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The 2019-2024 World Outlook for Manufacturing Metal Industrial Valves

The 2019-2024 World Outlook for Manufacturing Metal Industrial Valves

  • January 2018
  • 277 pages
  • ID: 1993190

Summary

Table of Contents

This study covers the world outlook for manufacturing metal industrial valves 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 manufacturing metal industrial valves. 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 manufacturing metal industrial valves 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 manufacturing metal industrial valves 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 manufacturing metal industrial valves. 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 manufacturing metal industrial valves. 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 manufacturing metal industrial valves.

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 manufacturing metal industrial valves 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 manufacturing metal industrial valves. 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 manufacturing metal industrial valves. 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 manufacturing metal industrial valves.

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 manufacturing metal industrial valves 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 manufacturing metal industrial valves 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 manufacturing metal industrial valves as defined by the North American Industrial Classification system or NAICS (pronounced "nakes").

The NAICS code for manufacturing metal industrial valves is 332911. It is for this definition that aggregate latent demand estimates are derived.

Manufacturing metal industrial valves is specifically defined as follows:
332911 This U.S. industry comprises establishments primarily engaged in manufacturing industrial valves and valves for water works and municipal water systems.
3329111 Gates, globes, angles, straightway (y-type) checks, stop and check, cross, etc.
33291111 Gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves, except parts
3329111101 Iron body gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves, including ductile or modular, all pressures (excl. IBBM, AWWA, and UL)
3329111103 Cast carbon steel gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves
3329111105 Forged carbon steel gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves
3329111107 Alloy steel and other metal gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves
3329111109 Brass and bronze (125 lb w.s.p. or more) gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves
3329111111 Actuators (power-operated, on-off mounted) for gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves
33291112 Parts for gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves
3329111213 Parts for gates, globes, angles, straightway (Y-type) check, stop and check, cross, 3- and 4-way, and other industrial valves
3329112 Valves for water works and municipal equipment (ibbw, awwa, and ul)
3329113 IBBM, AWWA, and UL Industrial Valves for Water Works and Municipal Equipment
33291131 Industrial valves for water works and municipal equipment (IBBW, AWWA, and UL), except parts
3329113101 Industrial IBBM gate line and tapping valves for water works and municipal equipment
3329113103 Industrial UL check valves (all pressures) for water works and municipal equipment
3329113105 All other industrial UL valves (all pressures), including pest indicators, for water works and municipal equipment
3329113107 Tapping sleeves and crosses for industrial valves for water works and municipal equipment (IBBM, AWWA, and UL)
3329113109 Fire hydrants
3329113111 Industrial AWWA check valves (all pressures) for water works and municipal equipment
3329113113 Industrial AWWA butterfly valves (all pressures) for water works and municipal equipment
33291132 Parts for industrial valves for water works and municipal equipment (IBBM, AWWA, and UL)
3329113215 Parts for industrial valves for water works and municipal equipment (IBBM, AWWA, and UL)
3329114 Butterfly valves (all metals, pressures, and types)
3329115 Industrial Ball Valves
33291151 Industrial ball valves, all metals, pressures, and types, including manual and power-operated, on-off valves, except parts
3329115101 Industrial iron (including ductile) ball valves (all pressures and types), manual and power-operated, on-off valves
3329115103 Industrial brass and bronze ball valves (all pressures and types), including manual and power-operated, on-off valves
3329115105 Industrial carbon steel (cast and fabricated) ball valves (all pressures and types), including manual and power-operated, on-off valves
3329115107 Industrial alloy steel and other metal ball valves (all pressures and types), including manual and power-operated, on-off valves
3329115109 Actuators (power-operated, on-off mounted) for industrial ball valves (all metals, pressures, and types)
33291152 Parts for industrial ball valves (all metals, pressures, and types), including manual and power-operated, on-off valves
3329115211 Parts for industrial ball valves (all metals, pressures, and types), including manual and power-operated, on-off valves
3329116 Industrial valves, n.e.c.
3329117 industrial butterfly valves and on-off valves
33291171 Industrial butterfly valves (all metals, pressures, and types), including manual and power-operated, on-off valves, except parts
3329117101 Industrial iron (including ductile) butterfly valves, except high-pressure types, including elastomer and fluroplastics lined, manual and power-operated, on- off valves
3329117103 Industrial brass and bronze butterfly valves, except high-pressure types, including elastomer and fluroplastics lined, manual and power-operated, on- off valves
3329117105 Industrial carbon steel (cast and fabricated) butterfly valves, except high- pressure types, including elastomer and fluroplastics lined, manual and power-operated, on-off valves
3329117107 Industrial alloy steel and other metal butterfly valves, except high-pressure types, including elastomer and fluroplastics lined, manual and power- operated, on-off valves
3329117109 Industrial high-pressure iron butterfly valves (shut-off to full ANSI class ratings), manual and power-operated, on-off valves
3329117111 Industrial high-pressure carbon steel (cast and fabricated) butterfly valves (shut-off to full ANSI class ratings), manual and power-operated, on-off valves
3329117113 Industrial high-pressure alloy steel and other metal butterfly valves (shut-off to full ANSI class ratings), manual and power-operated, on-off valves
3329117115 Industrial butterfly valve actuators (power-operated, on-off mounted)
33291172 Parts for industrial butterfly valves (all metals, pressures, and types), including manual and power-operated, on-off valves
3329117217 Parts for industrial butterfly valves (all metals, pressures, and types), including manual and power-operated, on-off valves
3329118 Automatic valves (regulating and control type) and parts (except nuclear)
3329119 Industrial plug valves (all metals, pressures, and types), including lubricated, cylindrical eccentric, and sleeve-lined
33291191 Industrial plug valves (all metals, pressures, and types), including lubricated, cylindrical eccentric, and sleeve-lined, except parts
3329119101 Industrial iron (including ductile) plug valves (all pressures and types), including lubricated, cylindrical eccentric, and sleeve-lined
3329119103 Industrial carbon steel plug valves (all pressures and types), including lubricated, cylindrical eccentric, and sleeve-lined
3329119105 Industrial alloy steel and other metal plug valves (all pressures and types), including lubricated, cylindrical eccentric, and sleeve-lined
3329119107 Industrial plug valve actuators (power~operated, on~off mounted)
33291192 Parts for industrial plug valves (all metals, pressures, and types), such as lubricated, cylindrical eccentric, and sleeve~lined
3329119209 Parts for industrial plug valves (all metals, pressures, and types), such as lubricated, cylindrical eccentric, and sleeve~lined
33291193 Parts for industrial plug valves (all metals, pressures, and types), including lubricated, cylindrical eccentric, and sleeve-lined
3329119308 Parts for industrial plug valves (all metals, pressures, and types), including lubricated, cylindrical eccentric, and sleeve-lined
332911B ALL OTHER MISCELLANEOUS INDUSTRIAL VALVES
332911B1 All other miscellaneous industrial valves
332911B101 Industrial valve cocks and stops (all metals, pressures, and types)
332911B103 Industrial diaphragm and pinch valves, including operators (all metals, pressures, and types), except automatic valves
332911B105 Industrial iron and steel pop safety valves and relief valves (more than 15 lb, w.s.p.)
332911B107 Industrial brass and bronze pop safety valves and relief valves (more than 15 lb, w.s.p.)
332911B109 Industrial compressed gas cylinder valves
332911B111 Industrial valve steam traps (more than 15 lb, w.s.p.)
332911B113 Industrial thru conduit pipeline valves
332911B115 Actuators for all other miscellaneous industrial valves, sold separately (power-operated, on-off mounted)
332911B117 Other industrial metal valves, excluding control valves, regulators, and solenoid valves
332911B118 All other miscellaneous industrial valves
332911D NUCLEAR VALVES (N-STAMP ONLY)
332911D1 Nuclear valves (N-stamp only), except parts
332911D101 Nuclear cast~carbon steel and low alloy gate, globe, and check valves (N~ stamp only)
332911D102 Gate, globe, and check valves
332911D103 Nuclear forged~carbon steel and low alloy gate, globe, and check valves (N~ stamp only)
332911D105 Nuclear corrosion~resistant alloy steel gate, globe, and check valves (N~ stamp only)
332911D107 Nuclear ball valves, butterfly valves, and plug values (on~off, N~stamp only)
332911D108 Valves
332911D109 Nuclear valve actuators (mounted power~operated, on~off) (N~stamp only)
332911D111 Nuclear automated control valves (N~stamp only)
332911D2 Parts for nuclear valves (N-stamp only)
332911D213 Parts for nuclear valves (N-stamp only)
332911F AUTOMATIC REGULATING AND CONTROL VALVES AND PARTS (EXCEPT NUCLEAR), POWER-OPERATED, DESIGNED FOR MODULATING (THROTTLING) SERVICE
332911F0 Automatic valves (regulating and control type, except nuclear)
332911F001 Automated control, pneumatic actuated, sliding stem, globe body valves
332911F003 Automated control, pneumatic actuated, sliding stem, all other type valves units . S MA334B
332911F005 Automated control, pneumatic actuated, rotary ball valves
332911F007 Automated control, pneumatic actuated, rotary butterfly valves
332911F009 Automated control, pneumatic actuated, all other rotary valves (including eccentric disk)
332911F011 Automated control, all other pneumatic power~operated control valves
332911F013 Parts for automated control, pneumatic actuated valves (sold separately)
332911F015 Automated control, all other actuation, sliding stem, globe body valves
332911F017 Automated control, all other actuation, sliding stem, all other type valves
332911F019 Automated control, all other actuation, rotary ball valves
332911F021 Automated control, all other actuation, rotary butterfly valves
332911F023 Automated control, all other actuation, all other rotary valves (including eccentric disk)
332911F025 Automated control, all other actuation, all other power~operated (except pneumatic) control valves
332911F027 Parts for all other power~operated (except pneumatic) automated control valves
332911F029 Automated control, valve actuators (sold separately)
332911F031 Remote~sensing direct actuated temperature regulator valves
332911F033 Self~contained direct actuated pressure regulator valves (except instrument type and safety relief valves)
332911F035 Pilot (internal and external) actuated pressure regulator valves
332911F037 Self~contained direct acting precision and instrument type pneumatic (air and gas) pressure regulator valves
332911F039 Flow regulator valves for gas, vapors, or liquids
332911F041 Other regulator valves
332911F043 Parts for regulator valves (sold separately)
332911F1 Automatic regulating and control valves and parts (except nuclear), power- operated, designed for modulating (throttling) service
332911F100 Automatic regulating and control valves and parts (except nuclear), power- operated, designed for modulating (throttling) service
332911F101 Automated control valves, pneumatic actuated, sliding stem, globe body type
332911F103 Automated control valves, pneumatic actuated, sliding stem, all other types
332911F105 Automated control valves, pneumatic actuated, rotary, ball
332911F107 Automated control valves, pneumatic actuated, rotary, butterfly
332911F109 Automated control valves, pneumatic actuated, rotary, all other (including eccentric disk)
332911F111 Automated control valves, all other pneumatic actuated
332911F113 Parts for automated control valves, pneumatic actuated (sold separately)
332911F115 Automated control valves, all other actuation (including electric and electro-hydraulic), sliding stem, globe body
332911F117 Automated control valves, all other actuation (including electric and electro-hydraulic), sliding stem, all other types
332911F122 Automated control valves, all other actuation (including electric and electro-hydraulic), rotary (including ball, butterfly, and eccentric disk)
332911F125 Automated control valves, all other power-operated (except pneumatic)
332911F127 Parts for automated control valves, all other power-operated (except pneumatic)
332911F129 Valve actuators (sold separately)
332911F131 Remote-sensing direct actuated temperature regulator valves
332911F133 Self-contained direct actuated pressure regulator valves (except instrument type and safety relief valves)
332911F135 Pilot (internal and external) actuated pressure regulator valves
332911F137 Self-contained direct acting precision and instrument type pneumatic (air and gas) pressure regulator valves
332911F139 Flow regulator valves for gas, vapors, or liquids
332911F141 Other regulator valves
332911F143 Parts for regulator valves (sold separately)
332911H SOLENOID-OPERATED VALVES AND PARTS, EXCEPT NUCLEAR AND FLUID POWER TRANSFER
332911H0 Solenoid~operated valves (except nuclear and fluid power transfer)
332911H001 Solenoid~operated valves (except power transfer valves), commercial~ industrial types, two~way
332911H003 Solenoid~operated valves (except power transfer valves), commercial~ industrial types, three~way
332911H005 Solenoid~operated valves (except power transfer valves), commercial~ industrial types, other
332911H007 Solenoid~operated valves (except power transfer valves), household appliance type
332911H009 Parts, components, and operators for solenoid~operated valves, except nuclear and power transfer valves (sold separately)
332911H1 Solenoid-operated valves and parts, except nuclear and fluid power transfer
332911H100 Solenoid-operated valves and parts, except nuclear and fluid power transfer
332911H101 Solenoid-operated valves (except nuclear and fluid power transfer), commercial/industrial types, two-way
332911H103 Solenoid-operated valves (except nuclear and fluid power transfer), commercial/industrial types, three-way
332911H105 Solenoid-operated valves (except nuclear and fluid power transfer), commercial/industrial types, other
332911H107 Solenoid-operated valves (except nuclear and fluid power transfer), household appliance type
332911H109 Parts, components, and operators for solenoid-operated valves (except nuclear and fluid power transfer) (sold separately)
332911M Miscellaneous receipts
332911P Primary products
332911S Secondary products
332911SM Secondary products and miscellaneous receipts

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 manufacturing metal industrial valves 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.

1.3.4 STEP 4. VARYING PARAMETER, NON-LINEAR ESTIMATION
Given the data available from the first three steps, the latent demand in additional countries is estimated using a "varying-parameter cross-sectionally pooled time series model".


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