VI Money Demand in a Small Open Economy: The Case of the Dominican Republic

Jaime Cardoso; Philip M Young

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Author: Mr. Jaime Cardoso and Mr. Philip M Young

Language:: English

Keywords:: OP; debt; differential semielasticity; monetary policy stance; money demand equation; output elasticity; domestic interest rate; Demand for money; Monetary aggregates; Monetary stance; Capital inflows; Monetary tightening

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Abstract

The formulation of monetary policy in the Dominican Republic is centered around an annual monetary program prepared by the BCRD and discussed with the government.67 The theoretical framework of the program is the monetary approach to the balance of payments. Given expected annual) real output growth, together with the inflation and exchange rate/foreign reserve objectives of the monetary authorities, an estimated money demand establishes a constraint on the assets and liabilities of the BCRD’s balance sheet. The program also specifies quarterly objectives for the intermediate targets (currency) and monetary policy instruments (for example, central bank paper). The quarterly objectives serve as guidelines for the Monetary and Exchange Affairs Committee as it monitors higher frequency indicators of the demand for money. Deviations from the projected path trigger a consultation with the governor of the BCRD and the Monetary Board, which ultimately decides which course of action to take.

The formulation of monetary policy in the Dominican Republic is centered around an annual monetary program prepared by the BCRD and discussed with the government.⁶⁷ The theoretical framework of the program is the monetary approach to the balance of payments. Given expected annual) real output growth, together with the inflation and exchange rate/foreign reserve objectives of the monetary authorities, an estimated money demand establishes a constraint on the assets and liabilities of the BCRD’s balance sheet. The program also specifies quarterly objectives for the intermediate targets (currency) and monetary policy instruments (for example, central bank paper). The quarterly objectives serve as guidelines for the Monetary and Exchange Affairs Committee as it monitors higher frequency indicators of the demand for money. Deviations from the projected path trigger a consultation with the governor of the BCRD and the Monetary Board, which ultimately decides which course of action to take.

The main instrument used for the implementation of monetary policy is central bank paper called certificados de participation. However, the BCRD also manages liquidity in the system using direct measures such as credit controls and the occasional freezing of excess reserves held at the BCRD by financial institutions. The BCRD intervenes in the free (commercial bank) foreign exchange market mostly with the objective of smoothing the irregular and seasonal components of exchange rate behavior, relinquishing in those cases the control of monetary aggregates.⁶⁸ Since late 1991, interest rates have been freely determined by market forces.

The objective of this chapter is to estimate a money demand equation for the Dominican Republic. The motivation is threefold. The key role that money demand plays in the formulation and implementation of monetary policy in the Dominican Republic contrasts with the doubt, both in academia and among policymakers (Leiderman and Svensson, 1995; and Blinder, 1998), that there is a long-run relationship (cointegration) between real money aggregates and real income.⁶⁹ The first motivation for estimating a money demand equation for the Dominican Republic is thus to test whether there is a long-run (cointegrating) relationship between real monetary aggregates, real income, and interest rates.

The second motivation for this study is to have a more informed view on the ability of the BCRD to control money market conditions and insulate them from foreign influences. Since the seminal work by Mundell (1963) on capital mobility and stabilization policy under fixed and flexible exchange rates, it has been recognized that the ability of monetary authorities in a small open economy to set monetary conditions, independent of foreign factors, decreases as capital mobility increases.⁷⁰ In a small open economy with capital mobility, a policy-induced increase in interest rates encourages capital inflows, which eliminate the incipient change in the interest rate differential and appreciate the domestic currency. In the Dominican Republic, as the domestic financial market and the capital account were liberalized, and as the economy started an extended period of high growth, monetary policy experienced a growing difficulty in maintaining a desired interest rate differential. The exchange rate effects stemming from changes in the domestic interest rate have been countered by foreign exchange market intervention, which has not always been fully sterilized. As a result, the stock of certificados de participatión has increased over time, and the growth of monetary aggregates has been endogenized.⁷¹ This is not the end of the story, however. As those capital inflows are intermediated by the banking system, they have resulted in a relatively higher rate of credit growth and have put downward pressure on interest rates. The main point is that the final effect of the original monetary policy tightening on overall monetary conditions seems to have been smaller than its initial effect, both on M2 and on the interest rate. Appendix VI.I develops an open economy model to illustrate this point.

The third motivation, a corollary of the last point, is to relate the issue of the ability of the BCRD to control domestic monetary conditions independently of foreign influences to the recent debate on how to assess the stance of monetary policy (see Christiano and others, 1998). The literature normally finds that a contractionary monetary policy increases domestic interest rates and appreciates the domestic currency. This highlights the role of capital flows in open economies discussed above. This was at the heart of much debate on the recent Asian crisis. The press has argued that high interest rates in Asia indicated a “tight” monetary policy. Based on the growth of monetary aggregates, Corsetti and others (1998) have characterized the monetary policy stance in Asia as “loose.” This debate suggests that the “monetary policy stance” may not be well measured by interest rates alone, or by the growth of monetary aggregates alone, whenever there is rapid feedback between monetary aggregates, credit, and interest rates, as is the case in small open economies. Interest rates contain both policy- and market-determined elements, and it is important to consider the evolution over time of financial variables in accurately assessing the stance of monetary policy (Tanner, 1999).

Econometric estimators of money demand equations should be able to deal with the suggested endogeneity of interest rates. This paper uses a Phillips-Loretan (1991) nonlinear dynamic least squares estimator to estimate three versions of a money demand equation—one that uses as a regressor a domestic interest rate, another one that uses the interest rate differential between the Dominican Republic and the United States, and a third one that uses the U.S. interest rate.

The Estimated Equations and the Estimation Technique

Given the theoretical framework of the Dominican Republic’s monetary program, this paper uses two measures of real monetary aggregates, M1 and M2, and investigates whether they are cointegrated with real output and nominal interest rates. Different specifications of equation (A7) in Appendix VI.1 are estimated.⁷² The basic money demand equation (A7), with alt variables except interest rates expressed in logs, is repeated here for convenience:

\begin{matrix} {(\frac{M}{P})}_{t} = b_{0} + b_{1} y_{t} + b_{2} i_{t} + ε_{t}^{m^{d}} & (1) \end{matrix}

The coefficients in equation (1) have the standard interpretation seen in studies of money demand dynamics: b₁ measures the output elasticity of money while b₂ measures the semielasticity of substitution between money and other domestic assets (that is, financial and real assets). It should be noted that the only interest-bearing financial assets readily available in the Dominican Republic are savings and time deposits, which are part of M2 but not M1. As a result, in the case of M2, b₂ is to be interpreted as the semielasticity of substitution between money and domestic real assets.

Because the Dominican Republic is a small economy with no capital controls, given uncovered interest rate parity (equation A8), equation (1) becomes:

\begin{matrix} {(\frac{M}{P})}_{t} = b_{0} + b_{1} y_{t} + b_{2} [i_{t}^{*} + (E_{t} e_{t + 1} - e_{t})] + ε_{t}^{m^{d}} & (2) \end{matrix}

The constant term in (2) now also includes a constant country risk premium. As before, the third term in equation (2) measures the semielasticity of substitution between money and other domestic assets. However, in an open economy, capital mobility equalizes the risk-adjusted expected return on domestic and foreign interest-bearing assets. So, in an open economy, the third term measures as well the degree of substitutability between domestic and foreign interest-bearing assets. This term poses special econometric problems because the expected change in the exchange rate is unobservable. The expected exchange rate change could be proxied by the difference between the forward and spot rates. Unfortunately, there is no forward market in the Dominican Republic, and as a result, equation (2) cannot be estimated in that form. Thus, given the objective of assessing the capacity of monetary policy to control domestic monetary conditions in isolation of foreign influences, one can use the coefficient on the interest rate differential (i_t−i_t*) as a proxy for the degree of substitutability between domestic and foreign interest-bearing assets. This follows a long tradition in money demand estimation in open economies (for example, Cuddington, 1983, and Siklos, 1996). The equation to estimate is:

\begin{matrix} {(\frac{M}{P})}_{t} = b_{0} + b_{1} y_{t} + b_{2} (i - i *)_{t} + ε_{t}^{m^{d}} & (3) \end{matrix}

As stated above, the estimate of b₂ from equation (2) measures either the semielasticity of substitution between money and domestic interest-bearing assets or the semielasticity of substitution between domestic and foreign interest-bearing assets. If the latter coefficient is statistically equal to the estimate of b₂ from equation (1)—which only measures the semi-elasticity of substitution between money and domestic interest-bearing assets—it is still possible to argue that the variance in the interest rate differential in equation (3) is driven mostly by the variance of the domestic interest rate. In that case, one could conclude that the home country monetary authorities can largely control domestic money market conditions independently of foreign influences, and that capital mobility is low. Therefore, for testing that hypothesis, as well as for completeness, a version of a money demand equation that uses the foreign interest rate is also estimated:⁷³

\begin{matrix} {(\frac{M}{P})}_{t} = b_{0} + b_{1} y_{t} + b_{2} i_{t} * + ε_{t}^{md} & (4) \end{matrix}

If there is a long-run relationship among real monetary aggregates, real output, and interest rates, there will be feedback between that long-run equilibrium relationship and the errors that drive the regressors (that is, real output and interest rates). Ordinary least squares (OLS), single equation error correction methods, and unrestricted vector autoregressions (VAR) will lead to estimators that are asymptotically biased and inefficient.⁷⁴ Therefore, equations (I), (3), and (4) are estimated using the nonlinear dynamic least squares estimator of Phillips and Loretan (1991), The authors show that this single-equation technique is asymptotically equivalent to a maximum likelihood estimator on a full system of equations under Gaussian assumptions. The technique provides estimators that are statistically efficient, and whose t-ratios can be used for inference in the usual way. Most importantly, the method takes into account both the serial correlation of the errors and the endogeneity of the regressors that are present when there is a cointegration relationship. The three estimated specifications are represented by equations (5)–(7).

\begin{matrix} \begin{matrix} \begin{matrix} {(\frac{M}{P})}_{t} = a + {by}_{t} + {ci}_{t} + Σ_{j = - k}^{k} [d_{j} Δ y_{t - j} + e_{j} Δ i_{t - j}] + \end{matrix} \\ ρ [(\frac{M}{P})_{t - 1} - a - {by}_{t - 1} - {ci}_{t - 1}] + ε_{t} \end{matrix} & (5) \end{matrix}

\begin{matrix} \begin{matrix} \begin{matrix} {(\frac{M}{P})}_{t} = a + {by}_{t} + c (i - i *)_{t} + Σ_{j = - k}^{k} [d_{j} Δ y_{t - j} + e_{j} Δ (i - i *)_{t - j}] + \end{matrix} \\ ρ [(\frac{M}{P})_{t - 1} - a - {by}_{t - 1} - c (i - i *)_{t - 1}] + η_{t} \end{matrix} & (6) \end{matrix}

\begin{matrix} \begin{matrix} \begin{matrix} {(\frac{M}{P})}_{t} = a + {by}_{t} + ci *_{t} + Σ_{j = - k}^{k} [d_{j} Δ y_{t - j} + e_{j} Δ i *_{t - j}] + \end{matrix} \\ ρ [(\frac{M}{P})_{t - 1} - a - {by}_{t - 1} - {ci}_{t} *] + ξ_{t} \end{matrix} & (7) \end{matrix}

Note that equations (5)–(7) include leads and not just lags. Phillips and Loretan, 1991, show that leads are required to produce valid conditioning (that is, to make the residuals ε_tη_t and ξ_t orthogonal to the entire history of the regressors). Similarly, the estimator includes not only lagged changes in the left-hand side variable ${(\frac{M}{P})}_{t - 1}$ but also the lagged equilibrium relationship. The reason is that lags of ${(\frac{M}{P})}_{t - 1}$ are not good good proxies for the past history of ε_t,η_t and ξ_t because of the persistence in effects of innovations from the unit roots in equations (1), (3), and (4). This requires the use of a nonlinear technique.

The standard interpretation of the coefficients b1 and b2 in equations (1), (3), and (4) was discussed above. That interpretation referred to the short-run dynamics of money demand and it is also applicable to the coefficients d_j and e_j in equations (5)–(7). However, equations (5)–(7) require the interpretation of the long-run values of the coefficients b and c as well. Those long-run values constitute the main focus of this study because they are the parameter estimates of the long-run relationship between money aggregates, real output, and interest rates. It is expected that b=1 for both M1 and M2 (at least when the interest rates used are the domestic interest rate or the interest rate differential). In the case of M1, it is expected that c<0 because holding noninterest bearing money is costly. However, it is also possible that MI is held in the long run only for transaction purposes, in which case c=0. As indicated earlier, because M2 includes foreign currency-denominated deposits, and given the frequent foreign exchange interventions of the BCRD, the long-run correlation between real M2 and the domestic interest rate or the interest rate differential may be positive, suggesting that c>0. Similarly, in the relatively underdeveloped Dominican financial markets, time deposits (quasi-money) serve as the main savings assets instrument, also suggesting that c>0 for M2.⁷⁵ Because i* proxies the rate of return on foreign assets, given an expected change in the exchange rate, the correlation between either real M1 or real M2 and the foreign interest rate is expected to be negative.

Equations (5)–(7) were estimated using quarterly data from 1992:Q1 to 1999;Q1. There are no indices of real activity available at a higher frequency in the Dominican Republic. Extending the sample back in time would imply going into a period when interest rates were not market-determined and important structural reforms had not yet taken place. The domestic interest rate used was the 90-day deposit rate and the foreign interest rate used was the 90-day U.S. treasury bill rate.

Unit Roots, Cointegration, and Long-Run Elasticities

Tables 30 and Tables 31 report the results for unit root tests.⁷⁶ In general, the tests tend to indicate that real M1, real M2, the domestic interest rate, and the interest rate differential are unit root processes. In the case of real output, however, only one of the two tests accepted the unit root hypothesis, but it was the more powerful of the two. Other econometric tests were also consistent with a unit root in real output. The behavior of the foreign interest rate during the sample period suggested that the unit root test should have power with respect to an alternative which allows for possible breaks either in the intercept or in the slope of the series. The Perron (l997) test did not reject the unit root hypothesis.

Table 30.

Dominican Republic: Unit Root Tests at 5 Percent Level

(1992:Q1–1999:Q1)

Sources: BCRD; and IMF staff estimates.

Note: IDOM = 9Q-day fending rate in the Dominican Republic.

IRD = interest rate differential; that is, 90-day lending rate in the Dominican Republic minus 90-day T-bill rate in the United States.
M1 D = M1 first differenced.
M2D = M2 first differenced.
GDPD = GDP first differenced.
IDOMD = 90-day lending rate in the Dominican Republic first differenced.
IRDD = 90-day lending rate in the Dominican Republic minus 90-day T-bill race in the United States first differenced.

^¹Lags were chosen according to the Akaike Information Criterion and for white noise of the residuals.

^²The power of ρ_μ (only constant) and ρ_t (constant and time trend) is higher than the power of T_μ (only constant) and T_t (constant and time trend) when the alternative is stationary.

^³The Newey-West weighting scheme was used for estimating the variances of S_μ² and S_t².

Table 30.

Dominican Republic: Unit Root Tests at 5 Percent Level

(1992:Q1–1999:Q1)

$Δ X_{t} = α + β_{t} + γ X_{t - 1} + Σ_{i = 1}^{p - 1} Φ i Δ X_{t - 1} + ε_{t}$
		Dickey-Fuller				Phillips-Perron
Variable	Lags¹	T_μ²	T_t²	ρ_μ³	ρ_t³	T_μ²	T_t²	ρ_μ³	ρ_t³
M1	2	−1.37	−3.66*	−2.62	−85.99*	−0.75	−2.27	−1.06	−10.35
M2	3	−0.10	−3.26	−0.14	154.84	−0.34	−2.02	−0.34	−8.68
GDP	5	−4.11*	−4.30*	−0.83	−2.64	−7.12*	−14.19*	−4.01	−8.29
IDOM	1	−2.53	−2.46	16.72*	−16.78	−1.86	−1.81	−7.77	−7.55
IRD	1	−1.94	−1.89	−9.93	−11.55	−1.63	−1.38	−5.93	−5.32
MID	3	−3.93*	−3.81*	55.66	55.46	−3.54*	−3.50	−18.26*	−18.11
M2D	3	−3.68*	−3.69*	151.63	429.76	−3.30*	−3.23	−18.15*	−18.09
GDPD	6	−1.50	−2.70	−1.86	−6.67	−15.52*	−12.42*	−5.40	−5.83
IDOMD	1	−3.13*	−3.40	−19.73*	−22.17*	−3.78*	−3.97*	−16.88*	−17.14
IRDD	1	−3.13*	−3.77*	−18.66*	−23.12*	−4.17*	−4.66*	−17.82*	−18.22*
Probability of a smaller value 5 percent		−2.99	−3.58	−12.63	−18.20	−2.99	−3.58	−12.63	−18.20

Sources: BCRD; and IMF staff estimates.

Note: IDOM = 9Q-day fending rate in the Dominican Republic.

IRD = interest rate differential; that is, 90-day lending rate in the Dominican Republic minus 90-day T-bill rate in the United States.
M1 D = M1 first differenced.
M2D = M2 first differenced.
GDPD = GDP first differenced.
IDOMD = 90-day lending rate in the Dominican Republic first differenced.
IRDD = 90-day lending rate in the Dominican Republic minus 90-day T-bill race in the United States first differenced.

^¹Lags were chosen according to the Akaike Information Criterion and for white noise of the residuals.

^²The power of ρ_μ (only constant) and ρ_t (constant and time trend) is higher than the power of T_μ (only constant) and T_t (constant and time trend) when the alternative is stationary.

^³The Newey-West weighting scheme was used for estimating the variances of S_μ² and S_t².

Table 30.

Dominican Republic: Unit Root Tests at 5 Percent Level

(1992:Q1–1999:Q1)

$Δ X_{t} = α + β_{t} + γ X_{t - 1} + Σ_{i = 1}^{p - 1} Φ i Δ X_{t - 1} + ε_{t}$
		Dickey-Fuller				Phillips-Perron
Variable	Lags¹	T_μ²	T_t²	ρ_μ³	ρ_t³	T_μ²	T_t²	ρ_μ³	ρ_t³
M1	2	−1.37	−3.66*	−2.62	−85.99*	−0.75	−2.27	−1.06	−10.35
M2	3	−0.10	−3.26	−0.14	154.84	−0.34	−2.02	−0.34	−8.68
GDP	5	−4.11*	−4.30*	−0.83	−2.64	−7.12*	−14.19*	−4.01	−8.29
IDOM	1	−2.53	−2.46	16.72*	−16.78	−1.86	−1.81	−7.77	−7.55
IRD	1	−1.94	−1.89	−9.93	−11.55	−1.63	−1.38	−5.93	−5.32
MID	3	−3.93*	−3.81*	55.66	55.46	−3.54*	−3.50	−18.26*	−18.11
M2D	3	−3.68*	−3.69*	151.63	429.76	−3.30*	−3.23	−18.15*	−18.09
GDPD	6	−1.50	−2.70	−1.86	−6.67	−15.52*	−12.42*	−5.40	−5.83
IDOMD	1	−3.13*	−3.40	−19.73*	−22.17*	−3.78*	−3.97*	−16.88*	−17.14
IRDD	1	−3.13*	−3.77*	−18.66*	−23.12*	−4.17*	−4.66*	−17.82*	−18.22*
Probability of a smaller value 5 percent		−2.99	−3.58	−12.63	−18.20	−2.99	−3.58	−12.63	−18.20

Sources: BCRD; and IMF staff estimates.

Note: IDOM = 9Q-day fending rate in the Dominican Republic.

IRD = interest rate differential; that is, 90-day lending rate in the Dominican Republic minus 90-day T-bill rate in the United States.
M1 D = M1 first differenced.
M2D = M2 first differenced.
GDPD = GDP first differenced.
IDOMD = 90-day lending rate in the Dominican Republic first differenced.
IRDD = 90-day lending rate in the Dominican Republic minus 90-day T-bill race in the United States first differenced.

^¹Lags were chosen according to the Akaike Information Criterion and for white noise of the residuals.

^²The power of ρ_μ (only constant) and ρ_t (constant and time trend) is higher than the power of T_μ (only constant) and T_t (constant and time trend) when the alternative is stationary.

^³The Newey-West weighting scheme was used for estimating the variances of S_μ² and S_t².

Table 31.

Perron (1997) Unit Root Test on the Foreign Interest Rate at 5 Percent¹

(1992:Q1–1999:Q1)

^¹The critical values used correspond to 60 observations tabulated in Perron (1997).

^²T_b is the value that minimizes the t-statistic for testing α = 1.

^³The k maximum was selected using the general to specific recursive procedure.

Table 31.

Perron (1997) Unit Root Test on the Foreign Interest Rate at 5 Percent¹

(1992:Q1–1999:Q1)

Model 1: $Y_{t} = u + Θ D U_{t} + β_{t} + δD {(T_{b})}_{t} + α γ_{t - 1} + Σ_{i = 1}^{k} c_{i} Δ y_{t - 1} + e_{t}$
T_b²	k ³	$\hat{α}$	${\hat{t}}_{α}$	${\hat{t}}_{θ}$
1995:3	10	0.62	6.09	n.a.
1996:2	10	1.24	n.a.	8.45
Model 2: $Y_{t} = u + Θ D U_{t} + β_{t} + δD {(T_{b})}_{t} + α γ_{t - 1} + Σ_{i = 1}^{k} c_{i} Δ y_{t - 1} + e_{t}$
T_b²	k³	$\hat{α}$	${\hat{t}}_{α}$	${\hat{t}}_{θ}$
1997:1	8	−3.20	−5.36	n.a.
1997:1	8	−3.20	n.a.	−5.36

^¹The critical values used correspond to 60 observations tabulated in Perron (1997).

^²T_b is the value that minimizes the t-statistic for testing α = 1.

^³The k maximum was selected using the general to specific recursive procedure.

Table 31.

Perron (1997) Unit Root Test on the Foreign Interest Rate at 5 Percent¹

(1992:Q1–1999:Q1)

Model 1: $Y_{t} = u + Θ D U_{t} + β_{t} + δD {(T_{b})}_{t} + α γ_{t - 1} + Σ_{i = 1}^{k} c_{i} Δ y_{t - 1} + e_{t}$
T_b²	k ³	$\hat{α}$	${\hat{t}}_{α}$	${\hat{t}}_{θ}$
1995:3	10	0.62	6.09	n.a.
1996:2	10	1.24	n.a.	8.45
Model 2: $Y_{t} = u + Θ D U_{t} + β_{t} + δD {(T_{b})}_{t} + α γ_{t - 1} + Σ_{i = 1}^{k} c_{i} Δ y_{t - 1} + e_{t}$
T_b²	k³	$\hat{α}$	${\hat{t}}_{α}$	${\hat{t}}_{θ}$
1997:1	8	−3.20	−5.36	n.a.
1997:1	8	−3.20	n.a.	−5.36

^¹The critical values used correspond to 60 observations tabulated in Perron (1997).

^²T_b is the value that minimizes the t-statistic for testing α = 1.

^³The k maximum was selected using the general to specific recursive procedure.

Tests for cointegration were based on the Johansen-Juselius (1990) method with critical values corrected for small sample bias using Cheung and Lai’s (1993) approach (Table 32).

Table 32.

The Johansen-Juselius Maximum Likelihood Test tor Cointegration

(1992:Q1–1999:Q1)

Sources: BCRD; and IMF staff estimates.r is the number of cointegrated vectors.p is the number of variables.The 99 percent (denoted with *) and 95 percent (denoted with **) critical values corrected for small samples using Cheung and Lai (1993) are used to evaluate the results.The models include a drift term in the variables but not in the cointegration space. The normality test is a multivariate version of the Shenton-Bowman test for normality for individual time series. The LMI and LM4 are the Langrange multiplier tests. p values are in parentheses.

Table 32.

The Johansen-Juselius Maximum Likelihood Test tor Cointegration

(1992:Q1–1999:Q1)

							λ max		Trace
		Eigenvalues	λ max	Trace	H₀:r	p-r	95%	99%	95%	99%	Lags
M1-inter. Rate		0.8517	51.53*	68.09*	0	3	17.69	19.13	37.01	43.94	2
		0.4582	16.55*	16.56	1	2	14.48	16.45	19.32	24.81
		0.0003	0.01	0.01	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	= 6.038		LMI ~χ₉²= 14.793				LM4 ~χ₉²= 8.923
		(0.42)				(0.10)				(0.44)
M2-inter. Rate		0.808	44.12*	63.50*	0	3	17.69	19.13	37.01	43.94	2
		0.5069	19.09*	19.38**	1	2	14.48	16.45	19.32	24.81
		0.0108	0.29	0.29	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	= 11.187		LMI ~χ₉²= 25.675				LM4 ~χ₉²= 13.593
		(0.08)				(0.00)				(0.14)
M1-inter.diff.		0.8873	58.94*	73.95*	0	3	17.69	19.13	37.01	43.94	2
		0.4254	14.96**	15.01	1	2	14.48	16.45	19.32	24.81
		0.0019	0.05	0.05	2.	1.	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=3.693		LMI ~χ₉²= 15.643				LM4 ~χ₉²=9.600
		(0.72)				(0.07)				(0.38)
M2-inter.diff.		0.8578	52.67*	72.44*	0	3	17.69	19.13	37.01	43.94	2
		0.5175	19.68**	19.77**	1	2	14.48	16.45	19.32	24.81
		0.0036	0.10	0.10	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=6.731		LMI ~χ₉²= 23.128				LM4 ~χ₉²= 15.882
		(0.35)				(0.01)				(0.07)
M1-foreign inter.		0.9026	62.89*	76.89*	0	3	17.69	19.13	37.01	43.94
rate		0.3182	10.34	14.00	1	2	14.49	16.45	19.32	24.81	2
		0.1268	3.66	3.66	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=7.949		LMI ~χ₉²=19.747				LM4 ~χ₉²=12.465
		(0.24)				(0.02)				(0.19)
M2-foreign inter.		0.7960	42.92*	61.54*	0	3	17.69	19.13	37.01	43.94	2
rate		0.4547	16.37**	18.61	1	2	14.49	16.45	19.32	24.81
		0.0797	2.24	2.24	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=9.865		LMI ~χ₉²= 9.716				LM4 ~χ₉²= 13.976
		(0.13)				(0.37)				(0.12)

Table 32.

The Johansen-Juselius Maximum Likelihood Test tor Cointegration

(1992:Q1–1999:Q1)

							λ max		Trace
		Eigenvalues	λ max	Trace	H₀:r	p-r	95%	99%	95%	99%	Lags
M1-inter. Rate		0.8517	51.53*	68.09*	0	3	17.69	19.13	37.01	43.94	2
		0.4582	16.55*	16.56	1	2	14.48	16.45	19.32	24.81
		0.0003	0.01	0.01	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	= 6.038		LMI ~χ₉²= 14.793				LM4 ~χ₉²= 8.923
		(0.42)				(0.10)				(0.44)
M2-inter. Rate		0.808	44.12*	63.50*	0	3	17.69	19.13	37.01	43.94	2
		0.5069	19.09*	19.38**	1	2	14.48	16.45	19.32	24.81
		0.0108	0.29	0.29	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	= 11.187		LMI ~χ₉²= 25.675				LM4 ~χ₉²= 13.593
		(0.08)				(0.00)				(0.14)
M1-inter.diff.		0.8873	58.94*	73.95*	0	3	17.69	19.13	37.01	43.94	2
		0.4254	14.96**	15.01	1	2	14.48	16.45	19.32	24.81
		0.0019	0.05	0.05	2.	1.	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=3.693		LMI ~χ₉²= 15.643				LM4 ~χ₉²=9.600
		(0.72)				(0.07)				(0.38)
M2-inter.diff.		0.8578	52.67*	72.44*	0	3	17.69	19.13	37.01	43.94	2
		0.5175	19.68**	19.77**	1	2	14.48	16.45	19.32	24.81
		0.0036	0.10	0.10	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=6.731		LMI ~χ₉²= 23.128				LM4 ~χ₉²= 15.882
		(0.35)				(0.01)				(0.07)
M1-foreign inter.		0.9026	62.89*	76.89*	0	3	17.69	19.13	37.01	43.94
rate		0.3182	10.34	14.00	1	2	14.49	16.45	19.32	24.81	2
		0.1268	3.66	3.66	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=7.949		LMI ~χ₉²=19.747				LM4 ~χ₉²=12.465
		(0.24)				(0.02)				(0.19)
M2-foreign inter.		0.7960	42.92*	61.54*	0	3	17.69	19.13	37.01	43.94	2
rate		0.4547	16.37**	18.61	1	2	14.49	16.45	19.32	24.81
		0.0797	2.24	2.24	2	1	4.84	8.36	4.84	8.36
Residuals
Normality	~χ₆²	=9.865		LMI ~χ₉²= 9.716				LM4 ~χ₉²= 13.976
		(0.13)				(0.37)				(0.12)

Tests of the residuals indicated that they were not serially correlated. Overall, there is strong statistical evidence of a long-run cointegration relationship between real monetary aggregates, real output, and interest rates in the Dominican Republic during the sample period. For more information on the tests also see Appendix VI.2.

The Long-Run Elasticities of the Model

Although the main objective of this paper is to test the existence of a long-run relationship between real monetary aggregates, real output, and interest rates, it was also thought important to look into the dynamics of the short-run disequilibrium. As a result, Table 33 reports not only the long-run parameters of the models, but also the parameters of the short-run dynamics from the Phillips-Loretan nonlinear dynamic least squares estimator.⁷⁷

Table 33.

The Phillips-Loretan Nonlinear Dynamic Least Squares Estimator

(1992–99:Q1)

Sources: BCRD; and IMF staff estimates.T ratios are in parentheses. Bartlett-Kolmogorov-Smirnov (B-K-S) 10 percent critical value is 0.305.

Table 33.

The Phillips-Loretan Nonlinear Dynamic Least Squares Estimator

(1992–99:Q1)

Equation 5: ${(\frac{M}{P})}_{t} = a + b y_{t} + c i_{t} + Σ_{j = - k}^{k} (d_{j} Δ y_{t - j} + e_{j} Δ i_{t - j}) + ρ [{(\frac{M}{P})}_{t - 1} - a - b y_{t - 1} - c i_{t - 1}] + ε_{t}$
M1					M2
Constant		−4.87		(−2.68)	Constant		−7.09		(−3.29)
Y_t		0.73		(4.50)	Y_t		0.95		(4.65)
i_i		0.02		(0.65)	i_i		0.05		(2.17)
ΔY_t-1		−0.27		(−2.76)	ΔY_t-2		−0.63		(−1.79)
Δi_t-1		−0.02		(−5.06)	Δi_t-2		−0.01		(−0.86)
ΔY_t		0.30		(0.78)	ΔY_t-1		0.28		(0.77)
Δi_t		−0.03		(−1.06)	Δi_t-1		−0.02		(−3.63)
ΔY_t+1		0.24		(0.64)	ΔY_t		0.00		(0.00)
Δi_t+1		−0.00		(−1.08)	Δi_t		−0.04		(−1.94)
ρ		−0.83		(−11.98)	ΔY_t+1		1.58		(1.46)
					Δi_t+1		0.00		(0.03)
					ΔY_t+2		2.05		(2.76)
					Δi_t+2		0.01		(1.29)
					ρ		−0.68		(−4.56)
	$\bar{R^{2}} = 0.98$		SE =0.02			$\bar{R^{2}} = 0.98$		SE = 0.02
	χ₁²= 0.04		χ₄²= 1.58			χ₁²= 0.05		χ₄²= 1.21
	B-K-S=0.27		b=1~χ₁²=2.75			B-K-S=0.22		b=1~χ₁²=0.05
Equation 6: ${(\frac{M}{P})}_{t} = a + b y_{t} + c {(i - i )}_{t} + Σ_{j = - k}^{k} [d_{j} Δ y_{t - j} + e_{j} Δ {(i - i )}_{t - j}] + ρ [{(\frac{M}{P})}_{t - 1} - a - b y_{t - 1} - c {(i - i *)}_{t - 1}] + η_{t}$
Constant		−6.01		(−3.28)	Constant		−4.41		(−2.29)
Y_t		0.84		(4.87)	Y_t		0.75		(4.29)
(i-i^*)_t		0.02		(1.36)	(i-i^*)_t		0.06		(2.48)
ΔY_t-1		−0.26		(−2.40)	ΔY_t-1		−0.22		(−2.25)
Δi_t-1		−0.02		(−4.98)	Δi_t-1		−0.02		(−4.08)
ΔY_t		0.41		(1.13)	ΔY_t		0.39		(1.04)
Δ(i-i^*)_t		−0.03		(−2.20)	Δ(i-i^*)_t		−0.06		(−2.54)
ΔY_t+1		0.47		(1.26)	ΔY_t+1		0.04		(0.08)
Δ(i-i^*)_t+1		−0.01		(−1.54)	Δ(i-i^*)_t+1		0.00		(0.20)
ρ		−0.79		(−11.99)	ρ		−0.80		(−13.59)
	$\bar{R^{2}} = 0.98$		SE =0.02			$\bar{R^{2}} = 0.98$		SE = 0.02
	χ₁²= 0.02		χ₄²= 2.06			χ₁²= 0.06		χ₄²= 0.89
	B-K-S = 0.23		b=1~χ₁²= 0.82			B-K-S =0.18		b=1~χ₁²= 2.08
Equation 7: ${(\frac{M}{P})}_{t} = a + b y_{t} + {ci}_{t} * + Σ_{j = - k}^{k} [d_{j} Δ y_{t - j} + e_{j} Δ {i^{}}_{t - j}] + ρ [{(\frac{M}{P})}_{t - 1} - a - b y_{t - 1} - c {i^{}}_{t - 1}] + ξ_{t}$
Constant		−0.54		(−0.78)	Constant		0.16		(0.45)
Y_t		0.36		(4.95)	Y_t		0.41		(12.23)
i_t^*		−0.05		(−2.63)	i_t^*		−0.10		(−10.70)
ΔY_t-2		−0.24		(−2.16)	ΔY_t		0.08		(1.00)
Δi^*_t-2		−0.05		(−2.81)	Δi_t^*		0.05		(3.18)
ΔY_t-1		−0.07		(−0.33)	ΔY_t+1		−0.09		(−0.47)
Δi^*_t-2		−0.03		(−1.78)	Δi^*_t+1		−0.03		(−3.15)
ΔY_t		−0.68		(−2.17)	ρ		−0.50		(−5.58)
Δi_t^*		0.01		(0.54)
ΔY_t+1		1.80		(3.10)
Δi^*_t+1		0.03		(1.59)
ρ		0.50		(−2.96)
	$\bar{R^{2}} = 0.97$		SE =0.03			$\bar{R^{2}} = 0.99$		SE = 0.02
	χ₁²= 0.31		χ₄²= 2.89			χ₁²= 0.40		χ₄²= 0.89
	B-K-S = 0.16		b=1~χ₁²= 80.22			B-K-S =0.17		b=1~χ₁²= 308.05

Sources: BCRD; and IMF staff estimates.T ratios are in parentheses. Bartlett-Kolmogorov-Smirnov (B-K-S) 10 percent critical value is 0.305.

Table 33.

The Phillips-Loretan Nonlinear Dynamic Least Squares Estimator

(1992–99:Q1)

Equation 5: ${(\frac{M}{P})}_{t} = a + b y_{t} + c i_{t} + Σ_{j = - k}^{k} (d_{j} Δ y_{t - j} + e_{j} Δ i_{t - j}) + ρ [{(\frac{M}{P})}_{t - 1} - a - b y_{t - 1} - c i_{t - 1}] + ε_{t}$
M1					M2
Constant		−4.87		(−2.68)	Constant		−7.09		(−3.29)
Y_t		0.73		(4.50)	Y_t		0.95		(4.65)
i_i		0.02		(0.65)	i_i		0.05		(2.17)
ΔY_t-1		−0.27		(−2.76)	ΔY_t-2		−0.63		(−1.79)
Δi_t-1		−0.02		(−5.06)	Δi_t-2		−0.01		(−0.86)
ΔY_t		0.30		(0.78)	ΔY_t-1		0.28		(0.77)
Δi_t		−0.03		(−1.06)	Δi_t-1		−0.02		(−3.63)
ΔY_t+1		0.24		(0.64)	ΔY_t		0.00		(0.00)
Δi_t+1		−0.00		(−1.08)	Δi_t		−0.04		(−1.94)
ρ		−0.83		(−11.98)	ΔY_t+1		1.58		(1.46)
					Δi_t+1		0.00		(0.03)
					ΔY_t+2		2.05		(2.76)
					Δi_t+2		0.01		(1.29)
					ρ		−0.68		(−4.56)
	$\bar{R^{2}} = 0.98$		SE =0.02			$\bar{R^{2}} = 0.98$		SE = 0.02
	χ₁²= 0.04		χ₄²= 1.58			χ₁²= 0.05		χ₄²= 1.21
	B-K-S=0.27		b=1~χ₁²=2.75			B-K-S=0.22		b=1~χ₁²=0.05
Equation 6: ${(\frac{M}{P})}_{t} = a + b y_{t} + c {(i - i )}_{t} + Σ_{j = - k}^{k} [d_{j} Δ y_{t - j} + e_{j} Δ {(i - i )}_{t - j}] + ρ [{(\frac{M}{P})}_{t - 1} - a - b y_{t - 1} - c {(i - i *)}_{t - 1}] + η_{t}$
Constant		−6.01		(−3.28)	Constant		−4.41		(−2.29)
Y_t		0.84		(4.87)	Y_t		0.75		(4.29)
(i-i^*)_t		0.02		(1.36)	(i-i^*)_t		0.06		(2.48)
ΔY_t-1		−0.26		(−2.40)	ΔY_t-1		−0.22		(−2.25)
Δi_t-1		−0.02		(−4.98)	Δi_t-1		−0.02		(−4.08)
ΔY_t		0.41		(1.13)	ΔY_t		0.39		(1.04)
Δ(i-i^*)_t		−0.03		(−2.20)	Δ(i-i^*)_t		−0.06		(−2.54)
ΔY_t+1		0.47		(1.26)	ΔY_t+1		0.04		(0.08)
Δ(i-i^*)_t+1		−0.01		(−1.54)	Δ(i-i^*)_t+1		0.00		(0.20)
ρ		−0.79		(−11.99)	ρ		−0.80		(−13.59)
	$\bar{R^{2}} = 0.98$		SE =0.02			$\bar{R^{2}} = 0.98$		SE = 0.02
	χ₁²= 0.02		χ₄²= 2.06			χ₁²= 0.06		χ₄²= 0.89
	B-K-S = 0.23		b=1~χ₁²= 0.82			B-K-S =0.18		b=1~χ₁²= 2.08
Equation 7: ${(\frac{M}{P})}_{t} = a + b y_{t} + {ci}_{t} * + Σ_{j = - k}^{k} [d_{j} Δ y_{t - j} + e_{j} Δ {i^{}}_{t - j}] + ρ [{(\frac{M}{P})}_{t - 1} - a - b y_{t - 1} - c {i^{}}_{t - 1}] + ξ_{t}$
Constant		−0.54		(−0.78)	Constant		0.16		(0.45)
Y_t		0.36		(4.95)	Y_t		0.41		(12.23)
i_t^*		−0.05		(−2.63)	i_t^*		−0.10		(−10.70)
ΔY_t-2		−0.24		(−2.16)	ΔY_t		0.08		(1.00)
Δi^*_t-2		−0.05		(−2.81)	Δi_t^*		0.05		(3.18)
ΔY_t-1		−0.07		(−0.33)	ΔY_t+1		−0.09		(−0.47)
Δi^*_t-2		−0.03		(−1.78)	Δi^*_t+1		−0.03		(−3.15)
ΔY_t		−0.68		(−2.17)	ρ		−0.50		(−5.58)
Δi_t^*		0.01		(0.54)
ΔY_t+1		1.80		(3.10)
Δi^*_t+1		0.03		(1.59)
ρ		0.50		(−2.96)
	$\bar{R^{2}} = 0.97$		SE =0.03			$\bar{R^{2}} = 0.99$		SE = 0.02
	χ₁²= 0.31		χ₄²= 2.89			χ₁²= 0.40		χ₄²= 0.89
	B-K-S = 0.16		b=1~χ₁²= 80.22			B-K-S =0.17		b=1~χ₁²= 308.05

Sources: BCRD; and IMF staff estimates.T ratios are in parentheses. Bartlett-Kolmogorov-Smirnov (B-K-S) 10 percent critical value is 0.305.

Analysis of the residuals indicated that they were white noise; there is agreement between the nonparametric test (Bartlett-Kolmogorov-Smirnov) at the 10 percent level and the visual observation of the residuals in Figures 5–10.⁷⁸ The residuals are also ho-moscedastic according to two chi-square tests using one and four lags.⁷⁹

The constant and the long-run output elasticity are significant at the 99 percent level. As expected, the long-run output elasticity is not statistically different from one in equations (5) and (6) at the 90 percent level (and above) as denoted by the x² statistic. The long-run output elasticity is different from one only when the foreign interest rate is used in the regression.

The long-run interest rate semielasticity of real M1 is not statistically different from zero at conventional confidence levels. A possible rationalization of this result requires appealing to the steady state of the model of Appendix VI.1, solved in Nadal-De Simone (2001). In the long run (steady state), the rate of growth of real monetary aggregates equals the rate of productivity growth, that is, the rate of potential output growth. Given that the model assumes long-run money neutrality, the results of regressions (5) and (6) are not surprising. It could also be argued that a good representation of the long-run real demand for M1 seems consistent with a cash-in-advance model where money is a means of payment (Lucas and Stokey, 1987).

In contrast, the long-run interest rate semielasticity of real M2 is positive, and strongly significant, either with the domestic interest rate or with the interest rate differential. Its value, however, is small (0.05). The strongly significant negative interest semielasticity of the foreign interest rate (0.10) argues against the interpretation that the interest rate differential is driven mostly by the variance of the domestic interest rate. The significant positive interest semielasticity of real M2 may be due to the fact that M2 includes the only domestic interest-bearing assets that economic agents have available in the Dominican Republic. It is also possible that this is the result of the frequent BCRD foreign exchange market interventions that, in the presence of large capital inflows, have tended to keep interest rates higher than otherwise.⁸⁰

The coefficients on the interest rate changes reflect the short-run dynamics of the model. It is noteworthy that all significant coefficients of changes either in the domestic interest rate or in the interest rate differential (lagged, contemporaneous, led) are negative, as it is customary to find in money demand estimations (Johansen and Juselius, 1990). Moreover, they are not statistically different across specifications.

The negative coefficients of changes in the domestic interest rate (or in the interest rate differential), together with the positive long-run interest rate semi-elasticity of real M2 (and the zero long-run interest rate semielasticity of real Ml), are consistent with the open economy paradigm of Mundell-Fleming. Those results suggest that the efficacy of monetary policy in the Dominican Republic, measured by its ability to affect domestic interest rates, is lower in the long run than in the short run.⁸¹ A tightening of monetary policy, for instance, increases the domestic interest rate, encouraging capital inflows, and appreciates the currency.⁸² If the authorities let the currency appreciate, as the banking system intermediates the capital inflow, real M2 increases and domestic credit also rises. If the monetary authorities intervene to prevent the appreciation of the exchange rate, the monetary base may increase (increasing real M2, other things being equal) as long as the intervention is unsterilized. If sterilized, the intervention would put upward pressure on interest rates, attracting further capital inflows.

The varying results for short- and long-run coefficients illustrate that in assessing the stance of monetary policy in open economies, it is important to distinguish the long-run equilibrium from the short-run dynamics.⁸³ Otherwise, the identification of the effects of policy shocks (and nonpolicy shocks) on interest rates is likely to be difficult. For example, a policy-induced monetary tightening will increase interest rates and reduce money demand in the short run. However, because of the feedback between interest rates and capital flows, we may find over time that the initial monetary tightening produces an increase in monetary aggregates. In addition, if inflation expectations embedded in interest rates decline (as they could with a monetary policy tightening), interest rates will eventually decline, although this should not be interpreted as a loosening of monetary policy.

Finally, the highly significant values of the coefficients measuring the previous-period deviation from long-run equilibrium indicate that adjustment to changes in the domestic interest rate or in the interest rate differential takes place between two and four quarters. This is consistent with most accounts of the lags with which monetary policy normally operates in the Dominican Republic. The coefficient measuring the previous-period deviation from long-run equilibrium following a change in the foreign interest rate indicates that adjustment takes place relatively more rapidly; it takes place in one quarter.

Conclusion and Policy Implications

This study reports the estimation of three money demand equations for two real monetary aggregates (M1 and M2), one using the domestic interest rate, another using the interest rate differential between the 90-day domestic deposit rate and the 90-day U.S. treasury bill rate, and the last one using only the U.S. interest rate. The results suggest that in the sample period 1992:Q1–1999:Q1 there is cointegration between real monetary aggregates (M1 and M2), real output, and interest rates in any of the three forms used in this study.

The long-run income elasticity is not statistically different from one where the domestic interest rate, or the interest rate differential with the United States, is used. The long-run interest rate semielasticity, or the long-run interest rate differential semielasticity, is significant and positive for real M2 demand, but not for real M1 demand. The long-run semielastici-ties have a low value when the interest rate used is the domestic rate or the interest rate differential. In contrast, the long-run foreign interest rate semielasticity is negative and strongly significant for both real M1 and real M2. Real M2 is more responsive to the foreign interest rate than it is to the domestic interest rate.

By relating the overall results to the three motivations of this study, it can be concluded that, first, the data support the central role of money demand in the monetary program of the BCRD. Second, it seems that the efficacy of monetary policy in the Dominican Republic, measured by its ability in affecting the domestic interest rate in a lasting manner, is lower in the long run than in the short run. Finally, the monetary policy stance is not well measured by interest rates alone, or by the growth of monetary aggregates alone. As the varying results for short- and long-run coefficients illustrate, in assessing the stance of monetary policy in open economies, it is important to distinguish the long-run equilibrium from the short-run dynamics. Otherwise, the identification of the effects of policy shocks (and nonpolicy shocks) on interest rates is likely to be difficult, and lead to contradictory results, as the recent debate on the monetary policy stance in Asia shows.

Despite the robustness of the results of the paper, it should be kept in mind that the short sample available prevented any meaningful stability test. Similarly, a meaningful out-of-sample simulation could not be performed. Finally, the use of the terms “long-run cointegration relationships” between real monetary aggregates, real output, and interest rates in this paper should be put in the context of the seven-year length of the sample available.⁸⁴

Appendix VI.I A Stylized Open Economy Model

This appendix uses a version of the standard textbook IS-LM model to illustrate the behavior of a small open economy following a monetary policy shock. In two recent articles, McCallum and Nelson (1996, 1999) showed that the standard IS-LM framework for a small open economy is compatible with explicit analysis of the maximizing behavior of rational economic agents, provided that the IS curve includes expected future output on the right-hand side, and that there is no habit formation in consumption.⁸⁵

Assume a small open economy that produces two goods, some of which are exported. The economy also imports and consumes foreign goods. The price of domestic goods (pt) is determined mostly by domestic forces while the price of foreign goods (pt*) is determined in world markets. With all variables except interest rates in logs, the model is

\begin{matrix} y_{t}^{d} = a_{0} + E_{t} y_{t + 1^{d}} + a_{1} r_{t} + a_{2} q_{t} + a_{3} y_{t}^{*} + {ε_{t}}^{y^{d}} & (A 1) \\ r_{t} = i_{t} - E_{t} (P_{t + 1} - P_{t}) & (A 2) \\ q_{t} = e_{t} + p_{t} * - p_{t} & (A 3) \\ y_{t}^{s} = {\bar{y}}_{t} + d_{1} (p_{t} - E_{t - 1} {\bar{p}}_{t}) + {ε_{t}}^{y^{s}} & (A 4) \\ {\bar{y}}_{t} = δ + {ε_{t}}^{\bar{y}} & (A 5) \\ P_{t} = α p_{t} + (1 - α) (e_{t} + p_{t} *) & (A 6) \\ m_{t} - P_{t} = b_{0} + b_{1} y_{t} + b_{2} i_{t} + ε_{t}^{m^{d}} & (A 7) \\ i_{t} = i_{t} * + E_{t} (e_{t + 1} - e_{t}) + ρ & (A 8) \\ m_{t} = c_{0} + {Γ m}_{t - 1} + ε_{t}^{m^{s}} & (A 9) \end{matrix}

where $y_{t}^{d}$ is the demand for the domestic good, a₀ is a constant, r_t is the real interest rate, q_t is the real exchange rate, $y_{t}^{*}$ is foreign output, e_t is the nominal exchange rate (defined as the number of domestic currency units necessary to buy a unit of foreign currency), $p_{t}^{*}$ is the price of foreign output, P_t is the price of domestic goods, ${\bar{y}}_{t}$ is potential output, δ is a constant productivity rate, P_t is the general price level as measured by the consumer price index, α is the share of domestic goods in the price index, m_t is the money stock, b₀ is a constant, i_t is the nominal interest rate, $i_{t}^{*}$ is the foreign nominal interest rate, ρ is a constant country risk premium, and c₀ is a constant. E_i is the expectational operator based on information available at time i. All disturbance terms, ε_t are assumed to be white noise for simplicity. All coefficients except a₁ and b₂ are positive.

Equation (A1) is an is curve for a small open economy that includes the expected value of next period’s output as suggested by McCallum and Nelson. Equation (A2) is the Fisher equation; there is an identical relation for the rest of the world. Equation (A3) defines the real exchange rate. Equations (A2) and (A3) represent real interest rate parity.⁸⁶

Aggregate supply behavior is represented by equation (A4), which embodies the “natural rate” hypothesis. Following McCallum and Nelson (1996), “price stickiness” is introduced simply by assuming that producers set domestic goods prices in period t at the value $({\bar{p}}_{t})$ that is expected to clear the market $p_{t} = E_{t - 1} {\bar{p}}_{t}$ , given information available at time (t-1). The idea is that market participants find it optimal to preset prices at levels that are expected to clear the market next period.⁸⁷ Therefore, p_t is the price that would prevail in the goods market if there were no unexpected shocks. Unexpected demand and supply shocks will make output realizations different from expected values. As a result, current period output is demand-determined given the price preset for the current period by producers, based on their information at the end of previous period.

While the standard IS-LM model is frequently regarded as implying the existence of capital adjustment costs, the model here has no explicit capital adjustment costs. Therefore, equation (A5) assumes that potential output $({\bar{y}}_{t})$ , consistent with the assumption that there are no contemporaneous responses of output to monetary shocks, grows at the exogenously given productivity rate δ.⁸⁸

Equation (A6) defines the overall price level in terms of the prices of domestic and foreign goods. Equation (A7) describes the demand for money. Equation (A8) is uncovered interest parity, and assumes a constant country risk premium for simplicity.⁸⁹ Equation (A9) describes the behavior of the nominal money supply which follows an AR(1) process such that when Г=1, the monetary shock is permanent, and when Г≠1, the monetary shock is transitory.

After some algebra and assuming for simplicity zero expected inflation abroad,

\begin{matrix} \begin{matrix} y_{t}^{d} = a_{0} + E_{t}^{{yd}_{t + 1}} + a_{1} [i_{t} - E_{t} (P_{t + 1} - P_{t})] + \\ a_{2} (e_{t} + p_{t}^{*} - p_{t}) + a_{3} y_{t}^{*} + {ε_{t}}^{y^{d}} \end{matrix} & (A 10) \\ y_{t}^{s} = δ + d_{1} (p_{t} - E_{t - 1} {\bar{p}}_{t}) + {ε_{t}}^{y^{s}} & (A 11) \\ \begin{matrix} m_{t} - P_{t} = b_{0} + b_{1} y_{t} + b_{2} [i_{t} * + E_{t} (e_{t + 1} - e_{t})] \\ + {ε_{t}}^{m^{d}} \end{matrix} & (A 12) \end{matrix}

Equations (A10)–(A12) determine the price and the output of the domestic good, together with the exchange rate (or the interest rate via interest rate parity).⁹⁰ Various versions of equation (A12) were estimated.⁹¹

To illustrate the behavior of the economy, it is convenient to view the expected value of a variable as its long-run value. For example, E_te_t+1 is the long run value of the nominal exchange rate, the value that will prevail under full employment and full price adjustment.

The behavior of the economy described by the system (A10)–(A12) is exhibited in Figures 11 and Figures 12. In the upper panels, all output-interest rate combinations for which there is equilibrium in the goods market and in the money market are represented by the downward-sloping IS curve and the upward-sloping LM curve, respectively. The upward-sloping BP curve in the upper panels describes all the output-interest rate combinations for which there is balance of payments equilibrium. The BP curve is less steep than the LM curve to indicate a large degree of capital mobility (normally, a BP curve steeper than an LM curve is used to represent a case of low capital mobility). The larger the increase is in the capital inflow for a given increase in the interest rate, the smaller will be the increase in the interest rate required to maintain balance of payments equilibrium as output rises; that is, the flatter the BP curve will be. In the lower panels, upward-sloping IS and BP curves show all the combinations of exchange rates and output for which there is equilibrium in the goods market and in the balance of payments.

Figure 11 shows the behavior of the economy following a temporary reduction in the money supply, that is, all expected values equal their long-run equilibrium levels. A monetary tightening—prior to the change in the exchange rate—increases the interest rate from i₁ to i₂ decreases output to y₂ and the balance of payments shows an incipient surplus. Point 2 is not an equilibrium. As a result, the exchange rate appreciates from e; to e₁ to e₃ to preserve interest rate parity. The interest rate falls somewhat to i₃ as capital flows in. The appreciation of the exchange rate shifts the BP curve upward and restores balance of payments equilibrium. The appreciation of the exchange rate also shifts the IS curve downward because imports rise and exports fall. Output falls further to y₃ After the temporary monetary contraction, the economy has moved from point 1 to point 3, where output is below potential. As the contractionary monetary policy is reversed over time, the economy will return to point 1.

In Figure 12, because the monetary tightening is permanent, not only the exchange rate but also the expected exchange rate will appreciate. As a result, the increase in the interest rate, the fall in output, and the spot exchange rate appreciation are larger than in the case of the temporary monetary shock. Point 4 is the new short-run equilibrium. However, at point 4, output is below potential. Thus, over time, domestic prices will start to fall to their new long-run equilibrium. That reduction will be proportional to the fall in the money supply. The fall in prices discourages imports and encourages exports, and therefore the IS and BP curves move to the right. Because the fall in prices increases real money balances, LM shifts downward, and the interest rate falls. The curves stop shifting when the price level and the exchange rate fall in proportion to the fall in the money supply and output is back lo potential. The new equilibrium will be at point 1 in the upper panel, and at 5 in the lower panel.

If the monetary authority partially offsets the exchange rate appreciation that follows the monetary policy tightening via an unsterilized intervention in the foreign exchange market, the stock of money will be relatively larger and the interest rate will be relatively lower than otherwise. As a result, the money stock behavior will be endogenized and, in the short run, all the curves will shift relatively less than in the case of a pure exchange rate float.

Appendix VI.2 Unit Roots and Cointegration

The literature on unit roots and cointegration is vast and will not be reviewed here. Suffice it to say that there is a valid concern among economists about the appropriateness of the tests for unit roots and their power against stationary alternatives. The choice of a particular testing methodology is not straightforward. Ultimately, one may not be able to determine whether there is a unit root in a given time series. Inevitably, however, a choice has to be made. In testing for unit roots and cointegration, the strategy followed in this study was to use different tests. A decision was then made based on whether or not the results of these various tests converge. Two popular methods to test unit roots were used: the ADF test (Dickey and Fuller, 1979, 1981 and Said and Dickey, 1984), and the Phillips-Perron test (Phillips, 1987, and Perron, 1988). Given the behavior of the 90-day T-bill rate in the period 1994–1995, the Perron (1997) test, which allows for a break in the intercept and or the slope of the series, was used for that series.

Tables 30 and Table 31 report the results for unit root tests.⁹² In general, the tests considered tend to agree that real M1, real M2, the domestic interest rate, the interest rate differential, and the foreign interest rate are unit root processes. However, while the T_μ and the T_τ versions of the ADF and the Phillips-Perron tests reject the null of a unit root in real output, the ρ_µ and the ρ_τ versions of those tests accept the null. As the latter versions of the tests are more powerful against a stationary alternative, it was decided that real output may contain a unit root. That decision was also based on the observation that the spectrum of the first difference of real output has Granger’s typical spectral shape.⁹¹

Gonzalo (1994) compared five different residual-based tests for cointegration. Among them, he recommends using the Johansen-Juselius (1990) method. Although very popular in the literature, this test has been highly criticized for its lack of power in finite samples, and—among other problems—by its sensitivity to the choice of the lag length. This test was used and the results are reported in Table 32. Given the relatively short sample period available, the critical values were corrected for small sample bias using Cheung and Lai’s (1993) approach. Lag length was evaluated as follows. A general lag model was estimated. Then, unnecessary lags were eliminated by testing backward using the Schwarz Criterion. The residuals of the models were checked for white noise each time using LM(1) and LM(4) tests, and for normality using a multivariate version of the Shenton-Bowman test. In all cases the tests accepted the null of Gaussian residuals. The LM(1) tests for real M2-domestic interest rate, real M2-interest rate differential, and real Mi-foreign interest rate indicated some serial correlation. The LM(4) tests—and LM tests with longer lags—however, accepted the null of white noise for the residuals at reasonable confidence levels.

At the 99 percent level and in all cases analyzed in this study, the λ_trace statistic strongly rejected the null hypothesis of no cointegrating vectors against the alternative of one or more cointegrating vectors (r > 0). Similarly, at the 99 percent level and in all cases, the λ_max statistic rejected the null hypothesis of no cointegrating vectors against the alternative of one cointegrating vector (r = 1). For M2, the λ_trace statistic rejected the null hypothesis of r≤1 cointegrating vectors against the alternative of two or more cointegrating vectors at the 95 percent level, except when the foreign interest rate was used. For Ml, that rejection occurred at the 90 percent level, again with exception of the system with the foreign interest rate. The λ_max statistics rejected the null of one cointegrating vector (r = 1) against the specific alternative of two cointegrating vectors (r = 2) at the 95 percent level at least in all cases, except in the case of real M1 and the foreign interest rate.⁹⁴

Finally, if real output were stationary, one more cointegrating vector would be required. As a result, multivariate tests of non stationary were performed. They did not reject the null of a unit root for real output when the aggregate was real Ml. but they did reject the null of a unit root for real output in the case of real M2. This confirmed the decision taken based on Dickey-Fuller and Phillips-Perron tests for the case of M1. As a result, real GDP was also detrended assuming a deterministic trend, and all the cointegration tests were run again. At the 99 percent level, the statistic rejected the null hypothesis of two cointegrating vectors against the alternative of three cointegrating vectors for real M2 and the domestic interest rate. That rejection occurred at the 95 percent level for real M2 and the interest rate differential.

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Abstract

The Estimated Equations and the Estimation Technique

Unit Roots, Cointegration, and Long-Run Elasticities

The Long-Run Elasticities of the Model

Conclusion and Policy Implications

Appendix VI.I A Stylized Open Economy Model

Appendix VI.2 Unit Roots and Cointegration

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