# Measuring the effects of economic diversity on growth and stability.

I. INTRODUCTIONThe relationship between regional economic diversity and growth and stability has been a topic of debate for nearly 60 years. While the logic of the policy - diversification of the economic base as a means to achieve the policy goals of economic stability and growth - is clear and straightforward, the empirical literature has been inconsistent. These inconsistencies have prompted some to step back and challenge the logic accepted and promoted by policymakers (Kort 1991; Siegel, Alwang, and Johnson 1994, 1995b; Malizia and Ke 1993). The current regional economic diversity debate has been two pronged, with some challenging the integrity of the empirical work while others have focused on the theoretical consistency of the policy.

As argued by Kort (1981), Malizia and Ke (1993), and Siegel, Alwang, and Johnson (1995b), the principal causes of this empirical inconsistency are the use of (1) small sample sizes, (2) highly aggregated data sets, (3) theoretically or empirically poor measures of diversity and regional economic stability, and (4) overly simplistic statistical methods. Others have questioned if there is an internal theoretical inconsistency of jointly pursuing economic growth and stability through the one policy approach of diversification (Kort 1991; Siegel, Alwang, and Johnson 1994, 1995b). Specifically, the notion of comparative advantage implies that growth requires specialization, which is polar opposite to diversification.

We attempt to address both of these issues in this article by examining the theoretical question within the framework of short- and long-term policy goals and by offering an alternative way of thinking about and measuring economic diversity. The hypothesis extended here is that part of the empirical inconsistencies in previous studies is related directly to the way in which we conceptually and empirically approach economic diversity. Specifically, most diversity measures focus on the distribution of economic activity across industries and do not account for inter-industry linkages and the relative size (i.e., number of industries) of the regional economy.

As a partial step in this direction, we propose a scalar diversity measure by combining the size, density, and condition number of the static (I - A) matrix of a regional input-output model. We suggest that by accounting for inter-industry linkages explicitly, our measure more fully captures the structure of the regional economy. In addition, the proposed index has the flexibility to allow researchers and policy analysts to address a range of policy issues, including policies that might affect the structure of a regional economy. The applied research reported here is not intended to develop a unified theory of regional growth, stability, and diversity, but to address a policy question within an empirical framework. Specifically, we ask the question, does a given level of diversity in time t lead to higher levels of growth and stability in time t + i.

The article is composed of five sections. First, we review the logic behind diversification as an economic policy. Second, we briefly review existing measures of diversity then introduce our approach to conceptualize and measure economic diversity in detail. Then, we put forth a relatively simple empirical model of economic growth and stability. Next, we estimate our diversity index for the U.S. and the 50 states and discuss it within the context of our model of economic growth and stability. Finally, the article closes with a brief summary section and discussion of policy implications.

II. DIVERSIFICATION AND ECONOMIC POLICY

As noted by Siegel, Alwang, and Johnson (1994, 1995a, 1995b), and Kort (1979, 1981, 1991), regional scientists have historically promoted the policy of economic diversification as a means to achieve certain economic goals. As a region's economy becomes more diversified, it becomes less sensitive to fluctuations caused by factors outside the region (Nourse 1968; Richardson 1969). Policymakers hold the "conventional wisdom" that economic diversification not only promotes stability, but also promotes the broader goals of economic growth and low unemployment levels (Malizia and Ke 1993; Attaran 1987).

Elementary economic theory suggests that growth should be derived from economic specialization based on comparative advantage. Theory also suggests that stability is achieved through diversity by spreading risk (or opportunities) over many activities. Theory, therefore, seems to suggest that regional policymakers are forced to choose between two polar goals of growth and stability, and the corresponding set of policy options. This trade-off is one that most, if not all, policymakers are unwilling to accept or act upon when designing policy. When policymakers attempt to pursue both goals simultaneously, contradictions seem to appear.

We suggest that the simultaneous pursuit of growth and stability is not contradictory when viewed in terms of the short and long run. Short-run policy can be viewed as more growth oriented where policymakers craft strategies that target growth industries. These strategies can capitalize on the comparative advantage of the region by specializing in a few select industries. Limiting policy to the short run may create a trap where policymakers fall into a "job is done" syndrome. This can be dangerous because as the industry matures a dampening pressure on growth levels will develop. In addition, if the targeted growth industries fail, the region may be worse off than before the policies were implemented.

We suggest that policymakers pursue these short-run strategies within the long-run policy of diversification. Diversification policies should be viewed as the long-run envelope of the region's short-run efforts. Long-run policy can be viewed as promoting stability with growth. As stability and diversity increase, so should the potential for growth. Diversity is not the absence of specialization, but reflects the presence of multiple specializations (Malizia and Ke 1993). The apparent contradictory goals and policies can be pursued simultaneously and consistently.

Consider a region whose true comparative advantage is agriculture. Short-term growth strategies might be to establish a production agricultural base in select commodities. Over time additional short-term strategies may be to expand the commodity base to include a number of alternative commodities, introduce value-added processing, and tighten the linkages among endogenous industries by reducing imported inputs. Such a strategy will enhance the region's ability to capture economic benefits from the gains of trade with final products as opposed to raw or intermediate products. The short-run strategies are focused on growth, but the long-run envelope moves the economy towards diversity. By expanding our thinking about what diversity entails, the policies of vertical integration and linkage tightening are introduced.

III. AN ALTERNATE DIVERSITY MEASURE

Historically, diversity has been defined as "the presence in an area of a great number of different types of industries" (Rodgers 1957, 16); as "the extent to which the economic activity of a region is distributed among a number of categories" (Parr 1965, 22); or "in terms of balanced employment across industry classes" (Attaran 1987, 45). An implicit premise being that an economy with more industries is better. This notion of diversity and the resulting family of entropy measures (Stigler 1968; Cowell 1987) has been adopted in several regional economic diversity studies (Kort 1981; Attaran 1987; Smith and Gibson 1987; Deller and Chicoine 1989; Malizia and Ke 1993).(1)

Entropy measures of economic diversity, such as the Herfidahl index, have been questioned empirically and theoretically. Empirically, Wasylenko and Erickson (1978) found many regions defined as highly specialized by the entropy approach were economically relatively stable. Kort showed that policy results were sensitive to the specific entropy measure used. Attaran showed that more specialized regions experienced greater economic growth and the relationship between levels of diversity and unemployment was minimal. Theoretically, Conroy (1972, 1974, 1975), and later Brown and Pheasant (1985), stated that the ideal of an equal distribution of activities across sectors is not based on any a priori rationale and is arbitrary. Bahl, Firestine, and Phares (1971) and Conroy (ibid) suggested that the key is not an equal distribution of activities, but rather the specialization in "inherently" stable industries. In addition, these measures do not account for any inter-industry linkages, and the number of industry sectors is usually fixed and not allowed to vary.

An approach advanced by Conroy (1974), Brown and Pheasant (1985), and Hunt and Sheesley (1994), which adapts portfolio theory from the finance literature (Markowitz 1959; Sharpe 1970), has received less attention within the empirical literature. Local policymakers select a set of industries in which to invest - analogous to an investor selecting a set of financial instruments - in creating a "community industrial portfolio" (Conroy 1974, 32). This framework focuses on the individual industry's net returns, the stability of these net returns, and the covariance of these net returns among industries within the portfolio.(2) This combination provides a measure of the relationships "among elements of the portfolio which is possibly a key element in the analysis of the diversification of that portfolio" (Conroy 1974, 32). But as noted by Siegel, Alwang, and Johnson (1995b) and Sherwood-Call (1990), the use of the covariance approach is not independent of stability itself, indeed, the region's total variance in economic activity is a frequently used measure of economic instability. Therefore, while the approach promoted by Conroy may help us conceptualize the problem, its use as an empirical tool is inappropriate.

A third approach that has recently been suggested in the literature builds on the importance of interindustry linkages and economic structure in growth and stability (Siegel, Alwang, and Johnson 1994, 1995a, 1995b: Wundt and Martin 1993). By using an input-output model, a region's structure can be rigorously modeled in terms of production, consumption, and trade relationships. Specifically, economic performance can be modeled as a direct function of regional economic structure. The methods adopted in this latter approach either incorporate the structure of an input-output model into a more traditional portfolio model or as a stand-alone measure of stability over time. Unfortunately, these studies have tended to rely on some aspect of the variance-covariance matrix capturing economic performance. As such, the "measure" of diversity is not independent of stability itself, thus not lending themselves to subsequent statistical tests of the hypothesis linking diversity with growth and stability.

The method that we propose builds on the importance of these inter-industry linkages and economic structure by developing a scalar measure of economic structure based on a static regional input-output model. We empirically implement our approach by using the regional modeling system MicroIMPLAN (Alward et al. 1989) to construct 51 separate input-output models for each of the 50 states, plus the entire U.S. Because of the flexibility of the regional databases contained within the MicroIMPLAN system, the analysis presented here is for the 50 states and the U.S., and could be repeated for every county, or multi-county combination, in the U.S.(3,4) We defined the study region to be the state given two reasons. First, since most comprehensive policies are enacted at a state level, from a policy perspective, a state-level analysis is meaningful. Second, data for the modeling of growth and stability are more readily available at the state level.

We posit that a measure of regional economic diversity can be constructed from three scalars that describe the regional input coefficients matrix of an input-output model and contain information useful in measuring diversity relative to a reference base economy. First is a measure of the size of the economy (i.e., the number of endogenous industries). An economy with only a handful of industries is less likely to absorb a shock than an economy composed of many different types of industries. The size of an economy, however, does not provide a measure of the degree of industry imports. In short, the more an economy imports, the smaller the responding effects used to generate additional economic activity. This would be captured by the second scalar; a measure of the density of the (I - A) matrix. Finally, the measure of degree of imports does not provide a complete measure of the linkages among industries; the flow of locally produced inputs between endogenous industries. Such linkages would be more fully captured by the third scalar. Note that all regional dimensions are relative to a base economy which is determined a priori as diversified. The purpose for defining a reference base economy is to facility comparisons and to place bounds on the index. Each of the three scalars is described in detail in turn.

The first scalar defines the relative size (SI) of a region's economy:

[SI.sub.i] = [N.sub.i]/[N.sub.be] [1]

where [N.sub.i] is the number of endogenous Standard Industrial Classification (SIC) code industries identified by MicroIMPLAN within region i and [N.sub.be] is the number of endogenous SIC industries in the base economy. If [N.sub.be] [greater than or equal to] [N.sub.i] [greater than] 0 [for every] i, then 0 [less than] [SI.sub.i] [less than or equal to] [SI.sub.be] = 1. The measure implies the greater the number of industries contained within the regional economy, as compared to the base economy, the better able the economy should be to absorb shocks. This measure increases as the number of endogenous industries increases. Note that size simply counts the number of industries (not firms) independent of output levels. This implies that firms within a given SIC code level are homogenous, which may not be the case empirically. The intent of this component is to identify the number of heterogeneous industries corresponding to the level of detail contained within the regional coefficients matrix. As this matrix becomes more detailed this scalar becomes more refined.

The second scalar measures relative matrix density. By definition, 0 [less than or equal to] [absolute value of [(I - A).sub.jk]] [less than or equal to] 1 [for every] j, k.(5) A nonzero element in the (I - A) matrix denotes a purchase of a locally produced input by a local industry and therefore an inter-industry linkage. Economies described by a relatively high number of zero elements in the (I - A) matrix are more open in our view of diversity. The density ([DEN.sub.i]) of the (I - A) matrix is defined as:

[Mathematical Expression Omitted] [2]

where [absolute value of [(I - [A.sub.i]).sub.jk]] and [absolute value of [(I - [A.sub.be]).sub.jk]] are the sum of the absolute value of the elements of the (I - A) matrix for region i and the base economy, respectively. If 0 [less than or equal to] [absolute value of [(I - [A.sub.i]).sub.jk]] [less than or equal to] [absolute value of [(I - [A.sub.be]).sub.jk]] [less than or equal to] 1 [for every] j, k and [Sigma][Sigma] [absolute value of [(I - [A.sub.be]).sub.jk]] [greater than or equal to] [Sigma][Sigma] [absolute value of [(I - [A.sub.i]).sub.jk]] [greater than or equal to] 0, then 0 [less than] [DEN.sub.i] [less than or equal to] [DEN.sub.be] = 1 [for every] i. Therefore, as [DEN.sub.i] increases, both the degree of the purchases of locally produced inputs and the possible inter-industry linkages would increase. We would expect the density measure would increase as the number of endogenous industries increases.

The last scalar measures the degree of inter-industry linkages:

[C.sub.i] = [CN.sub.i]/[CN.sub.be] [3]

where [CN.sub.i] and [CN.sub.be] define the condition numbers of the (I - A) matrix for region i and the base economy, respectively. The condition number is defined as:

CN = [[(I - A)]] [multiplied by] [[[(I - A).sup.-1]]] = [[Delta].sub.max](I - A)/[[Delta].sub.min] (I - A) [4]

where [[(I - A)]] is the 2-norm of the (I - A) matrix, [[[(I - A).sup.-1]]] is the 2-norm of the [(I - A).sup.-1] (the Leontief inverse matrix), and [[Delta].sub.max] (I - A) is the largest singular value and [[Delta].sub.min] (I - A) is the smallest singular value of the (I - A) matrix, respectively (Golub and Van Loan 1983).(6)

The condition number is a measure of linear independence between the rows and columns. Therefore, an identity matrix of any size has a condition number equal to one identically. Any divergence - nonzero off diagonal elements - from an identity matrix will cause the condition number to increase. In terms of regional economics, nonzero off diagonal elements in terms of the (I - A) matrix imply more purchases of locally produced inputs or a greater degree of inter-industry linkages. Thus, the condition number should increase as the inter-industry linkages of the economy increase.(7) Therefore, if 1 [less than or equal to] [CN.sub.i] [less than or equal to] [CN.sub.be], then 0 [less than or equal to] [C.sub.i] [less than or equal to] [C.sub.be] = 1 [for every] i.(8)

Our Diversity Index (DI) is defined as a combination of these three components. Since, we had no a priori reason to differentiate between a multiplicative (MDI) or an additive (ADI) form, we examined two different indices:

[MDI.sub.i] = [SI.sub.i] [multiplied by] [DEN.sub.i] [multiplied by] [C.sub.i] [5]

[ADI.sub.i] = ([w.sub.i] [multiplied by] [SI.sub.i]) + ([w.sub.2] [multiplied by] [DEN.sub.i])

+ ([w.sub.3] [multiplied by] [C.sub.i]) [summation of] [w.sub.j] where j = 1 to 3 = 1. [6]

In equation[5], if the base economy is the most diversified, then 0 [less than or equal to] [MDI.sub.i] [less than or equal to] [MDI.sub.be] = 1 [for every] i, where [MDI.sub.be] is the multiplicative diversity index for the base economy. In equation [6], if the base economy is the most diversified, then 0 [less than or equal to] [ADI.sub.i] [less than or equal to] [ADI.sub.be] = 1 [for every] i, where [ADI.sub.be] is the additive diversity index for the base economy. Since we had no a priori reason to place different weights on the components in equation [6], we assumed [w.sub.j] = 1/3, [for every] j. Naturally, a more complex algorithm could be developed to allow the weights to vary depending on the values of [SI.sub.i], [DEN.sub.i], and [C.sub.i]. A value of zero can only occur if there is no economic activity within the region, clearly impossible given our construction of the problem.

In our construction of MDI and ADI, three internal consistency checks are appropriate.

Consistency Check #1: The condition number for the U.S. is the largest.

Consistency Check #2: There is a positive relationship between the size of the economy (or the number of endogenous industries) and the condition number.

Consistency Check #3: There is a positive relationship between the density of the (I - A) matrix and the condition number.

First, if more diverse economies are characterized by higher condition numbers, then the U.S. should have the largest condition number. Second, if this is the case, does this mean, that a larger economy will have a larger condition number? As more off diagonal elements of the (I - A) matrix become nonzero or larger in magnitude as endogenous industries purchase more locally produced inputs, the (I - A) matrix will become more dense. Therefore, if the density of a matrix increases then the condition number should also increase. Congruity of these internal consistency checks, and the data's support of these checks, will lend credence o our measure of regional economic diversity.

Like any empirical measure, we acknowledge that our proposed index of diversity does have a few shortcomings. First, the measure is insensitive to industry output levels. Suppose that there are two regions that appear identical in all aspects of the (I - A) matrix, but the first has a high percentage of employment in risky industries. Then the relatively specialized region may be less stable in the economically important sense. That specialization is lost to our measure as it is currently constructed. In other words, potentially useful information contained in the transactions table of the input-output model is lost. By moving to the technical coefficients matrix (A), we may loose some useful information. A second critique is that the input-output model is by definition a static analysis and we are proposing to use it to address a dynamic policy question. One could conclude we are mixing apples and oranges. Recall, however, that the intent of this line of literature is to address the association between a given level of diversity with growth and stability. In other words, the hypothesis is whether a given level of diversity at time t affects growth and stability in time t + i. Measures of diversity that are dynamic (e.g., Conroy 1972, 1974, 1975; Seigel, Alwang, and Johnson 1994, 1995a, 1995b) are not conducive to statistical hypothesis testing because the diversity measure is not independent of stability by definition.

IV. A MODEL OF GROWTH AND STABILITY

To test the overriding hypothesis that higher levels of economic diversity result in higher levels of economic stability and growth, we define two empirical models. To do this we turn to six basic studies. First, we use Duffy's (1994) study to help conceptualize the model. Next, we use Kusmin's (1994) review of the empirical regional growth literature along with Malizia and Ke's (1993) study to help identify exogenous variables. Finally, we turn to the work of Miller (1976), coupled with the work of Barkley, Henry, and Bao (1995) and Doff and Emerson's (1978) study, to help formulate to empirical specification of the model. Data are derived from the Statistical Abstract of the United States, 1980, and the BEA-REIS CD-ROM for 1993. As such, the independent variables reflect the state of the regional economy in 1980 while the dependent variables are changes from 1969 to 1992.(9)

Conceptual Framework

Using the logic of Duffy (1994), we hypothesize that there are five broad classifications of factors influencing regional economic growth and stability: (1) markets, (2) labor, (3) taxes, (4) amenities, and (5) infrastructure. We suggest that regional economic growth and stability is determined through the interplay of these five broad sets of forces along with economic diversity.

Markets. In this broad category we are attempting to capture factors that influence the demand side of regional markets. Generally, these factors are designed to capture factors that describe the region's ability to buy (income measures) coupled with scale of market (population measures) and tastes and preferences (socio measures). The variables we propose that would capture market characteristics include:(10)

1. Income distribution (1980),(11)

2. Percent of the population that is nonwhite (1980),

3. Population (1980),

4. Growth in population (1969-91),

5. Per capita income (1980),

6. Cost of living (1981),(12)

7. Percent of individuals below the poverty level (1979),

8. Percent of children below the poverty level (1979),

9. Percent of persons over 65 years of age (1979), and

10. Percent of persons living in the region their entire life (1976).

Labor. This category is intended to capture the ability of regional markets to supply the goods and services needed to satisfy regional demand. We suggest that measures of human capital stocks and flows are sufficient to capture the influences of this side of the market on regional growth and stability. Human capital here refers to broad levels of education, health, and attitudes. The variables we propose that would capture labor characteristics include:

1. Right to work law (1982),

2. Percent of labor force unionized (1980),

3. Percent of persons with a high school diploma (1980),

4. Percent of persons with a college diploma (1980),

5. Average teacher (K - 12) salary (1980),

6. Number of doctors per 1,000 persons (1980),

7. Number of prisoners per 1,000 persons (1980), and

8. Infant death rate (1980).

Taxes. Again, relying on the work of Duffy (1994) and Kusmin (1994), the tax structure characterizing the regional economy is fundamental to the growth and stability potential of the region. High personal and business taxes are generally deemed to be detrimental to economic growth. For our purposes, we suggest that four tax measures captures the influence of regional tax policy:

1. Corporate tax rate (1981),

2. State sales tax rate (1981),

3. Composite effective tax rate (1981), and

4. Gasoline excise tax (1980).

Amenities. Increasingly, studies of regional migration and growth, particularly in rural areas, suggest that amenities are driving factors in the performance of the regional economy. For this study, four variables are advanced to capture the influence of amenities:

1. Percent of the regional population classified as rural (1980),

2. Percent of the region's surface area covered by lakes and rivers (1978),

3. Percent of the population with a fishing license (1978), and

4. Percent of the population with a hunting license (1978).

We propose that the latter three measures capture the potential to consume amenity-driven recreational activities.

Infrastructure. While the status of our nation's stock of infrastructure is well documented, the role of infrastructure in regional economic development and growth is less well understood (Deller 1991). Yet, the generally accepted position taken by most regional development economists is that public infrastructure is vital to the general performance and growth of regional economies (Immergluck 1993). While the types of public infrastructure vary widely, we suggest that the general level of infrastructure provision can be captured by:

1. Number of public airports per one million persons (1980),

2. Number of private airports per one million persons (1980), and

3. Highway density measured as miles of four-lane highway per square mile (1980).

Empirical Specification

Numerous studies of regional economic growth and stability have attempted to specify their empirical equations by including a "laundry list," much like the variables identified above, as right-hand-side variables in a regression style equation. Examples would include Malizia and Ke (1993) and the family of studies spurred by Carlino and Mills's (1987) study of county-level growth. Others, such as Duffy (1994), use statistical techniques such as step-wise regression to determine the final specification of the empirical model. Problems with these two approaches range from limited degrees of freedom, depending on the unit of analysis, to multicollinearity, to substituting data extraction for solid theory.

A third approach proposed by Miller (1976) suggests that blocks of variables, such as the Markets or Labor blocks outlined above, can be condensed into single scalar measures that capture the information contained in the original data. For example, Doff and Emerson (1978) reduced more than 100 different variables to 16 components that together serve as fairly reasonable predictors of each of the original variables. They then used these components to predict plant location. More recently, Barkley, Henry, and Bao (1995) compressed several blocks of variables into single regressor components to isolate the influence of local school quality on rural economic development. The primary advantage of this approach is that regional characteristics dictated as important by theory are not removed from the empirical analysis due to multicollinearity problems or limited degrees of freedom.

The limitation to this approach, as observed by Kusmin (1994), is that the individual components are difficult to interpret in terms of cause-and-effect relationships. In this study, much like Barkley, Henry, and Bao (1995), we are interested primarily in examining the influence of a single regional economic characteristic, economic diversity, on regional economic growth and stability while accounting for other characteristics as deemed by the theory. Therefore, to test statistically for the relationship in which we are interested, without accounting for these important factors, would lead to dubious statistical results.

The empirical specification approach adopted in this applied research is to use the tools of principal components to compress several individual variables into the five broad factors outlined above. These factors are, in essence, linear combinations of the original variable where the linear weights are the eigenvectors of the correlation matrix between the set of factor variables. For our analysis the empirical regression model to test the hypothesis surrounding the role of economic diversity in regional economic growth and stability takes the form:

Growth = f(Market, Labor, Taxes, Amenity, Infrastructure, DI) [7a]

Stability = g(Market, Labor, Taxes, Amenity, Infrastructure, DI). [7b]

Note that theory gives no insight into the appropriate functions form for either equations [7a] or [7b]. While much of the relevant literature assumes linear or logarithmic procedure, a superior approach would be to employ a nonlinear procedure capable of allowing the data to suggest the "correct" functional form. For this study a Box-Cox estimator is employed.

Measures of Growth and Stability

When assessing economic performance there are any number of measures that could be employed. For this study we measured economic performance of growth and stability using two proxy characteristics of the regional (state) economy: the unemployment rate and per capita income. These two measures are selected for consistency with previous studies of diversity and due to the popularity of these two measures in policy discussions. As noted earlier in this article, much of the empirical diversity literature has been challenged on measures of not only diversity, but also stability and growth. While our measures of stability and growth may be viewed as simplified, they reflect general patterns in the data.

Our suggested measure of economic growth is straightforward and is defined for the ith region as the average annual growth rate over the period examined:

[Mathematical Expression Omitted] [8]

where T is the number of periods examined (23) and Y is the proxy characterizing the economy (per capita income). Higher values of [AYGR.sub.i] indicate a faster growing region over the 23 periods we examine.

Malizia and Ke (1993) define stability as "the absence of variation in economic activity over time." Following this straightforward logic, our suggested measure of stability is the variance in the average annual unemployment rate for the same period. We suggest that larger swings (i.e., higher variances) in unemployment are associated with higher levels of economic instability. Naturally, the unemployment rate is fraught with empirical problems, but for our purposes it captures overall regional patterns.

V. EMPIRICAL RESULTS

Two sets of empirical results are reviewed, first we describe the results of our computations of our alternative measure of diversity followed by the results of our model of growth and stability.

Diversity Index

The results of calculating MDI and ADI are reported in Table 1, with the U.S. defining the base economy. To test for differences between the multiplicative and additive diversity measures a simple correlation coefficient between MDI and ADI was estimated. With a test statistic of 0.949, with a marginal significance level of 0.0001, we suggest that MDI and ADI were monotonic transformations of each other. For purposes of the empirical analysis we will limit our discussion to MDI.

The values, except the reference base economy of the U.S., ranged from a high of 0.5516 for the State of Alabama to a low of 0.0595 for the State of Alaska with an average value of 0.3217 and a standard deviation of 0.1469. The top three diversified states, by our measure are Alabama, Tennessee, and California, and the three least diversified are Wyoming, Hawaii, and Alaska. States which one would think of as more diversified, such as New York and Illinois, fell more in the middle of the range. New York, for example was ranked 33rd and Illinois was ranked 26th.

TABLE 1 EMPIRICAL ESTIMATES OF INPUT-OUTPUT based DIVERSITY MEASURES State DEN SI C MDI ADI AK 0.35273 0.43870 0.38438 0.05948 0.39193 AL 0.72364 0.85632 0.89014 0.55159 0.82337 AR 0.70455 0.83333 0.58684 0.34500 0.70855 AZ 0.69455 0.83525 0.53126 0.30819 0.68702 CA 0.86545 0.98276 0.59068 0.50240 0.81297 CO 0.76000 0.89655 0.50636 0.34503 0.72097 CT 0.67636 0.83333 0.51059 0.28779 0.67343 DE 0.48727 0.58238 0.52478 0.14892 0.53148 FL 0.77091 0.93678 0.50276 0.36308 0.73682 GA 0.76727 0.91379 0.64580 0.45279 0.77562 HI 0.43273 0.53065 0.50743 0.11652 0.49027 IA 0.73091 0.85249 0.55968 0.34873 0.71436 ID 0.56364 0.67241 0.51605 0.19558 0.58403 IL 0.78909 0.95977 0.43602 0.33022 0.72829 IN 0.72727 0.87739 0.51713 0.32998 0.70726 KS 0.71273 0.82375 0.60730 0.35655 0.71595 KY 0.72000 0.83908 0.60469 0.36532 0.72126 LA 0.69818 0.80268 0.62951 0.35278 0.71012 MA 0.76364 0.89847 0.52092 0.35740 0.72767 MD 0.71636 0.83716 0.63731 0.38220 0.73028 ME 0.57454 0.68582 0.52355 0.20630 0.59464 MI 0.75273 0.92912 0.44466 0.31099 0.70884 MN 0.77454 0.89272 0.59303 0.41005 0.75343 MO 0.78545 0.89847 0.61820 0.43627 0.76737 MS 0.65454 0.80077 0.59239 0.31050 0.68257 MT 0.53818 0.63218 0.58167 0.19790 0.58401 NC 0.74545 0.91954 0.70319 0.48202 0.78940 ND 0.49091 0.57088 0.59194 0.16589 0.55124 NE 0.56727 0.70498 0.49069 0.19623 0.58765 NH 0.61818 0.74330 0.50270 0.23099 0.62139 NJ 0.75273 0.91379 0.50195 0.34526 0.72282 NM 0.61091 0.72031 0.53881 0.23710 0.62334 NV 0.58909 0.70690 0.52318 0.21787 0.60639 NY 0.75636 0.94828 0.39016 0.27984 0.69827 OH 0.79273 0.93103 0.51412 0.37945 0.74596 OK 0.72727 0.84674 0.59194 0.36452 0.72199 OR 0.70909 0.87548 0.50596 0.31410 0.69684 PA 0.78182 0.94061 0.48563 0.35713 0.73602 RI 0.58545 0.69923 0.49888 0.20423 0.59452 SC 0.73091 0.86590 0.55213 0.34944 0.71631 SD 0.48727 0.58429 0.51861 0.14765 0.53006 TN 0.79273 0.92146 0.72815 0.53189 0.81411 TX 0.81454 0.95019 0.53309 0.41260 0.76594 UT 0.66545 0.79502 0.47840 0.25310 0.64629 VA 0.74909 0.87739 0.58647 0.38545 0.73765 VT 0.52727 0.64368 0.47896 0.16256 0.54997 WA 0.75273 0.89080 0.54387 0.36468 0.72913 WI 0.76000 0.89464 0.52376 0.35612 0.72613 WV 0.55636 0.67625 0.47485 0.17866 0.56915 WY 0.42909 0.52874 0.52976 0.12019 0.49586 US 1.00000 1.00000 1.00000 1.00000 1.00000 Data Source: MicroIMPLAN, 91-F.

Turning to our internal consistency checks, we see that the data supports our logic. The condition number for the U.S. was the largest at 5.81206, thus confirming internal consistency at one level. This means that the U.S. economy had the greatest degree of inter-industry linkages. This result also makes intuitive sense. The second and third internal consistency checks were tested using the Pearson Correlation Coefficient (Table 2). As reported in Table 2 there was a statistically significant positive correlation between the size variable (S[I.sub.i]) and the condition number as measured by [C.sub.i]. Therefore, the logic of our approach appears consistent with the data. This supports the generally held belief that the larger the size of the economy, the greater the degree of the possible interindustry linkages. There was also a statistically significant positive correlation between density of the (I - A) matrix ([DEN.sub.i]) and the condition number as measured by [C.sub.i]. Again, the logic of our approach appears consistent with the data. This implies that as the purchases of locally produced inputs increases so do the inter-industry linkages.

Each scalar component of our diversity measure has advantages and disadvantages. The condition number is a measure of linear independence between the rows and columns of any matrix. Consequently, two matrices of different size may have the same condition number. For example, the estimated condition numbers for Oklahoma and North Dakota's (I - A) matrices are approximately equal; however, they differ in the relative size ([SI.sub.i]) and density ([DEN.sub.i]) (see Table 1). In addition, endogenous industries with similar sale or expenditure patterns, as captured by the regional input coefficients matrix, will also cause the condition number to increase. These similar sales and expenditure patterns could result from comparable industries or the net result of estimating the effects of imports on different industries. Therefore, an economy like Idaho has a condition number greater than New York; but again they differ in relative size ([SI.sub.i]) and density ([DEN.sub.i]).

The measure of relative density ([DEN.sub.i]) is affected by the purchases of locally produced input. Thus, an economy with relatively few industries each importing a small amount could have the same [DEN.sub.i] estimate as an economy with relatively many industries each importing a large amount. For example, Michigan, New Jersey, and Washington had the same [DEN.sub.i] estimate. However, neither the internal structure of the (1 - A) matrix nor the relative size of the economy is captured by the [DEN.sub.i] estimate. These are captured by [C.sub.i] and [SI.sub.i], respectively.

TABLE 2 CORRELATION MATRIX OF KEY DIVERSITY MEASUREMENT ELEMENTS Variable(a) DEN SI C MDI DEN 1.00000 (0.0) S1 0.97619 1.00000 (0.0001) (0.0) C 0.43053 0.29274 1.00000 (0.0016) (0.0371) (0.0) MDI 0.87163 0.77394 0.78454 1.00000 (0.0001) (0.0001) (0.0001) (0.0) Notes: The correlations were calculated using the Pearson Correlation Coefficients. The terms in the parentheses are the Prob [greater than] [absolute value of R] under [H.sub.0]: [Rho] = 0/N = 51. a DEN denotes density as defined by equation [2]. SI denotes size as defined by equation [1]. C denotes a measure of interindustry linkages as defined the condition number in equation [4].

The relative size of an economy, as measured by [SI.sub.i], is a simplistic, easily estimated scalar. It describes one aspect of a region's economy but does not contain any information on the inter-industry linkages and structure of the (I - A) matrix nor the relative degree of purchases of locally produced inputs. These are captured by [C.sub.i] and [DEN.sub.i], respectively. For example, Georgia and New Jersey have the same relative size, but have different inter-industry linkages and degree of purchase of locally produced inputs.

Each scalar is individually insufficient for estimating diversity of a regional economy as described by the regional inputs coefficients matrix or analogously the (I - A) matrix. These results suggest that the logic of focusing on the combination of these three scalars that describe the (I - A) matrix as a locus for the analysis is reasonable.

Growth and Stability Results

In order to test the role of diversity in regional economic growth and stability, the hypothesized growth and stability relations outlined in equations [7a] and [7b] are estimated for 48 states. Two states were removed from the analysis due to missing data. First we will report on the results of the principal components analysis, then the Box-Cox estimation of equations [7a] and [7b] themselves.

Principal component analysis. Although there is no exact rule to selecting a specific principal component, there are two approaches relied upon in most applications. One is to select the first principal component regardless of the cumulative variation with the block of variables explained by the principal component. The other is to select the principal component that the eigenvalue of the correlation matrix is closest to one. For this analysis the second general approach is employed. Finally, note that due to scaling sensitivity, all variables used in the principal component analysis are standardized to zero mean and unit variance. The results of the principal component analysis are reported in Table 3.

The principal components for Amenities and Infrastructure can be interpreted directly; higher levels of both principal components are associated with higher levels of both variable blocks with the respective principal components explaining 64.03 and 72.86 percent of the variation in variable blocks. Here, a higher value of the Amenities principal component is associated with higher levels of three of the four variables defining the block. Note that the small (i.e., less than .5) eigenvector for the surface water measure suggests that this specific variable plays no real role in determining the final principal component. The principal components for Taxes captures tax structures that tend to favor businesses over consumers. In other words, higher values of the Taxes principal component are associated with regions (states) with lower corporate tax rates and higher sales and gasoline tax rates. The taxes principal component explains 67.45 percent of the variation in the variable block.

The Markets and Labor principal components are not as clearly interpreted. Regions with higher values of the Markets principal component are associated with regions that have higher income inequality, a higher percentage of persons living in the region their entire life, and a lower number of elderly persons. Here, 90.85 percent of the variation in the variable block is explained. The Labor principal component is perhaps the most difficult to interpret directly. While no single set of variables seems to define this principal component, higher values of the Labor principal component appear to be associated with higher levels of unionization and education. The Labor principal component explains 77.85 percent of the variation in the labor block of variables.

Growth and stability results. The results of the Box-Cox estimation of equations [7a] and [7b] are reported in Table 4.(13) Turning attention first to the growth model, we see that the data supports a nonlinear functional form (Box-Cox lambda equal to .63) and that three of the six hypothesized variable groups are statistically significant explaining about 17 percent of the variation in growth. The significant and negative coefficient on labor suggests that higher values of this principal component are associated with lower overall levels of growth. Given the dominate role of unionization in this principal component, this result is consistent with the existing literature. The positive and significant coefficient on the infrastructure principal component indicates that higher levels of infrastructure stock are also associated with economic growth.

TABLE 3 PRINCIPAL COMPONENT EIGENVECTORS Variable Block Eigenvector Markets Income distribution (1980) 0.373896 Percent of the population that is nonwhite (1980) -.210187 Population (1980) 0.037399 Growth in population (1969-91) 0.233518 Per capita income (1980) 0.052413 Cost of living (1981) 0.009444 Percent of individuals below the poverty level (1979) 0.001064 Percent of children below the poverty level (1979) -0.041890 Percent of persons over 65 years of age (1979) -0.406701 Percent of persons living in the region their entire life (1976) 0.768177 Cumulative Variance Explained 90.85% Labor Right to work law (1982) -0.131884 Percent of labor force unionized (1980) 0.454602 Percent of persons with a high school diploma (1980) -0.411921 Percent of persons with a college diploma (1980) -0.250696 Average teacher (K-12) salary (1980) 0.456971 Number of doctors per 1,000 persons (1980) 0.216706 Number of prisoners per 1,000 persons (1980) 0.381578 Infant death rate (1980) 0.376870 Cumulative Variance Explained 77.85% Taxes Corporate tax rate (1981) -0.600410 State sales tax rate (1981) 0.659553 Composite effective tax rate (1981) -0.126624 Gasoline excise tax (1980) 0.434125 Cumulative Variance Explained 67.45% Amenities Percent of the regional population classified as rural (1980) 0.500109 Percent of the region's surface area covered by lakes and rivers (1978) -0.275104 Percent of the population with a fishing license (1978) 0.564072 Percent of the population with a hunting license (1978) 0.596684 Cumulative Variance Explained 64.03% Infrastructure Number of public airports per one million persons (1980) 0.582335 Number of private airports per one million persons (1980) 0.517265 Highway density measured as miles of four-lane highway per square mile (1980) 0.627155 Cumulative Variance Explained 72.86% TABLE 4 EMPIRICAL RESULTS FOR THE GROWTH AND STABILITY MODELS Models(a) Variable Growth Stability Market 0.000465 0.010115 (0.27)(b) (0.37) Labor -0.006027 0.062298 (3.20) (2.22) Tax 0.001034 0.006637 (0.67) (0.27) Amenity 0.003097 0.058564 (1.18) (1.43) Infrastructure 0.005126 0.093217 (2.44) (3.03) Diversification Index 0.018444 -0.157680 (2.15) (1.70) Constant -1.25360 -2.12730 (154.72) (19.87) Box-Cox Lambda 0.6300 0.4100 Adj [R.sup.2] 0.1694 0.2560 F-stat 2.5980 3.696 a Measure of growth is the average annual growth rate in state per capita income and the measure for stability is the variance of the average annual unemployment rate for the period 1969-91. b Number in parentheses is the absolute value of the t-statistic.

The more interesting finding in the growth model is the statistical importance of our proposed diversity measure. This result suggests that, after accounting for several growth-inducing factors, there is evidence that supports the notion that higher levels of economic diversification lead to higher levels of economic growth as measured by changes in per capita income.

Results of the stability model are also reported in Table 4. Again the data supports a nonlinear functional form (Box-Cox lambda equal to .41) and two of the six hypothesized variables are significant at the 95 percent level of confidence, explaining about 26 percent of the variation in stability. The significant and positive coefficient on the labor principal component suggests that higher values of this variable are associated with higher levels of economic instability as measured by unemployment rates.

Again, given the dominant role of unionization rates in this variable, this result is also consistent with expectations given the literature. The positive and significant coefficient on the infrastructure principal component is not as intuitive as with the growth model result. Again, as with the growth model, the more interesting result is the negative and weakly significant coefficient on our proposed diversity measure. This result suggests, albeit weakly in a statistical sense, that higher levels of economic diversification are associated with lower levels of economic instability, ceteris paribus

VI. CONCLUSIONS

A commonly pursued regional economic development strategy is that of economic diversity in order to achieve the goal of economic stability and growth. While logic, and common sense, suggests that this is a reasonable approach, the empirical literature has not been able to affirm this strategy. We outline a theoretical approach to policy development in which we argue that the long-run envelope of a diverse set of short-run growth strategies can lead to the simultaneous goal of growth and stability. We further suggest an alternative way of empirically thinking about diversity which emphasizes inter-industry linkages.

Using the framework of regional input-output modeling, we construct an alternative measure of diversity which explicitly captures the size of the regional economy as well as the degree of inter-industry linkages. Using a simple model of growth and stability, empirical results suggest that higher levels of diversity are statistically associated with higher levels of growth and stability.

Given our results, a new layer of policy options are available to local economic development policymakers. Specifically, the notion of building a core set of industries on the comparative advantage of the region in the short run promotes the goal of growth. The traditional theory of diversity suggests that all the policymaker need worry about is that total economic activity is evenly distributed across those selected industries. Given our proposed view of the world, policymakers are given a wider range of options to pursue in the long run. Specifically, the role of vertical and horizontal integration through the pursuit of value-added industries and/or industry targeting in the name of import substitution becomes clearer and directly applicable. While our proposed measure of diversity is but one approach, the idea of exploring the role of structural inter-industry linkages as a means to tackle the diversity question warrants further attention.

1 For a more detailed review of the alternative empirical measures of diversity see Siegel, Alwang, and Johnson (1995b).

2 Net returns are viewed as economic growth rates of either employment or income.

3 The MicroIMPLAN database is created using non-survey methods. In addition, the regional input coefficients matrices are generated from the national technical coefficients matrix and estimated trade flows, We assume the resulting regional inputs coefficients matrices are reasonable representations of the regional economies.

4 The flexibility of the proposed measure is witnessed by the application of the method to California counties by Andrew and Goldman (1996).

5 The (I - A) matrix was used to be consistent with estimating the final scalar.

6 Condition numbers can be used to determine an upper bound on the relative error created in the solution by small perturbations in the D matrix or b vector of the linear system Dx = b. There are a number of different types of matrix norms and the magnitude of the condition number depends on the specific norm used. However, if a matrix is ill-conditioned using the 2-norm, it will be ill-conditioned using any other matrix norm. Furthermore, Golub and Van Loan (1983) define the mathematical relationships between matrix norms.

7 An extreme case would be were the (1 - A) matrix was diagonal with 0 [less than] [(I - A).sub.jj] [less than or equal to] 1 [for every] j and [(I - A).sub.jk] = 0 [for every] j [not equal to] k. In this case, the singular values of the matrix are defined by the diagonal elements and the size of the condition number would depend on the smallest and the largest elements. The economic interpretation of this matrix is that the endogenous industries import all their intermediate inputs. However, this is not a realistic concern.

8 The condition number estimated using the matrix 2-norm is invariant with respect to orthogonal transformations. Therefore, if the rows and columns of the regional input coefficient matrix are aggregated such that Q(I - A)Z defines the aggregation scheme with [Q.sup.T]Q = I and [Z.sup.T]Z = I, then [[Q(I - A)Z]] = [[(I - A)]] (Golub and Van Loan 1983). Thus, different size matrices may have the same condition number.

9 At first glance it may appear that we are subject to a problem with causation: our independent variables should be describing the regional economy at the beginning of the period examined (1969) as opposed to 1980, the middle of the period. This is due to the structure of MicroIMPLAN, the source of the input-output models upon which the diversity measure is constructed. The technical coefficients matrix used by MicroIMPLAN are based on the 1982 benchmark matrix of the Bureau of Economic Analysis, with the exception of the agriculture sectors which is based on pre-released portions of the 1987 benchmark matrix. Therefore, the internal structure of our diversity measure is reflective of 1982.

10 Space prevents a detailed discussion of each of these variables and the reader is referred to the wide empirical literature, particularly Kusmin's (1994) review.

11 Computing a Gini Coefficient for each of the 50 states examined in this analysis creates a scalar measure of income distribution.

12 Regional cost-of-living indices are available from McMahon (1991).

13 Note that to apply the Box-Cox estimator, all variables must be nonnegative. Because the principal components are scaled around zero, all principal component variables were shifted nonnegative by the smallest (negative) value.

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John E. Wagner and Steven C. Deller are, respectively, assistant professor at SUNY-College of Environmental Science and Forestry, Syracuse, and associate professor and community development specialist, Department of Agricultural and Applied Economics, University of Wisconsin-Madison/Extension. Support for this research was provided by the USDA Forest Service Southern Forest Experiment Station and the University of Wisconsin-Madison/Extension. This work benefited from the helpful comments of George Goldman, David Kraybill, Paul Siegel, Emil Malizia, and two journal reviewers. We would also like to thank Martin Shields for data analysis. An earlier draft of this article was released as a Center for Community Economic Development Staff Paper 93.3, Department of Agricultural and Applied Economics, University of Wisconsin-Madison/Extension and was presented at the NE-162 session at the Western Regional Science Association's annual meetings, Tucson, February 23-27, 1994. All errors and misinterpretations are the responsibility of the authors.

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Author: | Wagner, John E.; Deller, Steven C. |
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Publication: | Land Economics |

Date: | Nov 1, 1998 |

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