This study covers the world outlook for fractional horsepower motors and generators excluding hermetics across more than 190 countries. For each year reported, estimates are given for the latent demand, or potential industry earnings (P.I.E.), for the country in question (in millions of U.S. dollars), the percent share the country is of the region, and of the globe.

These comparative benchmarks allow the reader to quickly gauge a country vis-à-vis others. Using econometric models which project fundamental economic dynamics within each country and across countries, latent demand estimates are created.

This report does not discuss the specific players in the market serving the latent demand, nor specific details at the product level. The study also does not consider short-term cyclicalities that might affect realized sales.

The study, therefore, is strategic in nature, taking an aggregate and long-run view, irrespective of the players or products involved. This study does not report actual sales data (which are simply unavailable, in a comparable or consistent manner in virtually all of the countries of the world).

This study gives, however, my estimates for the worldwide latent demand, or the P.I.E., for fractional horsepower motors and generators excluding hermetics. It also shows how the P.I.E. is divided across the world’s regional and national markets. For each country, I also show my estimates of how the P.I.E. grows over time (positive or negative growth). In order to make these estimates, a multi-stage methodology was employed that is often taught in courses on international strategic planning at graduate schools of business.

**1.3 THE METHODOLOGY**

In order to estimate the latent demand for fractional horsepower motors and generators excluding hermetics on a worldwide basis, I used a multi-stage approach. Before applying the approach, one needs a basic theory from which such estimates are created.

In this case, I heavily rely on the use of certain basic economic assumptions. In particular, there is an assumption governing the shape and type of aggregate latent demand functions.

Latent demand functions relate the income of a country, city, state, household, or individual to realized consumption. Latent demand (often realized as consumption when an industry is efficient), at any level of the value chain, takes place if an equilibrium is realized.

For firms to serve a market, they must perceive a latent demand and be able to serve that demand at a minimal return. The single most important variable determining consumption, assuming latent demand exists, is income (or other financial resources at higher levels of the value chain). Other factors that can pivot or shape demand curves include external or exogenous shocks (i.e., business cycles), and or changes in utility for the product in question.

Ignoring, for the moment, exogenous shocks and variations in utility across countries, the aggregate relation between income and consumption has been a central theme in economics. The figure below concisely summarizes one aspect of problem.

In the 1930s, John Meynard Keynes conjectured that as incomes rise, the average propensity to consume would fall. The average propensity to consume is the level of consumption divided by the level of income, or the slope of the line from the origin to the consumption function.

He estimated this relationship empirically and found it to be true in the short-run (mostly based on cross-sectional data). The higher the income, the lower the average propensity to consume.

This type of consumption function is shown as "B" in the figure below (note the rather flat slope of the curve). In the 1940s, another macroeconomist, Simon Kuznets, estimated long-run consumption functions which indicated that the marginal propensity to consume was rather constant (using time series data across countries). This type of consumption function is show as "B" in the figure below (note the higher slope and zero-zero intercept).

The average propensity to consume is constant. For a general overview of this subject area, see Principles of Macroeconomics by N. Gregory Mankiw, South-Western College Publishing; ISBN: 0030340594; 2nd edition (February 2002).

Is it declining or is it constant? A number of other economists, notably Franco Modigliani and Milton Friedman, in the 1950s (and Irving Fisher earlier), explained why the two functions were different using various assumptions on intertemporal budget constraints, savings, and wealth. The shorter the time horizon, the more consumption can depend on wealth (earned in previous years) and business cycles.

In the long-run, however, the propensity to consume is more constant. Similarly, in the long-run, households, industries, or countries with no income eventually have no consumption (wealth is depleted).

While the debate surrounding beliefs about how income and consumption are related and interesting, in this study a very particular school of thought is adopted. In particular, we are considering the latent demand for fractional horsepower motors and generators excluding hermetics across some 190 countries.

The smallest have fewer than 10,000 inhabitants. I assume that all of these counties fall along a "long-run" aggregate consumption function.

This long-run function applies despite some of these countries having wealth; current income dominates the latent demand for fractional horsepower motors and generators excluding hermetics. So, latent demand in the long-run has a zero intercept. However, I allow firms to have different propensities to consume (including being on consumption functions with differing slopes, which can account for differences in industrial organization, and end-user preferences).

Given this overriding philosophy, I will now describe the methodology used to create the latent demand estimates for fractional horsepower motors and generators excluding hermetics. Since ICON Group has asked me to apply this methodology to a large number of categories, the rather academic discussion below is general and can be applied to a wide variety of categories, not just fractional horsepower motors and generators excluding hermetics.

**1.3.1 STEP 1. PRODUCT DEFINITION AND DATA COLLECTION**

Any study of latent demand across countries requires that some standard be established to define "efficiently served". Having implemented various alternatives and matched these with market outcomes, I have found that the optimal approach is to assume that certain key countries are more likely to be at or near efficiency than others.

These countries are given greater weight than others in the estimation of latent demand compared to other countries for which no known data are available. Of the many alternatives, I have found the assumption that the world’s highest aggregate income and highest income-per-capita markets reflect the best standards for "efficiency".

High aggregate income alone is not sufficient (i.e., China has high aggregate income, but low income per capita and cannot be assumed to be efficient). Aggregate income can be operationalized in a number of ways, including gross domestic product (for industrial categories), or total disposable income (for household categories; population times average income per capita, or number of households times average household income per capita).

Brunei, Nauru, Kuwait, and Lichtenstein are examples of countries with high income per capita, but not assumed to be efficient, given low aggregate level of income (or gross domestic product); these countries have, however, high incomes per capita but may not benefit from the efficiencies derived from economies of scale associated with large economies.

Only countries with high income per capita and large aggregate income are assumed efficient. This greatly restricts the pool of countries to those in the OECD (Organization for Economic Cooperation and Development), like the United States, or the United Kingdom (which were earlier than other large OECD economies to liberalize their markets).

The selection of countries is further reduced by the fact that not all countries in the OECD report have industry revenues at the category level. Countries that typically have ample data at the aggregate level that meet the efficiency criteria include the United States, the United Kingdom, and in some cases France and Germany.

Is it declining or is it constant? A number of other economists, notably Franco Modigliani and Milton Friedman, in the 1950s (and Irving Fisher earlier), explained why the two functions were different using various assumptions on intertemporal budget constraints, savings, and wealth. The shorter the time horizon, the more consumption can depend on wealth (earned in previous years) and business cycles.

In the long-run, however, the propensity to consume is more constant. Similarly, in the long-run, households, industries, or countries with no income eventually have no consumption (wealth is depleted).

While the debate surrounding beliefs about how income and consumption are related and interesting, in this study a very particular school of thought is adopted. In particular, we are considering the latent demand for fractional horsepower motors and generators excluding hermetics across some 190 countries.

The smallest have fewer than 10,000 inhabitants. I assume that all of these counties fall along a "long-run" aggregate consumption function.

This long-run function applies despite some of these countries having wealth; current income dominates the latent demand for fractional horsepower motors and generators excluding hermetics. So, latent demand in the long-run has a zero intercept. However, I allow firms to have different propensities to consume (including being on consumption functions with differing slopes, which can account for differences in industrial organization, and end-user preferences).

Given this overriding philosophy, I will now describe the methodology used to create the latent demand estimates for fractional horsepower motors and generators excluding hermetics. Since ICON Group has asked me to apply this methodology to a large number of categories, the rather academic discussion below is general and can be applied to a wide variety of categories, not just fractional horsepower motors and generators excluding hermetics.

**1.3.1 STEP 1. PRODUCT DEFINITION AND DATA COLLECTION**

Any study of latent demand across countries requires that some standard be established to define "efficiently served". Having implemented various alternatives and matched these with market outcomes, I have found that the optimal approach is to assume that certain key countries are more likely to be at or near efficiency than others.

These countries are given greater weight than others in the estimation of latent demand compared to other countries for which no known data are available. Of the many alternatives, I have found the assumption that the world’s highest aggregate income and highest income-per-capita markets reflect the best standards for "efficiency".

High aggregate income alone is not sufficient (i.e., China has high aggregate income, but low income per capita and cannot be assumed to be efficient). Aggregate income can be operationalized in a number of ways, including gross domestic product (for industrial categories), or total disposable income (for household categories; population times average income per capita, or number of households times average household income per capita).

Brunei, Nauru, Kuwait, and Lichtenstein are examples of countries with high income per capita, but not assumed to be efficient, given low aggregate level of income (or gross domestic product); these countries have, however, high incomes per capita but may not benefit from the efficiencies derived from economies of scale associated with large economies.

Only countries with high income per capita and large aggregate income are assumed efficient. This greatly restricts the pool of countries to those in the OECD (Organization for Economic Cooperation and Development), like the United States, or the United Kingdom (which were earlier than other large OECD economies to liberalize their markets).

The selection of countries is further reduced by the fact that not all countries in the OECD report have industry revenues at the category level. Countries that typically have ample data at the aggregate level that meet the efficiency criteria include the United States, the United Kingdom, and in some cases France and Germany.

Latent demand is therefore estimated using data collected for relatively efficient markets from independent data sources (e.g. Euromonitor, Mintel, Thomson Financial Services, the U.S. Industrial Outlook, the World Resources Institute, the Organization for Economic Cooperation and Development, various agencies from the United Nations, industry trade associations, the International Monetary Fund, and the World Bank).

Depending on original data sources used, the definition of fractional horsepower motors and generators excluding hermetics is established. In the case of this report, the data were reported at the aggregate level, with no further breakdown or definition. In other words, any potential products and/or services that might be incorporated within fractional horsepower motors and generators excluding hermetics fall under this category.

Public sources rarely report data at the disaggregated level in order to protect private information from individual firms that might dominate a specific product-market. These sources will therefore aggregate across components of a category and report only the aggregate to the public. While private data are certainly available, this report only relies on public data at the aggregate level without reliance on the summation of various category components.

In other words, this report does not aggregate a number of components to arrive at the "whole". Rather, it starts with the "whole", and estimates the whole for all countries and the world at large (without needing to know the specific parts that went into the whole in the first place).

Given this caveat, this study covers fractional horsepower motors and generators excluding hermetics as defined by the North American Industrial Classification system or NAICS (pronounced "nakes").

The NAICS code for fractional horsepower motors and generators excluding hermetics is 3353121. It is for this definition that aggregate latent demand estimates are derived.

**Fractional horsepower motors and generators excluding hermetics is specifically defined as follows:**

3353121 Fractional horsepower motors and generators (excluding hermetics)

33531210 Fractional horsepower motors (rated at less than 746 watts) (excluding hermetics)

3353121000 Fractional horsepower motors (rated at less than 746 watts) (excluding hermetics)

3353121001 AC and DC fractional horsepower motors used in automobile accessories (such as heaters, convertible tops, and automatic windows), excluding starter motors and generators (2 digit frame size)

3353121004 AC fractional horsepower motors used in aircraft and spacecraft, excluding generators (2 digit frame size)

3353121007 DC fractional horsepower motors used in aircraft and spacecraft, excluding generators (2 digit frame size)

3353121011 AC and DC fractional horsepower motors used in toys (all sizes) and clock type synch and subsynch timing (2 digit frame size)

3353121013 AC (noncommutated), skeleton type shaded pole single phase fractional horsepower motors, less than 2.75 inch diameter at widest pt (2 digit frame size)

3353121016 AC (noncommutated), skeleton type shaded pole single phase fractional horsepower motors, 2.75 inch diameter and over (2 digit frame size)

3353121019 AC (noncommutated), conventional type shaded pole fractional horsepower motors, less than 2.5 inch diameter (2 digit frame size)

3353121022 AC (noncommutated), 2 pole, conventional type shaded fractional horsepower motors, 2.5 to less than 3.75 inch diameter (2 digit frame size)

3353121025 AC (noncommutated), 4 pole, conventional type shaded fractional horsepower motors, 2.5 to less than 3.75 inch diameter (2 digit frame size)

3353121028 AC (noncommutated), 6 pole and over conventional type shaded fractional horsepower motors, 2.5 to less than 3.75 inch diameter (2 digit frame size)

3353121031 AC (noncommutated), conventional type shaded pole fractional horsepower motors, 3.75 to less than 4.375 inch diameter (2 digit frame size)

3353121034 AC (noncommutated), 2 through 4 pole conventional type shaded fractional horsepower motors, 4.375 to less than 5.375 inch diameter (2 digit frame size)

3353121037 AC (noncommutated), 6 pole and over, conventional type shaded fractional horsepower motors, 4.375 to less than 5.375 inch diameter (2 digit frame size)

3353121041 AC (noncommutated), conventional type shaded pole fractional horsepower motors, 5.375 inch diameter and over (2 digit frame size)

3353121043 AC (noncommutated), permanent split capacitor fractional horsepower motors, less than 2.5 inch diameter (2 digit frame size)

3353121046 AC (noncommutated), 2 pole permanent split capacitor fractional horsepower motors, 2.5 to less than 3.75 inch diameter (2 digit frame size)

3353121049 AC (noncommutated), 4 pole and over, permanent split capacitor fractional horsepower motors, 2.5 to less than 3.75 inch diameter (2 digit frame size)

3353121052 AC (noncommutated), 2 pole permanent split capacitor fractional horsepower motors, 3.75 to less than 4.375 inch diameter (2 digit frame size)

3353121055 AC (noncommutated), 4 pole permanent split capacitor fractional horsepower motors, 3.75 to less than 4.375 inch diameter (2 digit frame size)

3353121058 AC (noncommutated), 6 pole and over permanent split capacitor fractional horsepower motors, 3.75 to less than 4.375 inch diameter (2 digit frame size)

3353121061 AC (noncommutated), 2 pole permanent split capacitor fractional horsepower motors, 4.375 to less than 5.375 inch diameter (2 digit frame size)

3353121064 AC (noncommutated), 4 pole permanent split capacitor fractional horsepower motors, 4.375 to less than 5.375 inch diameter (2 digit frame size)

3353121067 AC (noncommutated), 6 pole and over, permanent split capacitor fractional horsepower motors, 4.375 to less than 5.375 inch diameter (2 digit frame size)

3353121071 AC (noncommutated), permanent split capacitor fractional horsepower motors, 5.375 to less than 6 inch diameter (2 digit frame size)

3353121073 AC (noncommutated), permanent split capacitor fractional horsepower motors, 6 inch diameter and over (2 digit frame size)

3353121076 AC (noncommutated), capacitor start fractional horsepower motors, less than 3.75 inch diameter (2 digit frame size)

3353121079 AC (noncommutated), capacitor start fractional horsepower motors, 3.75 to less than 4.375 inch diameter (2 digit frame size)

3353121082 AC (noncommutated), capacitor start fractional horsepower motors, 4.375 to less than 5.375 inch diameter (2 digit frame size)

3353121085 AC (noncommutated), capacitor start fractional horsepower motors, 5.375 to less than 6 inch diameter (2 digit frame size)

3353121088 AC (noncommutated), capacitor start fractional horsepower motors, 6 inch diameter and over (2 digit frame size)

3353121091 AC (noncommutated), split phase fractional horsepower motors, less than 3.75 inch diameter (2 digit frame size)

3353121094 AC (noncommutated), split phase fractional horsepower motors, 3.75 to less than 5.375 inch diameter (2 digit frame size)

3353121097 AC (noncommutated), split phase fractional horsepower motors, 5.375 to less than 6 inch diameter (2 digit frame size)

33531210A1 AC (noncommutated), split phase fractional horsepower motors, 6 inch diameter and over (2 digit frame size)

33531210A4 AC (noncommutated), other single phase fractional horsepower motors, less than 6 inch diameter (2 digit frame size)

33531210A7 AC (noncommutated), other single phase fractional horsepower motors, 6 inch diameter and over (2 digit frame size)

33531210B1 AC (noncommutated), synchronous stepper fractional horsepower motors, polyphase (servo and nonservo) (2 digit frame size)

33531210B4 Other AC (noncommutated), servo (induction rotor), polyphase fractional horsepower motors (2 digit frame size)

33531210B7 Other AC (noncommutated), nonservo, polyphase fractional horsepower motors less than 5.375 inch diameter (2 digit frame size)

33531210C1 Other AC (noncommutated), nonservo, polyphase fractional horsepower motors, 5.375 to less than 6 inch diameter (2 digit frame size)

33531210C4 Other AC (noncommutated), nonservo, polyphase fractional horsepower motors, 6 inch diameter and over (2 digit frame size)

33531210C7 AC cased or sleeved, mechanically commutated fractional horsepower motors, less than 2.875 inch diameter (2 digit frame size)

33531210E1 AC cased or sleeved, mechanically commutated fractional horsepower motors, 2.875 to less than 3.188 inch diameter (2 digit frame size)

33531210E4 AC cased or sleeved, mechanically commutated fractional horsepower motors, 3.188 to less than 3.563 inch diameter (2 digit frame size)

33531210E7 AC cased or sleeved, mechanically commutated fractional horsepower motors, 3.563 inch diameter and over (2 digit frame size)

33531210F1 AC uncased, mechanically commutated fractional horsepower motors, less than 2.875 inch diameter (2 digit frame size)

33531210F4 AC uncased, mechanically commutated fractional horsepower motors, 2.875 to less than 3.188 inch diameter (2 digit frame size)

33531210F7 AC uncased, mechanically commutated fractional horsepower motors, 3.188 to less than 3.563 inch diameter (2 digit frame size)

33531210G1 AC uncased, mechanically commutated fractional horsepower motors, 3.563 to less than 4.375 inch diameter (2 digit frame size)

33531210G4 AC uncased, mechanically commutated fractional horsepower motors, 4.375 inch diameter and over (2 digit frame size)

33531210G7 DC or universal servo, permanent magnet fractional horsepower motors (brushless), less than 4.0 inch case diameter (2 digit frame size)

33531210H1 DC or universal servo, permanent magnet fractional horsepower motors (brushless), 4.0 inch diameter and over (2 digit frame size)

33531210H4 DC or universal nonservo, permanent magnet fractional horsepower motors (brushless) less than 4.0 inch case diameter (2 digit frame size)

33531210H7 DC or universal nonservo, permanent magnet fractional horsepower motors (brushless), 4.0 inch diameter and over (2 digit frame size)

33531210J1 DC or universal wound field fractional horsepower motors (2 digit frame size)

33531210J4 DC or universal electronically commutated fractional horsepower stepper motors (2 digit frame size)

33531210J7 Other DC or universal commutated servo fractional horsepower motors (2 digit frame size)

33531210K1 Other DC or universal commutated nonservo fractional horsepower motors (2 digit frame size)

33531210K4 AC (noncommutated) single phase fractional horsepower motors (3 digit frame size)

33531210K7 AC (noncommutated) polyphase induction fractional horsepower motors, excluding synchronous (3 digit frame size)

33531211 Fractional horsepower motors (rated at less than 746 watts) (except hermetics)

3353121100 Fractional horsepower motors (rated at less than 746 watts) (except hermetics)

3353121101 Motors and generators, used in automobile accessories, excluding starter motors and generators (including AC and DC), less than 746 watts, under 1 hp, 2-digit frame sizes

3353121104 Motors, used in aircraft and spacecraft, AC, less than 746 watts, under 1 hp, 2-digit frame sizes

3353121107 Motors, used in aircraft and spacecraft, DC, less than 746 watts, under 1 hp, 2-digit frame sizes

3353121111 Motors and generators, used in toys (all sizes) and clock type sinch and subsynch timing (AC and DC), less than 746 watts, under 1 hp, 2-digit frame sizes

3353121112 Motors and generators, all other uses, AC (non-commutated), single phase, skeleton type shaded pole

3353121119 Motors and generators, all other uses, AC (non-commutated), conventional type shaded pole, less than 2.5 in. diameter

3353121122 Motors and generators, all other uses, AC (non-commutated), conventional type shaded pole, 2.5 to less than 3.75 in. diameter, 2 pole

3353121126 Motors and generators, all other uses, AC (non-commutated), conventional type shaded pole, 2.5 to less than 3.75 in. diameter, 4 pole and over

3353121131 Motors and generators, all other uses, AC (non-commutated), conventional type shaded pole, 3.75 to less than 4.375 in. diameter

3353121133 Motors and generators, all other uses, AC (non-commutated), conventional type shaded pole, 4.375 in. diameter and over

3353121145 Motors and generators, all other uses, AC (non-commutated), permanent split capacitor, less than 3.75 in. diameter, 2 pole

3353121148 Motors and generators, all other uses, AC (non-commutated), permanent split capacitor, less than 3.75 in. diameter, 4 pole and over

3353121151 Motors and generators, all other uses, AC (non-commutated), permanent split capacitor, 3.75 to less than 4.375 in. diameter

3353121162 Motors and generators, all other uses, AC (non-commutated), permanent split capacitor, 4.375 to less than 5.375 in. diameter, 2 and 4 pole

3353121167 Motors and generators, all other uses, AC (non-commutated), permanent split capacitor, 4.375 to less than 5.375 in. diameter, 6 pole and over

3353121172 Motors and generators, all other uses, AC (non-commutated), permanent split capacitor, 5.375 in. diameter and over, less than 746 watts, under 1 hp, 2-digit frame sizes

3353121181 Motors and generators, all other uses, AC (non-commutated), capacitor start, less than 4.375 in. diameter

3353121182 Motors and generators, all other uses, AC (non-commutated), capacitor start, 4.375 to less than 5.375 in. diameter

3353121186 Motors and generators, all other uses, AC (non-commutated), capacitor start, 5.375 in. diameter and over, less than 746 watts, under 1 hp, 2-digit frame sizes

3353121192 Motors and generators, all other uses, AC (non-commutated), split phase, less than 746 watts, under 1 hp, 2-digit frame sizes

3353121195 Motors and generators, all other uses, AC (non-commutated), all other single phase, less than 746 watts, under 1 hp, 2-digit frame sizes

3353121198 Motors and generators, all other uses, AC (non-commutated), all other polyphase, less than 746 watts, under 1 hp, 2-digit frame sizes

33531211B1 Motors and generators, all other uses, AC (non-commutated), polyphase (servo and nonservo), synchronous stepper motors

33531211C7 Motors and generators, all other uses, AC, mechanically commutated (brushes, etc.), cased or sleeved, less than 2.875 in. diameter

33531211E1 Motors and generators, all other uses, AC, mechanically commutated (brushes, etc.), cased or sleeved, 2.875 to less than 3.188 in. diameter

33531211E4 Motors and generators, all other uses, AC, mechanically commutated (brushes, etc.), cased or sleeved, 3.188 to less than 3.563 in. diameter

33531211E7 Motors and generators, all other uses, AC, mechanically commutated (brushes, etc.), cased or sleeved, 3.563 in. diameter and over, less than 746 watts, under 1 hp, 2-digit frame sizes

33531211G5 Motors and generators, all other uses, AC, mechanically commutated (brushes, etc.), uncased, less than 746 watts, under 1 hp, 2-digit frame sizes

33531211G7 Motors and generators, all other uses, DC or universal, permanent magnet (brushless), servo, less than 4 in. diameter

33531211H1 Motors and generators, all other uses, DC or universal, permanent magnet (brushless), servo, 4 in.

diameter and over

33531211H4 Motors and generators, all other uses, DC or universal, permanent magnet (brushless), non-servo, less than 4 in. diameter

33531211H7 Motors and generators, all other uses, DC or universal, permanent magnet (brushless), non-servo, 4 in. diameter and over

33531211J1 Motors and generators, all other uses, DC or universal, permanent magnet (brushless), wound field

33531211J4 Motors and generators, all other uses, DC or universal, electronically commutated

33531211J7 Motors and generators, all other uses, DC or universal, all other, servo

33531211K1 Motors and generators, all other uses, DC or universal, all other, non- servo

33531211K4 Motors, all other uses, AC (non-commutated), single phase, less than 746 watts, under 1 hp, 3-digit frame sizes

33531211K7 Motors, all other uses, AC (non-commutated), polyphase induction (excluding synchronous), all types (including energy efficient (EE)), less than 746 watts, under 1 hp, 3-digit frame sizes

This report was prepared from a variety of sources including excerpts from documents and official reports or databases published by the World Bank, the U.S. Department of Commerce, the U.S. State Department, various national agencies, the International Monetary Fund, the Central Intelligence Agency, various agencies from the United Nations (e.g. ILO, ITU, UNDP, etc.), and non-governmental sources, including ICON Group Ltd., Euromonitor, the World Resources Institute, Mintel, the U.S. Industrial Outlook, and various public sources cited in the trade press.

**1.3.2 STEP 2. FILTERING AND SMOOTHING**

Based on the aggregate view of fractional horsepower motors and generators excluding hermetics as defined above, data were then collected for as many similar countries as possible for that same definition, at the same level of the value chain. This generates a convenience sample of countries from which comparable figures are available.

If the series in question do not reflect the same accounting period, then adjustments are made. In order to eliminate short-term effects of business cycles, the series are smoothed using a 2-year moving average weighting scheme (longer weighting schemes do not substantially change the results).

If data are available for a country, but these reflect short-run aberrations due to exogenous shocks (such as would be the case of beef sales in a country stricken with foot and mouth disease), these observations were dropped or "filtered" from the analysis.

**1.3.3 STEP 3. FILLING IN MISSING VALUES**

In some cases, data are available for countries on a sporadic basis. In other cases, data from a country may be available for only one year.

From a Bayesian perspective, these observations should be given the greatest weight in estimating missing years. Assuming that other factors are held constant, the missing years are extrapolated using changes and growth in aggregate national income.

Based on the overriding philosophy of a long-run consumption function (defined earlier), countries which have missing data for any given year are estimated based on historical dynamics of aggregate income for that country.