POLICY RESEARCH WORKING PAPER 2825 Demand for Imports in Venezuela A Structural Time Series Approach Mario A. Cuevas TIhe World Bank Latin America and the Caribbean Region Colombia, Mexico, and Venezuela Country Management Unit April 2002 I POLICY RESEARCH WORKING PAPER 2825 Abstract Using structural time series models, Cuevas estimates a 0.4 percent increase in imports. And in the long-run, 1 common stochastic trends of real GDP and imports in percent real GDP growth is associated with 1.7 percent Venezuela from 1974-2000. The real imports trend real imports growth. The author also shows that the drifts upward at almost twice the rate of growth of GDP. GDP elasticity of imports tniformly falls with cycle This highlights the powerful structural tendency toward period, with the elasticity reaching 4.55 at the frequency increasing imports in Venezuela. The author also associated with the 5-year cycle. A powerful imports explicitly estimates common stochastic cycles, which he responsiveness at the higher cycle frequency is associated finds to have 5 and 17 year periods. In addition, he finds with the recurrence of external imbalances in Venezuela. that a 1 percent real exchange rate appreciation leads to This paper-a product of the Colombia, Mexico, and Venezuela Country Management Unit, Latin America and the Caribbean Region-is part of a larger effort in the region to encourage research on macroeconomic issues. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Michael Geller, room 14-046, telephone 202-458-5155, fax 202-676-0720, email address mgeller@worldbank.org. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at mcuevas@worldbank.org. April 2002. (15 pages) The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Produced by the Research Advisory Staff DEMAND FOR IMPORTS IN VENEZUELA: A STRUCTURAL TIME SERIES APPROACH Mario A. Cuevas The World Bank Latin America and the Caribbean Vice-Presidency Colombia, Mexico, and Venezuela Country Management Unit Washington, D.C. E-MAIL: MCUEVAS@WORLDBANK.ORG INTRODUCTION AND APPROACH' Stochastic Trend-Cycle Models of GDP and Real Imports In this framework, we will represent the log of real GDP, y, as yt=,g ,Y±+ Y+t+ , (1) where uty represents the stochastic trend (unit root) component of log real GDP, Vt< and df represent independent stochastic (trigonometric) cycles, and 6, is an innovation. Similarly, we represent the log of real imports, m,, as m, = ,, + X, + Xtm + r, + 7, (2) where pu' represents the stochastic trend (unit root) component of the log of imports, N ""- ' 000C It 10 00 CD 'I 1000 1 Nq It 100 C 000' 00 0 0 0c 0t 000a ' X X: 0 10 Y0 0 XW o N a a, a, I -Cycle] Log Real Imports -Cycle] Log Real GDP -Cycle 2 Log Real Imports Cycle 2 Log Real GDP The common higher frequency cycles have amplitude of 0.03 and 0.11 in the GDP and imports models, respectively. The common lower frequency cycles have amplitudes of 0.03 and 0.08 in the GDP and imports models, respectively. One of the salient featuies of the cyclical components is that they have relatively greater impact on 9This is very close to the potential GDP growth rate of 1.5 percent annually that we have estimated for the period 1981-2000, after adjusting for changes in the real price of oil. See Cuevas (October 2001). 'Olt is worth noting that these frequencies are parameters estimated from the data, not model assumptions. Demand for Imports in Venezuela; Mario A. Cuevas 5 real imports than on GDP. This is consistent with the higher R2 of the imports model (0.60), relative to the GDP model (0.50). This is especially interesting considering that real imports, unlike GDP, has been corrected for changes in the real exchange rate. In other words, for a given exchange rate level, cyclical variations in domestic economic activity (as measured by GDP) are associated with amplified cyclical changes in imports. However, as may be recalled, the ordinary goodness of fit measure of the imports model is in fact less than the GDP model (0.66 vs. 0.95). This suggests that despite the relatively greater amplitude of the imports cycles, there is also a lot more unexplained noise in the level of imports than in the GDP level series. In addition, it is worth noting that the higher frequency cycle is rather smooth- close to a theoretical stochastic (trigonometric) cycle with very little noise. By contrast, the lower frequency cycle displays a more important noise element. This is to be expected given the length of the data sample that we are using, as the scope for estimating a 5 year cyclical pattern from 1972 to 2000 is much greater than for estimating a 17 year cyclical pattern. With a longer time series, lower frequency cycles could be estimated with greater precision. Venezuela: GDP and Imports Cycle Parameters 1974-2000) Parameter Cycle iV/ Cycle C Amplitude 0.03 0.03 (GDP model) Amplitude 0.11 0.08 (Imports model) Period (in years) 4.98 17.10 Frequency 1.26 0.37 SUMMARY OF RESULTS AND POLICY IMPLICATIONS Analysis of Imports Elasticities in Venezuela We have obtained the real exchange rate elasticity of imports from the estimated coefficient associated with r. in the imports model equation. Using the estimated components series, we have also obtained estimates of the GDP elasticities of imports at frequencies 0, 0.37 and 1.26 (please see Table "Venezuela: Estimated Real Imports Elasticities (1974-2000)"). The elasticity coefficient associated with the real exchange rate has reasonable magnitude (0.4) and has the expected sign.'1 The GDP elasticity of imports increases "Our measure of the real exchange rate increases with a real depreciation, and falls with a real appreciation. As r, increases, the economy experiences a real depreciation and (other things held constant) imports should be expected to fall, and vice versa. This accounts for the negative sign before the real exchange rate elasticity of imports. Demand for Imports in Venezuela; Mario A. Cuevas 6 with frequency (or equivalently, falls as the period increases). For example, at the highest frequency, elasticity is 4.55. At the zero frequency, the elasticity is smaller, at 1.71.2 This clearly illustrates that the short-run imports responsiveness to variations in GDP is uniformnly higher than in the longer run (the imputed frequency profile of imports elasticities is shown in Chart "Venezuela GDP Elasticity of Imports"). The frequency profile of the imports elasticities turns out to be a line in the frequency-elasticity space, with a relatively steep slope of about 1.9 Venezuela: Estimated Real Imports Elasticities (1974-2000) Real Exchange Rate Elasticity -0.43 GDP Elasticity of Imports 1.71 (Frequency=0) GDP Elasticity of Imports 2.72 (Frequency=0.37) GDP Elasticity of Imports 4.55 (Frequency= 1.26) Higher frequency fluctuations in growth seem to generate unusually powerful responses from aggregate imports, a phenomenon which can be expected to lead to issues with the country's external balance on a recurrent basis. VenezibL GM tidtyofhWorts Moreover, if we assume that the F e potential rate of growth of the Venezuelan 5 economy is about 1.6 percent annually, 4 then the underlying rate of growth of real imports is about 2.7 percent (i.e. the GDP 3 elasticity of imports at the zero frequency 2 times the potential rate of growth of X GDP).13 This underlines the powerful I structural tendency towards increasing _ imports that characterizes the Venezuelan 0o 0 , , economy, even at slow rates of GDP .0 0.4 0.8 1.3 growth. F 12Elasticity parameters have been estimated by means of linear regressions of each component of imports against the corresponding GDP components. At the zero frequency, elasticity parameters are estimated super-consistently (since cointegration of the trend components is assured by construction of common trends. At other frequencies, parameter estimates are estimated consistently under classical assumptions. 13This calculation is consistent with the underlying rate of drift of imports directly estimated above, which is 2.8 percent annually. Demand for Imports in Venezuela; Mario A. Cuevas 7 Summary of Findings Using structural time series models, we have estimated common stochastic trends (with independent rates of drift) of real GDP and imports in Venezuela. The real imports trend has an underlying rate of drift of 2.8 percent annually; by contrast, the rate of drift of real GDP is 1.6 percent annually. We also estimated common stochastic cycles, which have been found to have approximately 5 and 17 year periods. In addition, we have found that a 1 percent real appreciation leads to 0.4 percent increase in imports. Moreover, the long-run GDP elasticity of imports is about 1.7. thus implying that 1 percent real GDP growth in the long-run is associated with 1.7 percent real imports growth. GDP elasticity of imports increases with frequency (or equivalently, falls with cycle period), reaching 4.55 at the frequency associated with the 5-year cycle. Demand for Imports in Venezuela; Mai io A. Cuevas 8 REFERENCES * Campbell, J. and Perron, P., "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots" (Princeton University, Econometric Research Program, Research Memorandum, April 1991). * Cuevas, M., "Potential GDP Growth in Venezuela: A Structural Time Series Approach" (World Bank mimeo, October 2001) * Davidson, J., "Econometric Theory" (Blackwell, 2000). * Doornik, J., et al, "STAMP: Structural Time Series Analyser, Modeller and Predictor" (Timberlake Consultants Ltd., 2000). * Greene, W., "Econometric Analysis " (Prentice Hall, 1997). * Hamilton, J., "Time Series Analysis" (Princeton, 1994). * Harvey, A., "Trends and Cycles in Macroeconomic Time Series" (Journal of Business & Economic Statistics, July 1985, 3(3), 216-227). *______,__ "Forceasting, Structural Time Series Models and the Kalman Filter" (Cambridge University Press, 1989). * _________, "Time Series Models" (Harvester Wheatsheaf, 1993). * ________, "Trends, Cycles and Convergence " (Proceedings of the Fifth Annual Conference of the Central Bank of Chile, 2002). * Johansen, S., "Likelihood-based Inference in Cointegrated Vector Autoregressive Models" (Oxford University Press, 1995). * Rao, B., "Cointegration for the Applied Economist" (St. Martin's Press, 1994). Demand for Imports in Venezuela; Mario A. Cuevas 9 ANNEX I DESCRIPTION OF GDP AND OIL PRICE STATISTICAL SERIES * Real GDP. The annual GDP series, spanning the 1974-2000 period, is based on National Accounts data published by the Central Bank of Venezuela. * Real Imports. The annual real imports series, spanning the 1974-2000 period is based on National Accounts data published by the Central Bank of Venezuela. * Real Exchange Rate (RER). The annual RER has been calculated as an index (1990=100) on a trade-weighted basis for Venezuela, using monthly information on exchange rates as well as domestic and foreign price indices obtained from the IMF's International Financial Statistics. The convention that an increase in the index represents a real depreciation was followed. Real Imports Real GDP RER 1974 43900 379800 62.12 1975 57100 390800 59.91 1976 76600 421000 58.60 1977 98800 447400 57.94 1978 95100 457900 59.33 1979 73600 461400 60.70 1980 72800 441000 57.09 1981 81200 439400 53.03 1982 94700 430300 48.55 1983 44700 414100 45.02 1984 69000 420000 63.73 1985 66500 420900 60.51 1986 66100 448400 57.86 1987 71800 464300 82.59 1988 88400 491400 70.27 1989 58900 449200 87.98 1990 55000 478300 100.00 1991 82200 524900 96.55 1992 103800 556700 93.46 1993 97000 558100 92.26 1994 79100 545000 92.72 1995 98004 566627 73.00 1996 86998 565506 87.10 1997 116476 601534 73.59 1998 127425 602557 63.00 1999 108839 565887 56.87 2000 130040 584073 56.04 Demand for Imports in Venezuela; Mario A. Cuevas ANNEX II ESTIMATED SPECTRAL DENSITIES AND PROBABILITY DISTRIBUTIONS Spectral Density Imports Model Residuals 0.3 + + 0.2 0.1 I , ~~~~~~~~~~+ 0 5 10 15 - Spectral Density. GDP Model Residuals 0.3 -+ -+ + Perg Spectrum| 0.2 - 0.1 ++ +~~~~ n)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _ 0 5 10 15 0.4 Density (Residuals, Imports Model) -. N(s=0.957)|/ X 0.3- 0.2 0.1 ==<.1 ..1,.,.1.., -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.4 S Density (Residuals, GDP Model) 0.3 s ) 0.2 - 0.1 I -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Demand for Imports in Venezuela; Mario A. Cuevas ANNEX III STRUCTURAL TIME SERIES MODELS AND THE VECM FRAMEWORK Long-Run Analysis. We have estimated stochastic trends common to real imports and GDP using the structural time series approach. We now compare the estimated imports trend with estimates obtained through an alternative conventional econometric framework-the VECM framework. We have estimated a Vector Error-Correction Model (VECM) using the same GDP, imports and real exchange rate data used elsewhere in this paper. GDP, impForts and the real exchange rate are treated as endogenous variables in the VECM.' . We find that the VECM framework performs well in the estimation of long-run relationships. First, it is important to notice that long-run imports elasticities implied by the VECM framework are very similar to those estimated following the structural time series approach. This is important, as it corroborates the robustness of long-run parameter estimates in the presence of cointegrating relationships, even when using alternative estimation methods.'5 The estimated trends (assumed to be random walks with a fixed rate of Venezuela: Real Imports Trends drift under both methodologies), turn out Time Series and VECM Models to be quite similar (see Chart "Venezuela: Real Imports Trends"). 12.0- This is consistent with the similarities of the estimated long-run elasticities. ; 11.5 - However, the VECM-based imports trend is below the alternative trend estimate for most of the 1980s. As will 11.0 be discussed later, it turns out that the VECM-based "cycle" lies above the 10.5 composite cycle estimated using structural time series throughout the same period (please refer to the discussion below). This appears to be a O ON O OX O O ON ON ON O O ON ON o0 4c case where the lack of a well-defined cyclical structure in the VECM Trend Log M VECM Trend Log M framework has interfered with estimation of long-run trends. '4We need to treat the real exchange rate as an endogenous variable in the VECM framework so as to be able to obtain the long-run real exchange rate elasticity of imports. 151t must be noted that in structural time series models, trend-cycle decompositions are not unique-some identifying restrictions are needed to specify a decomposition. Similarly, in the VECM framework there is also an identification problem (cointegrating relationships are not uniquely defined) which requires imposition of identifying restrictions. It is reassuring that, in our analysis, we appear to have found approximately the same underlying stochastic trend processes, thus suggesting that these particular trend- cycle decompositions are indeed comparable. Demand for Imports in Venezuela; Mario A. Cuevas Venezuela: Lon -Run Elasticities of Imports Modeling Methodology GDP Elasticity RER Elasticity Structural Time Series 1.71 -0.43 VECM Framework 1.73 -0.46 Short-Run (Cycle) Analysis. At this stage, it is worth noting that modeling short-run (cyclical) behavior via a VECM can be difficult, because of the uncertainty regarding the appropriate lag structure and lack of a priori knowledge on parameter restrictions to be applied to the short-run model.16 Even more importantly perhaps, a complex autoregressive lag structure in the VECM framework can become very parameter-intensive in the absence of a priori information regarding underlying short-run dynamics. In this regard, stochastic (trigonometric) cycles, explicitly defined and estimated using structural time series models, may turn out to be more parsimonious and use information more effectively in the estimation of short-run dynamics, than a VECM. For the purpose of comparing the two methodologies, we added up y7 and Venezuela: Real Ihorts Cycles rune Sen es and VECMModels X (which are independent trigonometric 1.0 - - -- - cycles) based on the structural time series decomposition, to generate a "composite" _ 0.5 cycle. It turns out that not only did the VECM attribute some of the trend 0o0 behavior to the cycles (as has already been discussed), but occasionally strong -0.5 - impulses in the irregular component have been "absorbed" as part of the short-run -1.0 . model (e.g. a transitory impulse in 1983). g 0 , s > a t , a I ° It turns out that a VECM that performed - well with regard to estimation of a long- -CyclesLogM-VECMCycIeLogM run relationship, has done a comparatively poor job at modeling short-run dynarnics. This is corroborated by inspection of the spectral densities of the VECM-based short-run dynamics-which, we hoped, would have captured a "cycle". Instead, the corresponding spectral density suggests that the short-run dynamics captured by the VECM are somewhat loaded towards higher frequencies, thus explaining the high level of noise of the series. At best, it could be said that the VECM has captured some short- 16This occurs because the VECM framework is asymmetric with regard to the specificity of definition of the model in the zero frequency and other frequencies. In general, it may be said that the model is sufficiently structured at the zero frequency, thanks to the role played by the cointegrating relationship(s). By contrast, the autoregressive structures used to model cyclical and other frequencies are, in fact, no more than reduced forms of a composite of underlying structural processes. '7Notice that under the VECM framework, V,7 and C7' are not independently estimated. Demand for Imports in Venezuela; Mario A. Cuevas run dynamics together with higher frequency noise. By contrast, the spectral density of the composite cycle associated with the structural time series models is loaded towards lower and medium frequencies,"8 which is where more interesting cyclical patterns have been found. With the structural time series model, higher frequencies have been effectively filtered out of our cycle estimates. This suggests that structural time series models display higher selectivity in the estimation of the cyclical band. 0.45 - Venezuela: Spectral Density of VECM-Based Imports Cycle 0.40 0.35 0.30 Pergr Spectrum 0.25 0.20 0.15 0.10 0.05 1 2 3 4 5 6 7 8 9 10 11 12 13 0.8 Venezuela: Spectral Density of Composite Imports Cycle 0.7 0.6 Pergr Spectrum 0.5 0.4 0.3 0.2 0.1 0 5 10 15 t5Notice also that the spectral density of the composite imports cycle is itself a combination of the spectral densities of the lower and medium frequency cycles estimated via structural time series models. Demand for Imports in Venezuela; Mario A. Cuevas Venezuela: Spectral Density of Higher Frequency Inports Cycle 3e7 2e7 - IO,,. 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