DIVERGENCE* Patricia E. Beeson and David N. DeJong** First Version: November 2000 This Revision: May 2001
**
Department of Economics, University of Pittsburgh, Pittsburgh, PA 15260 email:
[email protected];
[email protected] Corresponding author: DeJong *
We thank Matthew Kelley and Eileen Kopchik for excellent research assistance, and Michael Haines and Koleman Strumpf for providing county-level data and corrections. For their many valuable comments, we also thank Francesco Caselli, Dean Corbae, Steven Durlauf, Gerhard Glomm, Marla Ripoll, Jordan Rappaport, Jean-Francois Richard, and seminar participants at Carnegie -Mellon University, the Federal Reserve Bank of Atlanta, the Universities of Pittsburgh and Wisconsin, the 2000 Regional Science Association Meetings, and the 2001 Midwest Economic Association Meetings. The usual disclaimer applies.
DIVERGENCE Abstract We use population data from the U.S. Census to track regional patterns of growth from 1790 through 1990. At the county level, we find that an initial general tendency towards population convergence lasting roughly through the 1800s becomes reversed: particularly in the post-WWII period, regional populations have diverged. The finding of divergence hinges on two factors: the exclusion of transition dynamics and the level of aggregation. Regarding the former, statelevel populations exhibit consistent patterns of transitional population growth over roughly two- to six-decade periods surrounding the admission of states to the union, followed by long periods of relatively steady growth. When transitional periods are included in our county-level analysis, divergent steady state patterns of growth become masked. Regarding the latter, when we aggregate to the state level, divergent county-level patterns of growth are again masked: even when transitional periods are excluded, state-level populations exhibit tendencies towards convergence. I. Introduction. Recent theoretical analyses of economic growth have highlighted a wide range of endogenously arising sources of growth that carry the potential to generate divergent patterns of economic activity. Empirical research conducted at the micro (e.g. firm and industry) level has documented the existence of many of these sources, including knowledge spillovers, technology transfers, and increasing returns to industry concentration. However, across broad classes of comparable aggregated economies (e.g., OECD countries, U.S. states, and Japanese prefectures), there is no evidence that these sources have in fact generated divergent growth trajectories. County-level population data compiled by the U.S. Census offer a resolution of this puzzle. Measuring population growth on a decade-by-decade basis (and over longer sub-periods) over the period 1840 – 1990, we find evidence of divergent county-level growth: counties with relatively large initial populations have tended to experience relatively rapid subsequent growth, particularly in the post-1940 period. This result is robust to a large number of specifications, but turns out to be sensitive to two key facets of our analysis: the exclusion of “transition” dynamics, and the level of aggregation used to define a region. This sensitivity is important, because it suggests two reasons why previous empirical studies of cross-sectional growth may have failed to uncover tendencies towards divergence. Consider first the issue of transition dynamics. When territories initially opened for settlement, their growth rates tended to be unusually high relative to steady state: logged populations typically grew exponentially for several decades before transitioning to linear trajectories. This “frontier effect” may reflect efforts to capitalize on regional amenities generated by natural characteristics. For our purposes, it is important to isolate and focus on the behavior of steady state dynamics, because it is along this dimension that the predictions of endogenous and exogenous growth models are distinct. In our analysis,
1
the inclusion of dates during which frontier effects are present turns out to mask differences in steady state behavior; when frontier effects are eliminated, we find a clear post-war tendency towards divergence.1 The second key facet involves the level of aggregation. If we aggregate our county-level data to the state level, the state-level data show a tendency towards convergence, even controlling for frontier effects. The importance of the level of aggregation is perhaps not surprising, since many of the potential sources of endogenous growth highlighted in the literature (referred to hereafter as agglomeration economies) are facilitated by or result from spatial concentrations. For example, spatial concentrations are important for facilitating knowledge spillovers, which play a key role in the theoretical constructs of Jacobs (1969), Romer (1986) and Lucas (1988). They are also important for enabling firms operating in large labor markets to benefit from labor pooling, and to exploit complementarities in labor supply (Marshall, 1920 and Krugman, 1991). The contrasting results we obtain at the county and state levels indicate that agglomeration economies are operational or clearly evident only at the local level, and that the influence of these activities is masked in aggregating up to the state level. In examining relationships between initial regional populations and subsequent growth rates, we use several alternative definitions of initial populations, measure growth over a variety of time horizons, and condition on a broad range of fixed exogenous regional characteristics (e.g., proximity of oceans, navigable rivers, etc.). Our most striking finding is that initial population levels have highly persistent explanatory power in accounting for subsequent rates of population growth. For example, initial populations established as early as 1840 exhibit positive and significant (statistically and quantitatively) relationships with population growth measured between 1980 and 1990. In early decades, the relationship between initial populations and subsequent growth rates is negative: populations show a general tendency towards convergence up until around 1900. This pattern is then reversed: throughout most of the 1900s, regional populations generally diverged; this tendency is particularly dramatic in the post-1940 period. The post-war tendency towards divergence occurs roughly uniformly across regional size classifications. In particular, when we divide regions into decile classifications based on their initial populations, we find that average growth rates in the post-war period rise roughly monotonically with initial decile rankings. Thus our finding of divergence is not merely an artifact of the growth patterns exhibited by regions in the upper or lower tails of the population distribution. In contrast, the pre-1940 tendency towards convergence does not occur uniformly across decile classifications: growth rates fall roughly monotonically with decile rankings in the lower half of the distribution, and rise roughly 1
We use a statistical framework to obtain a systematic distinction between frontier effects and steady state behavior; the framework is described in detail in Section III.
2
monotonically in the upper half. Thus throughout the entire sample period, relatively large regions have tended to grow relatively rapidly. Analyses of sources and consequences of agglomeration economies follow Mills (1967) and Jacobs (1969), who respectively emphasized scale economies and knowledge spillovers as important sources of agglomeration economies. Henderson (1987), Quigley (1998), and Glaeser (1999) provide overviews of subsequent theoretical and empirical work in this area. Many different strands of empirical work within this literature are related to this study. One strand of related work has focused on determinants of differential growth experiences among urban areas (citie s and MSAs). Often, the goal of this work has been to determine whether differences in potential sources of agglomeration economies account for differences in urban growth experiences. The findings of this work are typically supportive. For example, Gla eser et al. (1995) found initial differences in the human capital of the local population to be an important determinant of differences in subsequent urban growth over the period 1960–1990; Simon and Nardinelli (1998) obtained a similar result over the period 1880–1980. In slight contrast, Chatterjee and Carlino (2001) documented a pattern of employment deconcentration among urban areas since the 1950s, a tendency they attribute to the dominance of congestion effects over agglomeration economies. Another strand of related work has highlighted persistence in population growth rates. Strong serial correlations in regional population growth rates have been documented by Barro and Sala -i-Martin (1991) and Blanchard and Katz (1992) at the state level; Rappaport (2000) at the state and county level; and Glaeser et al. (1995) among urban areas. (Serial correlation is also evident in our data; we control for this in examining links between initial populations and subsequent growth rates.) Rappaport emphasized the importance of capital- and labor-adjustment costs as a source of this persistence; alternatively, this may reflect persistence in regional productivity advantages, possibly due to agglomeration economies. Gabaix (1999) has shown that Ziph’s (1949) law (the number of urban areas with populations greater than S is proportional to 1/S) arises from another form of persistence, Gibrat’s (1931) law: urban growth rates are independent of initial populations, thus the relative size rankings of urban areas are highly persistent. In this way, the substantial literature devoted to establishing the empirical relevance of Ziph’s law among large cities pertains to this analysis. Our data provide mixed support for Ziph’s law. Among regions ranked in the top decile of our sample based on initial populations, average growth rates computed over the entire sample period show no systematic relationship with initial populations. However, there is a distinct tendency towards population divergence among these regions prior to 1900, and towards population convergence from 1940-1990. This latter result is consistent with the pattern of employment deconcentration among urban areas documented by Chatterjee and Carlino (2001).
3
Our analysis of population-growth patterns within the U.S. complements the substantial literature devoted to cross- and within-country analyses of income-growth patterns, which are often motivated as attempts to distinguish between predictions of neoclassical and endogenous growth models (see Durlauf and Quah, 1999, for a survey of this literature). Within this literature, Barro and Sala -i-Martin’s (1992) analysis of state-level patterns of income growth in the U.S. is perhaps most directly pertinent.2 Their analysis documented a clear tendency towards state-level income convergence. The pattern of countylevel population divergence we document does not contradict their findings, but rather reflects differences in the variables we study and the level of aggregation at which we study them. We have already discussed the importance of the level of aggregation: just as Barro and Sala -i-Martin found state-level income convergence, we find population convergence when we aggregate up to the state level. Regarding the analysis of population versus income growth, labor tends to be relatively mobility at the local level. Given labor mobility, regions with productivity and amenity advantages will experience relatively rapid population growth as long as these advantages persist. (The effect on income growth is less clear, since income growth also depends on the relative sizes of amenity and productivity effects.) In the presence of agglomeration economies arising from initial concentrations of economic activity, we would therefore expect to see divergent patterns of population growth until the productivity advantages they generate ultimately become swamped by congestion effects, or if severe labor shortages in less-populated regions themselves yield offsetting labor-productivity advantages. Like counties, cities are also attractive because they economize on aggregation. However, the political boundaries of cities often exclude suburbs, which typically constitute an important portion of the local economy. And while county borders occasionally change, they are less likely to do so in response to growing populations than city or metropolitan area borders. Most significantly, counties are defined for all areas, including not only those that grew and eventually became cities or metropolitan areas, but also those that stagnated, declined, or never came to be. Thus county-level data provide a large variety of growth experiences and avoid the selection problem noted in DeLong (1988) in reference to Baumol’s (1986) analysis of income convergence among OECD countries. A handful of previous growth studies have focused on county-level data. Notably, Carlino and Mills (1987) studied the effects of demographic and climatic characteristics on county-level growth during the 1970s. Rappaport (1998) documented systematic relationships between growth and county characteristics such as human capital, crime, poverty, and local fiscal conditions between 1970-1990. 2
A benefit of within-country growth analyses is that regional differences in, e.g., political, ethnic and cultural characteristics are kept to a minimum. As Brock and Durlauf (2000) emphasize, heterogeneity among such characteristics complicates the interpretation of cross-country income-growth regressions.
4
Rappaport and Sachs (2001) documented the high density of economic activity along U.S. coastlines, and attributed this to productivity effects. Finally, Beeson, DeJong and Troesken (2001) analyzed growth over the period 1840-1990 using counties in only those states in existence in 1840, and found a tendency towards population divergence. Here, we extend this work by studying counties covering the entire land area of the continental U.S., by measuring growth on a decade-by-decade basis, and by systematically controlling for transitional frontier effects in studying tendencies towards convergence or divergence.
II. The oretical Framework for Growth Regressions. Here we provide theoretical motivation for our empirical analysis of regional population growth. This construct closely follows Glaeser et al. (1995). It is sparse, yet sufficiently flexible to encompass the richer frameworks of, e.g., Henderson (1987) and Chatterjee and Carlino (2001). See Rappaport and Sachs (2001) for an alternative motivation. Let output in region j at time t, Yj,t , be given by (1)
Yj, t = A j, t Lαj, t
0 < α t* ;
ε t = ρε t-1 + ut , which is estimated subject to the restrictions: (10)
y0 + bt* + ct*2 = γ + δt* ; b + 2ct* = δ.
The first restriction imposes equality between the linear and quadratic components at date t* ; the second imposes tangency between the components at t* . Note that the parameter ρ permits the innovations {ut } to have persistent effects. The assumption of normality for the innovations {ut } yields a likelihood function associated with (9) and (10), which we maximize with respect to {γ, δ, ρ, t* }; given ML estimates of these parameters, corresponding estimates of b and c are obtained using (10). Of particular interest to us are estimates of t* , which we use to define initial regional population levels in our growth regressions. We estimated (9) – (10) for each state individually, using all available observations for the 40 states that did not experience breaks in their linear components. For the remaining eight states, we estimated the model using pre-break observations only. Alternatively, we could have modified (9) to accommodate a potential break; this would not have affected our characterizations of transition dynamics. Figure 2 illustrates the fitted model for the four representative states illustrated in Figure 1; Figure 3 illustrates the fitted model for four additional states that, like the total of 35 states in our sample, approach roughly stable log-linear trajectories from below. (Model estimates were obtained using the DavidonFletcher-Powell secant method, executed in GAUSS.)
8
Table 1 presents ML estimates of our model for each state. The first three columns report the state, region, and years of data used to estimate the model. Column 4 reports (γ - y0 ), the gap between our estimate of logged initial population along the estimated steady state trajectory and the actual logged population in the first year for which data are available. (By implication, e(γ - y0) represents the ratio of estimated initial steady state population to the actual initial value; thus an estimated value of 3 for (γ - y0 ) implies a ratio of 20.) For the nine states whose populations approach their linear trajectories from above this difference is negative. As noted, North Carolina and Virginia follow approximately linear trajectories throughout their samples; these are the only two states for which (γ - y0 ) is estimated as insignificantly different from zero at the 5% significance level. Excepting Nevada and the original thirteen states, estimates of (γ - y0 ) range from 0.286 (Florida) to 6.117 (Alabama), implying ratios of initial steady state to actual populations of 1.33 and 454. Estimated differences are on average highest in the East- and West-North-Central regions: average and median differences are approximately 4 in these regions, implying ratios of approximately 55. Average and median values of the absolute difference between γ and y0 are 2.22 and 1.77 across all 48 states, implying ratios of 9.21 and 5.87. So clearly, discrepancies between initial populations and their estimated steady state counterparts are substantial. The estimated durations of transition periods, t* , are reported in Column 7 of Table 1. With the exception of Florida, all estimates of t* are significant at the 5% level. Estimates of transition durations fall as one moves west: average and median durations are 61 and 63 in the New England, Mid- and SouthAtlantic regions; 47 and 43 in the four Central regions; and 41 and 34 in the Mountain and Pacific regions. Presumably, this pattern is due the fact that western regions were settled at relatively later dates, thus their settlements advanced more rapidly due to technological advances in transportation, construction, etc. Closely related behavior is seen in the estimated half-life of (γ - y0 ), reported in Column 10. Half-life is measured as the number of years required to cut the gap between yt and its estimated steady state trend line to half the value of (γ - y0 ). Average and median values of half-lives range from 18 to 13 to 10 years across the three groups of regions mentioned above. A third related measure reported in Table 1 is Merge Date, which is obtained by adding t* to the initial observation date for each state. A final difference between transitional and steady state behavior highlighted in Table 1 involves a comparison of population growth rates computed along the estimated log-linear trajectory (steady state growth, denoted as gss ) with the average growth rate observed over the entire sample period (denoted as gavg). Estimated steady state growth is reported in Column 5, the actual growth rate is reported in Column 12, and the t-statistic for the test of the hypothesis of equal growth rates is reported in Column 13. 6
6
Regarding steady state growth, since a one-unit movement in the variable t in (9) represents a onedecade time increment, the annual growth rate implied by the trend parameter δ is δ/10. 9
Multiplying this ratio by 100 yields steady state growth measured as an annual percentage rate, thus Table 1 reports ML estimates of gss = 10δ. The null hypothesis of equal growth is rejected at the 5% significance level for all but five states: Delaware, Maryland, New Mexico, North Carolina and Virginia. The largest difference in growth rates is observed for North Dakota: 4.25 percentage points. The average and median absolute difference in growth rates overall are 1.43 and 1.33 percentage points. Differences are highest in the West-North-Central region, where they average around 2.8 percentage points; they are also high in the East-North-Central and Pacific regions, where they average around 2.2 percentage points. Once again, discrepancies between transitional and steady state behavior are clearly apparent. Regarding steady state growth, four states feature average annual population growth rates of well over 3 percent: Nevada (3.9), Arizona (3.7), Florida (3.5), and California (3.4). Growth is highest on average in the Pacific and Mountain regions (2.5 and 2.2 percent), and lowest in the West-North-Central region (0.7 percent). Steady state growth rates estimated for the eight states that underwent trend breaks should be interpreted with this break in mind. For example, Pennsylvania’s rate of 1.8% is based on data through 1930; its average rate from 1930 – 1990 was only 0.35%. We conclude with comments on estimates of ρ, (reported in Column 6) which indicate the persistence of the innovations {ut }. Specifically, the half life of an innovation measured in years is given by 10*(ln(0.5)/ln(ρ)), so the estimated value of 0.67 obtained for Tennessee implies a half-life of approximately 17 years. Relatively high estimates of persistence indicate sustained periods over which the actual data lie either above or below the fitted curve. Note from Figure 2 that Connecticut and Tennessee each feature such periods (1910 – 1970 for Connecticut; 1880 – 1920 for Tennessee); thus their estimates of ρ are relatively high. In contrast, the populations of New Hampshire and Massachusetts regularly cross their trend lines, and their corresponding estimates of ρ are relatively low. Estimates of ρ are low in general: the average and median value across all states is 0.35, and ρ is estimated at or below 0.5 for 36 states. In contrast, unusually high estimates of ρ are obtained for New York (0.87) and Kentucky (0.92). In both cases, this reflects distinct departures from the log-linear specification after date t* . Instead of log-linearity, the data logged data exhibit hump-shaped patterns, and thus lie above their trend lines over several decades. As the estimates of ρ indicate in general, the relatively poor fits of (9) – (10) for New York and Kentucky are exceptional.
IV. Data Description. The U.S. Censuses of Population in 1840-1990 are our primary data sources. (Prior to 1840, states typically have so few counties that they are not suitable for conducting cross-sectional analyses.) Michael Haines provided an edited version of the Inter-university Consortium for Political and Social
10
Research (1978) 1840-1970 Census data files;7 the 1980-1990 data are from the Bureau of the Census. Decennial population growth rates are used as dependent variables in our analysis. Geographic boundaries of some counties changed over the time period covered in our analysis, and in some states these changes were substantial. To control for this, we use the template developed by Horan and Hargis (1995) to construct county groups with consistent geographic boundaries over the sample period. 8 The constructed county groups include all land area and population in each state. Horan and Hargis provide templates that group counties starting with any decade from 1840 to 1980; the county groupings and the number of county groups in each state vary depending on the starting date. For each state, we use the template that corresponds with our estimated merge date, thus county definitions and the number of counties in each state are consistent over time.9 Of course, the total number of counties included in the sample varies as time moves forward and additional states are estimated to have reached their steady state trajectories. Even after correcting known errors in the census data, outliers remain in the sample. In some cases population growth is extraordinarily high because starting populations are low. In other cases extraordinarily large, positive growth rates one year are followed by extraordinarily large, negative growth rates the following year, suggesting a recording error. There are two exclusions we make to deal with these outliers. First, we drop all observations with start-of-decade populations less than 500. Second, we drop all county-decade observations for which population levels are 25% higher than in both the previous and subsequent decades, or 25% lower. In addition to data-recording errors, this restriction of population spikes also excludes abnormal experiences (e.g., gold rushes) that we are not attempting to explain in any case. Table 2 provides summary statistics for county-level populations and population growth rates by decade. There are two potential concerns with these county data. First, counties are not uniform in geographic size, both because of our construction of conglomerate counties and because counties are not defined to have a fixed geographic area. To address this concern, we include the logarithm of land area as a control variable in the analysis that follows. This approach assumes the effects of land area are linear, but we have yet to verify the empirical validity of this assumption. A second potential concern with our constructed county groups is that county redefinitions may have been influenced by growth experiences, 7
These files were further edited to incorporate corrections made by Strumpf and Rhode (2000), and to eliminate additional minor inconsistencies. These edited data files are available upon request. 8
We actually use a modified template that corrects some minor inconsistencies; the modified template is available upon request. 9
We experiment with alternative definitions of merge dates in the analysis that follows; to do so, we work with alternative templates. 11
and thus county definitions are not strictly exogenous. To check this, we investigate whether conglomerate counties behave systematically differently from their non-conglomerate counterparts. As it turns out, they do not: when the models reported below are estimated separately for conglomerate and non-conglomerate counties, we find no notable differences in the estimates. The set of control variables we use consists of natural characteristics; these include measures indicating access to water transportation, climate, and mineral resources. We use four dummy variables to indicate access to natural transportation systems, which are coded using maps. The first identifies counties with Pacific, Atlantic or Gulf coast borders. The second identifies counties with a navigable river bordering or crossing through them. Navigable rivers are identified using the Army Corps of Engineers map of Inland Rivers/Navigable Waterways. The third identifies confluences of two navigable rivers, or of a navigable river and a coastline. The fourth indicates the presence of a mountain peak. Three variables measure climate: heating-degree days (HDD), cooling-degree days (CDD), and precipitation. HDD and CDD measure temperature extremes: higher values of HDD indicate colder climates, and higher values of CDD indicate warmer climates. These measures are reported by the U.S. National Oceanic and Atmospheric Administration (NOAA), and are collected from the U.S. National Climate Data Center web site. All variables are divisional normals constructed by the NOAA for the period 1931-1990.10 Wright (1990) argued that natural resources promoted the industrial development of America. To explore the role of natural resources we code three dummy variables. The first indicates the presence of a coal mine in the county; another indicates the presence of an iron ore mine; and the third indicates the presence of any other type of mine. These data come from the 1880 Census of Mining. The final physical characteristic, land area (total land area less water), is constructed using Census data, and is measured in thousands of square kilometers. Means and standard deviations of the natural characteristics for the samples of counties included in the 1860, 1900, 1940 and 1980 regressions are reported in Table 3. From this table, 4% of the counties in the 1860 regression sample are located on a coast. This percentage doubles by 1900, as a disproportionate number of coastal counties reached their steady state trajectories between these dates. Nearly 37% of the counties in the 1860 sample have at least one river running through them and nearly 9% have a confluence of two rivers; both percentages fall by about a third over time as counties are added to the sample. Approximately 15% of counties have iron ore deposits, one-third have coal, and less than 10
Climate data are reported for divisions, not counties. Divisions are sub-state regions designating areas of similar climate. For the most part these regions are groups of counties. The number of climate divisions in a state varies from one (Rhode Island) to ten (many states).
12
10% have other mineral deposits. Counties added to the sample in later years are less likely to have ironore deposits, but slightly more likely to have coal and other minerals than counties included in the 1860 sample. In terms of climate, counties that achieve steady state trajectories in later decades tend to have less rain and fewer heating-degree days. V. Distributional Characteristics of County Populations. We begin our county level analysis by characterizing the evolution of population distributions over time. We focus on the distributions of counties that were estimated to have reached their steady state growth traje ctories at or prior to 1870 in order to examine a consistent set of counties over time. These counties comprise only 13% of the total sample, but as Appendix Figure A1 (described below) illustrates, similar characterizations arise when the sample is expanded to include counties that reached their steady state trajectories in later decades. Figure 4 depicts 5%, 25%, 50%, 75%, and 95% quantiles of the pdfs of logged population densities on a decade-by-decade basis as they evolved from 1870 – 1990. The corresponding pdfs for each decade are presented in Figure 5. (Quantiles of the pdfs for distributions of counties estimated to have reached their steady state trajectories between 1870 and 1930 are reported in Appendix Figure A1.) These figures present clear evidence of divergence. The respective average per-decade growth rates of these quantile values over this period are 10.2%, 6.1%, 7.1%, 12.3% and 18.7%: on average, relatively dense counties have grown relatively rapidly. Two exceptions to this generalization are noteworthy, however. First, the 5% quantile value exhibits relatively rapid growth from 1870 – 1920 (11.8% per decade), and relatively slow growth thereafter (4.9% per decade). In anticipation of the regression results to follow, the relatively rapid growth of the least-dense counties early in the sample period seems to account for the general pattern of convergence we find prior to 1900. Second, the relatively rapid average growth of 18.7% per decade exhibited by the 95% value was interrupted twice: between 1930 and 1940 (6.7%), and between 1970 and 1980 (-0.7%). The upshot of this average pattern of behavior is that the pdfs of logged population densities have become increasingly diffuse and skewed to the right over time. This is illustrated in Figures 5 and A1, which clearly show the most densely populated counties (those in the top half of the distribution) splitting off from the rest of the counties. . Within these pdfs, the rank orderings of counties (ranked by population densities) are highly persistent among relatively heavily and sparsely populated counties: densely populated counties tend to remain dense, while sparsely populated counties tend to remain sparse. To illustrate this, we follow Quah (1993) by dividing population densities into five cells, and calculating the proportion of counties that start and end each decade in the same cell. At each date, the first cell contains counties whose densities are no greater than 25% of the sample average; ranges of the remaining cells are greater than 25% but no greater
13
than 50%; greater than 50% but no greater than 100%; greater than 100% but no greater than 200%; and greater than 200%. The proportions of counties remaining in each cell are presented by decade in Figure 6. The proportions indicate relatively high churning between the middle three cells, and high persistence in both the lower and upper cells: the average proportions computed across decades for the five cells (ordered from least- to most-densely populated) are 0.96, 0.81, 0.79, 0.82 and 0.98. There is substantial time variation in the proportions calculated for the middle three cells, and little variation in the lower and upper cells: standard deviations of the proportions are 0.032, 0.093, 0.110, 0.073, and 0.034. Note that the proportions calculated for the upper cell exceed 0.95 for each decade beyond 1880, and the proportions calculated for the lower cell exceed 0.95 in 9 of the 12 decade spans. Taken together, these distributional characterizations indicate a general tendency towards population divergence at the county level, with population densities remaining fairly constant in the lower tail of the distribution (following an initial ‘catch-up’ period for the least-populated counties) and a dramatic splitting off of the more-densely populated counties. We now turn to a regression analysis that provides further evidence of this tendency obtained by conditioning on a set of natural characteristics. We then examine the sensitivity of this finding of divergence to transition dynamics and aggregation.
VI. Initial Regional Populations and Subsequent Growth. In this section we use growth regressions to document a divergent pattern of population growth using county level data that have been purged of transition effects as discussed in Section III. The finding of divergence is shown to be robust to a variety of specifications of time horizons, starting dates, measures of initial population, and conditioning variables. We then demonstrate that the finding of divergence is not robust to the inclusion of transitional years, nor to aggregation to the state level. For ease of presentation we document this latter finding by measuring growth over extended sub-periods; these results are similar to those obtained by measuring growth on a decade-by-decade basis. VIi: Regression taxonomy In examining relationships between initial populations and subsequent growth, we considered many variations of the regression equations (6) and (6’). Variations were considered along four dimensions. One dimension involves the time horizons over which growth rates are measured. First, we measured growth over one-decade intervals, beginning in 1840. (Although periods of transitional growth were estimated to have concluded prior to 1840 for six states, 1840 is the first decade for which we have sufficient data to estimate the model.) Next, we measured growth over a set of longer intervals that were naturally suggested by our decade-by-decade results. The intervals reported here include the full interval
14
1840-1990; the pair of sub-intervals 1840-1900 and 1900-1990; and the pair of sub-intervals 1840-1940 and 1940-1990. We chose two pairs of sub-intervals because patterns of convergence/divergence are mixed in the intervening years 1900-1930. The second dimension involves the choice of dates used to determine whether the counties in a particular state were included in the sample for a particular regression. 11 In the decade-by-decade regressions, we used four alternative rules to determine inclusion dates; all are based on the ML estimates of convergence dates reported in Table 1. First, the counties in a particular state were included in the sample for a given decade only if the state’s estimated convergence date occurred prior to the beginning of that decade. Using Connecticut as an example (with an estimated convergence date of 1852 and a standard error of 12), its counties were included in the sample beginning in 1860 under this rule. We then considered three alternatives to this rule : add one standard deviation to the estimated convergence date and round up to the nearest decade; add two standard deviations to the estimated convergence date and round up; and add ten years to the estimated convergence date and round up. Returning to the example, Connecticut’s counties were included in the sample beginning in 1870, 1880 and 1870 under the three respective alternatives. In the growth regressions involving the entire time interval 1840-1990 and the four sub-intervals, all counties were included in the sample under a given rule if their earliest date of availability was defined prior to the end of the sub-interval. Since counties in these regressions are available over varying sub-intervals, average growth rates are measured in these regressions as sample averages over each available time period. Returning once more to the example, the measures of growth used for Connecticut’s counties in the 1840-1990 regressions are sample averages computed over the interval 1860-1990 using rule 1, etc. The third variation involves alternative measures of initial populations. Let tj,0 denote the earliest inclusion date for county j using one of the four alternative definitions just described. For each choice of tj,0 , we used six alternative measures of initial population size in the decade-by-decade regressions. The first is simply the size of the county’s logged population at date tj,0 . The second is the log of the ratio of the county’s population at date tj,0 relative to the size of the median population among the counties in the sample at date tj,0 . The third is the county’s logged population at the beginning of the decade in question. The final three measures are decile rankings, which we used to capture potential non-linearities in the relationship between initial size and subsequent growth rates. For a growth regression spanning period t through (t+10), with t > tj,0 , the first ranking is based on the county’s time-tj,0 population relative to the initial populations for the counties included in the sample at date t. As t increases and more counties are included in the sample, county j’s decile ranking can change under this method. For example, if initial 11
Here and in the subsequent discussion we use the term ‘county’ to refer to individual counties and groups of counties constructed to have consistent borders over time, as discussed in the data section. 15
population sizes increase systematically over time, county j’s decile ranking may fall using this measure as counties are added to the sample. The second ranking is the decile ranking of county j’s initial population computed relative to the sizes of all of the counties included in the sample at time tj,0 . This ranking is unaffected by the inclusion of additional counties in subsequent periods: once it is assigned, remains fixed. Finally, the third measure ranks county j’s time-t population relative to the time-t populations of the other counties in the sample at that date. The final variation involves the list of additional conditioning variables (besides the logs of initial population size and land area) we include in our regressions. In the decade-by-decade regressions, we considered seven alternatives: natural characteristics; natural characteristics and state dummies; natural characteristics, state dummies, and convergence year; and then in each of these four cases, we also included population growth in the previous decade. Of course, we could not include lagged population growth in the regressions spanning the longer time intervals, so we considered only four alternatives in these regressions. We considered this wide range of variations in the anticipation that they would yield alternative characterizations of the relationship between initial populations and subsequent growth rates. With the exception of the time horizons we considered, this turned out not to be the case: conditional on time horizon, our results are remarkably consistent across specifications. VIii. Decade-by-decade regression results. We begin by discussing the decade-by-decade growth regressions. Since we considered a large number of alternative regression specifications, and since our results are so robust across specifications, we report only a representative set of results. Our full set of results is available upon request. Regarding the choice of starting dates tj,0 for each county j, our main focus is on results obtained using the “ML estimate + one standard error” rule. This is primarily due to the fact that when we include convergence year as an explanatory variable in these regressions, its coefficient is always statistically insignificant; this is not the case in using the estimated convergence date rule. Although results regarding convergence/divergence are largely unaffected by the use of alternative starting dates (as we shall demonstrate), this choice strikes a good balance between the competing goals of excluding frontier effects from the analysis, and examining growth over long time horizons. Table 4 presents five sets of regression results obtained using this starting-date rule. The first three sets were obtained using logged populations at time of convergence to steady state (tj,0 ) as initial populations. The first set was obtained using land area, lagged growth, and the set of natural characteristics as additional conditioning variables. Hereafter, we will refer to this as our baseline regression specification. Note that the coefficient on lagged growth is statistically significant at the 1%
16
level in each decade (all standard errors used to judge significance are heteroskedastic -consistent, following White, 1980). This is true for every alternative regression scheme we considered; thus we focus exclusively on results obtained by including lagged growth in this discussion. (Remarkably, inferences regarding convergence/divergence are largely invariant to the exclusion of lagged growth as a regressor.) This coefficient indicates the proportional influence of an innovation to population growth realized in the preceding decade on growth in the current decade. The coefficient is estimated to be less than 1/3 in only two decades (0.32 in 1920 and 0.157 in 1930); it exceeds 0.5 in four decades; and is particularly large in the post-1940 decades, where its average estimated value is 0.56. Regarding the relationship between initial population and subsequent growth, there is a general but sporadic tendency towards convergence in the pre-1940 data. We obtain a negative coefficient estimate in five of the nine decades spanning 1850-1940; however, the coefficient is significant at the 10% level in only three of these five cases (1850, 1870 and 1930). Moreover, the coefficient is estimated to be positive and significant in 1900 and 1910. A much clearer pattern of divergence is evident in the post-1940 data, although the pattern was distinctly interrupted in the 1970s, reflecting the widely documented deconcentration of population that occurred during this decade (e.g., see Beale, 1977). With the exception of the 1970s, we obtain positive and significant estimates in each post-1940 decade, with values ranging from 0.007 in 1960 to 0.034 in 1940. Note that, even as late as 1980, population growth is significantly influenced by initial populations established as early as 1840. Regarding the quantitative significance of these estimates, consider the estimate of 0.023 obtained for the decade beginning in 1980. Let η denote the coefficient on initial logged population, and gj the annual growth rate of county j. Then controlling for all other measured factors, the difference between annual population growth rates across counties j and i associated with the difference in their initial populations (L) is given by (gj –gi ) = (η/10)ln(Lj,0 /Li,0 ), where η is divided by 10 to convert from decade to annual growth rates. In the 1980 regression sample, the logged difference between initial populations in the 90th -percentile and median county (ranked by initial population size) is 1.03, implying a difference in annual growth rates of 0.24 percentage points. If this difference were sustained indefinitely, the initial difference in populations in these counties would double in 289 years. Likewise, the difference between initial populations in the 90th - and 10th -percentile counties is 2.36 in the 1980 sample, implying a difference in annual growth rates of 0.54 percentage points and a years-to-double figure of 128 years. The next set of regression results in Table 4 was obtained by dropping the natural characteristics from the baseline specification, so land area, initial population, and lagged population growth are the only conditioning variables. This has three notable effects: the negative but insignificant estimate of η
17
obtained in 1920 roughly quadruples in absolute value, becoming negative and significant at the 5% level; the negative and significant estimate of η obtained in 1930 becomes positive but insignificant; and the positive and significant estimate of η obtained in 1900 becomes insignificant. The third set of results was obtained by adding state dummies to the baseline specification, so inferences regarding convergence/divergence are now interpreted as occurring within states. These results are remarkably similar to those obtained in the baseline regression: the decade-by-decade pattern of significance is identical across specifications, and η changes signs only in 1880 (from positive and insignificant to negative and insignificant). Thus within- and cross-state patterns of convergence/divergence exhibit close correspondence. (As noted, we also added convergence year as an explanatory variable in the baseline specification. Its coefficient is insignificant in all decades, and its inclusion has no impact on the remaining parameter estimates, thus these results are omitted from Table 4.) The fourth and fifth sets of results reported in Table 4 were obtained by modifying the definition of initial population in the baseline specification. In the fourth set, initial population is calculated as the log ratio of initial population at date tj,0 relative to the median population of counties included in the sample at that date. These results are virtually indistinguishable from the baseline regression (although in 1900, η remains positive but becomes insignificant). This is due to the relative stability of median populations over the period in which the large majority of counties were first included in the sample: the maximum logged difference in median populations is 0.23 between 1840-1920. In the fifth set, initial population is defined as the beginning-of-decade population, so this case represents a dramatic redefinition of initial population relative to the baseline case. Here, the general pattern of convergence observed in the pre-war data using the baseline model is slightly weakened. The negative estimate of η obtained in 1930 is no longer significant; and η switches from negative and insignificant to positive and insignificant in 1890. Also, the positive estimates of η obtained in 1860 and 1880 roughly triple in this case, although they remain insignificant. In the post-1940 data, there is one notable difference: the positive and significant estimate of η obtained in 1960 becomes negative and insignificant. Despite these differences, the general pattern of pre-war convergence and post-1940 divergence continues to hold. We now illustrate the influence of alternative choices of starting dates for each state. This is done in Table 5. The first set of results was obtained using the baseline specification, which are included for ease of comparison. In the remaining sets, the conditioning variables are the same as in the baseline regression: the only difference is in the definitions of tj,0 : in the second set, tj,0 is defined as the estimated convergence date rounded up to the nearest decade; the third set adds two standard errors to the estimated convergence date and rounds up to the nearest decade; and the fourth set adds ten years to the estimated convergence date and rounds up to the nearest decade.
18
The alternative choices of dates have virtually no impact on post-1940 inferences: magnitudes and patterns of statistical significance are uniform across choices. There are various differences across choices in the pre-war data; these differences tend to reflect a slightly weaker pattern of pre-war convergence relative to the baseline case. For example, consider the “ML estimate plus two standard error” choice of dates. Here, the estimate of η obtained in 1850 is reduced in absolute value by a factor of five and is no longer statistically significant; the positive estimate obtained in 1860 doubles but remains insignificant; the positive estimate obtained in 1880 triples but remains insignificant; and the negative and insignificant estimate obtained in 1890 becomes positive but insignificant. The major difference between the sample obtained using this choice of dates relative to the baseline model is that it excludes counties in states for which the end of transitional frontier periods is estimated with relative uncertainty in the early decades. This exclusion influences inferences regarding convergence/divergence early in the sample period: while there remains evidence of pre-war convergence in this sample during this period, it is weakened relative to the baseline case. Again, the post-1940 pattern of divergence remains unaffected. We conclude this subsection by reporting estimates obtained only for those counties ranked in the top decile by initial population at the time they were included in the sample. These estimates are reported in Table 6. Given the small number of counties available early in the sample period, the first decade for which we have results is 1870. A striking feature of these results is the general statistical insignificance of η, which is estimated as significant in only four decades: 1950 (η = -0.036); 1960 (-0.02); 1970 (-0.038); and 1980 (0.019). The general insignificance of η estimated for these counties is consistent with Ziph’s law: urban growth rates are independent of initial populations. In turn, the negative estimates of η obtained in the 1940 through 1970 data reflect the general pattern of suburbanization and urban deconcentration documented, e.g., by Chatterjee and Carlino (2001). Regarding quantitative significance, consider the estimate of -0.038 obtained for 1970. In this sample, the logged difference between initial populations in the 90th -percentile and median county is 0.87, implying a difference in annual growth rates of 0.33 percentage points; the difference between initial populations in the 90th - and 10th percentile counties is 1.38 in this sample, implying a difference in annual growth rates of 0.53 percentage points. VIiii. The influence of transitional growth and aggregation. For ease of presentation, we document the influence of transition dynamics and aggregation to the state level using measures of growth obtained using extended sub-periods. (As noted, results obtained on a decade-by-decade basis do not differ qualitatively from the sub-interval analysis presented here, and are available on request.) Given the decade-by-decade results, which indicate a general pattern of convergence prior to 1900 or 1940 and a subsequent pattern of divergence, we considered four subperiods (in addition to the entire span of our sample, 1840-1990): 1840-1900, 1900-1990, 1840-1940,
19
1940-1990. We measured growth as the decade-rate average over the relevant time span, so that estimates of η are directly comparable with those reported in the decade-by-decade regressions. To begin, we report results obtained using the baseline specification; these are given in the top row of Table 7. These results closely resemble those obtained in the decade-by-decade regressions. Over 1840-1990, η is estimated as negative and insignificant. But it is negative and significant at the 1% level in the 1840-1900 and 1840-1940 subsamples (-0.103 and -0.036); and positive and significant at the 1% level in the 1900-1990 and 1940-1990 subsamples (0.007 and 0.021). Regarding quantitative significance, consider the estimate of 0.021 obtained for the 1940-1990 subperiod. In this sample, the logged difference between initial populations in the 90th -percentile and median county is once again 1.03, implying a difference in annual growth rates of 0.22 percentage points, and a year-to-double figure of 315 years. And the difference between initial populations in the 90th - and 10th percentile counties is 2.33 in this sample, implying a difference in annual growth rates of 0.49 percentage points and a years-to-double figure of 141 years. Next, we demonstrate the impact of failing to control for periods of frontier transitional growth. This is done by redefining tj,0 as the first date at which the census was conducted for county j. Results obtained using this redefinition are reported in the second set of regressions in Table 7. Over 1840-1990, η is estimated as –0.039 (compared with –0.003 in the baseline case), and is significant at the 1% level. Through 1940 there is also a much stronger tendency towards convergence when frontier effect are not excluded: η is estimated as –0.114 over 1840-1900 (compared with –0.103 in the baseline case), and is estimated as –0.062 over the 1840-1940 sub-period (compared with –0.036 in the baseline case). In the post-1940 period the strong evidence of divergence disappears when the frontier effects are not excluded: η is estimated as –0.004 over the 1900-1990 period, indicating convergence (though the coefficient is significantly insignificant), and 0.001 over the 1940-1990 period, indicating divergence (though the coefficient is very small relative to the baseline estimates and significantly insignificant). Thus controlling for frontier effects has a substantial influence on the analysis. Next, we demonstrate the impact of aggregating to the state level. Results obtained using statelevel population growth given the exclusion of frontier transitional behavior (i.e., using the estimated initial steady state dates employed in the baseline model) are reported in the third set of regressions in Table 7. These contrast sharply with the county-level regressions. Over the full time span, η is estimated as –0.037, which is significant at the 10% level. Prior to 1900 and 1940, there is only a weak tendency towards convergence: η is negative but insignificant in these regressions. In the 1900–1990 and 1940– 1990 regressions the tendency towards convergence is stronger: η is estimated as –0.041 and –0.047 in these cases, respectively. Regarding quantitative signific ance, the estimate of –0.047 implies a
20
differential growth rate of 0.44 percentage points among states whose logged initial populations differ by one standard deviation (the standard deviation of logged initial populations at the state level is 0.94). Thus, while post-war divergence is clearly evident among county-level populations, state-level populations show a strong tendency towards convergence over the same time period. At least in this context, the level of aggregation thus plays a critical role in influencing inferences regarding convergence/divergence. VIiv. Decile breakdowns Table 7 presents two additional sets of regressions. The first additional set (the fourth overall) was obtained by replacing initial populations with decile rankings of initial populations in the baseline case. We made this replacement in all of the decade-by-decade regressions, but report only those obtained for the longer sub-periods because once again they are broadly reflective of our general findings. Besides the coefficient estimates reported in Table 7, we also plot the coefficient estimates and their 95% confidence intervals in Figure 7. The omitted dummy in these regressions is that for the lowest-decile counties. Consider first the dummies estimated for the full sample (Figure 7a). Each dummy is estimated as negative and significant, indicating significantly more rapid growth in lowest-decile counties over the full sample. However, note that the estimated dummies increase roughly monotonically beginning at the median of the sample, indicating relatively rapid growth among counties with initial populations in the upper tail of the distribution relative to those in the middle of the distribution. In particular, note that the median-decile dummy exceeds the 9th -decile dummy in absolute value by a factor of nearly 5. Similar patterns are evident in the 1840-1940 and 1900-1990 sub-periods. In contrast, the 1840-1900 dummies fall roughly monotonically from the 1st -8th deciles, then rise from the 8th to the 9th . And the 1940-1990 dummies rise roughly monotonically from the 1st -7th deciles, and are flat from the 7th -9th deciles. So even though there is an overall tendency towards convergence early in the sample period, counties with relatively large initial populations tended to grow more rapidly than counties with median-level populations even during this period. Coupled with the more universal pattern of divergence observed in the post-1940 data, the overall tendency towards divergence is clearly evident. The final set of regressions in Table 7 reports results obtained for top-decile counties. Results in this case turn out to differ from those obtained on a decade-by-decade basis, thus the two sets of results warrant comparison. In contrast to the generally insignificant estimates of η obtained for top-decile counties in the decade-by-decade regressions early in the sample period, there is a discernable pattern of divergence among these counties prior to 1900, and it is quite distinct: η is estimated as 0.069, whic h is significant at the 1% level. This difference is due to two factors. First, there are a larger number of available counties over this sub-period than in the decade-by-decade regressions, thus η is estimated with
21
greater precision (recall that this is the case because if a county was not available prior to, say, 1880, it was still included in the 1840-1900 sub-sample – its average growth rate was calculated only between 1880-1900). Second, behavior during the 1840s and 1850s is reflected in the 1840-1900 and 1840-1940 subsamples, but not in the decade-by-decade regressions. The pattern of post-1940 convergence among these counties observed in the decade-by-decade regressions remains evident: η is estimated as -0.038, and is significant at the 1% level between 1940-1990. Vv. Discussion There are many potentially complementary factors that may account for the pattern of population divergence we have documented. While it is not possible to pinpoint the relative importance of each of these factors, it is nevertheless useful to consider their potential role in influencing post-1940 divergence. One factor concerns the steady decline of the farm population, which has been driven in part by technological advances that have reduced labor intensity in the agriculture industry. While this phenomenon is not isolated to the post-1940 period, it is relatively distinct during this period. Census data indicate that, as a percentage of the total population, farm population fell by nearly 21 percentage points (from 43.8% to 23.2%) between 1880 – 1940; it fell by an additional 21 percentage points to 2.2% between 1940 – 1990. These figures imply that the pre-1940 gap between the growth rates of the farm population and the total population averaged 1.06 percentage points, while the post-1940 gap averaged 4.9 percentage points. This post-1940 acceleration of the relative decline in the farm population is thus a potential contributing factor to the aggregate pattern of post-1940 divergence. But while the most direct influence of this post-1940 acceleration is on the growth behavior of low-decile counties, its implications for the aggregate pattern of divergence is less obvious. Indeed, as the decile -dummy parameters in Figure 7a indicate, post-1940 population growth increases roughly monotonically with decile rankings, so divergence is not merely due to stagnant growth among low-decile counties. Another potentially important and related factor concerns the migration of African Americans from the relatively rural south to the relatively urban north. Once again, this phenomenon is not merely isolated to the post-1940 period, and in fact, census data indicate that in this case the phenomenon is most distinct in the pre-1940 period. Specifically, the growth rate of the urban African-American population outstripped that of the African-American population as a whole by 2.2 percentage points in the pre-1940 period, and by 1.7 percentage points in the post-1940 period. A third issue relates to the construction of our sample. Specifically, the sample of counties included in our analysis changes as time passes and additional states achieve their steady state growth trajectories. For example, in the regressions reported in Table 7, the 159 counties in Florida, Idaho, Nevada, and New Mexico are included in the post-1940 regressions but not in the pre-1940 regressions
22
because these states did not reach their estimated steady state growth trajectories until 1940 or 1950. To determine the influence of this change in samples on our results, we re-estimated the post-1940 regression by including only those counties included in the pre-1940 regressions. The resulting estimate of η is virtually unchanged: it becomes 0.022, while the previous estimate was 0.021. There are other potentially important contributors to the observed patterns of population growth that we have not explored. These include the effects of wars (including the Civil War and reconstruction, as well as the mobilization associated with the first and second world wars); the role of industrial shifts in addition to the decline of the population dedicated to farming; the introduction of the interstate highway system; etc. A comprehensive examination of these and related factors is beyond the scope of this paper, but certainly seems like a promising topic for future research. Finally, agglomeration economies may have been important in generating the pattern of population divergence we have identified, but it is not possible to isolate their role. Nevertheless, the remarkable persistence of initial population patterns in accounting for subsequent patterns of population growth is supportive of the prominent theoretical role that has been assigned to agglomeration economies in accounting for economic growth. Of course, initial populations alone do not account for the patterns of population growth evident in our sample. In the following section, we examine the relationship between growth and the fixed county characteristics we conditioned on in examining convergence/divergence. VII. Fixed Regional Characteristics and Growth. Table 8 reports estimated effects of natural characteristics on growth for the pre-1940 and post1940 periods. For the post-1940 period, we report coefficient estimates obtained using two samples of counties: all counties, and only those counties that are also in the pre-1940 sample (that is, excluding counties in Florida, Idaho, Nevada, and New Mexico). These estimates were obtained jointly with the estimates of η reported in Table 7. Mean values of the natural characteristics for each sample are reported in Columns 1 and 2, and the coefficient estimates are reported in Columns 3, 4 and 5. Columns 6 and 7 report the estimated effect of a one-standard deviation increase in each continuous variable, and a 0-1 change in each of the discrete variables, both for the pre-1940 regressions and the post-1940 regressions based on the pre-1940 sample. Since the natural characteristics of a county do not change over time, the difference in means between the pre- and post-1940 samples is accounted for by the 159 counties in Florida, Idaho, Nevada, and New Mexico, which have merge dates in 1940 and 1950. The addition of Florida accounts for the higher share of counties with a coastline in the post-1940 sample, while the addition of the other states accounts for the higher share of mountain counties and other
23
minerals. Similarly, the shift in the composition of states accounts for the lower rainfall and heatingdegree days, and higher cooling-degree days in the 1940-1990 sample. Turning to the coefficient estimates in Columns 3 and 5, over the full time period populations were drawn to places with access to water transportation systems (rivers, oceans), and areas with more temperate climates, and away from coal deposits but toward areas with iron and other minerals. Focusing on the parameter estimates based on the pre-1940 sample (Columns 3 and 5), there are several striking contrasts between the estimates for the pre- and post-1940 periods. First, though access to water transportation networks (particularly as measured by locations near oceans and rivers) was an important source of growth in both periods, contrary to our expectations the estimated effects of both are considerably larger in the post-1940 period. (Rappaport and Sachs, 2001, provide more detailed evidence regarding this tendency.) The estimated coefficients indicate that other things equal, counties located on rivers experienced a 2.3 percentage point per decade growth advantage in the post-1940 period, compared with a 1.3 percentage point advantage in the pre-war period. For counties with coastal locations the change is even more dramatic. Pre-1940, coastal locations experienced a 1.9 percentage point per decade growth advantage; post-1940, they experienced a 7.4 percentage point advantage. Locations at the confluence of two waterways did not have any particular growth advantage in either period. Mountains, which may impede transportation, had a distinct growth disadvantage in the early period that was overcome by the post-1940 period. The importance of these measures of access to transportation networks probably extends beyond their roles of facilitating the transport of people and goods. Information also tends to flow along these waterways, and so our estimates likely reflect the influence of the exchange of ideas as well as the exchange of commodities (Sokoloff, 1988; Simon and Nardinelli, 1998). Consistent with Wright (1990) we find that mineral resource endowments influenced growth. This is particularly true in the latter period, when growth rates were significantly higher in counties with iron ore and other mineral deposits (though lower in coal-mining counties). Growth rates were also related to weather: counties with less rain and relatively moderate temperatures grew more rapidly than counties with less-desirable weather. Finally, counter to our expectations, the estimated growth advantage of locations with less extreme climates did not decline between the pre- and post–1940 periods. In fact, the point estimates indicate an increase in the attractiveness of locations with temperate climates after 1940, despite the subsequent widespread availability of air conditioning. VIII.
Conclusion. We have studied regional patterns of population growth in the U.S. at the state and county level.
State-level populations exhibit consistent patterns of transitional growth over roughly two-to six-decade
24
periods surrounding their admission to the union, followed by long periods of relatively steady log-linear growth. County-level populations exhibit an initial general tendency towards population convergence lasting roughly through the 1800s, which then becomes reversed: particularly in the post-1940 period, county populations have diverged. Relatedly, initial population levels have highly persistent explanatory power in accounting for subsequent rates of population growth. For example, initial populations established as early as 1840 exhibit positive and significant (statistically and quantitatively) relationships with population growth measured between 1980 and 1990. Two features of our analysis played an important role in revealing the pattern of divergence we have documented. The first is the elimination of the influence of transitional frontier dynamics from the analysis. This is important because in early stages of settlement, regional populations tended to follow a pattern of explosive growth; if this behavior is not isolated, we found that it masks subsequent steady state differences in regional patterns of growth. The second feature is the focus on county-level as opposed to state-level population behavior. If agglomeration economies are operational or clearly evident only among a relatively small number of heavily concentrated local economies within a given state, then the influence of these activities may be masked by focusing on state-level behavior. We found this to be the case in the post-war U.S.: while state-level populations exhibit a tendency towards convergence, county-level populations exhibit a tendency towards divergence.
25
References Barro, Robert J. and Sala -i-Martin, Xavier, 1991. “Convergence across States and Regions,” Brookings Papers on Economic Activity, no. 1, pp. 107-82. Barro, Robert J. and Sala -i-Martin, Xavier, 1992. “Convergence,” Journal of Political Economy, vol. 100, no. 2 (April), pp. 223-51. Barro, Robert J. and Sala -i-Martin, Xavier, 1995. Economic Growth, McGraw-Hill: New York. Baumol, William J., 1986. “Productivity Growth, Convergence, and Welfare: What the Long-Run Data Show,” American Economic Review, vol. 76, no. 5 (December), pp. 1072-85. Beale, C. 1977. “The recent shift of United States Population to Nonmetropolitan Areas, 1970-75,” International Regional Science Review, vol. 2, pp. 113-122. Beeson, Patricia E., DeJong, David N., and Troesken, Werner, 2001. “Population Growth in U.S. Counties: 1840-1950,” Regional Science and Urban Economics, forthcoming.. Blanchard, Olivier J., and Katz, Lawrence F., 1992. “Regional Evolutions,” Brookings Papers on Economic Activity, vol. 1, pp. 1-76. Brock, William A. and Durlauf, Steven, 2000. “Growth Economics and Reality,” Working Paper, University of Wisconsin. Carlino, Gerald A. and Mills, Edwin. 1987. “The Determinants of County Growth,” Journal of Regional Science, vol. 27, no. 1, pp. 39-54. Chatterjee, Satyajit and Carlino, Gerald, 2001. “Aggregate Employment Growth and the Deconcentration of Metropolitan Employment,” Journal of Monetary Economics, forthcoming. DeLong, J. Bradford, 1988. “Productivity Growth, Convergence, and Welfare: Comment,” American Economic Review, vol. 78, no. 5 (December), pp. 1195-99. Durlauf, Steven N. and Quah, Danny T., 1999. “The New Empirics of Economic Growth,” Handbook of Macroeconomics, John Taylor and Michael Woodford, eds. Elsevier: New York, pp. 235-308. Gabaix, Xavier, 1999. “Zipf’s Law for Cities: An Explanation,” The Quarterly Journal of Economics, vol. 113, no. 3 (August), pp. 739-767. Gibrat, R. 1931. Les Inegalites Economiques. Paris: Librairie du Recueil. Glaeser, Edward L., 1999. “Essays on Urban Growth,” Working Paper, Harvard University. Glaeser, Edward L., Scheinkman, Jose A., and Shleifer, Adrei. 1995. “Economic Growth in a CrossSection of Cities,” Journal of Monetary Economic, vol. 36, pp. 117-43. Henderson, J. Vernon, 1987. “General Equilibrium Modeling of Systems of Cities,” Handbook of Regional and Urban Economics, Volume II: Urban Economics, E.S. Mills, ed. Elsevier: New York, pp. 927-956. 26
Horan, Patrick M., and Hargis, Peggy G., 1995. County Longitudinal Template, 1840-1990 [Computer file]. ICPSR version. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor]. Inter-university Consortium for Political and Social Research. Historical, Demographic, Economic, and Social Data: the United States, 1790-1970 [Computer file]. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [producer and distributor], 1978. Jacobs, Jane, 1969. The Economy of Cities. New York: Random House. Krugman, Paul, 1991. Geography and Trade. Cambridge, Mass.: MIT Press. Marshall, Alfred, 1920. Principles of Economics. London: Macmillian. Mills, E.S., 1967, “An Aggregative Model of Resource Allocation in a Metropolitan Area,” American Economic Review, 57, pp. 197-210. Quah, Danny, 1993. “Empirical Cross-Section Dynamics in Economic Growth,” European Economic Review, 37 (2/3), pp. 426-434. Quigley, John M., 1998. “Urban Diversity and Economic Growth,” Journal of Economic Perspectives, vol. 12, no. 2 (Spring), pp. 127-138. Rappaport, Jordan 1998. “Local Economic Growth,” Harvard University Working Paper. Rappaport, Jordan, 2000. “Why Are Population Flows so Persistent?” Working Paper, Federal Reserve Bank of Kansas City. Rappaport, Jordan, and Sachs, Jeffrey, 2001. “The U.S. as a Costal Nation,” Federal Reserve Bank of Kansas City Working Paper. Simon, Curtis, and Nardinelli, Clark, 1998. “The Rise of American Cities, 1880-1980," Clemson University Working Paper. Sokoloff, Kenneth. 1988. “Inventive Activity in Early Industrial America: Evidence from Patent Records, 1790-1846,” Journal of Economic History, vol. 48, pp. 813-50. Stumpf, Koleman, and Rhode, Paul, 2000. “A Historical Test of the Tiebout Hypothesis: Local Heterogeneity from 1850 to 1990, Working Paper, University of North Carolina. White, H., 1980. “A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity,” Econometrica, vol. 48, pp. 817-838. Wright, Gavin. 1990. "The Origins of American Industrial Success, 1879-1940," American Economic Review, vol. 80, no. 4 (September), pp. 651-68. Zipf, G., 1949. Human Behavior and the Principle of Last Effort. Addison Wesley: Cambridge, MA.
27
Table 1: Maximum Likelihood Estimates of State-Level Transition Dynamics *
State
Region
Data Range
γ - y0
(1) CN
(2) 1
(3) 1790 - 1990
MA
1
1790 - 1920
ME
1
1790 - 1990
NH
1
1790 - 1950
RI
1
1790 - 1920
VT
1
1790 - 1950
NJ
2
1790 - 1930
NY
2
1790 - 1990
PA
2
1790 - 1930
IL
3
1810 - 1990
IN
3
1800 - 1990
MI
3
1820 - 1990
OH
3
1800 - 1990
WI
3
1840 - 1990
(4) -0.445 (0.086) -0.257 (0.061) 1.444 (0.05) 0.417 (0.03) -0.586 (0.042) 1.138 (0.036) -0.431 (0.094) 1.677 (0.169) 0.595 (0.078) 4.847 (0.152) 4.773 (0.088) 4.154 (0.125) 3.127 (0.11) 3.416 (0.111)
gss = 10δ (%) (5) 1.595 (0.066) 1.975 (0.036) 0.519 (0.082) 0.571 (0.026) 2.171 (0.044) 0.222 (0.031) 2.458 (0.073) 1.192 (0.096) 1.826 (0.114) 1.202 (0.078) 1.152 (0.115) 1.789 (0.069) 1.338 (0.108) 1.175 (0.087)
ρ
t*
b
c
(6) 0.664 (0.195) 0.393* (0.591) 0.649 (0.188) 0.310* (0.263) 0.100* (0.15) 0.174* (0.224) 0.472* (0.319) 0.868 (0.103) 0.739 (0.182) 0.509 (0.213) 0.117* (0.227) 0.004* (0.06) 0.503 (0.281) 0.259* (0.29)
(7) 62 (12) 46 (17) 67 (3) 41 (6) 57 (6) 38 (3) 56 (13) 78 (7) 75 (0) 71 (3) 57 (2) 55 (3) 41 (3) 30 (4)
(8) 0.017* (0.028) 0.085 (0.042) 0.480 (0.017) 0.260 (0.026) 0.013* (0.016) 0.623 (0.039) 0.092 (0.032) 0.549 (0.037) 0.341 (0.014) 1.487 (0.047) 1.796 (0.051) 1.683 (0.066) 1.647 (0.101) 2.394 (0.238)
(9) 0.011 (0.004) 0.012* (0.009) -0.032 (0.002) -0.025 (0.007) 0.018 (0.003) -0.079 (0.011) 0.014 (0.006) -0.028 (0.004) -0.011 (0.001) -0.096 (0.007) -0.148 (0.009) -0.136 (0.013) -0.183 (0.026) -0.379 (0.084)
28
Halflife of γ - y0 (10) 18 (3.598) 13 (4.942) 20 (0.868) 12 (1.803) 17 (1.788) 11 (0.861) 16 (3.81) 23 (2.135) 22 (0.016) 21 (0.953) 17 (0.607) 16 (0.886) 12 (0.944) 9 (1.056)
Merge Date (11) 1852 (12) 1836 (17) 1857 (3) 1831 (6) 1847 (6) 1828 (3) 1846 (13) 1868 (7) 1865 (0) 1881 (3) 1857 (2) 1875 (3) 1841 (3) 1870 (4)
gavg (%) (12) 1.313
H0 : gss = gavg
1.785
5.28
1.271
9.17
0.827
9.86
1.668
11.44
0.930
22.82
2.206
3.45
1.984
8.24
2.215
3.41
3.811
33.44
3.594
21.24
4.082
33.23
2.887
14.34
3.374
25.28
(13) 4.26
Table 1, continued: Maximum Likelihood Estimates of State-Level Transition Dynamics *
State
Region
Data Range
γ - y0
(1) IA
(2) 4
(3) 1840 - 1990
KS
4
1860 - 1990
MN
4
1850 - 1990
MO
4
1810 - 1990
NB
4
1860 - 1990
ND
4
1870 - 1990
SD
4
1870 - 1990
DE
5
1790 - 1990
FL
5
1830 - 1990
GA
5
1790 - 1990
MD
5
1790 - 1990
NC
5
1790 - 1990
SC
5
1790 - 1990
VA
5
1790 - 1940
(4) 3.582 (0.074) 2.470 (0.037) 4.875 (0.183) 4.408 (0.064) 3.499 (0.044) 5.234 (0.261) 3.342 (0.191) -0.369 (0.102) 0.286 (0.144) 1.666 (0.125) -0.331 (0.087) -0.061* (0.06) 0.303 (0.05) -0.050* (0.071)
gss = 10δ (%) (5) 0.454 (0.107) 0.508 (0.070) 1.318 (0.043) 0.643 (0.196) 0.405 (0.049) 0.551 (0.051) 0.688 (0.287) 1.373 (0.199) 3.506 (0.087) 1.346 (0.279) 1.500 (0.118) 1.468 (0.086) 1.168 (0.053) 0.933 (0.117)
ρ
t*
b
c
(6) 0.358* (0.282) 0.017* (0.069) 0.120* (0.256) 0.011* (0.051) 0.082* (0.21) 0.473* (0.348) 0.733 (0.232) 0.662 (0.155) 0.572 (0.303) 0.670 (0.16) 0.683 (0.149) 0.303* (0.203) 0.457 (0.188) 0.479 (0.209)
(7) 42 (2) 35 (1) 30 (3) 81 (2) 40 (1) 30 (3) 26 (1) 70 (17) 50* (65) 72 (7) 63 (15) 90 (49) 21 (8) 80 (5)
(8) 1.743 (0.057) 1.467 (0.044) 3.376 (0.3) 1.151 (0.014) 1.791 (0.044) 3.512 (0.214) 2.651 (0.155) 0.031* (0.027) 0.465 (0.116) 0.600 (0.036) 0.044* (0.027) 0.133 (0.01) 0.408 (0.104) 0.081 (0.012)
(9) -0.201 (0.014) -0.203 (0.013) -0.540 (0.105) -0.067 (0.002) -0.219 (0.011) -0.571 (0.079) -0.499 (0.051) 0.008 (0.004) -0.011* (0.026) -0.032 (0.005) 0.008 (0.004) 0.001* (0.001) -0.070* (0.05) 0.001* (0.001)
29
Halflife of γ - y0 (10) 12 (0.498) 10 (0.355) 9 (0.944) 24 (0.457) 12 (0.336) 9 (0.758) 8 (0.412) 20 (5.057) 15* (19.1) 21 (2.088) 18 (4.326) 26 (14.325) 6 (2.282) 23 (1.365)
Merge Date (11) 1882 (2) 1895 (1) 1880 (3) 1891 (2) 1900 (1) 1900 (3) 1896 (1) 1860 (17) 1880 (65) 1862 (7) 1853 (15) 1880 (49) 1811 (8) 1870 (5)
gavg (%) (12) 2.777
H0 : gss = gavg
2.416
27.25
4.700
78.65
3.080
12.44
3.079
54.57
4.806
83.43
3.384
9.39
1.211
0.81*
3.695
2.18
2.181
2.99
1.352
1.25*
1.410
0.67*
1.319
2.85
0.902
0.26*
(13) 21.71
Table 1, continued: Maximum Likelihood Estimates of State-Level Transition Dynamics *
State
Region
Data Range
γ - y0
(1) WV
(2) 5
(3) 1790 - 1930
AL
6
1800 - 1990
KY
6
1790 - 1990
MS
6
1800 - 1990
TN
6
1790 - 1990
AR
7
1810 - 1990
LA
7
1810 - 1990
OK
7
1890 - 1990
TX
7
1850 - 1990
AZ
8
1870 - 1990
CO
8
1870 - 1990
ID
8
1870 - 1990
MT
8
1880 - 1990
NM
8
1870 - 1990
(4) 0.324 (0.058) 6.117 (0.108) 1.738 (0.126) 4.309 (0.162) 2.573 (0.075) 5.908 (0.362) 1.523 (0.065) 1.795 (0.079) 1.682 (0.075) 1.471 (0.076) 2.016 (0.084) 2.699 (0.1) 2.167 (0.082) 0.311 (0.088)
gss = 10δ (%) (5) 2.257 (0.044) 1.250 (0.040) 1.129 (0.078) 0.831 (0.066) 1.202 (0.102) 1.134 (0.063) 1.445 (0.117) 0.693 (0.053) 1.935 (0.056) 3.710 (0.097) 2.006 (0.105) 1.242 (0.115) 0.816 (0.110) 2.116 (0.328)
ρ
t*
b
c
(6) 0.202* (0.252) 0.032* (0.202) 0.922 (0.064) 0.372* (0.231) 0.670 (0.174) 0.425 (0.229) 0.174* (0.274) 0.347* (0.306) 0.004* (0.033) 0.244* (0.252) 0.448 (0.251) 0.000* (0.018) 0.000* (0.006) 0.001* (0.015)
(7) 71 (14) 45 (2) 30 (2) 72 (4) 48 (2) 60 (7) 61 (5) 27 (2) 48 (4) 22 (3) 22 (2) 59 (3) 34 (3) 64 (15)
(8) 0.318 (0.012) 2.870 (0.099) 1.269 (0.078) 1.275 (0.052) 1.198 (0.04) 2.069 (0.161) 0.641 (0.03) 1.378 (0.097) 0.892 (0.047) 1.689 (0.149) 2.027 (0.121) 1.042 (0.03) 1.342 (0.081) 0.309 (0.018)
(9) -0.007 (0.002) -0.308 (0.023) -0.192 (0.024) -0.082 (0.008) -0.113 (0.008) -0.162 (0.029) -0.040 (0.005) -0.238 (0.036) -0.073 (0.01) -0.295 (0.067) -0.414 (0.055) -0.078 (0.005) -0.183 (0.025) -0.008 (0.003)
30
Halflife of γ - y0 (10) 21 (4.021) 13 (0.539) 9 (0.65) 21 (1.251) 14 (0.561) 18 (1.921) 18 (1.332) 8 (0.648) 14 (1.145) 7 (0.788) 6 (0.467) 17 (0.776) 10 (0.77) 19 (4.381)
Merge Date (11) 1861 (14) 1845 (2) 1820 (2) 1872 (4) 1838 (2) 1870 (7) 1871 (5) 1917 (2) 1898 (4) 1892 (3) 1892 (2) 1929 (3) 1914 (3) 1934 (15)
gavg (%) (12) 2.450
H0 : gss = gavg
4.371
78.01
1.956
10.60
3.039
33.45
2.454
12.28
4.313
50.46
2.225
6.66
2.497
34.04
3.129
21.33
4.920
12.48
3.679
15.93
3.506
19.69
2.745
17.54
2.334
0.67*
(13) 4.38
Table 1, continued: Maximum Likelihood Estimates of State-Level Transition Dynamics *
State
Region
Data Range
γ - y0
(1) NV
(2) 8
(3) 1870 - 1990
UT
8
1850 - 1990
WY
8
1880 - 1990
CA
9
1840 - 1990
OR
9
1850 - 1990
WA
9
1870 - 1990
(4) -1.481 (0.277) 2.049 (0.106) 1.616 (0.083) 3.592 (0.089) 2.551 (0.133) 3.070 (0.115)
gss = 10δ (%) (5) 3.897 (0.101) 2.158 (0.109) 1.391 (0.111) 3.440 (0.095) 2.182 (0.139) 1.875 (0.137
ρ
t*
b
c
(6) 0.298* (0.259) 0.529 (0.239) 0.001* (0.014) 0.433* (0.281) 0.179* (0.249) 0.000* (0.005)
(7) 65 (1) 33 (3) 34 (4) 23 (1) 49 (5) 48 (3)
(8) -0.066* (0.055) 1.460 (0.084) 1.082 (0.084) 3.514 (0.157) 1.270 (0.083) 1.475 (0.061)
(9) 0.035 (0.007) -0.189 (0.026) -0.137 (0.026) -0.699 (0.069) -0.108 (0.018) -0.135 (0.014)
*
Halflife of γ - y0 (10) 19 (0.246) 10 (0.783) 10 (1.066) 7 (0.341) 14 (1.339) 14 (0.831)
Merge Date (11) 1935 (1) 1883 (3) 1914 (4) 1863 (1) 1899 (5) 1918 (3)
gavg (%) (12) 2.785
H0 : gss = gavg
3.610
13.32
2.794
12.64
5.698
23.77
3.905
12.40
4.427
18.63
(13) 11.01
Notes. Region codes are as follows: 1 = New England; 2 = Mid Atlantic; 3 = East North Central; 4 = West North Central; 5 = South Atlantic; 6 = East South Central; 7 = West South Central; 8 = Mountain; 9 = Pacific. The ML estimate of γ is reported in terms of its difference from y0 to indicate the initial displacement of logged population from its corresponding value along the estimated log-linear trajectory; a negative value of (γ - y0 ) denotes convergence of logged population to its log-linear trajectory from above. The parameter gss denotes annual steady state growth implied by the estimated log-linear trajectory; gavg denotes average annual growth computed over the entire sample period. Statistics reported in the final column are t statistics of the null hypothesis H0 : gss = gavg. Standard errors are reported in parentheses; standard errors of functions of {γ, δ, ρ, t* } were computed using the delta method. Asterisks denote insignificance at the 5% significance level.
31
Table 2: Median Starting Population and Growth Rate, by Decade .
Year
Number of Median Merge Median MergeMedian Start-ofStd. Dev. Std. Dev. Obs. Date Date Population Decade Population
Median Decennial Growth Rate
Std. Dev.
1850
90
1840
14,517
(51,046)
17,180
(57,521)
0.069
(0.140)
1860
187
1850
18,177
(46,009)
21,627
(57,052)
0.068
(0.142)
1870
317
1850
17,352
(41,437)
20,805
(55,049)
0.173
(0.116)
1880
575
1860
16,286
(45,395)
22,921
(66,406)
0.090
(0.179)
1890
1,111
1870
15,181
(55,214)
20,304
(82,667)
0.109
(0.156)
1900
1,420
1880
15,574
(58,491)
21,466
(106,588)
0.059
(0.172)
1910
1,760
1880
14,968
(54,875)
20,624
(126,119)
0.026
(0.164)
1920
2,158
1890
14,411
(50,455)
19,351
(138,376)
0.021
(0.221)
1930
2,285
1890
14,496
(49,222)
19,412
(167,801)
0.037
(0.135)
1940
2,449
1890
14,654
(48,922)
20,126
(172,975)
0.005
(0.189)
1950
2,520
1900
14,510
(48,303)
19,729
(199,116)
0.009
(0.200)
1960
2,614
1900
14,519
(49,185)
19,627
(238,743)
0.024
(0.169)
1970
2,620
1900
14,501
(49,136)
19,946
(273,744)
0.110
(0.170)
1980
2,618
1900
14,510
(49,154)
23,481
(290,675)
0.013
(0.145)
32
Table 3: Means of Natural Characteristics, 1860, 1900, 1940, 1980 1860
1900
1940
1980
0.037
0.076
0.062
0.072
(0.190)
(0.265)
(0.242)
(0.258)
River
0.369 (0.484)
0.280 (0.449)
0.218 (0.413)
0.217 (0.412)
Confluence
0.086 (0.280)
0.065 (0.246)
0.050 (0.218)
0.052 (0.221)
Mountain
0.075 (0.264)
0.082 (0.275)
0.106 (0.308)
0.121 (0.326)
Iron Ore
0.166 (0.373)
0.157 (0.364)
0.130 (0.336)
0.127 (0.333)
Coal
0.316 (0.466)
0.354 (0.478)
0.353 (0.478)
0.338 (0.473)
Other Minerals
0.053 (0.226)
0.054 (0.227)
0.072 (0.259)
0.093 (0.291)
Precipitation /1000
4.487 (0.689)
4.094 (0.974)
3.655 (1.276)
3.618 (1.339)
Heating-Degree Days /1000
4.607 (1.338)
5.224 (1.967)
5.109 (2.066)
5.053 (2.141)
Cooling-Degree Days /1000
1.240 (0.485)
1.117 (0.638)
1.230 (0.730)
1.251 (0.784)
Log Growth Rate
0.090 (0.142)
0.089 (0.172)
0.027 (0.189)
0.030 (0.145)
187
1,420
2,449
2,618
Ocean
Number of Counties
33
Table 4: Decade -by-Decade Regressions * Model
Baseline
Initial Population Lagged Growth R-squared
pooled 0.008*** [5.91] 0.424*** [38.18] 0.32
1850 -.096*** [3.39] 0.357*** [3.43] 0.64
1860 0.015 [0.55] 0.448*** [5.73] 0.4
1870 -0.032** [2.44] 0.333*** [7.27] 0.33
1880 0.005 [0.42] 0.510*** [4.53] 0.31
1890 -0.001 [0.13] 0.348*** [12.77] 0.37
1900 0.012* [1.73] 0.486*** [11.04] 0.31
1910 0.023*** [4.57] 0.357*** [12.31] 0.31
1920 -0.004 [0.49] 0.320*** [6.96] 0.19
1930 -0.007* [1.68] 0.157*** [6.32] 0.2
1940 0.034*** [8.37] 0.474*** [7.93] 0.35
1950 0.018*** [4.41] 0.699*** [21.81] 0.53
1960 0.007* [1.87] 0.469*** [22.98] 0.43
1970 -.030*** [9.29] 0.578*** [21.17] 0.46
1980 0.023*** [11.19] 0.589*** [31.90] 0.62
No Natural Characteristics
Initial Population Lagged Growth R-squared
0.008*** [5.64] 0.452*** [39.84] 0.3
-.096*** [3.36] 0.438*** [4.47] 0.52
0.025 [1.22] 0.462*** [7.85] 0.35
-.037*** [3.34] 0.221*** [4.77] 0.18
0.005 [0.53] 0.512*** [5.38] 0.26
-0.007 [1.18] 0.333*** [12.44] 0.34
0.009 [1.49] 0.408*** [9.41] 0.22
0.022*** [5.16] 0.371*** [12.74] 0.3
-0.017** [2.00] 0.377*** [8.03] 0.12
0.002 [0.62] 0.142*** [5.57] 0.05
0.024*** [5.72] 0.532*** [8.93] 0.18
0.014*** [3.94] 0.721*** [24.65] 0.51
0.011*** [3.15] 0.476*** [25.18] 0.38
-.030*** [9.39] 0.630*** [24.12] 0.39
0.020*** [10.01] 0.646*** [37.69] 0.57
Initial Population Lagged Growth R-squared
0.009*** [5.81] 0.397*** [35.66] 0.34
-.112*** [3.38] 0.338*** [3.02] 0.66
0.035 [1.30] 0.486*** [6.16] 0.48
-.029*** [2.69] 0.346*** [7.86] 0.45
-0.01 [0.82] 0.474*** [4.21] 0.36
-0.006 [0.78] 0.329*** [11.04] 0.41
0.021*** [2.97] 0.473*** [10.44] 0.38
0.030*** [5.75] 0.376*** [12.50] 0.4
-0.003 [0.39] 0.317*** [6.70] 0.3
-0.008* [1.90] 0.146*** [6.07] 0.29
0.039*** [8.22] 0.454*** [7.30] 0.41
0.016*** [3.50] 0.673*** [20.70] 0.58
0.011** [2.49] 0.453*** [19.86] 0.49
-.028*** [7.97] 0.544*** [19.81] 0.53
0.020*** [8.79] 0.570*** [29.47] 0.68
Initial Deviation From Median Population
Initial Population Lagged Growth R-squared
0.008*** [5.85] 0.424*** [38.19] 0.32
-.096*** [3.39] 0.357*** [3.43] 0.64
0.035 [1.22] 0.489*** [6.03] 0.41
-0.030** [2.29] 0.335*** [7.31] 0.33
0.003 [0.28] 0.508*** [4.53] 0.31
-0.001 [0.20] 0.347*** [12.74] 0.37
0.011 [1.57] 0.484*** [11.01] 0.31
0.023*** [4.65] 0.358*** [12.34] 0.31
-0.003 [0.46] 0.320*** [6.96] 0.19
-0.006* [1.66] 0.157*** [6.32] 0.2
0.033*** [8.29] 0.473*** [7.92] 0.35
0.018*** [4.36] 0.699*** [21.81] 0.53
0.007* [1.92] 0.469*** [22.99] 0.43
-.030*** [9.30] 0.578*** [21.17] 0.46
0.023*** [11.04] 0.589*** [31.88] 0.62
Beginning-ofDecade Initial Population
Initial Population Lagged Growth R-squared
0.010*** [7.28] 0.408*** [34.54] 0.32
-.096*** [3.39] 0.453*** [4.48] 0.64
0.04 [1.45] 0.451*** [7.55] 0.41
-0.029* [1.91] 0.374*** [8.06] 0.32
0.016 [1.36] 0.501*** [4.49] 0.31
0.001 [0.13] 0.349*** [13.38] 0.37
0.022*** [2.95] 0.467*** [10.83] 0.32
0.039*** [7.19] 0.319*** [10.86] 0.33
-0.003 [0.38] 0.326*** [6.79] 0.19
-0.006 [1.32] 0.166*** [5.72] 0.2
0.054*** [12.55] 0.404*** [7.03] 0.4
0.017*** [4.06] 0.662*** [17.44] 0.53
-0.001 [0.35] 0.479*** [19.29] 0.43
-.038*** [14.01] 0.675*** [21.37] 0.49
0.021*** [13.53] 0.557*** [30.03] 0.63
Observations
22724
90
187
317
575
1111
1420
1760
2158
2285
2449
2520
2614
2620
2618
State Dummies
*
Notes: t statistics are in brackets. *denotes 10% significance, **denotes 5% significance, ***denotes 1% significance.
34
Table 5: Alternative Definitions of Merge Dates* Definition Baseline: ML Estimate Plus One S.E .
ML Estimate
ML Estimate Plus Two S.E.s
ML Estimate Plus 10 Years *
Initial Population
pooled 0.008*** [5.91]
1850 -.096*** [3.39]
1860 0.015 [0.55]
1870 -0.032** [2.44]
1880 0.005 [0.42]
1890 -0.001 [0.13]
1900 0.012* [1.73]
1910 0.023*** [4.57]
1920 -0.004 [0.49]
1930 -0.007* [1.68]
1940 0.034*** [8.37]
1950 0.018*** [4.41]
1960 0.007* [1.87]
1970 -.030*** [9.29]
1980 0.023*** [11.19]
Lagged Growth Observations R-squared
0.424*** [38.18] 22724 0.32
-.357*** [3.43] 90 0.64
0.448*** [5.73] 187 0.4
-.333*** [7.27] 317 0.33
0.510*** [4.53] 575 0.31
0.348*** [12.77] 1111 0.37
0.486*** [11.04] 1420 0.31
0.357*** [12.31] 1760 0.31
0.320*** [6.96] 2158 0.19
0.157*** [6.32] 2285 0.2
0.474*** [7.93] 2449 0.35
0.699*** [21.81] 2520 0.53
0.469*** [22.98] 2614 0.43
0.578*** [21.17] 2620 0.46
0.589*** [31.90] 2618 0.62
Initial Population Lagged Growth Observations R-squared
0.009*** [6.71] 0.405*** [37.94] 23768 0.31
-0.046* [1.87] 0.531*** [5.92] 103 0.6
0.035** [2.00] 0.528*** [10.20] 222 0.48
-.046*** [4.06] 0.306*** [7.12] 359 0.39
-0.007 [0.62] 0.542*** [5.84] 775 0.3
-0.004 [0.65] 0.339*** [12.36] 1102 0.34
0.01 [1.49] 0.466*** [11.16] 1542 0.33
0.017*** [3.79] 0.278*** [11.44] 2196 0.23
-0.007 [1.13] 0.360*** [8.03] 2272 0.21
-0.002 [0.63] 0.150*** [6.48] 2438 0.19
0.031*** [7.67] 0.482*** [8.00] 2507 0.33
0.019*** [4.73] 0.708*** [23.00] 2564 0.53
0.011*** [3.24] 0.463*** [21.48] 2560 0.42
-.028*** [8.61] 0.575*** [20.29] 2565 0.44
0.025*** [11.99] 0.573*** [31.17] 2563 0.6
Initial Population Lagged Growth Observations R-squared
0.008*** [4.79] 0.448*** [36.82] 22788 0.32
-0.019 [0.69] 0.544*** [6.25] 79 0.66
0.031 [1.29] 0.378*** [5.27] 148 0.35
-0.031** [2.47] 0.284*** [5.70] 281 0.28
0.018 [1.54] 0.768*** [7.78] 423 0.38
0.004 [0.56] 0.407*** [7.83] 859 0.32
0.01 [1.03] 0.487*** [11.29] 1206 0.28
0.021*** [4.50] 0.513*** [17.35] 1657 0.38
-0.007 [0.76] 0.340*** [7.83] 2347 0.2
-0.005 [1.27] 0.165*** [6.79] 2393 0.2
0.046*** [10.59] 0.504*** [9.11] 2607 0.36
0.012*** [2.70] 0.727*** [22.94] 2661 0.53
0.009** [2.08] 0.459*** [21.36] 2706 0.4
-.037*** [10.70] 0.585*** [21.30] 2711 0.45
0.026*** [11.78] 0.572*** [31.91] 2710 0.32
Initial Population Lagged Growth Observations R-squared
0.011*** [7.09] 0.415*** [35.62] 21643 0.31
-0.04 [1.14] 0.523*** [6.34] 56 0.7
0.013 [0.58] 0.407*** [6.15] 207 0.37
-.066*** [4.83] 0.183*** [2.92] 210 0.38
-0.005 [0.37] 0.474*** [3.71] 444 0.35
0.017*** [2.61] 0.334*** [11.16] 738 0.36
0.019*** [2.78] 0.473*** [11.35] 1460 0.31
0.023*** [4.57] 0.355*** [12.43] 1802 0.3
-0.002 [0.23] 0.318*** [6.97] 2200 0.19
-0.005 [1.28] 0.165*** [6.38] 2238 0.2
0.036*** [8.61] 0.487*** [8.32] 2395 0.36
0.017*** [4.07] 0.696*** [21.40] 2466 0.53
0.011*** [2.87] 0.464*** [20.54] 2463 0.4
-.030*** [8.97] 0.564*** [19.70] 2467 0.43
0.024*** [11.31] 0.566*** [30.21] 2497 0.58
Notes: t statistics are in brackets. *denotes 10% significance, **denotes 5% significance, ***denotes 1% significance.
35
Table 6: Top-Decile Counties* Regression Model Baseline
TopDecile Counties
*
Initial Population Lagged Growth Observations R-squared
pooled 0.008*** [5.91] 0.424*** [38.18] 22724 0.32
Initial Population Lagged Growth Observations R-squared
-0.011** [2.25] 0.526*** [16.49] 1151 0.49
1850 -.096*** [3.39] 0.357*** [3.43] 90 0.64
1860 0.015 [0.55] 0.448*** [5.73] 187 0.4
1870 -0.032** [2.44] 0.333*** [7.27] 317 0.33
1880 0.005 [0.42] 0.510*** [4.53] 575 0.31
1890 -0.001 [0.13] 0.348*** [12.77] 1111 0.37
1900 0.012* [1.73] 0.486*** [11.04] 1420 0.31
1910 0.023*** [4.57] 0.357*** [12.31] 1760 0.31
1920 -0.004 [0.49] 0.320*** [6.96] 2158 0.19
1930 -0.007* [1.68] 0.157*** [6.32] 2285 0.2
1940 0.034*** [8.37] 0.474*** [7.93] 2449 0.35
1950 0.018*** [4.41] 0.699*** [21.81] 2520 0.53
1960 0.007* [1.87] 0.469*** [22.98] 2614 0.43
1970 -.030*** [9.29] 0.578*** [21.17] 2620 0.46
1980 0.023*** [11.19] 0.589*** [31.90] 2618 0.62
-0.052 [1.13] 0.461*** [3.32] 25 0.87
0.037 [1.52] 0.853*** [4.47] 44 0.7
0.018 [1.42] 0.565*** [10.59] 73 0.75
-0.008 [0.55] 0.527*** [5.52] 86 0.64
0 [0.02] 0.728*** [5.99] 93 0.62
-0.008 [0.35] 0.608*** [3.43] 103 0.43
-0.011 [1.50] 0.198*** [3.92] 105 0.48
-0.01 [0.67] 1.064*** [7.41] 114 0.49
-0.036** [2.20] 0.933*** [7.36] 114 0.59
-0.020** [2.51] 0.455*** [9.21] 123 0.7
-.038*** [4.06] 0.484*** [8.61] 123 0.82
0.019* [1.88] 0.750*** [8.82] 123 0.7
Notes: t statistics are in brackets. *denotes 10% significance, **denotes 5% significance, ***denotes 1% significance.
36
Table 7: Sub-Period Regressions * Model Initial Population Baseline Observations R-squared Transition Effects Not Eliminated
Initial Population Observations R-squared Initial Population
State-level Aggregation
Observations R-squared
Decile 1 Decile 2 Decile 3 Decile 4 Decile Dummies
Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Observations R-squared Initial Population
Top-Decile Counties
*
Observations R-squared
1840-1990 -0.003 [1.08] 2622 0.19
1840-1900 -0.103*** [8.20] 1430 0.32
1900-1990 0.007*** [2.93] 2615 0.21
1840-1940 -0.036*** [8.10] 2449 0.16
1940-1990 0.022*** [8.02] 2608 0.22
-0.039*** [16.02] 1681 0.27
-0.114*** [21.29] 1484 0.43
-0.004 [1.56] 1646 0.26
-0.062*** [19.63] 1674 0.36
0.001 [0.22] 1668 0.24
-0.037* [1.85] 48 0.18
-0.009 [0.64] 30 0.19
-0.041** [2.04] 48 0.21
-0.020 [1.26] 44 0.07
-0.047** [2.35] 48 0.22
-0.053*** [4.69] -0.054*** [5.00] -0.062*** [5.73] -0.069*** [6.39] -0.074*** [6.57] -0.063*** [5.73] -0.043*** [3.82] -0.041*** [3.82] -0.016 [1.42] 2622 0.22
-0.174*** [4.79] -0.196*** [5.27] -0.284*** [7.72] -0.289*** [7.61] -0.329*** [8.61] -0.352*** [9.27] -0.356*** [9.15] -0.393*** [9.73] -0.363*** [8.48] 1430 0.37
-0.038*** [3.73] -0.038*** [3.85] -0.042*** [4.26] -0.038*** [3.82] -0.048*** [4.64] -0.029*** [2.88] -0.005 [0.48] -0.001 [0.07] 0.019* [1.95] 2615 0.24
-0.126*** [7.86] -0.130*** [8.28] -0.172*** [11.55] -0.171*** [11.26] -0.189*** [12.29] -0.185*** [12.36] -0.182*** [11.92] -0.168*** [11.05] -0.137*** [8.60] 2449 0.23
0.000 [0.02] 0.003 [0.29] 0.02 [1.59] 0.013 [1.11] 0.02 [1.59] 0.038*** [3.10] 0.064*** [5.06] 0.062*** [5.40] 0.068*** [5.69] 2608 0.23
-0.001 [0.13] 123 0.42
0.069*** [2.84] 87 0.24
-0.012 [1.11] 122 0.46
0.028* [1.82] 114 0.25
-0.036*** [2.87] 123 0.46
Notes: t statistics are in brackets. *denotes 10% significance, **denotes 5% significance, ***denotes 1% significance.
37
Table 8: Coefficient Estimates, Natural Characteristics * Mean
log Land Area Ocean=1 River=1 Confluence=1 Mountain=1 Iron ore=1 Coal=1 Other minerals=1
Avg. annual rainfall /1000 Avg. annual heating degree days/1000 Avg. annual cooling degree days/ 1000
1940-1990, Merge Merge Date 1940-1990 Merge Date 1940-1990 pre-1940 Date to 1940-1990 to 1940 to 1940 sample 1940 (1) (2) (3) (4) (5) (6) (7) 6.547 6.590 0.046*** 0.000 0.000 0.037 0.000 0.815
0.825
[11.86]
[0.08]
[0.00]
0.062
0.072
0.019
0.139***
0.074***
0.258
0.259
[1.55]
[12.35]
[6.45]
0.218
0.218
0.013*
0.025***
0.023***
0.412
0.413
[1.82]
[3.69]
[3.60]
0.050
0.052
0.008
-0.032**
-0.001
0.221
0.222
[0.59]
[2.37]
[0.04]
0.106
0.119
-0.032***
0.035***
0.006
0.326
0.324
[2.97]
[3.49]
[0.61]
0.130
0.127
0.008
0.017**
0.020**
0.333
0.333
[1.06]
[2.15]
[2.77]
0.353
0.339
-0.023***
-0.043***
-0.035***
0.474
0.473
[4.25]
[8.08]
[7.09]
0.072
0.091
-0.018
0.059***
0.057***
0.291
0.287
[1.51]
[5.53]
[5.23]
3.655
3.623
0.000
-0.008***
-0.012***
1.340
1.337
[0.12]
[2.93]
[4.50]
5.109
5.051
-0.030***
-0.026***
-0.039***
2.144
2.141
[9.25]
[8.76]
[13.08]
1.230
1.251
-0.077***
-0.046***
-0.099***
0.785
0.784
[8.87]
[5.81]
[12.39]
0.386***
0.062
0.220***
[8.79]
[1.49]
[5.44]
2449
2608
2449
Constant Observations
1 std dev. Change, or 0-1 change
Coefficient
2449
2608
0.160 0.220 0.217 R-squared Notes: t-statistics are in brackets * denotes 10% significance; ** denotes 5% significance; *** denotes 1% significance.
38
0.019
0.139
0.013
0.025
0.008
-0.032
-0.032
0.035
0.008
0.017
-0.023
-0.043
-0.018
0.059
0.000
-0.011
-0.064
-0.056
-0.060
-0.036
Figure 1: Log State-Level Populations
Figure 2: Transitional and Steady State Trajectories Legend: CCCCC raw data; _____ fitted log-linear segment; ------- fitted log-quadratic segment
Figure 3: Additional State-Level Population Trajectories Legend: CCCC raw data; ______ fitted log-linear segment; --------- fitted log-quadratic segment
7.5
log population density
6.5
5.5
4.5
3.5
2.5
1.5 1870
1890
1910
1930
1950
1970
1990
year==1880
year==1890
year==1900
year==1910
year==1920
year==1930
year==1940
year==1950
year==1960
year==1970
year==1980
year==1990
0
0
0 -1.8
9.9
-1.8
9.9
-1.8
9.9
-1.8
9.9
1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 < 0.25
0.25 -0.5
0.5 - 1
1-2
Fraction of Mean Density at Start of Decade, 1870 - 1980
Figure 6: Persistence of Population Density Rankings: 1870 Sample
2+
0.15
0.1 0.05
0 1
2
3
4
5
6
7
8
9
8
9
-0.05 -0.1
-0.15 -0.2
-0.25 Decile Rank
Figure 7a: * = 1840-1940; ♦ = 1940-1990; + = 1840-1990 0.1
0 1
2
3
4
5
6
7
-0.1
-0.2
-0.3
-0.4
-0.5 Decile Rank
Figure 7b: * = 1840-1900; ♦ = 1900-1990
Figure 7: 95-Percent Confidence Intervals for Decile Dummies 40
1840
1850
1860
1870
1880
1890
1900
1910
1920
8 6 4 2 0 8 6 4 2 0
8 6 4 2 0 1840 1870 1910 1950 1990
1840 1870 1910 1950 1990
1840 1870 1910 1950 1990
5th, 50th, and 95th percentiles
Figure A1: Population Density Percentiles
