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Right theory, wrong variable: foreign variables and monetary policy in Jamaica/Bonne theorie, mauvaise variable les variables etrangeres et la politique monetaire en Jamaique/Teoria indicada, variable incorrecta: variables exteriores y politica monetaria en Jamaica.

ABSTRACT

The quantity theory of money suggests there is an unambiguous causal relationship between money supply and price level. Quarterly data from Jamaica for a 28-year period (1980-2008) reveal that two other variables exert influence on the price level. The first causal relationship is between changes in the exchange rate and the price level. The second is between US money supply and Jamaica's price level. These results suggest that monetary policy in small open economies may not, by itself, tame inflationary pressures (JEL E31, F31).

La teoria cuantitativa del dinero indica que existe una clara relacion causal entre la oferta de dinero y el nivel de precios. Los datos trimestrales de Jamaica para un periodo de 28 anos (1980-2008) indican que hay otros dos variables que influyen en el nivel de precios. La primera relacion causal existe entre los cambios en la tasa de cambio y el nivel de precios. La segunda existe entre la oferta de dinero de los Estados Unidos y el nivel del precio de Jamaica. De acuerdo con los resultados, la politica monetaria de las economias pequenas y abiertas, por si sola, no llega a controlar las presiones inflacionarias (JEL E31, F31).

Palabras claves: Nivel de Precios; Inflacion; Deflacion; Divisas

La theorie quantitative de la monnaie suggere qu'il existe un lien univoque de causalite entre la masse monetaire et le niveau des prix. Les donnees trimestrielles de la Jamaique d'une periode de 28 ans (1980-2008) revelent que deux autres variables exercent une influence sur le niveau des prix. Le premier lien de causalite est entre les variations du taux de change et le niveau des prix. Le deuxieme est entre la masse monetaire aux Etats-Unis et le niveau des prix en Jamaique. Ces resultats indiquent qu'il est possible que la politique monetaire des petites economies ouvertes ne dompte pas seule les pressions inflationnistes (JEL E31, F31).

Mots-cles: Niveau des prix; Inflation; Deflation; Devises Etrangeres Los Hindus en las Islas Virgenes Norteamericanas

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A perfunctory survey of macroeconomic literature is enough to reveal a consensus around the quantity theory of money. A profession known for wide differences of opinion agrees in general that there is an unambiguous causal relationship between money supply and prices. According to De Long (2000) and Mankiw (2000), among other textbook authors, the direction of that causality goes from money supply to price level. In mainstream economics, money is exogenous; a change in money supply will change price level in a proportionate manner and not the other way around.

The exogeneity of money supply is central to mainstream monetary policy. If money supply is exogenous (and if velocity of money is constant) then controlling the money supply can help stabilize an economy. De Long (2000) even sustains that this is the principal policy implication of the quantity theory of money. This theory has defined, in large part, the role of central banks in economies such as the European Union. Arestis and Chortareas (2006) argue that one of the main goals of mainstream monetary policy is to achieve price stability by keeping money supply growth in check.

According to Roncaglia (2005) the quantity theory of money is also one of the oldest theories in economics, first formulated in the late sixteenth century. However, as mentioned by Friedman and Schwartz (1982), it is arguably one of the most controversial theories in the social sciences and, without a doubt, one of the most tested in economics. Its modern conception is a result of Milton Friedman's work over the course of the second half of the twentieth century. Friedman's research had a considerable effect on economic policymaking all over the world. His conclusions on appropriate monetary policy became policy prescriptions. De Long (2000) even asserts that "Monetarism" rose to become an ideology.

A close examination of quarterly data from Jamaica, over a 28-year time span, reveals that the causality between money supply and price level is potentially bidirectional. In other words, sometimes changes in the price level may actually affect the quantity of money in these economies. Is this an indication that the quantity theory of money is incorrect? Not quite.

Cointegration analysis, together with Granger causality tests, reveals that the Jamaican consumer price index is sensitive to foreign variables. It turns out that for Jamaica, changes in the US money supply trigger changes in the domestic price level. Changes in the exchange rate, the price of one US dollar, also cause changes in the cost of living in Jamaica.

Thus, the quantity theory of money is the right theory for describing the relationship between money supply and price level in Jamaica. However, the independent variable, money supply, is incorrectly specified. There is an unambiguous, unidirectional relationship between US money supply and Jamaica's price level.

MONETARY POLICY IN JAMAICA

Monetary policy can be viewed as the set of procedures undertaken by the monetary authorities to manage the money supply exchange rates and interest rates, and to influence credit conditions to achieve economic objectives (Chibba 2007, Palley 1994). Ultimately monetary policy is one of various stabilization policies implemented in countries as a means of addressing economic imbalances (Chibba 2007). Sufficient coordination is required between the authorities creating monetary policy and other participants trying to stabilize an economy, since monetary policy on its own has its limitations.

The Bank of Jamaica is the authority which manages monetary policy for Jamaica. The stated intention of the Bank is to regulate growth in both money and credit, in accordance with the primary objective of achieving price stability. This is done by coordinating the resources that finance economic activity and generate employment. Low inflation is considered the best contribution monetary policy can provide to the economic and financial welfare of residents.

The Bank of Jamaica takes into consideration a variety of market information when formulating monetary policy, including current and future developments in the macro-economy, external sector developments, and fiscal operations. All of the relevant information influences liquidity conditions in Jamaica and ultimately price levels, making the identification of liquidity sources a key concern of the Bank.

Since the Bank of Jamaica does not have the ability to directly impact the prices of goods and services, it targets various operating and intermediate variables that directly influence inflation. As a result, monetary targeting plays a significant role in the Bank's framework and strategy when attempting to maintain a desired price level.

The operating target of the Bank is the monetary base and it is used to exercise control over the amount of liquidity that exists in the economy. The monetary base is the monetary aggregate that is controlled by the Central Bank. This is the avenue the Bank uses to manage liquidity levels. By adjusting the monetary base, the level of credit and the money supply is affected by the movement in interest rates. The expected effects of the changes are stable price levels and exchange rates.

The transmission process works in a manner that monetary policy is initially expected to influence the monetary base. The impact on monetary changes influences domestic prices either through adjustments in exchange rates or through the money supply. The Bank of Jamaica has one direct policy tool at its disposal, namely the reserve requirement. It is the percentage of cash which it is recommended that financial institutions deposit at the Bank of Jamaica or keep on hand.

Alternatively, the Bank controls liquidity by making direct sales or purchases in the foreign exchange market. For the flexible exchange rate to be managed efficiently the Central Bank occasionally intervenes to smooth out supply conditions and ensure relative stability of the exchange rate. As a result, monetary policy tools are used to manage the flow of foreign currency and other pressures stemming from the foreign exchange market.

WHICH WAY IS WHICH?

A. The Orthodox View

The equation of exchange is one of the simplest and oldest models in economics:

(1) M x V = P x Y,

where M is the money supply, P is the price level, and Y is aggregate output. The variable V stands for "velocity of money," which is defined by Mankiw (2000) as the number of times a unit of legal tender changes hands. The standard model assumes velocity is constant in the long run. Because aggregate output, Y, is determined by what occurs in factor markets and the state of technology, any change in the supply of money will cause only a proportionate change in price level. In other words, a percentage change in M triggers a percentage change in P:

(2) %[DELTA]M = %[DELTA]P.

The quantity theory of money has been tested in many countries and in different historical periods. The two seminal works in favor of the policy implications of the quantity theory of money are A Monetary History of the United States by Milton Friedman and Anna J. Schwartz (1963) and "Two Illustrations of the Quantity of Money" by Robert Lucas (1980).

There is considerable empirical research supporting the unidirectional causality from money supply to price level. Lothian (1985) uses cross-sectional data from member countries of the Organization for Economic Co-operation and Development (OECD), reporting unanimous support for unidirectional causality just as the quantity theory would predict. Gupta and Moazzami (1991: 1088) find a "unidirectional and instantaneous causality" between money supply and price level for six countries: Canada, France, Germany, Italy, the United Kingdom, and the United States. Other studies like Jadhav (1994), Nachane and Nadkarni (1985) and Rao (1994) have found this kind of clear-cut causal direction in India. Karfakis (2002) found the same causality in Greece, and Riley (1983) and Officer (2005) found similar results for the seventeenthcentury in France and eighteenth-century in New England respectively

B. The Heterodox View

There are alternative models in heterodox economics which suggest that price level actually affects money supply and not the other way around. Examples of this view can be found in Kaldor (1982), Moore (1979), Palley (2002), and Rousseas (1992). In these PostKeynesian models the endogeneity of money arises from changes in two theatres of economic action.

One is a change in factor prices, in particular, wages. According to Atesoglu (1997) and Moore (1979), central banks supply money such that wage agreements between large unions and large firms can be met. The other medium of money creation is through bank loans. Money supply, according to this model, is expanded as banks lend more money; it contracts when debt is repaid as in Palley (2002). Thus, according to Post-Keynesians, the interest rate at which money is borrowed plays an important role in determining the (endogenous) supply of money.

Post-Keynesian economists have produced empirical evidence consistent with their views on money supply. The first empirical studies were done for the United States and the United Kingdom, examples of these are Moore (1988), Moore and Threadgold (1985) and Palley (1994). Later on, Post-Keynesians like Howells and Hussein (1998) tested their hypothesis on the G7 countries, just as Shanmugan et al. (2003) and Palacio-Vera (2001) did in Malaysia and Spain respectively.

Endogenous money in mainstream economics.

One can certainly walk away with the impression that endogenous money is a belief held by heterodox economists only. This certainly seems to be the conclusion in many Post-Keynesian literature reviews like Fontana (2004) and some surveys of monetarist models by mainstream economists like De Long (2000) and Laidler (2002). According to De Long (2000: 85), generally speaking, most mainstream economists could be considered "neo-monetarists." Nevertheless, the notion that the quantity theory of money has hegemonic influence over mainstream economics is far from true.

In the late nineteenth century, explanations of the origins of money began with commodity money. Menger (1982) argued that money originated endogenously, in the sense that what constituted money and its supply was determined by relative transaction costs. This tradition continued with some general equilibrium models which used Karl Menger's concept of money as can be seen in Kiyotaki and Wright (1992) and Niehaus (1971).

Money in real business cycle theory is also endogenous, to the chagrin of Neo-Keynesian economists, and it "responds to fluctuations in output" as noticed by Mankiw (1989: 88). King and Plosser (1984: 367) began building a model where money is "inside money". When there is a positive economic shock, banks lend more money as firms wish to finance their expansion through debt. Ironically, the believers of neo-Walrasian macroeconomics hold a view similar to Post-Keynesian monetary economics.

On the empirical front there are many studies which demonstrate an ambiguous causal direction between money supply and price level. Sargent and Wallace (1973) argued that it is more appropriate to model causality of money supply and price level as bidirectional. For India there is some evidence that money is endogenous starting with Ramachandra (1983). Other studies like Ramachandra (1986) and Saunders and Biswas (1990) supported the result of bidirectional causality between India's supply of money and price level. Bidirectional causality has also surfaced in studies based on Latin American countries as in Dutton (1971) as well as Indonesia according Aghlevi and Khan (1977). Ozmen (2003) confronts Karfakis (2002) demonstrating that money in Greece is not exogenous.

A large part of this literature examines data from large economies (e.g. the United States, the European Union). Many of these large economies are not as dependent on foreign goods and inputs as smaller economies such as Jamaica. Small open economies are subject to foreign monetary shocks and shocks in the exchange rate for important currencies such as the US dollar. A central bank in a small open economy cannot control these outside variables. Could these factors affect the relationship between money supply and price level?

COULD THERE BE ANOTHER EXPLANATION?

Virtually no economist disputes the basic implication of the quantity theory of money, if velocity were constant. What is disputed is that equation (2) is the only policy implication from the equation of exchange. Furthermore, equation (1) by itself may offer an incomplete picture of what goes on in many developing economies.

A. Exchange Rate Pass-through

It is well-known that small developing economies such as Jamaica's are highly dependent on foreign inputs and technology. According to Cline (1981) and Durreval (1998) this is also true for larger emerging economies such as Brazil where increases in oil prices and other foreign inputs and goods have generated episodes of inflation. Thus, changes in the exchange rate for these countries trigger simultaneous changes in money supply and price level.

Typically, in mainstream models changes in exchange rates arise from changes in money supply; this can certainly be the case. However, if foreign factor prices increase, production costs rise considerably, and thus the general price level will increase as well. There is a considerable body of work done on precisely this inflationary transmission mechanism: it is known as the "exchange rate pass-through."

For Goldberg and Knetter (1997) this concept essentially measures the sensitivity of import prices to a 1 percent change in the exchange rate. Several studies, like Dornbusch (1987), Krugman (1987), Kim (1998), and McCarthy (2000), have been done on the influence exchange rates have on price levels. Robinson (1996) and McFarlane (2002) study this particular transmission mechanism for Jamaica. They find that the exchange rate influences wage and price levels considerably.

According to Choudhri and Hakura (2001) developing economies are more susceptible to exchange rate pass-through than developed ones. Ho and McCauley (2003) explain this stylized fact as a result of Engel's Law, more so than the degree of openness in an economy. Consumers in developed countries spend their money mostly on non-tradable services. Consumers in developing countries, on the other hand, devote most of their expenditure to tradable goods, directly imported or produced with imported inputs, such as food.

However, an increase in the exchange rate will also affect money supply. The demand for imported inputs and goods is relatively inelastic in small open economies. Consumers and producers will have to spend more for the same amount of foreign currency to buy the same amount of inputs and goods. The increase in domestic currency supply has a mirror image in an increase in foreign currency demand.

These results are consistent with those of McFarlane (2002). He shows that the nominal exchange rate Granger-causes money supply and also price level. If the exchange rate can cause money supply and price level to fluctuate in these countries, then the policy implication is clear. Monetary policy by itself may be inadequate to control inflation in these small open economies.

B. Foreign Money Supply

Jamaica's main trading partner is the United States. According to the Bank of Jamaica (2010) 39 percent of its imports come from and 40 percent of its exports go to this nation. The same source reports that Jamaica also receives 50 percent of all its foreign exchange through its tourism industry, the most important sector in the Jamaican economy, absorbing around 65 percent of the employed labour force. The majority of these tourists, according to the Government of Jamaica (2009) come from the United States. In fact, much of the sector's infrastructure is in the northern part of the island, in order to be readily accessible to visitors from the United States.

All these factors make the US dollar an important currency in Jamaica. Jamaican establishments accept both Jamaican and US dollars (at varying rates of exchange, of course). This flexibility contrasts greatly with that of many developing countries, such as Mexico, where the US dollar is used as a medium of exchange only in certain areas such as the Mayan Riviera and parts of the border with the United States.

If the Jamaican and US dollar are both valid as exchange media, then this gives rise to two questions. First, how important are changes in US money supply, in other words US monetary policy, in Jamaica's economy? The second question is equally important and even more uncomfortable. Given the large flows of US dollars throughout the Jamaican economy, how important is domestic central bank policy in Jamaica?

WHAT DOES THE DATA SAY?

The quarterly data examined below comes from two main sources: the International Monetary Fund's Balance of Payments Yearbooks (1980, 1988, 1996, 2004a), International Financial Statistics (2004b) and the United States Federal Reserve. The data consists of five time series: consumer price index (CPI), deposit rate, exchange rate, Jamaican money supply, and US money supply. The deposit rate is the average interest rate paid for bank deposits. The exchange rate is the price of one US dollar in Jamaican dollars. Both Jamaican and US money supplies are measures of Ml (currency and checking deposits, among other liquid assets). All of the series, except deposit rate, cover a span of 110 quarters, from the last quarter of 1980 to the first quarter of 2008.

The quantity theory of money predicts that a percentage change in the money supply is equal to a percentage change in the price level, ceteris paribus. This is why the data is examined in terms of percentage changes, rather than levels. At the outset, Table 1 reveals that on average, the money supply in Jamaica has increased considerably. The average percentage change in money supply looms over the average percentage changes in other variables. So while the median percentage change for money supply is 10.18 percent, the median percentage change for inflation is only 3.85 percent.

In and of itself, this is not evidence of a lack of causality between money supply and the price level. But it is an indication that the causal relationship may be inelastic. In other words, it takes a considerable percentage change in domestic money supply to trigger a percentage change in the cost of living in Jamaica.

Figure 1a reveals that, in general, money supply and price level do move together. The price level does oscillate considerably in Jamaica during this time. The inflation rate for the fourth quarter of 1991, for example, equals a peak value of 22.13 percent. However, for that same quarter, money supply increased 27.88 percent. In addition, severe drops in money supply growth are not accompanied by equally drastic rates of deflation. For example, in the first quarter of 2000, money supply decreased by 35 percent, but the price level increased 1.32 percent.

The price level in Jamaica becomes less volatile after 1996, when the percentage changes in the cost of living rarely exceed 4 percent. The same cannot be said about percentage changes in the money supply. Money supply continues to oscillate, with considerable troughs and upswings in 2000, 2001, and 2003. Figure la thus reiterates what Table 1 suggests. There may be a causal relationship from money supply to price level. However, price level appears to be relatively insensitive to changes in Jamaica's monetary policy.

Figure 1b juxtaposes the deposit interest rate with the CPI. The graph reveals a similar story to that of Figure la: deposit rates move together with the price level. But from 1980 to 1998, the deposit rate oscillates much more than the price level. The highest peak in the percentage change of the price level, 22.13 percent in the third quarter of 1991, pales in comparison with the 31.34 percent increase in the deposit rate that same quarter.

After 1998, percentage changes in the deposit rate become muffled, akin to those of the consumer price index. This coincides with the intensification of the structural adjustment process prescribed by the International Monetary Fund. After 1998 it seems the central bank began to have greater control of inflation through manipulation of the interest rate.

Figure 1c reveals an impressive similarity between percentage changes of the exchange rate and the cost of living during this time period. The data not only show that exchange rates and price levels move together. The price of the US dollar and the cost of living move closely together; closer in fact, than any other variable examined.

This pattern in the data makes sense when one remembers two features of the Jamaican economy. Like most small open economies, Jamaica is highly dependent on foreign inputs and goods. Jamaica, like other Caribbean countries, also has a large tourism industry. These characteristics should make Jamaica's price level sensitive to changes in the price of foreign currency, in particular, the price of US dollars. Figure 1c corroborates this result. However, what is surprising is how percentage changes in domestic money supply are not as important as percentage changes in the exchange rate.

The percentage changes in the US monetary base are shown in Figure Id, compared to percentage changes in the Jamaican price level. The similarity between movements in the US money supply and movements in the Jamaican price level are quite striking. What is even more striking is the fact that Jamaica's cost of living follows US money supply closer than the country's own money supply or interest rate.

Oddly enough, the quantity theory of money may explain inflation in Jamaica relatively well. It is, after all, percentage changes in money supply that has the largest percentage changes in the price level. But the money supply in question is not the Jamaican one: it is the money supply of Jamaica's most important trading partner, the United States.

METHODOLOGY AND RESULTS

The econometric methodology follows four main steps. The first is to test for unit root processes in the five series of data. The second is to perform cointegration tests for the four series given that, in all five cases, the series are integrated of order one (1(1)). The third step is to perform a vector error correction model in order to find long-run equilibrium relationships between the variables. The fourth step is to perform Granger-Wald causality tests (pairwise and multivariate) to determine the direction of the causal relationships found with the previous tests.

Naturally there are other tests performed. For example, before performing the causality tests, a vector autoregression (VAR) had to be done for the four series. The cointegration tests could not be performed without first establishing the optimal number of lags, which were chosen using the Akaike Information Criteria (AIC), the Final Prediction Error (FPE) and the Likelihood-Ratio test (LR).

A. Dickey-Fuller and Phillips-Perron tests

The objective of these tests is to determine whether or not the series follow a unit root process. The Augmented Dickey-Fuller (ADF) test is the most common and is based on the following regression model:

(3) [y.sub.t] = [mu] + [rho][y.sub.t-1] + [[epsilon].sub.t]

By subtracting [y.sub.t-1] from both sides we get:

(4) [[increment of y].sub.t] = [mu] + [gamma][y.sub.t-1] + [[epsilon].sub.t]

where [[increment of y].sub.t] = ([y.sub.t] - [y.sub.t-1]) and [gamma] = [rho] - 1.

In addition, the Augmented Dickey-Fuller test takes into account higher order serial autocorrelation by adding lagged differences of the dependent variables. Thus, the regression the ADF test uses for an autoregressive process of order k (AR(k)) would be:

(5) [[increment of y].sub.t] = [mu] + [[gamma].sub.1][y.sub.t-1] + [[delta].sub.1] [[increment of y].sub.t-1] + ... + [[delta].sub.k] [[increment of y].sub.t-k] + [[epsilon].sub.t],

where k is the number of lags.

The ADF test juxtaposes the null hypothesis [H.sub.0]: = [gamma] 0 against the alternative [H.sub.1] : = [gamma] < 0. The test statistic follows a Dickey-Fuller distribution (instead of a Student's t distribution). If that statistic is to the left of the critical value, the test fails to reject the null hypothesis; thus, the series would not be 1(1).

Both unit root tests are performed on variables in natural logarithmic form. The small perturbations found in these data series can be annihilated by transforming them into natural logarithms. Furthermore, our interpretation of the estimated regression coefficients becomes independent of units of measure when variables are in natural logarithmic form (they are elasticities).

In the case of the Augmented Dickey-Fuller test, all of the variables are to the right of the critical value at the 5 percent level of statistical significance. Therefore, according to this test, all four series are integrated of order one (1(1)) and we can proceed with cointegration tests.

The Augmented Dickey-Fuller test is one way to test for unit roots. In particular, research has found that the ADF test has very low power in certain instances. This is why we include results from another test designed by Phillips and Perron (1988), together with Augmented Dickey-Fuller tests in Table 2. The Phillips-Perron test takes into account higher-order serial autocorrelation non-parametrically. The test statistic is thus robust to heteroskedasticity or unknown serial autocorrelation. The interpretation of the test statistic is the same as in the ADF test. It is clear that the results of the Phillips-Perron test completely concur with those of the ADF test. Again, for all four series, the null hypothesis of the presence of a unit root process is rejected at the 5 percent statistical significance level.

B. Cointegration tests and vector error correction model

Now that we know our series are 1(1), we can test for whether or not a linear combination of them is integrated of order zero (1(0)) or stationary. A stationary linear combination of series is one with a time-invariant variance. This can be interpreted as a long-run equilibrium relationship between the variables. The test performed follows the methodology from Johansen (1991, 1995) and is based on vector autoregressions (VAR).

Essentially we take a vector autoregression of the following form:

(6) [y.sub.t] = [A.sub.1][y.sub.t-1] + [A.sub.2][y.sub.t-2] + [A.sub.3][y.sub.t-3] + [A.sub.4][y.sub.t-4] + B[x.sub.t] + [[epsilon].sub.t],

where [y.sub.t] is an m-vector of endogenous variables and [x.sub.t] is a j-vector of exogenous variables.

For the VAR, and for the vector error correction model (VECM) that follows, the number of lags was set to four according with the Final Prediction Error (FPE), Likelihood Ratio (LR), and Aikake Information Criterion (AIC) tests. All three tests suggest the same number of lags. Other tests such as the Schwarz's Bayesian Information Criteria (BIC) and the Hannan and Quinn Information Criteria (HQIC) suggest the use of two lags in the model. We decided to use four instead of two lags because underspecifying the number of lags in a VECM would increase the sample bias and lead to serial correlation.

This VAR is transformed by subtracting [y.sub.t-1] from both sides, together with adding and subtracting other terms. In the end, we obtain:

(7) [[increment of y].sub.t] = [PI][y.sub.t-1] + [p.summation over (i=1)] + [p.summation over (i=1)] [[GAMMA].sub.i] [[increment of y].sub.t-1] + B[x.sub.t] + [[epsilon].sub.t]

(8a) [PI][y.sub.t-1] = ([p.summation over (i=1)] [A.sub.i]) - I

(8b) [[GAMMA].sub.i] = [p.summation over (j = i + 1)] [A.sub.j]

In this case, p is the number of lags, and in our specification it is equal to four.

The key to Johansen's test is in the rank of the matrix [PI], denoted as r and referred to as the cointegrating rank. If r < m, then there exist two (m x r) matrices, [alpha] and [beta], such that [PI] = [alpha][beta]' and [beta][[gamma].sub.t] is stationary. The interpretation of the test results would then be that rank r is "the number of cointegrating relations" according to Quantitative Micro Software's 2000 Manual (520). The matrix [beta] would contain all the long run relationship coefficients. The matrix [alpha] in turn would contain the short-run adjustment coefficients for the vector error correction model (VECM).

The test results indicate there is one cointegrating equation. In other words, among the four series we find one long-run equilibrium relationship among them. Table 3 shows the results for the VECM.

Focusing on the long-run relationships, the Beta column, these results should be interpreted as an estimated equation that would read:

(9) In (CPI) + 1.756 * In (Deposit Rate) - 2.003 * In (Exchange Rate) - 0.612 * In (Money) + 4.256 * In (US Money) - 51.076.

Thus, a 1 percent change in the deposit rate, for example, triggers a -1.76 percent change in the CPI; an increase in the interest rate lowers the price level, as expected. The relationship between money supply and price level has the expected sign but a lower magnitude perhaps than the standard quantity theory of money would suggest. The price level as measured by the CPI tends to be relatively inelastic to changes in the money supply.

One interesting result for the purposes of this paper is the magnitude of the relationship between the exchange rate and the prices level. A 1 percent change in the Jamaican money supply, for example, increases the CPI by only 0.6 percent. However, a 1 percent change in the exchange rate increases the price level by 2 percent. The Jamaican CPI seems to be more sensitive to exchange rate shocks than to monetary shocks. This is consistent with our paper's thesis: small open economies, dependent on foreign goods and inputs, may suffer from considerable inflation independent of central bank policies.

The Jamaican CPI is relatively inelastic to changes in the Jamaican money supply. However, it is very sensitive to changes in the money supply of the United States. The long-run effect of a 1 percent change in the US money supply is a decrease of 4.23 percent in the Jamaican CPI. An increase in the US money supply, ceteris paribus, decreases the price of a US dollar in Jamaica. Given the country's dependence on foreign inputs and goods, this would naturally lower costs of production and the cost of living in Jamaica.

C. Granger-Wald Causality

The Granger-Wald Causality tests are performed after a vector auto regression (VAR) is estimated. The VAR model treats every endogenous variable as a function of its own lagged values, as well as lagged values of all the other endogenous variables. The causality tests we perform have a mathematical formulation similar to equation (4) above. For any pair of variables ([x.sub.t], [y.sub.t]):

(10a) [x.sub.t] = [[alpha].sub.0] + [[alpha].sub.1] [x.sub.t-1] + ... + [[alpha].sub.p][x.sub.t-p] + [[beta].sub.1][x.sub.t-1] + ... + [[beta].sub.p][y.sub.t-p] + [[epsilon].sub.t].,

(10b) [y.sub.t] = [[alpha].sub.0] + [[alpha].sub.1] [y.sub.t-1] + ... + [[alpha].sub.p][y.sub.t-p] + [[beta].sub.1][x.sub.t-1] + ... + [[beta].sub.p][y.sub.t-p] + [[xi].sub.t].,

where [[epsilon].sub.t] and [[xi].sub.t] are error terms for period t. The null hypothesis for the test is simply [H.sub.0] : [[beta].sub.1] = [[beta].sub.2] ... = [[beta].sub.p] = 0 for (8a) and (8b).

The results of the pairwise causality tests are shown below. There is limited evidence for monetary endogeneity; the hypothesis of no causality however, cannot be rejected at the 5 percent level. Interestingly enough, at variance with the standard quantity theory of money, changes in the domestic money supply do not cause changes in Jamaica's price level.

However, there is bidirectional causality between the exchange rate and the price level. Coupled with our results from the VEC estimates, and the descriptive analysis, this means that the exchange rate plays a very important role in inflationary dynamics in the Jamaican economy. In fact, it is safe to say that it plays an even more important role than domestic money supply.

Obviously, none of the Jamaican variables Granger-cause US money supply. US money supply does influence the Jamaican price level, as well as other variables. Compared to the domestic money supply, it is certainly true that US money supply exerts a greater influence in the Jamaican economy.

The results from the Granger-Wald causality tests make sense given the nature of the Jamaican economy. The small Caribbean nation has an open economy, highly dependent on foreign inputs and a large tourism industry. Naturally, the foreign exchange rate and foreign money supplies would exert influence on Jamaican prices for inputs and goods.

What is somewhat unexpected is that domestic money supply does not seem to exert the same level of influence. In other words, monetary policy, if uncoordinated or unaided by foreign exchange and trade policies, may be ineffective in curbing inflation. In fact, the Jamaican economy may be "importing inflation" as a result of its openness.

WHAT IS TO BE DONE?

The main objective of this paper is to identify the key determinants of the consumer price index in Jamaica. Using a vector error correction model and quarterly data for the period 1980-2008 we found that changes in deposit rate and in the US money supply are negatively cointegrated with elastic responses in the CPI of Jamaica (-1.76 percent and -4.23 percent respectively). Furthermore, we found evidence indicating that the causality is bidirectional between deposit rate and CPI, and unidirectional in the other case. In other words, US money supply causes changes in the CPI of Jamaica but not the other way around.

The results also show that the exchange rate and the CPI are cointegrated in a positive elastic way. Granger-Wald causality tests suggest that this cointegrated relationship is causal in both directions. Interestingly enough, and contrary to the traditional quantity theory of money, we found a positive cointegrated relationship between the money supply and CPI. This relationship is not only inelastic (0.61 percent) but also without causality going from money supply to CPI. A possible explanation can be found in the nature of the Jamaican economy, which is a small and open economy, highly dependent on foreign inputs and with a large tourism sector.

The most important determinants of the CPI of Jamaica are not Jamaica's money supply or the domestic interest rate. The US money supply and the exchange rate play a preponderant role in Jamaican inflation.

Small open economies like Jamaica face a great challenge. Typically, as emerging market economies develop, the non-tradable services sector generates a larger percentage of their GDP. Ho and McCauley (2003) point out that those economies are less vulnerable to changes in exchange rates. However, Jamaica's services sector is already large: tourism generates a considerable percentage of Jamaica's GDP. Furthermore, Jamaica's economy will never be completely independent of foreign inputs. It is likely that US money supply and the US-Jamaican dollar exchange rate will always have a large influence on Jamaica's price level.

This is why the Bank of Jamaica should always keep abreast with developments in US monetary policy. It can anticipate large oscillations in its price level and take measures to ameliorate brusque changes in the consumer price index. The descriptive analysis above revealed that the interest rate (since the 1990s) has been able to keep pace with the price level. The Granger causality tests also show that the interest rate does have an effect on the exchange rate and the price level.

The Jamaican case, however, should serve as a cautionary tale for other small economies emerging as open economies. Monetary authorities should prepare for the increased influence of foreign policies in their economies. They will also have to adopt flexible and judicious combinations of intervention (e.g. purchase and sale of foreign denominated bonds, direct or verbal intervention, etc.) in order to keep inflation under control, heeding the sound advice of Ho and McCauley (2003).

APPENDIX

Impulse Response Functions

The impulse response analysis analyzes the dynamic interactions between endogenous variables. An impulse response function (IRF) describes the expected impact (response) of a variable [y.sub.i,t+s] to a unit change (shock) in variable [y.sub.j]. An IRF is useful because the cointegration equation, equation (7), explains the long-run relationship among the analyzed variables but falls short in explaining the impact of an impulse variable over the response variable over time. I

An orthogonal impulse response function (OIRF) is an IRF for which a Cholesky decomposition is applied to the error variance covariance matrix. According to Pfaff (2008) the OIRF is used when the underlying shocks are less likely to occur in isolation. This is reflected in the correlation among the components of the error.

The orthogonal impulse response function graphs (see Figure Al) show the effect on the natural logarithm of the CPI of a onetime, one percent shock in one of the explanatory variables. None of the curves return to zero, suggesting that the one-time shocks permanently affect the price level in Jamaica. Nevertheless, shocks in the exchange rate and the US money supply have a permanent impact of a higher magnitude than shocks in the deposit rate and domestic money supply.

The graphs also show a similar pattern of behaviour (not the same magnitude) of a shock in the deposit rate and US monetary base over the Jamaica's CPI. A different pattern is presented in price level as response to a shock in the exchange rate and as a response to a one-time change in the monetary base of Jamaica. At first there is a positive short-term effect (three quarters) of both variables over the CPI. But that is followed by a decrease in the response of Jamaica's price level. The magnitude of this reduction is bigger than the original increase in the case of the monetary base of Jamaica.

The analysis of orthogonal impulse response functions corroborates our results. Foreign variables such as the exchange rate and the US money supply exert a greater influence on Jamaica's cost of living than its own monetary policy.

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Caption: Figure 1a: Percentage Changes: Money Supply and CPI

Caption: Figure 1b: Percentage Changes: Deposit Rate and CPI

Caption: Figure 1c: Percentage Changes: Exchange Rate and CPI

Caption: Figure 1d: Percentage Changes: US Money Supply and CPI

Caption: Figure A1: Impulse Response Functions
Table 1: Summary Statistics for Percentage Changes

                 Consumer Price   Jamaican Money   Deposit   Exchange
                     Index            Supply        Rate       Rate

Mean                 3.413            9.612         2.675     2.831
Median               3.846            10.178        2.697     3.500
Std. Deviation       1.424            1.589         0.478     1.221

Table 2: Dickey-Fuller and Phillips-Perron Tests (Constant with
Trend)

Test              In (CPI)   In (Deposit   In (Exchange   In (Money)
                                Rate)         Rate)

Dickey-Fuller      0.095       -1.849         -0.909        -0.790
Phillips-Perron    -1.838      -1.894         -1.349        -0.748

Test              In (US Money)

Dickey-Fuller         0.844
Phillips-Perron      -0.789

Notes: The number of observations is 109 except for
ln(Deposit Rate) for which there are 108 observations. The critical
value for 5% statistical significance for both tests is -3.449.

Table 3: Vector Error Correction Model Estimates

Variable              Beta      Alpha

In (CPI)              1.000     0.031
                       --      (0.007)
In (Deposit Rate)     1.756    -0.099
                     (0.154)   (0.032)
In (Exchange Rate)   -2.003     0.052
                     (0.283)   (0.032)
In (Money)           -0.612    -0.023
                     (0.155)   (0.044)
In (US Money)         4.256    -0.006
                     (0.825)   (0.005)
Constant             -51.076     --
Note: Standard errors in parentheses.

Table 4: Pairwise Granger-Wald Causality Test Results

Null Hypothesis                                           Chi-Squared
                                                          Statistic

In (Money) does not Granger-Wald cause In (CPI)                 6,431
In (CPI) does not Granger-Wald cause In (Money)                 9,252
In (Deposit Rate) does not Granger-Wald cause In (CPI)         22,640
In (CPI) does not Granger-Wald cause In (Deposit Rate)         13,153
In (Exchange Rate) does not Granger-Wald cause In (CPI)        52,528
In (CPI) does not Granger-Wald cause In (Exchange Rate)        23,477
In (Deposit Rate) does not Granger-Wald cause In                2,736
  (Money)
In (Money) does not Granger-Wald cause In (Deposit             13,746
  Rate)
In (Deposit Rate) does not Granger-Wald cause In               13,750
  (Exchange Rate)
In (Exchange Rate) does not Granger-Wald cause In              10,520
  (Deposit Rate)
In (Exchange Rate) does not Granger-Wald cause In              11,673
  (Money)
In (Money) does not Granger-Wald cause In (Exchange            12,471
  Rate)
In (US Money) does not Granger-Wald cause In (CPI)             24.507
In (CPI) does not Granger-Wald cause In (US Money)              4.463
In (US Money) does not Granger-Wald cause In (Money)           12.411
In (Money) does not Granger-Wald cause In (US Money)            4.455
In (US Money) does not Granger-Wald cause In (Exchange         16.359
  Rate)
In (Exchange Rate) does not Granger-Wald cause In (US           2.349
  Money)
In (US Money) does not Granger-Wald cause In (Deposit           3.955
  Rate)
In (Deposit Rate) does not Granger-Wald cause In (US            3.795
  Money)

Null Hypothesis                                           Probability

In (Money) does not Granger-Wald cause In (CPI)                 0.169
In (CPI) does not Granger-Wald cause In (Money)                 0.055
In (Deposit Rate) does not Granger-Wald cause In (CPI)          0.000
In (CPI) does not Granger-Wald cause In (Deposit Rate)          0.020
In (Exchange Rate) does not Granger-Wald cause In (CPI)         0.000
In (CPI) does not Granger-Wald cause In (Exchange Rate)         0.000
In (Deposit Rate) does not Granger-Wald cause In                0.603
  (Money)
In (Money) does not Granger-Wald cause In (Deposit              0.008
  Rate)
In (Deposit Rate) does not Granger-Wald cause In                0.008
  (Exchange Rate)
In (Exchange Rate) does not Granger-Wald cause In               0.033
  (Deposit Rate)
In (Exchange Rate) does not Granger-Wald cause In               0.020
  (Money)
In (Money) does not Granger-Wald cause In (Exchange             0.014
  Rate)
In (US Money) does not Granger-Wald cause In (CPI)              0.000
In (CPI) does not Granger-Wald cause In (US Money)              0.347
In (US Money) does not Granger-Wald cause In (Money)            0.015
In (Money) does not Granger-Wald cause In (US Money)            0.348
In (US Money) does not Granger-Wald cause In (Exchange          0.003
  Rate)
In (Exchange Rate) does not Granger-Wald cause In (US           0.672
  Money)
In (US Money) does not Granger-Wald cause In (Deposit           0.412
  Rate)
In (Deposit Rate) does not Granger-Wald cause In (US            0.435
  Money)

Notes: The number of observations in all of the Granger-Wald tests
is 105, with four degrees of freedom. The null hypothesis, no
causation, is rejected if the probability is less than 0.05.
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