Abstract
Canada has experienced drastic changes in its economy during the global financial crisis. This Selected Issues paper discusses the evolution of equilibrium real home prices in key Canadian provinces in the post-crisis period, Canadian dollar movement during and after the global financial turmoil in line with other world currencies, assessment of impacts on Canada’s potential growth, development of Canadian automotive sector—namely, NAFTA partners during the crisis, and the role of Canada Mortgage and Housing Corporation (CMHC) in Canada’s housing market.
II. Interpreting Canada’s Currency Movements During the Crisis 1
The Canadian dollar oscillated sharply during the global financial turmoil in line with other world currencies. Using different statistical tools, we find that this has been driven by “flight-to-safety” effects possibly related to swings in commodity prices—rather than carry-trade activity—similar to what happened with other advanced commodity exporters’ currencies. Results suggest, however, that the link between the CAD/USD and the terms of trade have become more attenuated recently.
A. Background
1. At the onset of the global financial crisis the Canadian dollar depreciated strongly with respect to the U.S. dollar and in real effective terms. This is largely believed to have been the result of three forces. First, given Canada’s large net exports of commodities, the collapse in world demand triggered a sharp correction in commodity prices weakening the Canadian dollar. Second, investors flew initially to safety toward U.S. dollar-denominated assets and away from most non-U.S. assets (including Canadian assets) in an aim to protect capital. Finally, Canada’s trade balance started to deteriorate as a result of the drop in U.S. income and relatively modest weakness of domestic demand, putting downward pressure on the loonie. As a result, the CAD/USD bilateral rate rose by 31 percent between May 2008 and March 2009.
ExchangeRate During the Crisis
(Index March 2005=100)
(CAD/USD, right)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: Haver Anaytics and Fund staff calculations.ExchangeRate During the Crisis
(Index March 2005=100)
(CAD/USD, right)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: Haver Anaytics and Fund staff calculations.ExchangeRate During the Crisis
(Index March 2005=100)
(CAD/USD, right)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: Haver Anaytics and Fund staff calculations.2. As the crisis matured, an improved global outlook and positive Canadian financial and economic news strengthened the value of the Canadian dollar. By March 2010, the Canadian dollar had recovered much of its strength on the back of a strong rebound in commodity prices, a rapid economic recovery in Canada in the second half of 2009 and the first half of 2010, a strong fiscal position vis-á-vis peers, and a resilient financial system.
3. This paper examines possible drivers of the value of the Canadian currency during the crisis. We use two methods: (1) an uncovered interest parity (UIP) decomposition focusing on portfolio considerations, namely the contribution of expected risks and return factors on Canadian dollar-denominated assets relative to U.S. dollar-denominated assets; and (2) a co-integration analysis that goes beyond relative return and risk factors to focus on long-run fundamental drivers of the Canadian dollar, namely Canada’s net foreign asset position and terms of trade. For analytical purposes, we mark the beginning of the financial crisis as February 27, 2007.2 This allows us to focus on exchange rate changes over a timeframe more than one year longer than used in existing studies of 2007-2009 crisis-related exchange rate movements. Among these, for example, Fratzcher (2009) rationalizes exchange rate swings during the recent crisis by telling a safe-haven story in which the global nature of the slowdown led investors to believe that negative shocks originating in the U.S. would affect foreign markets even more acutely. Kohler (2010), however, argues that exchange rate movements during this crisis were characterized by both safe-haven effects and carry trade that resulted from interest rate differentials.
4. Results show that the behavior of the loonie during the crisis seems to have been dominated primarily by safe haven effects and swings in commodity prices. This is similar to what is found for the Australian and the New Zealand dollar—the currencies of two other advanced commodity exporters.3 By contrast, we find that cumulative revisions to the nominal forward differentials between the Bank of Canada’s target for the overnight rate and the Fed Funds rate played a little or no role in the loonie’s movements during the crisis, an indication that carry trade activity or other return considerations did not dominate exchange rate changes during the crisis. Section II summarizes the results. An Appendix details the methodology used and the statistical tests.
B. Empirical Results
Results Based on the UIP Decomposition Method
5. The Uncovered Interest Parity (UIP) condition is used to assess the contribution of monetary policy news in the United States to exchange rate developments in Canada during the crisis.4 In practice, the UIP states that:
| expected change in | = | difference in interest | + | difference in risk | ||
| exchange rates between | rates between those two | between the assets of | ||||
| two countries | countries | the two countries | ||||
| expected change in | = | difference in interest | + | difference in risk | ||
| exchange rates between | rates between those two | between the assets of | ||||
| two countries | countries | the two countries | ||||
So, theoretically, if the interest rate differential between two countries is 3 percent, then the currency of the nation with the higher interest rate would be expected to depreciate 3 percent against the other currency, controlling for differences in the perceived riskiness of country A’s assets relative to country B’s assets. Employing the instantaneous forward interest rate differentials in an adapted UIP framework, we can thus decompose exchange rate movements into changes attributable to monetary policy and a residual (see the Appendix for a detailed description of the methodology used).
Decomposition Results
(Percent)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: Bloomberg, Haver Analytics, and Fund staff calculations.Decomposition Results
(Percent)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: Bloomberg, Haver Analytics, and Fund staff calculations.Decomposition Results
(Percent)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: Bloomberg, Haver Analytics, and Fund staff calculations.6. Results suggest that shifts in the Canadian dollar during the crisis were likely driven by flight-to-safety (first away then into the loonie) rather than by return considerations. The CAD/USD depreciated by over 40 percent during the initial phase of the crisis (i.e., in the “trough-to-peak” period), then recouping some ¼ of its pre-crisis value by early 2010 (in the “peak-to-April 2010” period).5 Changes in expectations about forward differentials between Canadian and U.S. interest rates can explain neither the weakening nor the strengthening of the loonie during the crisis: the revisions would have suggested opposite movements in the currency. Thus, the UIP decomposition lends support to the view that swings in the CAD were driven by shifts in investors’ sentiment first away and then into Canadian-dollar-denominated assets.
7. The finding that the weakening of the CAD/USD reflected a flight-to-safety effect is in line with views of exchange rate developments at the time. Most commentators saw the strength in the U.S. dollar at the beginning of the financial turmoil as a sign of panic and risk aversion, as investors liquidated investments bought at a time when interest rates heavily favored European or other non-U.S. assets. Institutional investors, faced with losses suffered on U.S. investments, were also liquidating overseas assets to meet margin calls. All these factors added to the U.S. dollar’s strength as major foreign currencies were sold for U.S. dollars; returns ceased being the driver for investors, instead paving the way for strategies aimed at capital protection. This is in stark contrast to the Asian crisis of 1997–98 and the crisis following the Russian debt default in 1998 during which investors fled the currencies of the countries in crisis.
8. The likelihood of an initial flight to safety away from the Canadian dollar is corroborated by the steep rise in 2009 in the volatility of the loonie.1 In Canada, and other commodity exporters like Australia, and South Africa the volatility hike likely reflected increased uncertainty about the course of commodity prices at the onset of the turmoil. Several formerly planned economies—Russia, Poland, the Czech Republic, and Hungary—also saw more exchange rate volatility than other countries, reflecting the depth of the crisis there. Remarkably, the euro saw less volatility in effective terms in 2009 than it did in previous years.
Nominal Effective Exchange Rate Volatility
(Standard Deviation of Monthly Data)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: INS and Fund staff calculations.Nominal Effective Exchange Rate Volatility
(Standard Deviation of Monthly Data)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: INS and Fund staff calculations.Nominal Effective Exchange Rate Volatility
(Standard Deviation of Monthly Data)
Citation: IMF Staff Country Reports 2010, 378; 10.5089/9781455213559.002.A002
Sources: INS and Fund staff calculations.9. The view that then the loonie strengthened because confidence returned also tallies with the conventional wisdom. The decision in April 2009 of the Bank of Canada to slash rates to virtually zero while promising to hold them until mid-2010 ruled out future revisions to nominal rate differentials vis-á-vis the Fed Funds rate—that was already at the zero bound. This eliminated any market incentive to speculate on forward differentials between the Canadian and the U.S. dollar, implying that interest rate differentials could not be a driver of changes in the exchange rate after April 2009. According to the UIP set up, the appreciation in the CAD/USD must hence lie in the fact that these currencies started to be seen as safe havens in early 2009 (or that the U.S. lost part of its “heavenliness”). This is likely, considering that like other advanced commodity exporters, Canada experienced a milder recession and a swifter recovery vis-á-vis other advanced G-20 countries thanks to the early rebound in commodity prices.
Results Based on Cointegration Analysis
10. Co-integration analysis is used as a second tool to unveil potential drivers of the CAD/USD during the crisis. Along the lines of Coletti and van Norden (1993), Lafrance and van Norden (1995), and Charron (2001), we estimate an error correction model that exploits the long-run relationship between the real exchange rate, commodity prices (measured by the Chain Fisher BoC Commodity Price Index (NSA, 2002=100) deflated by Canadian CPI), and Canada’s net foreign asset position.2 In the short-run specification, the model includes the differential between nominal monetary policy rates in Canada versus the United States as well real growth in emerging Asia among the set of exogenous regressors. Thus, while it does not exactly nest the Uncovered Interest Parity model, the model can help gauge whether interest rate differentials drive the exchange rate in the short run.
11. Statistical tests confirm that, historically, the real exchange rate, commodity prices, and net foreign assets have moved together in the long run (see the Appendix for more details on stationarity and co-integrating tests). Results indicate that at any point in time about a tenth of the deviation of the Canadian dollar from its fundamentals (i.e., commodity prices and net foreign assets) has been corrected every quarter. Our estimates of the long-run relationship are broadly in line with the previous literature (the long-run coefficient on commodity prices is 0.50, within the 0.5–0.8 range of point estimates for commodity prices in Coletti-Murchison, 1998; and Amano-van Norden, 1993). Importantly, the co-integrating vector is significant in the short-run equation, indicating that in the past, the CAD/USD real exchange rate has tended to slowly re-approach its co-trended variables following shocks. In the short run, the Canadian dollar is also driven by the first lag of the difference in the real exchange rate. However, the differential between Canadian and U.S. monetary policy rates is not statistically significant, thus results do not seem to support short-term interest rate parity between Canada and the United States.
12. However, we find two signs of parametric instability post 2008, suggesting that the crisis may have changed fundamentally how the CAD/USD adjusts to changes in commodity prices:
The long-run relationship displays a break in mid-2008, suggesting that since then the real exchange rate is substantially stronger for given levels of commodity prices and net foreign assets.
In the short-run specification, the error correction term shows signs of parametric instability in mid-2008 (indeed a slope dummy—with the dummy taking a value of 1 from 2008 Q3 onwards—interacting with the coefficient of the lagged dependent variable is highly significant). The coefficient on the slope dummy is greater than one, likely a sign of the unprecedented volatility of the exchange rate since 2008 and of its possible decoupling from fundamentals.
13. The finding of a break corroborates the hypothesis that the CAD/USD during the crisis has indeed been dominated by flight-to-safety considerations. Since expectations about future movements in commodity prices have in part reflected sentiment with regard to commodity exporters’ currencies and commodity importers’ economic performance during the turmoil, it is however difficult to identify a good model of the intra-crisis exchange rate movements using commodity prices among fundamentals. On the other hand, it is not obvious how to control for “flight-to-safety” effects in an episode like the financial crisis where investors were likely trading off expected volatilities on several currencies at once. Proxies capturing perceptions of volatility on U.S. assets, like changes in the VIX for example, are not statistically significant when included in the error correction model.
Prepared by Nicoletta Batini and Thomas Dowling (both WHD).
The Federal Reserve Bank of St. Louis (2009) also chooses this date to mark the beginning of the crisis. On that day, the Federal Home Loan Mortgage Corporation (Freddie Mac) announced that it would no longer buy the most risky subprime mortgages and mortgage-related securities, spurring a wave of panic toward such assets that in turn led to a series of bankruptcies and the subsequent cascade of well-known events.
For results on other countries including Australia and New Zealand, see: Batini, N. and T. Dowling, 2010, “Interpreting Currency Movements During the Crisis”, International Monetary Fund Working Paper, forthcoming.
In theory, the UIP condition is accepted as intuitive, but debate over whether or not UIP is empirically valid continues. For the purpose of decomposition into its components, however, we need only to assume that interest rate differentials and exchange rate movements have a one-to-one relationship, an assumption that seems plausible (see Fisher et al, 1990).
The trough (11/06/2007) is defined as the minimum exchange rate (Canadian dollar/U.S. dollar) from the start of the crisis to April 1, 2010. The peak (3/9/2009) is defined as the maximum exchange rate from the trough to April 1, 2010.
Volatility is here defined as the standard deviation of monthly exchange rates in a given year.
We also experiment with the terms of trade instead of commodity prices, but results are less stark.
References
Adams, K., & van Deventer, D. (1994). Fitting Yield Curves and Forward Rate Curves with Maximum Smoothness. The Journal of Fixed Income June, pp. 52–62.
Brigden, A., et al. (1997). Decomposing Exchange Rate Movements According to the Uncovered Interest Rate Parity Condition. Bank of England Quarterly Bulletin, May, pp. 377–389.
Chaboud, A., & Wright, J. (2003). Uncovered Interest Parity: It Works, But Not for Long. Federal Reserve International Finance Discussion Papers, January, No. 752.
Federal Reserve Bank of St. Louis (2009). The Financial Crisis Timeline. Retrieved from: http://timeline.stlouisfed.org/.
Fisher, P., Tanna, S., Turner, D., Wallis, K., & Whitley, J. (1990). Econometric Evaluation of the Exchange Rate. Economic Journal, 100, pp. 1,230–44.
Frankel, J., & Poonawala, J. (2006). The Forward Market in Emerging Currencies: Less Biased Than in Major Currencies. NBER Working Paper, August, No. W12496.
Fratzcher, M. (2009). What Explains Global Exchange Rate Movements During the Crisis? European Central Bank Working Paper Series, June, No. 1060.
Gurkaynak, R., et al. (2007). The U.S. Treasury Yield Curve 1961 to the Present. Journal of Monetary Economics, November, pp. 2291–2304.
Kohler, M. (2010). Exchange Rates During Financial Crises. Bank of International Settlements Quarterly Review, March, pp. 39–50.
Krippner, L. (2006). A Yield Curve Perspective on Uncovered Interest Parity. University Of Waikato: Working Papers in Economics, 06/16.
Krippner, L., & Thorsrud, L. (2009). Forecasting New Zealand’s Economic Growth Using Yield Curve Information. Reserve Bank of New Zealand Discussion Papers, DP2009/18.
Nelson, C., & Siegel, A. (1987). Parsimonious Modeling of Yield Curves. The Journal of Business, October, pp. 473–489.
Svensson, L. (1994). Estimating and Interpreting Forward Interest Rates: Sweden 1992–1994. NBER Working Paper, September, No. 4871.
Appendix 1. Methodology and Diagnostic Tests
A. UIP Decomposition
To determine the interaction between interest rates and exchange rates, we use the Uncovered Interest Parity (UIP) condition. The UIP’s underlying assumptions enable us to identify the contribution of these shocks as the UIP condition holds for any period of time, thereby reducing the amount of noise and allowing for better identification.
In symbols, the UIP condition can be generally expressed as:
Where
We use a log-linearized adaptation of the UIP condition following the Bridgen (1997) methodology to determine what portion of the unexpected change is attributable to interest rate differentials. Forward substitution allows us to derive the cumulative forward differentials from the UIP and generates the following generalized expression:
where
In Equation (2), the first RHS term is the forward interest differential, precisely, the cumulative revision to nominal forward interest differentials which expresses the expected difference between interest rates in country x and U.S. interest rates over some period. The forward differential is a measure of how much the expected rate of depreciation/appreciation of country x’s currency changed between t and t+k, subject to the choice of n. The next term on the RHS is the expected value of the nominal exchange rate of country x’s currency at time n. The last term on the RHS is the net change in country x’s currency risk premium between t and t+k, also subject to the choice of n. Since only the first term is observable, we treat the two other terms as a single residual.
The UIP decomposition requires the use of instantaneous forward rates to calculate the cumulative revision to nominal forward interest differentials. Following Svensson (1994), zero-coupon rates are needed to estimate these instantaneous forward rates. Canada’s zero-coupon rates were obtained from the Bank of Canada.
The instantaneous forward rates are provided for the United States (Federal Reserve Bank) while the rates for Canada are estimated using the parsimonious Nelson-Siegel (1987) parametric method, which is preferable to other types of estimation when fitting Nelson-Siegel models as explained in Gurkaynak et al. (2007). The zero-coupon rates are used to estimate the instantaneous forward rates in a two-step process according to the model:
Where r(t, T) is the interest rate at time t, for maturity T; α is a constant that represents the rate as T approaches infinity; β1 and β2 are parameters that define the curvature of the yield curve; and λ is a decay parameter that represents the persistence of short and medium term rates into the long run. To fit Equation (3), we first estimate the parameters α, β1, β2, and λ using ordinary least squares (OLS) iteratively to minimize the sum of squared residuals by varying the parameters with r(t, T) equal to the zero-coupon rates at time t. The initial value for each parameter is set at 1. We then derive the forward rates from Equation (3) by varying T over the maturities desired using the estimated parameters.
To quantify the contribution of changes in U.S. monetary policy on our sample of eight bilateral exchange rates using the UIP condition we follow five steps.
1) First, we identify the trough and peak of the Canadian dollar vis-à-vis the U.S. dollar from the beginning of the financial crisis until April 1, 2010. The trough is defined as the minimum exchange rate (Canadian dollar/U.S. dollar) from the start of the crisis to April 1, 2010. The peak is defined as the maximum exchange rate from the trough to April 1, 2010. Our decomposition results will examine how much of the trough-peak depreciation against the U.S. dollar and how much of the peak-to-April 1, 2010 appreciation can be explained using the UIP condition.
2) Second, for the trough-peak-April 1, 2010 dates, we obtain forward differentials by fitting zero-coupon rates to forward curves following the parametric estimation methodology of Nelson-Siegel.
3) Third, we obtain a measure of “news”. This quantifies what proportion of the change in the overnight nominal exchange rate can be attributed to an expected change—the exchange rate change implied by the interest rate differential according to the UIP—and to an unexpected change over the dates that we examine. This unexpected change is what we will call “news”.
4) Fourth, we decompose the “news” into: (i) changes in the differential between expected U.S. and Canadian interest rates up to some arbitrary terminal point and (ii) a residual term that includes changes in the expected value of the nominal exchange rate at that terminal point and changes in the currency risk premium.
5) Fifth, we attribute the “news” to monetary policy and non-monetary policy factors, based on a set of assumptions about the impact of monetary policy on interest rates at various maturities. This step implies a judgment about the ultimate cause of the change in the exchange rate, which is why we focus specifically on announcements during the crisis that pushed analysts to modify their expectations about the path of official rates.
The table below summarizes what we have discussed so far. Line one lists the actual percentage change of the bilateral exchange rate of country x vis-á-vis the United States. Lines two and three show the breakdown of the exchange rate movement on t+k into the expected change (which we have stated is zero) and the “news”. The fourth and fifth rows of the table summarize the results obtained by applying the above cumulative forward revision and reflect the first term of the RHS of Equation (2). We calculate the term with n=8 and n=12 to generate a sensitivity band of 8 to 12 years since the value of the term depends on the n chosen. Put otherwise, these rows show how much of the “news” can be explained by changes in the forward nominal differential, once we assume that changes in the risk premium are independent of the changes in the long-run forecast of nominal exchange rates.
Decomposition Results Table
Decomposition Results Table
| Trough 11/6/2007 | Peak 3/9/2009 | Current 4/1/2010 | |||
|---|---|---|---|---|---|
| Actual change against: | 41.37 | -22.49 | |||
| of which | |||||
| Expected | 0.00 | 0.00 | |||
| “News” | 41.37 | -22.49 | |||
| Cumulative revision to nominal | |||||
| forward interest differentials | |||||
| range as terminal horizon varies from 8 to 12 years | 8 years | -11.54 | 1.48 | ||
| 12 years | -16.41 | 1.86 | |||
| of which | |||||
| Estimated real component | -2.90 | 0.16 | |||
| Sensitivity band | |||||
| estimated range as p-horizon varies from 4 to 8 years | 4 years | -1.64 | 0.39 | ||
| 8 years | -4.84 | 0.16 | |||
| Residual | 44.27 | -22.64 | |||
| Sensitivity band | |||||
| estimated range as p-horizon varies from 4 to 8 years | 4 years | 43.01 | -22.87 | ||
| 8 years | 46.22 | -22.64 | |||
Decomposition Results Table
| Trough 11/6/2007 | Peak 3/9/2009 | Current 4/1/2010 | |||
|---|---|---|---|---|---|
| Actual change against: | 41.37 | -22.49 | |||
| of which | |||||
| Expected | 0.00 | 0.00 | |||
| “News” | 41.37 | -22.49 | |||
| Cumulative revision to nominal | |||||
| forward interest differentials | |||||
| range as terminal horizon varies from 8 to 12 years | 8 years | -11.54 | 1.48 | ||
| 12 years | -16.41 | 1.86 | |||
| of which | |||||
| Estimated real component | -2.90 | 0.16 | |||
| Sensitivity band | |||||
| estimated range as p-horizon varies from 4 to 8 years | 4 years | -1.64 | 0.39 | ||
| 8 years | -4.84 | 0.16 | |||
| Residual | 44.27 | -22.64 | |||
| Sensitivity band | |||||
| estimated range as p-horizon varies from 4 to 8 years | 4 years | 43.01 | -22.87 | ||
| 8 years | 46.22 | -22.64 | |||
B. Co-Integration Analysis
(i) Model and Data
The general form of the model estimate in this paper is:
The sample period used for the estimation is 1992Q4 to 2010Q2.
The variable rer represents the logarithm of the nominal exchange rate expressed as U.S. dollars per Canadian dollar, adjusted for inflation by the ratio of Canada to U.S. GDP implicit price deflators. An increase in the variable denotes an appreciation.
The variable pcomm represents the logarithm of the ratio of the Chain Fisher BoC Commodity Price Index (NSA, 2002=100) deflated by Canadian CPI.
The variable nfa represents the ratio of Canada’s net foreign asset position to GDP.
The variable ΔgdpEAt, represents quarterly GDP growth rate (s.a.a.r) in emerging Asia.
The variable intdifft measures the difference between the Canadian target for the overnight rate and the target for the Federal Fund rate.
The operator ‘Δ’ represents first differences. t are calendar quarters.
(ii) Empirical Results
Pre-test for Order of Integration
We begin our empirical analysis by examining the time series properties of each series. To this end we use the augmented Dickey-Fuller (1979), the Phillips and Perron (1988) and the Kwiatkowski, Phillips, Schmidt and Shin (1992) tests.1
The tests suggest that the real exchange rate, real commodity prices, and the net foreign assets to GDP ratio are well characterized by I(1) processes (see Table 1).
Tests for Unit Roots and Stationarity
(sample period: 1992Q4 to 2010Q2)
Tests for Unit Roots and Stationarity
(sample period: 1992Q4 to 2010Q2)
| Variable | ADF lag length | ADF | PP | KPSS |
|---|---|---|---|---|
| rer | 1 | -1.0347 | -0.3345 | 0.6304*** |
| pcomm | 2 | 0.3455 | 0.5296 | 0.8974*** |
| nfa | 0 | -1.2676 | -1.2255 | 1.0615 |
Tests for Unit Roots and Stationarity
(sample period: 1992Q4 to 2010Q2)
| Variable | ADF lag length | ADF | PP | KPSS |
|---|---|---|---|---|
| rer | 1 | -1.0347 | -0.3345 | 0.6304*** |
| pcomm | 2 | 0.3455 | 0.5296 | 0.8974*** |
| nfa | 0 | -1.2676 | -1.2255 | 1.0615 |
Co-Integration Tests
We use the Johansen (1988) procedure which estimates the system simultaneously, allowing for the possibility of endogenous regressors (Table 2). The preferred system includes the log of the real exchange rate, the log of the Bank of Canada-real-U.S. dollar-non-energy commodity price, and the NFA to GDP ratio in the co-integrating vector. The short-run dynamics include one lag of the first difference of the real exchange rate, as well as two lags of the first difference of commodity prices.
Co-Integration Tests
Unrestricted Cointegration Rank Test (Trace)
denotes rejection of the hypothesis at the 0.05 level
MacKinnon-Haug-Michelis (1999) p-values
Co-Integration Tests
Unrestricted Cointegration Rank Test (Trace)
| Hypothesized | Trace | 0.05 | ||
|---|---|---|---|---|
| No. of CE(s) | Eigenvalue | Statistic | Critical Value | Prob.** |
| None * | 0.313685 | 40.04452 | 35.19275 | 0.0139 |
| At most 1 | 0.123215 | 14.44806 | 20.26184 | 0.2597 |
| At most 2 | 0.077786 | 5.506517 | 9.164546 | 0.2324 |
denotes rejection of the hypothesis at the 0.05 level
MacKinnon-Haug-Michelis (1999) p-values
Co-Integration Tests
Unrestricted Cointegration Rank Test (Trace)
| Hypothesized | Trace | 0.05 | ||
|---|---|---|---|---|
| No. of CE(s) | Eigenvalue | Statistic | Critical Value | Prob.** |
| None * | 0.313685 | 40.04452 | 35.19275 | 0.0139 |
| At most 1 | 0.123215 | 14.44806 | 20.26184 | 0.2597 |
| At most 2 | 0.077786 | 5.506517 | 9.164546 | 0.2324 |
denotes rejection of the hypothesis at the 0.05 level
MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test
(Maximum Eigenvalue)
denotes rejection of the hypothesis at the 0.05 level
MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test
(Maximum Eigenvalue)
| Hypothesized | Max-Eigen | 0.05 | ||
|---|---|---|---|---|
| No. of CE(s) | Eigenvalue | Statistic | Critical Value | Prob.** |
| None * | 0.313685 | 25.59645 | 22.29962 | 0.0167 |
| At most 1 | 0.123215 | 8.941547 | 15.89210 | 0.4401 |
| At most 2 | 0.077786 | 5.506517 | 9.164546 | 0.2324 |
denotes rejection of the hypothesis at the 0.05 level
MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test
(Maximum Eigenvalue)
| Hypothesized | Max-Eigen | 0.05 | ||
|---|---|---|---|---|
| No. of CE(s) | Eigenvalue | Statistic | Critical Value | Prob.** |
| None * | 0.313685 | 25.59645 | 22.29962 | 0.0167 |
| At most 1 | 0.123215 | 8.941547 | 15.89210 | 0.4401 |
| At most 2 | 0.077786 | 5.506517 | 9.164546 | 0.2324 |
denotes rejection of the hypothesis at the 0.05 level
MacKinnon-Haug-Michelis (1999) p-values
Johansen (1992) demonstrates that estimation and inference on the single equation system will be equivalent to that of the full system only if all other cointegrating variables are weakly exogenous (in the sense of Engle, Hendry, and Richard (1983) with respect to the first variable in consideration in our case, the real exchange rate), and if there is only one cointegrating vector. The Johansen procedure allows us to perform a weak exogeneity test on the full system using the likelihood ratio test described in Johansen and Juselius (1992). This is simply a test of whether the speed of adjustment is significantly different from zero in the equations for the variables tested.
Results reported in Table 3 show that we cannot reject the hypothesis that commodity prices and the NFA-to-GDP ratio are all weakly exogenous, but we can reject weak exogeneity for the real exchange rate. This allows us to estimate the model as a single equation errorcorrection model (ECM) using non-linear least squares.
Test for Weak Exogeneity: LR Test for Binding Restrictions
Test for Weak Exogeneity: LR Test for Binding Restrictions
| Rank (n) | Chi-square(2) | rer | pcomm | nfa |
|---|---|---|---|---|
| 1 | 20.18613 | -30.26778 | -0.033030 | 0.275469 |
Test for Weak Exogeneity: LR Test for Binding Restrictions
| Rank (n) | Chi-square(2) | rer | pcomm | nfa |
|---|---|---|---|---|
| 1 | 20.18613 | -30.26778 | -0.033030 | 0.275469 |
Estimation Results
For model selection we follow the general to specific approach of Hendry (1980). In addition, we focus on parameter stability as the important criteria for model selection. To study the stability of the individual coefficients associated with the I (0) variables, we use the stability test developed in Hansen (1991). The final specification is:
Estimation results are reported in Table 4 below. Note that the estimated speed of adjustment parameter has the correct sign and a low value (-0.11), which suggest a slow adjustment of the real exchange rate toward its long-run equilibrium value.
Estimation Results
(Sample: 1992Q4 to 2010Q2)
Estimation Results
(Sample: 1992Q4 to 2010Q2)
| Coefficient | Value | Standard Error |
|---|---|---|
| β1 | 0.1980 | 0.0938** |
| β2 | 1.0240 | 0.1472*** |
| γ | -0.1196 | 0.0679* |
| ξ1 | -0.5020 | 0.0319*** |
| ξ2 | 0.0062 | 0.0008*** |
Estimation Results
(Sample: 1992Q4 to 2010Q2)
| Coefficient | Value | Standard Error |
|---|---|---|
| β1 | 0.1980 | 0.0938** |
| β2 | 1.0240 | 0.1472*** |
| γ | -0.1196 | 0.0679* |
| ξ1 | -0.5020 | 0.0319*** |
| ξ2 | 0.0062 | 0.0008*** |
It is well known that the two first tests may lack power against the alternative of stationarity if the data do not span a long enough time period. Therefore, we also use the Kwiatkowski, Phillips, Schmidt, and Shin (1992) test, which allows us to test the null hypothesis of stationarity against a unit root alternative.
