Commodity prices and labour market dynamics in small open economies

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Commodity prices and labour market dynamics in small open economies Martin Bodenstein, Gunes Kamber, and Christoph Thoenissen 2017-039 Please cite this paper as: Bodenstein, Martin, GunesKamber, andChristophThoenissen(2017). “Commodityprices and labour market dynamics in small open economies,” Finance and Economics Discussion Series 2017-039. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2017.039. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Commodity prices and labour market dynamics in small open economies ∗ Martin Bodenstein Gu¨ne¸s Kamber Christoph Thoenissen Federal Reserve Board Bank for International Settlements University of Sheffield April 4, 2017 Abstract We investigate the connection between commodity price shocks and unemployment in advanced resource-rich small open economies from an empirical and theoretical perspective. Shocks to commodity prices are shown to influence labour market conditions primarily through the real exchange rate. The empirical impact of commodity price shocks is obtained from estimating a panel vector autoregression; a positive price shock is found to expand the components of GDP, to cause the real exchange rate to appreciate, and to improve labour market conditions. For every one percent increase in commodityprices,ourestimatessuggestaonebasispointdeclineintheunemploymentrateandatitspeaka0.3%increase inunfilledvacancies. Wethenmatchtheimpulseresponsestoacommoditypriceshockfromasmallopeneconomymodel with net commodity exports and search and matching frictions in the labour market to these empirical responses. As in the data, an increase in commodity prices raises consumption demand in the small open economy and induces a real appreciation. Facing higher relative prices for their goods, non-commodity producing firms post additional job vacancies, causingthenumberofmatchesbetweenfirmsandworkerstorise. Asaresult,unemploymentfalls,evenifemploymentin the commodity-producing sector is negligible. JEL classifications: E44, E61, F42. Keywords: commodity prices, search and matching, unemployment ∗ Theviewsexpressedinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviews oftheBoardofGovernorsoftheFederalReserveSystem,theBankforInternationalSettlement,oranyotherpersonassociatedwith the Federal Reserve System or the Bank for International Settlements. We are grateful to seminar participants at the CEF 2016 in Bordeaux, the 2015 ABFER in Singapore, University of Auckland, Victoria University of Wellington, University of Sheffield, the University of Durham and Heriot Watt University in Edinburgh. We thank Panos Nanos for valuable comments and Junzhu Zhao fromtheNationalUniversityofSingaporeforprovidinguswithoutstandingresearchassistance. ∗∗ Contact information: Martin Bodenstein, E-mail martin.r.bodenstein@frb.gov; Gu¨ne¸s Kamber, E-mail Gunes.Kamber@bis.org; ChristophThoenissen,E-mailc.thoenissen@sheffield.ac.uk. 1

1 Introduction Withemploymentremainingbelowitspre-GreatRecessionlevelinmanyadvancedeconomies, thelabourmarket has taken the centre stage of policy discussions. Even economies that did not experience the symptoms of a financial crisis directly have seen a slow recovery of their labour markets. Among these economies are Australia, Canada, New Zealand, and Norway, all of which are net exporters of commodities. Other factors aside, the run-up in commodity prices prior to 2008, followed by steep price declines during the crises, and their incomplete recoveries since appear to have crucially influenced the labour markets of these small open economies. Togarnerabetterunderstandingofthenexusbetweencommoditypricesandunemploymentintheseresourcerich small open economies we investigate this connection from an empirical and a theoretical perspective. Shocks to commodity prices influence labour market conditions primarily through the real exchange rate. For a small commodity producing economy, an increase in the prices of its exported commodities raises wealth and consumption demand and induces a real appreciation. Facing higher relative prices for their goods, non-commodity producing firms post additional job vacancies, causing the number of matches between firms and workers to rise. Asaresult, unemploymentfalls, evenifemploymentinthecommodity-producingsectorisnegligible. Documenting and analysing this hitherto unexplored link between commodity prices, the real exchange rate, and labour market conditions is the key contribution of this paper. Theeconomiesinourpanelvectorautoregression(PVAR)analysisincludeAustralia,Canada,NewZealandand Norway, allofwhicharenetexportersofcommoditieswithhighqualitydataonunfilledvacancies, hoursworked, and unemployment. Restricting attention to net exporters allows for side stepping the issue of incomplete passthroughfromimportpricestoconsumerpricesfacedbynetcommodityimporters. Instead,ashocktocommodity prices has a direct effect on the terms of trade and the real exchange rate of net exporters. Commodity price shocks are identified recursively as in other empirical contributions that study the impact of commodity price or terms of trade shocks on small open economies. A positive price shock is found to expand the components of GDP, to cause the real exchange rate to appreciate, and to improve labour market conditions. For every one percent increase in commodity prices, our estimates suggest a one basis point decline in the unemployment rate and at its peak a 0.3% increase in vacancies. Webuildasmallopeneconomymodelwithnetcommodityexportsthatfeaturessearchandmatchingfrictions in the labour market as proposed by Diamond (1982), Mortensen (1982), and Pissarides (1985) (DMP) to obtain an economic interpretation of these empirical findings. Firms post vacancies and workers search for jobs. When a firm and a worker meet, wages are determined by Nash bargaining between the two parties. In departure from most of the search and matching literature, we assume that preferences over consumption and labour are not separable as in Greenwood et al. (1988), which gives rise to a consumption differential between employed and unemployed agents to compensate the employed for the disutility from labour. To keep matters simple, all goods are traded and commodity production is fixed in our baseline model. We proceed to show that, conditional on commoditypriceshocks,thistypeofmodeliscapableofgeneratingdatacongruentlabourmarketdynamics. Since our empirical identification scheme identifies commodity price shocks in the data, the results from estimating the PVARprovideacleanyardstickagainstwhichtoassesstheperformanceofthetheoreticalmodelthroughimpulse response function matching. This exercise yields estimates of key structural model parameters with implications 2

for the consumption differential between employed and unemployed agents and the degree of international risk sharing through financial markets. To achieve sufficient shock amplification for labour market tightness (the ratio of unfilled vacancies and job searchers), our formulation of the DMP model trades off between the replacement ratio, i.e., the ratio between unemployment benefits and wages, and the consumption differential between employed and unemployed agents whichcompensatestheemployedforthedisutilityfromlabour. Whenthisconsumptiondifferentialiszero,agiven amountofshockamplificationcanbeachievedwithahighreplacementratioonlyasinstandardformulationsofthe DMPmodelwithCRRApreferencesoverconsumption. Whenfixingthereplacementratioat40%,ourformulation of the DMP model requires that the consumption of the unemployed does not exceed 60% of the consumption of employed workers in order for the model to match the high volatilities of vacancies and unemployment in the data. This finding is reminiscent of the argument in Hagedorn and Manovskii (2008) to counter the criticism of the DMP framework by Shimer (2005). Most of the search and matching literature focuses on the impact of movements in labour productivity — generallythoughtofasstemmingfromtechnologyshocks—onthelabourmarketinaclosedeconomy. Forshocks that impact labour productivity directly, labour market tightness and therefore unemployment and vacancies are governed by the behaviour of labour productivity; a result that withstands introducing open economy features despite (relatively minor) movements in the real exchange rate. The increase in labour productivity raises the value of a match for the firm and thus the total surplus of a match. Firms increase vacancy postings, more matches are realized and unemployment drops. Output rises. Commoditypriceshocks,however,donottransmittothelabourmarketthroughchangesinlabourproductivity primarily, but rather through changes in the real exchange rate. We show that labour market tightness is approximately proportional to labour productivity and an appreciation of the real exchange rate. Commodity price shocks are closely related to wealth shocks in our theoretical framework and hence a positive price shock results in an immediate real appreciation and pushes up consumption demand. Facing a higher relative price for their goods, firms post additional vacancies, matches rise, and unemployment falls. Labour productivity, however,isslowtorespondreflectingthepaceoftheexpansionofthecapitalstock. Thus,thedynamicsoflabour market tightness, unemployment, and vacancies are dominated by the behaviour of the real exchange rate after a commodity price shock. International financial risk sharing plays an important role in the transmission of the commodity price shock. If the economy was characterised by financial autarky, the windfall profits from an unexpected price increase would cause consumption and investment to rise sharply. Apart from missing out completely on the dynamics of the trade balance, such a model would predict a strong appreciation of the real exchange rate, which in turn would push up vacancies and lower unemployment by more than in our empirical analysis. Thus, the countries in our sample must be able to smooth shocks through financial markets as corroborated by our impulse response function matching procedure. To assess the sensitivity of our findings, several variations of the model are considered. First, we explore the idea in Hall and Milgrom (2008) of replacing Nash bargaining by an alternating offer bargaining game. The estimation shows that this framework can deliver a high degree of shock amplification to labour market tightness 3

foralowreplacementratioevenwhenemployedandunemployedagentsconsumeequalamountsasunderadditive separablepreferences. However, shockamplificationdependssensitivelyonthe splitofvacancypostingcosts into variable and fixed components — this is not the case in our baseline specification. Second, in principle, our frameworkcanalsocapturethedynamicsofanewsshockaboutincreasedfuturecommodityproductionanalysed in Arezki et al. (2015). The remainder of the paper is structured as follows. Section 2 discusses the related literature. We estimate structuralpanelVARsinSection3. Section4presentsasimpleopeneconomymodelwithcommodityexportsand search and matching frictions in the labour market. Section 5 introduces alternative labour market arrangements to the model. The impulse responses to commodity price shocks derived from these models are matched to the empirical impulse response functions in Section 6 and the economic implications are discussed. Section 7 offers sensitivity analysis before Section 8 concludes. A Data Appendix is provided and a separate Technical Appendix documents details not provided in the main text. 2 Related literature Our work contributes to two broad strands of the literature: The literature on the transmission of shocks in open economies and the literature on labour market dynamics in the presence of search and matching frictions. Few studies analyse commodity price shocks from the point of view of advanced economies that are net exporters of commodities. One notable exception is Pieschacon (2012) in comparing the effects of oil shocks in Norway and Mexico with emphasis on different fiscal regimes. There is, however, a large literature on the effects of oil price shocks from the perspective of oil-importing countries. For example, Leduc and Sill (2004) analyse the monetary policy response to oil shocks, and Bodenstein et al. (2011) investigate the transmission channel of oil shocks in an open economy framework.1 In analysing the business cycle determinants of small open economies most contributors focus on movements in the terms of trade instead of the narrower concept of commodity prices. For developing economies, Mendoza (1995), Kose (2002), and Broda (2004) conclude that terms of trade shocks explain up to half of the estimated volatility in aggregate output at business cycle frequency. Reexamining the conventional view, Schmitt-Groh´e and Uribe (2015) uncover substantial heterogeneity across countries with respect to the contribution of terms of trade shocks to business cycle fluctuations. In particular, developing economies that depend on commodity exports appear to be vulnerable as limited access to financial markets and an insufficient macroeconomic policy framework exasperate the impact of commodity price movements. An important element of these studies is the assumption of the terms of trade to be exogenous. Themajorityofstudiesonsmalldeveloped economiesdifferinthisregardfromthoseondevelopingeconomies. The terms of trade are considered to be an endogenous variable and, similar to the closed economy literature on thebusinesscycle,fluctuationsareviewedastheresultofstructuraldisturbancestotechnologyandothersources. Examples of this approach are Gal´ı and Monacelli (2005), Justiniano and Preston (2010), and Adolfson et al. (2007). However, two exceptions in the literature, Correia et al. (1995) and Guajardo (2008) argue that shocks 1Bodensteinetal.(2011)andBodensteinetal.(2012)discusstheliteratureontheimpactofoilshocksonoil-importingcountries. 4

to the terms of trade can be helpful in accounting for aggregate fluctuations in developed small open economies just as they are in the case of developing economies. The open economy literature on commodity prices has emphasized the importance of wealth effects and has modelled commodity price shocks as changes in transfer payments across countries. Recently, the literature on openeconomymacroeconomicshasalsostressedthesubstitutioneffectstemmingfromcommoditypricechangesif commoditiesareanimportantproductioninputinthecountryunderconsideration—seeforexampleBodenstein et al. (2011). Wealth effects can also arise from technology shocks, particularly if these are long lasting or anticipated. Corsetti et al. (2008) have highlighted the role of wealth effects in open economies that arise from very persistent technology shocks; these shocks have both a wealth and a supply effect. Kamber et al. (2016) analysewealtheffectsinopeneconomiesthatareassociatedwithnewsaboutfuturetechnologyshocks;inthiscase the wealth effect precedes the actual increase in supply. In both cases, positive wealth effects generate economic expansions. Our paper focuses on the labour market dynamics in commodity-exporting developed small open economies. Morespecifically,weinvestigatetheempiricalperformanceoftheDMPsearchandmatchingframeworkconditional on commodity price shocks. Our selection of countries provides a good laboratory for this purpose. First, the labour markets in these countries are in general liberalised and the DMP framework captures key features of the labour market institutions in place. Second, high quality data in employment, unemployment, and vacancies are available. Third, despite enormous progress over the years empirical identification of structural shocks continues tobeatopicofcontroversy.2 Withregardtothelabourmarket, theimpactofneutraltechnologyshocksremains unclear. For example, Canova et al. (2013) and Balleer (2012) find that neutral technology shocks with positive long run effects on labour productivity raise unemployment in the short run, whereas Ravn and Simonelli (2008) document a decline in unemployment.3 Turning to the open economy offers the possibility to incorporate shocks that can be identified with less controversy and that have robust implications for the labour market. Small open economies have negligible impact on world commodity prices; assuming a recursive identification scheme (with commodity prices ordered first) or commodity prices to be exogenous appear to be defensible empirical specifications leading to possibly better yardsticks against which to assess the performance of theoretical models. The search and matching framework has emerged as the leading approach for embedding labour markets into macroeconomic equilibrium models. With few exceptions, most contributions building on the DMP framework assume the economy to be closed and to be driven by (labour) productivity shocks only. In this standard formulation,Shimer(2005)pointstothedifficultyoftheDMPframeworktogenerateunemploymentandvacancy flows that are of comparable volatility as in the U.S. data. The strong response of the real wage to labour productivity shocks dampens the incentives of firms to post new vacancies. Shimer (2005) stimulated efforts to improve the propagation of technology shocks in the DMP framework.4 2Since Gal´ı (1999) it has become standard to identify technology shocks in structural VARs by imposing the restriction that only technology shocks can impact labour productivity in the long run. However, this identification approach has not remained uncriticised. Faust and Leeper (1997) argue that structural VARs with long-run restrictions perform poorly in practice given sample size limitations. Furthermore, Lippi and Reichlin(1993)discusshowashort-orderedVARmayfailtoprovideagoodapproximationofthedynamicsofthevariablesintheVARifthetrue data-generatingprocesshasaVARMArepresentation. ForarecentanalysisoftheseissuesandfurtherdetailsseeErcegetal.(2005). 3This debate resembles the one on the hours-worked puzzle raised in Gal´ı (1999) and its explorations by Christiano et al. (2003) and Francis andRamey(2005). 4Candidate solutions to the DMP framework to overcome the shortcomings pointed out in Shimer (2005) are numerous: Shimer (2005) and Hall (2005) propose to real wage rigidities; Hagedorn and Manovskii (2008) argue that the opportunity cost of employment is too low in Shimer 5

Early contributions to embed the standard DMP framework into a model of the business cycle are Andolfatto (1996)andMerz(1995). However,openeconomymodelsrarelyfeaturesearchandmatchingfrictionsinthelabour market. Hairault (2002) and Campolmi and Faia (2011) show how augmenting a standard open economy model by the DMP framework impacts the transmission of shocks across countries. Christiano et al. (2011) develop a detailed small open economy DSGE model with search and matching frictions that can be employed for policy analysis. Finally, Bozetal.(2009)studysearchandmatchingfrictionsinasmallopeneconomymodelcalibrated to Mexican data. 3 Commodity price shocks in advanced small open economies Amongdevelopedeconomies,netexportsofcommoditiesaresignificantonlyforasmallsetofcountries. According totheIMF(2012), netcommodityexportsaccountformorethan30%oftotalexportsinAustralia, Iceland, New Zealand and Norway, and around 20% in Canada. Furthermore, net commodity exports account for 5% to 10% of GDP on average.5 Because of data limitations Iceland is excluded from our analysis. To quantify the impact of commodity price shocks on economic activity and labour markets we estimate structural vector autoregressive (SVAR) models. 3.1 Data description Our dataset consists of quarterly data for Australia, Canada, New Zealand, and Norway spanning from 1994 Q3 to 2013 Q4.6 For each country, we include a trade-weighted real commodity price index, expressed in US dollars, except for Norway for which we use the price of Brent crude oil. Nine country-specific macroeconomic time series complete the dataset: GDP per capita, consumption per capita, investment per capita, the unemployment rate, unfilled vacancies, net exports of goods and services relative to GDP, the real effective exchange rate, the real wage deflated by consumer prices, and hours worked per capita. With the exception of the unemployment rate and net exports, the data are transformed into logs. All data are de-trended. For the baseline VAR, we subtract a quadratic trend from the data. To assess the importance of trade in commodities, Table 1 lists the three most important commodities for the four countries in the sample, based on net exports. Iron ores and concentrates account for 33% of Australia’s net exports. In Canada and Norway exports of crude oil account for 30% and 43% net exports, respectively. 24% of New Zealand’s net exports are accounted for by milk concentrates. Some countries in our sample may be considered to be important players in selected commodity markets. For example, Australia is the world’s largest exporter of iron ore. However, Australia’s total production of iron ore is significantly below China’s and worldproductionofironores. Similarly,NewZealand’slargeexportsofmilkproductspaleincomparisontomilk production in India, the United States, and the European Union. Economic areas with large domestic markets (2005); Hall and Milgrom (2008) suggest departures from Nash bargaining over wages. Yashiv (2007) provides a comprehensive summary of the debateandabroaderassessmentofthesearchandmatchingframework. 5Thesamereportshowsthatnetcommodityexportstototalexportsexceed20%inSouthKorea,butnetcommodityexportsaccountforless than2.5%ofGDP. 6ThestartofthedatasampleinourpanelVARisdictatedbytheavailabilityofquarterlyvacancydataforNewZealand. Wealsoexperimented withlongertimeserieswhenestimatingcountry-specificVARsdependingondataavailability. Detailsonthedatausedinouranalysisareprovided intheDataAppendix. AseparateTechnicalAppendixgivesdetailsonadditionalestimationresults. 6

produce and consume a significantly larger share of commodities, but nevertheless export less. As we focus on a country’sroleacrossallcommoditiesandweusecountry-specifictrade-weightedcommoditypricesinouranalysis, assuming price taking behaviour in commodity markets for the countries in our sample appears justified. For all fourcountries, commoditypriceshaveexperiencedhighvolatilityoverthesampleasvisualisedbyFigure1which plots the quarterly percentage change in four commodity price series. Relative to real GDP, commodity prices are between 5 and 21 times more volatile. 3.2 Estimation strategy TheeffectsofcommoditypriceshocksonthelabourmarketareestimatedusingapanelSVARapproach.7 Asthe relevanttimeseriesareshort,butthecountriesinoursampleexperiencecommonalitiesintheireconomicstructure, combing the data across countries can improve the quality of the coefficient estimates. Furthermore, estimation ofapanelprovidesasinglebenchmarkformatchingtheimpulseresponsefunctionsimpliedbytheoreticalmodels to their empirical counterparts. As in Ravn et al. (2012) and Akinci (2013), the baseline specification assumes that heterogeneity across countries is constant, i.e., we conduct a pooled estimation with fixed effects of a reduced form VAR: y =µ +A(L)y +u . (1) i,t i i,t−1 i,t The factor A(L) ≡ A +A L+A L2 +... denotes a lag polynomial where L is the lag operator. The vector 0 1 2 u summarises the mean-zero, serially uncorrelated exogenous shocks with variance-covariance matrix Σ and i,t u µ denotes the country fixed effect. The lag length is set at 2 in our baseline.8 i The prices of the commodities traded by the countries in our sample are determined in the world markets. Commoditypriceshocksareidentifiedthrougharecursiveidentificationscheme. Withcommoditypricesordered first in the Cholesky decomposition, country-specific shocks are ruled out from affecting commodity prices contemporaneously. However, domestic developments in our sample countries can in principle feed back into the world market at all other horizons.9 3.3 Estimation results Figure 2 plots the median impulse responses, denoted by the black solid lines, together with the 90% confidence intervals of the panel SVAR to a one-standard-deviation increase in commodity prices. The shock to commodity prices is both hump-shaped and persistent. The median response of commodity prices indicates a rise by about 8 percent by the second quarter. Commodity prices return to trend after 12 quarters. Risingcommoditypricesleadtoaboominthecommodity-exportingeconomies. Output,consumptionandinvestmentriseonimpact. Outputandinvestmentincreasegraduallyandpeakatabout0.15%and1%,respectively. 7Canovaetal.(2013)offersacomprehensivesurveyofpanelVARmodelsusedinmacroeconomics. 8TheAkaike(AIC)andSchwarz(SIC)informationcriteriasuggestoneandthreelags,respectively. Ourbaselinespecificationsetsthelag-length at two, the mid-point of the two criteria. Ventzislav and Kilian (2005) find that SIC might be more accurate in small samples. The results for threelagswerebothqualitativelyandquantitativelyverysimilartoourbaseline. 9Bycontrast,otherempiricalstudiesoftherelationshipbetweencommodityprices(orthetermsoftrade)anddomesticmacroeconomicvariables imposecommodityprices(oreventhetermsoftrade)tobeexogenous. Forrecentexamplesemployingthismorerestrictiveidentificationassumption seePieschacon(2012)orSchmitt-Groh´eandUribe(2015). SeetheTechnicalAppendixforresultsderivedfromthisalternativespecification. 7

Theincreaseinprivateconsumptionisfrontloadedandreaches0.17%. InlinewiththeHarberger-Laursen-Metzler prediction, the net trade position improves by as much as 0.6% of GDP. The dynamic patterns of the trade balance follow closely those of the commodity price index. Accounting for the share of commodity net exports in GDP (averaging around 7.5%), we infer that the movements in the trade balance reflect primarily price rather than quantity changes suggesting a low (short-term) price elasticity of supply for commodities. The measure of the real exchange rate appreciates following an increase in commodity prices, thus increasing the international purchasing power of domestic households and firms. Labour market conditions improve on impact and continue to do so beyond the rise in commodity prices. At its peak, the median response of vacancies reaches almost 2% and the unemployment rate drops by 7 basis points. CPI deflated real wages decline on impact but recover quickly, whereas hours worked rise by about 0.2% on impact and remain elevated for several periods. Asarobustnesscheck,Figure2alsoreportstheimpulseresponsesfromVARsestimatedwithdatatransformed by a linear as well as an Hodrick-Prescott filter. The shape and the magnitude of the impulse response functions appear robust to the de-trending method. The results of the panel VAR are also robust to the exclusion of individual countries from the data set. Dropping one country at a time, i.e., estimating four different VARs with only three countries, the resulting impulse responses suggest that our findings are not solely driven by one country in the data set. This and other checks are reported in the Technical Appendix. There we also examine thesensitivityofourfindingstochangesintheVAR’slaglengthaswellastotheassumptionofblock-exogeneity of commodity prices. In all of these cases the baseline results are found to be robust. The effects of an increase in commodity prices on commodity-exporting countries mirror those found on developed commodity-importing countries. For example, Blanchard and Gal´ı (2007) report that a shock that raisesthepriceofoilunexpectedlyleadstoacontractionineconomicactivitywithGDPfallingandunemployment rising. As in other recent studies, commodity price shocks have a significant, yet quantitatively modest effect on domestic economic activity in commodity-exporting countries. After adjusting the magnitude of the shock, Pieschacon(2012)findsthatforNorwayan8%increaseinthepriceofoilpushesupprivateconsumptionby0.2%.10 The qualitative movements and overall magnitudes of the non-labour market variables are also comparable to those shown in Schmitt-Groh´e and Uribe (2015) for terms of trade shock (rather than commodity prices) in less developed economies. None of these studies, however, reports results for labour market variables. Medina and Naudon (2012) provide some labour market details for Chile. After an increase in mining terms of trade, vacancies expand and the unemployment rate falls by similar magnitudes as in our sample. Both the traded and the non-traded goods sector account for the increase in employment. 4 Baseline model Ourresultssuggestthatacommoditypriceboomisassociatedwithapersistentfallinunemploymentandlasting increases in unfilled job vacancies, consumption and investment. To gain a deeper theoretical understanding of theeconomicchannelsatwork, we buildasimple modelofasmallopeneconomythatexports commodities. The 10In Pieschacon (2012) a one standard deviation increase in the shock implies the price of oil to rise by 20% and Norwegian consumption to increaseby0.5%. 8

modelfeaturessearchandmatchingfrictionsinthelabourmarkettoobtainsatisfyingconceptsofunemployment andvacanciesasintheseminalcontributionsofDiamond(1982), Mortensen(1982), andPissarides(1985)—the DMP framework. The empirical analysis above provides guidance on the roles of wealth effects on the labour supply and international risk sharing. First, an increase in commodity prices raises the revenues from commodity exports. If the increase in revenues induces a strong (negative) wealth effect on the labour supply in the form of hours worked, employment, investment, and non-commodity output could contract depending on the importance of capital and labour in producing commodities in the short-term. Such wealth effects on hours worked after a commodity shock are ruled out in our framework by specifying preferences as in Greenwood et al. (1988) or by assuming individual hours worked to be inelastic. Second, the response on the trade balance suggests that the countries in our sample are limited in their capacity to share risk in international financial markets. Under a low supply elasticity for commodities, the commodity price increase (fall) constitutes a pure wealth transfer to (from) the commodity-producingcountry. IffinancialmarketswerecompleteinthesenseofArrowandDebreu(1954),these transfers would be very small and would have a negligible impact on the domestic economy. Apart from explicitly modelling the labour market, our model is standard. The small open economy is populated by a large number of households normalised to 1. Each household consists of a continuum of agents of measureone. Inordertobeemployed,anagentmustfirstbematchedtoaspecificjobatafirm. Nashbargaining between the agent and the firm determines the terms of employment. Employed agents (workers) supply labour inelastically and receive the real wage w . Unemployed agents receive unemployment benefits in the amount of t bu. Finally, the agents of a household share consumption risk by pooling their resources following the contributions of Andolfatto (1996) and Merz (1995).11 A household consumes goods (a domestically produced traded good and an imported traded good) financed through wages, unemployment benefits, firm profits, and financial assets. The only asset that trades internationally is a foreign bond. Firms accumulate capital, produce goods, and commodities. All commodities are exported. For the purpose of the subsequent discussion we refer to our baseline model as the DMP model. 4.1 Labour flows Firms post vacancies which are filled with workers looking for jobs. The number of new matches, m , resulting t from this process is described by the constant returns to scale matching function: m =χuζv1−ζ. (2) t t t v is the number of vacancies and u is the number of unemployed household members searching for a job at t t the beginning of the period. Newly formed matches increase the total number of employed workers immediately. 11TheapproachofAndolfatto(1996)andMerz(1995)preservesthesimplicityofthetextbookDMPmodelwithriskneutralagentsbutallows embedding labour market search and matching frictions into a standard business cycle framework with risk averse households. Without the construct of risk-sharing through the household, introducing risk averse agents into the DMP model complicates the analytics of the framework; nonlinear numerical methods are required to obtain a solution. Recent contributions that allow for risk pooling at the household level include ArseneauandChugh(2012),GertlerandTrigari(2009),andRavennaandWalsh(2012). 9

Existing matches are destroyed at the exogenous rate ρ.12 As a result, employment, n , evolves according to: t n =(1−ρ)n +m . (3) t t−1 t With the labour force being normalised to unity, u is given by: t u =1−(1−ρ)n . (4) t t−1 Whereas u is the number of unemployed workers searching for a job at the beginning of the period, the t unemployment rate following standard definitions is given by: u˜ =1−n . (5) t t Finally, labour market tightness, θ , is defined as: t v θ = t (6) t u t which allows us to express the matching function in terms of the job finding probability, s : t m s = t =χθ1−ζ (7) t u t t or the job filling probability, q : t m q = t =χθ−ζ. (8) t v t t 4.2 Households Households are modelled following the early contributions of Andolfatto (1996) and Merz (1995). At any point in time, n agents of the household are employed and 1−n agents are unemployed. Each household maximises t t the weighted utility of the employed (w) and unemployed (u) agents subject to a set of constraints. The inter-temporal preferences of the household are given by: ∞ (cid:88) E βt[n U(cw,1)+(1−n )U(cu,0)]. (9) 0 t t t t t=0 The period utility function U(c ,h ) of an agent is strictly concave and twice-continuously differentiable in cont t sumption. The labour supply of an agent, h , equals 1 if the agent is employed and 0 otherwise. We refrain from t the common assumptions that the preferences of the individual agent over consumption feature constant relative risk aversion (CRRA) and that agents do not incur disutility from working. Total consumption of the final consumption good by all household agents is defined as: c =n cw+(1−n )cu. (10) t t t t t 12Endogenousseparationcanbeintroducedbyadaptingtheframeworkoffirm-specificproductivityshockssuggestedbyRameyetal.(2000). 10

The final consumption good, c , consists of a domestically produced good, ch, and an imported good, cf. More t t t precisely, the final good is defined as a constant elasticity of substitution (CES) aggregate: c t = (cid:20) vθ 1 (cid:0) ch t (cid:1)θ− θ 1 +(1−v)θ 1 (cid:16) cf t (cid:17)θ− θ 1(cid:21) θ− θ 1 . (11) θ denotes the elasticity of substitution between these two types of goods and v is the share of the domestically produced good in final consumption. The price index of the final good, P , is chosen to be the numeraire. t Consequently, all other prices are expressed relative to the home final good. For example, the relative price of domestically produced goods, ph, denotes the ratio P t h . t Pt The inter-temporal budget constraint of the household is defined as: n cw+(1−n )cu+pfb =w n +(1−n )bu+(1+r )pfb +π +T . (12) t t t t t t t t t t−1 t t−1 t t Households smooth consumption by trading in one-period bonds, b , that pay out in units of the foreign intermet diate good, pfb . The interest rate payable on these bonds, r , is equal to the world interest rate adjusted for a t t t debt elastic risk-premium. The spread (or discount) relative to the world interest rate, r∗, depends on the debt t position of the economy: −φb (cid:18) pf tbt−¯b (cid:19) 1+r =(1+r∗)e gdpt . (13) t t With households owning all firms, profits from selling goods and commodities, π , are passed to the household. t Additionalincomeisderivedfromemploymentintheamountw n andunemploymentbenefitsbu(1−n ). Lumpt t t sum taxes, T , are collected by the government to finance unemployment insurance. t The household maximises lifetime utility (9) subject to the budget constraint (12), and equations (10) and (11) by choosing c , cw,t, cu,t, and b . The first order conditions associated with this problem can be written as: t t λ = U (cw,1) (14) t c t λ = U (cu,0) (15) t c t (cid:34) (cid:35) 1 λ pf = E β t+1 t+1 . (16) 1+r t t λ t pf t λ denotes the Lagrange multiplier on the household budget constraint. Equations (14) and (15) reveal that due t to efficient risk pooling marginal utility is equalised across household agents irrespective of their employment status. The optimal choices for ch and cf are derived from minimising the costs of obtaining one unit of the t t aggregate consumption good subject to condition (11): ch = v (cid:0) ph(cid:1)−θ c (17) t t t (cid:16) (cid:17)−θ cf = (1−v) pf c . (18) t t t The import price in terms of the final consumption good, pf, and the price of the domestically produced good, t 11

ph, are related through: t 1 = v (cid:0) ph(cid:1)1−θ +(1−v) (cid:16) pf (cid:17)1−θ . (19) t t Note, that the household is not choosing the level of total employment, n , or wages, w . Wages are set in a t t bargaining game between individual workers and firms over the surplus of the match. However, the marginal value of employment to the household is a key component in determining the surplus of the match. Let s t = m ut t denote the probability that an unemployed agent finds a new match. Applying this definition in equation (3) yields: n =(1−ρ)n +s u =(1−ρ)(1−s )n +s (20) t t−1 t t t t−1 t and the marginal (monetary) value of employment to the household, H , is shown to evolve according to: t U(cw,1)−U(cu,0) (cid:20) λ (cid:21) H = t t +w −bu−(cw−cu)+(1−ρ)E β t+1H (1−s ) t λ t t t t λ t+1 t+1 t t (21) by applying the envelope theorem. Expression(21)isobtainedfromthevaluefunctionofthehouseholdandtheconstraints(12)and(20)asshown in Cheron and Langot (2004) and Hall and Milgrom (2008) for arbitrary time-separable preferences. Moving one household member into employment affects utility of the overall household in three ways. First, the utility of the agent changing employment status adjusts by U(cw,1)−U(cu,0). Second, total household resources rise by the t t differencebetweenwagesandunemploymentbenefits,w −bu. Finally,totalexpenditureschangebythedifference t between consumption provided to working and unemployed household members. Household utility increases by the product of the net increase in available resources, w −bu−(cw −cu), and the marginal utility of wealth to t t t thehousehold, λ . Finally, thegainsfrommatchingahouseholdmemberwithafirmalsooccurinfutureperiods. t To express the utility gain to the household in units of the final consumption good we divide by the marginal utility of wealth. MostauthorsinthelaboursearchDSGEliteratureassumeaCRRAutilityfunctionandsetthedisutilityfrom labour to zero: ci1−σ U(ci)= t . (22) t 1−σ Under CRRA-utility, it is not only true that all household members have the same marginal utility; in fact, each agent will experience the same utility level as consumption levels do not differ by employment status. Thus, equation (21) reduces to the form commonly found in the literature: (cid:20) (cid:21) λ H = w −bu+(1−ρ)E β t+1H (1−s ) . (23) t t t λ t+1 t+1 t AssumingCRRA-utilityincombinationwithefficientrisk-poolingatthehouseholdlevelimpliesthatthemarginal value of employment to the household coincides with the value of employment in the standard DMP model with risk-neutral agents. 12

By contrast, we specify preferences as in Greenwood et al. (1988) (GHH), but start with the assumption that the hours worked by an employed agent are constant: (cid:16) ci− φ0 (cid:0) hi(cid:1)1+φ (cid:17)1−σ U(ci,hw)= t 1+φ (24) t 1−σ with hw =1 and hu =0. Defining Φ= φ0 (hw)1+φ, equations (14), (15), (21) imply: 1+φ Φ = cw−cu (25) t t λ = (c −n Φ)−σ (26) t t t (cid:20) (cid:21) λ H = w −bu−Φ+(1−ρ)E β t+1H (1−s ) . (27) t t t λ t+1 t+1 t Under GHH preferences, all agents enjoy the same utility level, but employed agents consume more than unemployed agents. The difference in consumption levels between the employed and the unemployed, Φ, turns out to be fixed over the business cycle. 4.3 Firms Domestic firms combine labour and capital to produce an intermediate good, yh, with the relative price, ph. The t t present discounted cash flow of these firms, πh, is defined as: t ∞ ∞ E (cid:88) βtλ πh =E (cid:88) βtλ (cid:0) phyh−w n −x −κ(v ,v )−q κ¯ (cid:1) . (28) 0 t t 0 t t t t t t t t−1 t t=1 t=1 The real wage, w , is expressed in terms of the consumer price index. The firm’s investment into its capital stock t is captured by x . In order to hire new workers, the firm needs to post vacancies. The cost function for posting t a vacancy is denoted κ(v ,v ) with v measuring the number of vacancies. To improve the empirical fit of our t t−1 t model we allow the costs of posting vacancies to depend on the rate at which vacancies are posted: (cid:32) φv (cid:18) v (cid:19)2 (cid:33) κ(v ,v )=κvv 1+ t −1 . (29) t t−1 t 2 v t−1 Pissarides (2009) assumes that the firm has to pay a fixed cost, κ¯, before the start of the bargaining process. He interprets these costs “as costs that are paid after the worker who is eventually hired arrives but before the wage bargain takes place; for example, they may be the costs of finding out about the qualities of the particular worker, ofinterviewing, andofnegotiatingwithher. Theyaresunkbeforethewagebargainisconcludedandthe worker takes up the position, but this property is not important for volatility, because training costs that are not sunk play a similar role.” At the aggregate level κ¯q units of the final good are used to pay for initialising the t bargaining process. We refer to κ¯q as the fixed component of the costs of filling a vacancy and κ(v ,v ) as the t t t−1 variable component. As with the aggregate consumption good, posting vacancies and physical investment require the use of the domestically produced good and the imported good. We assume the functional forms for these aggregate goods 13

to be identical to the ones for aggregate consumption: x t = (cid:20) vθ 1 (cid:0) xh t (cid:1)θ− θ 1 +(1−v)θ 1 (cid:16) xf t (cid:17)θ− θ 1(cid:21) θ− θ 1 (30) and similarly for vacancies. The optimal choices of producing the aggregate investment good and the payments for vacancy posting follow equations (17) to (19). Eachfirmmaximisesitspresentdiscountedcashflow(28)subjecttothreeconstraints: itsproductionfunction, the capital accumulation equation, and the evolution of employment. The Cobb-Douglas production function is defined over capital, total employment as well as total factor productivity: yh =a kα n1−α. (31) t t t−1 t The capital accumulation constraint is given by: k =(1−δ)k +ι(x ,x ) (32) t t−1 t t−1 with the conventional investment adjustment cost function (cid:32) φx (cid:18) x (cid:19)2 (cid:33) ι(x ,x )=x 1− t −1 . (33) t t−1 t 2 x t−1 Due to the presence of search and matching frictions in the labour market, firms are also constrained by the evolution of employment. Defining the probability of filling an open vacancy as q t = m vt t, equation (3) can be expressed as: n =(1−ρ)n +q v . (34) t t−1 t t The first order conditions with respect to capital and investment imply the usual restrictions: (cid:20) λ (cid:18) ph yh (cid:19)(cid:21) tq = E β t+1 α t+1 t+1 +(1−δ)tq (35) t t λ k t+1 t t (cid:20) (cid:21) ∂ι(x ,x ) λ ∂ι(x ,x ) 1 = tq t t−1 +βE t+1tq t+1 t (36) t ∂x t λ t+1 ∂x t t t where tq denotes Tobin’s q. t The first order condition for vacancies can be written as: (cid:20) (cid:21) ∂κ(v ,v ) λ ∂κ(v ,v ) q (J −κ¯) = t t−1 +E β t+1 t+1 t , (37) t t ∂v t λ ∂v t t t where J is the Lagrange multiplier on equation (34). The expected benefit from posting a vacancy, q (J −κ¯), t t t equals the marginal costs of posting a vacancy. Equation (37) is commonly referred to as the free entry into production condition. As shown next, J measures the value that the firm assigns to an additional unit of employment. Following t similar steps as for households, J is obtained from the firm’s value function associated with its optimisation t 14

problem. By the envelope theorem: (cid:18) phyh (cid:19) (cid:20) λ (cid:21) J = (1−α) t t −w +(1−ρ)E β t+1J (38) t n t t λ t+1 t t By employing one additional worker, the firm raises profits in the current period when the marginal product of labour, mpl t = (1−α)p n h t y t t, exceeds the wage payment, w t . Furthermore, the firm receives a continuation value if the match survives. Under standard assumptions, the marginal costs of posting vacancies do not depend on past posting choices, i.e., φv =0, and there are no sunk costs of bargaining, i.e., κ¯ =0. In this case, equations (37) and (38) reduce to the familiar system: q J = κv (39) t t (cid:20) (cid:21) λ J = mpl −w +(1−ρ)E β t+1J . (40) t t t t λ t+1 t 4.4 Wage bargaining When a match occurs between a worker and a firm, the two negotiate over the real wage, w . The surplus of t the match is measured by H +J . Assuming (efficient) Nash bargaining, the solution of the bargaining game is t t derived from the optimisation program: maxHξJ1−ξ (41) t t wt subject to equations (21) and (38) which describe the evolution of the variables H and J over time. The term t t ξ ∈(0,1) denotes the bargaining power of the household. The power of the firm is given by 1−ξ. The surplus of the match is shared according to: 1−ξ J = H . (42) t ξ t 4.5 Real exchange rate We define the real exchange rate, rer , in terms of the consumer price indices. As is standard in the small open t economy literature, the negligible size of the domestic country relative to the rest of the world implies that the domestic import price roughly equals the consumption real exchange rate, pf ≈rer . From equation (19) it then t t follows: 1 = v (cid:0) ph(cid:1)1−θ +(1−v)(rer )1−θ. (43) t t 4.6 Commodities The commodity supply of the small open economy to the world market is assumed to be price inelastic and fixed over time.13 In addition, we abstract from the use of commodities in domestic consumption or production as for the countries in our sample the share of domestic use is minuscule relative to the overall commodity output. 13Evenintheinterwarperiodwhencommoditypricesdeclinedsharply,overallproductionofcommoditiesdidnotcontractsignificantlyasshown inKindleberger(1973),Chapter4,Figure2. 15

Abstracting from endogenous movements in the supply of commodities focuses our work on the transmission of commodity price changes through their impact on wealth. Changes in the supply of commodities are often slow to occur. Unless sizeable excess capacity persists in the commodity-producing sector, the supply response is muted. Focussingonoil-producingNorway,Pieschacon(2012)includesoilproductionintoastructuralVAR.The estimatedresponseofoilproductionafteranoilpriceshockissmallandinsignificant. Bycontrast,theexpansion innon-oiloutputishighlysignificantandabout5to8timeslargerthantheexpansioninoilproductiondepending on the horizon. Furthermore, the direct impact of the commodity-producing sector on the labour market is likely to be small and cannot explain exclusively the economy-wide dynamics of unemployment and vacancies. For example, Australian employment in mining accounts for less than 3% of total employment although mining constitutes around 9% of GDP. Only 2% of Norwegian workers are employed in the extraction of oil and gas while the oil and gas industry accounts for 22% of Norwegian GDP.14 With commodity production being capital-intensive, employing only a small share of the domestic labour force, and being slow to respond to price shocks empirically, we deem itdefensibletoassumethatcommoditypriceshocksprimarilytransmittotheremainderoftheeconomythrough their impact on transfers and thus wealth. We denote the price of the commodities by pc and their supply by yc. Profits from commodity extraction, t t πc =pcyc, are distributed to the households. Commodity prices are determined in world markets and are set in t t t foreignconsumptionunits, pc∗. Thedomesticpriceofthecommodity, pc, isrelatedtoitsworldpricethroughthe t t real exchange rate, rer : t pc =rer pc∗. (44) t t t 4.7 Market clearing and net trade Demand for the domestically produced good arises from consumption, investment, filling vacancies and from abroad. Given the relative price of the domestically produced good, ph, and aggregate consumption demand, c , t t theoptimalconsumptiondemandforthedomesticallyproducedgoodfollowsequation(17),i.e.,ch =v (cid:0) ph(cid:1)−θ c . t t t With similar relationships applying to the demand for the purpose of investment and covering vacancy posting costs, market clearing for the domestically produced good implies: yh =v (cid:0) ph(cid:1)−θ (c +x +κ¯q +κ(v ,v ))+exh. (45) t t t t t t t−1 t Export demand from abroad is assumed to be of the form: (cid:18) rer (cid:19)θ∗ exh =v∗ t y∗ (46) t ph t t with y∗ denoting total foreign demand for the domestic good. t Finally, the evolution of the net foreign asset position of the domestic country is obtained from the budget constraint of the household (12) and the definition of profits by goods and commodity producers. Combining 14Thesharerisesjustbelow4%ifadministrativeandservicepositionsareincluded. 16

these equations yields: pfb =(1+r )pfb +pcyc+phyh−c −x −κ¯q −κ(v ,v ). (47) t t t−1 t t−1 t t t t t t t t t−1 5 Alternative models To contrast the labour market dynamics after a commodity price shock in the DMP model with the dynamics derived under alternative approaches taken in the literature, we consider an equivalent model with a Walrasian labour market and the alternating offer bargaining model proposed in Hall and Milgrom (2008). Thesearchandmatchingframeworkisappealingnotonlybecauseitissuitableforunderstandingthedynamics of unemployment and vacancies. In principle, the framework can also give rise to sticky real wages and volatile employment without requiring an unreasonably high labour supply elasticity. Under a Walrasian labour market, the flexible real wage adjusts instantly to induce market clearing. If the elasticity of the labour supply is set at the low values found in microeconometric studies, the real wage is too volatile a variable in comparison to the time series data. A high elasticity is necessary to match the high variability of hours worked, together with the low variability of the real wage.15 Shimer (2005) casts doubt on whether the quantitative performance of the DMP model is indeed superior to thatofamodelfeaturingaWalrasianlabourmarket. Atleastsimpleversionsofthesearchandmatchingapproach havedifficultyinaccountingforthehighvolatilityoflabourmarketvariablesunderwhatShimer(2005)considers a reasonable calibration of the model — a view challenged by Mortensen and Nagypal (2007) and Hagedorn and Manovskii (2008). To reduce the volatility in the real wage and thus to raise the volatility of unemployment and vacancies Hall and Milgrom (2008) propose replacing the idea of Nash bargaining between a worker-firm pair by an alternating offer bargaining game. 5.1 Walrasian labour market Under a Walrasian labour market, the labour supply of each agent is taken to be elastic to account for the variation in the labour input in production at the aggregate level. Household preferences over consumption and leisure follow Greenwood et al. (1988). Using preferences without a wealth effect on the labour supply are key in replicating the expansion of employment after an increase in commodity prices in our setting. All household members are employed and have preferences: (cid:16) (cid:17)1−σ c − φ0 (h )1+φ t 1+φ t U(c ,h )= . (48) t t 1−σ Furthermore, we follow Blanchard and Gal´ı (2007) in introducing real wage rigidities to improve the empirical performance of this model. The real wage evolves according to: w = ηw +(1−η)mrs (49) t t−1 t 15Analternativeapproachtoovercomethesetensionsbetweentheoryanddataandtopreservewageflexibilityassumesthatlabourisindivisible asinRogerson(1988). 17

with the standard Walrasian model arising under the assumption of η =0. The optimality conditions pertaining to the labour market are: (cid:18) φ (cid:19)−σ λ = c − 0 h1+φ (50) t t 1+φ t mrs = φ hφ (51) t 0 t phyh w = (1−α) t t (52) t n t h = n (53) t t w = ηw +(1−η)mrs . (54) t t−1 t 5.2 Alternating offer bargaining model Under Nash bargaining, the threat points are for the worker to return to unemployment and for the firm to leave thevacancyunfilled. HallandMilgrom(2008)suggestanoncooperativealternatingofferbargainingmodelwhich implies a change in the outside options of the negotiating parties.16 While a breakdown in the negotiations still leadstounemploymentfortheworkerandanunfilledvacancyforthefirm,themainthreatistoextendbargaining rather than to terminate it. Patience determines the threat points. By breaking the tight connection between wages and outside conditions in Mortensen and Pissarides (1994), the alternating offer bargaining model implies higher volatility of unemployment than the standard DMP model for parameters that are deemed realistic by Hall and Milgrom (2008). Christiano et al. (2016) imbed the model by Hall and Milgrom (2008) into a standard monetary business cycle model and attest to it superior statistical performance based on a Bayesian procedure. The main departure of the alternating offer bargaining model from Nash bargaining lies in the idea that a worker and a firm negotiate over a finite time span with Maob subperiods. The starting offer by the firm can be rejected by the worker by formulating a counteroffer. γaob is the cost to the firm of making a counteroffer. This process continues until an agreement is reached, the time span for negotiation is over, or bargaining has broken down. The exogenous probability of a breakdown in bargaining is denoted by δaob. Christiano et al. (2016) show that the surplus sharing rule in the alternating offer bargaining model can be written as: J =β H −β γaob+β (mpl −bu) (55) t 1 t 2 3 t with β =α /α for i=1,2,3 and i i+1 1 α = 1−δaob+(1−δaob)Maob (56) 1 α = 1−(1−δaob)Maob (57) 2 1−δaob α = α −α (58) 3 2 δaob 1 1−δaob α α = 2 +1−α (59) 4 2−δaobMaob 2 where mpl t = (1−α)p n h t y t t denotes the marginal product of labour. We start by assuming that households have 16ThealternatingofferbargainingmodelwasintroducedbyBinmoreetal.(1986). 18

CRRApreferences,i.e.,consumptionbetweenemployedandunemployedhouseholdmembersisequalised;wealso discuss the implications of relaxing this assumption below. Furthermore the firm has to pay a fee κ¯ to initialise the bargaining process as in the DMP model — see equation (37). Inthelimit, ifthenumberofsubperiodsoverwhichbargainingoccurs, Maob, islargeandthecostforthefirm to make a counteroffer is low, γaob, the surplus sharing rule of the alternating offer bargaining model converges to the surplus sharing rule under Nash bargaining with ξ = 1−δaob. 2−δaob However,forasmallervalueofMaob —Christianoetal.(2016)suggestsettingMaob equalto60—thesurplus sharing rules (55) can mimic the surplus sharing rule (42) only if the bargaining power of the household under Nashbargaining,ξ,islowandtheprobabilityofabargainingbreakdownunderalternatingofferbargaining,δaob, is high. To see this, choose δaob to satisfy the condition: 1−(1−δaob)Maob 1−ξ β = = . (60) 1 1−δaob+(1−δaob)Maob ξ Notice that β is increasing in δaob. Furthermore, the coefficient β can be approximated as 1 3 1 1−α β ≈ + 2. (61) 3 2Maob α 1 Foralargevalueofδaob (say>0.1)andMaob =60, β willbeclosetozero. Withtheappropriatechoicesofγaob 3 and δaob, the alternating offer bargaining model can be equivalent to the Nash bargaining model for arbitrary (even) values of Maob provided the household’s bargaining power under Nash bargaining, ξ, is sufficiently low.17 We refer to the model with noncooperative bargaining as the AOB model in our subsequent discussion. 6 Reconciling model and VAR Which of the labour market models is preferred by the empirical estimates provided in Section 3? To shed light on this question we estimate a number of model parameters for each model using a minimum distance strategy and assess the plausibility of the estimates. Theparametersaredividedintotwogroups: calibratedandestimatedparameters. Thecalibratedparameters are listed in Table 2. The first eight parameters are common to all models. The discount factor, β, implies a real interest rate of 4% per annum. The parameter σ governs the intertemporal elasticity of substitution and is set at 1.1. The share of capital in the production function, α is 0.33, the depreciation rate, δ is 2.5% per quarter. All these values are standard in the literature. The elasticity of substitution between home and foreign-produced goods, θ, is set at 2.0, which is within the relatively wide range of values commonly used in the literature. To assess robustness of our findings, we experiment with this parameter in Section 7. In 2013, the goods-export to GDP ratio averaged at 20% across the economies in the sample.18 The Harvard AtlasofEconomicComplexityisusedtodeterminetheshareofcommoditiesintotalexports. In2013,theaverage share of commodities in net exports in our four countries was 85%, which is significantly higher than the values 17Ifpreferencesandthecostsofinitialisingthebargainingprocess,κ¯areidenticalintheDMPandAOBmodel,thecostofmakingacounteroffer, γaob,needstobezerotoachieveequivalence. Ifpreferencesdiffer,asassumedinouranalysis,γaob willneedtobeasmallpositivenumber. 18ThisratioistakenfromtheOECDnationalaccountsdata. 19

suggested by IMF (2012), which range from 30% to 40%, albeit over a sample dating back to 1960. To err on the side of caution, we set the share of commodity exports in total exports at 75%. The share of non-commodity exports in GDP is set at 5%. With these target values in hand, the implied value for ν is 0.8. For the search and matching models, we set the probability that an existing match breaks up within a given quarterat0.1,whichissomewhatlowerthanthevalueof0.15suggestedbyAndolfatto(1996),butisequaltothe choiceinChristianoetal.(2016). Weassumeareplacementratio,ru = bu ,of40%ofwages. Inthesteadystate, wss we set employment equal to 0.95, which implies a steady state unemployment rate of 5%. The implied value for the scale parameter in the matching function, χ, is 0.67. Finally, we fix the share of all (expected) vacancy costs in (non-commodity) output, κvvss+qssκ¯, at 0.005. yh ss We estimate those parameters for which there is little or no empirical evidence. Given its importance in transmitting wealth shocks, we estimate the bond holding cost parameter, φb. To allow the models to better match the shape of the response in vacancies to the shock, the vacancy adjustment cost parameter, φv, is also estimated, as is the investment adjustment cost parameter, φx. For the search and matching model we also estimate the share of unemployment in the matching function, ζ. As will be highlighted in our discussion of the estimation results, for a given choice of the replacement ratio the dynamics of unemployment and vacancies are crucially influenced by our estimate of the relative consumption share of the unemployed to the employed agents, cu, in the DMP model. Under the alternative of alternating offer bargaining, the probability of breakdown in cw bargaining, δaob, is a key determinant of unemployment and vacancies given our choice of Maob equal to 60 as in Christiano et al. (2016). Thus, we estimate δaob in the AOB model with CRRA preferences. Finally, while we calibrate the overall costs of filling vacancies, we estimate the relative importance of the variable and the fixed component, sfixed. Equipped with an estimate for sfixed we can then compute the parameters κv and κ¯. Under the assumption of a Walrasian labour market, we estimate the inverse of the Frisch labour supply elasticity, φ, as well as the parameter η that introduces real wage rigidity. Giventhevaluesofthecalibratedparameters—stackedinthevectorΘc —weestimatetheremainingones— stackedinthevectorΘe —byminimisingtheweighteddistancebetweentheempiricalimpulseresponsefunctions from the VAR in Section 3, denoted by G, and the impulse response function implied by one of our theoretical models, denoted by G(Θc,Θe): Θˆe =argmin [G−G(Θc,Θe)](cid:48)Ω−1[G−G(Θc,Θe)]. (62) Θe The diagonal weighting matrix Ω is obtained from the empirical variance-covariance matrix of the estimated impulse response functions Ψ by setting all off-diagonal elements in Ψ to zero.19 Ω penalises those elements of the estimated impulse responses with wide error bands. We minimise the objective (62) over the first six periods of the VAR which allows our model to closely match the initial response of the data, but leaves the subsequent dynamics of the model unrestricted. The values assigned to the calibrated parameters are provided in Table 2. The estimated values of the remaining parameters are collected in Table 3. Standard errors are constructed from 19Theestimateofthevariance-covariancematrixΨisobtainedbymeansofbootstrappinginSection3. 20

the asymptotic covariance matrix of the estimator Θˆe given by (cid:2) Γ(Θe)(cid:48)Ω−1Γ(Θe) (cid:3)−1 Γ(Θe)(cid:48)(cid:2) Ω−1ΨΩ−1(cid:3) Γ(Θe) (cid:2) Γ(Θe)(cid:48)Ω−1Γ(Θe) (cid:3)−1 (63) where Γ(Θe)= ∂G(Θc,Θe). ∂Θe 6.1 Performance of the DMP model TheredsolidlinesinFigure4denotethefittedimpulseresponsesofthebaselinemodelwhileTable3reportsthe parameter estimates and standard errors. By minimising the objective in (62), the DMP model is able to closely replicate the behaviour of commodity prices as well as the VAR’s median impulse response for net trade. Importantly, the DMP model matches the approximate paths of unemployment and vacancies. To account for the slight “hump” shaped path of vacancies, the estimation yields a value for the vacancy adjustment cost parameter, φv, of 1.1, and the accompanying standard errors are small. The DMP model is able to reproduce the initial decline and the following gradual decrease in unemployment, albeit compared to the data, the path of unemployment is somewhat more persistent. The model cannot account for the initial decline or indeed the shape of the path of real wages, and it is silent (by construction) on the behaviour of individual hours. The commodity price rise transmits like a wealth shock to the economy as it induces additional transfers to households. These transfers are used to boost consumption and domestic investment and to increase savings in the form of foreign bonds. Consumption rises by 0.15% and remains elevated thereafter. The DMP model captures the initial magnitude of the increase in GDP (at constant prices) and its gradual rise, but it under predicts the response of GDP in the first 5 quarters following the commodity price shock. For investment, the model generates the same peak response as the data, but fails to capture the ‘hump’ shaped response in the first couple of periods. The persistent rise in consumption pushes up demand for both the domestic and the foreign non-commodity good, although the appreciation in the real exchange rate holds back demand for the former. In theshort-run, theoutputexpansionisdrivenbytheincreaseinemployment, whileovertimethegradualbuildup of the capital stock also contributes to the modest rise in production of the domestic non-commodity good. The shape and the magnitude of the impulse responses depend on the real interest rate movement induced by the shock and the household’s decision on how to allocate the additional transfers towards savings in foreign bonds, consumption, and investment. In our framework the interest rate faced by households and firms is equal to the world interest rate adjusted by a small risk premium that depends on the country’s net foreign asset position. The elasticity of this risk premium to the net foreign asset position of the home country is estimated at 0.0085 which is in line with values commonly used in the open economy literature.20 Although the estimate is statistically different from zero, its value implies that the interest rate faced by households is largely exogenous. As a result, the model generates a virtually flat consumption profile following a commodity price shock. In the data as in the model, the rise in domestic consumption occurs alongside a real exchange rate appreciation suggesting that country-specific consumption risk coming from wealth shocks cannot be effectively shared via relative price movements or trade in bonds. This feature differs from the transmission of a technology shock in 20For estimation purposes, we express the elasticity of the interest rate to deviations in the net foreign asset position from steady state as a percentage(multipliedby100)inTable3. 21

the open economy. Cole and Obstfeld (1991) point out that movements in the terms of trade provide a powerful source of insurance against technology shocks independently of the financial market arrangements — with the exceptions of a low trade elasticity of substitution or permanent technology shocks stressed in Corsetti et al. (2008). Theinvestmentadjustmentcostparameter, φx, requiredtominimise(62)iscloseto, butstatisticallydifferent from zero at 0.04. The share of unemployment in the matching function, ζ, is highly significant and comes out at 0.72; this estimate is remarkably robust across all specifications of the search and matching models we consider. Based on a variety of econometric studies Mortensen and Nagypal (2007) consider the range from 0.3 to 0.5 to be plausible for the elasticity of the matching function — in our notation 1−ζ. Implied by the estimated and calibrated parameters of the model is the bargaining power of households, ξ. It assumes the value of 0.4 which suggests that firms have a rather higher weight in the wage bargaining process than workers. Finally,weturntowardsthoseparametersthatprimarilygovernthevolatilityofunemploymentandvacancies: the share of consumption going to the unemployed, cu/cw, and the relative importance of the fixed and variable cost components in filling a vacancy, sfixed. The data are highly informative on the share of consumption going to the unemployed. Our estimates suggest that unemployed members of a household enjoy about 60% of the consumptionofemployedagents. Withthereplacementratiosetat40%ofsteadystatewages, thereisamodest, but far from complete, requirement to reduce consumption inequality between household members. By contrast, the estimate of sfixed is basically zero suggesting that the fixed costs to start bargaining, κ¯, are negligible. We embedthediscussionoftheroleoftheseparametersininfluencinglabourmarketdynamicsandoftheplausibility of their estimated values into a broader analysis of the transmission mechanism following next. 6.2 Transmission in the DMP model To structure the discussion of the transmission mechanism, the Technical Appendix establishes an approximate relationship between labour market tightness, θ , and the marginal product of labour, mpl , which in turn is t t determined by the real exchange rates and labour productivity. Abstracting from vacancy adjustment costs, the surplus sharing rule under Nash bargaining and the definitions of the marginal values of employment to the household and the firm — H and J — imply: t t (cid:20) (cid:21) λ J +(1−ξ)(bu+Φ)=(1−ξ)mpl +(1−ρ)E β t+1 (1−ξs )J (64) t t t λ t+1 t+1 t with J = κvθζ +κ¯ for φv = 0. Equation (64) can be used to obtain an approximate decomposition of the t χ t log-deviationoflabourmarkettightnessfromitssteadystatevalue, θˆ, intomovementsoftherealexchangerate, t rer , and labour productivity, yˆh−nˆ : (cid:99)t t t (cid:18) (cid:19) 1 mpl 1−ν θˆ ≈ ss yˆh−nˆ − rer . (65) t Υ (1−ru)mpl +ru(1−(1−ρ)β) (cid:16) κv +κ¯ (cid:17) −Φ t t ν (cid:99)t ss qss As detailed in the Technical Appendix, the parameter Υ assumes a positive value. For suitable choices of the replacement ratio, ru, and the consumption difference between employed and unemployed household members, 22

Φ, the second factor in equation (65) is also positive. The roles of the real exchange rate and labour market productivity in shaping the response of labour market tightness to the commodity price shock differ by time horizon. The top panel in Figure 5 plots the response of labour market tightness in the DMP model (with positive vacancy adjustment costs as estimated) together with the right hand side of equation (65) and its decomposition into movements due to changes in the real exchange rateandinlabourproductivity,respectively. Theapproximationtolabourmarkettightnessproposedinequation (65), depicted by the dashed red line, tracks the value of θˆ derived from the estimated DMP model, depicted by t the solid blue line, reasonably well in particular once the impact of the vacancy adjustment costs has worn off. Decomposingthemovementsinlabourmarkettightnessshowsthatearlyonlabourmarketconditionsimprove primarilyduetotheappreciationoftherealexchangerate. AdaptingthelogicinBodensteinetal.(2011),thenoncommoditytradebalancemustgointodeficitfollowingtheimprovementinthecommoditytradebalancesincethe rational expectations solution imposes that the net foreign asset position is bounded away from infinity. To slow non-commodity exports, the relative price of the domestically produced good has to rise swiftly which translates intoanappreciationoftherealexchangerate. Themagnitudeoftheexchangerateresponseisdeterminedbythe country’s ability to smooth the commodity price shock through the overall trade balance. If trade was required to be balanced period by period (financial autarchy), the non-commodity trade balance would need to go deeper into deficit on impact which would precipitate a larger appreciation. Although the domestic good has become more expensive, domestic demand increases for both the domestic and the foreign produced good because of the shock’sincomeeffect. Facingahigherrelativepricefortheirgoods, firmspostadditionalvacancies, matchesrise, andunemploymentfalls,whichpushesupθˆ. Thecontributionoftherealexchangeratetomovinglabourmarket t tightness is depicted by the dash-dotted green line. For the first eight quarters after the shock, the real exchange rate appreciation accounts for the bulk the change in θˆ in the DMP model. t Over time, as the real exchange rate slowly returns to its steady state value, labour market conditions remain favourable given a lasting improvement of labour productivity. Since international risk sharing is limited in our model, the real interest rate faced by domestic agents experiences a mild decline; the marginal product of capital, by contrast, rises on impact as a result of the real exchange rate appreciation and the expansion in domestic production. Thus, the wealth increase stemming from the commodity price shock is partially invested into expanding the capital stock as the marginal product of capital would otherwise exceed the real interest rate. As the capital stock is augmented, labour productivity rises and firms find it profitable to keep labour demand and employment persistently above their steady state values. As the black dotted line in the top panel of Figure 5 reveals, the improvement in labour productivity is slow to occur, but very persistent. Hence, the fall in unemployment and the rise in vacancies continue well after commodity prices have returned to steady state. The transmission of a commodity price shock differs significantly from the transmission of a technology shock both with respect to its domestic and international dimension. A positive neutral technology shock raises labour productivity on impact; but, with the price of the domestically produced good falling, the real exchange rate depreciates persistently. The bottom panel in Figure 5 decomposes the response of labour market tightness after a neutral technology shock into the movements due to labour productivity and due to the real exchange rate. Labour productivity dominates in shaping the response of labour market tightness at all horizons while the real 23

exchange rate dampens the improvement in labour market conditions not unimportantly. Open economy aspects areimportantinunderstandinglabourmarketdynamicsanditisnotsufficienttoviewlabourmarketmovements solely through the lens of changes in labour productivity as in much of the macro-labour literature referenced here. Shocks other than to technology can have a limited impact on labour productivity, but nevertheless have a sustained impact on the labour market through an adjustment in the real exchange rate. Shiftingthefocusfromthetransmissionoftheshocktoitsamplification,weturntointerpretingthecoefficient in equation (65): 1 mpl ss . (cid:16) (cid:17) Υ (1−ru)mpl +ru(1−(1−ρ)β) κv +κ¯ −Φ ss qss Although not made explicit in our notation, the value of Υ depends on the replacement ratio, ru, and the consumption difference between employed and unemployed household members, Φ. However, Υ is not very sensitive to the values of ru and Φ. In fact, for κ¯ =0 as implied by our estimation of the DMP model ,Υ can be showntolieintheinterval[ζ,1]. Muchmorerelevantfordeterminingtheimpactofthecommoditypriceinduced real exchange rate and labour productivity changes is the second factor. For a given value of the replacement ratiothedenominatorcanbemadearbitrarilysmall, yetpositive, bymakingtheconsumptiondifferencebetween employed and unemployed household members suitably large, i.e., lowering the share cu. If, however, Φ equals cw zero, as would be the case under CRRA preferences, a high value of the replacement ratio may be required to get sufficient amplification in θˆ.21 t This interplay between the parameters ru and Φ in amplifying the labour market response is not unique to the open economy context. Since Shimer (2005) has pushed the view that the textbook DMP model — in our context characterised by Nash bargaining and CRRA preferences — explains less than 10% of the volatility in U.S.unemploymentandvacancieswhenfluctuationsaredrivenbyproductivityshocks, the“correctvalue”ofthe replacement ratio, ru = bu , has been the subject of lively discussion. Hagedorn and Manovskii (2008) and Hall wss (2008) argue that the flow value of unemployment ought to capture more than direct insurance payments to the unemployed. Byappealingtothevalueofleisureandhomeproduction,HagedornandManovskii(2008)raisethe flow value of unemployment to imply a replacement ratio of 95.5% and demonstrate that the DMP model can be brought in line with the data. Hall (2008) attempts to discipline the calibration and models explicitly the value of leisure. By deviating from CRRA preferences and opting for preferences that feature complementarity between consumptionandhoursworkedourframeworkexplicitlyincorporatesakeyaspectadvocatedinHall(2008). Asshown in equation (27), employed household members are compensated for the disutility from labour with additional consumption: (cid:18) cu(cid:19) φ cw−cu = 1− t cw = 0 (hw)1+φ =Φ. (66) t t cw t 1+φ t Using U.S. data on consumption of nondurables and services from the Consumer Expenditure Survey (CE) and the Panel Study for Income Dynamics (PSID), Chodorow-Reich and Karabarbounis (2013) measure the relative 21Ifvacancycostsarecalibratedtobeasmallnumber,theterm κv +κ¯ willbesmallandthedenominatorcanbemade(arbitrarily)smallby qss raising ru towards unity even if Φ = 0. In principle, the relative importance of the fixed and variable costs components in filling vacancies and theimpliedvalueforκv andκ¯ canbeanalternativesourceofamplification. However, numericallytheeffectsaresmallintheDMPmodel. The TechnicalAppendixprovidesfurtherelaborationonthispoint. 24

consumption of an unemployed agent, cu t , to be 70% to 80% of an employed agent which is comparable to other cw t estimates discussed in the literature — see Chodorow-Reich and Karabarbounis (2013) for a review. In order for ourversionoftheDMPmodeltoimplyasatisfyingmatchtotheVARimpulseresponses,therelativeconsumption of an unemployed agent is estimated at the lower value of 60%. Although most of the evidence in the literature is derived from U.S. data, we do not expect the ratio cu t to differ dramatically for the countries in our sample. cw t However, at least the results in Chodorow-Reich and Karabarbounis (2013) do not account for housing, health care, education, anddurablegoodsconsumption. Withoutpursuingthedebateovertheratio cu t anyfurther, our cw t parameterestimatesimplyaflowvalueofunemployment, bu+Φ,of96%ofsteadystatewages. Usingdifferentdata wss and conditioning on commodity price shocks, we recover basically the same value for the flow value as Hagedorn and Manovskii (2008) studying unconditional U.S. data and productivity shocks. 6.3 Walrasian labour markets The dash-dotted black lines in Figure 4 show the fitted impulse responses for a standard model with Walrasian labour markets. Whereas the simple RBC model is silent on key labour market variables such as unemployment andvacancies,itdoesassumeanelasticindividuallaboursupplythatproducesadata-consistentincreaseinhours worked in response to a positive commodity price shock. The assumption of GHH preferences is vital to generate the expansion in hours worked. If the wealth effect on the labour supply was not eliminated — as would be the case under standard additive separable preferences — hours worked would fall and not rise! The fitted impulse responses for investment and the real exchange rate are almost identical to those of the DMP model. A key difference between the two models is found in the response of output and consumption. In both cases, the RBC model yields a larger initial response than the DMP model. Compared to the DMP model, there is a larger increase in employment which allows both output and consumption to increase by more. The dashed blue lines show the fitted impulse responses of the RBC model with real wage rigidities as in Blanchard and Gal´ı (2007). The estimated value of η is high at 0.84. Compared to the standard RBC model, the modelwithrealwagerigiditiesgeneratesmorevolatilityinoutputandconsumption,but,asexpected,slightlyless volatility in the real wage. As a result, the model generates a more volatile, and more data congruent, response of hours worked. The dynamics of the remaining variables are very similar to the baseline DMP model or the standard RBC model. A closer look at Table 3 reveals the reason for the relative performance of the two RBC models. To generate a flat real wage response, the simple RBC model requires a labour supply elasticity that is twice as high as in the RBC model with the real wage rigidity. 6.4 Alternative search and matching models To compare the results in the DMP model with alternative formulations of the search and matching framework, Figure 6 reports the fitted impulse responses for the alternating offer bargaining (AOB) model, depicted by the dashedbluelines, andaversiontheDMPmodelwithanelasticlaboursupply, depictedbythedash-dottedblack lines.22 22TheextensionoftheDMPmodeltoincludeanelasticlaboursupplyisrelegatedtotheTechnicalAppendix. 25

Allowing for an elastic labour supply does not alter the dynamics of the DMP model in significant ways. Because of the endogenous response of hours worked, output, consumption and investment are somewhat more responsiveonimpact. ThedynamicsofhoursworkedaresimilartothosegeneratedbytheRBCmodelsanalysed intheprevioussection. Theremaininglabourmarketvariablesarenotaffectedbytheinclusionofanendogenous labour supply. The value of the bargaining share of households, ξ, that is implied by the set of calibrated and estimated parameters, turns out to be 0.3. This lower value compared to the baseline DMP model accounts for theslightlysmallerrealwageresponseintheDMPmodelwithelasticlaboursupply. Thelaboursupplyelasticity inthismoreflexibleversionoftheDMPmodelisultimatelydeterminedbythedifferenceinconsumptionbetween employed andunemployedagents, Φ. UnderGHHpreferences andfullrisk poolingthe consumptiondifference to compensate employed agents for their labour effort satisfies: φ Φ =cw−cu = 0 (hw)1+φ (67) t t t 1+φ t at each instant in time. In periods of increased labour demand and higher hours worked, the consumption differential increases. With φ being determined by other aspects of our calibration strategy, less consumption 0 inequality (a lower steady state value Φ ) maps into a higher value of the inverse of the labour supply elasticity ss φ. Although the estimated value of the inverse of the labour supply elasticity rises to 0.74 compared to 0.48 in the simple RBC model, the implied labour supply elasticity is still above unity. The elevated estimate of the labour supply elasticity goes hand in hand with the somewhat small estimate of the relative consumption of the unemployed. As in Christiano et al. (2016), there is virtually no difference between the DMP and the AOB model. The similar dynamics trace back to virtually identical estimates of the bond holding cost parameter, φb, and the investment adjustment cost parameter, φx. Interestingly, the data prefers setting the breakdown probability of bargaining, δaob, as closely as possible to its lower bound in the estimation which is set at 0.001. Despite the similar impulse responses, the AOB model differs along important dimensions from the DMP model: the bargaining setup and parameter estimates. To isolate the role of the differences in the bargaining process, we estimate two restricted versions of the AOB models. In the first version, all parameters that are common across models are set at their respective point estimates in the DMP model. The parameter Maob is set to 60 and δaob is estimated. Given the values of Maob and δaob, the steady state relationships pin down the value of γaob. The second version we consider is identical to the first one with the one exception of including the parameter κ¯ into the estimation. In the DMP model this parameter assumes the value of zero. Figure7plotstheimpliedimpulseresponsesofunemploymentandvacanciesoftheDMPandtheAOBmodels and the two restricted versions of the AOB model. The first restricted version of the AOB model, shown by the dashed blue lines in the figure grossly understates the responses of the labour market variables. Changing the nature of the bargaining process is not sufficient to obtain empirically plausible responses in a model with search and matching frictions. In going from the DMP model to the first version of the restricted AOB model, we also abandoned the assumption that unemployed workers consume less than employed workers by reverting to the standard assumption of a CRRA utility function for the household members and simultaneously keeping the 26

replacement ratio at 0.4. Instead of estimating the replacement ratio, our second version, the dash-dotted green lines, takes the alternative approach of estimating the fixed cost of bargaining, κ¯. In terms of reconciling the constraints imposed by the model’s steady state relationships and the implied dynamics, κ¯ plays a role similar to the one played by the replacement ratio.23 Estimation of our second version of the restricted AOB model assign the value of 0.0131 to κ¯ — close to its value of 0.0095 in the unrestricted AOB model. The dynamics of unemployment and vacancies of this second version of the AOB model are hard to distinguish from those obtained under Nash bargaining. As for the DMP model, we can derive an approximation that establishes the link between labour market tightness, the real exchange rate, and labour productivity. The Technical Appendix treats the general case, but since the probability of a breakdown in bargaining, δaob, is estimated to be close to zero, we proceed differently. If δaob ≈0, the surplus sharing rule under alternating bargaining (55) reduces to: 1 J ≈−β γaob+ (mpl −bu) (68) t 2 2 t since β ≈ 0 and β ≈ 1. The marginal value of employment to the household, H , is (basically) irrelevant for 1 3 2 t wage determination if δaob is small. Abstracting again from vacancy adjustment costs, we apply the first order condition with respect to vacancies (37) and log-linearise the resulting equation to obtain: (cid:18) (cid:19) 1mpl 1−ν θˆ = ss yˆh−nˆ − rer . (69) t 2 ζκv t t ν (cid:99)t qss In this case, the amplification of shocks is unaffected by the value chosen for the replacement ratio, ru. In the AOB model, amplification of given movements in the real exchange rate and labour productivity is achieved by setting the term κv suitably small. For a calibration strategy that targets the share of total vacancy filling costs in non-commodity output, κvvss+qssκ¯, choosing a small value for κv may require to apportion a large yh ss shareofthevacancyfillingcoststoitsfixedcomponent,κ¯. Ifκ¯ isforcedtobezeroasinthefirstrestrictedversion of the AOB model in Figure 7, the AOB model fails to deliver sufficient amplification under CRRA preferences. For the final estimates of the AOB model, the coefficient 1mplss in equation (69) assumes a value similar to the 2 ζκv qss corresponding coefficient in the DMP model in equation (65). The approximation in equation (69) also suggests that the AOB model admits high values (or at least higher than our estimate) for the probability of bargaining breakdown only if tight restrictions prevail on the parameter κv such as a too low calibration target for the share of total vacancy filling costs in output, or sufficiently tight “priors” as in the Bayesian procedure applied by Christiano et al. (2016). The sensitivity of the parameter estimates to the calibration of the total vacancy posting costs relative to output is unique to the AOB model. In the DMP model a drastic reduction in these costs barely influences the parameter estimates. 23In a third version of the AOB model we estimated δaob and the replacement ratio. The estimate of the latter was 0.856 and δaob was close to1. Inthiscase,theimpliedweightβ1 inthesurplussharingrule(55)approachesinfinityandtheAOBmodelresemblesaversionoftheDMP modelwithaverylowbargainingweightξ forthehousehold. SeealsothediscussioninSection5.2. 27

7 Sensitivity analysis The real exchange rate plays a pivotal role in the labour market response to a commodity price shock. The three modelfeaturesthatdeterminethedynamicsoftherealexchangeratearethedegreeofinternationalrisksharing, trade openness, and the trade elasticity of substitution. The degree of international financial risk sharing is controlled by the parameter φb in our model. For φb very close to zero, the model converges to a simple permanent income model with an exogenously fixed real interest rate.24 In this case, the impact of commodity price shocks is smoothed through the trade balance; except for a permanent rise in consumption, the economy remains basically unaffected. Most importantly, the real exchange rate hardly moves. By contrast, under financial autarchy, i.e., φb is very large, even a small increase in the net foreignassetpositionwouldlowertheinterestratefacedbydomesticagentsininternationalmarketsandredirect spending towards consumption and investment. The rise in the commodity trade balance following a commodity price increase needs to be fully offset by a deterioration in the non-commodity trade balance which requires a sharp appreciation in the real exchange rate. Domestic macroeconomic aggregates bear the full burden of the adjustment process. The top panel of Figure 8 illustrates this discussion graphically for φb ={0.0085,0,∞} with all other parameters set as estimated in the baseline DMP model for comparability. Thebottompanelofthefigureshedslightontheroleoftradeopennessandthetradeelasticityofsubstitution for the response of the real exchange rate. Again, we refrain from re-estimating the model and adjust only the parameters of interest. In an even more open economy, the lower degree of home bias, i.e., ν = 0.7, causes the real exchange rate to appreciate by less. The labour market response, however, depends on the product of the real exchange rate with the term 1−ν, which is decreasing in ν. As this product barely changes, the responses of ν vacanciesandunemploymentarehardlyaffected. Therealexchangerateappreciationisamplifiedwhendomestic and foreign goods are more complimentary under the low trade elasticity of substitution of θ =0.8. The impact of the shock on the labour market is less pronounced under the parameter estimates of the baseline model. If the model was re-estimated under the assumption of a low trade elasticity, the estimated relative consumption of the unemployed would turn out to be higher than in our baseline case to bring the labour market responses back in line with the empirical impulse response functions. 7.1 Commodity supply Twopotentiallycontroversialassumptionsofthebaselinemodelaffectthesupplyofcommoditiesandtheabsence of non-traded goods. The production of commodities is assumed to be price inelastic and fixed over time. This assumption helps focus the attention on the transmission mechanism of wealth shocks, but comes at the risk of under predicting the response in GDP. If the supply of commodities reacts positively to an increase in prices, we would expect a direct effect on GDP through higher supply of commodities as well as an indirect one working via the traded goods sector. If commodity production required labour input, the effects on unemployment and vacancies would be amplified beyond the impact from the non-commodity sector. Abstracting from the supply of commodities therefore makes fitting the model to the data somewhat more challenging, but helps us to isolate 24OpeneconomypapersutilisingthisframeworkareSchmitt-Groh´eandUribe(2003)andAguiarandGopinath(2007). 28

the response of the non-commodity sector to commodity price shocks. Even if the production of commodities is fixed,the(net)supplyofcommoditiestotheworldmarketcanbemadeendogenous. Ifthecommodity-producing country uses some of its commodity output domestically, a rise in world commodity prices may cause domestic useofthecommoditytofalland(price-inelastic)commodityexportstorise. Withtheoverallsupplytotheworld market increased, transfers from commodity sales to the household are larger than in our baseline model. An alternative way of making the world supply elastic is through a simple storage technology. The main findings, however, remain unaffected by these changes. Overall, the price-elasticity of supply in the short-term is regarded to be low for most commodities. Longterm considerations appear to be much more relevant in this regards as expanding production requires expensive investment over several years. From this perspective, the findings in Arezki et al. (2015) are of great interest to our work. Arezki et al. (2015) explore the empirical relationship between “news” on giant oil discoveries and macroeconomic variables for open economies in a panel VAR. Upon the breaking of the “news,” consumption rises as future permanent income has increased. Until revenues flow from the newly discovered fields roughly five yearsaftertheirdiscovery,(oil-field)investmentandconsumptionarefinancedbyborrowingfromabroadandthe trade balance turns into deficit. GDP declines until commodity production starts whereas employment remains suppressed well beyond that point in time. Figure 9 shows that our model without investment into commodity supply can replicate these observations when the elasticity of substitution between traded goods is high with the obvious exception being investment. As in Arezki et al. (2015), the news shock occurs five years prior to production going online. Under the baseline parameterisation (solid blue lines) with a trade elasticity equal to 2, the model implies a rise in consumption and a trade balance deficit. However, the appreciation in the real exchange rate causes unemployment to fall and vacancies to rise. Although the domestically produced good has become relatively more expensive, the overall increase in consumption spending leads to higher demand for all goods given the relatively low degree of substitutability. If we follow Arezki et al. (2015) instead and assume perfect substitutability between goods (dashed red lines), domestic production can fall and with it vacancies and employment. Undersomewhatlessextremeassumptionsontheelasticityofsubstitution(dash-dottedgreenline) or the case of a trade elasticity of 2 combined with high openness to trade (dotted black line), the decline in employment is less pronounced but still present. Thus our framework is in principle suited to imply a decline in unemploymentafterapriceshockandanincreaseinunemploymentaftera“news”shockofhigherfuturesupply. 7.2 Non-traded goods The effects of commodity price shocks are frequently discussed in a modelling framework that also includes nontradedgoods,ofteninthecontextofthe“Dutchdisease”literature. Inthiscase,therealappreciationthatresults from a positive commodity price shock also leads to a shift in resources from the traded goods to the non-traded goods sector. Theincreaseinoverallspendingbydomestichouseholdsnowconcentratesontherelativelycheapernon-traded good and imports while demand for the domestically produced traded good expands little or even contracts depending on the degree of home bias and substitutability. In contrast to the model with traded goods only though, a larger share of the additional spending falls on domestically produced goods (traded and non-traded 29

combined) thus giving a stronger impetus to investment. To reconcile model and data, the point estimate for the adjustment cost parameter in investment turned out to be significantly above our baseline estimate (around 3 instead of close to zero).25 As the qualitative and quantitative implications of the model with non-traded goods resemble those of the baseline model in particular with regard to the labour market, we omit a more formal treatment. 7.3 A final look at the data Instead of embarking onto a quest for theoretical features that help bring the model even closer to the data, we offerafinalassessmentoftheDMPlabourmarketframeworkwiththehelpoftheapproximationoflabourmarket tightness in equation (65).26 To this end, we use the conditional responses of labour productivity and the real exchange together with the labour market parameters estimated for the DMP model to construct a prediction for labour market tightness. Figure 10 compares this approximation (dashed red line) to the empirical impulse response of labour market tightness which is depicted by the solid blue line.27 After increasing the relative consumption of the unemployed to the more realistic value of 65%, the DMP framework predicts labour market tightness to respond similarly to its counterpart in the data after a commodity price shock. Judged by their respectivepeaksthemagnitudesoftheresponsesaresimilar, althoughthetimingoftheresponsesisshiftedsince the approximation in (65) does not account for time leads and lags. 8 Conclusion Weanalysetheeffectsofcommoditypriceshocksonasetofadvanced-economycommodityexportersandfindan importantlinkbetweentherealexchangerateandlabourmarkettightness. Ouranalysishasbothanempiricalas wellasatheoreticaldimension. Theempiricalpartdocumentstheeffectsofcommoditypriceshockson, amongst others, labour market variables and the real exchange rate using panel VARs. The impulse responses from the VAR are then used as a yardstick against which to assess a number of small open economy models with search and matching frictions in the labour market to provide an economic interpretation. The impulse response matching exercise shows that in the data and the model, an increase in commoditypricesraisesconsumptiondemandinthesmallopeneconomyandinducesarealappreciation. Facing higher relative prices for their goods, non-commodity producing firms post additional job vacancies, causing the number of matches between firms and workers to rise. As a result, unemployment falls, even if employment in the commodity-producing sector is negligible. The careful analysis of transmission mechanism of commodity or wealth shocks onto the labour market in search and matching models is a key contribution of this paper. Openeconomyaspectsareimportantinunderstandinglabourmarketdynamicsanditisnotsufficienttoview 25We assume a nested CES framework, with non-traded and traded goods being combined to the final consumption good. Production of nontradedgoodsrequirestheinputoflabourandcapital. Thelabourmarketisassumedtobeintegratedwithahiringagencynegotiatingwageswith workers. Wagesarethereforeequalisedacrosssectors. Wefixedtheshareofnon-tradedgoodsinGDPat70%inthesteadystateandassumedan elasticityofsubstitutionbetweentradedandnon-tradedgoodsof0.75. 26Under the assumption of an integrated labour market, additional model features do not fundamentally change this approximation although thedynamicsoftheendogenousvariablesmayofcoursechange. 27We construct the responses of labour market tightness and labour productivity conditional on a commodity price shock from the empirical impulseresponsesinSection3byapplyingtherelevantrelationshipsobtainedfromtheDMPmodel. 30

labourmarketmovementssolelythroughthelensofchangesinlabourproductivityasinmuchofthemacro-labour literaturereferencedhere. Shocksotherthantotechnologycanhavealimitedimpactonlabourproductivity,but nevertheless have a sustained impact on the labour market through an adjustment in the real exchange rate. 31

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Figure 4: Decomposing the response in labour market tightness 0 5 10 15 20 25 30 35 40 quarters .SS morf .veD .tnecreP Commodity price shock 2.5 DMP model 2 approximated contribution real exchange rate contribution labour productivity 1.5 1 0.5 0 -0.5 0 5 10 15 20 25 30 35 40 quarters .SS morf .veD .tnecreP Neutral technology shock 2.5 2 1.5 1 0.5 0 -0.5 Note: Decompositionoftheresponseinlabourmarkettightnessusingtheapproximationprovidedinequation(65). Theapproximateresponseis givenbythedashedredline;thecontributionoftherealexchangerateisdepictedbythedash-dottedgreenlineandthedottedblacklineshows thecontributionoflabourproductivity. ThesolidbluelineistheactualmovementoflabourmarkettightnessgeneratedbytheDMPmodel. The toppanelshowsthemovementsthatareinducedbyacommoditypriceshock,thebottompanelshowsthecaseofaneutraltechnologyshock. 39

RAV susrev dna dekrow sruoh citsale htiw ledom PMD dna ,BOA ,PMD :5 erugiF tnemyolpmenU tnemtsevnI noitpmusnoC tuptuO secirp ytidommoC 40.0 52.0 52.0 8 20.0 2.0 2.0 1 0 51.0 51.0 6 20.0- 1.0 1.0 4 5.0 50.0 40.0- 50.0 2 0 60.0- 0 0 50.0- 0 80.0- 50.0- 1.0- 1.0- 2- 1.0- 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 dekrow sruoH egaw laeR etar egnahcxE ecnalab edarT seicnacaV 8.0 3 3.0 51.0 5.0 5.2 1.0 6.0 2 2.0 50.0 0 5.1 4.0 1 1.0 0 5.0- 5.0 50.0- 2.0 0 0 1.0- 0 5.0- 1- 1.0- 51.0- 1- 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 sruoh .tsale PMD BOA PMD RAV etamitse tniop RAV dnab ecnedifnoc enilesab eht susrev )kcalb dettod-hsad( dekrow sruoh citsale htiw ledom PMD eht dna ,)eulb dehsad( ledom BOA eht ,)der dilos( ledom PMD eht fo sesnopser eslupmi dettiF :etoN sretemarap ledom gniniamer eht fo seulav eht ;3 elbaT ni dedivorp era seulav retemarap detamitse ehT .)aera dedahs yerg( sdnab ecnedfinoc %09 sti dna )kcalb dilos( setamitse RAV .2elbaTninwohsera 40

Figure 6: Restricted estimation of the AOB model Unemployment Vacancies DMP -0.015 AOB AOB-restricted(v1) AOB-restricted(v2) 1.3 -0.02 1.2 -0.025 -0.03 1.1 -0.035 1 -0.04 0.9 -0.045 0.8 -0.05 0.7 -0.055 -0.06 0.6 -0.065 0.5 2 4 6 8 10 12 2 4 6 8 10 12 Note: Fitted impulse responses of the DMP model (solid red), the AOB model (dotted red), and the two restricted versions of the AOB model (dashed blue and dash-dotted green). AOB restricted(v1) uses the same parameters as the DMP model except for the probability of breakdown in bargaining, δaob, which is estimated at 100δaob =0.001. AOB restricted(v2) uses the same parameters as the DMP model, but estimates the probabilityofbreakdowninbargaining(againat100δaob=0.001)andtherelativeimportanceofthefixedandvariablecostcomponentsinposting vacancies, sfixed = 0.52. The estimated parameter values are provided in Table 3; the values of the remaining model parameters are shown in Table2. 41

sdoog fo ytilibatutitsbus dna ,ssennepo edart ,stnemegnarra tekram laicnanfi ot ytivitisneS :7 erugiF etar egnahcxE ecnalab edarT seicnacaV tnemyolpmenU noitprosbA citsemoD 1 5.4 0 20.0- 2.0 4 2.0- 8.0 40.0- 5.3 4.0- 60.0- 6.0 3 6.0- 51.0 80.0- 5.2 8.0- 4.0 1.0- 2 1- 21.0- 1.0 2.0 5.1 2.1- 41.0- 4.1- 0 1 61.0- 6.1- 5.0 81.0- 50.0 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 ledom HIP ymonocE nepO yhcratua .niF enilesab PMD etar egnahcxE ecnalab edarT seicnacaV tnemyolpmenU noitprosbA citsemoD 1.0- 8.0 30.0- 531.0 8.1 2.0- 6.0 40.0- 31.0 6.1 50.0- 3.0- 521.0 4.0 60.0- 4.1 21.0 4.0- 2.0 70.0- 511.0 2.1 5.0- 80.0- 0 11.0 6.0- 1 90.0- 501.0 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 21 01 8 6 4 2 erahs edart hgiH yticitsale edart woL enilesab PMD a ot srefer )neerg dettod-hsad( ykratua laicnaniF .gnirahs ksir lanoitanretni fo eerged eht ni segnahc ot ledom PMD detamitse eht fo ytivitisnes eht setartsulli lenap pot ehT :etoN eht fo noitarbilac a ot sdnopserroc )eulb dehsad( ledom HIP ymonoce nepo ehT .ytinfini gnihcaorppa si ,bφ ,retemarap tsoc gnidloh dnob eht erehw ledom enilesab eht fo noitarbilac eradoogngierofdnaemohehtnehwdna51.0= s h sxe gnittesyb)eulbdehsad(nepoeromsiymonoceehtnehwytivitisnessetartsullilenapmottobehT .0≈ bφerehwledomenilesab sspdg noitprosbacitsemoD .2=θdna,50.0= s h sxe ,548.0=bφeraseulavgnidnopserroceht)slenapllanider(ledomPMDdetamitseehtnI .8.0=θ,)neergdettod-hsad(elbatutitsbusssel sspdg .tnemtsevnidnanoitpmusnocfoegarevadethgiewehtsadetupmocsi 42

skcohS weN :8 erugiF tnemyolpmenU tnemtsevnI noitpmusnoC tuptuO 1 80.0 10.0 4.0 8.0 570.0 70.0 6.0 3.0 0 560.0 4.0 60.0 2.0 10.0- 2.0 550.0 50.0 1.0 20.0- 0 540.0 2.0- 40.0 0 30.0- 06 04 02 06 04 02 06 04 02 06 04 02 egaw laeR etar egnahcxE ecnalab edarT seicnacaV 6.0 0 3.0 30.0 20.0- 52.0 4.0 20.0 2.0 40.0- 51.0 2.0 10.0 60.0- 1.0 80.0- 50.0 0 0 0 1.0- 10.0- 50.0- 2.0- 21.0- 1.0- 06 04 02 06 04 02 06 04 02 06 04 02 ssennepo desaercnI yticitsale edart hgiH setutitsbus tcefreP yticitsale edart enilesaB enilesabehtrednusesnopserehtwohssenileulbdilosehT .)kcohsswenehtretfasraey5(noitcudorpytidommocerutufniesaercninatuobaswenotesnopserehtswohserugfiehT :etoN a morf devired era senil neerg dettod-hsad eht ;senil der dehsad eht yb detciped si sdoog dedart neewteb ytilibatutitsbus tcefrep fo esac ehT .ledom PMD eht rof setamitse retemarap .5.0= s h sxe gnittesybsaibemohfoeergedrewolarofwollaotdegnahcsawnoitaziretemarapenilesabeht,senilkcalbdettodehtniatbooT .7=θfoyticitsaleedartahtiwledom sspdg 43

Figure 9: labour market tightness — data and model predictions 2.5 data model approximation 2 1.5 1 0.5 0 -0.5 0 2 4 6 8 10 12 Note: The blue line depicts the response of labour market tightness constructed directly from the VAR estimates. The dashed red line is the predicted response of labour market tightness using equation (65) based on the empirical responses of the real exchange rate and labour market productivity. 44

Table 1: Share of top three commodity exports %ofcountry netexports Australia Ironoresandconcentrates 33 Coal;briquettes 18 Petroleumgases 8 Canada Petroleumoils,crude 30 Petroleumgases 4 Wheatandmeslin 4 NewZealand Milk&creamconcentrated 24 Lambmeat 8 Butter 7 Norway Petroleumoils,crude 43 Petroleumgases 24 Fish,excludingfillets 7 Notes: Source: HarvardAtlasofEconomicComplexity,2014data. 45

Table 2: Calibrated parameters Models Parameter Description DMP DMP(l) AOB RBC RBC(rr) β Discountfactor 0.99 (allmodels) σ Curvatureof 1.10 utilityfunction (allmodels) α Shareofcapital 0.33 (allmodels) δ Depreciationrate 0.025 (allmodels) θ Tradeelasticity 2.00 (allmodels) exh ss Steadystategoodsexport 0.05 gdpss GDPratio (allmodels) ys c s Steadystatecommodityexport 0.15 gdpss GDPratio (allmodels) v Home-biasparameter 0.80 (allmodels)[implied] nss Steadystate 0.95 0.95 0.95 – – employment qss Steadystateprob. 0.7 0.7 0.7 – – offillingvacancy κvvss+qκ¯ Shareofvacancy 0.005 0.005 0.005 – – yshs costinoutput ρ Probabilitythat 0.1 0.1 0.1 – – matchbreaksup bu/wss Replacementratio 0.4 0.4 0.4 – – χ Scaleparameter 0.67 0.67 0.67 – – inmatchingfunction [implied] [implied] [implied] Notes: DMP=baselinemodel,DMP(l)=baselinemodelwithelasticlaboursupply,AOB=alternatingofferbargainingmodel,RBC=Real businesscyclemodelwithWalrasianlabourmarkets,RBC(rr)=RBCmodelwithrealwagerigidities. 46

Table 3: Estimated parameters Models Parameter Description DMP DMP(l) AOB RBC RBC(rr) φb Bondholdingcost 0.85 0.72 0.86 0.70 0.68 (×100) [0.004] [0.004] [0.004] [0.004] [0.004] φv Costofvacancies 1.10 0.96 0.84 – – [0.020] [0.018] [0.027] – – φ Investment 0.04 0.005 0.04 0.02 0.02 adjustmentcosts [0.001] [0.001] [0.001] [0.001] [0.001] ζ Matchingfunction 0.72 0.74 0.70 – – parameter [0.001] [0.001] [0.001] – – δaob AOBparameter – – 0.001 – – (×100) – – [0.03] – – cu/cw Consumptionshare 0.60 0.58 – – – ss ss oftheunemployed [0.000] [0.000] – – – sfixed Fixedcostofbargaining 0.001 0.001 0.46 – – [0.03] [0.03] [0.03] – – ξ Household’s 0.40 0.30 – – – bargainingweight [implied] [implied] φ Inverseoflabour – 0.74 – 0.48 0.93 supplyelasticity – [implied] – [0.003] [0.01] η Realwagerigidity – – – – 0.84 – – – – [0.003] Notes: DMP=baselinemodel,DMP(l)=baselinemodelwithelasticlaboursupply,AOB=alternatingofferbargainingmodel,RBC=Real businesscyclemodelwithWalrasianlabourmarkets,RBC(rr)=RBCmodelwithrealwagerigidities.Numbersinbracketsarestandarderrors. 47

A Data description and definitions Table4liststherawdatausedintheVARs. AllseriesaretakenfromHaverAnalytics,andthedatasetisavailable by request from the authors. For each country in the panel, ten time series are used, which are transformations of the raw data: (cid:18) (cid:19) COM pcor = ln (A.1) US CPI (cid:18) (cid:19) GDP y = ln (A.2) POP (cid:18) (cid:19) C c = ln (A.3) POP (cid:18) (cid:19) I i = ln (A.4) POP (cid:18) (cid:19) NXE nxm = (A.5) GDP(L) (cid:18) (cid:19) UNE urate = (A.6) LAF vac = ln(VAC) (A.7) fxr = ln(REER) (A.8) (cid:18) (cid:19) WAGE wprr = ln (A.9) CPI (cid:18) (cid:19) Total HRS thp = ln (A.10) POP 48

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