Investment Specific Technology Shocks and Emerging Market Trade Balance Dynamics

Transcription

1 Investment Specific Technology Shocks and Emerging Market Trade Balance Dynamics Aydan Dogan University of Kent September 26, 215 Abstract Understanding the trade balance dynamics has a central role in studies of emerging market business cycles. In this paper, we investigate the driving sources of emerging market trade balance fluctuations by developing a two country, two sector international real business cycle model with investment and consumption goods sectors. We estimate the model for Mexico and US data and find that a slowly diffusing permanent investment specific technology shock that originates in the US accounts for most of the trade balance variability in Mexico. This shock is also the key driver of business cycle fluctuations in Mexico. Keywords: Emerging markets, Net exports, Investment specific technology shocks, International business cycles, Bayesian Estimation. JEL codes: C11, F41, F44. I would like to thank to my supervisor Miguel León-Ledesma for his helpful insights, guidance and support. All errors are mine. School of Economics, University of Kent, Canterbury, Kent, CT2 7NP, UK. ad416@kent.ac.uk. 1

2 Investment Specific Technology Shocks and Emerging Market Trade Balance Dynamics 1 Introduction Trade balance dynamics has a central role in studying emerging market business cycle fluctuations. Emerging market economies experience large economic crises that are related to significant current account and trade balance reversals. these countries compared with the advanced economies. The trade balance to GDP ratio is significantly more volatile in In this paper, we ask if investment specific technology shocks can be important determinants of emerging market trade balance dynamics within an international real business cycle IRBC framework. An important aspect of the post-war US economy is the significant decline in the relative price of investment goods and the increase in the investment rate. Greenwood et al explained this empirical feature by showing the important role of investment specific technology shocks for the US economic growth. Since then, the contribution of investment specific technology shocks in driving the US business cycle fluctuations has been examined in several papers such as Greenwood et al. 2, Fisher 26, Justiniano et al. 21 and Schmitt-Grohe and Uribe 211. Considering the increase in globalisation, a natural step would be to inquire into the international transmission of these shocks through trade linkages. In fact, empirical evidence suggests that the imports of emerging market economies are mostly concentrated on investment goods see Serven 1995 or Mutreja et al This implies that changes in the relative price of investment goods will have spillover effects through fluctuations in the trade balance. The aim of this paper is to investigate the transmission of investment specific technology shocks that originate in the US into emerging market economies by focusing on the trade channel. Specifically, we explore the trade dynamics between the US and Mexico as these two countries have strong trade linkages. Using the data for Mexico, we find that the share of US exports and imports are 78% and 49%, respectively. The import share of investment goods is 55% while its export share is 48% 1. In fact, Mexico is the third largest trading partner of the US 2. As imports are capital goods intensive, relative price movements in the US will transmit into the Mexican economy. This transmission operates through the substitution effects terms of trade movements, wealth effects technological progress as well as the relative investment absorption of both countries expenditure on investment goods. These will in turn affect the trade balance. Motivated by the empirical evidence, we build a two country, two sector IRBC model with consumption and investment goods sectors. In the model set-up, we allow country size to differ so that we can outline a small open economy with the calibration. The general convention in the business cycle literature is to represent investment goods and consumption goods as output of a single sector. In our model, there are two separate sectors with different technologies. First, as explained by Basu and Thoenissen 211, in an open economy framework changes in the relative price of investment goods do not necessarily imply a technical improvement. When investment goods are also tradable, changes in the aggregate investment price index do not truly reflect the changes in the domestic production of investment goods. This explanation is of particular interest for this paper as, in the model set-up, both goods can be tradable. Second, the two sector structure allow us to study the effects of technological improvements in the consumption and investment sectors separately. We introduce sector specific total factor productivity TFP shocks and an exogenous uncovered interest rate parity UIP shock to the model. The investment specific technology shock is assumed to be non-stationary to capture the trend in the relative price of investment 1 We used the data from OECD STAN Bilateral Database. We report the values from 211 as it is the latest available data. 2 The largest trading partners of the US are Canada and China respectively. The related data is taken from the US Census Bureau for June,

3 goods. We allow this shock to be persistent in growth rates. The technology shock in the consumption sector, on the other hand, is temporary. The permanent shock in the investment sector is assumed to originate in the developed economy. It, then slowly diffuses into the emerging market economy through an error correction structure. This formulation implies a cointegration in the long run. Intuitively, we capture the fact that technological improvements usually occur in advanced economies and take time to be acquired and implemented in emerging markets. We estimate the model for Mexico and US data by Bayesian likelihood methods. One interesting fact that emerges from our estimations is the significantly low posterior value of the speed of adjustment of the investment technology of Mexico. The estimated value implies an annual convergence to the common trend of 4% per year only. Hence, it is almost a non-stationary asymmetric shock. We check the model performance by comparing the second moments of the data with the ones we obtain from our model. The model successfully addresses the counter-cyclicality of the trade balance. Furthermore, the sign of the correlation between the trade balance and real exchange is positive as it is in the data. However, it overpredicts the volatility and persistence of the trade balance. Although not matching the correct persistence, it generates a downward sloping autocorrelation function in line with the data. The model does a good job at explaining the persistence of other variables. It also generates substantial investment and real exchange rate volatility. Given the reasonable empirical fit of the model, we present the variance decomposition to understand the contribution of shocks to the fluctuations of the trade balance. We find that, over the business cycle, around 9% of the trade balance variability is explained by the permanent, slowly diffusing investment specific technology shock that originates in the US. The analysis shows that this shock is the key source of business cycle fluctuations of Mexico. To understand the transmission mechanism, we present the dynamic response of the trade balance to a permanent investment specific technology shock that originates in the US. We find that the response of the trade balance is positive. This shock also successfully accounts for the counter-cyclicality of the trade balance. We decompose the trade balance into its price and quantity components to have a full understanding of the transmission. We find that both quantity and relative price components of the trade balance contribute to this countercyclicality positively except for the real exchange rate. This paper relates to several strands of the international real business cycle literature. The implications of investment specific technology shocks to address different questions in an international dimension have been studied in other papers previously, such as Boileau 22, Raffo 21 or Mandelman et al This paper is more closely related to Jacob and Peersman 213. They examined the driving sources of the US trade balance variability and found that the marginal efficiency investment shock -a shock that increases the efficiency of transforming investment goods into physical capital- accounts for most of the US trade balance fluctuations. As we focus on the emerging market trade balance dynamics, our paper also builds on the literature on emerging market business cycles. Aguiar and Gopinath 27 suggested that the business cycle characteristics of these countries can be addressed in a standard RBC framework when the main driving source of fluctuations is a shock to trend growth. We show that the business cycle fluctuations are mainly driven by a permanent shock as presented by Aguiar and Gopinath 27 but this shock is a slowly diffusing permanent investment specific technology shock that originates in the US. In this respect, our finding also relates to the literature that explores the importance of US shocks for the business cycle fluctuations of emerging market countries see, for instance, Canova 25 or Mackowiak 27. Motivated by the empirical regularities of the US economy, we add to this literature by introducing a permanent investment specific technology shock to an otherwise standard two sector IRBC model. The rest of the paper is structured as follows. We begin by describing the model in Section 2. In Section 3, we outline the Bayesian estimation of the model. We present the results in Section 4 by 3

4 discussing the second moments, variance decomposition and the impulse response analysis. Finally, we conclude in Section 5. 2 The Model The model we present here, is a two country, two sector small open economy general equilibrium model. The two countries, Home H and Foreign F, are populated by a mass of infinitely lived households with a fraction of n and 1 n of the world total, respectively. Firms can produce either consumption goods or investment goods and they can sell those goods in the domestic and foreign markets. There are deviations from the purchasing power parity PPP through the existence of home bias in preferences which depends on the degree of openness and the country size. We allow for some other real frictions that are common in the literature. Specifically, we introduce external habit formation in consumption, incomplete international asset market structure and investment adjustment costs. There are country and sector specific technology shocks as well as a UIP shock. We also include a permanent investment specific technology IST shock which is assumed to be cointegrated across economies. We will denote the foreign country variables by an asterisk,. 2.1 Households The preferences over intertemporal decisions are identical across countries. The representative home household, i, receives utility from consumption C i t, and disutility from supplying labour L i t. The representative home household s, i, lifetime utility function can be expressed as: U i t = E t t= [ ] β t logct i hc t 1 Li t 1+η, < β < η where E t denotes the expectations operator conditional on time t information, β is the discount factor, h is the degree of external habit formation and the parameter η is the inverse of the Frisch elasticity of labour supply. The log consumption utility ensures the existence of a balanced growth path in the model as there is a permanent IST shock. Households obtain income through renting labour and capital to the domestic firms. Households also receive nominal profits from the ownership of the domestic firms. It is assumed that the international asset markets are incomplete, in the sense that households are able to trade non-state-contingent bonds to invest in new capital and purchase consumption goods. Here, we follow Benigno 21 to model incomplete asset market structure. Households in the home country can hold two kinds of bonds which are denominated in the units of the home currency and the foreign currency. However, the bonds issued by the home country are not traded internationally. In order to have a stationary distribution of wealth between countries there is an additional cost for the households in the home country when they trade in the foreign asset market. The representative home household, i, maximises 1 subject to the budget constraint: Bi H,t Ct i + P x,txt i i + S tbf,t i t StB 1 + i F,t t Θ BH,t 1 i + S tbf,t 1 i + Wt i L i t + P x,trt K Kt i + Π i t 2 where BH,t i and BF,t i are the household i s holdings of the domestic and foreign currency denominated 4

5 nominal risk-free bonds. The nominal interest rates on these bonds in time t are i t and i t respectively, S t is the nominal exchange rate defined as the home currency price of buying one unit of foreign currency. P C,t and P X,t are the price of consumption and investment goods respectively, in the home country. The cost function Θ ensures a well defined steady state and is given for domestic households as it depends on the holdings of foreign currency denominated bonds of the world. 3 W i t represents the nominal wage rate, Xt i is the investment, Kt 1 i is the capital stock, Rt K denotes the real rental rate of capital in investment units and Π i t is the profit income from domestic firms. The law of motion for capital is given by: K i t = 1 δ K K i t 1 + [ ] X i 1 S t X i Xt 1 i t 3 where δ K is the capital depreciation rate. The functional form of the investment adjustment cost, S, has the following properties as in Christiano et al. 25: S1 = S 1 = and S 1 >. The equilibrium conditions of the household in the home country for labour, domestic and foreign bond holdings, capital and investment are characterised by: w t = L η t C t hc t 1 4 [ ] Ct hc t 1 Pc,t 1 = β1 + i te t C t+1 hc t +1 [ ] 1 = β1 + i Ct hc t 1 Pc,t St+1 t ΘS tb F,t/E t C t+1 hc t +1 S t [ ] Ct hc t 1 Px,t+1 Q t = βe t Rt+1 K + 1 δ K Q t+1 C t+1 hc t P x,t It It Q t 1 S S It = I t 1 I t 1 I t 1 βe t [ Ct hc t 1 C t+1 hc t Q t+1 S It+1 I t ] 2 It+1 I t 8 where w t is the real wage in consumption units and Q t is the shadow price of capital in consumption units. Equation 7 shows that the cost of installing an additional unit of capital is equal to the sum of present discounted future value and the rental rate. Notice that changes in the relative price of investment goods will affect the marginal value of acquiring an extra unit of capital. A fall in the relative price of investment goods will lower the cost of installing an additional unit of capital. The situation of foreign households is analogous. 2.2 Final Goods Sector Final goods in both sectors is a combination of home and foreign produced intermediate goods. Countries only trade intermediate goods; final goods can not be traded. 3 In order to prevent non-stationarity in the model, we impose the following restrictions on the cost function: Θ is a differentiable decreasing function in the neighbourhood of steady state level of net foreign assets and when the net foreign assets are in the steady state level BF,t i =, the cost function is equal to 1 Θ = 1. See Benigno 21 for details. 5

6 The final good in the home consumption sector consists of home produced consumption goods C H,t and imported goods C F,t and in the foreign country, it consists of foreign produced consumption goods CF,t and imported goods CH,t. The aggregate consumption index has the following constant elasticity of substitution CES aggregation form in the home and foreign country, respectively: C t = ω 1 θ CH,t θ 1 θ + 1 ω θ 1 CF,t θ 1 θ θ 1 θ 9 C t = ω 1 θ C F,t θ 1 θ + 1 ω θ 1 C H,t θ 1 θ θ 1 θ 1 where θ is the elasticity of substitution between home and foreign produced intermediate consumption goods. The parameter that determines the share of foreign produced intermediate goods in the production of the final consumption good at home, 1 ω, is a function of the degree of openness in the consumption sector, ρ, and the relative country size, 1 n 4 : 1 ω = 1 n ρ. The value of ω determines the degree of home bias in consumption preferences. And in the foreign country, 1 ω = n ρ. The final good producers in the consumption sector maximises 9 subject to nominal expenditure which gives the following demand functions for the home and foreign country respectively: C H,t = ω PH,t θ C t, C F,t = 1 ω PF,t θ C t 11 P θ CF,t = ω H,t C Pc,t t, CH,t = 1 ω P F,t P c,t θ C t 12 The corresponding consumer price indices are: = ωp 1 θ H,t + 1 ωp 1 θ 1 1 θ F,t 13 P c,t = ω P F,t 1 θ + 1 ω P H,t 1 θ 1 1 θ 14 We assume that law of one price LoOP holds such that: P F,t = S tp F,t and P H,t = P H,t/S t. Thus in our framework there are deviations from PPP only through the existence of home bias. Similarly, the final good in the investment sector is a combination of domestically produced investment goods -X H,t at home, X F,t at foreign country- and imported goods -X F,t at home, X H,t at foreign countryand has the CES aggregation form: X t = ν 1 α XH,t α 1 α α ν α XF,t α 1 α α 1 15 X t = ν 1 α X F,t α 1 α α + 1 ν α 1 X H,t α 1 α α 1 16 where α is the elasticity of substitution between home and foreign produced intermediate investment goods. The share of foreign produced intermediate goods for the production of the final investment good, 1 ν, is similarly a function of the degree of openness in the investment sector, φ and φ, 4 See, De Paoli 29 for a similar preference specification in a two country, small open economy general equilibrium framework. 6

7 and the relative country size, 1 n and n: 1 ν = 1 n φ and 1 ν = n φ. The value of ν and ν determines the degree of home bias in the investment sector. The optimal choice of final good producers in the investment sector yields: X H,t = ν Px H,t P x,t α X t, X F,t = 1 ν Px F,t P x,t α X t 17 X F,t = ν P x F,t Px,t α P Xt, XH,t = 1 ν x H,t P x,t α X t 18 The corresponding price indices for the investment goods are: P x,t = νp 1 α x H,t 1 1 α 1 α + 1 νpx F,t 19 P x,t = ν P x F,t 1 α + 1 ν P x H,t 1 α 1 1 α 2 As a result of LoOP; imported investment good prices will simply be the price that foreign producers set for those goods, corrected by the nominal exchange rate: P x F,t = S tp x F,t, P x H,t = P x H,t/S t 2.3 Intermediate Goods Sector Here, we describe the production functions and the price setting mechanism for both sectors. intermediate good producers in both sectors can sell their goods to the final good producers from the home and foreign country. Firms produce output by using labour and capital and production has the standard constant returns to scale functional form. The production function of the consumption goods in the home country is given by: The Y c,t = K αc c,t A c,tl c,t 1 αc 21 where A c,t is the sector specific exogenous technology shock, L c,t is the total labour supply employed in the home consumption intermediate sector, K c,t denotes the use of capital in the home consumption intermediate sector and finally the parameter α c is the capital s share of output. The technology shock in the consumption sector has the following stochastic process: where ρ a c < 1 and ε a c,t N, σ 2 a c. lna c,t = ρ a c lna c,t 1 + ε a c,t 22 Firms in the intermediate sector maximise the nominal profit function: subject to the production function 21. Π c,t = P H,tY c,t W tl c,t P x,tr K t K c,t 23 7

8 The first order conditions for the choice of capital and labour are: R K t = α c PH,t A 1 αc c,t P x,t w t = 1 α c PH,t A 1 αc c,t 1 α c Lc,t K c,t α c Kc,t L c,t And the capital-labour ratio is: w t Rt K = 1 αc α c K c,t L c,t P x,t 26 The production function of the investment goods sector is similar to the consumption goods one but with an additional non-stationary component: Y x,t = K αx x,tz x,tl x,t 1 αx 27 where L x,t is the total labour supply employed, K x,t is the use of capital and the parameter α x is the capital s share of output in the home investment intermediate sector. Different from the consumption sector, the investment specific technology shock assumed to be non-stationary. formalise the permanent investment specific shock in Section 2.5. As in the intermediate consumption sector, firms maximise the nominal profit function: We discuss how we Π x,t = P x H,tY x,t W tl x,t P x,tr K t K x,t 28 subject to the production function 27. The first order conditions for the choice of capital and labour are: 1 α x Rt K = α x Px H,t Z x,t 1 αx Lx,t P x,t K x,t w t = 1 α x Px H,t α x Z x,t 1 αx Kx,t L x,t 29 3 And the capital-labour ratio is: w t Rt K = 1 αx α x K x,t L x,t P x,t 31 The capital-labour ratio of two sectors imply that capital and labour will be allocated between the two sectors depending on the share of the inputs in the production functions: 1 α c α c K c,t L c,t = 1 αx α x K x,t L x,t 32 The foreign country s intermediate goods sectors are symmetric to the home country. 2.4 Equilibrium Conditions and the Current Account We close the model by using the market clearing conditions for each sector. The output of both sectors can be consumed at home and foreign country. Equivalently, the output in the consumption investment 8

9 sector will be equal to the sum of total consumption investment at home and the demand for exports minus the imports: P H,t Y c,t = PH,t C H,t + = C t P F,t S t C F,t + 1 n PH,t CH,t n 1 n n PH,t C H,t 33 P x H,t Y x,t = P xh,t X H,t + 1 n n = Px,t X t P xf,t S t X F,t + Px H,t XH,t 1 n Px H,t XH,t n We measure the total output in the home economy with CPI as we do not have an explicit GDP deflator: 34 Y t = PH,t Y c,t + P xh,t Y x,t 35 that is, the sum of production in the consumption and investment sectors. As a results of the incomplete international asset market structure, we can track the dynamics of the current account 5 : S tb F,t 1 + i t Θ S tb F,t StBF,t 1 1 n = n PH,tC H,t P F,tS tc F,t 1 n + n Px H,tX H,t P xf,t StXF,t 36 Notice that, the right hand side of the current account equation is equivalent to the net exports. It is the exports of both consumption and investment sectors minus the imports of both sectors. We define the trade balance as a ratio of GDP: T B t = 1 [ 1 n Y t Y t n PH,tC H,t Finally, the total labour and capital will be: P F,tS tc F,t + 1 n n Px H,tX H,t P ] xf,t StXF,t 37 L t = L c,t + L x,t 38 K t = K c,t + K x,t The Shock Structure The technology shock in the investment sector is a permanent shock in both countries. We assume that these two non-stationary shocks are cointegrated across countries. Specifically, we assume that the permanent IST shock in the foreign country carries a unit root while the technology of the investment sector in the home country adjusts to it slowly. 5 To see the fluctuations of the current account, we aggregate the individual budget constraints 2 and plug in the aggregate profits Π t = P x H,t Yx,t WtLx,t Px,tRK t Kx,t + P H,tY c,t W tl c,t P x,trt K Kc,t. Then we apply the equilibrium conditions, Equations 33 and 34. We also take into account the assumption that asset markets are complete at domestic level; meaning home bonds are in zero net supply. 9

10 One can think of a permanent IST shock that is persistent in growth rates. This shock assumed to originate in the foreign economy: lnz x,t lnz x,t 1 = ρ z xlnz x,t 1 lnz x,t 2 + ε z x,t 4 However, the technology of the investment sector of the home economy adjusts to this shock slowly: lnz x,t lnz x,t = ρ z xlnz x,t 1 lnz x,t 1 + ε z x,t 41 where the parameter ρ z x is the persistence of adjustment. We introduce a stochastic component ε z x,t to the adjustment of home investment technology to the technological improvement in the foreign country. To have a stationary equilibrium we transform the trended variables and work with a stationarised model. The derivation of the trends and the de-trending procedure can be found in Appendix A. Thus, in total there are four technology shocks in the model. As mentioned before, in addition to the IST shocks, there are temporary country specific technology shocks in the consumption sector of each country. We also introduce an exogenous UIP shock to the Equation 6: where [ ] 1 = βζ t1 + i Ct hc t 1 Pc,t St+1 t ΘS tb F,t/E t C t+1 hc t +1 S t lnζ t = ρ ζ lnζ t 1 + ε ζ,t, ρ a c < 1, ε a c,t N, σa 2 c Estimation We use Bayesian estimation methods to estimate the model 6. The stationary log-linearised model that we use for our estimations can be found in Appendix C. To obtain the posterior distributions, we run two parallel chains of 25 replications of the Metropolis Hastings algorithm and discard the first half of the draws. We monitor the convergence by using the Brooks and Gelman 1998 statistics Data We estimate the model for the period 1995:Q1-214:Q3. We assume that the home country is Mexico and foreign country is the US. We use series on Mexico and US real consumption, the ratio of relative price of investment goods between the two countries as well as the bilateral real exchange rate and the trade balance to GDP ratio as observables. We calculate the real exchange rate such that an increase is a depreciation as it is in the model. The trade balance to GDP ratio is the difference between the exports and imports of Mexico and US, divided by the Mexican GDP 8. Details on the data sources can be found in Appendix D. 6 See, An and Schorfheide 27 for a detailed description of implementation of Bayesian estimation. 7 To conduct estimations, we use the MATLAB version of Dynare see, Adjemian et al The bilateral export and import data are only available in nominal terms. What we observe in the data is then: T B t Y t = 1 Y t [ 1 n n P H,tCH,t P F,t StC F,t + 1 n ] n P x H,t X H,t P x F,t StX F,t This could create measurement issues given that in the model we present all variables in relative prices. But we avoid such problem since the above stated equation is observationally equivalent to the Equation 37. 1

11 We plot the observables in Appendix E where we present the additional tables and figures see, Figure 3. We take the natural logarithms of all series and demean them. Having a permanent shock in the model allows a consistent way of de-trending between the model and the data. Even though the relative price of investment goods is non-stationary in levels, we do not de-trend the series since we are using the difference of relative price of investment goods between the two countries. In our calibration, the capital share on the production of intermediate goods is assumed to be symmetric across sectors and countries α c = α x = αc = αx. This parameter choice implies a common stochastic trend between these two variables, making the relative measure stationary. As consumption and trade balance to GDP ratio are trended variables, we measure them in first differences. To match the data, we define the following observables in the model: c obs,t = c t c t 1 + α z x,t 44 c obs,t = c t c t 1 + α z x,t 45 rel rx,t = rx t rx t 46 tb obs,t = tb t tb t 1 47 where z x,t is the first difference of the global IST shock z x,t z x,t 1 = ε z x,t, rx t and rx x,t are the relative price of investment goods in the home and foreign country respectively rx t = p x,t p c,t, rx t = p x,t p c,t. As the real exchange rate is stationary in levels, the demeaned series is equivalent to the model specification. 3.2 Priors and Calibration Table 2 shows the prior distributions of the estimated coefficients. Our prior choice is standard. We use gamma distribution for the inverse Frisch elasticity of labour supply and trade elasticities for both sectors. We allow for a large standard deviation as the estimates of these parameters vary among studies. We choose beta distribution for the parameters that are bounded between zero and one. The prior choice of the consumption habit parameter is standard among estimated general equilibrium models for instance, see Smets and Wouters 23. We set the prior mean of the autoregressive components to.75 which implies high persistence. We choose inverse gamma distribution for the standard error of shocks with a mean of.1 and standard deviation of 2. We calibrate the remaining parameters. We set the discount rate, β, to.99 so that the annual steady state interest rate is around 4%. We set the size of the home country to.2 as Mexico is a small open economy. The cost of intermediation in the bond markets, δ, is fixed to.1 following Benigno 21. The depreciation rate, δ K, is set to.25 per quarter, implying a 1% annual depreciation on capital. The share of imported goods in both sectors are country size adjusted in the model: 1 ω = 1 n ρ in the consumption goods and 1 ν = 1 n φ in the investment goods. To calculate the degree of openness parameters, we took the data from World Input Output Database and used the national input output tables for Mexico and the US. We set the degree of openness in the consumption sector, ρ to.7 and φ to.15. These values imply that the size adjusted degree of home bias is higher in the US ω =.94, ω =.98, ν =.85 and ν =.97 and investment sectors have higher import intensity in both countries but particularly in Mexico 9. We fix the capital share in each sector and country to 9 To measure the import share of consumption and investment goods, we used the final consumption expenditure of households and the gross fixed capital formation respectively. We calculated the import shares of each sector for 5 years 2, 23, 26, 29, 211 and averaged them. We found the share of imports in investment sector.17 and.12 in Mexico and US respectively. For consumption goods sector these values are respectively.7 and.5 for Mexico and US. We fix the value of the degree of openness parameter in the consumption sector to the value that we obtain from the Mexican data as the values are similar 11

12 .36 to be consistent with the literature. The investment adjustment cost in both countries, φ = φ, is calibrated following Christiano et al. 25. Table 1: Calibrated Parameters Parameter Description Value β discount factor.99 n relative country size.2 δ cost of intermediation.1 δ K depreciation rate.25 ρ = ρ degree of openness-consumption.7 φ = φ degree of openness-investment.15 α c = α x = αc = αx capital share.36 µ = µ investment adjustment costs 2.5 between Mexico and the US. In fact, the degree of home bias in the consumption sector in the US is equal to.98 with both values. But because this is not the case for the investment goods sector, for the value of the degree of openness in the investment sector, we choose.15 as an intermediate value. This value matches the US home bias but it gives a slightly higher home bias for Mexico compared with the data- with the exact data calibration, the degree of home bias in the investment sector in Mexico equals to.85 while with our choice it is

13 Table 2: Prior and Posterior Distributions Parameter Description Prior Posterior Density Mean Std.dev Mode Std.dev Mean [5,95] η inverse frisch elasticity gamma [.97, 2.] θ trade elasticity-consumption gamma [.47,.56] α trade elasticity-investment gamma [.64, 1.6] h consumption habit-mex beta [.36,.56] h consumption habit-us beta [.88,.9] ρa ρ a c consumption tech. shock-mex c beta [.94,.97] consumption tech. shock-us beta [.1,.19] ρζ UIP shock beta [.55,.73] ρ x z ECM beta [.99,.99] ρ z x global IST shock beta [.82,.9] εa ε a c consumption tech. shock-mex c inv.gamma [.2,.4] consumption tech. shock-us inv.gamma [.5,.7] εζ UIP shock inv.gamma [.1,.2] ε x z ECM inv.gamma [.5,.9] ε z x global IST shock inv.gamma [.2,.3] 13

14 3.3 Posteriors Table 2 reports the estimation results. We present the posterior mode and the standard deviation along with the mean and the 5th and 95th percentiles of the posterior distribution. The posterior distributions of the estimated parameters can be found in Appendix E see, Figure 4. The estimate of the inverse Frisch elasticity is in line with the estimates of other studies. For instance, the posterior mean of the inverse Frisch elasticity in Smets and Wouters 23 is The posterior mean estimate of the trade elasticities seems fairly low. These two parameters are crucial for the fluctuations of the trade balance. The estimation results imply that the substitutability of goods is low between Mexico and US and even lower among consumption goods. Our estimate is similar to the estimates of the trade elasticity for small open economies by Justiniano and Preston 29. They found a posterior median of.63 for Australia,.69 for Canada and.73 for New Zealand. Similarly, Jacob and Peersman 213 estimate the trade elasticity between the US and the rest of the world to be.56 for both consumption and investment goods. We allow the degree of habit formation to be different between the two countries. The posterior distribution shows that consumption habits play a smaller role in Mexico than in the US. We find a fairly high persistence for the consumption sector productivity shock in Mexico. But this value is much lower for the US. We checked if this result is related to the high persistence of the growth rate of permanent IST shock. We fixed the ρ zx to.2 and re-estimated the model. The persistence of the US consumption technology shock with this estimation increases to.8. This shows that the persistence of the TFP shock in the consumption sector is partly captured by the persistence of the permanent IST shock in our estimations. In terms of the adjustment of Mexican investment technology to the permanent IST shock, the posterior value is quite high ρ x z =.99, indicating a weak cointegrating relationship between the US and Mexico total factor productivities in the investment sector. The estimated value implies an annual convergence to the common trend of 4% per year only. Hence, it is almost a non-stationary asymmetric shock. 4 Results 4.1 Second Moments We now turn to analysing the quantitative performance of the model. We present the second moments of key macroeconomic variables and compare them with the ones obtained from the model. Given our interest in the business cycle properties of the data, we HP-filter 1 output, consumption, investment, relative price of investment goods and trade balance series 11. To have a like for like comparison between the model and the data, we define new variables in the stationarised model by adding back the stochastic trends to the non-stationary variables. We report the HP-filtered theoretical moments of these nonstationary variables. Table 3 presents the standard deviation, autocorrelation and the cross-correlation of some selected variables. Overall, the model does reasonably well in matching the moments of the data. However, it fails to account for the volatility and persistence of the trade balance. The failure of RBC models in accounting for the volatility and persistence of the trade balance has been discussed by Garcia-Cicco et al. 21. Our finding is in line with their argument. Garcia-Cicco et al. 21 showed that a standard RBC model predicts that the autocorrelation function of the trade balance to GDP ratio is flat and close to unity. They argued that this is related to the parameterisation of debt elasticity δ which provides a stationary 1 As we are working with quarterly data, we choose 16 for the smoothing parameter of the HP-filter. 11 Information on the data sources can be found in Appendix D. 14

15 Table 3: Selected HP-filtered Moments Std.dev. relative to Y Autocorrelations Data Model Data Model TB/Y Y C X RER P x/p c Cross-Correlations Data Model Data Model TB/Y-Y Y-Y* RER-TB/Y C-C* C-TB/Y X-X* I-TB/Y X-Y RER-Rel.C C-Y Note: The standard deviation of all variables is divided by the standard deviation of Mexican GDP except for the TB/Y. As this variable is already a ratio of GDP, its standard deviation is the standard deviation of the observed ratio. All variables are in logs and the data on consumption, output, investment and relative price of investment goods is HP-filtered. We only keep the TB/GDP in levels. It is the HP-filtered nominal trade balance over the nominal GDP. We use the Mexican and the US data for the period 1995:Q1-214:Q3. The relative consumption is the log difference between the consumption of Mexico and US. The model counterpart of the statics is calculated by using the posterior mean. 15

16 distribution of wealth. The standard approach is to fix the value of this parameter to a small value that is sufficient enough to induce stationarity in the model. They pointed out that there exists a small enough value of debt elasticity which ensures stationarity but at the same time results in a flat, close to unity autocorrelation function for the trade balance to GDP ratio. This argument is particularly important for our results because their calibration of debt elasticity is the same as ours. To test the sensitivity of our results, to the calibration of δ, we increase the value to.7,.1 and 2.5. We find that, even with a calibration of 2.5 -which is not a common calibration choice- the persistence of the trade balance only decreases to.81. This implies that the high autocorrelation we obtain is not only related to the value of the cost of intermediation in the asset markets. We further test the sensitivity of the results to the value of some structural parameters. We find that the value of the degree of habit persistence and trade elasticities are crucial in addressing the autocorrelation of the trade balance. When we change the posterior mean of the consumption habit formation in both countries to.1 the persistence falls to.41. Alternatively, increasing trade elasticities in both sectors to 1.5 lowers the persistence to.69. The impact of trade elasticities transmit to the persistence of the trade balance through the relative price channel. An increase in the trade elasticity lowers the terms of trade volatility and since the terms of trade are mean reverting, a higher elasticity lowers its persistence too. Another interesting finding that Garcia-Cicco et al. 21 presented is that the RBC model predicts a flat autocorrelation function while in the data, this function slopes downward. In Figure 1, we show the autocorrelation function of the trade balance that we obtain from the data and the model. The autocorrelation function that the model delivers slopes downwards at a rate very close to the data although the level is higher for the model. Hence our model performs better than a standard RBC in this respect. The predicted volatility of the trade balance is much higher than what it is in the data. The existence of a permanent IST shock, increases the volatility of consumption and the trade balance since it generates significant wealth effects. In fact, when we shut down the permanent IST shock ε zx =, the volatility of the trade balance is equal to.2. But this then also lowers the consumption volatility significantly. In fact, our model underpredicts the volatility of consumption. An important business cycle feature of emerging market countries is that consumption volatility is higher than output volatility. Even though the model does not fit the data perfectly, it generates a volatility that is close to 1. Absence of a permanent IST shock reduces the performance of the model even further in terms of matching the consumption volatility. The slow diffusion of the permanent IST shock amplifies the wealth effects. When the growth rate of permanent shock is highly persistent, the impact of technological improvement on output is gradual. This generates further incentives to smooth consumption. Intuitively, when the shock is persistent in growth rates, consumers borrow initially as a result of higher income expectations in the future periods. This increases the volatility of both consumption and the trade balance. In fact, when we specify the permanent shock as a pure random walk ρ zx =, the volatility of the trade balance falls to.3. However, this improvement comes at the cost of even lower consumption volatility. The impact of the persistence and the standard deviation of the growth rate of the non-stationary shock was also discussed in Garcia-Cicco et al. 21. They showed that lowering the persistence and standard deviation of the growth rate of the non-stationary shock in a standard RBC model improves the model performance in terms of accounting for the volatility of the trade balance to output ratio but this improvement comes at the cost of low consumption volatility. The trade-off remains in our framework. The counter-cyclical behaviour of the trade balance is a well known feature of the emerging market economies 12. Our model successfully accounts for this feature as there are several channels that generate wealth effects in the set-up. One important parameter that has an impact on the sign of the correlation between the trade balance and output is the trade elasticity, as the elasticity of substitution parameter 12 See, Aguiar and Gopinath

17 determines the dominance of the substitution effect. In our model, the low substitutability between goods combined with high degrees of home bias dampens the impact of the expenditure switching channel 13. In addition, when the risk is not shared perfectly across countries, unexpected shocks create wealth effects. Hence, the incomplete market structure contributes to this counter-cylicality. The previously discussed wealth effect channel that operates through the persistence of the growth rate of the non-stationary shock provides extra uninsurable risk on top of the incomplete market structure. The model also generates the positive correlation between the trade balance and real exchange rate, confirming the Mundell-Fleming proposition. Figure 1: The Autocorrelation of the Trade Balance to GDP Ratio 1.9 Data.8.7 Model Lags The model is able to replicate the persistence of other variables of interest. This is a consequence of the rich shock structure along with the external habit formation in consumption. The persistence of the growth rate of the permanent IST shock contributes to the autocorrelations we obtain. The model performs reasonably well in terms of the volatility of investment and real exchange rate, although both volatilities are still less than what we observe in the data. The substantial real exchange rate volatility, we obtain is related to the low trade elasticity. The estimated value of elasticity of substitution between consumption goods is fairly low, implying a high terms of trade volatility. The fluctuations of terms of trade have an influence on real exchange rate as long as preferences are biased towards home produced goods. Given the high degree of home bias in our framework, the movements of terms of trade and real exchange rate are highly correlated. Hence, the high terms of trade volatility implies a high real exchange rate volatility as well. Finally, the model explains the cross-country correlation of output, consumption and investment reasonably well but not so much the correlation of real exchange rate and the relative consumption. Nevertheless, it successively generates a low correlation as international real business cycle models often predict a correlation close to one Corsetti et al. 28 show that with a sufficiently low trade elasticity the world demand for a good can fall with a fall in its price. 14 International real business cycle models predict a one to one correlation between the relative consumption and the real exchange rate. However, in data real exchange rate and relative consumption are negatively correlated. The inability of models to replicate this feature of data is known as the consumption-real exchange rate anomaly. See, Chari et al

18 4.2 Variance Decomposition In this section, we present the variance decomposition and specifically, examine the sources of fluctuations of the trade balance. The striking result we reach is that 9% of the variability of the trade balance is explained by the growth rate of permanent IST shock that originates in the US see, Table 4. The growth rate of permanent IST shock has a dominant role in driving the business cycle fluctuations of the economy. The exception to this is the volatility of the relative price of investment goods. 51% of its volatility is explained by the shock to the adjustment of the investment technology of Mexico. Expectedly, the second important driving source of the fluctuations is the consumption technology shock for the output, consumption and investment. But compared with the contribution of the permanent IST shock, the role of the consumption technology shock is still negligible. This result is important for understanding the sources of business cycle fluctuations of emerging market economies. Aguiar and Gopinath 27 suggested that the business cycle characteristics of these countries can be addressed in a standard RBC framework when the main driving source of fluctuations is a shock to trend growth. The importance of the permanent IST shock in our estimations is in line with their explanation. But we explore the implications of such shock in a two country, two sector framework. We show that the business cycle fluctuations are mainly driven by a permanent shock as suggested by Aguiar and Gopinath 27 but this shock is a slowly diffusing permanent IST shock that originates in the US. Our finding also relates to the literature that explores the importance of US shocks for the business cycle fluctuations of emerging market countries see, for instance, Canova 25 or Mackowiak 27. Motivated by the empirical regularities of the US economy, we add to the literature by emphasising the role of permanent IST shocks. A permanent supply side improvement in the US investment sector is the primary source of business cycle fluctuations of Mexico. Our finding proves the importance of trade linkages in the transmission of US shocks. Table 4: Variance Decomposition in percentages Vbl. Name ε a c ε a c εuip εzx ε z x NX/GDP GDP Cons Inv P x/p c RER Note: We only present the variance decomposition for Mexico home country variables. We report the variance decomposition of the HP-filtered variables based on the posterior mean. 4.3 Impulse Response Analysis Given the prominent role of the growth rate of investment specific technology shock, in this section we analyse the dynamic response of the trade balance to GDP ratio when the US economy is hit by a slowly diffusing permanent IST shock. 18

19 The structure of the IST shock in this model has important implications for the dynamic adjustment. When the permanent IST shock hits the US economy, its impact will not be immediate on either economies. It will diffuse slowly as it is persistent in growth rates. So, the impact on the US output will be gradual such that, in levels, agents will expect further TFP gains in the following periods. It will take much longer for the Mexican economy to adjust its technology to this innovation, considering the estimated persistence. countries. These features have implications on the trade dynamics between the two We can decompose the trade balance into its price and quantity components to have a full understanding of the transmission. This decomposition will allow us to disentangle the contribution of each component to the trade balance dynamics. By doing so, we can trace whether the dynamic response of the trade balance is dominated by the relative price movements or the quantity components 15. For tractability we use the log-linearised version of Equation 37. First, we will define the relative prices: rx t = p x,t p c,t, rx t = p x,t p c,t, rx H,t = p x H,t p c,t, rc H,t = p H,t p c,t, rx F,t = p x F,t p c,t, rc F,t = p F,t p c,t and rer t = p c,t + s t p c,t is the real exchange rate based on consumer prices. The trade balance to GDP ratio in linear terms is equal to: tb t = 1 n n C H Ỹ c h,t + rc H,t C F Ỹ cf,t + rc F,t + rer t + 1 n n X H Ỹ x h,t + rx H,t X F Ỹ xf,t + rx F,t + rer t 48 Re-writing this by substituting the optimal demand functions and using steady state conditions yield: tb t = c abs t + x abs t tot C,t tot X,t rel pxpc wrer t 49 where c abs t = C Ỹ 1 ωc t c t 5 x abs t = X Ỹ 1 νx t x t 51 tot C,t = C Ỹ 1 ω1 θrc F,t rc H,t 52 tot X,t = X Ỹ 1 ν1 αrx F,t rx H,t 53 rel pxpc t = X Ỹ 1 ν α rxt rx t 54 C X wrer t = 1 ω1 2θ + 1 ν1 2α rer t 55 Ỹ Ỹ 15 Jacob and Peersman 213 present a very similar definition of trade balance to the one we show here. Raffo 28 decomposes it into demand and price components in a different way. It is not a full decomposition as ours, because in their decomposition, the demand functions are affected by the relative price movements. 19

20 The first two components of the trade balance to GDP ratio, c abs t and x abs t, reflect the weighted cross-country relative consumption and investment absorptions. Considering the differences in the degree of openness between the two sectors, the weight of consumption and investment sectors will be significantly different. On the other hand, the impact of the terms of trade will also depend on the trade elasticities. With an elasticity higher than one, the substitution effect has a positive impact on the trade balance. Intuitively, when home produced goods become cheaper terms of trade increase consumers substitute imports with home produced goods, implying a trade balance improvement. But this is not the case when the substitution parameter is lower than one. In this case, increase in the terms of trade raises the demand for home produced goods as a result of the dominant income effect, implying a trade balance deterioration. The estimated values for both trade elasticities in our model is lower than one implying a negative relationship between the terms of trade and the trade balance. But, since the trade elasticity is higher in the investment sector, changes in the terms of trade in the investment sector will have a relatively smaller impact on the dynamics of the trade balance. As a consequence of the two sector structure, the international relative price of investment goods has an influence on the trade dynamics. Notice that in the absence of a separate investment sector, rel pxpc t would disappear. The final component, wrer t, is the weighted real exchange rate. The changes in the real exchange rate has a positive impact on the trade balance as a result of the negative value of the weight; a depreciation increase of the real exchange rate implies an improvement in the trade balance. Now, we can trace the impact of the IST shock on the trade dynamics by looking at the reaction of each component. Figure 2 shows the dynamic response of the current account, trade balance to GDP ratio, home output along with the response of the components of the trade balance. In response to this shock, the cost of producing investment goods falls in the US which in turn leads to a rise in the output of the investment sector. As the imports become cheaper for Mexico, the terms of trade improve in both sectors tot C,t, tot X,t 16. The increase in the terms of trade of both sectors has a positive impact on the trade balance. The dynamics of the current account is related to the persistence of the growth rate of the nonstationary IST shock and the behaviour of the terms of trade. The shock structure generates remarkable wealth effects in the dynamics. The improvement in the terms of trade induces a fall in the current account of Mexico, initially as a result of the increase in the import demand of investment goods. The deterioration of the current account lasts only for a short period of time; households in Mexico then save in order to ensure higher future expenditure while the households in the US borrow with the expectation of higher income in the later periods. The Mexican output falls and the real exchange rate appreciates. Expectedly, in both countries, consumption falls and expenditure moves towards investment goods. However, the fall in the home consumption is more severe. The slow diffusion of the innovation, combined with high lending is compensated by the big fall in consumption. Thus the weighted relative consumption c abs t increases, positively contributing to the trade balance. Appreciation of the real exchange rate leads to a fall in the aggregate home investment good price index and an increase in the aggregate foreign investment good price index. For both countries the behaviour of aggregate investment price index is dominated by the movement in the import prices. That is, for Mexico US price of domestically produced goods increases falls while the home foreign currency price of imports falls increases. This indicates a fall in the difference between the relative price of investment goods rel pxpc t across countries contributing to the trade balance dynamics positively. The real exchange appreciation deteriorates the trade balance since they move in the same direction wrer t. In fact, the only component that indicates a fall in the trade balance is the weighted real 16 The improvement in the terms of trade is a result of the value of the trade elasticity. With an elasticity higher than one tot C,t and tot X,t would actually increase. 2