## 1. Optimality Test

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---

### Introduction and background
- Early development of composite and coincident indicators:
  - Mitchell and Burns (1938) estimated first leading indicators of cyclical revival.
  - Moore and Shiskin (1967) produced first composite leading indicators for the U.S., a weighted average of four time series: industrial production, personal income less transfers, employees on non-agricultural payrolls and manufacturing, and trade sales.
  - Subsequent applications across OECD and emerging markets cited (Layton and Moore (1989), Zarnowitz (1996), Fabiano and others (2000), Lamy and Sabourin (2001), Albu (2008)).

### Motivation for LICs and SSA countries
- High-frequency GDP data in most low-income countries (LICs), especially sub-Saharan African (SSA) countries, are either unavailable or come with long lags and are often irrelevant for contemporaneous policymaking.
- Indicators of short-term dynamics serve as summary statistics and proxies for aggregate economic activity, facilitating timely policy responses.
- Few SSA countries currently use leading, coincident, or lagging indicators (examples cited: South Africa, Ghana, Mozambique).
- Growing emphasis on managing short-term aggregate demand in LIC monetary policymaking increases the need for indicators that can track and predict turning points.

### Methodological contributions and innovations
- Augments existing methodology to accommodate low-quality and frequently omitted variables common in developing economies.
- Extensions include:
  - Test for optimality in selecting components for estimation.
  - Test for stability of the estimated index.
  - A combined algorithm, within the same framework, for using the Composite Index of Economic Activities (CIEA) to interpolate quarterly GDP for countries lacking high-frequency GDP data.

### Key findings and evidence
- Correlation and tracking:
  - The estimated CIEA is highly correlated with official quarterly GDP estimates for all countries in the sample: Average correlation: 0.95
  - The CIEA closely tracks both short- and medium-term turning points in economic activity when benchmarked against official GDP estimates in all selected countries.
- Counterfactual policy insight:
  - Evidence indicates that monetary policy could have been enhanced, in hindsight, with high-frequency assessment of economic activity as central banks aim to minimize the output and inflation loss function.
- Interpolated quarterly GDP using the CIEA:
  - Shows a strong correlation with official estimates for all selected countries.
  - Supports using the CIEA as an important variable in projecting GDP for LICs lacking high-frequency GDP estimates.

### Policy relevance, scope, and limitations
- Purpose:
  - Construct an aggregate and comprehensive measure of overall economic activity that would be available on a timely basis at appropriate frequencies.
- Policy relevance:
  - The CIEA is useful as countries move to more flexible monetary management that requires responding to short-term changes in aggregate demand.
- Limitations:
  - The CIEA is not a replacement for standard measures of economic activity (i.e., GDP); it is intended to complement them by providing timely high-frequency information useful for short-term monitoring and policy response.
- Main practical roles:
  - An early signal on the direction of the economy.
  - A tool to anticipate the future direction of output to support policymaking in the absence of timely and high-frequency GDP data.

### Structure of the paper (overview)
- Section I: Background of indicators of economic activity and methodology outline for estimating the index.
- Section II: Criteria for selecting components for the index and the model for estimating the index.
- Section III: Application of the model to a selected set of SSA countries, including optimality tests.
- Section IV: Techniques for interpolating high-frequency GDP using the estimated CIEA.
- Section V: Stability and robustness tests of the CIEA index.
- Section VI: Conclusions.

### Appendix I — Indicator weights by country (selected entries)
- Botswana
  - Broad money — Weight on Real Index: 27.90; Weight on Nominal Index: 18.59
  - BSE Index — Weight on Real Index: 20.86; Weight on Nominal Index: 13.69
  - Diamond exports — Weight on Real Index: 25.05; Weight on Nominal Index: 32.29
  - Imports of machinery — Weight on Real Index: 26.20; Weight on Nominal Index: 35.44
- Kenya
  - Cement production — Weight on Real Index: 13.86; Weight on Nominal Index: 13.23
  - Car sales — Weight on Real Index: 5.27; Weight on Nominal Index: 5.04
  - Electricity consumption — Weight on Real Index: 18.63; Weight on Nominal Index: 17.79
  - Capital imports — Weight on Real Index: 11.35; Weight on Nominal Index: 11.14
  - Credit to private Sector — Weight on Real Index: 50.86; Weight on Nominal Index: 52.80
- Rwanda
  - VAT — Weight on Real Index: 10.46; Weight on Nominal Index: 10.25
  - Imports — Weight on Real Index: 6.03; Weight on Nominal Index: 5.90
  - Exports — Weight on Real Index: 3.74; Weight on Nominal Index: 3.66
  - Breweries — Weight on Real Index: 6.02; Weight on Nominal Index: 5.92
  - Reserve money — Weight on Real Index: 21.68; Weight on Nominal Index: 22.67
  - Key manufacturing — Weight on Real Index: 8.30; Weight on Nominal Index: 8.20
  - CPS — Weight on Real Index: 39.75; Weight on Nominal Index: 39.40
  - NCG — Weight on Real Index: 4.02; Weight on Nominal Index: 3.99
- Tanzania
  - Travel reciepts — Weight on Real Index: 7.19; Weight on Nominal Index: 7.01
  - Manufacturing exports — Weight on Real Index: 11.77; Weight on Nominal Index: 11.92
  - Capital imports — Weight on Real Index: 11.45; Weight on Nominal Index: 11.61
  - VAT — Weight on Real Index: 9.53; Weight on Nominal Index: 9.27
  - Development spending — Weight on Real Index: 6.43; Weight on Nominal Index: 6.28
  - M3 — Weight on Real Index: 53.63; Weight on Nominal Index: 53.90

### Appendix I — Co-movement chart captions and scales (selected)
- Botswana
  - Index; 2007 = 100
  - Millions of Pula, 1993-94
  - Time span shown: 2004Q1, 2004Q3, 2005Q1, 2005Q3, 2006Q1, 2006Q3, 2007Q1, 2007Q3, 2008Q1, 2008Q3, 2009Q1, 2009Q3, 2010Q1, 2010Q3
  - Vertical index markers: 40, 60, 80, 100, 120, 140, 5000, 5200, 5400, 5600, 5800, 6000, 6200, 6400, 6600, 6800, 7000
- Kenya
  - Index; 2007 = 100
  - Billions of Kenyan Shillings, 2001
  - Time span shown: 2002Q1, 2002Q3, 2003Q1, 2003Q3, 2004Q1, 2004Q3, 2005Q1, 2005Q3, 2006Q1, 2006Q3, 2007Q1, 2007Q3, 2008Q1, 2008Q3, 2009Q1, 2009Q3, 2010Q1, 2010Q3
  - Vertical index markers: 1, 40, 60, 80, 100, 120, 140, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400
- Rwanda
  - Index; 2007 = 100
  - Billions of Rwandan Francs, 2006
  - Time span shown: 2008Q1, 2008Q2, 2008Q3, 2008Q4, 2009Q1, 2009Q2, 2009Q3, 2009Q4, 2010Q1, 2010Q2, 2010Q3, 2010Q4
  - Vertical index markers: 40, 60, 80, 100, 120, 140 and 100, 200, 300, 400, 500, 600, 700
- Tanzania
  - Index; 2007 = 100
  - Billions of Tanzanian Shillings, 2001
  - Time span shown: 2003Q1, 2003Q3, 2004Q1, 2004Q3, 2005Q1, 2005Q3, 2006Q1, 2006Q3, 2007Q1, 2007Q3, 2008Q1, 2008Q3, 2009Q1, 2009Q3, 2010Q1, 2010Q3
  - Vertical index markers: 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 2000, 2500, 3000, 3500, 4000, 4500, 5000
- Trend analysis conducted using HP Filter.

*Source: _wp12119*

### 1. Optimality Test .....................................................................................................

### 1. Optimality Test

### Introduction
- Turning points of economic activity are critical for macroeconomic management because existing models have performed poorly at predicting recessions.
- Early work: Mitchell and Burns (1938) estimated the first leading indicators of cyclical revival.
- Moore and Shiskin (1967) produced the first composite leading indicators for the U.S., calculated as a weighted average of four time series: industrial production, personal income less transfers, employees on non-agricultural payrolls and manufacturing, and trade sales.
- Subsequent applications extended composite and coincident indicator methodologies across OECD and emerging market economies (examples cited: Layton and Moore (1989), Zarnowitz (1996), Fabiano and others (2000), Lamy and Sabourin (2001), Albu (2008)).

### Motivation for LICs and SSA countries
- High-frequency GDP data in most low-income countries (LICs), especially sub-Saharan African (SSA) countries, are either unavailable or come with long lags and are therefore often irrelevant for contemporaneous policymaking.
- Indicators of short-term dynamics of economic activity serve as summary statistics and proxies for aggregate economic activity, facilitating timely policy responses.
- Few SSA countries (examples: South Africa, Ghana, Mozambique) currently use leading, coincident, or lagging indicators.
- Growing emphasis on managing short-term aggregate demand in LIC monetary policymaking increases the need for indicators that can track and predict turning points.

### Novelty and methodological contributions of the paper
- Augments existing methodology to accommodate low-quality and frequently omitted variables common in developing economies.
- Extends the process to:
  - Test for optimality in selecting components for estimation.
  - Test for stability of the estimated index.
- Introduces a combined algorithm, within the same framework, for using the Composite Index of Economic Activities (CIEA) to interpolate quarterly GDP for countries lacking high-frequency GDP data.

### Key findings and evidence
- The estimated CIEA is highly correlated with official quarterly GDP estimates for all countries in the sample:
  - Average correlation: 0.95
- The CIEA closely tracks both short- and medium-term turning points in economic activity when benchmarked against official GDP estimates in all selected countries.
- Counterfactual policy insight:
  - Evidence indicates that monetary policy could have been enhanced, in hindsight, with high-frequency assessment of economic activity as central banks aim to minimize the output and inflation loss function.
- Interpolated quarterly GDP using the CIEA:
  - Shows a strong correlation with official estimates for all selected countries.
  - Supports using the CIEA as an important variable in projecting GDP for LICs lacking high-frequency GDP estimates.

### Structure of the paper (as presented)
- Section I: Background of indicators of economic activity and methodology outline for estimating the index.
- Section II: Criteria for selecting components for the index and the model for estimating the index.
- Section III: Application of the model to a selected set of SSA countries, including optimality tests.
- Section IV: Techniques for interpolating high-frequency GDP using the estimated CIEA.
- Section V: Stability and robustness tests of the CIEA index.

*Source: _wp12119 - 1. Optimality Test .....................................................................................................*

### Section VI concludes the paper.

### Section VI concludes the paper

### Key problem
- The lack of high-frequency real sector data in most LICs, particularly SSA countries, poses challenges in making macroeconomic policy proactive and flexible enough to anticipate, and where possible provide a timely response to, changes in macroeconomic fundamentals.

### Purpose of the study
- Construct an aggregate and comprehensive measure of overall economic activity that would be available on a timely basis at appropriate frequencies.

### Main findings
- The estimated CIEA is highly correlated with and closely tracks official estimates of GDP in all the selected countries.
- The CIEA helps close the gap in high-frequency real sector data that currently poses a challenge to policymaking in most developing countries.
- The CIEA is particularly helpful in gauging short-term dynamics of economic activity, serving as:
  - an early signal on the direction of the economy;
  - a tool to anticipate the future direction of output to support policymaking in the absence of timely and high-frequency GDP data.

### Scope and limitations
- The CIEA is not a replacement for the standard measures of economic activity (i.e., GDP); it is intended to complement them by providing timely high-frequency information useful for short-term monitoring and policy response.

### Policy relevance
- The CIEA is useful as countries move to more flexible monetary management that requires responding to short-term changes in aggregate demand.

*Source: Section VI, _wp12119 - Section VI concludes the paper.*

### Appendix I

### Appendix I

### Indicator weights by country
- Botswana
  - Broad money — Weight on Real Index: 27.90; Weight on Nominal Index: 18.59
  - BSE Index — Weight on Real Index: 20.86; Weight on Nominal Index: 13.69
  - Diamond exports — Weight on Real Index: 25.05; Weight on Nominal Index: 32.29
  - Imports of machinery — Weight on Real Index: 26.20; Weight on Nominal Index: 35.44
- Kenya
  - Cement production — Weight on Real Index: 13.86; Weight on Nominal Index: 13.23
  - Car sales — Weight on Real Index: 5.27; Weight on Nominal Index: 5.04
  - Electricity consumption — Weight on Real Index: 18.63; Weight on Nominal Index: 17.79
  - Capital imports — Weight on Real Index: 11.35; Weight on Nominal Index: 11.14
  - Credit to private Sector — Weight on Real Index: 50.86; Weight on Nominal Index: 52.80
- Rwanda
  - VAT — Weight on Real Index: 10.46; Weight on Nominal Index: 10.25
  - Imports — Weight on Real Index: 6.03; Weight on Nominal Index: 5.90
  - Exports — Weight on Real Index: 3.74; Weight on Nominal Index: 3.66
  - Breweries — Weight on Real Index: 6.02; Weight on Nominal Index: 5.92
  - Reserve money — Weight on Real Index: 21.68; Weight on Nominal Index: 22.67
  - Key manufacturing — Weight on Real Index: 8.30; Weight on Nominal Index: 8.20
  - CPS — Weight on Real Index: 39.75; Weight on Nominal Index: 39.40
  - NCG — Weight on Real Index: 4.02; Weight on Nominal Index: 3.99
- Tanzania
  - Travel reciepts — Weight on Real Index: 7.19; Weight on Nominal Index: 7.01
  - Manufacturing exports — Weight on Real Index: 11.77; Weight on Nominal Index: 11.92
  - Capital imports — Weight on Real Index: 11.45; Weight on Nominal Index: 11.61
  - VAT — Weight on Real Index: 9.53; Weight on Nominal Index: 9.27
  - Development spending — Weight on Real Index: 6.43; Weight on Nominal Index: 6.28
  - M3 — Weight on Real Index: 53.63; Weight on Nominal Index: 53.90

- Component Standarization Factors

### Co-movement between real GDP and real CIEA (chart captions and scales)
- Botswana
  - Index; 2007 = 100
  - Millions of Pula, 1993-94
  - Chart series labels: Real GDP; left scale — Real CIEA; right scale
  - Time span shown: 2004Q1, 2004Q3, 2005Q1, 2005Q3, 2006Q1, 2006Q3, 2007Q1, 2007Q3, 2008Q1, 2008Q3, 2009Q1, 2009Q3, 2010Q1, 2010Q3
  - Vertical index markers: 40, 60, 80, 100, 120, 140, 5000, 5200, 5400, 5600, 5800, 6000, 6200, 6400, 6600, 6800, 7000
- Kenya
  - Index; 2007 = 100
  - Billions of Kenyan Shillings, 2001
  - Time span shown: 2002Q1, 2002Q3, 2003Q1, 2003Q3, 2004Q1, 2004Q3, 2005Q1, 2005Q3, 2006Q1, 2006Q3, 2007Q1, 2007Q3, 2008Q1, 2008Q3, 2009Q1, 2009Q3, 2010Q1, 2010Q3
  - Vertical index markers: 1, 40, 60, 80, 100, 120, 140, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400
- Rwanda
  - Index; 2007 = 100
  - Billions of Rwandan Francs, 2006
  - Time span shown: 2008Q1, 2008Q2, 2008Q3, 2008Q4, 2009Q1, 2009Q2, 2009Q3, 2009Q4, 2010Q1, 2010Q2, 2010Q3, 2010Q4
  - Vertical index markers: 40, 60, 80, 100, 120, 140 and 100, 200, 300, 400, 500, 600, 700
- Tanzania
  - Index; 2007 = 100
  - Billions of Tanzanian Shillings, 2001
  - Time span shown: 2003Q1, 2003Q3, 2004Q1, 2004Q3, 2005Q1, 2005Q3, 2006Q1, 2006Q3, 2007Q1, 2007Q3, 2008Q1, 2008Q3, 2009Q1, 2009Q3, 2010Q1, 2010Q3
  - Vertical index markers: 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 2000, 2500, 3000, 3500, 4000, 4500, 5000

- Trend analysis conducted using HP Filter.

### References (selected entries from appendix)
- Albu, Lucian-Liviu, 2008, “A Model to Estimate the Composite Index of Economic Activity in Romania,” IEF-RO, Romanian Journal of Economic Forecasting.
- Fabiano, S, A. Locarno, G. Oneto, and P. Sestito, September 2000, “The Sources of Unemployment Fluctuations: An Empirical Application to the Italian Case,” ECB Working Paper No. 29.
- Friedman Milton, 1962, “Interpolation of a Time Series by Related Series,” Journal of the American Statistical Association, Vol. 57, No. 3000 (December), pp. 729–757.
- Lamy, R., and P. Sabourin, 2001, “Monitoring Regional Economies in Canada with New High-Frequency Coincident Indexes,” Working Paper 2001-05, Department of Finance, Government of Canada.
- Layton, A., and G.H. Moore, 1989, “Leading Indicators for the Service Sector,” Journal of Business and Economic Statistics, 7 (3), pp. 379-386.
- Mitchell, W., and A.F. Burns, 1938, “Statistical Indicators of Cyclical Revivals and Recessions,” Bulletin, 69, National Bureau of Economic Research, reprinted in G.H. Moore (1961), ed., Business Cycle Indicators: Contributions to the Analysis of Current Business Conditions, Vol. I, National Bureau of Economic Research.
- Moore, G. H., 1950 “Statistical Indicators of Cyclical Revivals and Recessions,” Occasional Paper 31 (New York: National Bureau of Economic Research).
- Moore, G. H., 1983 “Business Cycles: Business Cycles, Inflation, and Forecasting in Studies in Business Cycles,” National Bureau of Economic Research, Volume 24, (Chicago: University of Chicago Press).
- Moore, G.H., and, J. Shiskin, 1967, “Indicators of Business Expansions and Contractions”. (New York: National Bureau of Economic Research.)
- Stock, J. H., and M. W. Watson, 1989, “New Indexes of Coincident and Leading Economic Indicators,” NBER Macroeconomics Annual (Cambridge, Mass.: MIT Press).
- Zarnowitz, V., 1996, Business Cycles: Theory, History, Indicators and Forecasting, in Studies in Business Cycles, NBER, Volume 27 (Chicago: The University of Chicago Press).

*Source: _wp12119 - Appendix I*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12119.pdf_