Republic of Madagascar: Selected Issues
Author: International Monetary Fund
Publication Date:
13 Jul 2007
eISBN:
9781451825435
Language:
English
Keywords:
ISCR; CR; Madagascar; trade; tariff; E. core inflation; inflation expectation; energy inflation; inflation volatility; nonfood inflation; Consumer price indexes; Energy prices; Agricultural prices
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This Selected Issues paper on the Republic of Madagascar reports on the several key themes associated with longer-term development issues in Madagascar. As one of the poorest countries in sub-Saharan Africa, Madagascar suffers from low levels of social indicators across all fronts including education, health, water and sanitation, and infrastructure. To make progress toward the Millennium Development Goals, the country will need to scale up substantially both public and private investment while taking actions to increase absorptive and institutional capacity and implementing supportive policies in each of the priority sectors.

Abstract

This Selected Issues paper on the Republic of Madagascar reports on the several key themes associated with longer-term development issues in Madagascar. As one of the poorest countries in sub-Saharan Africa, Madagascar suffers from low levels of social indicators across all fronts including education, health, water and sanitation, and infrastructure. To make progress toward the Millennium Development Goals, the country will need to scale up substantially both public and private investment while taking actions to increase absorptive and institutional capacity and implementing supportive policies in each of the priority sectors.

IV. The Measurement and Use of Core Inflation in Madagascar 1

A. Introduction

1. The high volatility of Madagascar’s inflation rate over the past several decades makes early identification of trends difficult for policy makers. This paper proposes the development of a measure of “core” inflation for Madagascar to provide an alternative measurement of the underlying rate of inflation by volatile components that are subject to frequent supply shocks from the overall index. This indicator should better identify the current trend in inflation and thereby help policymakers avoid reacting to false signals as they manage monetary and fiscal policies.

2. Core inflation has numerous meanings, but generally refers to a measure of inflation that excludes food and energy prices because these elements are viewed as volatile and supply-driven. Core inflation is often used as a policy variable for monetary policy because it is aligned to demand pressures yet remains an unbiased indicator of inflation.2

B. Historical Inflation Volatility

3. It’s useful to review past inflation volatility to understand the challenge posed to policymakers. Madagascar benefited from relative price stability during the first two decades after independence (1960–80). There were two periods of high inflation in the 1980s (Figure IV.1). The first spike followed years of large net bank financing of fiscal deficits, high money growth, persistent terms of trade shocks, and, in 1982, the replacement of the exchange rate peg to the French franc by a crawling peg with frequent adjustments. The second inflationary shock was an official devaluation in 1987, part of a wider liberalization effort supported by the IMF’s Structural Adjustment Facility.

Figure IV.1.
Figure IV.1.

Madagascar: Historical Inflation Trends

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

4. Inflation soared again in 1994–96 in response to three shocks: (i) a large depreciation of the exchange rate (almost 60 percent) after the shift to a floating exchange rate and introduction of an interbank foreign exchange market (MID) in May 1994; (ii) the January 1994 cyclone, which damaged the rice crop and led to a surge in rice prices; and (iii) a rapid expansion of the money supply in 1993–94 to accommodate a significant increase of credit to both government and nongovernment sectors. Inflation rose to over 70 percent at mid-1995 before declining to about 40 percent at year-end and further to 16 percent at the end of 1996, as a result of tightened monetary policy and a sharp reduction in the government budget deficit in 1996.

5. There have been two inflationary surges since 2000. The first occurred in 2002 in the aftermath of the 2001 presidential election and the civil disruption that followed, which triggered an oil shortage in much of the industrial area. The second, which began in mid-2004 and peaked in February 2005, was attributed to: (i) the impact of two cyclones in early 2004; (ii) a subsequent 50 percent depreciation in the exchange rate during that time; and (iii) a significant rice shortage. An energy shock at the end of 2005 that continued through mid-2006 led to only a small rise in overall inflation, largely because declining rice prices had an offsetting effect.

6. The volatility of Malagasy inflation has frequently made early identification of the inflation trend very difficult. This volatility arises from: (i) domestic shocks (from monetary and fiscal policies as well as food production and political events); (ii) external shocks (energy prices, the terms of trade, and cyclones); and (iii) the exchange rate. For policymakers trying to control inflation, early identification of a change in trend is crucial. Thus, other measures of inflation that may reduce some of the noise in overall inflation may help identify the current trend.

C. Background on Core Inflation

7. The most general model of inflation has four components: a long-term persistent trend, which may vary with time; cyclical factors, which may be linked to excess demand; periodic seasonality; and transient disturbances, which are often supply-related.

Лoverall=Лtrent+Лcycilfactors+Лseasonalfactors+Лtransientshocks+random  error  (Eq. 1)

There have been various interpretations of core inflation.3 Some viewed core inflation as most closely linked to the trend component. Others interpreted core inflation as the component reflecting expectations of consumers and producers about future inflation, which had no impact on real output in the medium to long term—most closely captured by the trend and the cyclical and seasonal factors. The transient shock component reflects relative price changes and is often described as “noise” blurring the more general trend of inflation over the medium to long term.

8. Frequently, core inflation is measured as aggregate inflation excluding a variety of items whose price movements are considered to distort the underlying price trend. Based on this approach, the overall headline inflation rate, usually measured by the Consumer Price Index (CPI), can be decomposed into core inflation, which is associated with expectations and demand pressures, and a transient component consisting of supply shocks.

Лoverall=Лcore+Лtransient  supply shocks  +randomerror    (Eq.2)

9. Central banks typically target and monitor multiple measures of inflation to decide whether additional monetary policy actions may be needed. For example, an increase in overall inflation resulting from a rise in food prices owing to an adverse weather shock would not necessarily trigger a monetary policy response. Policy makers want to avoid overreacting to supply shocks in either direction. Thus, the use of core inflation as a guide is somewhat like the use of the nominal income rule (targeting money growth in line with nominal GDP growth): it can prevent procyclical tightening when there are adverse price and output shocks.

10. There are three main approaches to the construction of alternative core inflation measures. In each case, the ‘core’ measure should remove highly volatile elements like certain food and energy prices, administered prices, and tax changes.

  • Exclusion-based approach–removes the price of fresh foods or other highly volatile food elements, energy, and all administered prices and tax/subsidy changes.

  • Volatility-weighted approach–does not exclude any component but reweights all components in inverse proportion to a measure of their volatility.

  • Trimmed mean approach–a percentage of the outlier components are trimmed from the consumer price index each period, the outliers varying with each period. (The median is one estimator in this class.)

11. Alternative measures of core inflation should be evaluated against the following range of criteria:

D. Construction of a Core Inflation Measure

Proposal for measuring core inflation

12. The reasons for establishing a measure of core inflation are to smooth the inflation path so that it will be easier for policy makers to identify inflation trends and avoid reacting to false signals. Below, we experiment with an exclusion-based measure of core inflation: overall inflation excluding rice and energy inflation.4

Identify and remove seasonality from the CPI

13. Stable seasonality is an important source of volatility that can easily be removed when calculating core inflation and thereby more clearly identify the underlying monthly change in the CPI. Technical analysis found stable seasonality in the overall CPI and the food CPI but not in the nonfood CPI (Item 2, Appendix IV.2).5 Food seasonality appears to be driven by predictable, cyclic patterns in the rice price (Figure IV.2), which can account for swings of up to 12 percent over the course of the year. Thus, monitoring changes in the CPI is best done on the seasonally adjusted values or using the annual rate of change to avoid distorting the underlying inflation trend.

Figure IV.2.
Figure IV.2.

Madagascar: Historical Seasonal Factors, Overall consumer price index and Food and Rice Prices 6

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

Identify and remove volatile components of the CPI

14. The most volatile categories in the CPI can be identified by calculating the standard deviation of the 10 main CPI categories (Table IV.1), which shows that food and transportation have the highest volatility. The source of the food volatility would appear to be rice, with a much higher volatility, and the transportation volatility would appear to originate from energy prices (Figure IV.3). All subcategories should also be tested to isolate other highly volatile elements.

Table IV.1.

Madagascar: Average Annual Inflation and Volatility 1

article image

Defined as log of the price level in the current period less the log of the price level 12 months earlier, times 100.

Figure IV.3.
Figure IV.3.

Madagascar: Rice and Energy Inflation

(year-over-year percentage change)

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

Calculation of core inflation

15. For this exercise, core inflation (Лcore) is a weighted average of the CPI for nonrice food products and nonenergy nonfood products 7 (see components in Table IV.1). While core inflation tracks the overall inflation rate, as expected, the period differences can reach up to 20 percent (Figure IV.4).

Лcore=(.3670/.7783)*Лnonricefood+(4.113/.7783)*Лnonenergy nonfood  (Eq.3)
Figure IV.4
Figure IV.4

Madagascar: Overall and Core Inflation, and Difference

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

Properties of core inflation

Unbiased

16. Core inflation should be an unbiased estimator of inflation. This was tested by regressing core inflation on overall inflation (from 1991 through 2006m9) to obtain the following significant parameters:

Лoverall=.011=.916*Лcore (R2= .931) (Eq.4)

Wald tests indicated that the coefficient on core inflation (.916) was not statistically different from 1, and the intercept (.011) was not statistically different from zero, thus establishing core inflation as an unbiased estimator of overall inflation. 8 An ECM (error correction model) was estimated for this long-run relationship, and estimated an error correction coefficient of -0.11, which implies that it takes up to nine months to fully adjust to shocks (Item 3, Appendix IV.2).

Causality

17. The Granger causality test between overall and core monthly inflation found that core inflation “Granger-causes” overall inflation but not vice versa (Table IV.2) 9. This was tested over alternate time periods to ensure consistency.

Table IV.2.

Madagascar: Granger Causality Test with 24 Lags, Alternative Periods

article image

Relationship between core inflation and supply and demand factors

18. Some statistical testing using correlation and simple regressions were done to estimate the effects of energy and rice prices, monetary growth, and the exchange rate on core inflation (Item 5, Appendix IV.2). Although core inflation is free of the first-round effects of energy and rice price changes, it captures these effects in the longer run as they filter into the economy. Changes in the exchange rate, money supply and output take time to fully filter into prices.

  • Energy price changes impacted core inflation for up to six months, with about 30 percent of the change in energy inflation being transmitted to core inflation.

  • Rice price changes impacted core inflation for roughly up to three months, with about 16 percent of the change in rice inflation finally being transmitted to core inflation.

  • Exchange rate changes had their maximum impact on core inflation at about three months but persisted for up to nine months, with about 20 percent of the exchange rate fluctuation ultimately transmitted into core inflation.

  • Output growth takes 4–6 months to have its maximum impact on core inflation.

  • Broad money growth appears to have its maximum impact on core inflation at around 6 months, with almost 50 percent of the change in money growth transmitted to core inflation.

Divergences

19. The divergences between core and overall inflation provide the most interesting information. During most of 2005, high rice prices (Figure IV.3) drove overall inflation higher than core inflation (Figure IV.5) despite some decline in energy prices. However, in the second half of 2006, overall inflation subsided to below the core rate as food prices fell and energy prices stabilized. Because overall inflation benefited from these positive price shocks, it would not have been appropriate to relax monetary policy until the core rate was clearly on a firm decline.

Figure IV.5.
Figure IV.5.

Madagascar: Overall Inflation vs. Core Inflation, 2004–06

(year-over-year percent change)

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

E. Core Inflation and Money Demand

20. Having established the statistical benefits of the core inflation measure in the prior section, it is also important for policy purposes to verify that the core inflation measure functions well in a demand for money equation. To this end, three alternative measures of inflation were compared—core, overall, and nonfood inflation—in a simple long-run money demand equation using monthly data from January 1999 through September 2006. 10

21. A standard money demand equation was used (Equation 5), with M3 as the intermediate monetary target variable (as previous work has demonstrated broad money to be most robust); real GDP 11; the monthly treasury bill auction rate (I_tb); and the relevant CPI. 12 This is similar to the work of Nassar (2005) except that he used the French interest rate as a measure for the price of money.

Long-run money demand:

LM3=β1LCPI*+β2LGDPR*-β3I*_tb+Constant+ε             (Eq.5)

Based on this long-run model, an ECM can be written as:

Error Correction Model:

ΔLM3t=α1*ε(t-1)(Eq.6)+α2iΣ*ΔLM3(t-i)+Σα3i*ΔLCPI(t-i)+Σα4i*ΔLGDPR(t-i)+Σα5i*ΣΔI-tb(t-i)+Constant+Seasonalfactors+error

Cointegration analysis

22. Separate long-run money demand equations were estimated using cointegration equations (CEs) for each of the three inflation measures for the period January 1999 through September 2006 based on the Johansen maximum likelihood cointegration procedure (Item 6, Appendix IV.2). 13 The core CPI performed best and had the best-behaved residuals. The coefficient on real GDP behaved badly in the equations with overall and nonfood CPI. However, some experimentation with different time periods suggests there may be some instability in the equation—possibly owing to structural changes over time and volatility created by the high-frequency data. Nevertheless, the estimated vector error correction model with core inflation seems reasonable (equations 7 and 8):

  • All signs are correct and magnitudes appropriate;

  • The elasticity of money (1.61) is rather high; and

  • The coefficient on the error term (–026) indicates an adjustment of 38 periods, about three years.

Eq.7.M3=1.608*LCPI-CORE+.528*LGDPR-.024*I-tb+3.371+ε
E.8.Δ3t=-0.02603728852*(LM3(-1)-1.607746674*LCPI-CORE(-1)-0.52813346*LGDPR(-1)+0.02397343965*ITB(-1)+3.371091312)+0.1284186266*D(LM3(-1))+0.02266933095*D(LM3(-2))--0.1995307975*D(LM3(-3))+0.008659468307*D(LCPI-CORE(-1))-0.01667417489*D(LCPI-CORE(-2))-0.1916719494*D(LCPI-CORE(-3))+0.6694231464*D(LGDPR(-1))-2.00316082*D(LGDPR(-2))+1.937552546*D(LGDPR(-3))-0.0003845249901*D(ITB(-1))+0.00214613933*D(ITB(-2))-0.001740720109*D(ITB(-3))+0.009184388483-0.006806614364*@SEAS(1)+0.009289837633*@SEAS(8)+0.02109985438*@SEAS(10)+0.01841122586*@SEAS(12)

23. Some standard statistical tests were performed on the long-run money CE and ECM with CPI_core (Equations 7 and 8), which produced the following interesting conclusions: 14

  • The coefficient on CPI_core is statistically different from 1.

  • The error correction terms in the short-run equations for changes in prices, GDP, and the interest rate are statistically different from 0.

  • Because the error correction coefficient on the error from the money equation is not statistically different from 0, money is weakly exogenous.

  • Given the assumption of weak exogeneity, a Granger causality test was done on the group of three short-run explanatory variables versus ΔLM3. Because it found no significant causality, there is some evidence of a strong exogeneity of money.

Impulse response analysis

24. Using the vector autoregression (VAR) for the money demand system of equations allows us to examine a shock of one standard deviation to each of the variables. The first column of graphs in Figure IV.6 shows that a positive shock on money translates into higher inflation fairly rapidly, creates a temporary increase in real output, and leads to a decline in interest rates—all as commonly expected.

25. Shocks to the other variables behave largely as expected: a positive shock to the CPI raises the interest rate and depresses output; it also leads to a slight decline in money. A positive shock to real output reduces inflation and creates a reinforcing cycle of further growth for just over one year, allowing interest rates to fall. The shock to the interest rate in the last column looks highly stylized and not particularly relevant. The initial increase in the interest rate reduces money and adds to the price level, but the interest declines somewhat over the first six months, triggering a rise in output and further pushing prices up.

Figure IV.6.
Figure IV.6.

Madagascar: Impulse Response to Shocks of One Standard Deviation

Response to Nonfactorized One S.D. Innovations

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

F. Conclusions

26. Preliminary results suggest it would be beneficial for the authorities to produce a monthly measure of core inflation. One such measure was estimated here and seems relevant, although other measures should be tested. Results also suggest that the authorities calculate a monthly seasonally adjusted measure of overall inflation so as to better identify inflation trends and expectations. The launching of a core inflation measure and a seasonally adjusted index should initially be directed to the central bank and the ministry of finance. It might subsequently be made publicly available with a campaign to raise public awareness of the meaning and value of such measures, in order to anchor public expectations to these measures.

27. The core inflation measure can highlight short-term underlying trends better than overall inflation by removing volatility due to energy and rice price fluctuations. For example, in the second half of 2006 overall inflation declined from June and was lower than core inflation. This appears to have been the result of favorable price shocks from rice and energy that were camouflaging still-present inflationary pressures. The monitoring of core inflation, however, would suggest that monetary policy should remain tight until the downturn in core inflation is clear. The above analysis also found that a certain share of rice and energy supply shocks work themselves into the underlying inflation rate fairly rapidly—and faster than the effects of exchange rate and monetary movements.

28. For monetary policy the measure of core inflation worked satisfactorily in identifying a long-run, stable money-demand relationship with M3. That relationship exhibits a moderately strong exogeneity of money, i.e., a causality from money to prices. The stability of the relationship means that monitoring the path of core inflation is beneficial for monetary policy. In practice, it would seem that policy makers are already implicitly targeting the core rate of inflation because they are not projecting future supply shocks nor would they plan to monetize them.

29. Many central banks have adopted explicit “inflation targeting” policies to anchor inflation expectations and thereby protect the value of money, make investment decision-making more effective, and dampen economic cycles. Inflation targeting policies frequently use core inflation as the intermediate or final target. While M3 remains the key intermediate variable for the transmission of inflation in Madagascar, equations using currency in circulation demonstrated interesting results and might be explored further.

APPENDIX IV.1—Madagascar: Existing System for Measuring Prices

Monitoring and collecting the data needed to compute the CPI is the responsibility of the National Institute of Statistics (INSTAT), which publishes monthly price movements. The main characteristics of the INSTAT collection and calculation mechanisms can be summarized as follows:

The monthly CPI suffers from limited geographic coverage; it comprises five major urban centers but no rural areas. Moreover, owing to lack of financial means and technical staff, INSTAT often has problems collecting data.

APPENDIX IV.2—Madagascar: Variable List and Statistical Results

Item 1. Madagascar: Variable List

article image

Item 2. Madagascar: Seasonal Tests and Indices

article image

Seasonal factor = Actual index/seasonally adjusted index

Item 3.
Item 3.

Madagascar: Real Money Balances, 1990 to 2006m9

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

Item 4.
Item 4.

ECM for Equation 4

Citation: IMF Staff Country Reports 2007, 239; 10.5089/9781451825435.002.A004

Item 5.

Madagascar: Relationship Between Core Inflation and Key Variables 1999 to 2006m9

article image

Based on 12 lags of variable correlated core inflation.

This is the sum of the coefficients from a regression on core inflation using a second order polynomial distributed lag (PDL) structure with 9 lags and an end point constraint. Impact on core inflation can be inferred from estimated coefficients of PDl. R2 is show in parenthesis.

Item 6.

Madagascar: Augmented Dickey-Fuller Statistics for Unit Root Tests

article image
All variables except the interest rate were expressed in log form.Test of null hypothesis (in level and first difference) that variable has a unit root.Probability level shown rather than statistic.

Possibly I(0)

Item 7.

Madagascar: Long-run Money Demand Relationship Using M3

article image
Estimated coefficients of cointegrating equation (CE) are significant (**) or not significant (ns).All CE’s were estimated with seasonal dummy variables for months 1, 8,10 and 12, which were the only significant ones for M3.

Lag length estimated on the basis of Schwarz and Hannan-Quinn ciriteria.

Test for only one cointegrating vector based on trace test and maximum eigenvalue.

Type of CE.(a)(b)(c)(d)(e)
Linear data trendnonoyesyesQuadratic
Test
interceptnoyesyesyesyes
trendnononoyesyes

Test for normality by testing for skewness and kurtosis. CE passes, fails or has some problems (SP).

Test for no first order autocorrelation.

Test for no heteroscedasticity.

References

  • Armour, Jamie (2006), ‘An Evaluation of Core Inflation Measures,’ Bank of Canada Working Paper 2006–10.

  • Bryan, Michael and Cecchetti, Stephen (1994), ‘Measuring Core Inflation,’ in Monetary Policy, edited by N. Gregory Mankiw, 1994.

  • Inflation Targeting (1999), edited by B. Bernake, T. Laubach, F. Mishkin, and A. Posen.

  • Nassar, Koffie (2005), ‘Money Demand and Inflation in Madagascar,’ IMF Working Paper WP/05/236.

  • Roger, Scott (1998), ‘Core Inflation: concepts, uses and measurement,’ Reserve Bank of New Zealand Discussion Paper G98/9.

  • Sacerdoti, Emilio and Xiao, Yuan (2001), ‘Inflation Dynamics in Madagascar, 1971-2000,’ IMF Working Paper WP/01/168.

  • Silver, Mick (2006), ‘Core Inflation Measures and Statistical Issues in Choosing Among Them,’ IMF Working Paper WP/06/97.

1

Prepared by Mark Ellyne.

2

Countries like New Zealand, the UK, and Canada use measures of core inflation as an intermediate target in their inflation targeting strategy (Inflation Targeting, 1999).

3

See Roger (1998) for a good review of the various concepts of core inflation.

4

Alternative measures of core inflation should also be considered and tested statistically against previously mentioned criteria (¶11). Some background on the existing measurement system for the CPI is explained in Appendix IV.1.

5

The US Bureau of Census X12 seasonal adjustment program in EVIEWS was used to identify statistically significant seasonality.

6

See Item 2, Appendix IV.2, for details.

7

Administered prices and interest payments would also normally be removed, but the necessary data were not available.

8

The two series are cointegrated as the residuals of the equation were found to be stationary using the ADF test.

9

Because the Granger statistical test does not determine true causality but measures ‘time precedence,’ the term “Granger-causes” is used instead of “causes”. Nevertheless, Granger-causality tends to be a useful concept in considering directionality of action.

10

Although some criticize the use of high-frequency monthly data for such modeling, others, like Bryan and Cecchetti (1994) have successfully employed it. The time period for estimation was chosen based on data limitations and structural changes in the financial sector, in particular, a major shift occurred after the 1994 financial sector liberalization, as evidenced by the shift in real money balances (Item 3, Appendix IV.2)

11

Annual GDP was interpolated monthly using the cubic spline distribution in EVIEWS; alternative interpolation methods were examined.

12

Item 1, Appendix IV.2 contains a list of variable definitions.

13

All variables were found to have first order integration, so that a first difference of their log values made them stationary for cointegration (see Item 6, Appendix IV.2).

14

The goal of this exercise was to determine which measure of inflation performs best in a simple demand for money equation. Further work should be done to perfect the money demand equation.

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Cover IMF Staff Country Reports
Republic of Madagascar: Selected Issues
Author: International Monetary Fund
Volume/Issue:
Volume 2007: Issue 239
Publisher:
International Monetary Fund
ISBN:
9781451825435
ISSN:
1934-7685
Pages:
75
DOI:
https://doi.org/10.5089/9781451825435.002
  • View in gallery

    Madagascar: Historical Inflation Trends

  • View in gallery

    Madagascar: Historical Seasonal Factors, Overall consumer price index and Food and Rice Prices 6

  • View in gallery

    Madagascar: Rice and Energy Inflation

    (year-over-year percentage change)

  • View in gallery

    Madagascar: Overall and Core Inflation, and Difference

  • View in gallery

    Madagascar: Overall Inflation vs. Core Inflation, 2004–06

    (year-over-year percent change)

  • View in gallery

    Madagascar: Impulse Response to Shocks of One Standard Deviation

    Response to Nonfactorized One S.D. Innovations

  • View in gallery

    Madagascar: Real Money Balances, 1990 to 2006m9

  • View in gallery

    ECM for Equation 4

Madagascar: Historical Inflation Trends

Madagascar: Historical Seasonal Factors, Overall consumer price index and Food and Rice Prices 6

Madagascar: Rice and Energy Inflation

(year-over-year percentage change)

Madagascar: Overall and Core Inflation, and Difference

Madagascar: Overall Inflation vs. Core Inflation, 2004–06

(year-over-year percent change)

Madagascar: Impulse Response to Shocks of One Standard Deviation

Response to Nonfactorized One S.D. Innovations

Madagascar: Real Money Balances, 1990 to 2006m9

ECM for Equation 4