Diversifying Via Sectors

This article examines international diversification using new sets of global, regional, and sector indexes of multinational companies. It remains true that U.S. investors cannot aspire to strategically bal-anced portfolios through positioning in global indexes. That's partly because U.S.-based companies still largely impacted by the same monetary and fiscal policies that affect a portfolio of purely domestic firms fre-quently dominate these indexes.

On the other hand, the puzzle seems to be more than adequately answered when regional and sector indexes of multinational companies are used. There are diversification advantages to be gained from direct investment in these indexes.

A relatively new generation of investable stock indexes representing multinational companies the Dow Jones Global Titans Index, the FTSE Global 100 Index, and the S&P Global 100 Index has been introduced as important tools for global equity diversification. More recently, Dow Jones launched the Dow Jones Asian Titans, an index of blue-chip companies headquar-tered in the Asia/Pacific region, and the Dow Jones Sector Titans Indexes, representing the world's most important companies in each of 18 market sectors.

With barriers to trade coming down and global deregulations of various industries such as  telecommunications, banking, or utilities in full swing, these indexes are thought to allow investors to pick up true multinational companies, no matter where they are headquartered.

The impetus for these new indexes comes from various directions including the multinationals and the index compilers themselves. The multinationals see them as an answer to their request to have their per-formance measured against their global competitors rather than their domestic peers. As to the index providers, they are hoping to capture more business from fund managers no longer investing with traditional national criteria, such as fund managers in Europe that are switching to a regional approach in their investment strategies after the arrival of the euro.

The rush of new indexes also underlines the growing popularity of exchange-traded funds in the United States. since their birth in 1993 when they were largely seen as obscure products reserved for institutional investors. The new multinational indexes are expected to expand the use of exchange traded funds to retail investors, seen as a bigger target, by moving these products from their birthplace
on the American Stock Exchange to larger arenas such as the New York Stock Exchange and Deutsche Börse. The business press is filled with examples of mutual funds already filing registration documents with the Securities and Exchange Commission for a number of exchange-traded funds tied to global indexes.

However, it remains to be seen whether these multinational indexes offer investors true international diversification. After all, this idea has had its skeptics as early as the 1970s. For example, in 1978 Jacquillat and Solnik investigated whether the gains from international diversification could be realized by multinational firms. They tested the assumption that firms doing business in many countries may be viewed as a diversified international portfolio by examining  multinational firms from nine countries and found that their stock prices behave very much like those of purely domestic firms.

Clearly, their results did not support the hypothesis that positioning in multinational firms provides additional diversification benefits to a portfolio of purely domestic firms.¹

To have a full understanding of what is at stake here, we will first briefly review the merits of international diversification and some of the reasons for the ongoing home bias that seems to restrict its implementation in spite of its demonstrated benefits. We will then review the aforementioned three global indexes by comparing them against each other. The Dow Jones Asian Titans Index (DJAT) and the Dow Jones Sector Titans (DJST) are not included at this stage of the analysis because of their narrower focus. We will finally determine, using standard industry tests, whether this new generation of global, regional, and sector indexes of multinational companies provide any further explanation to the international diversification puzzle.

Diversification Is Great, but..
A key contribution of the Markowitz diversification strategy is the formulation of an asset's risk in terms of a portfolio of assets, rather than in isolation. Markowitz diversification seeks to combine assets in a portfolio with returns that are less than perfectly positively correlated, in an effort to lower portfolio risk without sacrificing return. Investment portfolios that satisfy this requirement are called efficient portfolios.²

Since Markowitz's seminal work, many studies have explored the merit of holding international assets as a part of a strategically balanced portfolio.³

In fact, international diversification has become one of the major themes of modern portfolio theory. In addition to holdings of many different assets including traditional securities such as stocks and bonds and less traditional ones such as options and futures, these studies have investigated whether investors should also consider holdings of foreign securities as a means to further enhance their portfolios' efficiency.

They point to the fact that nonsystematic risk at the national level can be reduced with international portfolio diversification. After all, business cycles do not happen uniformly across countries; when one country is expe-riencing rapid growth, another may be in a recession. By investing across countries, investors should logically eliminate from their portfolios part of the cyclical fluctuations that would arise from the domestic business cycle. Thus, limiting one's investments to securities representing firms located in only one part of the world would most likely result in a relatively low rate of return
per unit of risk.

In spite of the theoretical and matter-of-fact groundings of international diversification, many studies have demonstrated that investors nevertheless hold portfolios that consist nearly exclusively of domestic assets. This violation of standard theories of portfolio choice is known as the international diversification puzzle. In the past, it could be explained by the lack of international financial integration and national barriers to capital flows. However, the growth and integration of capital markets over the past two decades has not led to similarly dramatic portfolio reallocations.

For example, in 1991 French and Porteba reported that U.S. investors held about 94% of their financial assets in the form of U.S. securities. For Japan, the United Kingdom, and Germany, the share of domestic assets in each case exceeded 85%. In 1995 Tesar and Werner showed that domestic assets continued to overwhelmingly dominate portfolios despite the rapidly growing volume of international financial trade.⁴

They examined the foreign investment positions of major industrial countries and found that international investment as a fraction of the total domestic market of stocks and bonds equaled about 3% for the U.S., 4% for Canada, 10% for Germany, 11% for Japan, and 32% for the U.K. Of course, calculations of an optimal investment portfolio would have much higher fractions devoted to international assets.

Why do investors seem to have this bias in favor of securities of their home country? Standard models of optimal portfolio choice cannot rationalize this pattern of asset holdings, even in the presence of unhedged foreign exchange risk. Of the several possible reasons, taxes and transactions cost are considered the most significant irritants.⁵

But these reasons can be easily dismissed. Taxes paid to foreign governments can usually be credited against domestic taxes whereas the fact that investors trade their foreign securities more frequently than domestic securities (per Tesar et. al. findings) suggests that transactions costs cannot explain home bias in investment either.

Others find an explanation to the apparent tendency for investors to overweight their own equity market in other explicit limits on cross-border investment. In the U.S. for example, pension funds still interpret the prudent man rule as limiting their degree of international exposure. In Japan, insurance companies cannot hold more than 30% of their assets in foreign securities whereas in France a foreign investor may not hold more than 20% of any firm without prior approval from the Ministère de l'Economie et des Finances.
But again, the current level of international portfolio investment seems to be well below these institutional constraints. Obviously, the home bias has not been answered adequately. It may be that there is no answer that can be related easily to financial models of investment. Or perhaps, evidence given by Gatti and Tverski in 1990 that households behave as though unfamiliar gambles are riskier than familiar gambles  even when they assign identical probability distributions to the two gambles  should be given serious thought in future investment portfolio research.⁶

New Global Multinational Equity Indexes
Three global multinational equity indexes were launched within a relatively short period of time: the Dow Jones Global Titans Index in July 1999, the FTSE Global 100 Index in September 1999, and the S&P Global 100 Index in February 2000. These indexes are being marketed as a solution to the home bias problem in international investment because they measure the performance of true global multinational corporations.

Most importantly, they offer all the diversification benefits available from direct investment in foreign securities such as ADRs, yet they do not expose participants to the difficulties and costs involved in foreign capital markets. Also, for the U.S. fund manager, better information is available on these global multinational companies than on many of the less familiar firms quoted in distant stock markets. Lastly, like other regional and sectoral indexes they can be used for comparative performance and risk measurement. Figure 1, which summarizes both background and construction methodologies of

 

Figure 1	Index Characteristics
	Dow Jones Global Titans	FTSE Global 100	S&P Global 100
Background
Components	50	100	100
Launch date	7/1999	9/1999	2/2000
History from	1992	1999	1989
Total market capitalization	US$ 7.4 trillion1	US$ 7.7 trillion1	US$ 9.4 trillion1
Sponsorship	Dow Jones	FTSE Int'l.	Standard & Poor's
Top five companies	General Electric [8.3%, US]	General Electric [5.9%, US]	General Electric [6.2%, US]
Exxon Mobil [5.2%, US]	Microsoft [4.2%, US]	Pfizer [3.9%, US]
Microsoft [4.7%, US]	Exxon Mobil [3.7%, US]	Exxon Mobil [3.8%, US]
Citgroup [4.4%, US]	Pfizer [3.6%, US]	Microsoft [3.7%, US]
Intel [3.4%, US]	Intel [2.6%, US]	Citgroup [3.4%, US]
Main Sectors	Technology [29.1%]	Technology [25.5%]	Info Tech [18.1%]
	Telecom [18.3%]	Healthcare [18.0%]	Financials [15.8%]
	Financials [15.0%]	Financials [11.7%]	Healthcare [15.7%]
Regional Weightings	USA [67.2%]	USA [58.2%]	USA [59.4%]
	Europe [28.6%]	Europe [35.3%]	Europe [34.2%]
	Asia [4.2%]	Asia [5.7%]	Asia [5.3%]
		Others [0.8%]	Others [1.1%]
Construction Methodology
Selection Criteria
Primary:	Dow Jones Global Index	FTSE World Index	S&P Global 1200 Index
Secondary:	Top 100 by adj market cap	Global exposure	Global exposure (significant foreign
		(30% of sales must be foreign)	sales and foreign employment)
• Tertiary	Fundamental factors	Top 100 by market cap	³ US$ 5 B adj. market cap
Weighting by	Float-adjusted market cap2	Float-adjusted market cap2	Float-adjusted market cap2
Calculation frequency	Daily	Daily	Daily
Review of constituents	Quarterly	Quarterly	Quarterly
	(March, June, Sep, Dec)	(March, June, Sep, Dec)	(March, June, Sep, Dec)
1 Float adjusted
2 Based on shares that are available for trading, but may vary slightly across index providers

these global indexes, highlights a number of similarities but also shows differences that could be material in the management of equity portfolio and other financial products linked to these indexes.

There seems to be significant overlaps among these indexes. The most important overlap is the result of the current bent of equity markets worldwide. Technology firms dominate the composition of these global equity indexes, followed by telecommunication, healthcare, and financial firms.7 One canalso easily notice a bias in favor of U.S. firms in the composition of these indexes as quite a few of them have positioned themselves as technology leaders. Regardless of the methodology used in the compilation of these indexes, they seem to be included more frequently and as a result tend to dominate.

Although the providers of these indexes claim that the methodology underlying their compilation is inherently different, one can see that the selection criteria are closely related. To start with, they all use membership in their respective global indexes as a starting point in their selection procedures. The rest of the criteria such as importance of foreign sales, proportion of foreign employment, or liquidity of the company as measured by adjusted market capitalization are similar although not applied in the same order. The Dow Jones Titans seems to be the only index that puts some emphasis on specific financial factors such as book value and net profits. This does not seem to affect the end result, however, in view of the striking similarities observed on the list of the top multinationals comprising these indexes.

Dow Jones also tracks only the top 50 multinationals as identified by its selection methodology compared to the other two indexes with 100 each. Figure 2 shows the correlations of the three global indexes with the S&P 500 and selected regional indexes such the Dow Jones STOXX in Europe, the Dow Jones Asian Titans, and the Nikkei 225. As a rule of thumb, two variables are strongly positively correlated if their coefficient of correlation is at least 0.50. (The interested reader can find a source for this informal rule in Farrar and Glauber's discussion of a related topic.8) On average, they all tend to move up and down together, showing almost perfect synchronization.

This indicates that, to some extent, increasingly common world factors are equally affecting expected cash flows of the multinational firms comprising the indexes. Logically, increasingly closer economic and government policies between the countries where most of these multinationals are domiciled could contribute to the observed commonality in the indexes' performance behavior.

But most likely, these strong co-move-ments are justified by the aforementioned fact that, without exception, U.S.-based multinationals comprise an important fraction of these indexes. For example, as of March 1, 2001, the FTSE Global 100 included no less than 46 U.S. multinationals that account for 58.2% of the index gross market capitalization.

In the case of the S&P Global 100, 39 U.S. multinationals account for approximately 59.4% of the index gross market capitalization as of February 28, 2001. As to the Dow Jones Global Titans, out of the 50 multinational firms that comprise the index, 27 are headquartered in the U.S. and make up 67% of the index market capitalization as of February 25, 2001. This means that although a sizable portion of their revenues is generated outside the U.S., their performance is still largely determined by the same monetary and budgetary policies that guide U.S. economic growth. This could explain why, as shown in Figure 2, the performance of these multinational indexes is highly correlated with that of the S&P 500, widely recognized as a good gauge of the U.S. market portfolio.

The fact that these indexes are moving in step with each other could also indicate that, to some extent, increasingly common world factors are equally affecting expected cash flows of the multinational firms com-prising the indexes. Logically, increasingly closer economic and government policies between the countries where most of these multinationals are domiciled could contribute to the observed commonality in the indexes' performance behavior. Although the U.S. clearly dominates these indexes, they are also loaded with multinational firms headquartered in countries such as the U.K. and other European countries with economic policies known to be similar to those applied in the U.S.

However, before the U.S.-based globally minded investor becomes alarmed, one thing to keep in mind is that the correlation matrix is based on only 12 months of daily data since the historical data on the FTSE Global 100 could only be secured from September 30, 1999, to September 29, 2000. To be sure, correlation coefficients are not constant and although the data used in this analysis are high frequency daily data thereby more capable of capturing in step movements of the indexes than, say, monthly data evidence of a systematic trend toward a synchronization of world markets needs to be grounded on a much larger his-torical database.

What Now?
Figure 2 shows that there is still some room for international diversification through the regional indexes. Without exception, the correlation coefficients of the S&P 500 and of the multinational indexes with the DJAT are at best modest. This result seems to be quite reasonable considering that Japan, a country that dominates the DJAT, and the U.S. have experienced different business cycles in the 1990s. The 1990s saw the U.S. in a long and strong business cycle expansion, but the decade brought severe recession in Japan.

Japan's dominance of the DJAT is explained by the main selection criteria underlying the index, which are significantly different from those underlying the other multinational indexes. For example, rather than emphasize the importance of foreign sales, which usually favors U.S. corporations, the DJAT first includes only those companies from the Asia/Pacific region. Of the 50 companies included in the index, 25 are automatically selected from Japan with the rest going to the region's other major countries, such as Australia, Hong Kong, South Korea, and Taiwan. Due to this substantial allocation and the relatively larger size of its companies, Japan alone accounts for a whopping 75.8% of the index's market capitalization as of October 31, 2000.

Although a similarly strong conclusion between the S&P 500 and the Dow Jones STOXX Europe does not hold, a correlation of 0.34 indicates that there is nonetheless an argument to be made in favor of diversifying in Europe for an investor who holds the S&P 500. Most importantly, however, these results indicate that for now the global multinational indexes are best marketed in the Asia/Pacific region, where the benefits from diversification seem much greater thanks to the paltry performance of the economy of the country that tends to dominate the DJAT and Nikkei 225. The results also show that although policymakers from the U.S. and the other major economies are increasingly coordinating their macroeconomic economic decisions, it is still too soon to say whether the gradually visible integration of their markets is the consequence of these concerted policies or due to the current dominance of these global indexes by U.S. multinational firms resulting in a high average correlation of 0.87 with the S&P 500.

How About Sector-based Indexes?
Recently, the most prominent index providers are each offering sector indexes that are subsets of their respective broad-based global indexes. These sector indexes include companies that are market leaders in their sectors regardless of their location. Simply because this approach is sector-based, it could prevent companies satisfying the current bent of the equity markets (a serious flaw in the global indexes' current methodologies) from dominating multinational indexes. Case in point, investors' appetite for telecommunication and technology firms have fueled their market capitalization, especially in the late 1990s, which in turn enhanced their overall rank and led to their recent dominance of the global multi-national indexes. To make matters worse, the technological leadership of the U.S. in these two areas has clearly compounded the problem as indicated by the correlation of these indexes with the S&P 500.

Of course, one might rightly argue that if telecommunications stocks (or whatever sector is most popular) soared the world over, they would contribute significantly to the per-60 formance of a telecom-overweight global multinational index. But, if they plummeted  as they have done recently  portfolios relative to that benchmark would suffer significant losses. What that means is that the outperformance of such an index is not curbed under its current methodology, but more importantly, the underperformance one might expect from the same bet is not reduced.

The importance of sector investing in global asset allocation can be explored using the same standard industry tests on a set of 18 sector-based multinational indexes available from Dow Jones. To evaluate their role in global asset allocation, we will assess whether they provide additional diversification benefits to a U.S. investor holding the S&P 500. Although only recently released, historical daily data on the Dow Jones Sector Titans (DJST) Indexes are available starting from December 31, 1991, when each was assigned a base value of 100. Because the DJST Indexes are composed of stable companies, it has facilitated backtesting and the development of index histories. For the sake of a fair comparison with the previously assessed global indexes, the historical correlations shown in Figure 3 are also based on the same September 30, 1999, to September 29, 2000, period. Assuming that the S&P 500 represents the U.S. market portfolio, its average correlation of 0.02 with the sector indexes seems to clearly indicate that this approach could be effective in offering investors true global diversification.

Further Issues
However, before we state that sector indexes of multinational corporations repre sent an effective answer to the international diversification puzzle, we need to withhold our judgment until several other important questions are answered. Is their correlation coefficient with the S&P 500 likely to persist if a more substantial historical database is used? Is additional diversification gained by adding all the sector indexes or only a selected few to the U.S. market portfolio? How should these sector indexes fit into asset allocation?

To answer the first question we used the entire index history provided by Dow Jones (i.e., January 1, 1992, to December 31, 2000) and correlated it with that of the S&P 500. The result is an average correlation coefficient with the S&P 500 (-0.01) that is barely different from the one we obtained from a much shorter history. The consistency of this result supports the sector indexes as practical international diversification tools from the point of view of a U.S. investor seeking global exposure.

Although the second question is less straightforward, the answer can be found in the correlation matrix shown in Figure 3. Although individually these indexes show insignificant links to the S&P 500, a pairwise comparison indicates that some sectors show stronger correlations with each other than others. This means that the advantages from diversifying in sector indexes could easily come undone if they are indiscrimi-nately selected. Undoubtedly, a core portfolio of S&P 500 stocks is more likely to be considered diversified if it adds stocks from two sector indexes weakly correlated with each other such as ENG and TEL (-0.02) rather than adding stocks from two sector

 

Figure 2		Correlations Of Selected Global And
	Regional Multinational Indexes With The S&P 500 Index
	Based on September 30, 1999 to September 29, 2000 daily returns (US$)
	S&P	FTSE	DJ	DJ			DJ
	100 Global	Global 100	Global Titans	Asian Titans	S&P 500	NIKKEI 225	STOXX Europe
S&P 100 GLOBAL	1.00
FTSE GLOBAL 100	0.92	1.00
DJ GLOBAL TITANS	0.91	0.83	1.00
DJ ASIAN TITANS	0.12	0.09	0.19	1.00
S&P 500	0.87	0.86	0.88	0.02	1.00
NIKKEI 225	0.17	0.11	0.10	0.27	-0.01	1.00
DJ STOXX Europe	0.63	0.53	0.49	0.13	0.34	0.27	1.00

 

					Correlations Of Multinational Indexes
Figure 3			Based on September 30, 1999 to September 29, 2000 daily returns (US$)
S&P 500		ATO	BAK	BAS	CGS	CHE	CNS	ENG	FOB	FVS	HCA	IGS	INN	MDI	NCG	RET	TEL	THE	UTS
S&P 500	1
ATO	0.07	1
BAK	0.07	0.5	1
BAS	0.03	0.44	0.44	1
CGS	0.07	0.32	0.39	0.3	1
CHE	0.05	0.59	0.47	0.61	0.23	1
CNS	0.04	0.46	0.43	0.45	0.37	0.54	1
ENG	-0.03	0.15	0.21	0.39	0.05	0.22	0.18	1
FOB	0.04	0.24	0.38	0.31	-0.06	0.42	0.12	0.24	1
FVS	-0.03	0.35	0.71	0.27	0.50	0.37	0.32	0.12	0.2	1
HCA	-0.06	0.22	0.34	0.28	0.11	0.37	0.11	0.23	0.55	0.26	1
IGS	-0.02	0.37	0.46	0.25	0.60	0.33	0.39	0.12	0.01	0.61	0.14	1
INN	0.04	0.44	0.66	0.38	0.29	0.54	0.47	0.27	0.49	0.6	0.4	0.44	1
MDI	-0.04	0.26	0.36	0.15	0.66	0.21	0.45	0.1	-0.15	0.5	0.02	0.64	0.35	1
NCG	-0.03	0.31	0.41	0.23	0.38	0.37	0.18	0.02	0.43	0.44	0.42	0.38	0.44	0.25	1
RET	0.08	0.34	0.42	0.30	0.49	0.37	0.35	0.16	0.23	0.52	0.33	0.45	0.44	0.41	0.46	1
TEL	-0.06	0.28	0.35	0.13	0.58	0.18	0.4	-0.02	-0.10	0.5	0.02	0.62	0.31	0.71	0.29	0.4	1
THE	0.06	0.28	0.28	0.10	0.53	0.11	0.24	0.02	-0.18	0.43	-0.02	0.72	0.19	0.57	0.3	0.33	0.53	1
UTS	0.05	0.33	0.40	0.31	0.21	0.36	0.41	0.29	0.32	0.32	0.2	0.32	0.49	0.34	0.26	0.21	0.26	0.16	1
ATO - Automobiles; BAK - Banks; BAS - Basic Resources; CHE - Chemicals; CNS - Construction; CGS - Cyclical Goods & Services; ENG - Energy; FVS - Financial Services; FOB - Food & Beverage;HCA -
Healthcare; IGS - Industrial Goods & Services; INN - Insurance; MDI - Media; NCG - Non-Cyclical Goods & Services; RET - Retail; TEL - Telecommunications; THE - Technology; UTS - Utilities.

indexes moving in step with each other such as BAK and FVS (0.71). The strong comovement of BAK and FVS indicate that the underperformance of one is more likely to be mirrored by the underperformance of the other, resulting in a less than expected over-all portfolio performance. Because Figure 3 indicates that quite a few sector indexes exhibit borderline significance when correlated individually with the S&P 500 and with each other, we are confident in saying that the diversification properties of more narrowly focused indexes based on sectors are much more evident than those of globally focused indexes.

Finally, the case for treating the sector indexes as a new asset class invariably begins with their low correlation with each other and with other asset classes such as the S&P 500. But as is the case with stocks and bonds, the classic example of asset class division, low correlation is neither necessary nor sufficient for establishing separate asset class status. More persuasive than correlations is the need to demonstrate that these indexes have unique risk characteristics such as unpredictable liquidity, dis-tinct legal structures (such as different claims to firms' net income streams), and perhaps links to political factors that are unrelated to global markets. These considerably complex questions would need to be addressed in a different study. For now, it is sufficient to focus on the important fact that, much more so than global indexes, sector indexes could be treated as legitimate segments of an investor's core portfolio because they present, on average, compelling arguments for their use as effective foreign diversification tools.

Conclusion
From the perspective of a U.S.-based investor, the gains from diversification depend on the correlation of returns between the S&P 500, a widely recognized gauge of the U.S. equity market, and cross-border holdings. Using a set of three methodologically different multinational indexes, we have established a solid case in favor of combining regional and/or selected sector-based equity indexes with the S&P 500 as a means to build strategically diversified portfolio.

By the same token, we have also addressed the concerns of previous researchers who concluded that international diversification couldn't be effectively achieved through positioning in multinational corporations. Obviously, if the sample used is dominated by multinational corporations domiciled in the U.S. or in countries whose monetary policies are synchronized with those of the U.S., it is only normal to dismiss them as effective contributors to a strategically diversified portfolio. Therefore these studies need to be revisited in light of the constituents of the samples on which their results are based.

On a different note, a switch to a sectoral approach to global asset allocation also solves the problem of cross-borders deals that force country-indexed fund managers to sell stocks that are deleted from an index. DaimlerChrysler is a good example. Actually, the recent successive waves of mergers and acquisitions have made nationality one of the top issues in the agenda of both portfolio managers and index providers.

Footnotes

1. B. Jacquillat and B. Solnik, 'Multinationals are Poor Tools for International Diversification,' Journal of Portfolio Management, Winter 1978.
2. Harry M. Markowitz, 'Portfolio Selection,' Journal of Finance (March 1952), 77-91.
3. See, in particular, K. French and J. Poterba, 'International Diversification and International Equity Markets,' American Economic Review (May 1991), 222-226.
4. L. Tesar and I.M. Werner, 'Home Bias and High Turnover,' Journal of International Money and Finance (August 1995).
5. T. Horst, 'American Taxation of Multinational Firms,' American Economic Review (1977), pp. 376-89.
6. I. Gatti and A. Tverski, 'A Differential Weighting of Comment and Distinctive Components,' Journal of Experimental Psychology: General (1990), pp. 30-41
7. With all but a very few technology firms rapidly falling out of favor in today's highly volatile equity markets, this dominance is highly questionable in the future.
8. D.E. Farrar and R.R. Glauber, 'Multicollinearity in Regression Analysis: The Problem Revisited,' Review of Economics and Statistics, vol. 49, 1967, pp.92-107.