality. On the other hand, the use of household wealth does not require that households are eventually sophisticated enough to understand that government debt is a household liability. On balance, EMMA assumes that households target household wealth. The approach to modelling household consumption is a key and noteworthy point of differentiation of EMMA and the two other Australian macroeconometric models from a DSGE model. The use of an A-M consumption function is common in macroeconometric models, but DSGE models typically use the Euler equation from the Ramsey model. In its basic form, this is derived from intertemporal utility maximisation for a representative consumer who behaves as a dynasty and forms expectations of the future based on the model. DSGE models are built on a consistent theoretical framework of optimising households and firms, which provides a clear interpretation of the causal mechanisms in the model and an explicit role for forward-looking expectations. The assumption of fully optimising households in the Ramsey Euler equation is conceptually appealing. However, Murphy (2020) notes that it has two main drawbacks. First, unlike in the A-M approach, in the basic Euler equation there is no link from current after-tax income to consumption, making counter-cyclical fiscal policy implausibly ineffective. Second, in an open economy where the cost of capital, 𝑟𝑟, is determined abroad, the rate of growth in consumption from the Euler equation will usually not match the rate of growth in GDP in the long run, that is, growth is unbalanced. Longrun balanced growth can be enforced by imposing a constraint on the rate of time preference, known as a knife-edge condition. Other solutions for achieving long-run balanced growth are discussed from a theoretical perspective in Turnovsky (2002) and an econometric perspective in Schmitt-Grohé and Uríbe (2003). Coenen et al. (2012) discuss how seven DSGE models in use at government authorities modify the basic Euler equation approach to generate more realistic dynamics in the relationship between consumption and current after-tax income. These modifications incorporate additional theory of household behaviour and deviations from fully rational forward-looking households. They include the introduction of hand-to-mouth consumers not subject to the Euler equation, a reduced elasticity of intertemporal substitution, allowing for habit persistence in consumption, and loosening the dependence of the local cost of capital on the cost abroad. These modifications arguably come at the cost of reduced clarity of the causal links in the model and additional demands on model estimation. These issues with the fully optimising approach of the Ramsey Euler equation are partly addressed by Blanchard (1985) in his overlapping generations model (OLG). In his model, instead of behaving as a dynasty, the representative consumer has no concern for future generations, introducing a negative wealth effect on the rate of growth in consumption. The Blanchard OLG model replaces the knife-edge condition on the rate of time preference with a less restrictive condition often referred to in the OLG literature as the medium-term impatience condition. Under this condition, The Treasury Macroeconometric Model of Australia - Modelling approach 16 households consume a proportion out of their wealth, such that assets don’t accumulate explosively. The model also introduces a link from current income to consumption. However, empirical evidence indicates this link is considerably stronger in practice. For forecasting and short-term policy and scenario analysis, it is important to realistically model the link from fluctuations in current after-tax income to fluctuations in consumption. And, it is appealing to require of households a less demanding framework from which to base their consumption decisions, partly as the framework is more intuitive to policymakers. The A-M consumption function has these properties within a relatively parsimonious framework, noting this comes at the cost that the causal mechanisms are less clear than in a fully optimising approach, such as in the Ramsey or Blanchard OLG models. Consumer demand The total value of consumption determined in EMMA’s A-M consumption equation is in turn allocated across four different consumer goods and services. These are supplied by EMMA’s three industries – agriculture, mining and non-commodities – and its quasi-industry of housing services or ownership of dwellings. Housing services are singled out for special treatment in modelling consumer demand in EMMA. This is because in the short-term the quantity of housing services is determined by the available supply, whereas the quantities of the other three consumer goods and services can be assumed to be demand determined. The market for housing services clears by the rental price gradually adjusting to match demand with the available supply. At present, the three other goods and services are assumed to be consumed in fixed proportions. However, allowing for price-sensitive substitution between them is a possible area for future model development work. The Treasury Macroeconometric Model of Australia - Modelling approach 17 4. Approach to businesses The business sector describes the behaviour of firms in demanding primary factor inputs and intermediate inputs into production, combining domestic production with imports to construct total supply, and then supplying outputs to the domestic and export markets. Firms decision making is driven by a desire to maximise profits. These decisions determine the productive output of the economy. In EMMA, a unified technology structure (shown in Figure 1) is used to model all of the firm’s decisions, both in demanding inputs to production and in supplying output to markets. As a consequence, in the long run, a single profit maximisation problem explains the behaviour of firms and ensures internal consistency between the firm’s input demand and supply decisions. It also ensures that factor inputs are paid their marginal product and that the zero pure profit condition is met. That is, all first order conditions necessary to maximise profits are satisfied. All firm behaviour converges to a long-run equilibrium in which profit is maximised. In the mining and agriculture sectors, the adjustment process is driven by the costs of adjusting capital stocks. In the non-commodities sector, nominal price rigidities are also important drivers of the path to equilibrium, in addition to capital stock adjustment. Firms do not jointly optimise across all of their decisions along the transition path to long-run equilibrium. The production and trade technology and the approach to these business decisions is discussed in turn. Production and trade technology In EMMA, the modelling of business behaviour is based around a production and trade technology that is shown in Figure 1. A similar technology is used for each of the three industries – agriculture, mining and non-commodities. The representative firm in each industry simultaneously makes decisions across four stages of the process of the production and distribution of output. At the centre of the technology, the firm uses a production function in which the primary factors of capital (K), labour (N) and a fixed factor (F) are substitutable inputs in producing value-added output (V) (Stage 1). Labour input is measured in hours worked. The firm then combines value-added production with intermediate inputs to produce domestic production (D) (Stage 2). The firm also acts as a distribution agent by combining domestic production with imports (M), which determines the firm’s total supply (Y) (Stage 3), and then deciding how much of total supply will be allocated to the domestic (E) and export (X) markets (Stage 4). EMMA’s modelling of the production of domestic output (Stages 1 and 2) includes two refinements to the standard production technology. The first refinement is that EMMA extends the usual production function involving primary factors of capital and labour to allow for an industry-specific fixed factor. This fixed factor is included in the production function for each industry, other than for the non-commodities industry, which is the largest industry in EMMA. The economic interpretation of the fixed factor varies with the industry. In agriculture it represents agricultural land, in mining it represents mineral resources, and in the quasi-industry of housing services, it represents housing land. The Treasury Macroeconometric Model of Australia - Modelling approach 18 Figure 1: Production and trade technology Noncommodity Leontief Leontief Mining Agriculture Intermediate 𝐽𝐽 Value-added output 𝑉𝑉 Domestic output 𝐷𝐷 Imports 𝑀𝑀 Total supply 𝑌𝑌 CES CES Labour 𝑁𝑁 Capital 𝐾𝐾 Fixed Factor 𝐹𝐹 CET Exports 𝑋𝑋 Domestic Expenditure 𝐸𝐸 Leontief Consumption 𝐶𝐶 Investment 𝐼𝐼 Public 𝐺𝐺 Intermediate 𝐽𝐽 The Treasury Macroeconometric Model of Australia - Modelling approach 19 In each of these industries, it is useful to allow for the fixed factor for two reasons. First, the presence of a fixed factor reduces the flexibility of an industry’s supply and taking this into account makes the model more realistic. Second, the fixed factor receives a significant share of industry income and ignoring that would mean the return to capital would be over-stated, leading to difficult-to-justify excessive industry risk premia. The second refinement is that, as a multi-industry model, EMMA includes intermediate inputs as another factor of production. All three industries use intermediate inputs produced by all three industries. The inclusion of intermediate inputs allows for a deeper understanding of the interconnections between industries and the flow-on implications of industry level shocks. Regarding functional form, in the first stage of the production process the primary factors of capital, labour and, where applicable, a fixed factor, are combined in a Constant Elasticity of Substitution (CES) production function to produce value added output. The elasticity of substitution differs between industries but are estimated to be nearer to 0.5 than to the Leontief case of zero or the Cobb-Douglas case of unity. Along the balanced growth path all productivity growth is labouraugmenting. Further details on productivity are included in Appendix C. In the second stage of the production process, value added output is combined with the intermediate inputs to produce domestic output. In this stage, Leontief technology is assumed. That is, intermediate inputs are combined in fixed proportions, and the resulting bundle of intermediates is then combined in fixed proportions with value added output. This assumption of fixed proportions for intermediate inputs seems reasonable given that EMMA’s three industries are very broad. It becomes more important to allow for substitutability between intermediates in models with finer industry disaggregation. Examples of this include models that distinguish different forms of energy, for example the G-cubed model of McKibbin and Wilcoxen (1999), or different modes of transport. As mentioned, EMMA uses a unified technology structure to model both trade and production (Figure 1). As a consequence, in the long run, a single profit maximisation problem leads to industry decisions about import demand and export supply that are fully consistent with industry decisions about inputs to production. Regarding functional form, in the third stage of the production and distribution process, imports (M) are substitutable with domestic output (D) in generating total supply (Y) according to a CES function. In the fourth stage, that supply is transformable in meeting demands for exports (X) and domestic expenditure (E) according to a Constant Elasticity of Transformation (CET) function. Trade in EMMA is modelled under the plausible assumption that Australia approximates a small open economy. Australia is assumed to be a price taker for imports. Australia is almost a price taker for exports from agriculture and mining, with high price elasticities, while in the remaining industry of non-commodities, export demand is also price elastic, but less so. These high export demand elasticities would be likely to lead to implausibly volatile export volumes if export supply were similarly price elastic. Export supply in each industry would be highly price elastic in the long run under the following set of assumptions: constant returns to scale in production, all factors of production are variable, perfect competition, perfect labour mobility between industries and frictionless switching of industry supply between the domestic and export markets. Under those assumptions, each industry’s export supply curve will be close to horizontal, with the supply price equal to the largely given unit cost of production. The Treasury Macroeconometric Model of Australia - Modelling approach 20 To overcome this potential problem of volatile export volumes when highly price elastic export demand is combined with highly price elastic export supply, EMMA introduces two frictions in export supply. The first friction is the presence of the fixed factor of production in the agriculture and mining industries, which was mentioned above. These fixed factors impart upward slopes on the export supply curves for these two industries. Following Powell and Gruen (1968), the second friction is that there is less than perfect transformability between supplying the domestic and export markets. As a consequence, a CET function is used in allocating total supply between exports and local expenditure. This means that there is an increasing opportunity cost in an industry switching supply from the domestic market to the export market, implying an upward sloping export supply curve. Convergence to equilibrium EMMA bases its long-run modelling of producer behaviour on standard economic theory. That is, in each of the three industries, in the long-run equilibrium a representative business maximises profit subject to the production and trade technology shown in Figure 1. At this stage the simple assumption is made that, in the long run, profit is maximised under perfect competition. Allowing for imperfect competition is under consideration as part of future model development. Firms simultaneously make inter-dependent decisions about the level of production, the price to charge, and the use of variable, intermediate and fixed inputs to production in order to maximise profit. Firms do not jointly optimise across all of their decisions along the transition path to long-run equilibrium. Over time, variables converge to their equilibrium value, resulting in a convergence toward a long-run equilibrium across all decision variables. The first order conditions have been arranged to reflect stylistic features of the adjustment process for prices, volumes and factor inputs to their equilibrium values. In the non-commodity industry, a hierarchical adjustment approach is employed in using the first order conditions for profit maximisation to drive the economy from the Keynesian short run to the Classical long run. In the Keynesian short run, equilibrium employment demand is obtained by inverting the production function. A sticky expenditure price then gradually adjusts to an equilibrium value based on short-run marginal cost. Once this equilibrium value is reached, the marginal product of labour condition is satisfied, so there is a medium-run equilibrium. Investment demand is based on Tobin’s-q theory of investment so the capital stock is costly to adjust. Once the capital stock adjustment process is complete, the q-ratio equals unity implying that the zero pure profit condition is satisfied. In this Classical long run, all profit maximising first-order conditions are met: the firm operates on its production function and the marginal product of labour and zero pure profit conditions are satisfied. The dynamic adjustment process in the non-commodity industry is broadly speaking driven by two main economic elements: sticky prices and sluggish adjustment of capital stocks based on adjustment costs. The assumption of New Keynesian ‘sticky prices’ leads output to be demand determined in the short run. These nominal price rigidities are important in explaining short-run disequilibrium and provide a role for monetary and fiscal policy in managing aggregate demand. In contrast, the adjustment process in the two commodities industries – agriculture and mining – is somewhat simpler. For reasons explained below, prices are assumed to be flexible so there is no Keynesian short run. Hence, the adjustment process is driven only by the costs of adjusting capital stocks. The Treasury Macroeconometric Model of Australia - Modelling approach 27 This higher production will raise marginal cost, leading to gradual upward adjustment of price. In a Classical medium run, price has adjusted fully to marginal cost. This brings the marginal product of labour back into line with the real wage and producers revert to operating on their supply curves. Equation 5: Price of local sales of industry in the non-commodities industry ∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝐸𝐸) = 𝛽𝛽1�log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡−1 𝐸𝐸)−log (𝑃𝑃𝑖𝑖,𝑡𝑡−1 𝐸𝐸∗)�+𝛽𝛽2∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡−1 𝑀𝑀) + 𝛽𝛽3∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝐸𝐸∗) +(1−𝛽𝛽2−𝛽𝛽3)𝜋𝜋𝑡𝑡𝑇𝑇 (5) Equilibrium price of local sales, 𝑃𝑃 𝐸𝐸∗, of industry i is determined recursively in a series of four equations as follows. Equilibrium price of gross value added, 𝑃𝑃𝑉𝑉∗, is equal to its marginal cost of production, satisfying the marginal product of labour condition. 𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝑉𝑉∗=�𝑉𝑉𝑡𝑡 𝜆𝜆𝑁𝑁𝐶𝐶,𝑡𝑡 𝑁𝑁�⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 1−𝜃𝜃𝑁𝑁𝐶𝐶 𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉�𝐾𝐾𝑖𝑖,𝑡𝑡−1 𝑉𝑉𝑖𝑖,𝑡𝑡 ∗�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉 𝜃𝜃𝑁𝑁𝐶𝐶 𝑁𝑁⎦ ⎥ ⎥ ⎥ ⎥ ⎤ 1 𝜎𝜎𝑖𝑖𝑉𝑉−1 (5a) Equilibrium price of domestic production, 𝑃𝑃 𝐷𝐷∗ , is then determined as a weighted average of the equilibrium price of gross value added, 𝑃𝑃𝑉𝑉∗ and intermediate input prices. 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷∗=𝛽𝛽𝑣𝑣 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉∗+�𝛽𝛽𝑗𝑗,𝑖𝑖𝑃𝑃𝑗𝑗,𝑡𝑡 𝐸𝐸 𝑗𝑗 (5b) Equilibrium price of total supply, 𝑃𝑃𝑌𝑌∗, is then determined as a CES cost function in the equilibrium price of domestic production, 𝑃𝑃𝐷𝐷∗, and import prices, 𝑃𝑃𝑀𝑀. 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗=�𝛼𝛼𝑖𝑖𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷∗1−𝜎𝜎𝑖𝑖𝑌𝑌+(1−𝛼𝛼𝑖𝑖)𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀1−𝜎𝜎𝑖𝑖𝑌𝑌�1 1−𝜎𝜎𝑖𝑖𝑌𝑌 (5c) Finally, the equilibrium price of local sales, 𝑃𝑃𝐸𝐸∗, is determined residually from a CET revenue function in which the equilibrium price of total supply, 𝑃𝑃𝑌𝑌∗, reflects the equilibrium price of local sales, 𝑃𝑃𝐸𝐸, and export prices, 𝑃𝑃𝑋𝑋. 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗=�𝜙𝜙𝑖𝑖𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗1+𝜎𝜎𝑖𝑖𝑇𝑇+(1−𝜙𝜙𝑖𝑖)𝑃𝑃𝑖𝑖,𝑡𝑡 𝐸𝐸∗1+𝜎𝜎𝑖𝑖𝑇𝑇�1 1+𝜎𝜎𝑖𝑖𝑇𝑇 (5d) Where: 𝜋𝜋𝑇𝑇 is the mid-point of the RBA’s inflation target band, 𝜆𝜆𝑁𝑁is labour augmenting technical change, 𝜃𝜃𝐾𝐾 is capital’s share of output, 𝜃𝜃𝑁𝑁is labour’s share of output, 𝜎𝜎𝑉𝑉 is the elasticity of substitution between factors of production, 𝛽𝛽𝑣𝑣 is input share of value-added in domestic production, 𝛽𝛽𝑗𝑗,𝑖𝑖 is the input share of intermediate inputs from industry j to domestic production in industry i, 𝜎𝜎𝑌𝑌is the elasticity of substitution between domestic production and imports in production total supply and 𝜎𝜎𝑇𝑇is the elasticity of transformation in transforming domestic sales into exports. The Treasury Macroeconometric Model of Australia - Modelling approach 28 Hours worked The modelling of producer behaviour around the main production function is completed by the modelling of labour demand. As noted above, labour demand is measured using total hours worked. The equilibrium level of total hours worked, 𝑁𝑁𝑁𝑁∗, is obtained by simply inverting the main production function, as seen in equation (6a). Actual total hours worked, 𝑁𝑁𝑁𝑁, then adjusts to equilibrium using the ECM of equation (6). Equation 6: Total hours worked in the non-commodities industry ∆log (𝑁𝑁𝑁𝑁𝑁𝑁𝐶𝐶,𝑡𝑡) = 𝛽𝛽1�(𝑁𝑁𝑁𝑁𝑁𝑁𝐶𝐶,𝑡𝑡−1)−log (𝑁𝑁𝑁𝑁𝑁𝑁𝐶𝐶,𝑡𝑡−1 ∗)�+𝛽𝛽2∆log (𝑁𝑁𝑁𝑁𝑁𝑁𝐶𝐶,𝑡𝑡 ∗) +(1−𝛽𝛽2)(∆log (𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡∗) + ∆log (𝑁𝑁𝑡𝑡∗) + ∆log (𝜌𝜌𝑡𝑡∗)) (6) Equilibrium total hours worked (by inverting this CES production function) 𝑉𝑉𝑁𝑁𝐶𝐶,𝑡𝑡 ∗=𝐼𝐼𝑁𝑁𝐶𝐶,𝑡𝑡�𝜃𝜃𝑁𝑁𝐶𝐶 𝑁𝑁1 𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉�𝜆𝜆𝑁𝑁𝐶𝐶,𝑡𝑡 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝐶𝐶,𝑡𝑡 ∗�𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉−1 𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉+𝜃𝜃𝑁𝑁𝐶𝐶 𝐾𝐾1 𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉𝐾𝐾𝑁𝑁𝐶𝐶,𝑡𝑡−1𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉−1 𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉�𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉 𝜎𝜎𝑁𝑁𝑁𝑁 𝑉𝑉−1 (6a) Where: 𝑃𝑃𝑃𝑃𝑃𝑃∗ is trend population, 𝑁𝑁𝑁𝑁∗ is trend average hours worked and 𝜌𝜌∗ is trend labour force participation This inverted production function approach links labour demand to output. Thus, both output and employment are demand determined in a Keynesian short run but producers operate on their supply curves in a Classical medium run once prices have fully adjusted. In the long run, the business sector meets the conditions to maximise profit in relation to the main production function through the combined effect of business investment, key price and labour demand equations. These ensure that there is zero pure profit, labour is paid its marginal product and the business operates on its production function respectively. Because labour input is measured using total hours worked, it is necessary to decompose this into employment on a heads basis, which is used in modelling unemployment, and average hours worked. Trend average hours worked is exogenous to the model and is based on an aggregation of average hours worked projections across age gender cohorts. Average hours worked are modelled to vary pro-cyclically with total hours worked in equation (7). Employment on a heads basis is then obtained by dividing total hours worked by average hours worked. Equation 7: Average hours worked in industry i log (𝑁𝑁𝑖𝑖,𝑡𝑡 𝑐𝑐) = 𝛽𝛽1∆log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 𝑐𝑐) + 𝛽𝛽2log (𝑁𝑁𝑖𝑖,𝑡𝑡−1 𝑐𝑐) (7) Cyclical average hours worked in industry i log (𝑁𝑁𝑖𝑖,𝑡𝑡 𝑐𝑐)≡log (𝑁𝑁𝑖𝑖,𝑡𝑡)−log (𝑁𝑁𝑖𝑖,𝑡𝑡 ∗) (7a) Cyclical total hours worked in industry i log (𝑁𝑁𝑁𝑁 𝑖𝑖,𝑡𝑡 𝑐𝑐)≡log (𝑁𝑁𝑁𝑁 𝑖𝑖,𝑡𝑡 )−log (𝑁𝑁𝑁𝑁 𝑖𝑖,𝑡𝑡 ∗) (7b) The Treasury Macroeconometric Model of Australia - Modelling approach 29 Import demand and export supply In EMMA, trade flows are integrated with the production technology. This means producer behaviour determines demand for imports and supply of exports. The modelling of producer behaviour and trade flows is based around total supply/demand. In each industry, producers meet demand for local sales and for exports by transforming goods and services for each market using a CET function. This total demand is met using a CES combination of local production and competing imports. In equilibrium in each industry, the representative producer chooses the combination of local production and competing imports that minimises cost and the combination of local sales and exports that maximises revenue. The focus here is on how that operates in the non-commodities industry. Cost minimisation determines the equilibrium import propensity in equation (8a). This import propensity depends negatively on the price of imports. Actual imports then adjust to equilibrium imports, 𝑀𝑀∗, in the ECM of equation (8). Equation 8: Imports that compete with industry i ∆log (M) = 𝛽𝛽1�log (𝑀𝑀𝑖𝑖,𝑡𝑡−1)−log (𝑀𝑀𝑖𝑖,𝑡𝑡−1 ∗)�+𝛽𝛽2∆log (𝑌𝑌𝑖𝑖,𝑡𝑡) +𝛽𝛽3�∆log�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀�−∆log�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌��+ (1 −𝛽𝛽2)∆log (𝑌𝑌𝑡𝑡∗) (8) Equilibrium imports in competition with industry 𝑖𝑖 (based on cost minimising combination of imports, 𝑀𝑀, and domestic production, 𝐷𝐷, in producing total supply, 𝑌𝑌) 𝑀𝑀𝑖𝑖,𝑡𝑡 ∗=(1−𝛼𝛼𝑖𝑖)𝑌𝑌𝑖𝑖,𝑡𝑡�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗ 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀�𝜎𝜎𝑖𝑖𝑌𝑌 (8a) This approach models a single import propensity for each industry that does not vary between different end uses. An alternative approach would be to allow for different import propensities for, say, an industry’s intermediate goods, investment goods and consumption goods. That disaggregation may have advantages in the industry policy setting of a computable general equilibrium (CGE) model. However, the EMMA approach of disaggregating imports by industry but not by end use seems suitable for its purpose of analysing macroeconomic fluctuations. Under revenue maximisation, the optimal ratio of exports to local sales depends positively on their relative price. However, in the non-commodities industry, the representative producer does not directly control these quantities because they are demand determined in the Keynesian short run. Instead, the producer gradually adjusts the sticky export price until export demand is matched to the revenue-maximising export supply. The equilibrium supply price of exports is modelled in equation (9a). The actual price of exports then adjusts to the equilibrium price in the ECM of equation (9). The Treasury Macroeconometric Model of Australia - Modelling approach 30 Equation 9: Price of exports for the non-commodities industry ∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝑋𝑋) = 𝛽𝛽1�log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡−1 𝑋𝑋)− 𝛽𝛽2𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝑋𝑋𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡𝑑𝑑−log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡−1 𝑋𝑋∗)�+𝛽𝛽3�∆log �𝑃𝑃𝑡𝑡𝑊𝑊 𝜀𝜀𝑡𝑡�� + (1−𝛽𝛽3)∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝑋𝑋∗) (9) Equilibrium price of exports for the non-commodities industry (based on revenue-maximising combination of exports and domestic sales from total supply). 𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝑋𝑋∗=𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝐸𝐸∗�1−𝜙𝜙𝑁𝑁𝐶𝐶 𝜙𝜙𝑁𝑁𝐶𝐶 𝑋𝑋𝑁𝑁𝐶𝐶,𝑡𝑡 𝐸𝐸𝑁𝑁𝐶𝐶,𝑡𝑡�1 𝜎𝜎𝑁𝑁𝑁𝑁 𝑇𝑇 (9a) Where: 𝑃𝑃𝑊𝑊 is the world price for that good, 𝜀𝜀 is the nominal trade-weighted exchange rate and 𝜙𝜙 is the export share. The dynamics of export markets is quite different for EMMA’s commodity industries. As just discussed, for the non-commodities industry, export prices are sticky, so the quantity of exports is demand determined in the short run while the price is supply determined. Essentially, the reverse is true in the two commodities industries where prices are flexible and demand driven. Therefore, the equilibrium relationship is different to equation (9a) for the commodity industries. While this leads to different dynamics for the two types of export markets, the two approaches are equivalent once an equilibrium is reached in which markets clear. Inventory investment In modelling inventory investment, EMMA assumes that there is an equilibrium stocks to GDP ratio, as seen in equation (10a). Actual stocks, 𝐾𝐾𝐾𝐾𝑇𝑇, then adjust to equilibrium stocks, 𝐾𝐾𝐾𝐾𝑇𝑇∗, in the ECM of equation (10). Inventory investment, ∆(𝐾𝐾𝐾𝐾𝑇𝑇𝑡𝑡), is then calculated as the change in stocks. Equation 10: Inventory investment ∆log (𝐾𝐾𝐾𝐾𝑇𝑇𝑡𝑡) = 𝛽𝛽3[log(𝐾𝐾𝐾𝐾𝑇𝑇𝑡𝑡−1)−log(𝐾𝐾𝐾𝐾𝑇𝑇𝑡𝑡−1 ∗)] +𝛽𝛽4∆𝑙𝑙𝑙𝑙𝑔𝑔(𝐾𝐾𝐾𝐾𝑇𝑇𝑡𝑡−1) +(1−𝛽𝛽4)∆log (𝑌𝑌𝑡𝑡∗) (10) Equilibrium stock of inventories log (𝐾𝐾𝐾𝐾𝑇𝑇𝑡𝑡∗) = 𝛽𝛽1+𝛽𝛽2𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+log (𝑌𝑌𝑡𝑡) (10a) Where: 𝐾𝐾𝐾𝐾𝑇𝑇 is the stock of inventories and 𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 is a linear time trend. The Treasury Macroeconometric Model of Australia - Modelling approach 31 5. Approach to Foreign Sector In modelling international trade, the foreign sector demands exports and supplies imports. Trade in EMMA is modelled under the assumption that Australia approximates a small open economy (SOE). For imports, EMMA adopts the SOE assumption that Australia is a price taker on world markets. However, this is adopted as an equilibrium assumption only. In equilibrium, changes in foreign prices and the exchange rate pass through fully into import prices, PM*, in equation (11a) for non-commodities. The speed of this pass through is determined by an ECM in equation (11). Equation 11: Price of imports of industry i ∆log (𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀) = 𝛽𝛽1�log�𝑃𝑃𝑖𝑖,𝑡𝑡−1 𝑀𝑀�−𝛽𝛽2−𝛽𝛽3𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡−1−log�𝑃𝑃𝑖𝑖,𝑡𝑡−1 𝑀𝑀∗��+𝛽𝛽4∆log (𝜀𝜀𝑡𝑡) +𝛽𝛽5∆log(𝑃𝑃𝑖𝑖,𝑡𝑡 𝐹𝐹) + (1−𝛽𝛽5)∆log(𝑃𝑃𝑖𝑖,𝑡𝑡−1 𝐹𝐹) (11) Equilibrium price of imports that compete with industry i 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀∗=𝑃𝑃𝑖𝑖,𝑡𝑡 𝐹𝐹 𝜀𝜀𝑡𝑡 (11a) Where: 𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 is a linear time trend, 𝜀𝜀 is the nominal trade-weighted exchange rate and 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐹𝐹 is trade-weighted foreign prices for industry i. For exports, the SOE assumption is relaxed somewhat on the basis that some Australian exports are differentiated from the competing exports of other countries, giving some degree of pricing power. This is especially the case for non-commodity exports. This is a diverse category that includes tourism and education services, where Australian product differentiation is important, as well as manufactures where product differentiation is less marked. In modelling equilibrium exports of non-commodities in equation (12a), the freely estimated price elasticity of demand (𝜖𝜖) was negative but inelastic, implying an implausibly high degree of pricing power. This elasticity has been constrained to reflect a more moderate amount of pricing power. Actual non-commodity exports adjust to equilibrium in the ECM of equation (12). Equation 12: Export demand for non-commodities industry ∆log�𝑋𝑋𝑁𝑁𝐶𝐶,𝑡𝑡�=𝛽𝛽1�log�𝑋𝑋𝑁𝑁𝐶𝐶,𝑡𝑡−1�−𝛿𝛿𝑡𝑡−log(𝑋𝑋𝑛𝑛𝑐𝑐,𝑡𝑡−1 ∗)�+𝛽𝛽3Δ�log(𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝑋𝑋/𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝐹𝐹 ) ∙𝜀𝜀𝑡𝑡�+ β4Δlog(𝑌𝑌𝑡𝑡𝐹𝐹) + (1−𝛽𝛽4)Δlog(𝑌𝑌𝑡𝑡∗) (12) Equilibrium exports for the non-commodities industry 𝑋𝑋𝑖𝑖,𝑡𝑡 ∗=𝑌𝑌𝑡𝑡𝐹𝐹�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗𝜀𝜀𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐹𝐹�𝜖𝜖 (12a) Where: 𝛿𝛿𝑡𝑡 is a time-varying intercept estimated from a state-space model. It is assumed that Australia is closer to being a price taker for exports from agriculture and mining. This is on the basis that product differentiation is less marked than for non-commodity exports. The Treasury Macroeconometric Model of Australia - Modelling approach 32 6. Approach to government The approach to government includes the modelling of the government budget and monetary policy. Government budget In modelling the government budget, the government is defined as the general government sector. This excludes public corporations, which are treated as part of the business sector. All levels of government – commonwealth, state and local – are consolidated together in a single government sector, although they may be separated as part of future model development work. The baseline scenario for government expenditures and revenues is taken from official government projections. However, to support alternative scenarios, the government budget is modelled. This budget modelling allows the macroeconomic effects of alternative fiscal settings to be explored, including settings that change tax rates or expenditures. It also means that other model simulations take into account the likely broad effects on the budget when there are fluctuations in prices, incomes and expenditures. For the government budget modelling, government expenditures on goods and services are assumed to vary with GDP in the long run. More specifically, equilibrium real government consumption expenditure, 𝐺𝐺𝑐𝑐∗ , (exclusive of depreciation) is specified as a fixed share of real GDP in equation (13a). Actual government consumption, 𝐺𝐺𝑐𝑐 , then adjusts to this equilibrium in the ECM of equation (13). Real government investment expenditure, 𝐺𝐺𝑖𝑖, is modelled in an analogous way in equations (14a) and (14). Equation 13: General government consumption (exclusive of depreciation) ∆log (𝐺𝐺𝑡𝑡𝑐𝑐) = 𝛽𝛽2�log (𝐺𝐺𝑡𝑡−1 𝑐𝑐)−log (𝐺𝐺𝑡𝑡−1 𝑐𝑐∗) �+ ∆log (𝑌𝑌𝑡𝑡∗) (13) Equilibrium government consumption (exclusive of depreciation) log (𝐺𝐺𝑡𝑡𝑐𝑐∗)≡𝛽𝛽1+log (𝑌𝑌𝑡𝑡) (13a) Equation 14: General government investment ∆log (𝐺𝐺𝑡𝑡𝑖𝑖) = 𝛽𝛽2�log (𝐺𝐺𝑡𝑡−1 𝑖𝑖)−log (𝐺𝐺𝑡𝑡−1 𝑖𝑖∗) �+ ∆log (𝑌𝑌𝑡𝑡∗) (14) Equilibrium government investment (exclusive of depreciation) log (𝐺𝐺𝑡𝑡𝑖𝑖∗)≡𝛽𝛽1+log (𝑌𝑌𝑡𝑡) (14a) The Treasury Macroeconometric Model of Australia - Modelling approach 33 This approach to government expenditure is adopted so that the model can converge to a balanced growth path in the long run, with GDP and its components, including government final demand, growing at the same rates. The equilibrium government share of GDP is adjusted as a model input. Tax revenues are divided into five categories including personal income tax, company income tax, product taxes net of subsidies, other production taxes net of subsidies and taxes on non-residents. These taxes are modelled in identities that apply an effective tax rate to a model construct for the tax base. Hence, at the margin, tax revenues vary proportionately with each tax base. Future work may consider incorporating progressivity of the tax system into the model’s shock dynamics. Progressivity in the income tax system is captured in the model’s baseline projections by using the Government’s official projections for revenue. Changes in tax rates flow through to changes in prices and incomes. While this modelling of the government budget suffices for shorter-term analysis, for longer-term scenario analysis it is augmented to ensure that the government budget is sustainable. This involves specifying a rule in which fiscal policy adjusts gradually to stabilise government debt relative to GDP in the long term. Debt stabilisation relative to GDP will only be achieved without such fiscal adjustments under the condition that the nominal interest rate on government debt is lower than the growth rate in nominal GDP. While that condition holds in the current low interest rate environment, this need not always be true. Hence, EMMA includes a fiscal policy rule to ensure that the government budget is sustainable, as is standard practice in macroeconomic models. The EMMA fiscal policy rule defines a trend, 𝐵𝐵∗, for the ratio of government net debt, 𝐵𝐵, to trend nominal GDP, 𝑌𝑌𝑌𝑌∗ (which is calculated as potential GDP 𝑌𝑌∗ inflated by prices growing at the mid-point of the RBA’s target band). While in practice the trend may be restored through a variety of measures such as tax increases or expenditure cuts, for scenario analysis EMMA makes the common simplifying assumption that fiscal sustainability is achieved through gradual adjustments in the average rate of personal income tax, ∆𝜏𝜏𝐻𝐻𝐻𝐻. This considerable simplification of choosing a single swing fiscal instrument is common in macroeconomic models and means fiscal policy rules are often calibrated, as is the case here, rather than estimated. Other swing instruments can also be used, depending on the simulation. In any case, whatever the choice of swing instrument, the model can be used to simulate the use of virtually any type of fiscal measures to achieve debt stabilisation. To the extent that other fiscal measures are used to achieve debt stabilisation, little or no adjustment may be required in whatever is the designated swing instrument. In general B* is set to be consistent with the trajectory for net debt in the baseline projections based on current government policy. This trend share can be readily adjusted as a model input. Given the use of the fiscal policy rule for scenario and policy analysis, 𝐵𝐵∗ can be used to ensure that net debt as a share of GDP returns to its projected level under the baseline projections. In the fiscal policy rule (equation 15), the rate of personal income tax increases if debt is above 𝐵𝐵∗or if this debt gap increases. The change in the debt gap is included in addition to the level of the debt gap because this improves the performance of adjustments in the tax rate in achieving𝐵𝐵∗. The values of the two parameters appearing in the rule are chosen based on model simulation properties. Specifically, in model simulations that open a debt gap, the fiscal policy rule closes that gap in about 10 years under the chosen parameter values. The two parameter values can be adjusted to achieve 𝐵𝐵∗either more slowly or more quickly. The values of the two parameters are the same as those that were used by the TRYM model. The Treasury Macroeconometric Model of Australia - Modelling approach 34 Equation 15: Fiscal policy rule ∆𝜏𝜏𝑡𝑡𝐻𝐻𝐻𝐻=−0.007 �𝐵𝐵𝑡𝑡 𝑌𝑌𝑌𝑌𝑡𝑡∗−𝐵𝐵𝑡𝑡∗�−0.12 ∆�𝐵𝐵𝑡𝑡 𝑌𝑌𝑌𝑌𝑡𝑡∗−𝐵𝐵𝑡𝑡∗� (15) The fiscal policy rule is designed to achieve the stated purpose of ensuring fiscal sustainability in the long run during model simulations. In the short run, counter-cyclical fiscal policy can be modelled in a flexible way by varying a wide range of individual fiscal inputs. In short, the approach to modelling fiscal policy is flexible rather than prescriptive. Monetary policy Besides a fiscal policy rule to achieve long-run stabilisation of government debt, EMMA also requires a monetary policy rule to ensure long-run stabilisation of inflation. Macroeconomic models often use the Taylor rule for that purpose, which is shown below using textbook notation. 𝑖𝑖𝑡𝑡=𝜋𝜋𝑡𝑡+𝑟𝑟𝑡𝑡∗+𝛼𝛼𝜋𝜋 (𝜋𝜋𝑡𝑡−𝜋𝜋𝑡𝑡∗)+𝛼𝛼𝑦𝑦 (log (𝑌𝑌𝑡𝑡)−log (𝑌𝑌𝑡𝑡∗)) Under the Taylor rule, monetary policy is used to achieve a chosen inflation target. Monetary policy is said to be tight or loose when the policy interest rate, 𝑖𝑖, is above or below a neutral nominal rate. The neutral nominal rate is calculated as a neutral real rate,11 𝑟𝑟∗, plus the inflation rate, π . Monetary policy is tighter when inflation, π , is above its target, π ∗, or output, 𝑦𝑦, exceeds its potential, 𝑦𝑦∗. That is, monetary policy is driven by inflation and output gaps. EMMA uses the version of the Taylor rule that appears in the RBA’s MARTIN model (Ballantyne et al., 2020). MARTIN varies the standard Taylor rule shown above by replacing the output gap with an unemployment gap, calculated as the difference between the unemployment rate and the NAIRU. It also assumes that the actual interest rate adjusts gradually, rather than contemporaneously, to the rate indicated by the basic rule. The adjustment is also influenced by the change in the unemployment gap (the unemployment rate 𝑈𝑈 relative to the NAIRU 𝑈𝑈∗). 𝑖𝑖𝑡𝑡= 𝛽𝛽 𝑖𝑖𝑡𝑡−1+(1−𝛽𝛽) [𝜋𝜋𝑡𝑡+𝑟𝑟𝑡𝑡∗+𝛼𝛼𝜋𝜋 (𝜋𝜋𝑡𝑡−𝜋𝜋𝑡𝑡∗)+𝛼𝛼𝑢𝑢 (𝑈𝑈𝑡𝑡−𝑈𝑈𝑡𝑡∗)]−𝛼𝛼𝑐𝑐Δ2𝑈𝑈𝑡𝑡 This rule as it appears in EMMA can be seen in equations (16a) and (16). The interest rate from the rule is shown in equation (16a), while the adjustment of the actual interest rate to that rule is shown in equation (16). Equation 16: Monetary policy rule for cash rate ∆𝑖𝑖𝑡𝑡= 0.3 (𝑖𝑖𝑡𝑡∗−𝑖𝑖𝑡𝑡−1)−∆2(𝑈𝑈𝑡𝑡−𝑈𝑈𝑡𝑡∗) (16) 𝑖𝑖𝑡𝑡∗=𝑟𝑟𝑡𝑡∗+𝜋𝜋𝑡𝑡𝑇𝑇𝑀𝑀+(𝜋𝜋𝑡𝑡𝑇𝑇𝑀𝑀−𝜋𝜋𝑡𝑡∗)−2 (𝑈𝑈𝑡𝑡−𝑈𝑈𝑡𝑡∗) (16a) 11 As discussed in the section on Financial Markets, EMMA assumes uncovered interest parity (UIP). The combination of UIP and relative PPP means that the neutral real rate appearing in the monetary policy rule should ultimately be driven by the foreign real interest rate. This is taken into account in model simulations by adjusting the neutral real rate in line with any shock to the foreign real interest rate. The Treasury Macroeconometric Model of Australia - Modelling approach 35 All of the parameter values in the policy interest rate rule are imposed rather than estimated. Ballantyne et al. (2020) state that this approach is taken ‘in light of the well-known difficulties in estimating the parameters of monetary policy reaction functions’. The MARTIN version of the Taylor rule is one way of representing monetary policy in EMMA. The alternative way is to use optimal control of monetary policy. Under optimal control, there is still the same general idea that monetary policy is driven by the inflation and unemployment gaps. There is also the same aim of adjusting the policy interest rate gradually rather than abruptly. To achieve the optimal trade-off between these three potentially conflicting targets, optimal control minimises a loss function. That function includes the squared inflation gap, the squared unemployment gap and the squared change in the policy interest rate. Subjective weights are attached in combining these three sources of loss into a single measure of loss. A discount rate is used so lower weights are placed on losses the further that they occur into the future. In the literature, there are two versions of optimal control, closed loop and open loop. Under closed loop optimal control, the Taylor rule can continue to be used. Multiple simulations are conducted in which the model is subjected to a typical range of shocks. The loss function is used to determine the optimal values for the Taylor rule parameters (𝛽𝛽, 𝛼𝛼 π and 𝛼𝛼𝑢𝑢). This closed loop approach has the advantage that the policy approach can be easily understood from the Taylor rule and the disadvantage that this may be overly restrictive. Instead, EMMA uses open loop optimal control. This discards the Taylor rule. Instead, the loss function is used in determining the optimal entire path for the policy interest rate, and this is done separately for each shock. To avoid the problem of time inconsistency that may occur using closed loop optimal control, for any given shock, the monetary authority is assumed to commit to a path for the policy interest rate, and not re-optimise along that path. The Treasury Macroeconometric Model of Australia - Modelling approach 36 7. Approach to markets The main markets in EMMA include the product markets for the three industries, the labour market and financial markets. Prices are sticky in some of these markets and flexible in others, but in the long run all markets clear. This section describes the process of price adjustment to clear each market, taking the product, labour and financial markets in turn. Product markets As discussed previously, in modelling price adjustment in product markets, EMMA makes a distinction between its non-commodity industry and its two commodity industries, agriculture and mining. In broad terms, prices are sticky for the non-commodity industry, so in a Keynesian short run the representative business temporarily operates off its equilibrium supply curve by varying its factor utilisation, creating cyclical variation in productivity and total hours work, in order to accommodate demand at the prevailing price level. However, in the two commodity industries, prices are flexible, so that the representative business can vary its short-run supply. In each industry a distinction can be made between the product market for local sales, 𝐸𝐸, and the product market for exports, 𝑋𝑋, as seen in Figure 1. These two end uses of domestic production, 𝑌𝑌, are linked using CET technology. In equilibrium, the representative business chooses the combination of local sales and exports that maximises revenue given their relative prices. The operations of the market for non-commodities were partly explained in the section on the approach to businesses. It was pointed out that the stickiness in prices refers to local sales. More specifically, the actual price of local sales, 𝑃𝑃𝐸𝐸, adjusts gradually to the marginal cost of its supply, 𝑃𝑃𝐸𝐸∗. At that price, the market for local sales clears, with profit maximising supply matching price-sensitive demand. The price of exports of non-commodities is similarly sticky. In this case, the actual price of exports, 𝑃𝑃𝑋𝑋, adjusts gradually to the equilibrium price, 𝑃𝑃𝑋𝑋∗, at which the revenue maximising combination of exports and local sales is produced. As the actual price adjusts, export demand responds reflecting the price elasticity referred to in the discussion of the foreign sector. In contrast, price adjustment is flexible and export-driven in the two commodity industries. Australia is considered to be almost a price taker on these export markets. To reflect this idea, inverse export demand equations are specified in which the Australian share of the world market has a very limited effect on price. For mining, changes in world price (or the exchange rate) flow through contemporaneously into Australian export prices. For agriculture, the flow through is almost as quick, being spread over two quarters. Thus, prices are highly flexible in the two commodity export markets. While in the case of the non-commodity industry the principle of revenue maximisation over the two outputs was used in modelling the flow through of the price of local sales into export prices, this approach is reversed for the two commodities industries. That is, the actual price of local sales adjusts gradually to the shadow price at which the revenue maximising combination of exports and local sales are produced. This means that in the two commodities industries, price adjustment is less rapid for local sales than for exports. The Treasury Macroeconometric Model of Australia - Modelling approach 43 This focus in the design of EMMA on its steady state properties is useful in avoiding some modelling pitfalls. These pitfalls include projecting departures from steady, balanced growth in the long run because of accidents in model design, such as unintended departures from linear homogeneity in real variables in some equations, or a lack of consistency in the approach to setting model inputs. With those pitfalls avoided, EMMA can be used as a tool in developing a clear economic understanding of any likely departures from steady, balanced growth in the long run. Steady state structure In long-run equilibrium, EMMA has a structure that is almost recursive, which assists in understanding its long-run simulation properties. This almost recursive structure begins with the production technology, then flows to household consumption and the associated budget constraint and finally to trade volumes and the real exchange rate. Those three stages are now discussed in turn. The production and trade technology of Figure 1 is the first stage of the recursive structure. While there is a separate production technology for each of EMMA’s three industries, for simplicity this discussion of the model’s long-run structure abstracts from that industry detail. In EMMA, the effective supply of labour is determined by the so-called “Three Ps” of population, participation and productivity. In the long run, each of the 3Ps can be regarded as inputs to the model. The effective supply of labour in turn drives the effective use of labour because the unemployment rate is driven to the NAIRU by the wage equation. Thus, the explanation of long-run equilibrium in EMMA can begin with this effective labour input, 𝑁𝑁𝑁𝑁. Under the modelling assumptions, in the long run, the scale of production is essentially determined by effective labour input. Thus, in EMMA, the 3Ps broadly drive the scale of the economy. That is, when effective labour input expands, the other main variables in Figure 1 (capital (K), domestic output(D), imports (M), exports (X), consumption(C), investments (I) and government final demand (G)) will eventually expand by the same proportion. The two main qualifications to this also arose in the above discussion on the conditions for balanced growth in the steady state. First, as shown in Figure 1, there are fixed factors of production in the agriculture and mining industries. If these fixed factors are assumed to expand in tandem with the rise in effective labour input, then the result that the 3Ps drive the scale of the economy will continue to hold. Otherwise, the fixed factors will act as a mild brake on the general expansion in the economy when effective labour supply expands. Second, when effective labour supply expands, the induced general expansion in the economy includes the trade volumes, exports and imports. This can occur in a frictionless way if Australia is assumed to be a SOE with an exogenous terms-of-trade. However, as noted previously, in EMMA Australia only approximates an SOE. In particular, for the rest of the world to absorb an expansion in Australian exports, some endogenous fall in the terms of trade is required, particularly for non-commodities. This change in relative prices will have some effects on the pattern of economic activity in EMMA. For simplicity, the remaining discussion here of the model’s steady state properties makes the simplifying assumption that the scale of production in EMMA is driven by the level of effective labour input. The Treasury Macroeconometric Model of Australia - Modelling approach 44 The starting point in understanding the long-run properties of EMMA is the implied long-run zero pure profit (ZPP) condition involving trade values. Specifically, in Figure 1, the value of total supply consisting of domestic output and imports will equal the value of total use made up of exports, and expenditure, E. For present purposes, one can also make the simplifying assumption that the value of exports equals the value of imports to achieve external balance, although this will only by exactly true in an equilibrium in which net foreign liabilities are zero. In any case, under these assumptions the terms of trade, 𝑃𝑃𝑋𝑋/𝑃𝑃𝑀𝑀, entirely determines the price of output relative to the price of expenditure, 𝑃𝑃𝐷𝐷/𝑃𝑃𝐸𝐸. Hence, a higher terms of trade raises the price of output relative to the price of expenditure. As discussed previously, EMMA’s monetary policy rule targets consumer price inflation. For present purposes, we can think of that as determining the price of expenditure. Thus, when an increase in the terms of trade increases 𝑃𝑃𝐷𝐷/𝑃𝑃𝐸𝐸, this is likely to occur mainly via an increase in 𝑃𝑃𝐷𝐷 than via a decrease in 𝑃𝑃𝐸𝐸. Next, there is also a ZPP condition for factor use. As discussed earlier, this condition follows from the use of Tobin’s-q theory of investment under which the actual rate of return on capital equals the required rate of return in the long run. In terms of Figure 1, in the long run, the value of domestic output will equal the cost of capital plus the cost of labour. However, the price of domestic output and capital have already been determined by 𝑃𝑃𝐷𝐷 and 𝑃𝑃𝐸𝐸 respectively. Hence, the role of the ZPP condition for factor use is to determine the wage, 𝑉𝑉. That is, in EMMA, the real wage will adjust in the long run to ensure the actual rate of return on capital matches the rate required on world capital markets. For example, if labour productivity rises, the real wage will eventually rise proportionately, restoring the ZPP condition for factor use. Alternatively, if the terms of trade rises, increasing the price of output, 𝑃𝑃𝑌𝑌, relative to the price of new investment the potential pure profits will be neutralised by a rise in the wage relative to the price of output. Next, the marginal product of labour condition equates the marginal product of labour, which depends on the capital-to-labour ratio, with the real wage. As explained previously, this condition applies once the price of domestic output has adjusted to equal the marginal cost of production. With employment and the real wage already determined above, the capital stock adjusts to maintain the marginal product of labour condition. For example, if labour input rises with population, the capital stock will rise proportionately, maintaining the ratio of the capital stock to effective labour input. Next, the main production function determines domestic output. From Figure 1, domestic output depends on the inputs of capital and effective labour which have already been determined. Then, the process of capital accumulation determines the level of investment. With the capital stock already determined, investment needs to cover depreciation plus growth in the capital stock in line with growth in the real economy. This completes the first stage of the recursive model structure in long-run equilibrium. In the second stage of the recursive structure, household consumption and wealth are determined as explained in the section on the approach to households. There it was shown that the A-M consumption function combined with the long-run household budget constraint simultaneously determine household consumption and household wealth as ratios to after-tax labour incomes, in the long run. Labour incomes have already been determined in the first stage through wages and effective labour. The Treasury Macroeconometric Model of Australia - Modelling approach 45 Government final demand can also be determined as it is modelled as a ratio to domestic output which was determined in the first stage. From Figure 1, consumption, investments and government final demand can now be summed to determine total real expenditure, 𝐸𝐸. The third stage deals with trade volumes and the real exchange rate. Figure 1 shows are exports and imports enter the production technology. In EMMA, the profit-maximising producer chooses the ratio of imports to domestic output that minimises the cost of total supply. This means that imports depend on domestic output and price of domestic output which are already known from the first stage, as well as the foreign currency price of imports, which is exogenous. However, the choice of imports also depends on the exchange rate which is not known yet. Similarly, the profit-maximising producer chooses the ratio of exports to home market supply that maximises revenue from total supply. This means that exports depend on total expenditure and the price of expenditure, which are already known from the second and first stages respectively, as well as the foreign currency price of exports, which is exogenous. However, the choice of exports also depends on the exchange rate, which is not known yet. The final model relationship in the third stage is the trade technology of Figure 1. This links the supply of domestic output and imports to their use for home expenditure and exports. Domestic output was determined in the first stage and domestic expenditure in the second stage. Thus, the trade technology links the volume of exports and imports. Indirectly this reflects a requirement for external balance that has been introduced via the determination of domestic expenditure in the second stage.15 Thus, in the third stage there are three relationships – for import demand, export supply and the trade technology. These three relationships simultaneously determine exports, imports and domestic expenditure. In effect, the exchange rate adjusts until the level of exports relative to the level of imports is consistent with external balance. 15 In the second stage, E depends on C which depends on the household budget constraint which reflects a requirement for external balance. The Treasury Macroeconometric Model of Australia - Modelling approach 46 9. Conclusion A macroeconomic model is never finished. This paper has outlined the structure of Version 1.0 of EMMA. Several areas for further development have been identified in this paper. The model will continue to be developed over time to ensure it remains fit-for-purpose to meet the needs for the model to analyse the evolving economic and policy environment. This paper outlines the first version of the model. Further details on the model’s equations, empirical properties and dynamics will be published over time. The Treasury Macroeconometric Model of Australia - Modelling approach 47 REFERENCES Aron, J, Duca, J, Muellbauer, J, Murata, K, and Murphy A 2012, ‘Credit, Housing Collateral, and Consumption: Evidence from Japan, the U.K., and the U.S.’, Review of Income and Wealth, 58:3, pp. 397–423. Auerbach AJ, Kotlikoff LJ 1987. Dynamic Fiscal Policy. Cambridge University Press, Cambridge, U.K. Ballantyne, A, Cusbert, T, Evans, R, Guttmann, R, Hambur, J, Hamilton, A, Kendall, E, McCririck, R, Nodari, G, and Rees, D 2020, ‘MARTIN Has Its Place: A Macroeconometric Model of the Australian Economy’, Economic Record, 96, pp. 225–251. Blanchard, O 1985, ‘Debt, Deficits, and Finite Horizons’, Journal of Political Economy, 93:2, pp. 223–247. Blanchard, O 2018, ‘On the future of macroeconomic models’, Oxford Review of Economic Policy, 34, pp. 43–54. Christiano, L, Eichenbaum, M, and Evans, C 2005, ‘Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy’, Journal of Political Economy, 113:1, pp. 1-45. Coenen, G, Erceg, C, Freedman, C, Furceri, D, Kumhof, M, Lalonde, R, Laxton, D, Lindé, J, Mourougane, A, Muir, D, Mursula, S, Resende, C, Roberts, J, Roeger, W, Snudden, S, Trabandt, M, and Veld, J 2012, ‘Effects of Fiscal Stimulus in Structural Models’, American Economic Journal: Macroeconomics, 4, pp. 22–68. Downes, P., Hanslow, K. and Tulip, P. (2014), The Effect of the Mining Boom on the Australian Economy’, RBA Research Discussion Paper 2014-08, Reserve Bank of Australia, Sydney. Dungey, M, and Pagan, A 2000, ‘A Structural VAR Model of the Australian Economy’, Economic Record, 76, pp. 321–42. Dungey, M, and Pagan, A 2009, ‘Extending a SVAR Model of the Australian Economy’, Economic Record, 85, pp. 1–20. Fukač, M, and Pagan, A 2010, ‘Limited Information Estimation and Evaluation of DSGE Models’, Journal of Applied Econometrics, 25, pp. 55-70. Fukač, M, and Pagan, A 2011, ‘Structural Macroeconometric Modelling in a Policy Environment’, in Ullah, A. and Giles, D. (eds), Handbook of Empirical Economics and Finance, Chapman and Hall/CRC, Boca Raton. Gibbs, C, Hambur, J, and Nodari, G 2018, ‘DSGE Reno: Adding a Housing Block to a Small Open Economy Model’, Research Discussion Paper 2018-04, Reserve Bank of Australia, Sydney. Grohé, S, and Uríbe, M 2003, ‘Closing small open economy models’, Journal of International Economics, 61, pp. 163–185. Groth, C, and Khan, H 2010, ‘Investment Adjustment Costs: An Empirical Assessment’, Journal of Money, Credit and Banking, 42:8, pp. 1469-1494. The Treasury Macroeconometric Model of Australia - Modelling approach 48 Hawkins, J 2005, ‘Economic forecasting: history and procedures’, Economic Roundup Autumn 2005, Australian Treasury: Canberra. Higgins, C 1970, ‘A model for national income forecasting’, paper presented to ACT branch of Economic Society of Australia. Higgins, C and Fitzgerald, V 1973, ‘An econometric model of the Australian economy’, Journal of Econometrics, 1, pp. 229-65. Kaldor, N 1963, Capital Accumulation and Economic Growth. MacMillan, London. Kudrna, G, and Woodland, A 2011, ‘An inter-temporal general equilibrium analysis of the Australian age pension means test’, Journal of Macroeconomics, 33, pp. 61–79. Laforte, J 2018, ‘Overview of the Changes to the FRB/US Model’, Fed Notes, Board of Governors of the Federal Reserve System, Washington, December 7, 2018. Gustafsson, L 2021, ‘Australian Labour Force Participation: Historical Trends and Future Prospects’, Treasury Working Paper, 2021-2, Australian Treasury, Canberra. Murphy C 1988, ‘An overview of the Murphy Model’, in Burns M and Murphy (eds), Macroeconomic Modelling in Australia, Australian Economic Papers, Supp. McKibbin, W, and Wilcoxen, P 1999, ‘The theoretical and empirical structure of the G-Cubed model’, Economic Modelling, 16, pp. 123–148. Murphy, C 2017, Review of economic modelling at the Treasury, Independent Economics, Canberra. Murphy, C 2020, ‘Decisions in Designing an Australian Macroeconomic Model’, Economic Record, 96, pp. 252–270. Murphy, C, Bright, I, Brooker, R, Geeves, W, and Taplin B 1986, ‘A Macroeconometric Model of the Australian Economy for Medium-term Policy Analysis’, Office of the Economic Planning Advisory Council Technical Paper, No. 2, Canberra. Pagan, A, and Robinson, T 2016, ‘Investigating the Relationship between DSGE and SVAR Models’, NCER Working Paper 112, National Centre for Econometric Research, Brisbane. Pagan, A, and Wilcox, D 2016, ‘External Review – Reserve Bank of Australia Economic Group Forecasts and Analysis’, Reserve Bank of Australia Pagan, A 2019, ‘Australian Macro-Econometric Models and Their Construction - A Short History’, CAMA Working Paper 50/2019, Centre for Applied Macroeconomic Analysis, Canberra. Powell, A, and Gruen F 1968, ‘The Constant Elasticity of Transformation Production Frontier and Linear Supply System’, International Economic Review, 9, pp. 315-328. Powell, A, and Murphy, C 1995, Inside a Modern Macroeconomic Model – A Guide to the Murphy Model, 1st edition, Springer-Verlag, Berlin. Rees, D, Smith, P, and Hall, J 2016, ‘A Multi-sector Model of the Australian Economy’, Economic Record, 92, pp. 374–408. The Treasury Macroeconometric Model of Australia - Modelling approach 49 Ruberl, H, Ball, H, Lucas, L and Williamson, T 2021, ‘Estimating the NAIRU in Australia’, Treasury Working Paper, 2021-01, Australian Treasury, Canberra. Saxegaard, M 2017, ‘The Use of Models in Finance Ministries – An Overview’, Work Note 2017/1, Norwegian Ministry of Finance. Schmitt-Rohe, S and Uribe, M 2003, ‘Closing small open economy models’, Journal of International Economics, 61, pp. 163-185. Sims, C 1980, ‘Macroeconomics and Reality’, Econometrica, 48, pp. 1–48. Simes, R and Horn, P 1988, ‘Design of the NIF88 model’, Australian Economic Papers, supplement to volume 27, June, pp. 155-70. Smets, F, and Wouters, R 2007, ‘Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach’, American Economic Review, 97, pp. 586–606. Stock, J, and Watson, M 2001, ‘Vector Autoregressions’, Journal of Economic Perspectives, 15, pp. 101–15. Taplin, B, Jilek, P, Antioch, L, Johnson, A, Parameswaran, P, and Louis, C 1993, Documentation of the Treasury Macroeconomic (TRYM) Model of the Australian Economy, Australian Treasury, Canberra. Treasury 1981, The NIF-10 Model of the Australian Economy, AGPS, Canberra. Treasury 1984, Proceedings of the Conference on the NIF-10 model, AGPS, Canberra. Turnovsky, S 2002, ‘Knife-Edge Conditions and the Macrodynamics of Small Open Economies’, Macroeconomic Dynamics, 6, pp. 307–335. Uzawa, H 1961, “Neutral Inventions and the Stability of Growth Equilibrium,” Review of Economic Studies, Vol. 28 (2): pp. 117-124. Wren-Lewis, S, 2018, ‘Ending the microfoundations hegemony’, Oxford Review of Economic Policy, 34, pp. 55-69. The Treasury Macroeconometric Model of Australia - Modelling approach 50 Appendix A: Key equations Equation 1: Labour force participation rate (cyclical component) ∆log(𝜌𝜌𝑡𝑡)=𝛽𝛽1[log(𝜌𝜌𝑡𝑡−1)−log(𝜌𝜌𝑡𝑡−1 ∗)] +𝛽𝛽2�log �𝑁𝑁𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡�−log �𝑁𝑁𝑡𝑡∗ 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡∗�� +𝛽𝛽3∆log �𝑁𝑁𝑡𝑡−1 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡−1� (1) Equation 2: Household consumption ∆log (𝐶𝐶𝑡𝑡) = 𝛽𝛽6[log (𝐶𝐶𝑡𝑡−1)−log (𝐶𝐶𝑡𝑡−1 ∗)]+𝛽𝛽7∆log (𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁) + (1−𝛽𝛽7)∆log (𝑌𝑌𝑡𝑡∗) + 𝛽𝛽8∆𝑈𝑈𝑡𝑡 (2) Equilibrium household consumption log (𝐶𝐶𝑡𝑡∗) = 𝛽𝛽1+𝛽𝛽2𝑑𝑑𝑑𝑑𝑑𝑑_𝑐𝑐𝑡𝑡+log (𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁) + 𝛽𝛽3�𝑉𝑉𝑉𝑉𝑡𝑡−1 𝐻𝐻 𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁 �+𝛽𝛽4�𝑉𝑉𝑉𝑉𝑡𝑡−1 𝑁𝑁𝐻𝐻 𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁 �+𝛽𝛽5𝑅𝑅𝑡𝑡 (2a) Equation 3: Business investment rate in industry i (disequilibrium component) 𝐼𝐼𝐶𝐶𝑖𝑖,𝑡𝑡=𝛽𝛽1 �𝐼𝐼𝑅𝑅𝑖𝑖,𝑡𝑡−1−𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡−1�+𝛽𝛽2𝐼𝐼𝐶𝐶𝑖𝑖,𝑡𝑡−1 (3) Definition of disequilibrium component of business investment rate 𝐼𝐼𝐶𝐶𝑖𝑖,𝑡𝑡≡𝐼𝐼𝑖𝑖,𝑡𝑡 𝐾𝐾𝑖𝑖,𝑡𝑡−1−�∆log(𝑌𝑌𝑡𝑡∗) + 𝛿𝛿𝑖𝑖,𝑡𝑡 400� (3a) Actual rate of return on capital from cash flow 𝐼𝐼𝑅𝑅𝑖𝑖,𝑡𝑡=(1 −𝜏𝜏𝑖𝑖,𝑡𝑡 𝐶𝐶)�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉∙𝑉𝑉𝑖𝑖,𝑡𝑡−�𝑉𝑉𝑖𝑖,𝑡𝑡∙𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡+𝑟𝑟𝑖𝑖,𝑡𝑡 𝐹𝐹∙𝐹𝐹𝑖𝑖,𝑡𝑡�� 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐼𝐼∙𝐾𝐾𝑖𝑖,𝑡𝑡+𝜏𝜏𝑖𝑖,𝑡𝑡 𝐶𝐶𝛿𝛿𝑖𝑖,𝑡𝑡 400 (3b) Cost of capital 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡=(𝑖𝑖𝑡𝑡10−𝜋𝜋𝑡𝑡𝑒𝑒) 400 +�1 + 𝜋𝜋𝑡𝑡𝑒𝑒 400�𝛿𝛿𝑖𝑖,𝑡𝑡 400 +𝑅𝑅𝑖𝑖𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡 (3 c) Equation 4: Housing investment rate (disequilibrium component) 𝐼𝐼𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡=𝛽𝛽1�𝐼𝐼𝑅𝑅𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡−𝐶𝐶𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡�+𝛽𝛽2𝐼𝐼𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡−1+𝛽𝛽3∆4(𝑖𝑖𝑡𝑡−1−𝑖𝑖𝑡𝑡−1 10) (4) Definition of disequilibrium component of housing investment rate 𝐼𝐼𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡≡𝐼𝐼𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 𝐾𝐾𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡−1−�∆𝑦𝑦𝑡𝑡∗+ 𝛿𝛿𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 400 � (4a) The Treasury Macroeconometric Model of Australia - Modelling approach 51 Actual rate of return on capital 𝐼𝐼𝑅𝑅𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡=𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 𝑉𝑉∙𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡−𝑟𝑟𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 𝐹𝐹∙𝐹𝐹𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 𝐼𝐼∙𝐾𝐾𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡−1 (4b) Cost of capital 𝐶𝐶𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡=(𝑖𝑖𝑡𝑡10−𝜋𝜋𝑡𝑡𝑒𝑒) 400 +�1 + 𝜋𝜋𝑡𝑡𝑒𝑒 400�𝛿𝛿𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 400 +𝑅𝑅𝑖𝑖𝑅𝑅𝑅𝑅𝑜𝑜𝑜𝑜𝑜𝑜,𝑡𝑡 (4c) Equation 5: Price of local sales of industry in the non-commodities industry ∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝐸𝐸) = 𝛽𝛽1�log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡−1 𝐸𝐸)−log (𝑃𝑃𝑖𝑖,𝑡𝑡−1 𝐸𝐸∗)�+𝛽𝛽2∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡−1 𝑀𝑀) + 𝛽𝛽3∆log (𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝐸𝐸∗) +(1−𝛽𝛽2−𝛽𝛽3)𝜋𝜋𝑡𝑡𝑇𝑇 (5) Equilibrium price of local sales, 𝑃𝑃 𝐸𝐸∗ , of industry i is determined recursively in a series of four equations as follows. Equilibrium price of gross value added, 𝑃𝑃𝑉𝑉∗, is equal to its marginal cost of production, satisfying the marginal product of labour condition. 𝑃𝑃𝑁𝑁𝐶𝐶,𝑡𝑡 𝑉𝑉∗=�𝑉𝑉𝑡𝑡 𝜆𝜆𝑁𝑁𝐶𝐶,𝑡𝑡 𝑁𝑁�⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 1−𝜃𝜃𝑁𝑁𝐶𝐶 𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉�𝐾𝐾𝑖𝑖,𝑡𝑡−1 𝑉𝑉𝑖𝑖,𝑡𝑡 ∗�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉 𝜃𝜃𝑁𝑁𝐶𝐶 𝑁𝑁⎦ ⎥ ⎥ ⎥ ⎥ ⎤ 1 𝜎𝜎𝑖𝑖𝑉𝑉−1 (5a) Equilibrium price of domestic production, 𝑃𝑃 𝐷𝐷∗, is then determined as a weighted average of the equilibrium price of gross value added, 𝑃𝑃𝑉𝑉∗ and intermediate input prices. 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷∗=𝛽𝛽𝑣𝑣 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉∗+�𝛽𝛽𝑗𝑗,𝑖𝑖𝑃𝑃𝑗𝑗,𝑡𝑡 𝐸𝐸 𝑗𝑗 (5b) Equilibrium price of total supply, 𝑃𝑃𝑌𝑌∗, is then determined as a CES cost function in the equilibrium price of domestic production, 𝑃𝑃𝐷𝐷∗, and import prices, 𝑃𝑃𝑀𝑀. 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗=�𝛼𝛼𝑖𝑖𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷∗1−𝜎𝜎𝑖𝑖𝑌𝑌+(1−𝛼𝛼𝑖𝑖)𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀1−𝜎𝜎𝑖𝑖𝑌𝑌�1 1−𝜎𝜎𝑖𝑖𝑌𝑌 (5c) Finally, the equilibrium price of local sales, 𝑃𝑃𝐸𝐸∗, is determined residually from a CET revenue function in which the equilibrium price of total supply, 𝑃𝑃𝑌𝑌∗, reflects the equilibrium price of local sales, 𝑃𝑃𝐸𝐸, and export prices, 𝑃𝑃𝑋𝑋. 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗=�𝜙𝜙𝑖𝑖�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗�1+𝜎𝜎𝑖𝑖𝑇𝑇+(1−𝜙𝜙𝑖𝑖)�𝑃𝑃𝑖𝑖,𝑡𝑡 E∗�1+𝜎𝜎𝑖𝑖𝑇𝑇�1 1+𝜎𝜎𝑖𝑖𝑇𝑇 (5d) The Treasury Macroeconometric Model of Australia - Modelling approach 52 Equation 6: Total hours worked in industry i ∆log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡) = 𝛽𝛽1�(𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡−1)−log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡−1 ∗)�+𝛽𝛽2∆log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 ∗) +(1−𝛽𝛽2)(∆log (𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡∗) + ∆log (𝑁𝑁𝑡𝑡∗) + ∆log (𝜌𝜌𝑡𝑡∗)) (6) Equilibrium total hours worked (by inverting this CES production function) 𝑉𝑉𝑖𝑖,𝑡𝑡 ∗=𝐼𝐼𝑖𝑖,𝑡𝑡�𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 ∗�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉+𝜃𝜃𝑖𝑖𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉𝐾𝐾𝑖𝑖,𝑡𝑡−1𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 (6a) Equation 7: Average hours worked in industry i log (𝑁𝑁𝑖𝑖,𝑡𝑡 𝑐𝑐) = 𝛽𝛽1∆log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 𝑐𝑐) + 𝛽𝛽2log (𝑁𝑁𝑖𝑖,𝑡𝑡−1 𝑐𝑐) (7) Cyclical average hours worked in industry i log (𝑁𝑁𝑖𝑖,𝑡𝑡 𝑐𝑐)≡log (𝑁𝑁𝑖𝑖,𝑡𝑡)−log (𝑁𝑁𝑖𝑖,𝑡𝑡 ∗) (7a) Cyclical total hours worked in industry i log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 𝑐𝑐)≡log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡)−log (𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 ∗) (7b) Equation 8: Imports that compete with industry i ∆log (M) = 𝛽𝛽1�log (𝑀𝑀𝑖𝑖,𝑡𝑡−1)−log (𝑀𝑀𝑖𝑖,𝑡𝑡−1 ∗)�+𝛽𝛽2∆log (𝑌𝑌𝑖𝑖,𝑡𝑡) +𝛽𝛽3�∆log�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀�−∆log�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌��+ (1 −𝛽𝛽2)∆log (𝑌𝑌𝑡𝑡∗) (8) Equilibrium imports in competition with industry i (based on cost minimising combination of imports, M, and domestic production, D, in producing total supply, Y) 𝑀𝑀𝑖𝑖,𝑡𝑡 ∗=(1−𝛼𝛼𝑖𝑖)𝑌𝑌𝑖𝑖,𝑡𝑡�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗ 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀�𝜎𝜎𝑖𝑖𝑌𝑌 (8a) Equation 9: Price of exports for the non-commodities industry ∆log (𝑃𝑃𝑛𝑛𝑐𝑐,𝑡𝑡 𝑋𝑋) = 𝛽𝛽1�log (𝑃𝑃𝑛𝑛𝑐𝑐,𝑡𝑡−1 𝑋𝑋)− 𝛽𝛽2𝑃𝑃𝑛𝑛𝑐𝑐,𝑡𝑡 𝑋𝑋𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡𝑑𝑑−log (𝑃𝑃𝑛𝑛𝑐𝑐,𝑡𝑡−1 𝑋𝑋∗)�+𝛽𝛽3�∆log �𝑃𝑃𝑡𝑡𝑊𝑊 𝜀𝜀𝑡𝑡�� + (1−𝛽𝛽3)∆log (𝑃𝑃𝑛𝑛𝑐𝑐,𝑡𝑡 𝑋𝑋∗) (9) Equilibrium price of exports for the non-commodities industry (based on revenue-maximising combination of exports and domestic sales from total supply). 𝑃𝑃𝑛𝑛𝑐𝑐,𝑡𝑡 𝑋𝑋∗=𝑃𝑃𝑛𝑛𝑐𝑐,𝑡𝑡 𝐸𝐸∗�1−𝜙𝜙𝑛𝑛𝑐𝑐 𝜙𝜙𝑛𝑛𝑐𝑐 𝑋𝑋𝑛𝑛𝑐𝑐,𝑡𝑡 𝐸𝐸𝑛𝑛𝑐𝑐,𝑡𝑡�1 𝜎𝜎𝑛𝑛𝑛𝑛 𝑇𝑇 (9a) The Treasury Macroeconometric Model of Australia - Modelling approach 59 Fourth, in discounting future cash flows using the required rate of return, equation (A1.11) is unrealistic in implicitly assuming static expectations with respect to the discount rates that link each quarter. This is because there are well-developed bond markets in which the term structure of interest rates, and hence future expected short-term interest rates, are readily observable. Hence, in defining the required rate of return, the real discount rates used should not just refer to one quarter ahead, but rather should reflect the typical time horizon of investment decisions. This occurs automatically if model-consistent expectations are assumed. Under static expectations, it can be done in an approximate way by using a long-term interest rate. The real discount rate should also allow for risk. Taking these considerations into account, equation (A1.17) for the required rate of return uses as the real discount rate a nominal bond rate (𝑅𝑅𝐼𝐼10) net of expected inflation over the same time horizon (𝜋𝜋𝑡𝑡𝑒𝑒) plus an allowance for risk (𝑄𝑄𝑅𝑅𝐼𝐼𝐾𝐾𝐾𝐾). Annual, percentage rates are converted to quarterly, proportionate rates by dividing by 400. 𝑅𝑅𝑅𝑅𝐼𝐼𝑇𝑇𝑡𝑡=𝛿𝛿+𝑅𝑅𝐼𝐼10𝑡𝑡−𝜋𝜋𝑡𝑡𝑒𝑒 400 +𝑄𝑄𝑅𝑅𝐼𝐼𝐾𝐾𝐾𝐾𝑖𝑖,𝑡𝑡 (A1.17) This means that the investment equation for each industry is given by equation (A1.15), where disequilibrium investment is defined by equation (A1.6), the after-tax actual rate of return, 𝐼𝐼𝑅𝑅𝐼𝐼𝑇𝑇, by equation (A1.16) and the after-tax required rate of return, 𝑅𝑅𝑅𝑅𝐼𝐼𝑇𝑇, by equation (A1.17). This same set of equations appears in the list of key equations in Attachment A, after conversion to EMMA model notation and units of measurement. Specifically, equations (A1.15), (A1.6), (A1.16) and (A1.17) from here, appear there as equations (3), (3a), (3b) and (3c) respectively. The Treasury Macroeconometric Model of Australia - Modelling approach 60 Appendix C: Productivity This attachment describes the approach to modelling productivity in EMMA. Firm value-added production in each industry is explained by a constant elasticity of substitution (CES) production function with constant returns to scale. This production function explains how firms combine factor inputs of capital (𝐾𝐾), labour (𝑁𝑁𝑁𝑁) and a fixed factor (𝐹𝐹) to produce value added output (𝑉𝑉). 𝑉𝑉𝑖𝑖,𝑡𝑡=𝐼𝐼𝑖𝑖,𝑡𝑡�𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉+𝜃𝜃𝑖𝑖𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜉𝜉𝑖𝑖,𝑡𝑡𝐾𝐾𝑖𝑖,𝑡𝑡−1�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉+𝜃𝜃𝑖𝑖𝐹𝐹1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁𝐹𝐹𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 (A2.1) Where, for each industry 𝑖𝑖: 𝑉𝑉𝑖𝑖,𝑡𝑡 is GVA at basic prices; 𝐼𝐼𝑖𝑖,𝑡𝑡 is total factor productivity; 𝜃𝜃’s represent each factor’s respective contribution to output such that 𝜃𝜃𝑖𝑖𝑁𝑁+𝜃𝜃𝑖𝑖𝐾𝐾+𝜃𝜃𝑖𝑖𝐹𝐹= 1; 𝜎𝜎𝑖𝑖𝑉𝑉 is the elasticity of substitution between the factors; λ𝑖𝑖,𝑡𝑡 𝑁𝑁 represents the level of labour-augmenting technical change; 𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡is total hours worked; 𝜉𝜉𝑖𝑖,𝑡𝑡 is capacity utilisation; 𝐾𝐾𝑖𝑖,𝑡𝑡−1 is the capital stock; and, 𝐹𝐹𝑖𝑖,𝑡𝑡 is the fixed factor input. Labour productivity reflects the ability of labour to transform its input of hours worked into value-added production. Labour productivity can be derived by re-arranging the CES production function in Equation A2.1 (shown for the non-commodities industry which does not include a fixed factor): 𝑉𝑉𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡=�𝐼𝐼𝑖𝑖,𝑡𝑡λ𝑖𝑖,𝑡𝑡 𝑁𝑁�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1⎣ ⎢ ⎢ ⎡ 𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉+(1−𝜃𝜃𝑖𝑖𝑁𝑁)1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜉𝜉𝑖𝑖,𝑡𝑡𝐾𝐾𝑖𝑖,𝑡𝑡−1 λ𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉⎦ ⎥ ⎥ ⎤ 𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 (A2.2) Taking difference logs, it can be shown that labour productivity growth is equal to the sum of: • the growth rate of total factor productivity (𝐼𝐼𝑖𝑖,𝑡𝑡) (Hicks neutral productivity); • the growth rate of labour-augmenting technical change (λ𝑖𝑖,𝑡𝑡 𝑁𝑁) (Harrod neutral productivity); and • the rate of capital deepening (capital per effective unit of labour ( 𝜉𝜉𝑖𝑖,𝑡𝑡𝐾𝐾𝑡𝑡−1 λ𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝐻𝐻𝑖𝑖,𝑡𝑡 )) ∆log �𝑌𝑌𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡�=∆log�λ𝑖𝑖,𝑡𝑡 𝑁𝑁�+∆log�𝐼𝐼𝑖𝑖,𝑡𝑡�+∆log �𝜉𝜉𝑖𝑖,𝑡𝑡𝐾𝐾𝑖𝑖,𝑡𝑡−1 λ𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡� (A2.3) Total factor productivity (Hicks neutral) is defined as improvements in productivity that have a symmetrical impact on the productivity of labour and capital (and the fixed factor in the case of the commodity industries). That is, an increase in total factor productivity will increase the marginal productivity of labour (MPL) and capital (MPK) by the same percentage. The Treasury Macroeconometric Model of Australia - Modelling approach 61 Harrod neutral productivity means that improvements in productivity are specific to a factor of production. This is often called labour or capital-augmenting technical change. Improvements in the productive capacity of capital are embodied in the value of the capital stock itself rather than augmenting the capital stock.17 The focus is therefore on labour augmenting technical change. Balanced growth refers to an allocation where output grows at a constant rate and the capital-output ratio, the interest rate and factor shares remain constant. These are the so-called Kaldor facts (Kaldor, 1963). Balanced growth is a desirable property for a macroeconometric model like EMMA since it ensures the long-run stability of the model. The Kaldor facts are broadly consistent with Australian data. Notably, after accounting for changes in industry composition, factor income shares have remained broadly constant over the past 30 years. Uzawa’s theorem (Uzawa, 1961) shows that constant growth of output, capital and consumption combined with constant returns to scale implies that the aggregate production function must have a representation with Harrod-neutral (purely labour-augmenting) technological progress. The intuition of this result follows from the fact that capital accumulates whereas labour supply is exogenous. That is, increases in labour-augmenting technical change can induce increases in the productive capital stock and hence allows for factor inputs shares to be maintained, whereas increases in capital-augmenting technical change do not induce increases in labour supply.18 Labour augmenting technical change and total factor productivity cannot be distinguished in the labour demand equation without additional identifying assumptions. Following the business cycle literature, total factor productivity has been modelled as a first-order autoregressive stochastic process. Total factor productivity and capital deepening are assumed to be cyclical, and are therefore stationary in the long run. This means they contribute to productivity growth in the short run, but in equilibrium they are constant and so labour productivity grows in line with labour-augmenting technical change. Labour-augmenting technical change, total factor productivity and capital utilisation are unobserved. The first order condition on labour, combined with data on the real producer wage, has been used to extract the unobserved labour-augmenting technical change and total factor productivity components. It is then assumed that capital utilisation captures the remaining variation in observed value-added output. The first order condition for labour from the firm’s profit maximisation problem sets the marginal product of labour equal to the real producer wage (𝑊𝑊𝑡𝑡 𝑁𝑁𝑖𝑖,𝑡𝑡): 𝜕𝜕𝑌𝑌𝑖𝑖,𝑡𝑡 𝜕𝜕𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡=�λ𝑖𝑖,𝑡𝑡 𝑁𝑁𝐼𝐼𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉�𝑌𝑌𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡�1 𝜎𝜎𝑖𝑖𝑉𝑉=𝑉𝑉𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡 17 Cyclical variations in the utilisation of capital are captured through the term 𝜉𝜉𝑖𝑖,𝑡𝑡. 18 The Cobb-Douglas production function is a special case under which it is not possible to separately identify Hicks and Harrod neutral productivity. The Cobb-Douglas production function can be represented as purely labour-augmenting and so total factor productivity in a Cobb-Douglas production function is consistent with balanced growth. The Treasury Macroeconometric Model of Australia - Modelling approach 62 We rearrange the first order condition to give the following equilibrium labour demand equation: 𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡=�𝐼𝐼𝑖𝑖,𝑡𝑡λ𝑖𝑖,𝑡𝑡 𝑁𝑁�𝜎𝜎𝑖𝑖𝑉𝑉−1𝜃𝜃𝑖𝑖𝑁𝑁𝑌𝑌𝑖𝑖,𝑡𝑡�𝑉𝑉𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡�−𝜎𝜎𝑖𝑖𝑉𝑉 (A2.4) This long-run relationship can be log-linearised and fitted to data. Given the assumption that total factor productivity is stationary and mean-zero, it will capture deviations in the long-run relationship between employment and equilibrium employment (𝑡𝑡ℎ𝑡𝑡∗) as derived from the first order condition: 𝑡𝑡ℎ𝑖𝑖,𝑡𝑡 ∗=(𝜎𝜎𝑖𝑖𝑉𝑉−1)λ𝑖𝑖,𝑡𝑡 𝑛𝑛+𝜃𝜃𝑖𝑖𝑁𝑁+𝑦𝑦𝑖𝑖,𝑡𝑡−𝜎𝜎𝑖𝑖𝑉𝑉�𝑤𝑤𝑡𝑡−𝑝𝑝𝑖𝑖,𝑡𝑡� (A2.5) 𝑎𝑎𝑖𝑖,𝑡𝑡=𝑡𝑡ℎ𝑖𝑖,𝑡𝑡−𝑡𝑡ℎ𝑖𝑖,𝑡𝑡 ∗ (A2.6) Substituting in our assumption of cyclical total factor productivity gives our signal equation for identifying labour-augmenting technical change: ∆𝑡𝑡ℎ𝑖𝑖,𝑡𝑡=∆𝑡𝑡ℎ𝑖𝑖,𝑡𝑡 ∗+ (𝜌𝜌−1)�𝑡𝑡ℎ𝑖𝑖,𝑡𝑡−1−𝑡𝑡ℎ𝑖𝑖,𝑡𝑡−1 ∗�+(𝜎𝜎𝑖𝑖𝑉𝑉−1)𝑣𝑣𝑡𝑡 𝑣𝑣𝑡𝑡~(0, 𝜎𝜎𝑣𝑣2) (A2.7) We model the unobserved component of labour-augmenting technical change as a stochastic trend, in particular a random walk with time-varying drift (𝛿𝛿𝑡𝑡). The time-varying drift is the second state equation in the system. Signal equation: ∆𝑡𝑡ℎ𝑖𝑖,𝑡𝑡=∆�(𝜎𝜎𝑖𝑖𝑉𝑉−1)λ𝑖𝑖,𝑡𝑡 𝑁𝑁+𝜃𝜃𝑖𝑖𝑁𝑁+𝑦𝑦𝑖𝑖,𝑡𝑡−𝜎𝜎𝑖𝑖𝑉𝑉�𝑤𝑤𝑡𝑡−𝑝𝑝𝑖𝑖,𝑡𝑡�� + (𝜌𝜌−1)�𝑡𝑡ℎ𝑖𝑖,𝑡𝑡−1−�(𝜎𝜎𝑖𝑖𝑉𝑉−1)λ𝑖𝑖,𝑡𝑡−1 𝑁𝑁+𝜃𝜃𝑖𝑖𝑁𝑁+𝑦𝑦𝑖𝑖,𝑡𝑡−1−𝜎𝜎𝑖𝑖𝑉𝑉�𝑤𝑤𝑡𝑡−1−𝑝𝑝𝑖𝑖,𝑡𝑡−1��� +(𝜎𝜎𝑖𝑖𝑉𝑉−1)𝑣𝑣𝑡𝑡 𝑣𝑣𝑡𝑡~(0, 𝜎𝜎𝑣𝑣2) (A2.8) State equations: λ𝑖𝑖,𝑡𝑡 𝑁𝑁= 𝛿𝛿𝑡𝑡+λ𝑖𝑖,𝑡𝑡−1 𝑁𝑁 𝛿𝛿𝑡𝑡=𝛿𝛿𝑡𝑡−1+𝜖𝜖𝑡𝑡 𝜖𝜖𝑡𝑡~(0, 𝜎𝜎𝜖𝜖2) (A2.9) (A2.10) The Treasury Macroeconometric Model of Australia - Modelling approach 63 Capital utilisation has been identified as the residual of the production function: 𝜉𝜉𝑖𝑖,𝑡𝑡=𝑌𝑌𝑖𝑖,𝑡𝑡 𝐼𝐼𝑖𝑖,𝑡𝑡𝐾𝐾𝑖𝑖,𝑡𝑡−1 1 (1 −𝜃𝜃𝑖𝑖𝑁𝑁) 1 𝜎𝜎𝑖𝑖𝑉𝑉−1�1−𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑉𝑉�𝐼𝐼𝑖𝑖,𝑡𝑡λ𝑖𝑖,𝑡𝑡 𝑁𝑁∙𝑁𝑁𝑖𝑖,𝑡𝑡 𝑌𝑌𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 (A2.11) This identification strategy means that a change in total factor productivity or capital utilisation has a temporary effect on the level of measured labour productivity, while shocks to labour augmenting technical change have a permanent effect. The Treasury Macroeconometric Model of Australia - Modelling approach 64 Appendix D: Business Sector Equilibrium equations In EMMA, in the long run, a single profit maximisation problem explains the behaviour of firms and ensures internal consistency between the firm’s input demand and supply decisions. Different functional forms are used for non-commodities sector and the trade-orientated commodities sectors of mining and agriculture. The two commodity industries are assumed to be Classical, so that prices are flexible and producers operate on their supply curves. The non-commodity industry is assumed to be Keynesian, so that its price is sticky and output is demand determined in the short run. Variable Non-Commodities Commodities Imports (𝑴𝑴𝒊𝒊,𝒕𝒕) 𝑀𝑀𝑖𝑖,𝑡𝑡 ∗=(1−𝛼𝛼𝑖𝑖)𝑌𝑌𝑖𝑖,𝑡𝑡�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗ 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀∗�𝜎𝜎𝑖𝑖𝑌𝑌 𝑀𝑀𝑖𝑖,𝑡𝑡 ∗=�𝛼𝛼𝑖𝑖 1−𝛼𝛼𝑖𝑖�−1𝐷𝐷𝑖𝑖,𝑡𝑡�𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀�𝜎𝜎𝑖𝑖𝑌𝑌 Exports (𝑿𝑿𝒊𝒊,𝒕𝒕) 𝑋𝑋𝑖𝑖,𝑡𝑡 ∗=𝑌𝑌𝑖𝑖,𝑡𝑡 𝐹𝐹�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗𝜀𝜀𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐹𝐹�𝜖𝜖 𝑋𝑋𝑖𝑖,𝑡𝑡 ∗=𝜙𝜙𝑖𝑖1 𝜎𝜎𝑖𝑖𝑇𝑇+1�𝑌𝑌𝑖𝑖,𝑡𝑡 ∗𝜎𝜎𝑖𝑖𝑇𝑇+1 𝜎𝜎𝑖𝑖𝑇𝑇−(1 −𝜙𝜙𝑖𝑖)−1 𝜎𝜎𝑖𝑖𝑇𝑇𝐸𝐸𝑖𝑖,𝑡𝑡𝜎𝜎𝑖𝑖𝑇𝑇+1 𝜎𝜎𝑖𝑖𝑇𝑇�𝜎𝜎𝑖𝑖𝑇𝑇 𝜎𝜎𝑖𝑖𝑇𝑇+1 Domestic supply (𝑬𝑬𝒊𝒊,𝒕𝒕) Demand driven Demand driven Total supply (𝒀𝒀𝒊𝒊,𝒕𝒕) Demand driven 𝑌𝑌𝑖𝑖,𝑡𝑡 ∗=�𝛼𝛼𝑖𝑖1 𝜎𝜎𝑖𝑖𝑌𝑌�𝐷𝐷𝑖𝑖,𝑡𝑡 ∗�𝜎𝜎𝑖𝑖𝑌𝑌−1 𝜎𝜎𝑖𝑖𝑌𝑌+ (1 −𝛼𝛼𝑖𝑖)1 𝜎𝜎𝑖𝑖𝑌𝑌�𝑀𝑀𝑖𝑖,𝑡𝑡 ∗�𝜎𝜎𝑖𝑖𝑌𝑌−1 𝜎𝜎𝑖𝑖𝑌𝑌�𝜎𝜎𝑖𝑖𝑌𝑌 𝜎𝜎𝑖𝑖𝑌𝑌−1 Domestic production (𝑫𝑫𝒊𝒊,𝒕𝒕) 𝐷𝐷𝑖𝑖,𝑡𝑡 ∗=𝛼𝛼𝑖𝑖1 1−𝜎𝜎𝑖𝑖𝑌𝑌 �𝑌𝑌𝑖𝑖,𝑡𝑡𝜎𝜎𝑖𝑖𝑌𝑌−1 𝜎𝜎𝑖𝑖𝑌𝑌−(1 −𝛼𝛼𝑖𝑖)1 𝜎𝜎𝑖𝑖𝑌𝑌𝑀𝑀𝑖𝑖,𝑡𝑡 ∗𝜎𝜎𝑖𝑖𝑌𝑌−1 𝜎𝜎𝑖𝑖𝑌𝑌�𝜎𝜎𝑖𝑖𝑌𝑌 𝜎𝜎𝑖𝑖𝑌𝑌−1 𝐷𝐷𝑖𝑖,𝑡𝑡 ∗= 𝑉𝑉 𝑖𝑖,𝑡𝑡 ∗ (1−∑𝛽𝛽𝑖𝑖𝑖𝑖 ) The Treasury Macroeconometric Model of Australia - Modelling approach 65 Variable Non-Commodities Commodities Value added (𝑽𝑽𝒊𝒊,𝒕𝒕) 𝑉𝑉𝑖𝑖,𝑡𝑡 ∗=𝐷𝐷𝑖𝑖,𝑡𝑡 ∗�1−�𝛽𝛽𝑖𝑖 𝑖𝑖� 𝑉𝑉𝑖𝑖,𝑡𝑡 ∗=𝐼𝐼𝑖𝑖,𝑡𝑡�𝜃𝜃𝑖𝑖𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉𝐾𝐾𝑖𝑖,𝑡𝑡−1𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉+𝜃𝜃𝑖𝑖𝐹𝐹1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁𝐹𝐹𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 �1−𝜃𝜃𝑖𝑖𝑁𝑁�𝐼𝐼𝑖𝑖,𝑡𝑡𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁�𝜎𝜎𝑖𝑖𝑉𝑉−1�𝑉𝑉𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉�1−𝜎𝜎𝑖𝑖𝑉𝑉�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 Import price (𝑷𝑷𝒊𝒊,𝒕𝒕 𝑴𝑴) 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀∗=𝑃𝑃𝑡𝑡𝐹𝐹 𝜀𝜀𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀∗=𝑃𝑃𝑡𝑡 𝐹𝐹 𝜀𝜀𝑡𝑡 Export supply price (𝑷𝑷𝒊𝒊,𝒕𝒕 𝑿𝑿) 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗=𝑃𝑃𝑖𝑖,𝑡𝑡 𝐸𝐸∗�𝑋𝑋𝑖𝑖,𝑡𝑡 𝐸𝐸𝑖𝑖,𝑡𝑡∙1−𝜙𝜙𝑖𝑖 𝜙𝜙𝑖𝑖�1 𝜎𝜎𝑖𝑖𝑇𝑇 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗=𝑃𝑃𝑖𝑖,𝑡𝑡 𝑊𝑊 𝜀𝜀𝑡𝑡�𝑋𝑋𝑖𝑖,𝑡𝑡 𝑌𝑌𝑖𝑖,𝑡𝑡 𝐹𝐹�−1 𝜖𝜖 Domestic supply price (𝑷𝑷𝒊𝒊,𝒕𝒕 𝑬𝑬) 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐸𝐸∗=�1 1−𝜙𝜙𝑖𝑖𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗(1+𝜎𝜎𝑖𝑖𝑇𝑇)−𝜙𝜙𝑖𝑖 1−𝜙𝜙𝑖𝑖𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗(1+𝜎𝜎𝑖𝑖𝑇𝑇)�1 1+𝜎𝜎𝑖𝑖𝑇𝑇 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐸𝐸∗=𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗�𝐸𝐸𝑖𝑖,𝑡𝑡 𝑋𝑋𝑖𝑖,𝑡𝑡 ∗∙𝜙𝜙𝑖𝑖 1−𝜙𝜙𝑖𝑖�1 𝜎𝜎𝑖𝑖𝑇𝑇 Total supply price (𝑷𝑷𝒊𝒊,𝒕𝒕 𝒀𝒀) 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗=�𝛼𝛼𝑖𝑖∙𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷∗�1−𝜎𝜎𝑖𝑖𝑌𝑌�+(1−𝛼𝛼𝑖𝑖)∙𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀�1−𝜎𝜎𝑖𝑖𝑌𝑌��1 1−𝜎𝜎𝑖𝑖𝑌𝑌 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗=�𝜙𝜙𝑖𝑖∙𝑃𝑃𝑖𝑖,𝑡𝑡 𝑋𝑋∗�1+𝜎𝜎𝑖𝑖𝑇𝑇�+ (1 −𝜙𝜙𝑖𝑖)∙𝑃𝑃𝑖𝑖,𝑡𝑡 𝐸𝐸∗�1+𝜎𝜎𝑖𝑖𝑇𝑇��1 1+𝜎𝜎𝑖𝑖𝑇𝑇 Domestic production price (𝑷𝑷𝒊𝒊,𝒕𝒕 𝑫𝑫) 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷∗=�1−�𝛽𝛽𝑖𝑖 𝑖𝑖�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉∗+�𝛽𝛽𝑖𝑖𝑃𝑃𝑖𝑖,𝑡𝑡 𝐸𝐸 𝑖𝑖 𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷∗=𝛼𝛼𝑖𝑖1 𝜎𝜎𝑖𝑖𝑌𝑌−1�𝑃𝑃𝑖𝑖,𝑡𝑡 𝑌𝑌∗�1−𝜎𝜎𝑖𝑖𝑌𝑌�−(1 −𝛼𝛼𝑖𝑖)∙𝑃𝑃𝑖𝑖,𝑡𝑡 𝑀𝑀∗�1−𝜎𝜎𝑖𝑖𝑌𝑌��1 1−𝜎𝜎𝑖𝑖𝑌𝑌 The Treasury Macroeconometric Model of Australia - Modelling approach 66 Variable Non-Commodities Commodities Value added price (𝑷𝑷𝒊𝒊,𝒕𝒕 𝑽𝑽) 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉∗=1 𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉𝑉𝑉𝑡𝑡 𝐼𝐼𝑖𝑖,𝑡𝑡𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁�1 𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉 −𝜃𝜃𝑖𝑖𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉 𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉�𝐼𝐼𝑖𝑖,𝑡𝑡𝐾𝐾𝑖𝑖,𝑡𝑡−1 𝑉𝑉𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉�1 𝜎𝜎𝑖𝑖𝑉𝑉−1 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉∗=�𝑃𝑃𝑖𝑖,𝑡𝑡 𝐷𝐷 ∗ −∑𝛽𝛽𝑖𝑖𝑃𝑃𝑖𝑖,𝑡𝑡 𝐸𝐸 𝑖𝑖� (1−∑𝛽𝛽𝑖𝑖𝑖𝑖 ) Labour demand – total hours worked (𝑵𝑵𝑵𝑵𝒊𝒊,𝒕𝒕) 𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 ∗=�1 𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁�𝜃𝜃𝑖𝑖𝑁𝑁1 1−𝜎𝜎𝑖𝑖𝑉𝑉��𝑉𝑉𝑖𝑖,𝑡𝑡 𝐼𝐼𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉 −𝜃𝜃𝑖𝑖𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉𝐾𝐾𝑖𝑖,𝑡𝑡−1𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡 ∗=𝜃𝜃𝑖𝑖𝑁𝑁�𝐼𝐼𝑖𝑖,𝑡𝑡𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁�𝜎𝜎𝑖𝑖𝑉𝑉−1𝑉𝑉𝑖𝑖,𝑡𝑡�𝑉𝑉𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑉𝑉�−𝜎𝜎𝑖𝑖𝑉𝑉 The Treasury Macroeconometric Model of Australia - Modelling approach 67 Industry Production and Trade Technology Functions Value added output 𝑉𝑉𝑖𝑖,𝑡𝑡=𝐼𝐼𝑖𝑖,𝑡𝑡�𝜃𝜃𝑖𝑖𝑁𝑁1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜆𝜆𝑖𝑖,𝑡𝑡 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉+𝜃𝜃𝑖𝑖𝐾𝐾1 𝜎𝜎𝑖𝑖𝑉𝑉𝐾𝐾𝑖𝑖,𝑡𝑡−1𝜎𝜎𝑖𝑖𝑉𝑉−1 𝜎𝜎𝑖𝑖𝑉𝑉�𝜎𝜎𝑖𝑖𝑉𝑉 𝜎𝜎𝑖𝑖𝑉𝑉−1 Domestic output 𝐷𝐷𝑖𝑖,𝑡𝑡=min �𝑉𝑉𝑖𝑖,𝑡𝑡,𝐽𝐽𝑖𝑖,𝑡𝑡,���1−�𝛽𝛽𝑗𝑗 𝑗𝑗�𝑉𝑉𝑖𝑖,𝑡𝑡,�𝛽𝛽𝑗𝑗𝐽𝐽𝑗𝑗𝑖𝑖,𝑡𝑡 𝑗𝑗� Total supply (production) 𝑌𝑌𝑖𝑖,𝑡𝑡=�𝛼𝛼𝑖𝑖1 𝜎𝜎𝑖𝑖𝑌𝑌�𝐷𝐷𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑌𝑌−1 𝜎𝜎𝑖𝑖𝑌𝑌+(1−𝛼𝛼𝑖𝑖)1 𝜎𝜎𝑖𝑖𝑌𝑌�𝑀𝑀𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑌𝑌−1 𝜎𝜎𝑖𝑖𝑌𝑌�𝜎𝜎𝑖𝑖𝑌𝑌 𝜎𝜎𝑖𝑖𝑌𝑌−1 Total use (distribution) 𝑌𝑌𝑖𝑖,𝑡𝑡=�𝜙𝜙𝑖𝑖1 𝜎𝜎𝑖𝑖𝑇𝑇�𝑋𝑋𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑇𝑇−1 𝜎𝜎𝑖𝑖𝑇𝑇+ (1 −𝜙𝜙𝑖𝑖)1 𝜎𝜎𝑖𝑖𝑇𝑇�𝐸𝐸𝑖𝑖,𝑡𝑡�𝜎𝜎𝑖𝑖𝑇𝑇−1 𝜎𝜎𝑖𝑖𝑇𝑇�𝜎𝜎𝑖𝑖𝑇𝑇 𝜎𝜎𝑖𝑖𝑇𝑇−1 Notation Where 𝑉𝑉 is value added output; 𝐷𝐷 is domestic output, 𝑌𝑌 is total supply/use; 𝐽𝐽 is intermediate inputs; 𝑀𝑀 is imports, 𝑋𝑋 is exports, 𝐸𝐸 is domestic demand; 𝑁𝑁𝑁𝑁 is total hours worked; 𝐾𝐾 is capital; 𝐼𝐼 is total factor productivity; 𝜆𝜆𝑁𝑁 is labour augmenting technical change; 𝜉𝜉 is capacity utilisation; 𝜃𝜃, 𝛽𝛽, 𝛼𝛼 and 𝜙𝜙 represent input shares; and, 𝜎𝜎 is elasticity of substitution/transformation.