I. introduction

Inflation and money demand developments in Albania during 1993–97 took place in the context of a dramatic transition to a market economy, marked by substantial changes in institutional structures and in the policy-making environment. During 1993–95, significant progress was made in economic stabilization: inflation was brought down from near hyperinflation levels, real output grew rapidly, and reserves were built up to a comfortable level (Table 1, Figure 1). The stabilization effort was based on tight financial policies: the budget deficit was reduced substantially and monetary management was prudent. With the economy’s growing import needs financed by a large volume of remittances and generous foreign aid, Albania’s floating exchange rate moved within a small band over the three-year period, a feature that continued during 1996. This stability in the policy environment and the favorable outcome may have formed the basis for a decline in inflationary expectations and stable exchange rate expectations, making for stable relationships between the price level, money, and the exchange rate.

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Albania: Economic developments, 1993-97

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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Table 1.

Albania: Main economic indicators, 1992-97

Sources: Albanian authorities; and Fund staff estimates.

^1/Current account excluding net factor services and official transfers.

^2/Revenue (excluding grants) minus current expenditure.

^3/Commitment basis, excluding foreign financed investment.

^4/Excluding official transfers.

Table 1.

Albania: Main economic indicators, 1992-97

				1992	1993	1994	1995	1996	1997
									Est.
				(Percent change)
Real GDP				-7.2	9.6	9.4	8.9	9.1	-7.0
Retail prices (period average)				226.0	85.0	22.6	7.8	12.7	32.1
Retail prices (during period)				236.6	30.9	15.8	6.0	17.4	42.1
				(In percent of GDP)
Saving-investment balance
	Foreign saving 1/			57.1	28.7	14.4	9.7	11.5	14.2
	Domestic saving			-51.9	-15.5	3.5	11.3	9.0	-2.2
			Public 2/	-21.9	-8.7	-5.5	-3.3	-7.6	-8.7
			Private	-30.0	-6.8	9.0	14.6	16.6	6.6
	Investment			5.2	13.2	17.9	21.0	20.5	12.0
			Public	4.0	9.5	8.6	8.2	4.5	4.1
			Private	1.2	3.7	9.3	12.8	16.0	7.9
Fiscal sector
	Revenues			23.5	25.7	24.5	23.9	18.3	17.0
	Expenditures 3/			44.0	34.9	31.2	30.8	29.0	27.6
	Domestically financed deficit			20.0	9.1	7.0	6.6	11.0	10.9
	Overall deficit			20.3	14.4	12.4	10.3	12.1	12.7
Monetary indicators
	Broad money growth (in percent)			…	75.0	40.6	51.8	43.8	28.4
	Growth in private sector credit (in percent)			…	…	61.4	15.9	30.5	22.0
	Velocity of circulation			…	3.68	2.83	2.22	1.97	1.92
				(In millions of U.S. dollars)
External sector
	Current account balance			-104	-45	-118	-58	-168	-199
		(in percent of GDP)		-14.7	-3.7	-6.0	-2.4	-6.2	-8.6
	Official transfers			330	320	161	118	77	77
		(in percent of GDP)		46.5	26.1	8.2	4.9	2.9	3.3
	Current account balance 4/			-434	-365	-279	-176	-245	-276
		(in percent of GDP)		-61.1	-29.7	-14.1	-7.2	-9.1	-11.9
	Trade balance			-454	-490	-460	-474	-692	-519
		(in percent of GDP)		-64.0	-39.9	-23.4	-19.6	-25.7	-22.5
	Gross international reserves			72	147	204	240	280	306
		(in months of imports of goods  and nonfactor services)		1.4	2.3	3.2	3.4	3.1	4.5
Memorandum items:
	Real GDP (in billions of leks, 1990 prices)			11.2	12.3	13.5	14.7	16.0	14.9
	Nominal GDP (in billions of leks)			53.2	125.3	187.9	224.7	281.0	338.9
	Nominal GDP (in billions of U.S. dollars)			0.7	1.2	2.0	2.4	2.7	2.3

Sources: Albanian authorities; and Fund staff estimates.

^1/Current account excluding net factor services and official transfers.

^2/Revenue (excluding grants) minus current expenditure.

^3/Commitment basis, excluding foreign financed investment.

^4/Excluding official transfers.

View Table

Table 1.

Albania: Main economic indicators, 1992-97

				1992	1993	1994	1995	1996	1997
									Est.
				(Percent change)
Real GDP				-7.2	9.6	9.4	8.9	9.1	-7.0
Retail prices (period average)				226.0	85.0	22.6	7.8	12.7	32.1
Retail prices (during period)				236.6	30.9	15.8	6.0	17.4	42.1
				(In percent of GDP)
Saving-investment balance
	Foreign saving 1/			57.1	28.7	14.4	9.7	11.5	14.2
	Domestic saving			-51.9	-15.5	3.5	11.3	9.0	-2.2
			Public 2/	-21.9	-8.7	-5.5	-3.3	-7.6	-8.7
			Private	-30.0	-6.8	9.0	14.6	16.6	6.6
	Investment			5.2	13.2	17.9	21.0	20.5	12.0
			Public	4.0	9.5	8.6	8.2	4.5	4.1
			Private	1.2	3.7	9.3	12.8	16.0	7.9
Fiscal sector
	Revenues			23.5	25.7	24.5	23.9	18.3	17.0
	Expenditures 3/			44.0	34.9	31.2	30.8	29.0	27.6
	Domestically financed deficit			20.0	9.1	7.0	6.6	11.0	10.9
	Overall deficit			20.3	14.4	12.4	10.3	12.1	12.7
Monetary indicators
	Broad money growth (in percent)			…	75.0	40.6	51.8	43.8	28.4
	Growth in private sector credit (in percent)			…	…	61.4	15.9	30.5	22.0
	Velocity of circulation			…	3.68	2.83	2.22	1.97	1.92
				(In millions of U.S. dollars)
External sector
	Current account balance			-104	-45	-118	-58	-168	-199
		(in percent of GDP)		-14.7	-3.7	-6.0	-2.4	-6.2	-8.6
	Official transfers			330	320	161	118	77	77
		(in percent of GDP)		46.5	26.1	8.2	4.9	2.9	3.3
	Current account balance 4/			-434	-365	-279	-176	-245	-276
		(in percent of GDP)		-61.1	-29.7	-14.1	-7.2	-9.1	-11.9
	Trade balance			-454	-490	-460	-474	-692	-519
		(in percent of GDP)		-64.0	-39.9	-23.4	-19.6	-25.7	-22.5
	Gross international reserves			72	147	204	240	280	306
		(in months of imports of goods  and nonfactor services)		1.4	2.3	3.2	3.4	3.1	4.5
Memorandum items:
	Real GDP (in billions of leks, 1990 prices)			11.2	12.3	13.5	14.7	16.0	14.9
	Nominal GDP (in billions of leks)			53.2	125.3	187.9	224.7	281.0	338.9
	Nominal GDP (in billions of U.S. dollars)			0.7	1.2	2.0	2.4	2.7	2.3

Sources: Albanian authorities; and Fund staff estimates.

^1/Current account excluding net factor services and official transfers.

^2/Revenue (excluding grants) minus current expenditure.

^3/Commitment basis, excluding foreign financed investment.

^4/Excluding official transfers.

Macroeconomic performance weakened in 1996 and a full-blown crisis erupted in early 1997. The fiscal stance became lax ahead of the parliamentary elections in May 1996 and the demand pressures were reflected in higher inflation and in a worsening of the current account deficit. Events took a turn for the worse during the second half of 1996, when the growth of financial pyramid scheme went unchecked. The inevitable collapse occurred in March 1997. Widespread rioting over lost savings led to extensive civil disorder. Massive supply-side disruptions, a precipitous fall in revenue collection, and a collapse of remittances, contributed to a sharp depreciation of the exchange rate and generated strong inflationary pressures. A decisive response to the crisis and a return to responsible financial policies came only in the second half of 1997 with the formation of a new government.

This paper has two objectives. First, it seeks to uncover the quantitative relationships between the price level, money, and the exchange rate in Albania. So far, there has been little econometric analysis of inflation and money demand for Albania. In part, this reflects the short time series and the scarcity of basic data on real activity. Second, the paper seeks to assess the impact of the economic crisis of 1997 on inflation and money demand. At the onset of the crisis, the fiscal situation worsened sharply, and together with the steep depreciation of the exchange rate, prompted fears that the economy might revert to a period of very high inflation, even hyperinflation. The period was also marked by heightened uncertainty about the prospective behavior of money demand. However, except for a steep jump in March, monthly inflation was quickly brought under control. This was undoubtedly in part due to the strong policy response in the second half of 1997. There is, nevertheless, the issue of whether these developments generated a significant change in the underlying determinants of inflation and money demand.

This study is a part of a growing literature on inflation and money demand in transition economies. Reflecting the short length and paucity of the data series, the focus has mostly been on cross–country studies (Sahay and Vegh (1995), Fischer et. al. (1996), Begg (1996), Coorey et. al. (1997), De Broeck et. al. (1997)). These studies have produced stylized facts on, and cross—country panel data parameter estimates of, the determinants of inflation and money demand. Some individual country studies are also available (Griffiths and Pujol (1996), Domac (1997), and Ross (1998)). Albania’s early experience with inflation stabilization is analyzed in McNeilly and Schiesser-Gachnang (1998).

The remainder of the paper is organized as follows: Section II outlines a simple analytical framework involving the price level, the exchange rate, money, and the interest rate. Data issues are taken up in Section III. Integration and cointegration analyses are carried out in Section IV. Based on these, a parsimonious error-correction model for prices, money, and interest rates, conditional on the exchange rate, is estimated in Section V. Section VI concludes.

II. Analytical framework

The relationships between prices, money, and the exchange rate are examined using a simple two equation model of an economy with a goods market and a money market. In the goods market, the price level (P) is assumed to be a weighted average of tradable (P_T) and nontradables (P_NT) prices; the price of tradables is determined by the exchange rate (E) and foreign prices (P*) while nontradable prices are a markup over unit labor costs (W):

Substituting for the prices of tradables and nontradables in the price level equation, taking logs (all variables denoted in small letters) and using a suitable normalization, p is a function only of the exchange rate and time:

where α₁=α; and α₂ = [αν + (1−α)ϕ] > 0.

Equations (1)–(2) also define the evolution of the real wage (w) and the real exchange rate (x, the relative price of nontradables), using a suitable normalization, as:

The demand for money is represented as a function of the price level (P), the expected depreciation of the exchange rate (E), the interest rate (R), and the level of real activity (Y):

The transactions demand for nominal balances increases as the price level rises. The inclusion of the expected rate of depreciation in the money demand function captures the portfolio choice that asset holders face. In the Albanian context, foreign cash and deposits constitute virtually the only financial alternative to domestic currency and deposits. Movements in the exchange rate constitute an important element of the relative rate of return on alternative assets and are facilitated by the curb market in foreign exchange, which is relatively efficient and can mediate a substantial volume of small transactions at low cost.² A priori, the sign of f₂ is indeterminate and would depend on whether broad money is defined to include or exclude foreign currency denominated deposits.³ With regard to the interest rate, f₃ may be positive or negative. The demand for currency would fall with an increase in R but the demand for (interest bearing) demand and time deposits is likely to be higher. Finally, money demand is expected to be positively related to the level of activity.

We can therefore postulate the following (semi-log) relation between money demand, the price level, the exchange rate, the interest rate, and the level of activity:

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Albania: Daily lek/U.S. dollar exchange rate and fluctuation bands, 1993-96

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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III. data

Data for the period 1993–97 are used. The data are plotted in Figure 3. Monthly CPI data are available from the Albanian statistical institute, INSTAT. The price variable is the CPI index, excluding administered prices. The exchange rate is the monthly average of daily lek/US dollar rate. Data on broad money and the interest rate are available from the Bank of Albania. Broad money is defined to include domestic currency in circulation, and demand and time deposits (in domestic and foreign currency). The minimum 12–month deposit rate in state-owned commercial banks is used for the interest rate variable. In the absence of a suitable series, the nominal wage is assumed to be a function of time as in the analytical framework. With regard to the level of real activity, there are no official national income accounts. The scale variable Y is extrapolated to reflect the estimated growth of real GDP.⁴ All variables are used without seasonal adjustments.

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Albania: Money, prices, the exchange rate, and interest rates, 1993-97

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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IV. integration and cointegration

Unit root tests for the variables were conducted, and Johansen’s maximum likelihood procedure was applied to test for cointegration between the variables. Table 2 lists the augmented Dickey-Fuller (ADF) statistics. All the variables appear to be integrated of at most order one. Cointegration tests between p, e, and m (with R, y, and the time trend as nonmodeled variables) were conducted in a third–order vector autoregression with three lags of each variable in the autroregressive distributed lag equations; the test statistics and estimates for the Johansen procedure are reported in Table 3.⁵ The maximal and trace eigenvalues statistics (λ_max and λ_trace) give consistent indication of two cointegrating relationships. The three (recursively estimated) eigenvalues are reasonably constant (Figure 4). The standardized eigenvectors and adjustment coefficients of the cointegration analysis (γ’ and δ, respectively) are shown in Table 3.

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Albania: Cointegration analysis of prices, exchange rate, money, and interest rates

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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Table 2.

Albania: Augmented Dickey—Fuller statistics for testing for a unit root

Sample period: 1993(4)–96(12) ^1/2/

Sources: Albanian authorities; and Fund staff estimates.

^1/Two values are reported for each variable and null order—the augmented Dickey-Fuller statistic, and (in parentheses) the estimated coefficient on the lagged variable, where the coefficient should be zero under the null hypothesis of a unit root. For a given variable x and null order 1(0), the ADF statistic is testing a null hypothesis of a unit root in x against the alternative of a stationary root; for a null order 1(1), the statistic is testing a null hypothesis of a unit root in Δx against an alternative of a stationary root in Δx. Each estimated equation contains a constant and a time trend. The maximum available sample is used, and varies across the null order.

^2/Here, and in the remainder of the paper,* and ** denote significance at the 5% and 1% level, respectively.

Table 2.

Albania: Augmented Dickey—Fuller statistics for testing for a unit root

Sample period: 1993(4)–96(12) ^1/2/

	Variable
Null order	p	m	e	R
I(0)	−3.76* (0.36)	−5.84** (−0.05)	−3.70** 0.37)	−4.67** (0.16)
I(1)	−6.63** (−0.23)	−8.72** (−0.49)	−6.57** (−0.33)	−7.84** (0.36)

Sources: Albanian authorities; and Fund staff estimates.

^1/Two values are reported for each variable and null order—the augmented Dickey-Fuller statistic, and (in parentheses) the estimated coefficient on the lagged variable, where the coefficient should be zero under the null hypothesis of a unit root. For a given variable x and null order 1(0), the ADF statistic is testing a null hypothesis of a unit root in x against the alternative of a stationary root; for a null order 1(1), the statistic is testing a null hypothesis of a unit root in Δx against an alternative of a stationary root in Δx. Each estimated equation contains a constant and a time trend. The maximum available sample is used, and varies across the null order.

^2/Here, and in the remainder of the paper,* and ** denote significance at the 5% and 1% level, respectively.

View Table

Table 2.

Albania: Augmented Dickey—Fuller statistics for testing for a unit root

Sample period: 1993(4)–96(12) ^1/2/

	Variable
Null order	p	m	e	R
I(0)	−3.76* (0.36)	−5.84** (−0.05)	−3.70** 0.37)	−4.67** (0.16)
I(1)	−6.63** (−0.23)	−8.72** (−0.49)	−6.57** (−0.33)	−7.84** (0.36)

Sources: Albanian authorities; and Fund staff estimates.

^1/Two values are reported for each variable and null order—the augmented Dickey-Fuller statistic, and (in parentheses) the estimated coefficient on the lagged variable, where the coefficient should be zero under the null hypothesis of a unit root. For a given variable x and null order 1(0), the ADF statistic is testing a null hypothesis of a unit root in x against the alternative of a stationary root; for a null order 1(1), the statistic is testing a null hypothesis of a unit root in Δx against an alternative of a stationary root in Δx. Each estimated equation contains a constant and a time trend. The maximum available sample is used, and varies across the null order.

^2/Here, and in the remainder of the paper,* and ** denote significance at the 5% and 1% level, respectively.

Table 3.

Albania: Cointegration analysis of prices, exchange rate, money, and interest rates

Sample period: 1993(4)–96(12)

Sources: Albanian authorities; and Fund staff estimates.

^1/The statistics λ_max and λ_trace are Johansen’s maximal eigenvalue and trace eigenvalue statistics for testing cointegration. The null hypothesis is in terms of the cointegration rank r and, in the case of r=0 is evidence in favor of at least one cointegrating vector.

Table 3.

Albania: Cointegration analysis of prices, exchange rate, money, and interest rates

Sample period: 1993(4)–96(12)

Eigenvalues		0.45	0.34	021
Hypotheses 1/		r=0	r ≤ 1	r≤ 2
λmax		26.8 *	18.6	10.4
95% critical value		25.5	19.0	12.3
λtrace		55.7 **	28.9 **	10.4
95% critical value		42.4	25.3	12.3
		Standardized eigenvectors, γ’
p	e	m	R	y	Trend
1.00	0.07	−0.66	−0.19	1.52	0.003
16.59	1.00	23.66	−17.99	−53.87	−0.50
−0.79	4.80	1.00	−8.04	−7.12	0.001
		Standardized adjustment coefficients, δ
	p	−0.31	0.002	0.011
	e	−0.45	−0.002	−0.05
	m	−0.09	−0.02	0.002

Sources: Albanian authorities; and Fund staff estimates.

^1/The statistics λ_max and λ_trace are Johansen’s maximal eigenvalue and trace eigenvalue statistics for testing cointegration. The null hypothesis is in terms of the cointegration rank r and, in the case of r=0 is evidence in favor of at least one cointegrating vector.

View Table

Table 3.

Albania: Cointegration analysis of prices, exchange rate, money, and interest rates

Sample period: 1993(4)–96(12)

Eigenvalues		0.45	0.34	021
Hypotheses 1/		r=0	r ≤ 1	r≤ 2
λmax		26.8 *	18.6	10.4
95% critical value		25.5	19.0	12.3
λtrace		55.7 **	28.9 **	10.4
95% critical value		42.4	25.3	12.3
		Standardized eigenvectors, γ’
p	e	m	R	y	Trend
1.00	0.07	−0.66	−0.19	1.52	0.003
16.59	1.00	23.66	−17.99	−53.87	−0.50
−0.79	4.80	1.00	−8.04	−7.12	0.001
		Standardized adjustment coefficients, δ
	p	−0.31	0.002	0.011
	e	−0.45	−0.002	−0.05
	m	−0.09	−0.02	0.002

Sources: Albanian authorities; and Fund staff estimates.

^1/The statistics λ_max and λ_trace are Johansen’s maximal eigenvalue and trace eigenvalue statistics for testing cointegration. The null hypothesis is in terms of the cointegration rank r and, in the case of r=0 is evidence in favor of at least one cointegrating vector.

Two sets of restrictions were imposed on γ’ and δ:

• Identification: zero restrictions were imposed to establish whether the cointegration vectors could “identify” relationships of the form (2) and (4), i.e., whether the vectors (1, −γ₁₂, 0, 0, 0, −γ₁₆) and (−γ₂₁, −γ₂₂, 1, −γ₂₄, −γ₂₅, 0) lie in the cointegrating space. In addition, the restriction that nominal money demand is homogenous of degree 0 with regard to the price level was imposed on the second vector (γ₂₁ = 1).

• Weak exogeneity: The tests for weak exogeneity show that only the exchange rate fitted the bill (δ₂₁= 0, δ₂₂= 0; Table 4). In addition, the restriction that disequilibrium in the first cointegrating relationship did not affect the evolution of prices was imposed (δ₁₁ = 0).⁶

Table 4.

Albania: Restricted cointegration analysis of prices, exchange rate, money, and interest rates

Sample period: 1993(4)–96(l2)

Sources: Albanian authorities; and Fund staff estimates.

^1/The weak exogeneity test statistics are evaluated under the assumption that r=2 and so are asymptotically distributed as χ²(2) under the null of weak exogeneity of the specified variable.

Table 4.

Albania: Restricted cointegration analysis of prices, exchange rate, money, and interest rates

Sample period: 1993(4)–96(l2)

		Weak exogeneity test statistics 1/
		p	e	M
	χ2(2)	13.9 [0.00] **	6.88 [0.03]*	8.4 [0.01] *
		Restricted eigenvectors, γ’
p	e	m	R	y	Trend
1.000	−0.18144	0.000	0.000	0.000	−O.006174
−1.000	0.34835	1.000	−0.71165	−3.7308	0.000
		Standard errors of γ’
p	e	m	R	y	Trend
0.00	0.067	0.00	0.00	0.00	0.00034
0.00	0.164	0.00	0.359	0.145	0.000
Restricted adjustment coefficients, δ
p	0.000	0.224
e	0.000	0.000
m	−0.857	−0.430
Standard errors of δ
p	0.000	0.049
e	0.000	0.000
m	0.202	0.139

Sources: Albanian authorities; and Fund staff estimates.

^1/The weak exogeneity test statistics are evaluated under the assumption that r=2 and so are asymptotically distributed as χ²(2) under the null of weak exogeneity of the specified variable.

View Table

Table 4.

Albania: Restricted cointegration analysis of prices, exchange rate, money, and interest rates

Sample period: 1993(4)–96(l2)

		Weak exogeneity test statistics 1/
		p	e	M
	χ2(2)	13.9 [0.00] **	6.88 [0.03]*	8.4 [0.01] *
		Restricted eigenvectors, γ’
p	e	m	R	y	Trend
1.000	−0.18144	0.000	0.000	0.000	−O.006174
−1.000	0.34835	1.000	−0.71165	−3.7308	0.000
		Standard errors of γ’
p	e	m	R	y	Trend
0.00	0.067	0.00	0.00	0.00	0.00034
0.00	0.164	0.00	0.359	0.145	0.000
Restricted adjustment coefficients, δ
p	0.000	0.224
e	0.000	0.000
m	−0.857	−0.430
Standard errors of δ
p	0.000	0.049
e	0.000	0.000
m	0.202	0.139

Sources: Albanian authorities; and Fund staff estimates.

^1/The weak exogeneity test statistics are evaluated under the assumption that r=2 and so are asymptotically distributed as χ²(2) under the null of weak exogeneity of the specified variable.

The restricted cointegrating vectors and the estimated error correction parameters are presented in Table 4. The “identifying” restrictions on the cointegrating vectors and “zero” restrictions on the error correction factors were not rejected at the 1% level of significance. The restricted cointegrating relationships were reasonably stationary (Figure 4). These vectors are (standard errors in parentheses):

The coefficients in equations (2′) and (4′) have the anticipated signs, are highly significant, and measure the sensitivity of prices and money demand to the regressors:

• Equation (2′) implies that over the sample period the price level was positively related to the depreciation of the exchange rate with an elasticity of 0.17. The parameter estimates of α₁ and α₂ can also be used to retrieve other parameters of equation (2). Thus, α = α₁ = 0.18, and [0.18ν + 0.82 ϕ] = α₂ = 0.0062. Assuming ν = 0.002 (so that foreign prices increase at an annual rate of some 2½ percent), we can residually solve for ϕ. The monthly growth rate of the nominal wage was thus an estimated 0.0071 (annualized 8½ percent). Moreover, the evolution of the equilibrium real wage rate and the real exchange rate can be calculated as:

  $\begin{array}{l}{w}=0.0009{t}-0.18{e}\\ {x}=0.005{t}.\end{array}$

• The estimated equation implies that the real wage grew over the sample period; for real exchange rate, the parameters imply an annual appreciation (of about 6 percent); this qualitative result sits well with the stylized fact that in transitional economies there is a tendency for the real exchange rate to appreciate.

• Equation (4′) implies that in the long run, money demand rose by an estimated: (i) ⅓ percent for a one percent appreciation of the exchange rate; (ii) ¾ percent if the deposit interest rate were raised by a percent; this positive relationship provides support for the policy of providing incentives for savings through the formal banking system; and (iii) 3¾ percent if the level of real activity were one percent higher. The elasticity of money demand to the scale variable is higher than in industrial countries (½–1), but is consistent with estimates for developing and transitional economies, where velocity shows a downward trend on account of many factors, including financial deepening. These results are consistent with the theoretical literature on the determinants of money demand, and the claim in the early transition literature that the determinants of inflation during transition are largely the same as in market economies (Sahay and Vegh (1995)).

V. an error correction model of prices and money

An error correction model (ECM) of prices, money, and interest rates, conditional on the exchange rate, is developed in this section. The model is reduced to obtain a parsimonious ECM. The model parameters turn out to be statistically constant, a remarkable property given the changes in the institutional and structural changes in Albania over the sample period. The long- and short-run properties, and the adjustment mechanism of the conditional ECM are discussed. The estimated model is used to forecast the path of the price level and money demand during 1997. The outcomes are compared to forecast values to assess the impact of the crisis. The model is reestimated using a dummy variable for 1997 to take account of the structural break in the parameters. The reestimated model is constant.

A. A parsimonious, conditional error correction model

The vector autoregression which forms the basis of the relationships in (2)’ and (4)’ was mapped into an I(0) system, and the reformulated system was estimated using recursive least squares. Corresponding to the lag length of two in the ADL, the lag length in the I(0) system was one. Monthly seasonal dummies were included in the system. A process of model reduction was then undertaken: (i) weak exogeneity of the exchange rate was imposed on the system, making the exchange rate a nonmodeled variable; (ii) insignificant regressors were dropped from individual equations of the system; (iii) the first cointegrating vector was dropped from the price change equation (as postulated in the “zero” restrictions); and (iv) suitable parameter restrictions were placed to increase the available degrees of freedom. Tests for model reduction were conducted and the reductions were found to be acceptable at each stage. The model, presented in Table 5, has only 12 estimated coefficients (compared to 40 in the original ADL). The restrictions imposed on the I(0) system were not rejected (the test statistic is χ²(28) = 33.63 [0.21]).

Table 5.

Albania: A parsimonious full information maximum likelihood conditional error correction model ^1/

Sample period: 1993(4)–96(12)

Sources: Albanian authorities; and Fund staff estimates.

^1/“Δ” indicates the first difference in the variable, and subscripts denote lagged (first) differences, ordinary equation standard errors are in parentheses (.), S1–S11 are monthly seasonal dummies for January–November, and Ω is the estimated variance-covariance matrix of error terms.

Table 5.

Albania: A parsimonious full information maximum likelihood conditional error correction model ^1/

Sample period: 1993(4)–96(12)

${\Delta }{p}=\underset{(0.22)}{1.12}+\underset{(0.12)}{0.34}{\Delta }{{p}}_{-1}-\underset{(0.09)}{0.21}{\Delta }{{m}}_{-1}+\underset{(0.05)}{0.11}({\Delta }{e}-{\Delta }{{e}}_{-1})$			$+\underset{(0.04)}{0.21}({m}-{{m}}^{*})-1$
${\Delta }{m}=\underset{(0.62)}{2.78}$			$\underset{(0.008)}{-0.026}({S}1+{S}2+{S}6+{S}7)\underset{(0.008)}{-0.031}({S}3+{S}4+{S}5+{S}9+{S}10)\underset{(0.01)}{-0.02}{S}8\underset{(0.01)}{-0.23}{S}11\underset{(0.17)}{-0.87}{({p}-{{p}}^{*})}_{-1}\underset{(0.10)}{-0.44}{({m}-{{m}}^{*})}_{-1}$
Standard errors of equations:
Δp:0.009	Δm:0.015
Log likelihood=404.07
Log|Ω|=−17.96	|Ω|=1.59e−8
Number of observations=45
Likelihood ratio test of over-identifying restrictions:χ2(28)=33.63 [0.21]
Correlation of residuals
	Δp	Δm
Δp	1.000
Δm	−0.05	1.000

Sources: Albanian authorities; and Fund staff estimates.

^1/“Δ” indicates the first difference in the variable, and subscripts denote lagged (first) differences, ordinary equation standard errors are in parentheses (.), S1–S11 are monthly seasonal dummies for January–November, and Ω is the estimated variance-covariance matrix of error terms.

View Table

Table 5.

Albania: A parsimonious full information maximum likelihood conditional error correction model ^1/

Sample period: 1993(4)–96(12)

${\Delta }{p}=\underset{(0.22)}{1.12}+\underset{(0.12)}{0.34}{\Delta }{{p}}_{-1}-\underset{(0.09)}{0.21}{\Delta }{{m}}_{-1}+\underset{(0.05)}{0.11}({\Delta }{e}-{\Delta }{{e}}_{-1})$			$+\underset{(0.04)}{0.21}({m}-{{m}}^{*})-1$
${\Delta }{m}=\underset{(0.62)}{2.78}$			$\underset{(0.008)}{-0.026}({S}1+{S}2+{S}6+{S}7)\underset{(0.008)}{-0.031}({S}3+{S}4+{S}5+{S}9+{S}10)\underset{(0.01)}{-0.02}{S}8\underset{(0.01)}{-0.23}{S}11\underset{(0.17)}{-0.87}{({p}-{{p}}^{*})}_{-1}\underset{(0.10)}{-0.44}{({m}-{{m}}^{*})}_{-1}$
Standard errors of equations:
Δp:0.009	Δm:0.015
Log likelihood=404.07
Log|Ω|=−17.96	|Ω|=1.59e−8
Number of observations=45
Likelihood ratio test of over-identifying restrictions:χ2(28)=33.63 [0.21]
Correlation of residuals
	Δp	Δm
Δp	1.000
Δm	−0.05	1.000

Sources: Albanian authorities; and Fund staff estimates.

^1/“Δ” indicates the first difference in the variable, and subscripts denote lagged (first) differences, ordinary equation standard errors are in parentheses (.), S1–S11 are monthly seasonal dummies for January–November, and Ω is the estimated variance-covariance matrix of error terms.

Actual outcomes, fitted values, and forecasts of the dynamic equations of Table 5 are shown in Figure 5; the variables are closely tracked (and the residuals not shown here are well behaved). On the basis of the diagnostic test statistics for the system and the individual equations reported in Table 6, the model and individual equations were statistically satisfactory. The portmanteau statistics, testing for serial correlation in the error terms up to six lags, showed no evidence of serial correlation. There was no trace of heteroscedasticity, and the error terms were approximately normal.

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Albania: Inflation and money growth

Outcomes and fitted values of the conditional ECM

Sample period: 1993(4)–96(12)

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albania authorities; and Fund staff estimates.

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Table 6.

Albania: Diagnostic statistics for the full information maximum likelihood error correction model

Sample period: 1993(4)–96(12)

Sources: Albanian authorities; and Fund staff estimates.

^1/Single equation tests: The Portmanteau statistic is a degrees of freedom corrected version of the Box-Pierce statistic for residual autocorrelation and tests for autocorrelation upto 6 lags; small values should be treated cautiously as residual autocorrelation is biased towards 0 when lagged dependent variables are included in the estimated equations. The LM F-statistic test for residual autocorrelation is performed through the auxiliary regression of residuals on the original variable and lagged residuals; missing observations are set to zero. The Normality test amounts to testing whether the skewness and kurtosis of the residuals correspond to that of a normal distribution. The ARCH test tests the joint significance of lagged squared residuals (here 1–4 lags) in a regression of squared residuals on a constant and lagged squared residuals.

^2/Vector tests: The Vector Portmanteau statistic is the multivariate equivalent of the single equation portmanteau. For the LM test, lagged residuals are partialed out from the original regressors, and the likelihood of the re-estimated system is compared to the original system. The Normality test is a multivariate equivalent of the single equation test.

Table 6.

Albania: Diagnostic statistics for the full information maximum likelihood error correction model

Sample period: 1993(4)–96(12)

Single Equation Tests 1/

Portmanteau tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{Portmanteau}6\text{lags}=4.66\\ {\Delta }{m}:\text{Portmanteau}6\text{lags}=5.61\end{array}$

Lagrange Multiplier F-tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{AR}1-4{F}(4,21)={4.44[0.01]}^{*}\\ {\Delta }{m}:\text{AR}1-4{F}(4,21)=2.64[0.06]\end{array}$

Tests for Normality (Doornik and Hansen, 1994):

$\begin{array}{l}{\Delta }{p}:\text{Normality}{{\chi }}^2(2)=0.72[0.69]\\ {\Delta }{m}:\text{Normality}{{\chi }}^2(2)={8.67[0.01]}^{*}\end{array}$

LM test autocorrelated squared residuals (AutoRegressive Conditional Heteroscedasticity):

$\begin{array}{l}{\Delta }{p}:\text{ARCH}4{F}(4,17)=1.07[0.40]\\ {\Delta }{m}:\text{ARCH}4{F}(4,17)=1.33[0.30]\end{array}$

Vector Tests 2/

$\begin{array}{l}\text{Vector portmanteau}6\text{lags}=15.54\\ \text{Vector LM test}:\text{AR}1-4,{F}(16,60)=0.50[0.94]\\ \text{Vector normality}{{\chi }}^2(4)=9.38[0.06]\end{array}$

Sources: Albanian authorities; and Fund staff estimates.

^1/Single equation tests: The Portmanteau statistic is a degrees of freedom corrected version of the Box-Pierce statistic for residual autocorrelation and tests for autocorrelation upto 6 lags; small values should be treated cautiously as residual autocorrelation is biased towards 0 when lagged dependent variables are included in the estimated equations. The LM F-statistic test for residual autocorrelation is performed through the auxiliary regression of residuals on the original variable and lagged residuals; missing observations are set to zero. The Normality test amounts to testing whether the skewness and kurtosis of the residuals correspond to that of a normal distribution. The ARCH test tests the joint significance of lagged squared residuals (here 1–4 lags) in a regression of squared residuals on a constant and lagged squared residuals.

^2/Vector tests: The Vector Portmanteau statistic is the multivariate equivalent of the single equation portmanteau. For the LM test, lagged residuals are partialed out from the original regressors, and the likelihood of the re-estimated system is compared to the original system. The Normality test is a multivariate equivalent of the single equation test.

View Table

Table 6.

Albania: Diagnostic statistics for the full information maximum likelihood error correction model

Sample period: 1993(4)–96(12)

Single Equation Tests 1/

Portmanteau tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{Portmanteau}6\text{lags}=4.66\\ {\Delta }{m}:\text{Portmanteau}6\text{lags}=5.61\end{array}$

Lagrange Multiplier F-tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{AR}1-4{F}(4,21)={4.44[0.01]}^{*}\\ {\Delta }{m}:\text{AR}1-4{F}(4,21)=2.64[0.06]\end{array}$

Tests for Normality (Doornik and Hansen, 1994):

$\begin{array}{l}{\Delta }{p}:\text{Normality}{{\chi }}^2(2)=0.72[0.69]\\ {\Delta }{m}:\text{Normality}{{\chi }}^2(2)={8.67[0.01]}^{*}\end{array}$

LM test autocorrelated squared residuals (AutoRegressive Conditional Heteroscedasticity):

$\begin{array}{l}{\Delta }{p}:\text{ARCH}4{F}(4,17)=1.07[0.40]\\ {\Delta }{m}:\text{ARCH}4{F}(4,17)=1.33[0.30]\end{array}$

Vector Tests 2/

$\begin{array}{l}\text{Vector portmanteau}6\text{lags}=15.54\\ \text{Vector LM test}:\text{AR}1-4,{F}(16,60)=0.50[0.94]\\ \text{Vector normality}{{\chi }}^2(4)=9.38[0.06]\end{array}$

Sources: Albanian authorities; and Fund staff estimates.

^1/Single equation tests: The Portmanteau statistic is a degrees of freedom corrected version of the Box-Pierce statistic for residual autocorrelation and tests for autocorrelation upto 6 lags; small values should be treated cautiously as residual autocorrelation is biased towards 0 when lagged dependent variables are included in the estimated equations. The LM F-statistic test for residual autocorrelation is performed through the auxiliary regression of residuals on the original variable and lagged residuals; missing observations are set to zero. The Normality test amounts to testing whether the skewness and kurtosis of the residuals correspond to that of a normal distribution. The ARCH test tests the joint significance of lagged squared residuals (here 1–4 lags) in a regression of squared residuals on a constant and lagged squared residuals.

^2/Vector tests: The Vector Portmanteau statistic is the multivariate equivalent of the single equation portmanteau. For the LM test, lagged residuals are partialed out from the original regressors, and the likelihood of the re-estimated system is compared to the original system. The Normality test is a multivariate equivalent of the single equation test.

The model parameters were jointly statistically constant, implying that price formation and money demand processes remained unchanged over the sample period. Figure 6 shows the one-step residuals of the estimated equations and the corresponding equation standard errors. The one-step ahead Chow statistics and the “break-point” Chow statistics are also plotted, and constancy is clearly not rejected.

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Albania: Constancy statistics for the conditional error correction model

Recursive equation residuals and Chow statistics

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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Parameter constancy suggests that the determinants of inflation and money demand remained unchanged over the sample period. This constancy is remarkable considering the transition that the economy was undergoing, the proliferation of the pyramid scheme companies, and the changes in the policy environment in 1996. Although perhaps surprising, the constancy is explicable. A number of changes, including price and trade liberalization, had already taken place early in the transition in 1992 (see McNeilly and Schiesser (1998)). Also, a number of factors contributed to a stable economic environment, including tight financial policies, a steady pace of remittances, and substantial foreign aid. These factors helped to create stable expectations about inflation and exchange rate depreciation. Moreover, the pace of structural reform, especially in the banking system, was especially slow during 1995–96.

B. Model properties

The ECM provides information on the adjustment and transmission mechanisms. In particular, two results are significant. First, the error correction parameters have a number of interesting properties. They are higher than those typically reported in industrial country studies (e.g., Ericsson and Sharma (1996), Hendry and Ericsson (1991)) which suggests that adjustment to price and money demand shocks in Albania is faster than in industrial countries. The higher values are all the more remarkable, since the money demand functions for industrial countries are typically estimated using quarterly data. Even in the context of a “general equilibrium” structure, the error correction parameters have the appropriate signs: when the price level is higher than its long run equilibrium value, there is a fall in money demand and a rise in the interest rate, when money is higher than its long run equilibrium value, the price level rises, and money demand falls. The model also permits a comparison of the impact of different kinds of disequilibria—possible only in a model with more than one market. The parameters show that the impact effect of price level disequilibria—the absolute value of the coefficient is 0.87—is larger compared to money market disequilibria (coefficients range in absolute value between 0.15 and 0.25). The results are also interesting in the context of sticky-price models à la Dornbusch, where adjustment to asset market disequilibria is faster compared to goods market disequilibria.

Second, the lag structure of the model also has some interesting features: only one lag of the variables is enough to capture the dynamics of inflation and money demand; there is some inflationary inertia even in the absence of such factors as price stickiness, lagged adjustment to relative price changes (Coorey et. al. (1997)), and wage indexation (Ross (1998)); and as is not uncommon, the transmission of the shocks is highly nonlinear. Figures 7 and 8 show the impact and cumulative impact, respectively, of a unit innovation in the price and money equation on inflation and on money demand growth.

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Albania: Impulse response functions of the conditional error correction model

(for a unit innovation in the price and money equations)

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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Albania: Cumulative impulse response functions of the conditional error correction model

(for a unit innovation in the price and money equations)

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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C. Developments in 1997

Albania descended into a crisis in March 1997. The stable policies of 1993–95 gave way to a lax policy stance by the second half of 1996, and the economy was engulfed by the rapid growth and proliferation of financial pyramid schemes. The distorting effects of the operations of the pyramid scheme companies were evident in macroeconomic indicators, including in shifts in the currency-deposit ratio. The inevitable collapse occurred in early 1997, and the pyramid scheme mania turned into a panic. Fueled by large supply-side disruptions, a precipitous drop in revenue collection, and a steep depreciation of the exchange rate, inflation rose. These factors, together with the considerable uncertainty in the policy-making environment, prompted fears that inflation could get out of hand.

Inflation was quickly brought under control and money demand remained remarkably strong. The security environment improved with the arrival of a multinational force, and revenue collection was restored rapidly with external technical assistance. Economic policy became more decisive after a new government took office in June, and financial policies were tightened in the second half of 1997. Strong efforts were made to secure a rebound in tax collection, and to keep the domestically financed deficit under check. In addition, short-term deposit interest rates were raised significantly to prop up money demand. Given that the economic and social situation recovered quickly, it is of some interest to examine whether the crisis induced only a one-time jump in the exchange rate and the price level, leaving the underlying determinants of inflation and money demand unchanged.

The hypothesis that the crisis induced a one-time jump in the exchange rate and the price level, leaving the long-run determinants of inflation and money demand unchanged, is tested by reestimating the cointegrating relationships and the error correction model for the entire period 1993–97. A clue to the form that the extended framework should take is provided by the forecast Chow statistic for the conditional ECM for 1993–96 (Figure 9). The statistic jumps, is stable after April, and parallels the movement in the exchange rate. This indicates that a break may have occurred in April 1997, and suggests the use of dummy variable (D497) for the period April-December 1997. This variable was introduced into the analysis, and a new error correction model was estimated. Cointegration analysis once again reveals the existence of two cointegrating relationships. These cointegrating vectors were estimated under the same “identifying” restrictions and “zero” restrictions as before. Furthermore, the coefficients of all variables, except the dummy variable, were restricted to the values that were arrived at for the earlier set of cointegrating vectors. The reestimated restricted cointegrating relationships were once again fairly stationary. For the period 1993–96 the same values of the cointegrating vectors as before were obtained. The reestimated vectors, where D497=1 for April–December 1997, 0 otherwise, are (standard errors in parentheses):

$\begin{array}{lll}(2^{″})& & {{p}}^{**}=0.18{e}+0.006{t}+\underset{(0.02)}{0.12}{D}497\end{array}$

$\begin{array}{lll}(4^{″})& & {{m}}^{**}={p}-0.35{e}+0.71{R}+3.73{y}+\underset{(0.04)}{0.46}{D}497\end{array}$

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Albania: Forecast Chow statistics for the conditional error correction model

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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The coefficients on the dummy are highly significant and capture the level jump in the exchange rate. The elasticities of inflation to exchange rate depreciation and of money demand to the exchange rate, the interest rate, and the level of economic activity are the same as before.

The final step is to estimate an error correction model in which these cointegrating relationships are embedded. To further capture the one-time effect of the disturbances during March and April 1997, step dummies (SD397 and SD497, respectively) were introduced in the dynamic system. This reestimated model is presented in Table 7, and has some interesting features. First, all the coefficients are significant and the error correction parameters are of the same sign as before. Second, the effect of the disturbances of March 1997 is captured in the coefficient of SD397 in the price equation; out of a total monthly inflation of 14 percent, the effect of these disturbances is estimated at about 8¼ percent. The diagnostic statistics for this model are encouraging (Table 8). The fitted values of the log differences of the price level and money demand are plotted in Figure 10, and the Chow statistics for the model are presented in Figure 11; parameter constancy is not rejected.

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Albania: Inflation and money growth

Outcomes and fitted values of the conditional ECM

Sample period: 1993(4)-97(12)

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albania authorities; and Fund staff estimates.

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Albania: Chow statistics for the conditional error correction model

Sample period: 1993(4)-1997(12)

Citation: IMF Working Papers 1998, 101; 10.5089/9781451948585.001.A001

Sources: Albanian authorities; and Fund staff estimates.

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Table 7.

Albania: A parsimonious full information maximum likelihood conditional error correction model ^1/

Sample period: 1993(4)–97(12)

Sources: Albanian authorities; and Fund staff estimates.

^1/Dummy variables: SD397 is 1 for March 1997, 0 otherwise; SD497 is 1 for April 1997, 0 otherwise; and S1–S11 are monthly seasonal dummies for January–November.

Table 7.

Albania: A parsimonious full information maximum likelihood conditional error correction model ^1/

Sample period: 1993(4)–97(12)

${\Delta }{p}=\underset{(0.18)}{0.59}+\underset{(0.11)}{0.49}{\Delta }{{p}}_{-1}+\underset{(0.04)}{0.28}({\Delta }{e}-{\Delta }{{e}}_{-1})+\underset{(0.01)}{0.09}{S}{D}397-\underset{(0.02)}{0.08}{S}{D}497$			$+\underset{(0.04)}{0.21}{({m}-{{m}}^{**})}_{-1}$
${\Delta }{m}=\underset{(0.56)}{2.91}$			$-\underset{(0.008)}{0.027}({S}1+{S}2+{S}6+{S}7)-\underset{(0.007)}{0.031}({S}3+{S}4+{S}5+{S}9+{S}10)-\underset{(0.01)}{0.01}{S}8-\underset{(0.01)}{0.025}{S}11-\underset{(0.13)}{0.70}{({p}-{{p}}^{**})}_{-1}-\underset{(0.06)}{0.23}{({m}-{{m}}^{**})}_{-1}$
Standard errors of equations:
Δp:0.12	Δm:0.014
log likelihood=500.57
Log|Ω|=−17.56	|Ω|=2.36 e-8
Number of observations=57
Likelihood ratio test of over-identifying restrictions: χ2(27)=34.12 [0.16]
Correlation of residuals
	Δp	Δm
Δp	1.000
Δm	−0.09	1.000

Sources: Albanian authorities; and Fund staff estimates.

^1/Dummy variables: SD397 is 1 for March 1997, 0 otherwise; SD497 is 1 for April 1997, 0 otherwise; and S1–S11 are monthly seasonal dummies for January–November.

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Table 7.

Albania: A parsimonious full information maximum likelihood conditional error correction model ^1/

Sample period: 1993(4)–97(12)

${\Delta }{p}=\underset{(0.18)}{0.59}+\underset{(0.11)}{0.49}{\Delta }{{p}}_{-1}+\underset{(0.04)}{0.28}({\Delta }{e}-{\Delta }{{e}}_{-1})+\underset{(0.01)}{0.09}{S}{D}397-\underset{(0.02)}{0.08}{S}{D}497$			$+\underset{(0.04)}{0.21}{({m}-{{m}}^{**})}_{-1}$
${\Delta }{m}=\underset{(0.56)}{2.91}$			$-\underset{(0.008)}{0.027}({S}1+{S}2+{S}6+{S}7)-\underset{(0.007)}{0.031}({S}3+{S}4+{S}5+{S}9+{S}10)-\underset{(0.01)}{0.01}{S}8-\underset{(0.01)}{0.025}{S}11-\underset{(0.13)}{0.70}{({p}-{{p}}^{**})}_{-1}-\underset{(0.06)}{0.23}{({m}-{{m}}^{**})}_{-1}$
Standard errors of equations:
Δp:0.12	Δm:0.014
log likelihood=500.57
Log|Ω|=−17.56	|Ω|=2.36 e-8
Number of observations=57
Likelihood ratio test of over-identifying restrictions: χ2(27)=34.12 [0.16]
Correlation of residuals
	Δp	Δm
Δp	1.000
Δm	−0.09	1.000

Sources: Albanian authorities; and Fund staff estimates.

^1/Dummy variables: SD397 is 1 for March 1997, 0 otherwise; SD497 is 1 for April 1997, 0 otherwise; and S1–S11 are monthly seasonal dummies for January–November.

Table 8.

Albania: Diagnostic statistics for the full information maximum likelihood error correction model

Sample period: 1993(4)–97(12)

Sources: Albanian authorities; and Fund staff estimates.

^1/Single equation tests: The Portmanteau statistic is a degrees of freedom corrected version of the Box—Pierce statistic for residual autocorrelation and tests for autocorrelation upto 6 lags; small values should be treated cautiously as residual autocorrelation is biased towards 0 when lagged dependent variables are included in the estimated equations. The LM F-statistic test for residual autocorrelation is performed through the auxiliary regression of residuals on the original variable and lagged residuals; missing observations are set to zero. The Normality test amounts to testing whether the skewness and kurtosis of the residuals correspond to that of a normal distribution. The ARCH test tests the joint significance of lagged squared residuals (here 1–4 lags) in a regression of squared residuals on a constant and lagged squared residuals.

^2/Vector tests: The Vector Portmanteau statistic is the multivariate equivalent of the single equation portmanteau. For the LM test, lagged residuals are partialed out from the original regressors, and the likelihood of the reestimated system is compared to the original system. The Normality test is a multivariate equivalent of the single equation test.

Table 8.

Albania: Diagnostic statistics for the full information maximum likelihood error correction model

Sample period: 1993(4)–97(12)

Single Equation Tests 1/

Portmanteau tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{Portmanteau}7\text{lags}=6.78\\ {\Delta }{m}:\text{Portmanteau}7\text{lags}=5.28\end{array}$

Lagrange Multiplier F-tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{AR}1-4{F}(4,31)={3.93[0.01]}^{*}\\ {\Delta }{m}:\text{AR}1-4{F}(4,31)={3.38[0.01]}^{*}\end{array}$

Tests for Normality (Doornik and Hansen, 1994):

$\begin{array}{l}{\Delta }{p}:\text{Normality}{{\chi }}^2(2)=0.16[0.92]\\ {\Delta }{m}:\text{Normality}{{\chi }}^2(2)=1.72[0.42]\end{array}$

LM test autocorrelated squared residuals (AutoRegressive Conditional Heteroscedasticity):

$\begin{array}{l}{\Delta }{p}:\text{ARCH}4{F}(4,27)=0.50[0.73]\\ {\Delta }{m}:\text{ARCH}4{F}(4,27)=0.50[0.73]\end{array}$

Vector Tests 2/

$\begin{array}{l}\text{Vector portmanteau}7\text{lags}=26.68\\ \text{Vector LM text}:\text{AR}1-4,{F}(16,80)=1.08[0.38]\\ \text{Vector normality}{{\chi }}^2(4)=1.95[0.74]\end{array}$

Sources: Albanian authorities; and Fund staff estimates.

^1/Single equation tests: The Portmanteau statistic is a degrees of freedom corrected version of the Box—Pierce statistic for residual autocorrelation and tests for autocorrelation upto 6 lags; small values should be treated cautiously as residual autocorrelation is biased towards 0 when lagged dependent variables are included in the estimated equations. The LM F-statistic test for residual autocorrelation is performed through the auxiliary regression of residuals on the original variable and lagged residuals; missing observations are set to zero. The Normality test amounts to testing whether the skewness and kurtosis of the residuals correspond to that of a normal distribution. The ARCH test tests the joint significance of lagged squared residuals (here 1–4 lags) in a regression of squared residuals on a constant and lagged squared residuals.

^2/Vector tests: The Vector Portmanteau statistic is the multivariate equivalent of the single equation portmanteau. For the LM test, lagged residuals are partialed out from the original regressors, and the likelihood of the reestimated system is compared to the original system. The Normality test is a multivariate equivalent of the single equation test.

View Table

Table 8.

Albania: Diagnostic statistics for the full information maximum likelihood error correction model

Sample period: 1993(4)–97(12)

Single Equation Tests 1/

Portmanteau tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{Portmanteau}7\text{lags}=6.78\\ {\Delta }{m}:\text{Portmanteau}7\text{lags}=5.28\end{array}$

Lagrange Multiplier F-tests for residual autocorrelation:

$\begin{array}{l}{\Delta }{p}:\text{AR}1-4{F}(4,31)={3.93[0.01]}^{*}\\ {\Delta }{m}:\text{AR}1-4{F}(4,31)={3.38[0.01]}^{*}\end{array}$

Tests for Normality (Doornik and Hansen, 1994):

$\begin{array}{l}{\Delta }{p}:\text{Normality}{{\chi }}^2(2)=0.16[0.92]\\ {\Delta }{m}:\text{Normality}{{\chi }}^2(2)=1.72[0.42]\end{array}$

LM test autocorrelated squared residuals (AutoRegressive Conditional Heteroscedasticity):

$\begin{array}{l}{\Delta }{p}:\text{ARCH}4{F}(4,27)=0.50[0.73]\\ {\Delta }{m}:\text{ARCH}4{F}(4,27)=0.50[0.73]\end{array}$

Vector Tests 2/

$\begin{array}{l}\text{Vector portmanteau}7\text{lags}=26.68\\ \text{Vector LM text}:\text{AR}1-4,{F}(16,80)=1.08[0.38]\\ \text{Vector normality}{{\chi }}^2(4)=1.95[0.74]\end{array}$

Sources: Albanian authorities; and Fund staff estimates.

^1/Single equation tests: The Portmanteau statistic is a degrees of freedom corrected version of the Box—Pierce statistic for residual autocorrelation and tests for autocorrelation upto 6 lags; small values should be treated cautiously as residual autocorrelation is biased towards 0 when lagged dependent variables are included in the estimated equations. The LM F-statistic test for residual autocorrelation is performed through the auxiliary regression of residuals on the original variable and lagged residuals; missing observations are set to zero. The Normality test amounts to testing whether the skewness and kurtosis of the residuals correspond to that of a normal distribution. The ARCH test tests the joint significance of lagged squared residuals (here 1–4 lags) in a regression of squared residuals on a constant and lagged squared residuals.

^2/Vector tests: The Vector Portmanteau statistic is the multivariate equivalent of the single equation portmanteau. For the LM test, lagged residuals are partialed out from the original regressors, and the likelihood of the reestimated system is compared to the original system. The Normality test is a multivariate equivalent of the single equation test.