Empirical Modelling of Norwegian Import Prices

Bache, Ida Wolden Working Paper Empirical Modelling of Norwegian Import Prices Working Paper, No. 2002/1 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Bache, Ida Wolden (2002) : Empirical Modelling of Norwegian Import Prices, Working Paper, No. 2002/1, ISBN 82-7553-188-8, Norges Bank, Oslo, https://hdl.handle.net/11250/2498660 This Version is available at: https://hdl.handle.net/10419/209800 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Norges Bank's Working papers present research projects and reports (not usually in their final form), and are intended inter alia to enable the author to benefit from the comments of colleagues and other interested parties. Views and conclusions expressed in Working Papers are the responsibility of the authors alone. Empirical Modelling of Norwegian Import Prices∗ Ida Wolden Bache Research Department, Norges Bank (Central Bank of Norway) January, 2002 Abstract In this paper we investigate the formation of Norwegian import prices of manufactures over the period 1970(1)–1998(3), thereby extending the sample period used in the study by Naug and Nymoen (1996). If international goods markets are perfectly integrated and the law of one price holds, then for a small open economy we would expect import prices to be exogenously given in foreign currency and to fully respond to movements in the exchange rate. However, empirical studies of small open economies have shown that exchange rate changes are not fully reflected in import prices, and that domestic variables have significant effects on import prices. Applying both single-equation and multivariate cointegration analysis we find evidence of a long-run cointegrating relationship between Norwegian import prices, foreign export prices measured in domestic currency, domestic unit labour costs, and the domestic unemployment rate. Our results indicate that exchange rate pass-through is complete in the long run. In contrast, Naug and Nymoen (1996) report a long-run pass-through coefficient of 0.63. Keywords: Import prices; Exchange rate pass-through; Equilibrium-correction models JEL classification: C51, E31, F31 ∗This paper is an abridged version of my dissertation submitted to the Department of Economics, University of Oslo in fulfillment of the requirements for the cand.oecon degree in February 2000. The work on the dissertation was carried out during my internship at the Research Department, Norges Bank in the period from July 1999 to January 2000. I would like to thank my supervisor, Professor Ragnar Nymoen at the Department of Economics, University of Oslo for valuable comments. I am also grateful for help from Fredrik Wulfsberg, Gunnar B˚ardsen, Qaisar Farooq Akram and Øyvind Eitrheim. The views expressed in this paper are my own and should not be interpreted as reflecting those of Norges Bank. 1 Introduction Understanding the behaviour of import prices is important for a small open economy like Norway. First, growth in import prices is an important determinant of domestic inflation. Approximately 25 percent of the official Norwegian consumption basket consists of imported goods, and another 15 percent is made up of goods whose prices are influenced by the prices of imports through foreign competition or imported inputs. Second, by affecting the terms of trade, the development of import prices influences the trade balance. Of particular importance is understanding the relationship between import prices and nominal exchange rates. The degree to which changes in exchange rates are reflected in local currency import prices is referred to as the degree of exchange rate pass-through. If pass-through is complete, a one percent depreciation of the domestic currency will cause import prices to increase by one percent. Incomplete pass-through of exchange rate changes to import prices has important implications for macroeconomic policy. First, incomplete pass-through implies that exchange rate policy are less effective in inducing the adjustments in terms of trade needed to equilibrate trade imbalances, and second, the effects of an exchange rate depreciation on consumer price inflation are moderated. A common assumption in macro models of small open economies is that the “law of one price” holds, and that import prices are exogenously determined in foreign currency on the world market. In this situation, exchange rate pass-through will be complete, and domestic market conditions will not influence import prices. However, empirical studies of small open economies like Sweden, Finland, and Australia have shown that import prices do not fully respond to changes in exchange rates, and that domestic variables have significant effects on import prices.1Theoretically, these results could be explained in models of imperfect competition and segmented markets. The phenomenon of exchange rate induced price discrimination is referred to as “pricing to market” (Goldberg and Knetter (1996)). Naug and Nymoen (1996) investigate the formation of Norwegian import prices of manufactures over the period 1970(1)–1991(4). Using multivariate cointegration analysis they find evidence of a long-run cointegrating relationship between import prices, the exchange rate, foreign export prices, and domestic unit labour costs. The estimated long-run elasticity of import prices with respect to the exchange rate and foreign export prices is 0.63, and the long-run elasticity with respect to domestic unit labour costs is estimated to 0.37. Naug and Nymoen (op cit) also estimate a dynamic structural import price equation in which deviations from the cointegrating relationship enter as an equilibrium-correction mechanism. The import price equation contains significant 1See Alexius (1997), Kuismanen (1995), and Menon (1995b). 2 effects of variables proxying demand pressure in the domestic economy, and so the small open economy assumption is rejected in favour of the pricing to market hypothesis. The purpose of this dissertation is to investigate the robustness of the results reported in Naug and Nymoen (op cit) when the estimation period is extended to 1998(3). The dissertation is organised as follows: In Section 2 we briefly review the theoretical and empirical literature on exchange rates and traded goods prices discussing topics such as exchange rate pass-through, the law of one price, and pricing to market. We also derive an import price equation which will serve as a starting point for the empirical analysis. Section 3 reports results from an econometric analysis of the relationship between Norwegian import prices of manufactures, the exchange rate, foreign export prices, domestic unit labour costs, and the unemployment rate over the period 1970(1)–1998(3). Section 3.1 describes the data and investigates the time series properties of the variables. The unit root tests suggest that the series are non-stationary and integrated of order one. In Section 3. 2 we derive a dynamic conditional single equation model of import prices. The starting point is a general unrestricted equilibrium-correction model estimated by OLS. To obtain a simpler model that is easier to interpret, but which represents the data equally well, we simplify the general model by deleting insignificant variables and imposing restrictions on the parameters. Evaluating the final model by analysis of residuals and tests for parameter stability, we find that the model is well-specified with parameters that are relatively constant over the sample period. From the single equation analysis we find evidence of a cointegrating relationship between the variables in the model. This is consistent with the evidence in Naug and Nymoen (1996). However, the hypothesis of long-run unit homogeneity in foreign and domestic prices measured in the same currency is no longer accepted by the data, and the long-run elasticities of import prices with respect to the exchange rate and foreign export prices are close to one which is larger than those reported in Naug and Nymoen (op cit). The magnitude of the long-run elasticities is confirmed in the multivariate cointegration analysis in Section 3. 3. The hypothesis that the exchange rate, foreign export prices, and domestic unit labour costs are weakly exogenous for the cointegration parameters is not rejected by the data, implying that single equation estimation of the cointegration parameters is efficient. The data series used in the empirical analysis are taken from Norges Bank’s RIMINI model database and are available on request from the author. The numerical results are obtained using PcGive and PcFiml version 9.20.2 2See Hendry and Doornik (1999) and Doornik and Hendry (1997). 3 2 Theory and Existing Evidence In the following subsections we give a brief overview of the theoretical literature on exchange rates and import prices focusing on the law of one price, exchange rate passthrough and pricing to market. In Section 2.1.3 we derive a theoretical import price equation which will serve as the starting point for the econometric analysis in Section 3. 2.1 The law of one price and exchange rate pass-through As pointed out by Goldberg and Knetter (1996, p.3), when discussing the relationship between exchange rates and goods prices it is important to distinguish between integrated and segmented markets. An integrated market is defined as a market in which geography does not have a systematic effect on the prices of identical goods. In a perfectly integrated market identical products sells for the same price everywhere, that is, the absolute version of the law of one price (LOP) holds. For any product i, the LOP in its absolute form states Pi=EP∗ i(2.1) where Piis the price of good iin domestic currency, P∗ iis the analogous foreign currency price, and Eis the nominal exchange rate. The mechanism assumed to be enforcing the law of one price is arbitrage. If the LOP holds for all products between two countries, and assuming that the weights used in constructing each country’s price level are the same, then absolute purchasing power parity (PPP) holds between these two countries. For reasons such as transport costs, imperfect information, and government-imposed trade barriers, the absolute version of the LOP is unlikely to hold in practise. However, if the factors causing deviations from (2.1) give rise to a constant price differential between the two markets, a weaker version of the LOP, relative LOP, holds: Pi=αEP∗ i(2.2) where αis a constant. Letting lower-case letters denote natural logarithms and taking first differences we get ∆pi= ∆e+ ∆p∗ i(2.3) The relative version of the LOP thus examines the proportionate changes in the variables in (2.1). According to Goldberg and Knetter (1996, p.7), there are three main reasons why the empirical literature has focused on the relative version of the LOP. First, transport costs, tariffs and other trade barriers make arbitrage costly, implying that a complete equalisation of prices is unlikely. Second, the identical goods assumption is strong and likely to be violated in most datasets. Finally, information on Piand P∗ i 4 usually come in the form of price indices relative to a base year, making the levels of Pi and P∗ iarbitrary. The conventional definition of exchange rate pass-through (ERPT) is the percentage change in local currency import prices caused by a one percent change in the nominal exchange rate. If the exporting firm adjusts the home currency price to fully offset the exchange rate change, then pass-through will be zero. On the other hand, if the exporter leaves the home currency price unadjusted, then the exchange rate change will be fully reflected in the import price and pass-through is complete. In his examination of the relationship between the law of one price and exchange rate pass-through, Menon (1995c, p.551) asks the question of whether incomplete passthrough always implies violation of the law of one price. To see that it does not, we consider a simple supply and demand model.3Demand and supply for an imported good is given by QD=D(P) (2.4) QS=S(P∗) = S²P E³(2.5) where QDand QSdenote the quantity demanded and supplied of the imported good, P and P∗are the domestic and foreign currency prices of the good, and Eis the exchange rate. Total differentiation of (2.4) and (2.5) yields dQD=∂D ∂P dP (2.6) dQS=∂S ∂P∗º1 EdP −P E2dE»(2.7) Imposing the condition that dQDand dQSare equal in equilibrium we get ERPT = dP dE E P= ∂S ∂P ∗ ∂S ∂P ∗−E∂D ∂P =²1−εD εS³−1 (2.8) where εD=∂D ∂P P Dand εS=∂S ∂P ∗ P∗ S=∂S ∂P ∗ P ES are the elasticities of demand and supply. A small open economy is assumed to be a price taker in world markets and hence, to face a perfectly elastic supply of exports (corresponding to εS→ ∞).From (2.8) it follows that for a small open economy, the law of one price implies that pass-through will be complete. Changes in the exchange rates of large economies, however, could alter world prices, and ensure the co-existence of incomplete pass-through and the law of one price. Thus, for large countries the simple supply and demand model is sufficient to explain a failure of import prices to move in proportion to changes in the exchange rate. 3The model is based on Menon (1995a). 5 There is also the question of the relationship between the degree of segmentation and the degree of competition in a market. In a perfectly competitive market price is equal to marginal cost and so a perfectly competitive market must be integrated. However, an integrated market is not necessarily perfectly competitive. In an imperfectly competitve market producers may charge a price above marginal cost, but if markets are integrated, arbitrage could still eliminate differences in the common currency price of goods across markets. Moreover, if the producer has constant marginal costs of production and charges a constant markup over cost, exchange rate pass-through will be complete. Thus, we conclude that the relationship between the law of one price, the degree of exchange rate pass-through, and the nature and degree of competition is ambiguous. As noted by Rogoff (1996, p.652) the empirical support for the law of one price is weak. The LOP has been rejected in a large number of studies covering a broad range of product categories and countries. Moreover, the deviations from the law of one price appear to be highly correlated with exchange rate movements. Engel and Rogers (1995) find that the price differentials for consumer goods across cities in the United States and Canada are much larger and more volatile than the price differentials for the same goods across cities within the same country even when controlling for the distance between the cities. 2.2 Incomplete pass-through and pricing to market The theory presented above suggests that when identical goods are traded in an integrated world market, arbitrage should eliminate differences in the common currency prices of goods across countries. Exchange rate pass-through is complete and domestic market conditions are of no importance in the determination of import prices in small open economies. In this subsection we turn to the case where markets are segmented. Following Goldberg and Knetter (1996, p.3) we say that a product market is geographically segmented if the location of the buyers and sellers has a significant influence on prices. Market segmentation may be due to transportation costs, trade barriers or imperfect information. Now, if markets are imperfectly competitive as well as segmented, then profit maximisation could imply price discrimination. If so, market conditions in the importing country could affect import prices, and pass-through may be less than complete even in a small open economy. A concept that has received much attention in recent literature on exchange rates and traded goods prices is the concept of pricing to market (PTM). According to Krugman (1987, p.50) what is meant by PTM is that import prices respond “too little” to exchange rate appreciations or depreciations. However, as stressed by Krugman, PTM is not present whenever import prices fail to respond in proportion to the exchange rate change. Any effect of the exchange rate on world prices of the imported good should be excluded 6 (2.20) apriori. Finally, assuming that the variables are integrated of order one, the longrun version of LOP holds if pb,e, and, px cointegrate with cointegration parameters equal to one. . Adopting the analytical framework presented above Naug and Nymoen (op cit) find evidence of a single cointegrating relationship between Norwegian import prices of manufactures, foreign export prices, the exchange rate, and domestic unit labour costs over the period 1970(1)–1991(4). The estimated cointegrating vector is pb =const. + 0.63 (0.08)px + 0.63e+ 0.37ulc (2.21) where ulc denotes unit labour costs in domestic manufacturing. The unit labour cost variable is included as a proxy for the price of import competing goods. The authors thus find support for the hypothesis that import prices are homogenous of degree one in foreign and domestic prices measured in the same currency. The presence of the domestic cost variable in the cointegrating vector is interpreted as evidence of a long-run pricing to market effect. The significant effect of domestic costs on Norwegian import prices is consistent with the findings reported by von der Fehr (1987). An estimated long-run pass-through coefficient of 0.63 is close to the estimates reported in other studies of the pass-through to import prices in small open economies. In a study of Finnish import prices for total imports, Kuismanen (1995) finds a long-run pass-through coefficient of 0.68. In Alexius (1997) the long-run pass-through to Swedish import prices of manufactured goods is estimated to be in the range 0.6–0.8, while Menon (1995b) estimates the long-run elasticities of Australian import prices of manufactures to 0.66 (the exchange rate), 0.75 (foreign costs) and 0.37 (the price of import competing goods). Naug and Nymoen (op cit) also estimate a dynamic structural import price equation where deviations from (2.21) enter as an equilibrium-correction mechanism. The estimation period is 1970(1)–1991(4). The equation contains significant effects of variables proxying demand pressure in the domestic economy. The authors report a positive effect from domestic inflation and growth in domestic absorption, and a negative effect from the unemployment rate. Naug (1996) extends the sample to 1994(4) and finds that the estimated short-run coefficients remain relatively constant. 13 3 Empirical Modelling of Norwegian Import Prices of Manufactures 1970(1)-1998(3) In this section we present results from an econometric analysis of Norwegian import prices of manufactures over the period 1970(1)-1998(3). To start, Section 3.1 describes the data and investigates the time series properties of the variables. Section 3.2 presents estimation results for a single equation equilibrium-correction model of import prices. Then, in Section 3.3 we compare the results from the single equation analysis with the results from multivariate cointegration analysis, and test for weak exogeneity of the regressors with respect to the cointegration parameters. 3.1 The data Throughout the analysis we use quarterly, seasonally unadjusted data for the period 1970(1)–1998(3). Allowing for lags, estimation is over 1971(2)–1998(3) unless otherwise mentioned. Import prices, the exchange rate, and foreign export prices are indices taking the value 1 in 1996. All data series are taken from Norges Bank’s RIMINI model database. The sources of the original data are given in Appendix A. 3.1.1 Variable descriptions Taking equation (2.20) as the starting point for the empirical analysis we need data for import prices, exchange rates, foreign export prices, domestic prices of import competing products, and an indicator of domestic demand pressure. We consider these in turn. Import prices The import price series (denoted PB) is an implicit deflator for imports of manufactures with Norwegian substitutes. The products in the index are priced cif Norwegian port, that is, the prices include cost, insurance and freight, but exclude import duty. The implicit deflator is calculated by dividing the value of imports by the volume of imports. Implicit deflators of this kind are subject to well-known limitations such as not accounting for shifts in the quality of a product, and reflecting not only underlying price changes, but also changes in the composition of imports. For example, the implicit deflator gives increasing weight to computers over the same period during which prices of computers have fallen sharply. Because it gives a low weight to computers and because it abstracts from shifts in the commodity composition of imports, Hooper and Mann (1989) prefer to use a fixed-weight index. However, Naug and Nymoen (1996) constructed an index excluding computers and a fixed-weight import price index for Norwegian manufactured imports over the period 1968–1991 and found that both showed a development more or less like the implicit deflator. 14 Figure 1: Import prices of manufactured products 1970(1)–1998(3) 1970 1975 1980 1985 1990 1995 -1 -.5 0 pb 1970 1975 1980 1985 1990 1995 -.05 0 .05 .1 Dpb Figure 1 plots the log of the import price series (pb) and its quarterly growth rates (∆pb). In the period from 1970 to 1990 import prices increased steadily, while since 1990 growth in import prices has been markedly slower and the fluctuations from quarter to quarter appear to have been smaller. These are important features that our model should capture. Notice also the strong fluctuations in the index in 1989. Splitting the aggregate index into subindices according to the commodity classification in the quarterly national accounts, we find that these movements can be accounted for by fluctuations in the price of metals, which has an average quantity weight of about 9% in the aggregate index. Exchange rates The exchange rate index (denoted E) is a nominal effective import weighted exchange rate for Norwegian Kroner (NOK). The weights reflect the relative importance of Norway’s main trading partners. The 14 countries included in the index are the same as those that were included in Norway’s official exchange rate basket in the period from August 1982 to October 1990. Each country’s weight is the imports from this country as a share of total imports from the countries in the index. The weights are given in Table 1 and are calculated as the average import shares over the period 1978–87. Note that using a trade-weighted exchange rate index is not necessarily optimal. As pointed out by Menon (1995a), to get a true representation of the extent of exchange rate fluctuations faced by exporters we should instead use a currency-contract-weighted exchange rate. 15 Table 1: Average import shares 1978–87. Total = 100. Country Import share Sweden 20.6 Germany 17.5 Great Britain 13.4 USA 9.2 Denmark 7.7 Japan 6.3 Finland 4.9 France 4.4 Netherlands 4.1 Belgium 3.3 Italy 3.3 Canada 2.0 Switzerland 1.9 Austria 1.4 Figure 2 plots the log of the exchange rate (e) and the quarterly growth rates in the series (∆e). A rise in the index represents a depreciation of the NOK. The figure serves as a background for a brief overview exchange rate policy in Norway in the period 1970–1998. After the collapse of the Bretton Woods system in 1972, Norway joined the European snake arrangement leaving the NOK floating against the US dollar and other currencies outside the snake. After a 5 percent revaluation in November 1973, the NOK was devalued four times between 1976 and 1978 before Norway withdrew from the snake arrangement in 1978. In December 1978 a national currency basket with weights reflecting the relative importance Norway’s trading partners was introduced. In the period 1979–1986 there were several small devaluations until in May 1986 the central value of the exchange rate was changed from 100 to 112. One reason for the adjustment was the sharp fall in the oil price early in 1986. The devalution marked the beginning of a period during which only small fluctuations around the fixed target value were allowed. In 1990 the weights in the currency basket were changed to ECU weights. In December 1992, after extensive speculation against the krone following the ERM crisis, the central bank was forced to let the NOK float. After a period of relative stability following the crisis, the exchange rate fluctuated widely in 1997 and 1998. The new guidelines for monetary policy were set out in the Exchange Rate Regulation of May 6, 1994. Monetary policy should be directed at maintaining a stable exchange rate against European currencies, but no fluctuation margins are specified. 16 Figure 2: Import weighted exchange rate 1970(1)–1998(3) 1970 1975 1980 1985 1990 1995 -.2 -.1 0 e 1970 1975 1980 1985 1990 1995 -.025 0 .025 .05 De Foreign export prices Since foreign marginal costs are not directly observable, we follow Naug and Nymoen (1996) and use an import weighted foreign export price index (denoted PX) as a proxy variable. Previous studies have employed other proxies such as foreign producer price indices, foreign unit labour costs, and foreign consumer price indices. The import weighted foreign export price index is constructed with the same set of weights as the exchange rate index above. As pointed out in Section 2.3, using average foreign export prices as a proxy for marginal costs means that foreign exporters’ markups in all markets are contained in the disturbance term in equation (2.20). Then for (2.20) to form a cointegrating relationship, we must assume that this measurement error is I(0). Even if this assumption is satisfied, the measurement error may induce biases in the estimated cointegrating parameters in finite samples. Figure 3 plots the log of foreign export prices (px) and the quarterly growth rates (∆px). From the figure we see that export prices increased markedly following the oil price shocks in 1973–74 and 1979. In 1985–86 turbulent oil markets contributed to a fall in export prices. Average growth in foreign export prices appears to have been significantly lower after 1985 than in the period before. Domestic unit labour costs As a proxy for the domestic price of import competing goods we use domestic unit labour costs in manufacturing and construction (denoted ULC). Unit labour costs are defined as ULC =WC/Z where WC is hourly wage costs and Zis value-added labour productivity in manufacturing and construction. Again 17 Figure 3: Import weighted foreign export prices 1970(1)–1998 1970 1975 1980 1985 1990 1995 -1 -.5 0px 1970 1975 1980 1985 1990 1995 0 .025 .05 .075 Dpx there is a potential measurement problem. The markups of domestic producers of import competing goods are left in the disturbance term, and only if the measurement error is I(0) will (2.20) form a cointegrating relationship. Figure 4 plots the log of unit labour costs (ulc) and the quarterly growth rate of the series (∆ulc). The series has a strong positive trend and exhibits a marked seasonal pattern which stems from seasonal variations in value added labour productivity. Unemployment rate We use the unemployment rate (denoted U), measured as the number of registered unemployed as a fraction of the total labour force, as an indicator for demand pressure in the domestic economy. As noted by Naug and Nymoen (1996) the unemployment rate is easily observable and may therefore be used by foreign producers to assess demand conditions in Norway when detailed market information is costly. Figure 5 plots the log of the unemployment rate (u) and the quarterly changes in the series (∆u). We see that the level of unemployment was low throughout the 1970s, then started to increase in the beginning of the 1980s before reaching an all time high in 1992–93. The quarter to quarter fluctuations in the series are markedly smaller after 1983 than in the preceding period. 18 Figure 4: Unit labour costs 1970(1)-1998(3) 1970 1975 1980 1985 1990 1995 2000 -1.5 -1 -.5 ulc 1970 1975 1980 1985 1990 1995 2000 -.05 0 .05 .1 .15 Dulc Figure 5: Unemployment rate 1970(1)–1998(3) 1970 1975 1980 1985 1990 1995 -5 -4 -3 u 1970 1975 1980 1985 1990 1995 -.5 0 .5 Du 19 3.1.2 Unit root tests Prior to modelling it is important to determine the order of integration for the variables of interest. In Table 2 we report ADF-tests for the levels and first-differences of the variables in the model.11 As can been seen from the above figures import prices, foreign export prices, and unit labour costs all appear to be strongly trended. Thus, the appropriate alternative hypothesis seems to be that of trend stationarity, implying that the estimated model should include a deterministic trend. The test statistic for this specification is denoted ττ. For the unemployment rate and the exchange rate we also report the statistic τµwhich is computed from a model estimated without a deterministic trend term. In each test we started out with 5 lags and then used a sequence of t-tests to determine the lag length. Misspesification tests were performed to ensure that the residuals were white noise. It proved difficult to obtain white noise residuals in the tests for uand px so the results from these tests should be interpreted with caution. In the table asterisks (*) and (**) denote rejection at the 5% and 1% critical values respectively. The Dickey-Fuller critical values are taken from Table B.6 in Hamilton (1994). The sample is 1971(4)– 1998(3) for all series. Table 2: Augmented Dickey Fuller tests 1971(4)-1998(3) Variable Lag-length τu-statistic ττ-statistic pb 1 - -0.460 px 5 - -1.342 e2 -0.424 -2.726 ulc 5 - -1.818 u5 -1.655 -1.915 ∆pb 0 -11.490** – ∆px 5 -3.354* – ∆e2 -5.141** – ∆ulc 3 -17.347** – ∆u4 -3.535** – For the levels of the variables we fail to reject the null of a unit root in all cases, while for the first-differences the null is rejected at the 1% level for pb,e,ulc, and u and at the 5% level for px. These results suggest that all variables should be treated as non-stationary I(1) series. The assumption that the unemployment rate is I(1) may seem unreasonable, and previous studies such as Naug and Nymoen (1996) interpret the 11For a variable Ythe ADF test statistic is the tratio on φ0from the regression ∆Yt=φ0Yt−1+Xp j=1 φj∆Yt−j+ξ+ωt +ut, where pis the number of lags on ∆Y,ξis a constant term, tis a time trend and utis an error term which is assumed to be white noise. A unit root corresponds to φ0= 0. 20 unemployment rate as an I(0) series, but with possible structural breaks. Perron (1989) has shown that if the underlying process is stationary with a one time structural break in the trend or the constant term during the sample period, standard unit root tests cannot reject the null hypothesis of a unit root even asymptotically. Thus we cannot reject the interpretation of uas an I(0) series with structural breaks solely on the basis of the tests above. However, Bjørnstad and Nymoen (1999) note that although the rate of unemployment is conceptually integrated of order zero with a bounded variance, the actual time series of the transformed rate of unemployment behaves as if it was I(1) due to autocorrelation. In the subsequent analysis we follow Bjørnstad and Nymoen (1999) and treat uas an I(1) variable. 3.2 A conditional single equation model In this section we present estimation results for a single equation equilibrium-correction model of import prices. The formulation and interpretation of the general model is described in Section 3.2.1. The exposition is influenced by de Brouwer and Ericsson (1995). Estimation results are presented and interpreted in Section 3.2.2. 3.2.1 Formulation and interpretation of the general model The starting point for single equation modelling is an autoregressive distributed lag model in pb, px, e, ulc, and u. pbt=a0+ 5 X i=1 a1ipbt−i+ 5 X i=0 a2iet−i+ 5 X i=0 a3ipxt−i(3.1) + 5 X i=0 a4iulct−i+ 5 X i=0 a5iut−i+ 3 X i=1 a6iSit +vt where vtis a disturbance term assumed to be white noise, and Sit is a seasonal dummy taking the value 1 in quarter iand zero otherwise. As is common with quarterly data, the lag length is set to 5. Without loss of generality (3.1) may be reparameterised as an EqCM ∆pbt=a0+a20∆et+a30∆pxt+a40∆ulct+a50∆ut(3.2) +c1pbt−1+c2et−1+c3pxt−1+c4ulct−1+c5ut−1 + 4 X i=1 b1i∆pbt−i+ 4 X i=1 b2i∆et−i+ 4 X i=1 b3i∆pxt−i + 4 X i=1 b4i∆ulct−i+ 4 X i=1 b5i∆ut−i+ 3 X i=1 a6iSit +vt 21 where c1=P5 i=1 a1i−1, cj=P5 i=1 aji,and bji =−P5 k=i+1 ajk for j= 1,2,3,4,5 and i= 1,2,3,4.The EqCM in (3.2) contains both a static levels model and a pure difference model of import prices as special cases. The non-stochastic static-state equilibrium can be found by setting the error term vtand all growth rates to zero. Ignoring the seasonals and dropping time subscripts (3.2) can be solved for pb =−²a0 c1³−²c2 c1³e−²c3 c1³px −²c4 c1³ulc −²c5 c1³u(3.3) The coefficient c1measures the feedback from disequilibrium in period (t−1).This can be seen more clearly if we rewrite (3.2) so as to incorporate the long-run solution (3.3) directly ∆pbt=a0+a20∆et+a30∆pxt+a40∆ulct+a50∆ut(3.4) +c1(pb −γe −δpx −κulc −λu)t−1 + 4 X i=1 b1i∆pbt−i+ 4 X i=1 b2i∆et−i+ 4 X i=1 b3i∆pxt−i + 4 X i=1 b4i∆ulct−i+ 4 X i=1 b5i∆ut−i+ 3 X i=1 a6iSit +vt where γ=−c2/c1,δ=−c3/c1, κ =−c4/c1,and λ=−c5/c1. For dynamic stability we require c1<0 (subject to strong exogeneity of the regressors). Testing the null hypothesis H0:c1= 0 is a way of testing for cointegration between the variables in the model. Under the null of no cointegration the test statistic t=bc1/qdvard (c1) has a nonstandard distribution for which appropriate critical values can be found in MacKinnon (1991). Kremers et al. (1992) have shown that this test will have higher power against the alternative of cointegration than the standard residual-based ADF test suggested by Engle and Granger (1987) unless certain common factor restrictions are satisfied. An alternative is to move the levels terms in the EqCM to the longest lag: ∆pbt=a0+a20∆pxt+a30∆et+a40∆ulct+a50∆ut(3.5) +c1pbt−5+c2pxt−5+c3et−5+c4ulct−5+c5ut−5 + 4 X i=1 d1i∆pbt−i+ 4 X i=1 d2i∆pxt−i+ 4 X i=1 d3i∆et−i + 4 X i=1 d4i∆ulct−i+ 4 X i=1 d5i∆ut−i+ 3 X i=1 a6iSit +vt with d1i=Pi k=1 a1i−1 and dji =Pi k=1 ajk for i= 1,2,3,4.The coefficients of the levels terms are unaffected by this reparameterisation. However, as stressed by B˚ardsen 22 The import price equation contains a significant negative effect of current changes in the unemployment rate, ∆ut. Our results thus indicate that increases in domestic demand pressure result in price increases on imports of manufactures. This is consistent with the findings in Naug and Nymoen (op cit). In addition to a significant negative effect from the unemployment rate, their model contains positive effects from domestic inflation and growth in domestic absorption. The model also contains a significant negative effect from lagged changes in unit labour costs, ∆2ulct−1.Giving a clear interpretation of this result is difficult, and attempts to reparameterise the model such that the coefficients were easier to interpret were not successful. The speed of adjustment towards the long-run equilibrium path, given by the coefficient of the equilibrium-correction term, is −0.17 and implies that the correction of disequilibria from the estimated long-run relationship is fairly slow. 29 Figure 8: Recursive OLS estimates of final model 1971(2)–1998(3) 1980 1985 1990 1995 -.05 0 .05 Constant 1980 1985 1990 1995 -.75 -.5 -.25 Dpb_1 1980 1985 1990 1995 -.5 0 .5 1 De 1980 1985 1990 1995 .5 1 1.5 De_1 1980 1985 1990 1995 1 1.5 2Dpx 1980 1985 1990 1995 -.075 -.05 -.025 Du 1980 1985 1990 1995 -.2 0 .2 EqCM 1980 1985 1990 1995 -.3 -.2 -.1 0D2ulc_1 Figure 9: Recursive analysis of final model 1971(2)–1998(3) 1980 1985 1990 1995 -.05 -.025 0 .025 .05 1-stepresiduals 1985 1990 1995 .25 .5 .75 11% 1-stepChowtests 1985 1990 1995 .25 .5 .75 1 1% BreakpointF-tests 1985 1990 1995 .25 .5 .75 1 1% ForecastF-tests 30 3.3 Multivariate cointegration analysis In this section the results from the single equation analysis are compared with the results from applying the Johansen (1988) full information maximum likelihood (FIML) procedure. For the single equation approach to yield efficient estimates of the long-run coefficients we require that the regressors are weakly exogenous for the cointegration parameters.16 Moreover, with nvariables in the model there may be up to n−1 distinct cointegration vectors, and when estimating a single equation we can only obtain an estimate of a linear combination of these. Taking a multivariate approach we are able to determine the number of cointegration vectors empirically as well as testing the assumptions of weak exogeneity implicit in the single equation analysis. If weak exogeneity is absent, we must choose between efficient (but more complicated) inference from the system analysis and inefficient inference from the conditional model. Consider an n-dimensional vector equilibrium-correction model (VEqCM) of the type ∆Yt=Π0Yt−1+Xp−1 j=1 Πj∆Yt−j+ΦDt+εt,εt∼IN(0n,Σ) (3.8) where Yt= (Y1t, Y2t,...,Ynt)0is an (n×1) vector of I(1) variables,εt= (ε1t,ε2t, ...,εnt)0 is an (n×1) vector of independently and normally distributed disturbances and Dt is a vector of deterministic variables. If the variables in Ytare cointegrated Π0can be factored into αβ0where both αand βare (n×r) matrices of rank r. Hence, cointegration implies that the matrix Π0has reduced rank r < n. The columns of βcontain the coefficients in the rcointegrating vectors such that the linear combinations β0Ytare I(0).The matrix αis a matrix of “loading coefficients” giving the weight attached to each cointegrating vector for all nequations. Testing for cointegration thus amounts to determining the rank of Π0.The Johansen FIML procedure enables empirical determination of the cointegrating rank from (3.8). Application of Johansen’s procedure provides neigenvalues b λ1>b λ2> ... > b λn.The estimates of βare obtained as the eigenvectors corresponding to the rlargest eigenvalues. 16Consider two variables xtand ytwith joint density f(·).The joint density can be factored into a conditional density for ytgiven xtand a marginal density for xtas follows f(yt, xt;θ) = g(yt|xt;λ1)×h(xt;λ2) The concept of weak exogeneity is defined relative to the parameters of interest ψ:xtis weakly exogenous for ψif 1. ψ=ψ(λ1); that is, ψis a function of λ1alone 2. λ1and λ2are variation free These conditions ensure that ψneither directly (condition 1) nor indirectly (condition 2) depends on the parameters of the marginal model. Weak exogeneity is a sufficient condition for efficient inference on ψfrom the conditional model. (The definition is taken from Ericsson et al. (1998)) 31 A test of the null hypothesis that there are at most rcointegration vectors can be based on the trace statistic ηr=−T n X i=r+1 ln(1 −b λi), r = 0,1,2,...,n−1 (3.9) where Tis the number of observations. Under the hypothesis that there are rcointegrating relationships, the distribution of ηris nonstandard. Asymptotic critical values are tabulated by Osterwald-Lenum (1992). The appropriate critical values depend on whether a trend and/or a constant are included in the model and whether these are restricted to lie in the cointegration space. Testing is sequential η0, η1,...,ηn−1, and the cointegrating rank is selected as zero if η0is not significant and r+1 if the last significant statistic is ηr. When the full system is large, we are often restricted to making inferences on the basis of a conditional model only. As shown in Harbo et al. (1998) making inference on cointegrating rank from a conditional model is not straightforward. For the asymptotic distribution of the test statistics to be free of nuisance parameters, the conditional model should include a restricted highest-order deterministic term, and asymptotic inference should be based on the critical values provided by Harbo et al. (1998). Hence, if there is the possibility of a linear but not a quadratic trend in the variables, inference on cointegrating rank should be made from a model which includes an unrestricted constant term and a restricted trend term. After having determined the cointegrating rank we can test whether the linear trend in the cointegrating relations can be dropped by a conventional χ2-test. 3.3.1 Formulation and estimation of the VAR The starting point for multivariate cointegration analysis is a congruent unrestricted vector autoregressive model. Initially, we estimate a VAR for pb, e, px, and ulc with five lags on each variable and three centered seasonal dummies.17 An unrestricted constant term is included to allow for a linear trend in the levels of the variables. The rate of unemployment lagged two quarters, ut−2,is assumed to be weakly exogenous for the cointegrating relations and is included in the long-run part of the system as a nonmodelled variable. For inference purposes, following the analysis in Harbo et al. (1998), we also add a restricted linear trend. Finally, two conditioning variables are taken from the conditional single equation model above: Dumtand ∆ut. The results from estimating the fifth-order VAR by OLS over the full sample 1971(2)– 1998(3) strongly indicate that the system is misspecified. The diagnostic tests reveal 17Centered seasonal dummies sum to zero over time and thus do not affect the asymptotic distributions of the tests for cointegrating rank. See Harris (1995). 32 significant non-normality and autocorrelation in the equation for px, and significant ARCH effects in the equation for ulc. The vector normality test has a p-value of zero. Moreover, inspection of the residuals reveals a large outlier in the equation for px in 1974(1), and the recursively estimated 1-step residuals indicate nonconstancies in the equation for ein 1986 and 1997. To mop up the outliers and induce constancy in the equations we use 5 impulse dummies: One to account for the increase in px following the oil crisis in 1973 (PX74q1), one to allow for the devaluation of the krone in May 1986 (E86q2) and three to account for the strong fluctuations in the exchange rate in 1997 (E97q1, E97q2,and E97q4).18 The F-statistic for the null hypothesis that the fifth lag of the variables is zero is F(16,226) = 1.1683 (with a p-value of 0.295) and indicates that it is statistically acceptable to simplify the system to a fourth-order VAR. Reducing the lag-order further induces residual misspesification. Estimation of a fourth-order VAR with the five impulse dummies entering yields a more satisfactory representation of the system. Table 7 reports the residual standard errors and misspesification tests for the four equations individually and for the system.19 The sample period is 1971(2)–1998(3). None of the tests are significant at the 5% level. Furthermore, the 1-step residuals shown in Figure 10 all lie within their respective ±2 standard error bands. Thus, there are no strong indications of residual misspecification or parameter nonconstancies. The fourth-order VAR will form the basis of the cointegration analysis in the next subsections. Table 7: Diagnostics for conditional fourth-order VAR 1971(2)–1998(3) Single equation tests V ariable pb e px ulc bσ0.023 0.013 0.008 0.023 AR 1−5F(5,76) 1.168 [0.150] 0.846 [0.521] 1.130 [0.352] 0.378 [0.863] Normality χ2(2) 3.565 [0.168] 2.598 [0.273] 0.234 [0.890] 0.152 [0.927] ARCH 4F(4,73) 1.703 [0.159] 0.549 [0.701] 1.119 [0.354] 2.107 [0.089] Hetero F(36,44) 0.945 [0.566] 0.494 [0.984] 0.650 [0.907] 0.806 [0.746] System tests V ector AR 1−5F(80,231) 1.213 [0.137] V ector normality χ2(2) 9.428 [0.308] V ector heteroscedasticity F(360,366) 0.605 [1.000] 18The dummies are defined as follows: P X74q1 = 1 in 1974(1), 0 otherwise, E86q2 = 1 in 1986(2), 0 otherwise, E97q1 = 1 in 1997(1), 0 otherwise, E97q2 = 1 in 1997(2), 0 otherwise. 19See Doornik and Hendry (1997) for details and references. 33 Figure 10: 1-step residuals ±2 standard errors for fourth-order VAR 1971(2)–1998(3) 1985 1990 1995 -.05 0 .05 1-stepresidualspb 1985 1990 1995 -.02 0 .02 1-stepresidualse 1985 1990 1995 -.02 -.01 0 .01 .02 1-stepresidualspx 1985 1990 1995 -.05 0 .05 1-stepresidualsulc 3.3.2 Determining cointegration rank The next step is to determine the dimension of the cointegrating space. Table 8 reports the results from applying the Johansen procedure to the fourth-order VAR. It shows the four eigenvalues, the trace-statistics and the asymptotic 5% critical values taken from Table 2 in Harbo et al. (1998). Note that since the VAR includes several impulse dummies and a non-modelled differenced variable as conditioning variables, the reported critical values are only indicative. The trace statistic strongly rejects the null hypothesis of no cointegration (r= 0) in favour of at least one cointegrating vector, whereas the null of at most one cointegrating vector (r≤1) is not rejected at the 5% level. On the basis of these tests, we conclude that there is a single cointegrating vector. Table 8 also reports estimates of the eigenvectors β0and the adjustment coefficients α. The β0 matrix is presented in normalised form, having one element of each row set equal to 1. Next, we test for the absence of the linear trend in the cointegrating relations. The test is a conventional likelihood ratio (LR) test. Imposing the restriction r= 1,the model is in I(0) space and the LR-statistic will be asymptotically distributed as χ2(1). The observed value of the statistic is χ2(1) = 7.129 with a p-value of 0.008.Thus, the null hypothesis is rejected at the 1% significance level and the linear trend is retained in the model. 34 Table 8: Multivariate cointegration analysis Eigenvalues 0.332 0.153 0.119 0.090 Cointegration test Null hypothesis Trace-statistic 5% critical value r= 0 86.92 71.7 r≤1 42.57 49.6 r≤2 24.34 30.5 r≤3 10.35 15.2 Normalised eigenvectors pb e px ulc ut−2trend 1.000 −1.147 −1.105 −0.196 0.049 0.004 −1.736 1.000 0.648 1.8314 0.276 −0.018 −0.646 1.449 1.000 −0.123 0.009 −0.004 1.079 −0.126 −2.132 1.000 0.135 −0.011 Adjustment coefficients pb −0.488 0.026 −0.044 −0.004 px 0.009 0.006 −0.122 −0.013 e−0.043 0.002 −0.046 0.013 ulc −0.128 −0.093 −0.031 −0.006 Normalising the estimated cointegrating vector on import prices we find: pb = +1.147 (0.137)e+ 1.105 (0.107)px + 0.196 (0.117)ulc −0.049 (0.017)u−2−0.004 (0.001)trend (3.10) with standard errors in parentheses. Giving a precise economic interpretation of the presence of a deterministic trend in the cointegrating vector is difficult. The trend coefficient is −0.004 which implies that in the long-run equilibrium (3.10) import prices decrease by 1.6% per annum after the influence of the other variables in the cointegrating vector is taken into account. The trend term might perhaps capture the effect of the continued growth in world trade and the increasing competition between producers in international markets. Table 9: Testing the significance of a given variable in the cointegrating vector Variables pb e px ulc u trend χ2(1)-statistic 16.369 11.700 15.97 1.981 6.151 7.129 p-value 0.000 0.001 0.000 0.159 0.013 0.008 Table 9 reports LR-tests for the significance of each variable in the cointegrating vector. Except for the unit labour cost variable, all the variables are strongly signifi- 35 cant. This confirms the results from the single equation analysis. Moreover, seeing that the estimated coefficient of unit labour costs is positive, all the coefficients have their expected signs. The long-run elasticities of exchange rates and foreign export prices are close to one, again confirming the estimates derived from the single equation model. The numerical value of the coefficient on the unemployment rate has dropped from 0.09 to 0.04,but the coefficient is still significant and indicates that domestic market conditions affect import prices even in the long run. The adjustment coefficients in αmeasure the feedback from disequilibrium in the long-run relationship onto the variables in the VAR. The vector of adjustment coefficients corresponding to (3.10) is given by b α0= [−0.489 (0.080),0.009 (0.045),−0.043 (0.029),−0.128 (0.084)] (3.11) where, specifically, −0.489 is the estimated adjustment coefficient for the import price equation. A coefficient of −0.489 implies a relatively rapid correction of disequilibria in the cointegrating vector. The estimated adjustment coefficient is larger than what we found in the single equation analysis. 3.3.3 Testing cointegration restrictions Having identified the single cointegration vector it is still of interest to test hypotheses on αand β. Testing for weak exogeneity of a given variable for the cointegrating vector amounts to testing whether the corresponding row of αis zero. Table 10 reports likelihood ratio statistics for tests of weak exogeneity. The hypothesis that individually and jointly, exchange rates, foreign export prices, and unit labour costs are weakly exogenous for the cointegrating vector is supported by the data. Moreover, weak exogeneity of import prices is strongly rejected. These results imply that the cointegrating vector enters only the equation for import prices, and that single equation estimation of the long-run parameters is efficient. However, since we have included a restricted deterministic trend in the multivariate cointegration analysis, the results obtained from the single equation and the system analysis are not directly comparable. Table 10: Weak exogeneity tests Variable pb e px ulc Joint test {px, e, ulc} χ2(1)-statistic 24.231** 0.035 2.230 1.872 χ2(3)-statistic 4.289 p-value 0.000 0.852 0.135 0.171 p-value 0.232 Table 11 reports statistics for tests of overidentifying restrictions on the cointegration vector. The hypotheses are formulated as restrictions on the equation pb =γe +δpx + κulc +λu +µtrend, and the degrees of freedom in the χ2-distributions is equal to the 36 number of independent restrictions to be tested.Not surprisingly, the hypothesis that domestic macroeconomic conditions do not affect import prices in the long-run (κ= λ= 0) is strongly rejected by the data. The hypothesis that the coefficients on foreign export prices and exchange rates are equal (γ=δ) is accepted, as is the hypothesis that these coefficients are both equal to 1 (γ=δ= 1). The statistic for testing the restriction of long-run unit homogeneity (γ=δand κ= 1−γ) has a p-value of zero and thus is not supported by the data. Note that, while data accepts that the long-run elasticities of the exchange rate and foreign export costs are equal to one, imposing this restriction joint with the hypothesis of long-run unit homogeneity (γ=δ= 1 and κ= 0) is rejected. This casts doubts on the reasonableness of the equilibrium-correction term in the final single equation model of import prices in the previous section. Table 11: Test of overidentifying restrictions on the cointegrating vector Hypothesis Statistic p-value H1:κ=λ= 0 χ2(2) = 18.393** 0.000 H2:γ=δ χ2(1) = 0.123 0.726 H3:γ=δ= 1 χ2(2) = 1.050 0.592 H4:γ=δand κ= 1 −γ χ2(2) = 15.453** 0.000 H5:γ=δ= 1 and κ= 0 χ2(3) = 16.284** 0.001 Finally, imposing weak exogeneity of e,px, and ulc jointly with the restriction that the coefficients on exchange rates and foreign export prices are equal to 1 we get χ2(5) = 5.49 with a p-value of 0.359. The estimated cointegrating vector is found to be pb =e+px + 0.298 (0.039)ulc −0.026 (0.014)u−2−0.004 (0.001)trend (3.12) and the corresponding estimate of the feedback coefficient is −0.501 with a standard error of 0.082. 3.4 Concluding remarks In this section we have presented results from an econometric analysis of Norwegian import prices of manufactures over the period 1970(1)–1998(3). The purpose was to investigate the robustness of the results in Naug and Nymoen (1996) who found evidence of a cointegrating relationship between import prices, the exchange rate, foreign export prices, and domestic unit labour costs in a similar study covering the period 1970(1)– 1991(4). In addition to the extension of the sample period, several factors may contribute to differences in the results. These factors include revisions in the data and differences in 37 the construction of the variables.20 It is well-known from the empirical literature on exchange rates and traded goods prices that the selection of data can significantly affect the analysis. Another difference occurs in the treatment of the unemployment rate in the cointegration analysis. While Naug and Nymoen (op cit) treat the unemployment rate as stationary, the evidence in this and other studies21 suggests that the transformed rate of unemployment rate behaves as if it were an I(1) variable. Based on an untested assumption of weak exogeneity, we therefore include the unemployment rate as a non-modelled variable in the long-run part of the VEqCM. Then, for the asymptotic distribution of the cointegration test statistics to be free of nuisance parameters, we also add a restricted deterministic trend to the model. After having determined the cointegrating rank, the significance test on the trend coefficient leads us to retain the trend in the cointegrating vector. The presence of a deterministic trend in the cointegrating vector is one important difference between the results in this study and those of Naug and Nymoen (op cit). The results from both the single equation and the system analysis lead us to conclude that there is a single cointegrating relationship between the variables in the model. This is consistent with the results in Naug and Nymoen (op cit), as is the significant effect of the unemployment rate in the long-run solution. The result that increases in domestic demand pressure lead to increases in import prices thus appears to be robust. What is not clear from the economic theory discussed in Section 2, however, is how this apparently robust effect should be interpreted in relation to the pricing to market hypothesis. The hypothesis that there are significant pricing to market effects in Norwegian import prices is not supported by the data in the present study. Both the single equation estimates and the estimates obtained using the Johansen procedure suggest that the long-run pass-through of changes in exchange rates and foreign export prices is complete, and this conclusion is not altered if the deterministic trend is dropped from the model prior to the cointegration analysis. However, the presence of a deterministic trend in the cointegrating vector and the fact that we fail to find a long run equilibrium with homogeneity indicate that there is scope for further modelling. 20In particular, we employ data for unit labour costs in manufacturing and construction, while Naug and Nymoen (1996) employ data for unit labour costs in manufacturing only. 21See Bjørnstad and Nymoen (1999). 38