Monetary conditions index: a composite measure of monetary policy in Pakistan.
Accurate measures of the size and direction of changes in monetary policy are very important. A number of variables/indicators have been used as a measure of the stance of monetary policy the world over. These include growth rates of monetary aggregates and credit aggregates, short-term interest rate as used by Sims (1992), index of minutes of Federal Open Market Committee (FOMC), as suggested by Friedman and Schwartz (1963) and reintroduced by Romer and Romer (1989), monetary policy index constructed by employing Vector Autoregression (VAR) estimation technique with prior information from Central Bank such as Bernanke and Blinder (1992) and Bernanke and Mihov (1998), and Monetary Conditions Index (MCI)--which is the focus of this paper--constructed by and used by Bank of Canada [Freedman (1995)], taking into consideration the interest rate and exchange rate channel of monetary policy transmission mechanism in a small open economy.
In case Of open economy it is assumed that the monetary policy affects the economy and the prime objective of monetary policy, rate of inflation, through two important transmission mechanisms. These transmission channels are; interest rate channel and exchange rate channel. The working of the first channel is that the interest rate influences the level of expenditures, investment and subsequently domestic demand. The change in official interest rate effects the market rates of interest both short term as well as long term interest rates. This change in market rates of interest is transmitted to the bank lending rates and saving rates. The change in saving rate effects the spending behaviour of individuals (consumption) whereas the change in bank lending rate effects the investment behaviour of firms (investment). The change in aggregate consumption and investment has direct link to the gross domestic product (GDP).
The second channel is exchange rate. The exchange rate is the relative price of domestic and foreign money. In principle the rate of exchange depends on both domestic and foreign monetary conditions. This channel works in this way. The change in exchange rate leads towards the relative prices of domestic and foreign produced goods and services. This movement in prices affect the pattern of spending of economic agents that is individuals and firms. The exchange rate changes can also effect directly to the rate of inflation. This effect is transmitted through the Rupees prices of imported goods. In a modern interlinked world the imported goods are important determinants of many of the firm's costs and consumptions expenditures of individuals. Appreciation of Rupee lowers Rupee price of imported good and depreciation of Rupee increases the price of imported goods. Hence in a small open economy the exchange rate is another important channel through which actions of monetary policy are transmitted to the ultimate objectives of policy that is rate of inflation and economic activity.
Considering the importance of interest rate and exchange rate channels of monetary transmission mechanism in an open economy it is required to have comprehensive measure of monetary policy stance. This requirement is fulfilled by the introduction of monetary conditions index by bank of Canada. Hataiseree (2000) argued that MCI is better in assessing the monetary conditions of the economy.
There are numbers of studies that have estimated Monetary Conditions Index for different countries. Kesriyeli and Kocaker (1999) estimated MCI of inflation for Turkey. Weights of MCI are estimated from inflation model by using real interest rate and real effective exchange rate as determinants. MCI of inflation for Thailand is constructed by Hataiseree (2000). To estimate the weights autoregressive distributed lagged model of inflation is used. This inflation equation include interest rate, nominal effective exchange rate. Import prices index, agricultural price index and government fiscal indicator. The estimate ratio of weights of exchange rate and interest rate for Thailand is 3.3:1. Real interest rate and real effective exchange rate variables are used in the construction of MCI of output for Hong Kong by Monetary Authority (2000). By estimating reduced form equation of aggregate demand relevant weights are obtained. The ratio of exchange rate and interest rate weights is 4.25:1. Further, the MCI estimated for different countries are as; Duguay (1994) for Canada, Hansson and Lindberg (1997) for Sweden, Hataiseree (2000) for Thailand, Kesriyeli and Kocaker (1999) for Turkey.
Pakistan is one of the emerging economies of the world which have no estimates of composite measure of monetary policy stance. This study intends to estimate the MCI for inflation for Pakistan that could be used by the monetary authorities and policy-makers to evaluate the stance of monetary policy. The distribution of the rest of the paper is given below. Section two deals with the monetary policy in Pakistan whereas Sections 3-4 discuss the concept of MCI, its uses and approaches to estimate MCI. Section five presents the methodology of estimation of MCI. Next two Sections (i.e., 6 and 7) contain unit root and cointegration analysis. Section 8 presents estimated MCI whereas Section 9 deals with decomposition analysis. The last section concludes the study.
2. MONETARY POLICY IN PAKISTAN
State Bank of Pakistan, the central bank, was established for two clearly broad objectives; to secure monetary stability and to find fuller utilisation of country's productive resources. These objectives are confined under the head of 'Functions and Responsibilities of the Central Board' by making it responsible to secure monetary stability and soundness of the financial system. Section 9A.1 of the Act 1956 of the State Bank of Pakistan (amended) elaborates the targets of monetary policy in Pakistan. It states that the target rates of growth and inflation set by the Federal Government are the targets of monetary policy. Therefore the objectives of monetary policy in Pakistan are to achieve the target rates of growth and inflation that are set by the Federal Government.
One of the important and crucial intermediate target variables of monetary policy in Pakistan is money supply. The SBP has been using M2 aggregate (i.e., currency + demand deposits + time deposits) for policy purposes on the assumption that the demand for M2 function is stable in Pakistan. Utilising the estimated money demand function the target rate of growth of M2 is set. Another variable that is used as intermediate target of monetary policy in Pakistan is credit. Target rate of growth of credit is set by the SBP while preparing the annual credit plan. This credit plan is made considering the sectoral requirements of credit in the country. It is implicitly assumed by the SBP that M2 and credit aggregates can be effectively controlled by the effective use of monetary policy instruments.
Last two decades witnessed a number of changes in the monetary sector of Pakistan. In the beginning of 1980s monetary authorities in Pakistan has decided to abandon the fixed exchange rate mechanism and to adopt for floating exchange rate system. This is to initiate another important channel of monetary transmission mechanism in Pakistan. Further in late 1980s the authorities has started working on comprehensive financial sector reforms with the help of international financial agencies such as International Monetary Fund and World Bank. During these reforms a number of steps have been taken to modernise monetary sector. On this road monetary authorities have taken steps to utilise the market based instruments of monetary policy in Pakistan.
After the start of financial sector reforms Open Market Operation (OMO) has become an important instrument of monetary policy in Pakistan. The SBP earl influence/manage domestic liquidity through purchase or sale of government securities in the secondary market. The OMO can also be used to maintain the level of reserve money according to the operating target.
Further the SBP can impose cash reserve requirement on all deposits of scheduled banks as an instrument of monetary policy. Current weekly reserve requirement of every Bank is fixed as 5 percent of average weekly deposits. However, under another condition the amount of these reserves should not be less than 4 percent of daily deposits. Apart from the reserve requirement every Bank has to maintain 15 percent of total daily deposits as a liquidity requirement. For this purpose Bank can use cash, gold and government securities.
The SBP has been given responsibility to maintain the external value of currency by the government. For this purpose SBP has to maintain foreign currency reserve by intervening the foreign exchange market. This instrument has been used by the SBP during recent years to maintain and build foreign currency reserve. This intervention in the foreign exchange market helped to stabilise the external value of the Pak Rupee.
3. MONETARY CONDITIONS INDEX
In order to evaluate the monetary conditions in a country during different policy regimes there must be an indicator. The monetary conditions index is designed to serve as an indicator of monetary policy. It helps to evaluate the monetary policy stance. Weather monetary policy is tight or easy or just right.
Theoretically MCI is considered as movement in the two important variables that is rate of interest and exchange rate from the base period. For example, the MCI for inflation variable can be expressed in equation as
MCI[([pi]).sub.t] = [w.sub.r] ([r.sub.t] - [r.sub.b] ) + [w.sub.e] ([e.sub.t] - [r.sub.t] ) ... ... ... ... (1)
Where [r.sub.t] is interest rate at time t, [r.sub.b] is base period interest rate, et is exchange rate at time t, [e.sub.b] is base period exchange rate, w, is weight of interest rate and We is weight of exchange rate. It is assumed that the sum of two weights that is [w.sub.r] and [w.sub.e] is unity.
In the process of construction of MCI the most important parameters are weights of interest rate and exchange rate. These estimated weights contain information about the relative importance of interest rate and exchange rate channels of monetary transmission mechanism in the determination of economic activity or rate of inflation. These weights can be derived from the existing econometric models or by estimating appropriate econometric model by a researcher.
One of the important goals of monetary policy in Pakistan, as discussed earlier, is to achieve Federal Government's targeted rate of inflation. Considering the targeted rate of inflation as objective variable the estimated weights refer to the relative importance of rate of interest and rate of exchange in the determination of rate of inflation in Pakistan. Therefore the model explaining the behaviour of rate of inflation, one of the possible choice variables, is specified as:
[[pi].sub.t] = [[beta].sub.0] + [[beta].sub.1][r.sub.t] + [[beta].sub.2][e.sub.t] + [[epsilon].sub.t] ... ... ... ... ... (2)
The variable [[pi].sub.t] is the rate of inflation. This is potential target for the monetary condition index. Whereas [r.sub.t] is call money rate and [e.sub.t] is monthly average nominal exchange rate and [e.sub.t] is well behaved error term.
4. USES OF MONETARY CONDITIONS INDEX
In the literature multiple possible uses of MCIs are discussed. One possible use of MCI is that it can be used as operational target of monetary policy. For this purpose desired MCIs are constructed by taking into consideration of long run monetary policy objectives. As a policy target monetary authority is required to bring actual level of MCI to the targeted level. The central banks of Canada and New Zealand, among others, are using MCI as an operational target of monetary policy. Another use of MCI is that it can be used an indicator of monetary policy conditions in a particular time. It can measure monetary policy stance that is whether monetary policy is tight or loose with reference to particular period. Furthermore, Monetary Condition Index can also be used as a monetary policy rule. For this purpose the objective function of monetary policy rule can be obtained by rearranging MCI equation. Then normalising it on interest rate or exchange rate, as the case may be. For detailed discussion MCI as a monetary policy rule see for example Ball (1998).
5. APPROACHES TO ESTIMATE WEIGHTS OF MONETARY CONDITIONS INDEX
In the calculation of Monetary Conditions Index the estimation of weights of interest rate and exchange rate for an objective function are very important. Broadly speaking there are two ways to get these weights. Either these are obtained from already estimated econometric models or get freshly estimate by specifying the model. New estimates are made by modeling the objectives of monetary policy, that is either rate of inflation or economic growth or both at a time.
In the literature there are number of approaches available to estimate these weights of two monetary instruments while calculating MCI. First approach contains single equation based MCIs. This method is used by the IMF (1996), among others, to estimate the weights of MCI. The second is called trade share based MCIs which is being employed by J. P. Morgan's while calculating MCI for UK, such as Suttle (1996). Third approach deals with the estimation of weights by using multiple equations model, for example MCIs constructed by Davies and Simpson (1996) for Gold Sachs in UK. Recently the concept of dynamic MCIs is introduced by Batini and Turnbull (2000). They calculated dynamic MCI for the monetary policy committee of Bank of England.
There are a number of econometric issues in the construction of MCI which are needed to be addressed. These include dynamics, non-stationarity of data, cointegration and parameter constancy among others. These issues are related with the empirical model on which the value of weights is based. In this study we estimate weights by estimating above equation.
6. METHODOLOGY FOR ESTIMATION OF TI-IE MODEL
The important issue in the construction of MCI as compound measure of monetary policy stance in an open economy is the estimated value of weights of interest rate and exchange rate. These weights are important because they leads toward the construction of monetary condition ratio. This ratio indicates the relative importance of interest rate and exchange rate policy channels. The weights of MCI are not directly observable. They, however, could be obtained either from already estimated econometric models of the economy or by formulating empirical function by a researcher himself. It implies that MCIs are model dependent. In both cases, particularly new, estimates of the weights are subject to model building and estimation methodological criticism. This leads toward the econometric issues in estimating the weights. These issues include dynamics, time series properties of data, cointegration, exogeneity and parameters constancy [Eika, et al. (1996)].
Considering the importance of MCI in the analysis of monetary policy and criticism leveled against its measurement we start econometric methodology with the investigation of data generation process of individual time series. Specifically the testing of non-stationarity of time series data and order of integration. Since the seminal work of Nelson and Plosser (1985) on historical data of US economy, the time series data are assumed to be difference stationary. This finding of non-stationarity of time series data is confirmed by a number of researchers all over the world.
For the purpose of testing of order of integration of individual time series we used standard Augmented Dickey and Fuller (1979, 1981) method according to Hall's (1994) sequential rule. This ADF procedure for testing integration of series is still dominant method of testing the existence of unit roots in the time series data despite heavy criticism leveled against it, see for example Maddala and Kim (1998).
This is to estimate the following type of equation;
[DELTA][y.sub.t] = [alpha] + [beta]T + [rho][y.sub.t-1] + [n.summation over (i=1)] [lambda] [DELTA][y.sub.t-1] + [[epsilon].sub.t] ... ... ... ... ... (3)
for i=0, 1,2 ........... n
where [y.sub.t] is any time series to be tested for unit roots, t is time trend and e, is white noise error term. We test the hypothesis that [rho] = 0 in Equation 3 by [tau]-test by comparing the critical values of MacKinnon's (1991 ).
As a second and important step of analysis we estimate following model of inflation, one of the prime objectives of monetary policy in Pakistan. We include two policy variables as determinants of rate of inflation. Since we are considering an open economy, policy variable include the rate of interest and rate of exchange (Rupees in terms of Dollars). Each variable represents one monetary policy transmission mechanism explained earlier in the paper. The inflation model for Pakistan, a small open economy, is as;
[[pi.sub.t],= [[beta].sub.0] + [[beta].sub.1][r.sub.t], + [[beta].sub.2][e.sub.t] + [[epsilon.sub.t]
where [[pi].sub.t] is current rate of inflation measured by Log [CPI.sub.t]-Log [CPI.sub.t-1] [r.sub.t] is call money rate, [e.sub.t] is average exchange rate, and [e.sub.t] is well behaved error term. Following the lead of Bank of Canada (1994) we used interest rate and exchange rate in nominal form [Freedman (1995)]. It is argued that in the short run the distinction between the nominal and real variables is of little importance [Reserve Bank of New Zealand (1996)]. In the short run MCIs constructed from both real and nominal rates moves in a similar way because in the short run relative prices and inflation rates assumed to be remain constant [Eika, et al. (1996)].
At this stage we test existence of cointegrating relationship between the variables by using Likelihood ratio test based on maximal eigenvalue and trace of stochastic matrix as proposed by Johanson (1988). Full Information Maximum Likelihood Method of Johansen (1988) (1) would be used to estimate long run parameters of the objective function. This method use vector autoregressive methodology to estimate the model having non-stationary time series data. Another importance of VAR technique is that it does not require variables to be distinguished into endogenous and exogenous variables. We can estimate system of equation simultaneously. Hence we do not face the problem of simultaneity biasedness. The estimated parameters of the model can be interpreted as weights of rate of interest and rate of exchange in the objective function. These weights are to be used in the construction of MCI.
One approach to formulate the dynamic error correction function is Vector Autoregressive (VAR) system adopted by Johansen (1988), Johansen and Juselius (1990). It can be represented by the following function.
[X.sub.t] = [n.summation over (i=1)][[PI].sub.i][X.sub.t-i] + [mu].sub.t] + [PHI][D.sub.t] + [[epsilon].sub.t] (4)
Where [X.sub.t] is a vector of variables included in the model, [[mu].sub.t] is constant term, [D.sub.t] is a vector of dummy variables and [[epsilon].sub.t] is iid([LAMBDA]0, A) disturbance term. From this model, using [DELTA]=1-L, where L is the lag operator, we can deduce the following dynamic error correction model
[DELTA][X.sub.t] = [[GAMMA].sub.1][DELTA][X.sub.t-1] + ....+ [[GAMMA].sub.k-1][[DELTA].sub.t-k+1] + [PI][X.sub.t-k] + [[mu].sub.t] + [PHI][D.sub.i] + ... [[epsilon].sub.t] (5)
where [GAMMA].sub.i] = -I + [[PI].sub.1] + ..... + [[PI].sub.i], i=1, 2, .... k ... ... ... (6)
and [PI] = -I + [[PI].sub.1] + ... + [[PI].sub.k] ... ... ... ... ... (7)
This error correction model captures the short-run dynamics as well as long run properties of the inflation model because it includes variables both in levels and in differences. Under the assumptions all the variables included in the model are stationary. Therefore, this model can be estimated with the ordinary least square method [Granger and Lee (1989)]. However, the term [PI] is a cointegrating matrix, which consists of the long-run stable relationship among the rate of inflation, interest rate and exchange rate and loading vector. It implies that this relationship between the variables is stable and can be used for forecasting purposes and policy analysis.
7. TESTING OF STATIONARITY OF THE DATA
The property of data, whether these are stationary or not, is investigated by using standard ADF method. This test helps to estimate the order of integration of series. The order of integratedness would lead towards the appropriate action, for example differencing of the series to convert it into stationary series before estimation of weights of the MCI. As can be seem from the Table 1, the data for the variables to be used in the analysis are not stationary. The data have unit roots at frequency one, therefore all the series are I(1).
8. COINTEGRATION ANALYSIS
In the previous section we have established that the time series data of the variable to be used in the modeling of inflation for the estimation of weights are not stationary at their level. However, these series can be made stationary after differencing. This univariate analysis leads towards the utilisation of econometrics techniques, such as cointegration analysis, tailored for the non-stationary time series data.
Johanson (1988) full information maximum likelihood method is used to test the presence of any long run relationship between the rate of inflation, rate of interest and exchange rate. For this analysis we used order of VAR as 24 months, which is chosen on the basis of the white noise property of error term and standard lag selection criteria such as Akiake Information Criteria (CIA) and Schwartz Baysian Criteria (SBC). As can be seen from the Table 2, both Maximal eigenvalue and Trace statistics lead to the conclusion that there are two cointegrating vectors between these variable at the 5 percent level of significance. This result is inline with the theoretical prediction. There is long run relationship between the rate of inflation and rate of interest as predicted by Fisher. And there is long run relationship between the rate of inflation and exchange rate as predicted by the theory of open economy. Further studies in Pakistan found that external factor are significantly contributing the rate of inflation, see for example, Khan and Qasim (1996); Hasan, et al. (1995); Naqvi, et al. (1994) and Bilquees (1988), among others.
Following the tradition we used first cointegrating vector to estimate the coefficients of the inflation equation. The estimated equation is presented below (t-ratios are in the parentheses).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
From this estimated model we obtained weights of rate of interest and exchange rate that are to be used in the construction of monetary conditions index of inflation in Pakistan. The estimated coefficients of rate of interest and exchange rate give the weights of 0.736 and 0.264, respectively. With the help of these estimated weights we calculated monetary condition ratio, which is 2.79:1. The monetary conditions ratio is an indicator of the relative importance of interest rate channel and exchange rate channel in the monetary policy transmission mechanism to affect the rate of inflation. The estimated monetary condition ratio of 2.79:1 implies that one percentage point movement in the rate of interest is equivalent to the 2.79 percentage points movement in the nominal exchange rate in term of effect on the rate of inflation. In other words, we can say that one percentage point increase in the rate of interest can be offset by the 2.79 percentage point fall in the exchange rate. This opposite directions movement in the interest rate and exchange rate would leave monetary condition in putting pressure on rate of inflation unchanged.
9. MONETARY CONDITIONS INDEX OF INFLATION
Finally monetary conditions index (MCI) is constructed by utilising the weights that are estimated in the previous section. For this purpose we used monthly data from July-1990 to June-2001. The June-1990 is used as base period. There is no theoretical reason to select the base period, it is rather an arbitrary decision. Since financial sector reforms initiated by the government of Pakistan during the financial year 1989-90, this choice seem to be reasonable to analyse monetary condition in Pakistan during the previous decade. The estimated weight of rate of interest is 0.736 and it is 0.264 for nominal exchange rate.
Table 3 presents the MCI of inflation variable for Pakistan whereas Table 4 contains movement in the MCI. Respective series are presented in the Figures 1 and 2. Linear trend line is fitted and it is also presented in the Figure 1. The visual inspection of the graph of MCI reveals the fluctuating behaviour of monetary conditions during 1990s. However, the linear trend line shows increasing pressure on inflation by the monetary authorities during the decade under discussion.
We have also estimated proper trend line. The estimated trend line is concave to the time period that is x-axis. This shape of trend line indicates changing stance of monetary policy by the monetary authorities during the decade under study. It seemed that in the earlier period of 1990s the monetary policy aimed to exert pressure on rate of inflation and authorities are trying to reduce the rate of inflation up to the target level. On the close inspection of the graph of MCI it is evident that spell of tight monetary policy remained operative till 1997. It seems that the monetary authorities are easing monetary policy since 1997-98. However, it is also clearly in evident that the monetary authorities are careful in the conduct of monetary policy. This implies that monetary authorities in Pakistan are determined to contain rate of inflation within given target level without damaging other macroeconomic objectives of the Government.
10. DECOMPOSITION OF MONETARY CONDITIONS INDEX
In the previous section we have constructed monetary conditions index for the period from 1999M6 to 2001M6. In this section our objective is to analyse the series of MCI by time series techniques. For this purpose we decompose the series into different components. It is assumed that a given series have four components such as seasonal, trend, cycle and irregular. We assume these components are of multiplicative nature, like
[Y.sub.t] = [S.sub.t] x [T.sub.t] x [C.sub.t] x [I.sub.t]
First we estimate seasonally adjusted series that is MCISA. For this purpose we used both twelve months moving average method and X-11 method. To get the seasonal components from the series we divided original series (MCI) by the seasonal adjusted series (MCISA) that is S, = MCI / MCISA. As a second step we have estimated the long-term trend of the series. For this purpose we used Hodrick and Prescort (1997) method. Hodrick-Prescort method is two-sided linear filter that computes a smoothed series by minimising the variance of Y around S, that is
[SIGMA] [([Y.sub.t] - [S.sub.t])].sup.2] + [lambda][SIGMA] [[([S.sub.t+1] - [S.sub.t]) - ([S.sub.t] - [S.sub.t-1]].sup.2]
where [lambda] is penalty factor and it controls the smoothness of the series, larger the value of [lambda], the smoother the series. The value of [lambda], for the monthly series is proposed to be 14400.
This Hodrick and Prescort trend line is plotted in Figure 3 along with the original seasonally adjusted MCI series. The figure gives interesting picture about the stance of monetary policy during the last decade. It indicates tightening of monetary policy for rate of inflation during early and mid nineties, that is from 1990 to March 1997. After that the stance of monetary policy seems to be easing. This trend of easing monetary policy continues till December 1999. However policy stance is still tight with respect to the base period. From January 2000 monetary policy seems to be putting pressure on the rate of inflation. This trend of increasing pressure on inflation goes on up to June 2001.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
11. CONCLUSIONS AND POLICY RECOMMENDATIONS
This paper estimated Monetary Conditions Index (MCI) of inflation variable for Pakistan by using monthly data from June 1990 to June 2001. Before calculating MCI we have estimated weights of interest rate and exchange rate to be used in the construction of MCI. For this purpose we used unit root analysis and Johenson (1988) maximum likelihood method base on vector autoregressive technology. The estimated monetary conditions ratio for Pakistan is around 2.79:1. This is close to the estimated ratio of small developing countries as Turkey, Thailand etc. Finally we have constructed the MCI by utilising the estimated weights of rate of interest and exchange rate. For detailed analysis we decomposed the series into seasonal, trend, cycle and irregular factors. The trend factor is obtained by the application of Hodrick and Prescort (1997) filter. The analysis indicate overall tight monetary policy during the decade. However there is some easing spell during 1997 to 1999. This shows the determinedness of monetary authorities with objective of keeping inflation low. Low inflation at the end of the decade indicates the success of monetary authorities in the conduct of monetary policy in achieving the target of low inflation.
Author's Note: I am thankful to Dr Muzhar Iqbal of Quaid-i-Azam University and for his useful comments on an earlier version of this paper.
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(1) This method would take care of the criticism levelled by Eika, et al. (1997) against the underlying estimated models of MCIs such as Duguay (1994), and Hansson and Lindberg (1997) among others.
Abdul Qayyum is Associate Professor of Economics at the Pakistan Institute of Development Economics, Islamabad.
Table 1 ADF Test of Unit Roots Variables Order of Lag [tau]-Ratio [pi] 11 -2.42 Ex 12 -2.08 Cmr 10 -2.34 Variables Order of lag [tau]-Ratio [DELTA][pi] 0 -16.96 [DELTA]Ex 11 -4.97 [DELTA]Cmr 0 -26.05 Note: Lag length is selected on the basis of the white noise property of error term along with AIC and SBC. The critical value at 5 percent level is 2.87. Table 2 Cointegration; Likelihood Ratio Test Based on Maximal Eigenvalue/ Trace of the Stochastic Matrix Maximal Null Alternative Eigenvalue r = 0 r [less than or equal to] 1 119.56 * r [less than or equal to] 1 r [less than or equal to] 2 35.98 * r [less than or equal to] 2 r=3 5.15 Null Trace r = 0 160.70 * r [less than or equal to] 1 41.13 * r [less than or equal to] 2 5.15 Table 3 Monetary Conditions Index of Pakistan (1999M6 - 2001M6) OBS MCII OBS. MCII OBS. MCII 1990M6 99.9971 1994M7 122.8061 1998M8 83.3176 1990M7 101.2053 1994M8 93.6024 1998M9 67.6773 1990M8 101.2108 1994M9 100.9361 1998M10 127.2105 1990M9 98.6420 1994M10 95.5405 1998M11 92.0248 1990M10 97.3103 1994M11 117.3137 1998M12 108.1050 1990M11 99.9913 1994M12 117.5116 1999M1 131.1717 1990M12 103.6483 1995M1 129.1717 1999M2 110.8827 1991M1 104.3325 1995M2 120.8256 1999M3 97.8702 1991M2 102.5833 1995M3 111.0207 1999M4 129.1746 1991M3 107.2278 1995M4 126.0419 1999M5 114.3582 1991M4 90.2350 1995M5 118.5462 1999M6 72.3802 1991M5 91.8061 1995M6 120.7214 1999M7 116.2055 1991M6 91.4843 1995M7 113.5223 1999M8 112.0313 1991M7 78.3342 1995M8 119.3794 1999M9 110.662 1991M8 101.5816 1995M9 121.1339 1999M10 121.5921 1991M9 94.6043 1995M10 120.3660 1999M11 116.0295 1991M10 114.8401 1995M11 107.7205 1999M12 119.5114 1991M11 110.0901 1995M12 129.4301 2000M1 111.6898 1991M12 108.4142 1996M1 127.7208 2000M2 102.1873 1992M1 104.6455 1996M2 122.2359 2000M3 104.1921 1992M2 106.1363 1996M3 124.7475 2000M4 97.8178 1992M3 118.3299 1996M4 129.1601 2000M5 116.7180 1992M4 101.1485 1996M5 93.9643 2000M6 122.6732 1992M5 73.6892 1996M6 112.1252 2000M7 98.0675 1992MG 77.0846 1996M7 114.1062 2000M8 109.5979 1992M7 83.6303 1996M8 114.1770 2000M9 105.7583 1992M8 46.4118 1996M9 114.4224 2000M10 127.9761 1992M9 119.4532 1996M10 128.1883 2000M11 129.6603 1992M10 113.7991 1996M11 115.7311 2000M12 122.2142 1992M11 105.1336 1996M12 138.5339 2001M1 116.9945 1992M12 118.6222 1997M1 139.7258 2001M2 105.2279 1993M1 122.7103 1997M2 135.3751 2001M3 105.8019 1993M2 124.7216 1997M3 122.5178 2001M4 122.6207 1993M3 115.7573 1997M4 134.4620 2001M5 118.3507 1993M4 98.7652 1997M5 121.9490 2001M6 118.2465 1993M5 126.6061 1997M6 125.4804 1993M6 120.9148 1997M7 120.8547 1993M7 62.6480 1997M8 118.8520 1993M8 88.8515 1997M9 105.5242 1993M9 131.6691 1997M10 116.1496 1993M10 126.3744 1997M11 107.2425 1993M11 1l5.3238 1997M12 128.2175 1993M12 129.4122 1998M1 135.0194 1994M1 110.5034 1998M2 128.3300 1994M2 94.6461 1998M3 128.5053 1994M3 107.4143 1998M4 138.5559 1994M4 73.7216 1998M5 128.3862 1994M5 120.4602 1998M6 132.1760 1994M6 115.3460 1998M7 115.2710 Table 4 Change in Monetary Conditions Index of Pakistan (1999M6 - 2001 M6) OBS. CMCI OBS. CMCI OBS. CMCI 1990M6 -1.2722 1994M7 7.4601 1998M8 -31.9535 1990M7 1.2082 1994M8 -29.2037 1998M9 -15.6403 1990M8 0.01 1994M9 7.337 1998M10 59.5332 1990M9 -2.5687 1994M10 -5.3956 1998M11 -35.1857 1990M10 -1.3317 1994M11 21.7732 1998M12 16.0801 1990M11 2.6810 1994M12 0.19794 1999M1 23.0668 1990M12 3.6570 1995M1 11.6601 1999M2 -20.2890 1991M1 0.68418 1995M2 -8.3461 1999M3 -13.0125 1991M2 -1.7492 1995M3 -9.8049 1999M4 31.3044 1991M3 4.6445 1995M4 15.0211 1999M5 -14.8165 1991M4 -16.9928 1995M5 -7.4956 1999M6 -41.9779 1991M5 1.5712 1995M6 2.1752 1999M7 43.8252 1991M6 -0.32186 1995M7 -7.1991 1999M8 -4.1742 1991M7 -13.1501 1995M8 5.8571 1999M9 -1.3651 1991M8 23.2474 1995M9 1.7545 1999M10 10.9259 1991M9 -6.9773 1995M10 -0.76792 1999M11 -5.5626 1991M10 20.2359 1995M11 -12.6455 1999M12 3.4819 1991M11 -4.7500 1995M12 21.7096 2000M1 -7.8216 1991M12 -1.6759 1996M1 -1.7093 2000M2 -9.5025 1992M1 -3.7686 1996M2 -5.4849 2000M3 2.0048 1992M2 1.4907 1996M3 2.5116 2000M4 -6.3743 1992M3 12.1936 1996M4 4.4126 2000M5 18.9002 1992M4 -17.1814 1996M5 -35.1958 2000M6 5.9552 1992M5 -27.4593 1996M6 18.1609 2000M7 -24.6057 1992M6 3.3954 1996M7 1.9810 2000M8 11.53.5 1992M7 6.5456 1996M8 .070728 2000M9 -3.8396 1992M8 -37.2185 1996M9 .24543 2000M10 22.2178 1992M9 73.0413 1996M10 13.7659 2000M11 1.6842 1992M10 -5.654 1996M11 -12.4572 2000M12 -7.4461 1992M11 -8.6656 1996M12 22.8027 2001M1 -5.2196 1992M12 13.4886 1997M1 1.1920 2001M2 -11.7666 1993M1 4.0881 1997M2 -4.3507 2001M3 0.57398 1993M2 2.0113 1997M3 -12.8573 2001M4 16.8188 1993M3 -8.9643 1997M4 11.9442 2001M5 -4.2700 1993M4 -16.9921 1997M5 -12.513 2001M6 -0.10428 1993M5 27.8409 1997M6 3.5314 1993M6 -5.6913 1997M7 -4.6257 1993M7 -58.2667 1997M8 2.0027 1993M8 26.2034 1997M9 -13.3278 1993M9 42.8176 1997M10 10.6254 1993M10 -52947 1997M11 -8.9071 1993M11 -11.0505 1997M12 20.9749 1993M12 14.0883 1998M1 6.8019 1994M1 -18.9088 1998M2 -6.6894 1994M2 -15.8573 1998M3 0.17531 1994M3 12.7682 1998M4 10.0506 1994M4 -33.6927 1998M5 -10.1697 1994M5 46.7385 1998M6 3.7898 1994M6 -5.1141 1998M7 -16.9050
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|Title Annotation:||FINANCIAL SECTOR|
|Publication:||Pakistan Development Review|
|Date:||Dec 22, 2002|
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