Consumer Price Index Dynamics in a Small Open Economy: A Structural Time Series Model for Luxembourg

Transcription

1 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 Consumer Price Index Dynamics in a Small Oen Economy: A Structural Time Series Model for Luxembourg Bédia F. Aka * and P. Pieretti ** University of Luxembourg and Centre de Recherche en Economie Aliuée (CREA Abstract This aer examines relations between the consumer rice index (CPI and its theoretical exlanatory variables using a Structural Time Series (STS model in order to take into account unobserved comonents (trend, cycle, seasonal and irregular of the CPI. Theoretically, the consumer rice index is negatively related to labour roductivity but ositively to nominal wages and foreign rices. Emirical results for a small oen economy as Luxembourg indicate that the CPI is ositively related to foreign rices and negatively to labour roductivity as redicted by the theory, but surrisingly wages are not significant in exlaining the CPI of the Luxembourg economy. However the unit labour cost significantly exlains the CPI. Keywords: Consumer rice index, unobserved comonents models, structural time series JEL Classification: C22, E3. Introduction Although the understanding of the rocess of rice formation is crucial in macroeconomics, there is no consensus on which variables do articiate in the rice behaviour. While some authors consider that rices are determined by marginal cost, others state that rices deend on world rices through the urchasing ower arity mechanism. At the same time, some assume that both variables are imortant in the exlanation of rice formation (see Martin, 997. Investigating the rocess of rice formation, this aer is based on a model of rice setting, which derives from the new oen macroeconomics initiated by the seminal aer of Obstfeld and Rogoff (995. Subseuently, various works basing on microeconomic foundations and imerfect cometition have been devoted to the dynamics of rice formation. In this context, see Lane (999, Sarno (200, Bowman and Doyle (2003 for a survey. Earlier emirical studies have used autoregressive distributed lag (ARDL and vector autoregressions (VAR or vector error correction (VEC models to analyse the short and long run dynamics of rices (Martin, 997; De Brouwer and Ericsson, 998; Marcellino and Mizon, 200. In this aer we aim at comlementing these methods that give little information on structural comonents of the studied variables by adding more information about the trend and the cyclical and seasonal comonents of the series.

2 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 2 Our main emirical findings in the case of a very small oen economy like Luxembourg are that the consumer rice index (CPI is negatively related to labour roductivity and ositively to foreign rices, but wages are not significant at exlaining the CPI behaviour. While a 00% increase in foreign rices results in a 39% increase in the CPI, a 00% increase in labour roductivity results in a 7.7% decrease in the CPI. Although wages are not significant in exlaining the evolution of the CPI in Luxembourg, combining wage and labour roductivity in a unit labour cost (ULC index involves that the CPI is significantly exlained by ULC and foreign rices. A 00% increase in ULC results in a 5.4% increase in the CPI, while a 00% increase in foreign rices results in a 38% increase in the CPI. It clearly aears that the unit labour cost is more significant than nominal wages in the exlanation of the CPI behaviour, while foreign rices are the main variable imacting the CPI in Luxembourg. The rest of the aer is organized as follows. Section 2 briefly resents the model of rice formation extended with structural time series comonents. Section 3 resents the estimation results for Luxembourg and section 4 concludes. 2. The model 2. A Model of Price formation In the new oen macroeconomic framework rice formation is based on microeconomic foundations with monoolistic cometition (Obstfeld and Rogoff, 995 and 998; Lane, 999; Sarno, 200; Bowman and Doyle, 2003; Devereux and Engel, 998; Tille, 200. In this context, continuums of consumers maximize their utility and on the other hand reresentative firms maximize their rofit. The consumer rice index (CPI is defined as the minimal exenditure reuired for buying a unit of consumtion and derives from the cost minimization of the consumer rogram. The CPI is given by: ( P P Q r 0< <, ( where reresents the share of imorted goods in the consumer basket of goods, Pr is the roducer rice and Q reresents foreign rices (or imorts rice. On the roduction side, a reresentative firm in an imerfectly cometitive market roduces a single good for which imerfect substitutes are roduced abroad. The lanned rice of the good is determined as a mark-u over marginal costs. Using small letters for logarithmic variables, we can write the rice euation in an additive form: r μ mc, (2 where μ is the mark-u and mc the marginal cost. The mark-u can be non-constant and exressed as a function of the foreign rices and the roducer rice r :

3 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 3 μ κ ( r ξ, (3 where κ, and ξ are given arameters. In contrast to Gali and Gertler (2000, Pétursson (2002 and Martin (997 who secified a CES (Constant Elasticity of Substitution tye function, we choose a Cobb-Douglas roduction function with constant returns to scale: Y k N n AK,, > 0 and (4 k n k n Where Y reresents the outut, A the total factor roductivity (TFP, N is the total number of working hours, and K K is the caital considered as fixed in the short run. The marginal cost (MC is given by the ratio between the real wage ( W/P and the marginal roductivity of labour ( Y / N : MC W P Y N W P.. (5 Y / N Y The marginal roductivity of labour is given by AK k n n N. We thus get : N MC W P. Y / N W P. AK N kn n (6 MC W N W N.. (7 P A K k N n P Y n n Taking the log of E. (7, we get: cm w n log n y (8 After introducing the logarithm of labour roductivity (z y-n and relacing following euation : n by, we get cm w z log (9

4 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 4 Solving receding euations (by relacing the marku and the marginal cost in the rice euation gives the roducer rice as a margin over the unit labour cost (w-z and foreign rices (: ξ κ log ( z w r r (0 After few maniulations, we get the roducer rice: z w r ξ κ ( log ( Considering the consumer rice index P given in E. (, we get in logarithmic form: r (, (2 where reresents the share of imorted goods in the consumer basket of goods. From E. (2 the roducer rice becomes: r, (3 which can be euated to E. ( : z w ξ κ ( log (4 We then get: z w ξ κ ( log (5 In the long run, the CPI becomes: ξ κ log ( ( ( z w (6 The exchange rate e and foreign rices (as t t t Q e P imact the domestic rice through due to imorted goods, and the marku arameter μ through the modification in the rice of imorted goods in the domestic consumtion. Thus theoretical results indicate that the consumer rice index (P is related to nominal wages (W, labour roductivity (Z and foreign rices (Q. More recisely, the consumer rice index is

5 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 5 negatively related to labour roductivity but ositively to nominal wages and foreign rices. The consumer rice euation (that exlicitly take account of a time index t, can be formulated as follows: t wt δt ϕzt (7 Or using the unit labour cost (ULC: t ( w z t δt (7 Remember that indicates the log of the consumer rice index, w the log of nominal wages and the log of foreign rices, (w-z the unit labour cost,, δ and ϕ are real coefficients. The unit labour cost is exected to ositively imact the consumer rice index. 2.2 An Extended Structural Time Series Model of the Consumer Price Index The stochastic formulation of a structural time series (STS model for the logarithm of consumer rice index denoted with exlanatory variables is the following: t t μt βt μ μ β t ψ t εt t βt t ζ t t (8 where μt is the trend, ψ t is the cyclical comonent, and ε t the irregular comonent, all assumed to be stochastic. The arameter β t is the sloe of the trend comonent. The stochastic roerties of the level and the sloe are driven by t and ζ t. The seasonal (cyclical comonent in trigonometric form, see Harvey (989, may be exressed as follows: s 2 ψ ψ t, L T, (9 t jt, i with ψ jt determined by ψ jt cos j * ρ ψ jt sin j sin j ψ jt * cos j ψ jt ω jt * ω jt (for j,2, L, s / 2, t, L, T, (20 where 2πj s is the freuency in radians and ρ is the daming factor ( 0 < ρ. j /

6 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 6 Combining E. (7 or (7 with E. (8, we get the following two extended stochastic secifications: t t μ ψ δ ϕ ε t t w z t t (2 μ t ψ t ( w z δ t εt, (2 where, δ, ϕ, and are real coefficients. Es. (2 and (2 can be alternatively estimated to see which of these comonents exlains much the CPI behaviour. The results of the estimated model for Luxembourg are resented in the next section. 3. Emirical Results Models (2 and (2 are estimated using STAMP 6.02; see Kooman, Harvey, Doornik and Shehard (2000. The uarterly data used are rovided by the STATEC (Statistical Institute of Luxembourg and cover the eriod 995:-2005:4. Figure shows the time series in level (left anel and first difference (right anel. We can notice that the data show a non-constant uward trend over time. We test various models which combine the level and sloe characteristics for seasonal dummies and for trigonometric dummies. The results (see Table indicate that models -3 overcomes others regardless seasonal characteristics, but the log-likelihood of models including seasonal dummies are higher than those including trigonometric seasonal comonent. We therefore choose seasonal dummy model -3 in the next ste of the aer. The estimated variances of disturbance from model -3 indicate that the variance of the disturbance term connected with the stochastic sloe comonent is not significant (Table 2; we therefore move to model -5 with a fixed sloe. Next we notice that among the exlanatory variables the coefficient of the wage rate is not significant (Model -5, Table 4. Thus we removed the wage variable from the model -5 and estimated it again. The final result (model -6 with higher log-likelihood (86.477, see Table indicates that all remaining exlanatory variables are significant in terms of t-value (see Table 4, Model -6. When we examine the grah of residuals of model -6 (Figure 2, it aears that there is an outlier in 2002:. We reformulate the model to include an imulse dummy at this date in order to imrove its fit. This last model -7 reaches the highest log-likelihood ( and all variables are significant. This model is the most arsimonious estimate of the CPI function in Luxembourg. The results of the final state vector from the estimation of Model -7 (see Table 3 indicate that the comonents are significant. The trend level is estimated at with a sloe at The sloe estimate indicates that the consumer rice index increases at a rate of 2.44% er year.

7 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 7 Estimates of exlanatory variables in the final state vector show that the one-lag consumer rice index, labour roductivity and foreign rices are significant in the exlanation of the consumer rice behaviour (Table 4. The consumer rice index decreases with the labour roductivity while it increases with foreign rices. An increase of 00% in labour roductivity results in 7.7% decrease in the consumer rice index, while a 00% increase in foreign rices results in 39% increase in the consumer rice index. When we further examine the results of model -7, it aears that the estimated variances of disturbances of the irregular comonent are zero (Table 2. We reformulate the model using unit labor cost (ULC as exlanatory variable (E. 2. The estimated results of model 0 indicate a better fit to the data, all comonents and exlanatory variables being significant (Table 4. The results of the final state vector from the estimation of model 0 (see Table 3 indicate that all comonents are significant. The trend level is estimated at 2.00 with a sloe at indicating that the consumer rice index increases at a rate of 2.28% er year. The estimates of exlanatory variables in the final state vector show that the lag consumer rice index, the unit labour cost and foreign rices are significant in the exlanation of the consumer rice index behaviour (Table 4. The consumer rice index increases with the ULC and foreign rices. As exected, if the ULC increases by 00% it results in 5.4% increase in the consumer rice index, while a 00% increase in foreign rices results in 38% increase in the consumer rice index. 4. Conclusions This aer analyses the Luxembourg consumer rice index along with its unobserved comonents using a structural time series (STS model. The results indicate the stochastic nature of the trend of the CPI with a deterministic or fixed sloe. We find that the CPI is negatively related to labour roductivity and ositively to foreign rices but nominal wages are not significant in the exlanation of the CPI rice behaviour in Luxembourg. A 00% increase in foreign rices results in a 39% increase in the CPI, but a 00% increase in labour roductivity results in only a 7.7% decrease in the CPI. More surrisingly, nominal wages are not significant in the exlanation of the evolution of the CPI in Luxembourg. Further investigation indicates that the consumer rice index (CPI is significantly exlained by the unit labour cost (ULC and foreign rices. A 00% increase in ULC results in a 5.4% increase in the CPI while a 00% increase in foreign rices results in a 38% increase in the CPI. It aears that the unit labour cost is more significant than nominal wages in the exlanation of the rice behaviour in Luxembourg. Overall foreign rices are the main determinants of the evolution of the CPI in Luxembourg.

8 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 8 Endnotes * Corresonding author: Bédia F. Aka, Researcher, University of Luxembourg, Faculty of Law, Economics and Finance, and CREA, 62A, avenue de la Faïencerie, L-5 Luxembourg, Tel.: ( , francois.aka@uni.lu ** Patrice Pieretti, Professor of Economics, University of Luxembourg, Faculty of Law, Economics and Finance and Director of CREA (Cellule de Recherche en Economie Aliuée. We are grateful to S. Allegrezza (Director of Statec, Luxembourg and F. Adam (Statec for roviding the uarterly data (Project MODEL. Secial thanks to F. Adam for collaboration during the roject MODEL.. Setting the share of wage income or unit labor cost as Gali and Gertler (2000. W N t t S t gives Pt Yt MC S t, as in n References Bowman, D. and B. Doyle New Keynesian Oen-Economy Models and Their Imlications for Monetary Policy, International Finance Discussion Paers, FRS. De Brouwer, G. and N. R. Ericsson Modeling Inflation in Australia, Journal of Business and Economic Statistics, 6, Devereux, M. and C. Engel The Choice of Exchange-Rate Regime: Price Setting Rules and Internationalized Production, mimeo, University of British Colombia/Hong Kong University of Science and Technology and University of Washington. Gali, J. and M. Gertler Inflation Dynamics: A Structural Econometric Analysis, NBER WP 755. Harvey, A. C Forecasting Structural Time Series and the Kalman Filter. Cambridge University Press. Kooman, S., A. C. Harvey, J. A. Doornik and N. Shehard Stam: Structural Time Series Analyser, Modeller and Predictor, London: Timberlake Consultants Press. Lane, P. R The New Oen Macroeconomy: A Survey, Trinity Economic Paer Series, Paer No. 3. Marcellino, M. and G. E. Mizon Small-System Modelling of Real Wages, Inflation, Unemloyment and Outut Per Caita in Italy , Journal of Alied Econometrics, 6,

9 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 9 Martin, C Price Formation in An Oen Economy: Theory and Evidence for the United Kingdom, 95-99, The Economic Journal, 07, Obstfeld, M. and K. Rogoff Exchange Rate Dynamics Redux, Journal of olitical Economy, 03, Obstfeld, M. and K. Rogoff Risk and Exchange Rate, mimeo, University of California at Berkeley and Princeton University. Pétursson, T. G Wage and Price Formation in a Small Oen Economy: Evidence from Iceland, Central Bank of Iceland Working aers No. 6. Sarno, L Toward a New Paradigm in Oen Economy Modeling: Where Do We Stand? Federal Reserve Bank of St, Louis Review, 83, Tille, C The Role of Consumtion Substitutability in the International Transmission of Monetary Shocks, Journal of International Economics, 53,

10 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 0 Models Table : Summary Statistics (Model selection Comonents Level Sloe Variables Irregular With Dummy Seasonal Log- Likelihood -: No No Exl. Irregular : Fixed Fixed Exl. Irregular : Stoch. Stoch. Exl. Irregular : Stoch. No Exl. Irregular : Stoch. Fixed Exl. Irregular : Stoch. Fixed Exl. Irregular : Stoch. Fixed Exl. Irregular : Fixed No Exl. Irregular : Fixed Stoch. Exl. Irregular Using Unit Labour Cost (ULC -0: Stoch. Fixed Exl. Irregular With Trigonometric Seasonal 2-: No No Exl.. Irregular : Fixed Fixed Exl. Irregular : Stoch. Stoch. Exl. Irregular : Stoch. No Exl. Irregular : Stoch. Fixed Exl. Irregular : Fix No Exl. Irregular : Fixed Stoch. Exl. Irregular Table 2: Estimated variances of disturbances (Samle: (T 43 Comonents LP_CFIN (-ratio Model -3 Irregular e-006 ( Level.734e-005 (.0000 Sloe ( Seasonal.055e-007 ( Model -5 Irregular 4.057e-006 ( Level.734e-005 (.0000 Seasonal.055e-007 ( Model -7 Irregular ( Level (.0000 Seasonal (0.092 Model -0 Irregular 7.772e-007 ( Level.2957e-005 (.0000 Seasonal e-008 (0.0037

11 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 Table 3: Estimated coefficients of final state vector (Samle: (T 43 Variables Coefficient R.m.s.e. t-value Model 3 Level Sloe Sea_ Sea_ Sea_ Model -5 Level Sloe Sea_ Sea_ Sea_ Model -7 with intervention dummy 2002: Level Sloe Sea_ Sea_ Sea_ Model -0 with intervention dummy 2002: Level Sloe Sea_ Sea_ Sea_ Table 4: Estimated coefficients of exlanatory variables (Samle: (T 43 Variables Coefficient R.m.s.e. t-value Model -3 LP_CFIN_ LSALM LPRODE LP_XBSEU Model -5 LP_CFIN_ LSALM LPRODE LP_XBSEU Model -6 LP_CFIN_ LPRODE LP_XBSEU Model -7 with intervention dummy LP_CFIN_ LPRODE LP_XBSEU Irr_ ULC LP_XBSEU2 LP_CFIN_ Irr_2002. Model -0 with intervention dummy Note: LP_CFIN_ (log of CPI ; LSALM (log of wage; LPRODE (log of roductivity; LP_XBSEU2 (log of foreign rices; ULC (Unit labor cost

12 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 2 Figure : Level and first difference of variables 0.25 LP_CFIN DLP_CFIN LSALM 0.20 DLSALM LP_XBSEU DLP_XBSEU LPRODE DLPRODE ULC 0.03 DLULC

13 Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, -3 3 Figure 2: Residual of Model -6 2 Residual LP_CFIN Figure 3: Estimated Comonent of the CPI 0.0 LP_CFIN TrendX_LP_CFIN Trend_LP_CFIN Seas_LP _CFIN Irr_LP_CFIN Figure 4: Post-Samle Prediction of CPI (Model F-LP _CFIN Forecast F-LP _CFIN F-TrendX_LP_CFIN F-Seas_LP _CFIN