J-Curve, Oil Price, House Price and US-Canada Imbalance

Transcription

1 J-Curve, Oil Price, House Price and US-Canada Imbalance Tim Leelahaphan February 29 (Second Draft) Abstract We find that real exchange rate, real oil price and real new housing price index have significant effects on US real trade balance with Canada in the long-run. We acquire evidence of short-run J-curve both within linear and non-linear framework with an overall effect of -.62 percent and -.22 percent following a 1 percent depreciation in regime one and regime two, respectively. We find that short-run dynamic effects of real oil price is not so fearful, with statistically significant effect of -.14 percent following a 1 percent real oil price increase in non-linear framework, but confined to the regime where imbalance correction is not found. While house price could be argued as being strongly relevant for settlement and adjustment of US trade balance in the long-run with an elastic coefficient of US real new housing price index, our empirical findings shed light on the meaning and validity of the wealth effects in the short-run. Moreover, the role of real exchange rate and real oil price are found to be confined to a single regime whereas real new housing price index pervades both regimes. We argue that exchange rate manipulation could help the US gain balance since the role of such variable pervades in the regime where persistent correction is presented. With the transition probability matrix showing that moving to regime presenting correction is more likely than the opposite, we reasonably believe that a (small) chance to correct US-Canada imbalance prevails. However, our analysis argues that current asset (housing) price bubble reflation would not help improving US trade deficit (with Canada in particular) over the long-run. Furthermore, our results indicate that the medium-term out-of-sample forecastability is not much improved by real oil price and real asset price variables, which nonetheless actively explain in-sample movement of US real trade balance with Canada. JEL Classification: F4 Keywords: adjustment, asset price, bilateral trade, Canada, cointegration, correction, dynamic relationship, exchange rate, forecasting, global imbalance, international trade, J-curve, linear framework, long-run, Markov-switching, new housing price index, non-linear framework, oil price, out-of-sample, persistency, regime, short-run, trade balance, trade partner, transition probability matrix, the US, vector errorcorrection model, wealth effects Contact information: The Department of Economics, The University of Warwick, Coventry, CV4 7AL, United Kingdom; T.Leelahaphan@warwick.ac.uk. This draft is for Econometrics Workshop, The Department of Economics, The University of Warwick and to be submitted to Canadian Economics Association conference. 1

2 1 Introduction A massive US balance of trade deficit always highlights global imbalances. Figures released by the US Commerce Department in January 29 show that, as the economic slowdown led to lower demand for imports, the US trade deficit dropped to its lowest level in more than five years in November 28. In particular, the trade deficit shrank 28.7 percent from October 28 to 4.4 billion US dollars. Currently, economists have not reached consensus on the direction of US trade balance. Some believe that the US trade deficit is set to shrink while some claim that the US economy can continue to have enormous trade deficits for years or decades. Nevertheless, despite recent improvements, US trade deficit remains high priority and is one of the most striking features of the current global economy. For most economists, this is also one of the most worrying features. Over the past several years, three developments have been of international macroeconomists interest, besides the fall of the US dollar. First, large global external imbalances have persisted. These include a massive balance of trade deficit in the US. The aggregate US trade deficit has worsened significantly over the past seven years. The deficit as a share of GDP climbed over 6 percent in December 25 for the first time on record and settled at 5.1 percent for December 27. This is a significant increase since March 21, when the deficit accounted for 3.9 percent of GDP. It is also a larger deficit level than any point prior to March 24. Second, energy prices have risen sharply since 23. This is driven both by strengthening global demand and, most recently, by concerns about future supply. With limited excess capacity, the supply-demand balance in medium-term is expected to remain very tight. Oil prices would be expected to persist at high levels. And third, for many of the OECD countries, real housing prices have shown a rapid increase since the mid-199s. Table 1 shows these. 1 2 Motivation We are motivated by following arguments and findings regarding (i) trade between the US and Canada (ii) J-curve effects and global imbalance, (iii) oil price and global imbalance and (iv) asset price and global imbalance. These are explained in the followings. Firstly, we are motivated by the fact that the US and Canada conduct the world s largest 1 Sources are Bureau of Economic Analysis, IMF International Financial Statistics and Bureau of the Census, the US Department of Commerce. 2

3 Table 1: (a) US International Balance of Trade in Goods and Services (Percent of GDP), (b) Texas Spot Oil Price (US Dollar per Barrel) and (c) US Real New Housing Price Index Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan-6 (a) (b) (c) bilateral trade relationship, with the North American Free Trade Agreement implemented in In addition, Canada is the US s first-ranked trading partner, not China (the second-ranked). For the month of November 28, this accounts for billions of US dollar. For year to date, this is billions of US dollar. With China, this is 33.5 billions of US dollar in November 28. For year to date, this is billions of US dollar. The values given are for imports and exports added together. Table 2 shows this. 3 In 28, Canada represents percent of US imports and 2.24 percent of US exports in goods. In addition, Canada s main trading partner is the US. In particular, trading with the US accounts for roughly three-quarters of trade and the majority of capital moving in and out of Canada. From these facts provided which motivate us for an analysis emphasizing on the international trade between these two closely linked countries, we believe that international trade between the US and Canada is a very good bilateral trade case study due to the fact that they are the biggest trade partner of each other. 4 We are also motivated by the fact that Canada is the top source of US crude oil imports (2.55 million barrels per day for October 28) and by the continuing US trade imbalance with Canada, despite the weak US dollar. 5 See Table 3 and This is with total merchandise trade (imports and exports added together) exceeding billion US dollar in 26. See Fergusson [28]. 3 Sources are and 4 Note that empirical research on balance of trade could be usefully classified into two groups. The first one, on the one hand, is domestic and rest-of-the-world framework. A second group of research, on the other hand, focuses on trade between two partners only. Our analysis falls into the second group of research and also well represent the first group, due to the fact that they are the biggest trade partner of each other. 5 Canada is the only G7 country that is running current account (and government balance) surpluses these days. This might be due to the fact that Canada s overall trade balance has benefited from soaring global crude oil prices. 6 Source are Energy Information Administration, Official Energy Statistics from the US Government and US Census Bureau, Foreign Trade Division. 3

4 Table 2: Top Five Countries with which the US Trades, for the Month of November 28 Country name Total in Total in billions of US dollar billions of US dollar, Year to date Canada China Mexico Japan Federal Republic of Germany Table 3: US Crude Oil Imports Top Five Countries (Thousand Barrels per Day) Country 8-Oct 8-Sep YTD 28 7-Oct YTD 27 Canada 2,55 1,923 1,91 1,898 1,894 Saudi Arabia 1,427 1,429 1,519 1,37 1,416 Mexico 1, ,18 1,322 1,419 Venezuela 1, ,37 1,221 1,131 Nigeria ,184 1,55 Secondly, J-curve effects, worsening trade balance measured in local currency in response to exchange rate depreciation in the impact period, are believed to be able to produce a temporary increase in the nominal balance of trade deficit. This could help explain the fact that US current account imbalance has stayed rigidly high despite the decline in US dollar. 7,8 Thirdly, we are motivated by the argument that some of global imbalances have been exacerbated by higher energy prices. Clearly, in fuel importers, the rise in world oil prices worsens the trade balance. 9 In particular, the increase in oil prices since 23 has directly worsened the US current account deficit by over 1 percent of GDP. Fourthly, recent studies have started showing the link between asset price and the trade balance. This is essentially through wealth effects. In particular, an increase in asset prices, especially when it is expected to be permanent, raises expected household income and, hence, consumption. In 7 That is, the Marshall-Lerner condition, improving trade balance following a devaluation, is not met. 8 Note that current account is comprised of (i) merchandise trade balance, (ii) service trade balance and (iii) income balance. Following Kilian et al. [27], the trade balance should be recognized to refer to the merchandise trade balance. In fact, the trade in services is not included in trade balance. This is due to data availability and concerns about the poor quality of service trade data. In addition, the income balance, which is generally computed as the difference between the current account and trade balance, is excluded. This is due to the fact that it is difficult to interpret the income balance, without further knowledge of the country s asset position and that it could not be calculated accurately. For example, even when service trade data are available, the income balance could not be separated from transfer payments. Therefore, the merchandise trade balance in our analysis could reasonably stand for the current account. 9 Note that we focus on trade balance (not oil or non-oil trade balance). This is due to data availability, between the US and Canada. Also, we emphasize that our objective is to examine if oil price could be claimed as a major source of US-Canada (trade) imbalance. 4

5 Table 4: Continuing US Trade Imbalance with Canada (Millions of US Dollar) and US Dollars to One Canadian Dollar. -1,. -2,. -3,. -4,. -5,. -6,. -7,. -8,. -9, addition, this situation helps firms to finance opportunities for investment easily. Consequently, it causes a deterioration in a country s trade balance. Fratzscher et al. [28] show that falls in US asset prices such as housing and equities have a substantially more important role for reducing US trade imbalances, accounting for up to 35 percent of the movements of the US trade balance, than changes in the US dollar exchange rate, over the period Lastly, we are motivated by the lack of research on non-linear balance of trade. In particular, most of international trade studies (on J-curve effects in particular) have been carried out using linear vector error-correction models, assuming that macroeconomic variables examined have stable behavior. Nevertheless, it is clear and reasonable to believe that the balance of trade is likely to differ across the business cycle. In export led growth (such as oil and early industrial countries), the balance of trade would improve during an economic expansion. However, with domestic demand led growth (as in the US and Australia), the trade balance would worsen at the same stage in the business cycle. 1 Inspired by research on business cycle, we believe that linear models might not be able to explain well its behavior and, consequently, we might need to use non-linear models to cope with such behavior For the US, clear evidence is that US trade deficit dropped to its lowest level in more than five years in November 28 as the economic slowdown led to lower demand for imports. 11 See Clements and Krolzig [22] and Clements and Krolzig [24]. 5

6 3 Questions We Ask Motivated by arguments and findings set out in the previous section where we justify why exchange rate, oil price and asset price may be an important (additional) control in empirical trade balance equation, we would like to empirically examine, both within linear and non-linear framework, following questions. These are (i) if evidence of a short-run J-curve effects prevails for the US and Canada, (ii) if oil price could be claimed as a major source of global imbalances, US-Canada imbalance in particular and (iii) if asset price, house price in particular, undoubtedly explains the movements of the US trade balance as recent evidence shows. Our novel features include the use of non-linear model in the balance of trade analysis and the use of interesting variables recently claimed as sources of the US trade deficit to augment traditional functional relationship for the trade balance having only domestic income, trading partner s income and real bilateral exchange rate as explanatory variables. 12 To empirically explore the dynamic relationship between US real trade balance with Canada and real exchange rate, real oil price and real new housing price index and its adjustment, both in the short- and long-run, we use cointegration analysis and a linear and non-linear vector errorcorrection model with monthly data for January 1985 to May 25. In addition, we would like to evaluate our oil price and asset price-augmented model by performing simple forecasting exercise, comparing to forecastability of the traditional functional relationship for the trade balance. We would like to make an implication about global imbalance at the end of the chapter. We find that real exchange rate, real oil price and real new housing price index have significant effects on US real trade balance with Canada in the long-run. We acquire evidence of short-run J-curve both within linear and non-linear framework with an overall effect of -.62 percent and -.22 percent following a 1 percent depreciation in regime one and regime two, respectively. We find that short-run dynamic effects of real oil price is not so fearful, with statistically significant effect of -.14 percent following a 1 percent real oil price increase in non-linear framework, but confined to the regime where imbalance correction is not found. While house price could be argued as being strongly relevant for settlement and adjustment of US trade balance in the long-run with an elastic coefficient of US real new housing price index, our empirical findings shed light on the meaning 12 No one to date has formally examined the (traditional) functional relationship for the trade balance within non-linear framework, except Moura and Silva [25]. 6

7 and validity of the wealth effects in the short-run. Moreover, the role of real exchange rate and real oil price are found to be confined to a single regime whereas real new housing price index pervades both regimes. We argue that exchange rate manipulation could help the US gain balance since the role of such variable pervades in the regime where persistent correction is presented. With the transition probability matrix showing that moving to regime presenting correction is more likely than the opposite, we reasonably believe that a (small) chance to correct US-Canada imbalance prevails. However, our analysis argues that current asset (housing) price bubble reflation would not help improving US trade deficit (with Canada in particular) over the long-run. Furthermore, our results indicate that the medium-term out-of-sample forecastability is not much improved by real oil price and real asset price variables, which nonetheless actively explain in-sample movement of US real trade balance with Canada. The remainder of the chapter is set out as follows. In the following Section 4, we describe the methodology including variables of interest, cointegration analysis and linear vector errorcorrection model and non-linear vector error-correction model. In Section 5, we describe the data and report the estimation results including results from cointegration analysis, results from linear model and results from non-linear model. This is with a discussion. In Section 6, we perform forecasting exercise. We make some concluding comments in Section 7. 4 Methodology We divide this section into three subsections. These are (i) variables of interest, (ii) cointegration analysis and linear vector error-correction model and (iii) non-linear vector error-correction model. 4.1 Variables of Interest The selection of variables is usually based on economic theory and considerations. This also requires good judgment and sound intuitive analysis. For our analysis, chosen variables are mainly based on existing literatures, country specific and motivation set out in the Motivation section. In order to make our analysis consistent with literature, we start with a traditional functional relationship for the trade balance. Following Bahmani-Oskooee and Artatrana [24a], the tradi- 7

8 tional functional relationship for the trade balance is Real T rade Balance = f(domestic income, T rading partner s income, Real bilateral exchange rate). (1) We then introduce oil price and asset price to our analysis due to discussion in the Motivation section. We call our specification the oil price and asset price-augmented trade balance equation. Hence, variables are (i) US real trade balance with Canada, (ii) US real industrial production, (iii) Canada real industrial production, (iv) US (domestic) dollar real exchange rate relative to Canadian (foreign) dollar, (v) real oil price, (vi) US real new housing price index and (vii) Canada real new housing price index. Note that such variables are chosen for our analysis; however, variables are not necessarily limited to these. 13 Our functional relationship for the oil price and asset price-augmented trade balance is Real T rade Balance = f(us income, Canada income, Real exchange rate, Real oil price, US real new housing price index, Canada real new housing price index). (2) For US real trade balance with Canada, we follow Moura and Silva [25]. In particular, we take the export-import ratio to represent trade balance. This is common in literature. The advantage of doing so is to allow us to take logarithms of trade balance and, hence, to get growth rates (see Brada et al. [1997]). With the export-import ratio, remaining constant when measurement units change is another gain. In addition, the export-import ratio is able to serve as either nominal or real trade balance (see Bahmani-Oskooee and Tatchawan [21]). Alternatively, with the difference between exports and imports to represent trade balance, a deflator is needed in order to acquire real trade balance. However, this measurement is sensitive to different deflators. The US real trade balance with Canada (RTB) is 13 Variables that we have tried putting in our specification are (i) US real trade balance with Canada, (ii) US (domestic) dollar real exchange rate relative to the Canadian (foreign) dollar, (iii) real oil price, (iv) US real new housing price index, (v) Canada real new housing price index, (vi) US real industrial production, (vii) Canada real industrial production, (viii) difference of US and Canada real new housing price index and (ix) difference of US and Canada real industrial production. (i), (ii) and (iii) have to be in the specification, and choose between (iv) OR (iv) with (v) OR (viii), and choose between (vi) with (vii) OR (ix). 8

9 ( ) Export RT B t = ln (Export import ratio) t = ln = ln (Export) Import t ln (Import) t. (3) t For US and Canada real GDP (USRY and CNRY ), we use industrial production and consumer price index. That is ( ) US industrial production USRY t = ln (Real US industrial production) t = ln US CP I t (4) and ( ) Canada industrial production CNRY t = ln (Real Canada industrial production) t = ln. Canada CP I t (5) For US dollar real exchange rate relative to Canadian dollar, we use (domestic) US dollar unit to (foreign) Canadian dollar exchange rate, US consumer price index and Canada consumer price index. US dollar real exchange rate relative to Canadian dollar (RER) in our context is defined as the natural logarithm of (domestic) US dollars to one (foreign) Canadian dollar real exchange rate. Hence, a decrease (increase) in exchange rates corresponds to an appreciation (depreciation) of (domestic) US dollar against (foreign) Canadian dollar. We write RER t = ln (US dollars per Canadian dollar) t + ln (Canada CP I) t ln (US CP I) t. (6) For real oil price, we use price of West Texas intermediate crude in dollars per barrel. We use US consumer price index as the deflator to derive the real oil price (ROP). That is ROP t = ln (Oil price) t ln (US CP I) t. (7) For US and Canada real new housing price index (USRHPI and CNRHPI ), we use the US price index of new one-family houses under construction, Canada new housing price index and 9

10 consumer price index. That is USRHP I t = ln (Real US new housing price index) t = ( ) US price index of new one family houses under construction = ln US CP I t (8) and CNRHP I t = ln (Real Canada new housing price index) t = ( ) Canada new housing price index = ln Canada CP I. t (9) 4.2 Cointegration Analysis and Linear Vector Error-Correction Model To examine the dynamic relationship between US real trade balance with Canada and real exchange rate, real oil price and real new housing price recently believed to have impact on the US trade balance, both in the short- and long-run, we perform multivariate cointegration analysis and linear vector error-correction model. Cointegration tests look for linear combinations of I(d) non-stationary time series that are stationary. Such stationary combination is called the cointegrating equation. This might be interpreted as a long-run equilibrium relationship between the variables (see Engle and Granger [1987]). For our analysis, this might be written as RT B t = β +β 1 RER t +β 2 ROP t +β 3 USRHP I t +β 4 CNRHP I t +β 5 USRY t +β 6 CNRY t +u t, (1) where u t is the random error term. Each cointegrating coefficient, β i, shows the percentage change in US real trade balance with Canada for one unit percentage change in each of the explanatory variables in the long-run. The coefficients of these variables should enter with a sign according to the channels discussed in the Motivation section. That is, we expect that β 1 > for real exchange rate depreciation to improve real trade balance. This also satisfies the Marshall-Lerner condition. In particular, as a 1

11 devaluation of the exchange rate means a reduction on price of exports, quantity demanded for these will increase. At the same time, price of imports will rise and their quantity demanded will diminish. The net effect on the trade balance will depend on price elasticities. If goods exported are elastic to price, their quantity demanded will increase proportionately more than the decrease in price, and total export revenue will increase. Similarly, if goods imported are elastic, total import expenditure will decrease. Both will improve the trade balance. 14 With no doubt, β 2 is expected to be negative due to the fact that, in fuel importers, the rise in world oil prices worsens the trade balance and that Canada is the top source of US crude oil imports. Attributed to the wealth effects presented in the Motivation section, we expect that β 3 < and β 4 >. Following existing literature, we do not have priori expectations for β 5 and β 6. Coefficients of these two variables are purely empirical. 15 To find the number and estimation of cointegrating relations, we employ the Johansen [1988] and Johansen and Juselius [199] maximum likelihood procedure applied to a vector autoregressive (VAR) model, assuming that the errors are Gaussian. This is based on a pth-order structural and dynamic VAR model on the variables under consideration. In keeping with Granger representation theorem, this can be written as an unrestricted vector error-correction model (VECM) involving up to p lags represented in the following form x t = µ + p Γ i x t i + Πx t 1 + ξ t, (11) i=1 where is the first difference operator and x t = [RT B, RER, ROP, USRHP I, CNRHP I, USRY, CNRY ]. µ is the constant term and Γ i is the vector of coefficients of lagged variables in first difference dynamic terms to be estimated. Π contains the information on the speed-of-adjustment coefficient (α) to long-run equilibrium and the vector of cointegrating coefficients (β). That is, Π = αβ. ξ t is a purely white noise term. 14 Empirically, it has been found that goods tend to be inelastic in the short term, as it takes time to change consuming patterns. Thus, the Marshall-Lerner condition is not met, and a devaluation is likely to worsen the trade balance initially. In the long term, consumers will adjust to the new prices, and trade balance will improve. This effect is called J-curve effect. 15 It should be expected that β 5 < since an increase in US real GDP usually leads to an increase in imports from Canada. However, it would also be possible that β 5 > if an increase in US real GDP is attributed to an increase in the import substitute goods production, leading to less imports from Canada as economy grows. Hence, depending on the magnitude of demand side factors and supply side factors, β 5 could be either negative or positive. This argument also applies to β 6. 11

12 We explain the practical procedure for the cointegration analysis and the linear vector errorcorrection model estimation. Firstly, we consider whether each of seven time series of interest (US real trade balance with Canada, US dollar real exchange rate relative to Canadian dollar, real oil price, US real new housing price index, Canada real new housing price index, US real GDP and Canada real GDP) is integrated, that is, the order of difference before stationarity is achieved, of the same order. In particular, we test for unit roots to examine the stationary properties of the data. To do this, we consider the standard Augmented Dickey-Fuller (ADF) test. Secondly, we use the lag selection criterion as leading indicator for choosing the robust and stable cointegration test specification. To search for the number of multivariate cointegrating relationships, we use the Johansen [1988] and Johansen and Juselius [199] procedure. The cointegration rank, r, is the set from zero to k 1, where k = 7 is the number of endogenous variables. r is then determined with the trace and maximum eigenvalue test. The trace statistic, λ trace, tests the hypothesis that there are at most r cointegrating vectors. The maximum eigenvalue statistic, λ max, tests that there are r cointegrating vectors against the alternative that r +1 exists. The asymptotic critical values are given in Johansen and Juselius [199] and MacKinnon et al. [1999]. The form of test statistics are k LR tr (r k) = T log (1 λ i ) (12) i=r+1 where λ i is the i-th largest eigenvalue of the Π matrix and LR max (r r + 1) = T log (1 λ r+1 ) = LR tr (r k) LR tr (r + 1 k), (13) for r =, 1,... k 1. Note that lag selection for cointegration test specification will also be used in the vector autoregressive (VAR) in first difference part when estimating the vector errorcorrection mechanism. This is in order to acquire the same long-run (error-correction mechanism) relationship. Thirdly, we specify the long-run relationship between US real trade balance with Canada and the other six variables. In particular, this is the normalized cointegrating relationship estimated. Finally, we estimate the vector error-correction model by the Johansen procedure and examine the estimated coefficients of lagged variables in first difference dynamic terms in Γ i and the coefficient estimate of the error-correction term, that is, the adjustment parameter, α. 12

13 4.3 Non-Linear Vector Error-Correction Model We perform non-linear model due to the motivation set out in the Motivation section. This is in order to investigate the regime changes of our six variables and US real trade balance with Canada and to tackle the cyclical pattern in the time series. A cointegrated VAR(p) with M Markovian regimes model is dubbed MS(M )-VECM(p). This is the model we employ in particular. Generally, an MS-VECM model is a vector error (equilibrium)-correction model with shifts in the drift v (s t ) and in the long-run equilibrium µ (s t ). Note that the linear VECM(p) collapses to the particular case where M = 1. We write an MS-VECM as p x t µ (s t ) = α (s t ) βx t 1 + v (s t ) + A (s t ) k ( x t k µ (s t k )) + u t (14) and the innovations u t are conditionally Gaussian, u t s t NID(, (s t )). The (autoregressive) parameters are time-varying and also depend upon changes in a stochastic, unobservable regime variable, s t {1,... M}. This is with finite number of states. The stochastic process for generating changes in the unobservable regimes is an ergodic Markov chain defined by the transition probabilities k=1 p ij = Pr (s t+1 = j s t = i), M p ij = 1 i, j {1,... M}. (15) j=1 where p im = 1 p i1... p im 1 for i = 1,... M. By inferring the probabilities of the unobserved regimes conditional on an available information set, it is then possible to reconstruct the regimes, Krolzig [1993]. The important issue is how to perceive the proper number of regimes in and specification of an MS-VECM. Nevertheless, this could not be found directly. With the presence of nuisance parameters, the likelihood ratio could not be served as a criterion, turning out to be with no asymptotic distribution. With such situations, Hansen [1992] and Garcia [1998] have developed an approach to acquire the asymptotic distribution. Nevertheless, with practical purposes, this might not be useful since the distribution depends on both data and parameters of the model. As a result, every time performing a test, we need to acquire asymptotic distribution (see Krolzig [1993]). However, common in literature, both Akaike information criterion (AIC) and Schwarz criterion (SC) are believed to well serve as criteria, not underestimating the minimum number of 13

14 regimes to be examined in an MS-VECM (see Ryden [1995]). Therefore, we would use such criteria for our analysis. 5 Data and Results We divide this section into four subsections. These are (i) data, (ii) results from cointegration analysis, (iii) results from linear model and (iv) results from non-linear model. 5.1 Data As in section 4, variables are (i) US real trade balance with Canada, (ii) US real GDP, (iii) Canada real GDP, (iv) US dollar real exchange rate relative to Canadian dollar, (v) real oil price, (vi) US real new housing price index and (vii) Canada real new housing price index. Our data set is from January 1985 to May 28 (281 observations). Table 5 shows plots of these variables of interest, transformed as set out in Variables of Interest subsection, in level and in first difference. For US real trade balance with Canada, monthly US nominal trade balance (with Canada) data in millions of US dollars is from US Census Bureau, Foreign Trade Division. For US and Canada real GDP, we use monthly US industrial production, monthly Canada industrial production, monthly US consumer price index and monthly Canada consumer price index data from IMF International Financial Statistics. Note that they are in the same unit, price index, 2=1. For US dollar real exchange rate relative to Canadian dollar, monthly US dollar unit to Canadian dollar average exchange rate, monthly US consumer price index and monthly Canada consumer price index data are from IMF International Financial Statistics. Note that US consumer price index and Canada consumer price index are in the same unit, index, where 2=1. For real oil price, the monthly current price of West Texas intermediate crude in dollars per barrel, not seasonally adjusted, is from IMF International Financial Statistics. For deflator, we use monthly US consumer price index. Note that for US consumer price index, 2=1. 14

15 Table 5: Plots of Variables of Interest in Level (Blue) and in First Difference (Red) Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan-6 (RTB) (RER) Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan-6 (ROP) (USRHPI ) Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan-6 (CNRHPI ) (USRY ) Jan-85 Jan-88 Jan-91 Jan-94 Jan-97 Jan- Jan-3 Jan (CNRY ) 15

16 Table 6: Results from Augmented Dickey-Fuller (ADF) Test Variables Prob. Variables Prob. RTB.499 RT B.* RER.8896 RER.* ROP.752 ROP.* USRHPI.9986 USRHP I.* CNRHPI.7926 CNRHP I.4* USRY.8174 USRY.* CNRY.761 CNRY.* For US and Canada real new housing price index, the monthly US price index of new onefamily houses under construction and Canada new housing price index, not seasonally adjusted, are from Bureau of the Census, the US Department of Commerce and Cansim - Statistics Canada, respectively. Note that both of them are in the same unit, price index. Note also that from the original data set where 25=1 for the US price index of new one-family houses under construction and 1997=1 for Canada new housing price index, we construct time series of interest where 2=1. Note that, in estimating the model, we use data from January 1985 to May 25 (245 observations). The last 3-year observations (36 observations) are kept for forecasting exercise. 5.2 Results from Cointegration Analysis We analyze the stationarity in our seven variables, US real trade balance with Canada, US real GDP, Canada real GDP, US dollar real exchange rate relative to Canadian dollar, real oil price, US real new housing price index and Canada real new housing price index. This is from January 1985 to May 25. We use Augmented Dickey-Fuller (ADF) test, with trend and intercept. The maximum lag length for Schwarz Information Criterion is 15. The results are shown in Table 6 reporting Augmented Dickey-Fuller (ADF) test statistic with the unit root null hypothesis and MacKinnon [1996] one-sided p-values. We find that our seven variables have a unit root or, alternatively, are integrated of order one, I (1), at 1 percent significance level. We analyze cointegration among our seven variables. This is from January 1985 to May 25. We use Johansen cointegration test. We choose the cointegration test specification with 5 lags (1 to 2 and 4 to 5). 16 Moreover, we include intercept and trend in CE - no trend in VAR. The results 16 The lag length selection criteria we use for this specification are sequential modified LR test statistic (each test at 5 percent level), final prediction error and Akaike information criterion, selecting three lag order. Nevertheless, we choose 16

17 Table 7: Results from Johansen Cointegration Analysis No. hypothesized CEs Trace Max-eigen Trace Max-eigen Trace Max-eigen statistic statistic 5 percent 5 percent prob. prob. critical value critical value None *.13* At most *.2141 At most At most At most At most At most Table 8: The Estimated Cointegrating Vector (β) on US Real Trade Balance with Canada Cointegrating vector, ˆβ RTB RER ROP USRHPI CNRHPI USRY CNRY t ˆβ *.12439* * * (s.e.) (-) (.24974) (.5133) (.5574) (.23151) (.36327) (.4872) (.22) with MacKinnon et al. [1999] p-values are presented in Table 7. The results from the Trace and Maximum Eigenvalue statistics suggest (rank) r is strongly rejected but r 1 is not rejected (for Maximum Eigenvalue statistics) at 5 percent significance level. Therefore, we conclude that there is one cointegrating equation at the 5 percent significance level. 5.3 Results from Linear Model We provide results from the linear model and make an analysis. Table 8 reports the estimated cointegrating vector, β, normalized cointegrating coefficients, on US real trade balance with Canada. From results in Table 8, we can write our cointegrating relationship as RT B t = RER t.12rop t 1.36USRHP I t +.63CNRHP I t.1usry +.55CNRY. (16) We check whether all the coefficients of the variables of interest are correctly sign. Note that US dollar real exchange rate relative to Canadian dollar is natural logarithm of (domestic) US dollars to one (foreign) Canadian dollar real exchange rate. That is, a decrease (increase) in exchange rates corresponds to an appreciation (depreciation) of (domestic) US dollar against (foreign) Canadian the specification with 5 lags due to sound economic intuition acquired. 17

18 dollar. A 1 percent depreciation of US dollar real exchange rate relative to Canadian dollar will lead to a.49 percent increase of the US real trade balance with Canada in the long-run, with the t-statistic of This implies that the Marshall-Lerner condition for a currency devaluation to have a positive impact on trade balance holds in the long-run. A 1 percent increase in real oil price will lead to a.12 percent decrease of US real trade balance with Canada in the long-run. The estimate of this coefficient is statistically significant with the t-statistic of For real new housing price index, supporting the wealth effects discussed in the Introduction, results are of our interest and noteworthy. A 1 percent increase in US real new housing price index deteriorates US real trade balance with Canada beyond 1 percent in the long run. In addition, US real trade balance with Canada improves, in the long run,.63 percent with a 1 percent increase in Canada real new housing price index. The estimates of these two countries real new housing price index coefficients are statistically significant with the t-statistic of -2.7 and 2.7, respectively. For US and Canada real GDP, without the priori expectations for signs as discussed in the Cointegration Analysis and Linear Vector Error-Correction Model subsection, the estimates show that an increase in US real GDP leads to a rise of imports from its trading partner, Canada. However, these estimated real GDP coefficients of US and Canada are NOT statistically significant, with the t-statistic of -.3 and 1.15, respectively. Comparing among these six variables of interest, we believe that all variables, but US and Canada real GDP, significantly explain the long-run dynamics of US real trade balance with Canada. Noticeably, real new housing price index, US one in particular, could be argued as being strongly relevant for settlement and adjustment of US trade balance in the long-run. The meaning and validity of the wealth effects are strongly supported in the long-run. We now analyze the short-run dynamics of US real trade balance with Canada. The existence of at least one cointegrating vector among seven variables considered implies that a vector errorcorrection model can be estimated to investigate the short-run relationship. We estimate the vector error-correction model. The specification capturing the short-run dynamics with 5 lags (1 to 2 and 4 to 5) is exactly the same as one for Johansen cointegration test. Note that we include intercept and trend in CE - no trend in VAR. Looking at the system, we find that US real trade balance with Canada shows an adjustment due to the statistically significant 18

19 Table 9: Estimates from the Vector Error-Correction Model for One Cointegrating Vector Dependent Adjustment Constant Lagged variables in first difference dynamic terms variable coefficient, ˆα term RT B *.824 (s.e.) (.5639) (.316) RT B t 1 RT B t 2 RT B t 4 RT B t * * (.766) (.6767) (.6333) (.619) RER t 1 RER t 2 RER t 4 RER t * (.2613) (.27193) (.265) (.26724) ROP t 1 ROP t 2 ROP t 4 ROP t * (.4161) (.4) (.4185) (.481) USRHP I t 1 USRHP I t 2 USRHP I t 4 USRHP I t (.72715) (.7165) (.73482) (.7331) CNRHP I t 1 CNRHP I t 2 CNRHP I t 4 CNRHP I t * * (.6776) (.64834) (.66924) (.64835) USRY t 1 USRY t 2 USRY t 4 USRY t (.6569) (.63659) (.65493) (.6373) Note: The value of R 2 is CNRY t 1 CNRY t 2 CNRY t 4 CNRY t * * (.51291) (.5182) (.51323) (.51374) estimate of the error-correction term coefficient, with the t-statistic of Table 9 reports the error-correction model estimates (the lagged variables in first difference dynamic terms) for one cointegrating vector and standard errors. From results in Table 9, we find that past values of US dollar real exchange rate relative to Canadian dollar at lag 2, real oil price at lag 5, Canada, not US, real new housing price index at lag 2 and 4 and Canada real GDP at lag 2 and 4 statistically significantly explain the movement of US 17 This empirical evidence could be taken as a reason why we emphasize our analysis only on US real trade balance with Canada, not US dollar real exchange rate relative to Canadian dollar which might also be of interest. In particular, the estimate of the error-correction term coefficient (-.2) is not statistically significant at 5 percent significance level, with the t-statistic of

20 real trade balance with Canada in the short-run. This is with the t-statistics of -2.8, 2.28, -2.79, 2.4, 1.99 and -2.66, respectively. The magnitude of.57 for lagged US dollar real exchange rate relative to Canadian dollar in first difference, of.9 for lagged real oil price in first difference and of 1.81 and 1.36 for lagged Canada real new housing price index in first difference are noteworthy. We would like to make an argument that results from our linear vector error-correction model show the evidence of the J-curve effect where, in response to exchange rate depreciation, the trade balance measured in (local) US dollar worsens in the impact period. This effect could, therefore, be thought of as a short-run departure from Marshall-Lerner condition discussed above. This is due to the fact that the coefficient estimate of the significant past value (in first difference) of US dollar real exchange rate relative to Canadian dollar is negative, with the magnitude of.57 as reported earlier. And note that, in our context where US dollar real exchange rate relative to Canadian dollar is defined as the natural logarithm of (domestic) US dollars to one (foreign) Canadian dollar real exchange rate, an increase in exchange rates corresponds to a depreciation of (domestic) US dollar against (foreign) Canadian dollar. The impulse-response function is a convenient way of showing an estimate of a variable coefficient of a VAR model. In our context, it is particularly useful to capture the short-run dynamics of the response of US real trade balance with Canada to interested variables shocks. Table 1 shows response of US real trade balance with Canada to innovations of one standard deviation in US dollar real exchange rate with Canadian dollar, real oil price, US real new housing price index and Canada real new housing price index. We see that US real trade balance with Canada decreases in the aftermath of a shock to US dollar real exchange rate relative to Canadian dollar, real oil price and US real new housing price index. Note the fourth month. For US dollar real exchange rate relative to Canadian dollar, from accumulated figure, the minimum occurs after nearly five months. Therefore, we argue that the impulse-response function shows the evidence of the J-curve effect in this linear vector errorcorrection model. Afterwards, the Marshall-Lerner condition holds. This is due to the fact that the temporary negative impact of US dollar real exchange rate with Canadian dollar shock to US real trade balance with Canada is believed to be fully faded away after eight months have vanished from the accumulated figure. We also note the immediate negative response of US real trade balance with Canada to US real new housing price index shocks. 2

21 Table 1: The Response of US Real Trade Balance with Canada to Shocks (RER Shocks, Not Accumulated) (RER Shocks, Accumulated) (ROP Shocks, Not Accumulated) (ROP Shocks, Accumulated) (USRHPI Shocks, Not Accumulated) (USRHPI Shocks, Accumulated) (CNRHPI Shocks, Not Accumulated) (CNRHPI Shocks, Accumulated) 21

22 The estimate of the error-correction term coefficient (-.14) is statistically significant, with the t-statistic of as reported earlier. This is with the appropriate (negative) sign indicating existence of long-run relationship. Short-run US real trade imbalance with Canada is monthly corrected at a rate of 14 percent. We assess the performance of our linear model, performing the presence of serial correlation test and heteroskedasticity test. 18 The model does not have autocorrelations but problem of heteroskedasticity. This might be due to very long period of data analyzed. 5.4 Results from Non-Linear Model We estimate the non-linear model. Since we are interested to see whether our six variables of interest have a different effect on US real trade balance with Canada in separate regimes, we should estimate only models that allow for regime-dependent parameters. Hence, we choose the specification from the two specifications namely MSIA(2)-VECM(5) and MSIAH(2)-VECM(5). Both specifications are with regime-dependent intercept term and with regime-dependent (autoregressive) parameters. 19 The first specification is homoskedasticity. The second one is heteroskedasticity. A regime-dependent covariance structure of the process might be considered as additional feature (Krolzig [1998]). We are interested only in 2-regime specification. This is due to the fact that following results show that duration is very short. Hence, it might not be reasonable to increase the number of regimes. In addition, we use the same lag length as one in the linear model (1 to 2 and 4 to 5). This is for dynamic comparison reason. We estimate both specifications and report results from both AIC and SC criteria in Table 11. Note that the error-correction term (RT B t 1 ) in the MS-VECM model is the same one as in the linear VECM model. In particular, we use the error-correction term (cointegrating equation as (16)) from the linear VECM model as an exogenous variable when estimating the MS-VECM model. This is the two-stage procedure proposed in Krolzig [1999]. From these results, since the first specification MSIA(2)-VECM(5) shows the lowest values for 18 The multivariate LM test statistics (probability) for residual serial correlation up to 12 order, under the null hypothesis of no serial correlation of order h, are.6872,.3774,.651,.9157,.5835,.4564,.6387,.4361,.4862,.537,.5831 and With White heteroskedasticity test, under the null of no heteroskedasticity, the non-constant regressors are jointly significant with probability. 19 We are aware that, with regime-dependent (autoregressive) parameters, the problem of too few degrees of freedom (too many parameters) might occur. 22

23 Table 11: Results from Both AIC and SC Criteria Specification AIC Criterion SC Criterion MSIA(2)-VECM(5) MSIAH(2)-VECM(5) both the AIC criterion ( ) and the SC criterion ( ), we should look at such specification for our analysis. Nevertheless, we also put an eye on the second specification MSIAH(2)- VECM(5). And after deliberately considering both specifications, we reasonably select the MSIAH(2)- VECM(5) specification for our analysis. This is mainly due to an interesting economic interpretation made from this specification, comparing to the MSIA(2)-VECM(5). 2 MSIAH(2)-VECM (5) is written as x t = α (s t ) βx t 1 + v (s t ) + Our chosen model 5 A (s t ) k x t k + u t, (17) where x t = [RT B, RER, ROP, USRHP I, CNRHP I, USRY, CNRY ], α (s t ) is regime-dependent speed-of-adjustment coefficient to long-run equilibrium, β is vector of cointegrating coefficients, v (s t ) is regime-dependent intercept term, A (s t ) is vector of regime-dependent (autoregressive) parameters, u t is conditionally Gaussian, u t s t NID(, (s t )) and s t {1, 2}. The stochastic process for generating changes in the unobservable regimes is an ergodic Markov chain defined by the transition probabilities p ij = Pr (s t+1 = j s t = i), 2 j=1 p ij = 1 i, j {1, 2}, where p i2 = 1 p i1 for i = 1, 2. We normalize the model to make US real trade balance with Canada dependent variable. We try to make an analysis from results from the non-linear model reported in Table 12. From the chosen MSIAH(2)-VECM(5) specification, intercept is negative in regime one and positive in regime two. k=1 Hence, we could reasonably conclude that regime one stands for the periods with negative changes and that regime two stands for the periods with positive changes in (the rate of)??? US real trade balance with Canada. Also, these two values in regime one and regime two are statistically significant at 5 percent significance level with the t-statistics of The MSIA(2)-VECM(5) specification provides longer duration for regime two (5.67 months), comparing to the MSIAH(2)-VECM(5) (4.36 months). On the other hand, regime one duration from the MSIAH(2)-VECM(5) (3.56 months) is longer than that from the MSIA(2)-VECM(5) (2.2 months). Neither specification provides longer durations for both regime one and regime two, comparing with each other. We believe that specification providing longer durations might be meaningful for forecasting exercise. However, this could not be applied here. Nevertheless, we are aware that chosen specification might lose forecastability due to shorter duration in one of two regimes. 23