Identifying Monetary Policy in a Small Open Economy under Flexible Exchange Rates

Prior VAR studies of monetary policy in small open economies generate an “exchange rate puzzle” (a contractionary interest-rate shock perversely depreciates the currency) and a “price puzzle” (prices rise instead of fall), and Cushman and Zha argue these “derive from an identification of monetary policy that is inappropriate for such economies.” The standard recursive (Choleski) identification implicitly assumes the central bank cannot react contemporaneously to the exchange rate within the month, which the authors show is inconsistent with how the Bank of Canada actually behaves and is what generates the exchange rate puzzle.

The paper uses monthly Canada-US data from 1974 to 1993 – a window chosen to avoid the 1973 oil price shock and the unsettled pre-float period – drawn from Statistics Canada’s CANSIM database and the IMF’s International Financial Statistics. The Canadian (“home”) block comprises the exchange rate (US-dollar price of the Canadian dollar), M1, the three-month Treasury bill rate, the CPI, industrial production, and exports/imports to the US; the US (“foreign”) block comprises US industrial production, the US CPI, the federal funds rate, and a world export commodity price index. All variables are in logarithms except interest rates (decimal percentages), trade values are deflated by the Canadian CPI, and each equation includes seasonal dummies.

The model is a non-recursive structural VAR with block exogeneity: the restriction A_21(L) = 0 means the Canadian/home block never enters the US/foreign block’s equations contemporaneously or at any lag, reflecting Canada’s small-country status relative to the US – the foreign block is unrestricted in the other direction and freely enters the home block’s equations (e.g., Table 1’s policy equation includes the contemporaneous US federal funds rate and world commodity prices); the foreign block itself is left in reduced form, normalized lower-triangular in the order output, prices, interest rate, commodity prices. Within the Canadian block, the contemporaneous structure is organized into three sectors: a money market (a money-demand equation and a money-supply/policy-reaction equation), an information market (an exchange-rate equation), and a production sector (imports, exports, output, prices, ordered recursively, with contemporaneous foreign and financial variables excluded). The model is estimated by maximum likelihood with 12 lags, standard errors from the Hessian of the log-likelihood, and 5,000 Monte Carlo draws (82 discarded to keep the diagonal of A_0 positive) used to construct error bands following Zha (1996); a model-stability chi-square test with 364 degrees of freedom (346.1) passes.

The policy reaction function is specified to let the Bank of Canada respond within the month to the exchange rate, the money stock, the foreign (US) interest rate, and world commodity prices – but not contemporaneously to output or the price level – because the authors argue the central bank can observe and react to financial variables intra-month but output and prices are available only with a lag. This contrasts with the recursive/Choleski approach, which implicitly orders the policy variable so it cannot respond contemporaneously to the exchange rate; the authors identify this omission as the source of the exchange rate puzzle. A separate “information market” (exchange-rate) equation is specified to load on all eleven contemporaneous variables in the system, capturing efficient-market pricing of the exchange rate given all currently available information.

Yes: a contractionary policy shock (a positive innovation to the money-supply equation) produces an immediate and persistent decline in M1, an immediate and statistically significant appreciation of the Canadian dollar that lasts about 12 months, only a brief and small – though statistically significant – rise in the nominal interest rate that becomes insignificant for most of the remaining four-year horizon, and a price level that declines gradually rather than rising; the only exception is a slightly positive price response in month 2 that the authors describe as “neither strongly significant nor large.” Under the same data, a Choleski identification instead generates a persistent exchange-rate puzzle across a variety of orderings (“results were quite similar for a variety of other orderings”).

The Canadian interest-rate response to a policy shock is weak while the exchange-rate response is strong – the opposite emphasis from “the strong interest rate effects in recent studies of US monetary policy (e.g., Gordon and Leeper, 1994).” The authors interpret this as evidence that monetary transmission in a small open economy like Canada operates primarily through the exchange rate – and its effects on trade flows and expenditure – rather than through the domestic interest-rate channel emphasized in closed-economy models.

Following a contractionary shock, exports fall initially while imports fall by more before rising again – producing a classic J-curve in the trade balance, which improves initially and then worsens; imports have fallen by approximately 0.5% by month 4. The authors attribute the initial import decline partly to a valuation effect from the cheaper US dollar and partly to the income decline; toward the end of the four-year horizon, money and prices remain lower while other variables are not significantly different from their original levels.

Approximately: the UIP deviation – defined as Z = R - R + 4(Exc^f - Exc), where Exc^f is the three-month-ahead forecast exchange rate – is significantly negative for only about 4 months and insignificantly different from zero for the remainder of the four-year horizon.* The authors note this finding “contrasts with much of the literature” and suggest it may reflect the importance of correctly modeling the central bank’s contemporaneous policy reaction rather than assuming it away.

Very little: monetary-policy (money-supply) shocks account for roughly 1.00% of Canadian output’s forecast-error variance at a 12-month horizon and no more than 2.75% at any horizon out to 6 months, per the paper’s variance decomposition (reported at 6, 12, 24, and 48 months). The production and information sectors jointly dominate output variance in the first few months (the production sector alone accounts for 40.29% at 6 months), but foreign shocks come to dominate after 12 months, accounting for 74.33%, 72.51%, and 74.17% of output variance at 12, 24, and 48 months respectively. The authors caution that this evidence that “unpredicted monetary policy disturbances have no major effect on output by no means implies that endogenous monetary policy itself is ineffective.”