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MINISTRY OF FINANCE Discussion Papers 2/2013 Bayesian Estimation of Finnish Import Demand* Mikko Sariolay September 2013 Mikko Sariola Ministry of Finance, Snellmaninkatu 1 A, Helsinki, P.O. Box 28, FI-00023 GOVERNMENT. Tel. +358 400 12 77 43, [email protected] y *I am grateful to Mika Kuismanen, Jani Luoto and Meri Obstbaum for constructive and helpful comments. The usual disclaimers apply. This paper represents the views and analysis of the author and should not be thought to represent those of the Ministry of Finance. ISBN 978-952-251-500-1 Keywords: Bayesian Analysis: General, Time Series, Model Construction and Estimation, Empirical Studies of Trade JEL Codes: Bayesian C11, C32, Analysis: C51, F14 General, Time Series, Model Construction Keywords: and Estimation, Empirical Studies of Trade JEL Codes: C11, C32, C51, F14 1 Introduction Finland is a small open economy and its production structure has a relatively strong bias towards manufacturing products with high value added. Due to the small home market these products are mainly exported. The Finnish exports to GDP ratio of 47 per cent1 at the outburst of the global …nancial crisis highlights that feature. The majority of imported goods, over 70 per cent, are either investment or intermediate goods (appendix, …gure 1), probably echoing the needs of the exporting industry. The import ratio of goods and services to GDP has increased over the years and reached its highest level of 43 per cent in 2008. With these facts in mind coupled with high Finnish cost structure, Finnish products should be highly specialized, and perhaps di¤erentiated, in order to be competitive on the global market. Furthermore, given that Finnish export goods are highly specialized, an interesting question is to what extent foreign imports can be substituted to domestic inputs. Moreover, low subsitutability of foreign and domestic inputs would suggest that the price elasticity of import demand is also low. A review of past empirical work on import elasticities at industry level can be found for example in Erkel-Rousse and Mirza (2002). To gain a broader than industry level2 view some studies are disussed here in short. Bergstrand (1985) derives a model and estimates a gravity equation by using 15 OECD countries. Bergstrand …nds that the elasticity of substitution between domestic and import goods is below unity. Hooper et al. (2000) estimate and test the stability of the income and price elasticities of import demand for G-7 countries. They …nd that short run import price elasticity is not signi…cantly di¤erent from zero in all but one country. The income elasticity ranges from unity (DE, IT, JP, UK) to over 2 (US). Senhadji (1998) estimates a structural import demand equation for a large set of countries and argues that the price elasticity is di¤erent in the long run. The average price elasticity is close to zero in the short run and slightly over unity in the long run. Senhadji also notes that price elasticities are lower for industrialized countries. He extends his research to cover income elasticities as well. Compared to the …ndings of Hooper et al, Senhadji’s estimated income elasticities for G-7 countries are somewhat lower, ranging from 0.3 (JP) to 1.3 (DE). Erkel-Rousse and Mirza (2002) build their estimation on monopolistic competition where they apply gravity type of equations. Their …nding is that import price elasticities are low when estimated with OLS or …xed e¤ect methods but the instrumental variable approach tends to increase price elasticity. Furthermore, price elasticity is signi…cantly correlated with the degree of product di¤erentiation. In this paper Finnish imports and their substitutability is studied in a monopolistic competition framework. First, the import demand equation is derived analytically. Second, the analytical log-linearized conditional factor demand 1 Total exports to GDP in 2008. a di¤erent perspective than this paper but yet interesting, Anderton et al. (2005) investigate the substitution e¤ects of manufactured goods between intra- and extra euro area imports. They …nd signi…cant substitution e¤ects due to changes in relative prices. 2 From 1 form suggests that the data used in the estimation is stationary. Therefore, the data is detrended using Hodrick-Prescott …lter before estimation. Then, the import demand equation is estimated by Bayesian methods using …ltered Finnish national accounts and quarterly national accounts data from 1976Q1 to 2008Q4. By choosing this time frame, we have excluded the global …nancial crisis from the data set as being extremely rare event that does not represent economy’s normal ‡uctuations. A novelty in the chosen approach is that the unobservable variable for marginal costs of production is proxied by intermediate input de‡ator for …rms. The intermediate input de‡ator is a more correct measure for …rms’marginal costs than for example the output de‡ator. These two price concepts should be the same only if the …rms are operating in a perfect market but not in the monopolistic market. Therefore, using output prices in estimating a monopolistic market leads to a severe conceptual con‡ict and raises concerns about the reliability of such results. The main results of the Bayesian estimation suggest that i) imports are perfect complements in the production process. Therefore, Finnish production technology has the Leontief form. The zero price elasticity of import demand is in line with Senhadji (1998) and Hooper et al. (2000) results for short term elasticity in industrialized countries. ii) Income elasticity is clearly above unity (1.7) in Finland. Income elasticity of this magnitude is higher than in the most G-7 countries according to Senhadji (1998) and Hooper et al. (2000). Hence, the assumption of income elasticity equal to one does not hold for Finland and is not an advisable choice for example when calibrating macro models representing Finnish economy. Overall, the results suggest that import demand is driven by income elasticity and not much by relative prices within this time period. The paper is organized as follows. In chapter 2, the analytical import demand equation is derived and log linearized. In the third chapter the data is introduced, the equation is estimated and the results are discussed. The last chapter concludes. 2 2 Analytical model In the model …nal composite good Yt is produced in the competitive market by combining intermediate goods Yt (i) 21 Z Yt = 4 Yt (i) y 0 3 1 y di5 (1) It is assumed that intermediate goods are produced in the domestic market using constant elasticity of substitution (CES) production function. While assuming perfect …nal goods market, value added is in fact created in the intermediate goods market where two inputs, one domestic and one imported, are combined to produce the good i. Firms operating in the intermediate goods market are assumed to be monopolistically competetive. The constant elasticity of substitution (CES) production function for good i in the intermediate goods market is following Yt (i) = (1 ,where Y (i) MH MF = 1 +1 )(MtH ) + (MtF ) 1= (2) production of good i factor share of the foreign input used in production domestic input foreign input elasticity of substitution subsitution parameter, which determines the elasticity of substi- tution. Furthermore, elasticity of substitution between the inputs in CES leads to 1< <0 ) elasticity > 1 =0 0< ) elasticity = 1 <1 ) elasticity < 1: In order to get the conditional factor demand of the imported input, constrained cost minimization problem subject to technology constraint is applied minPtH MtH + PtF MtF MtF s.t. Yt (i) = (1 )(MtH ) 3 + (MtF ) 1= Lagrangean is following n L = PtH MtH + PtF MtF (1 )(MtH ) + (MtF ) 1= o Yt (i) (3) , where P H is the price of the domestic input and P F is price of the foreign input. First order condition, and the conditional factor demand, is then MtF = 1 +1 PtF 1 +1 Yt (i): (4) t The …rst order condition, equation 4, can be rewritten using elasticity notation MtF = PtF Yt (i): (5) t Due to the monopolistic competition assumption, represents the marginal cost of production. Finally, log linearization of the equation 5 around the steady state yields equation 6. It is assumed that one representative …rm produces one good. This will be the equation that is estimated. b m bF t = ( t pbF bt t )+y (6) The constant elasticity of scale production function implies that if the elasticity, , is close to unity, then the production function reduces to Cobb-Douglas form. If the elasticity is zero, then the factors of production are perfect complements and the production has Leontief form. More generally, if substitution pareameter, , is negative, then factors are substitutes. Positive value of substitution parameter implies that factors are complements. By estimating the import demand equation and elasticity parameter, it is simple to backtrack the substitution parameter. 4 3 3.1 Empirical estimation of the model Data In the model estimation, data from the national accounts (NA) and quarterly national accounts (QNA) is used. All the data is acquired from Statistics Finland and quarterly data is seasonally adjusted. It is easy to select observable variables for Yt , PtF and MtF but for t the choice is more open for judgement. Yt , PtF and MtF are real value added of total economy, de‡ator of imported goods and services and real import of goods and services respectively. The marginal cost of production, t , is unobservable variable but is proxied by the intermediate input de‡ator for …rms. Recently, Statistics Finland has adopted double de‡ation standard in calculation of value added. This means that there are separate de‡ators for output and intermediate inputs. Hence, the de‡ator for intermediate inputs should serve as a proxy for marginal cost of production. These two price concepts should be the same only if the …rms are operating in perfect market where price equals marginal cost of production. But this is not the case in monopolistic market. Therefore, using output prices in estimating monopolistic market leads to a severe conceptual con‡ict and raises concerns about the reliability of such results. The downside of this variable is its availability. Data (NA) is only available in annual terms, therefore annual observations are disaggregated into quarterly series. Hence the quarterly series of marginal cost of production is more rigid than perhaps in reality it would be. The four series are represented in appendix (…gure 2) In order to have stationary series as the log linearization around steady state in equation 6 requires, the data is …ltered with Hodrick-Prescott …lter. In …ltering the data, conventional smoothing parameter of 1600 is applied. The properties of the stationary variables for the period 1976Q1-2008Q4 are presented in table 1. As expected, the import price de‡ator is more persistent than the import volume (…gure 1). Perhaps for that reason the import volume appears to be twice as volatile than the import de‡ator (appendix, …gure 3). Total value added is very persistent and has small variance compared to imports. It is noteworthy, that it seems the import volume has become less volatile after Finland entered the EU. The proxy for marginal costs is very persistent partly due to the data interpolation. Table 1. Properties of the variables Maximum Minimum Autocorrelation Std. Dev. Skewness Kurtosis Observations m bF 0.160 -0.202 0.511 0.055 -0.094 4.488 132 pbF 0.073 -0.056 0.769 0.028 0.267 2.557 132 yb 0.058 -0.048 0.821 0.020 0.495 4.206 132 5 b 0.036 -0.047 0.939 0.019 -0.506 2.491 132 import volume total value added .2 .2 .1 .1 .0 .0 -.1 -.1 -.2 -.2 1980 1985 1990 1995 2000 2005 1980 import deflator 1985 1990 2000 2005 'MC', intermediate input deflator for firms .2 .2 .1 .1 .0 .0 -.1 -.1 -.2 -.2 1980 1985 1990 1995 2000 2005 1980 1985 1990 b Figure 1. Deviations from the steady state for m b F ; ybt ; pbF t and t 3.2 1995 Bayesian estimation In this section we carry on with Bayesian estimation. By this, we seek to incorporate prior knowledge to estimation and to increase understanding of the parameter distribution. Also we have a reason to believe there might be heteroscedasticity present and want to take care of the t-distributed errors appropriately by Bayesian approach3 .4 The selected approach will not only a¤ect 3 Another Bayesian tradition approach involving CES production structure is Luoma and Luoto (2011), who apply Bayesian methods in system estimation of CES production function and pro…t maximizing …rst order conditions. 4 For the interest of a classical econometrician, table 1 in the appendix presents the theorical model results when residuals are assumed normal. The coe¢ cient for is very close to zero 6 1995 2000 2005 the shape of the posterior distribution but may also change the posterior mode when compared to a linear model with normal errors. As usual, in the following notation, letters with underscores are priors and letters with bars are posteriors. Parameter vector is presented in equation 7. is as in equation 6 and denotes the coe¢ cient of the value added yb. As a starting point, prior propability density function p( ) is assumed to be multinormal and prior density function p(h) is assumed gamma5 . = (7) Furthermore, we expect that prior vector is independent of prior h. This implies we know neither joint posterior distribution for and h nor do we know their marginal posteriors. Therefore, Monte Carlo integration method is not available. In addition, we want to make sure that heteroscedastivity is taken into consideration and use the independent Student-t linear model. However, with these independent Normal-Gamma priors and Student-t regression model we resort to Metropolis-Within-Gibbs sampler in order to carry out Monte Carlo Markov Chain posterior simulation. We use relatively informative priors. ; the prior for the relative price variable is assigned to zero with high standard deviation. This prior expected value and standard deviation was chosen while our theoretical model does not give any advice whether negative or positive priors should be used. However, the zero price elasticity prior is in line with Senhadji’s (1998) results for short term elasticity in industrialized countries. On the contrary in case of , the prior for the value added6 is set at 1 as suggested by our theoretical model. However, we do not constrain to unity but apply somewhat smaller prior standard deviation compared to : So, it is set 0 1 = 0:52 0 var( ) = V = (8) 0 0:32 (9) and t-test reveals it is not statistically di¤erent from zero. Hence implying the foreign imports are perfect complements to domestic inputs. However, White test reveals heteroscedasticity with 1 % risk level. Residuals seem to be heteroscedastic even if assumptions concerning the theoretical model are relaxed and parameter restriction to unity for the coe¢ cient of the value added is lifted (appendix …gure 4 and 5). The pre 1995 era appears far more volatile than the time period after EU accession. Residuals of the OLS estimation where coe¢ cient restriction for value added is relaxed and not restricted to unity were tested also. Normality assumption was rejected with p-value 0.01. This may raise some concerns of the robustness of the results if the classical OLS estimation principle is violated. Residuals of the unrestricted model are not autocorrelated with 1 % risk level in Breusch-Godfrey LM test with lags 2 to 4. 5 More on density functions in question, see for example Koop (2003, p. 60). 6 This can be viewed as a scaling variable. 7 Other prior hyperparameters are prior degrees of freedom (13) and prior expected value for h (0.012 ). In total we have 132 observations in the data set meaning we are attaching around 10 % weight to our prior. Initial draw in the Gibbs procedure for the error precision is set at the inverse of 0.012 :7 The Metropolis-Within-Gibbs algorithm proceeds in a following manner. First in the Metropolis algorithm section we use random walk chain to get degrees of freedom parameter, , for the vector e h that is used as a weight to transform the data. e h is drawn from the 2 -distibution. These are the hierarcical priors of the model. In the random walk chain a new draw is taken from a normal distribution and added to the old accepted value . Then, the old value and and the new candidate value are evaluated at the conditional posterior density kernel of : If the acceptance probability is positive and is higher than a random number drawn from a uniform distribution [0,1], then the candidate value is accepted to the chain. After the Metropolis algorithm the observables are reweighted by the e h and the standard Gibbs sampling is carried out. This Metropolis-WithinGibbs loop is run S times. Value 0.01 is chosen for prior . The interested reader on methodology is referred to Geweke (2005, p. 205-208) and Lancaster (2004, p.185-164). In posterior simulation we take 500 000 draws and throw away …rst 30 000 draws as burn in period. According to Geweke’s CD statistics both chains have converged while test values are well below 1.96.8 By using central limit theorem, we can say that test statistic CD follows normal distribution N(0,1) and test value below 1.96 implies that there is 95 % propability remaining series is converged to its stationary distribution. Relevant prior and posterior properties are summarized in table 3. The posterior distribution of the degrees of freedom parameter ( ) for the vector e h that is used as a weight to transform the data is reported in appendix (…gure 6). The acceptance rate in the Metropolis algorithm is 0.49. 7 This value is roughly at the same magnitude as the OLS model variance reported in the appendix table 1. 8 Also chain for has converged as CD statistics is below 1.96. 8 Table 3. Bayesian estimation of (unrestricted) theoretical model m b F = (bt pbF ) + ybt t t Sample: 1976Q1 2008Q4 Included observations: 132 Prior and posterior results (standard deviations in parentheses) Prior 0 (0.5) 1 (0.3) Posterior -0.22 (0.1) 1.76 (0.13) Geweke’s CD -0.03 -1.26 Simulated posterior mean for is very close to zero and is not two standard deviations away from zero. Increasing the number of draws does not change the results. The prior and posterior distributions can be seen in …gure 3 (top). As zero is within two standard deviations from the posterior, this has straightforward economic implication suggesting foreign imports are perfect complements to domestic inputs (Leontief production). The implied zero price elasticity is in line with Senhadji (1998) and Hooper et al. (2000) results for short term elasticity in industrialized countries. To check whether the result is robust to the choice of marginal cost variable, two other proxy marginal cost variables are tested. When using other proxies for marginal costs, intermediate input de‡ator for manufacturing and intermediate input de‡ator for total economy, simulated posterior mean remains within two standard deviations from zero9 . Hence, result seems to be robust to the choice of marginal cost proxy. Finally, simulated posterior mean for the scale variable is 1.7. The prior and posterior distributions are reported in …gure 3 (bottom). is clearly above unity and in this case all the propability mass is located above one. Based on this we do not recommend restricting the model’s scale variable to unity. Higher than one income short term elasticity is in line with results by Hooper et al. (2000) for G-7 countries. Senhadji’s (1998) …ndings for G-7 are somewhat lower ranging from 0.3 (JP) to 1.3 (DE). The results suggest that import demand is driven by income elasticity and not much by relative prices within this time period. 9 Especially, when using intermediate input de‡ator for manufacturing, 17 % of the probability mass lays above 0. When Intermediate input de‡ator for total economy is used as proxy for marginal costs, results are in line with the baseline simulation. 9 Figure 3. Prior and posterior distributions. 10 4 Conclusions In this paper the import demand equation is …rst derived analytically by assuming constant elasticy of scale production function and then the import demand equation is estimated by Bayesian methods. Prior knowledge suggested by the theoretical model and empirical studies is introduced in the Bayesian estimation. The simulated posterior distribution suggests that imports are used as complements in the production process within this time period. Interestingly, the posterior distribution implies that they are perfect complements and hence the production technology would be of the famous Leontief form. The implied zero price elasticity is in line with Senhadji (1998) and Hooper et al. (2000) results for short term elasticity in industrialized countries. To assess the robustness of the …ndings, we tested that results hold when changing the unobservable marginal cost variable to other candidate proxy variables. What might then explain the perfect complementarity result? Intuitively, it is easier to substitute butter than brent. A small country producing highly specialized export products has limited options to substitute specialized import inputs needed in the production process to domestic ones. In the case of Finland, over 70 % of imported goods are investment, energy and raw materials (Customs Finland, 2009). In addition to price elasticity, the income elasticity of import demand was estimated. The simulated posterior mean for income elasticity is clearly above unity (1.7) and higher than in the most G-7 countries according to Senhadji (1998) and Hooper et al. (2000). Moreover, the whole posterior distribution lies above one. Hence, the assumption of income elasticity equal to one does not hold for Finland and is not an advisable choice for example when calibrating macro models representing Finnish economy. The results suggest that import demand is driven mainly by income elasticity and less by relative prices within this time period. This line of work could be continued in several ways. The method could be extended to cover export elasticities to gain a broader view on Finnish external trade in macro perspective. Another way forward could be estimating an equation at a more disaggregated level in order to capture substitution possibilities in the production technologies of for example consumption, investment or intermediate goods. The subsitutability or complementarity might namely depend on the type of produced good. Another interesting direction could be to break the data set into two and exploit the pre-EU era dataset in setting up the priors. Then Bayesian estimation could be carried out with EU era dataset to capture the potential change of market and competition setting. 11 References [1] Anderton, R., Baltagi, B., Skudelny, F. and Sousa, N. (2005). "Intra and Extra Euro Area Import Demand for Manufacturers". ECB Working Paper Series 532. [2] Bergstrand, J. (1985). "The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence". The Review of Economics and Statistics 67 (3), p. 474-481. [3] Customs Finland (2009). "Foreign Trade in Finland 2009: Finnish Trade in Figures". http://www.tulli.…/en/releases/ulkomaankauppatilastot/tiedotteet/ kuluvavuosi/pocketstatistics2009/index.html [4] Erkel-Rousse, H. and Mirza, D. (2002). "Import Price Elasticities: Reconsidering the Evidence". Canadian Journal of Economics 35 (2), p. 282-306. [5] Geweke, J. (2005). "Contemporary Bayesian econometrics and statistics". Wiley series in probability and statistics. [6] Hooper, P., Johnson, K. and Marquez, J. (2000). Trade Elasticitities for the G-7 Countries. Princeton Studies in International Economics. [7] Koop, G. (2003). "Bayesian Econometrics". John Wiley, ltd. [8] Lancaster, T. (2004). "An Introduction to Modern Bayesian Econometrics". Blackwell Publishing Ltd. [9] Luoto and Luoma (2011). "A Critique of the System Estimation Approach of Normalized CES Production Functions". HECER Discussion Paper No. 336. [10] Senhadji, A. (1998). "Time Series Estimation of Structural Import Demand Equations: A Cross-Country Analysis". IMF Sta¤ Papers 45 (2). 12 A Appendix Figure 1.Imports by use of goods in 2009. Source: Foreign trade in 2009 (Customs Finland, 2009) 13 import volume total value added 20,000 40,000 35,000 16,000 30,000 12,000 25,000 8,000 20,000 4,000 15,000 0 10,000 1980 1985 1990 1995 2000 2005 1980 import deflator 1985 1990 1995 2000 2005 'MC', intermediate input deflator for firms 120 120 100 100 80 80 60 60 40 40 20 20 1980 1985 1990 1995 2000 2005 Figure 2. Un…ltered series of Yt , PtF ; MtF and 14 1980 t 1985 1990 1995 2000 2005 total value added 20 25 16 20 Frequency Frequency import volume 12 8 4 15 10 5 0 0 -.2 -.1 i .0 .1 .2 -.2 import deflator -.1 .0 .1 .2 'MC', intermediate input deflator for firms 16 12 10 12 Frequency Frequency 8 8 6 4 4 2 0 0 -.2 -.1 .0 .1 b Figure 3. Distributions of m b F ; ybt ; pbF t and t 15 .2 -.2 -.1 .0 .1 .2 .2 .1 .0 .15 -.1 .10 -.2 .05 . -.3 .00 -.05 -.10 -.15 76 78 80 82 84 86 88 90 Residual 92 94 Actual 96 98 Fitted Figure 4. Unrestricted linear model with normal residuals assumed. 16 00 02 04 06 08 Figure 5. Squared residuals of unrestricted linear model with normal residuals assumed. 17 Figure 6. Posterior distribution. 18 Table 1. OLS estimation of theoretical model m b F = (bt pbF ) + ybt t t Sample: 1976Q1 2008Q4 Included observations: 132 Normal residuals assumed R-squared S.E. of regression Durbin-Watson stat Coe¢ cient -0.117 Std. Error 0.143 t-Statistic -0.817 0.413 0.042 1.394 S.D. dependent var Akaike info criterion Log likelihood 0.055 -3.492 231.454 19 Prob 0.415 Ministry of Finance Discussion Papers 1/2009 Mika Kuismanen – Ville Kämppi The effects of fiscal policy on economic activity in Finland 2/2009 Mikko Sariola Monetary policy and exchange rate shocks: effects on foreign trade in Finland 3/2009 Juha Itkonen Päästökauppajärjestelmien linkittämisen ilmastopoliittiset vaikutukset 1/2010 Samuli Pietiläinen The Bayesian Estimation of Private Investment in Finland 1/2011 Meri Obstbaum The Finnish unemployment volatility puzzle 1/2012 Ilari Ahola Kuntien finanssipoliittiset säännöt ja niiden toimivuus 1/2013 Marja Tuovinen Terveysmenojen kasvu