Regional Income Convergence in Sweden, 1911-2003: A Time Series Analysis

Regional Income Convergence in Sweden, 1911-2003: A Time Series Analysis Joseph DeJuan University of Waterloo Joakim Persson Karlstad University Marc Tomljanovich1 Drew University Abstract. The issue of income convergence is important for policy makers’ regional strategies aimed at redistributing funds to poorer regions in a country. We investigate the growth and convergence characteristics of 24 Swedish counties during the period 19112003. Using time series techniques, we find that shocks to relative county per capita incomes are temporary, and that initially poor (rich) counties tend to experience higher (lower) growth rates than the nation as whole. Our findings are consistent with the neoclassical model’s prediction of conditional convergence, and imply that market forces rather than interregional government redistribution are the main drivers behind our results. JEL Classification: C32, E10, O40, R00 Keywords: Regional per-capita income, time series models, β convergence, trend function, serial correlation 1. Introduction Regional income disparities have been a prominent feature of the Swedish economy throughout history. Indeed, some simple statistics reveal that the level of per capita income in the county of Stockholm was at least twice that of the poor northern counties for much of the twentieth century. Moreover, the rank ordering of counties by per capita income has undergone little change over time. There is evidence, however, that income disparities have been shrinking. Research based on the established cross section regression approach of Barro and Sala-i-Martin (1991), and used by Persson (1997), Aronsson, Lundberg and Wikström (2001) and others for Sweden, find a negative relationship between initial per capita income levels and subsequent growth rates across

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Swedish counties, indicating that the initially poorer counties on average grew faster and thereby caught-up with the richer ones, a phenomenon known in the literature as βconvergence. Much of the research on regional income convergence in Sweden is based on cross section approaches. To date, there has been no time series analysis undertaken using historical data on per capita income of Swedish counties spanning over more than 90 years. Yet, such research is worthwhile as it offers insights into how each individual county is growing through time relative to the nation as a whole. Consequently, this paper builds upon and extends previous research by using time series econometric techniques to examine whether per capita incomes of 24 Swedish counties converge to the national average during the period 1911-2003.2 We implement time series tests to determine whether relative county per capita incomes satisfy the two conditions which Carlino and Mills (1993, 1996) argue are both necessary for convergence: (i) shocks to relative county per capita incomes are temporary (that is, stochastic convergence), and (ii) counties having per capita incomes initially above (below) the national average exhibits slower (faster) growth than the nation as a whole (that is, β-convergence). The empirical methodology that we employ stems from the tests for detecting shifts in the trend function of a dynamic time series developed by Vogelsang (1997, 1998), which allow for both serial correlation and trending data and are valid irrespective of whether the data are stationary or contain a unit root. One benefit of these time-series tests over cross section and panel data tests of income convergence is that we can determine not only whether stochastic and β-convergence have been occurring for Swedish counties overall, but also whether each separate county converges or diverges from the other counties. In addition, relative to Persson (1997), this study extends the time period by ten years; to 2003. Our empirical results reveal that per capita income levels of Swedish counties have been converging in both the stochastic and β- sense since 1911. In particular, most of the convergence appears to have occurred during the first half of the twentieth century, and that the estimated rates of convergence were higher during this period. The results also indicate that the estimated degree to which counties converged to the national average depends to some extent on whether the break point of the trend function is treated as known or unknown (that is, endogenous), as well as on the robustness of test statistics with respect to the form and persistence of serial correlation in the errors. Our findings also suggest that government redistribution policies had a minimal impact on income convergence in Sweden. The remainder of the paper is organized as follows. Section 2 describes the longterm evolution of relative per capita income of Swedish counties. Section 3 presents the econometric methodology. Section 4 reports the estimation and results. Section 5 summarizes and concludes. 2. Regional Growth and Convergence in Sweden: A First Look Have regional income disparities in Sweden changed over the period 1911-2003?

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Figure 1 displays relative per capita income (that is, county per capita income relative to the national per capita income) of 24 Swedish counties over time.3 It is clear that per capita incomes differed widely across counties in the early part of the twentieth century. Stockholm, Gothenburg, and Malmohus, which were the three richest counties in 1911, had per capita incomes that were more than 33 percent above the national average. At the other extreme were Vasterbotten, Skaraborg, and Gotland, which had per capita incomes that were more than 46 percent below the average. It is also evident from Figure 1 that differences in per capita income had decreased dramatically over the 92 years after 1911, although the reduction was only moderate between 1911 and 1932. For example, per capita income in Stockholm was 164 percent above the national average in 1911, 121 percent above the average in 1932, and only 21 percent above average in 2003. In the case of Gothenburg, per capita income was 37 percent above average in 1911 and 1932, but only 2 percent above the average in 2003. For Kristianstad, per capita income was 36 percent below average in 1911, 35 percent below in 1932, and only 8 percent below in 2003. For the initially poorest county, Vasterbotten, per capita income was 56 percent below the average in 1911, 46 percent below in 1932, and only 10 percent below in 2003. It thus appears that poor counties made substantial gains in their per capita income level, while rich counties lost some ground over a period of Swedish economic history spanning more than ninety years. Figure 2 displays the cross-sectional standard deviation of relative per capita income across 24 Swedish counties, which we denote σ (for an extensive discussion of the concepts of convergence, see e.g. Barro and Sala-i-Martin, 1991). It is apparent that σ declined from 0.44 in 1911 to 0.34 in 1921, and then was quite stable until 1932. The 1920s was a period of declining relative prices of agricultural products (Myrdal, 1933) that adversely affected the relatively poor counties as their agricultural sectors (for example, as a share of total employment) typically were larger than those of relatively rich counties (see Persson, 1997, footnote 15). In 1933, σ resumed its downtrend, reaching a value of 0.06 in 1980. In 2003, σ was 0.07. Thus, the cross-sectional dispersion of relative per capita income was significantly reduced over the period 19112003, providing evidence of so-called σ-convergence. It is noteworthy that in 2003, per capita incomes of Swedish counties lie within 12 percent of the national average, except for Stockholm which exceeds the average by 21 percent, and the island of Gotland which falls short by 15 percent. Moreover, the dispersion of relative per capita income across counties did not decrease much during the last twenty-six years, which suggests that there are some structural differences between the counties (for example, with respect to human capital), or that more recent economic shocks have kept convergence from progressing further. In the foregoing analysis, we have utilized an income measure which does not account for inter-county differences in prices. One should recognize however that if absolute purchasing power parity does not hold, the levels of real per capita income are mismeasured, which potentially could lead to incorrect inference on convergence (see, for example, Barro and Sala-i-Martin, 1992). In Sweden, the cost of living is lower in

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poor counties than it is in rich counties, which is consistent with cross-country evidence. Persson (1997) reports that the cost of housing in Stockholm was around twice as high or more than in the Southeast or Northern counties for much of the twentieth century. As such, the cost-of-living adjusted income measure tends to raise estimates of per capita income in poor counties relative to an unadjusted income measure, while the opposite tends to be the case for rich counties. Figure 2 includes the cross-sectional standard deviation of adjusted relative per capita income (dotted line). It shows that accounting for regional differences in the cost of living compresses the cross-sectional distribution of relative per capita income such that the adjusted σ is always lower than the unadjusted σ during the period 1911-2003. 3. Econometric Methodology In this section, we describe the trend function tests proposed by Vogelsang (1997, 1998) which can be used to determine whether or not β-convergence has occurred over time among Swedish counties. Suppose that the logarithm of relative per capita income of county i, yit, is generated by a deterministic trend model of the form:

yit =  i   i t + uit

(1)

where i=1, 2, …, 24; t=1, 2, …, T; μ represents the initial level of y, β is the growth rate of relative per capita income, and u is a zero-mean random error process. According to the concept of β-convergence, counties that start out with above-average per capita incomes exhibit slower growth than the national average while counties that start out with below-average per capita incomes exhibit faster growth than the national average. In terms of the parameters of equation (1), β-convergence requires that if μ > 0 then β < 0, and if μ < 0 then β > 0. When u is I(0), it is well-known that the ordinary least squares (OLS) estimators of μ and β are asymptotically equivalent to the generalized least squares estimators and hence, are asymptotically efficient (Grenander and Rosenblatt, 1957). Yet, in practice, u is highly serially correlated and may be a unit root process. In such case, OLS loses its optimality properties and inference on estimates of μ and β is not straightforward in that their test statistics require consistent estimates of the serial correlation parameters of u which, in turn, necessitates an explicit model specification of the u dynamics. To get around these issues, Carlino and Mills (1993, 1996) assumes that u follows an AR(2) model and rewrite y as an autoregressive process. One drawback of this approach, however, is that the AR(2) model may not provide an adequate approximation to the correlation structure of u for all counties and hence, can lead to misspecification and invalid conclusions (see Tomljanovich and Vogelsang, 2002). To conduct valid inference on μ and β, we use a class of statistics proposed by Vogelsang (1997, 1998) which are asymptotically invariant to serial correlation in u and do not require estimation of the serial correlation nuisance parameters. The statistics are also valid whether the error series are I(0) or I(1) and hence, should prove very useful in practice as no unit-

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root pre-test is required of the series. Clearly, this is important as it is by now wellknown that standard unit root or stationarity tests have low power to discriminate between a unit root and a near unit root process in finite samples. The statistics proposed by Vogelsang are based on two regressions that are both estimated by OLS. We define DU1it=1 if tTb and 0 otherwise; DT1it=t if tTb and 0 otherwise. Tb represents the break date, the date of a shift in the parameters of the trend function of yit, t

which can either be considered known a priori or unknown. Let

z it   y ij ; j 1

t

t

t

j 1

j 1

j 1

SDT1it   DT1ij ; SDT2it   DT2ij ; Sit   uij ; the parameters μ1i and μ2i denote the relative per capita incomes of county i at periods 1 and Tb respectively, while β1i and β2i denote the growth rates before and after the break date Tb respectively. The two regressions are as follows:

yit =  1i DU 1it +  1i DT 1it +  2i DU 2it +  2i DT 2it + u it

(2)

z it =  1i DT 1it +  1i SDT 1it +  2i DT 2it +  2i SDT 2it + S it

(3)

β-convergence requires the estimates of μji and βji, j=1, 2 to be different from zero and have opposite signs. Vogelsang provides statistics that can be used to test the significance of the OLS estimates in the y and z regressions. Specifically, let ty and tz denote the t-statistics for testing the null hypothesis that the individual parameters in the y and z regressions are zero. For the y regression, the modified t-statistic is defined as T-½ty, where T is the sample size. For the z regression, the modified t-statistic is t-PST=T-½tzexp(-bJT), where b is a constant. JT denotes the standard Wald statistic normalized by T-1 for testing the joint hypothesis c2=c3=...=c9=0 in the regression: 9

yit =  1i DU 1it +  1i DT 1it +  2i DU 2it +  2i DT 2it +  c j t i + u it

(4)

j= 2

That is, JT=(RSSR-RSSUR)/RSSUR, where RSSR and RSSUR denote the sum of squared residuals obtained from the OLS estimation of (2) and (4) respectively. For a given level of significance, the constant b can be chosen such that t-PST asymptotically has the same critical values for both I(0) or I(1) errors. In effect, the JT modification results in t-tests from the z regression that are robust to I(1) errors. When b is zero, JT has no effect on tPST. b should be set to zero when the errors are known to be I(0) (see Vogelsang, 1997, for details).

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As noted by Vogelsang, the JT modification is not needed in the y regression because when u is I(1), T-½ty has a well-defined asymptotic distribution while when u is I(0), T-½ty converges to zero. Thus, the T-½ty statistic is designed to have power when u is I(1), but remains robust when u is I(0). The asymptotic distributions for the T-½ty and t-PST statistics are nonstandard and depend on whether the break date Tb is known a priori or unknown. If Tb is unknown, then it must be estimated from the data. A commonly used method to identify the unknown break date is to estimate the y regression sequentially for each break year with 10 percent trimming, that is, 0.10T < Tb < 0.90T. For each regression, the Wald statistic normalized by T-1 for testing the joint hypothesis that μ1=μ2 and β1=β2 (that is, the hypothesis that there is no break in the trend function of y) is calculated. The estimated break date is the value of Tb for which the normalized Wald statistic is maximized. Vogelsang (1997, 1998) tabulates the 5 percent and 10 percent asymptotic critical values of the T-½ty and t-PST statistics, and these values are reported at the bottom of Table 2. 4. Estimation and Results The foregoing discussion highlights an important property of the trend function test for β-convergence, namely, that the test is valid for both stationary and unit root data. It is important to note however that the value of the test statistics is much smaller when the data are characterized by a unit root. In this regard, we first examine the time series properties of y to determine whether shocks to y are permanent or temporary. We use a well-known stationarity test proposed by Kwiatowski, Phillips, Schmidt and Shin (1992), henceforth KPSS, to test the null hypothesis of trend stationarity against the alternative of a unit root for the relative per capita income of each county. The results of the KPSS tests are summarized in Table 1. It is apparent that the null hypothesis is not rejected at the 5 percent significance level for 15 of the 24 counties for the whole sample period, and when restricting the sample to post-World War II period, the trend stationarity null is not rejected at the 5 percent level for 20 counties, and at the 1 percent level for all counties. Taken together, these results indicate that shocks to relative county per capita incomes are temporary for a majority of the Swedish counties over the full sample period and for an overwhelming majority of the counties during the post-World War II period, a finding consistent with stochastic convergence. We now turn to examine the empirical validity of β-convergence which, according to Carlino and Mills (1993, 1996), is another necessary condition for true income convergence. As previously explained, β-convergence requires the estimates of μj and βj to have opposite signs. In other words, β-convergence implies that if per capita income of a county is initially below the national average, that is, μj<0, then it should grow faster than the nation, that is, βj>0. Similarly, if per capita income of a county is initially above the national average, that is, μj>0, then it should grow slower than the nation, that is, βj<0. Table 2 reports the estimates of μj and βj for the z regression for both the known and unknown break date models. The t-PST statistics with no JT correction are given in parentheses below each point estimate and the asymptotic critical

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values are given in the bottom two rows. The known break date is set at 1946, the year often chosen to account for World War II which altered the regional income distribution in many countries (see e.g. Carlino and Mills, 1993; 1996). The estimated Tb of the unknown break date model shown in last column are mostly either at the beginning or towards the end of World War II. Thus, assuming 1946 as the exogenous break year appears not unreasonable even though Sweden was not directly involved in World War II. The column headed μ1 shows the percentage change deviation of county per capita income from the national average, approximately, in 1911.4 The column headed β1 gives the estimated average annual rate of convergence by county during the prebreak (1911-1946) period. When the break date is exogenous, the estimates of μ1 and β1 are statistically significant with opposite signs for all but six counties, namely, Uppsala, Kronoberg, Gavleborg, Jamtland, Vasternorrland, and Norrbotten. These results indicate that initially richer (poorer) counties had a lower (higher) growth rate of per capita income than the nation as a whole. For example, per capita income in Malmohus was above the national average in 1911, and the county had an annual growth rate that was 30 percent below the national average during the 1911 to 1945 period. Similarly, per capita income in Sodermanland was about 15 percent below the national average in 1911, and the county had an annual growth rate that was 45 percent above the national average during the same period. Of the six counties enumerated above which do not meet the criteria for β-convergence, only three (Gavleborg, Jamtland, and Norrbotten) diverge from the national average in the sense that their estimates of μ1 and β1 are statistically significant with the same sign (negative). The remaining three counties (Uppsala, Kronoberg, and Vasternorrland), on the other hand, exhibit weak or no βconvergence in the sense that their estimates of μ1 and β1 have opposite signs but one or both of the estimates are not statistically significant. Similar qualitative results are obtained for the unknown break date model (see columns 5 and 6). The results on βconvergence are somewhat weaker in the sense that the estimates of μ1 and β1 are statistically significant with opposite signs for fewer counties (eleven), but stronger in the sense that estimates of μ1 and β1 are statistically significant with the same sign (negative) for only two counties. The column headed μ2 shows the percentage change deviation of county per capita income from the national mean, approximately, in 1946. The column headed β2 gives the estimated rate of convergence by county during the post-break (or 1946-2003) period. The estimates of μ2 and β2 are statistically significant with opposite signs for a large majority (twenty) of the counties. In three of these counties, namely, Stockholm, Gothenburg, and Malmohus, per capita incomes are downwardly convergent whereas in the other seventeen counties, they are upwardly convergent. For two of the remaining four counties (Orebro and Vastmanland), estimates of μ2 and β2 are statistically insignificant which suggests that these counties had converged to their equilibrium growth paths at the beginning of the post-break period. No county was diverging from the national average. Also for the period 1946-2003, the results on β-convergence are

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somewhat weaker for the unknown break date model in the sense that estimates of μ2 and β2 are statistically significant with opposite signs for fewer counties (sixteen). One county (Sodermanland) is diverging. Interestingly, Table 2 also reveals a general slowdown in the rates of convergence after 1946. In particular, the estimates of β2 for counties that exhibited convergence in the pre-break period are smaller in absolute value than their estimates of β1 for both the known and unknown break date models. This result is consistent with the neoclassical growth model which predicts that the rate of convergence is higher the further an economy is from its steady state. If assuming similar equilibrium growth paths across counties, we expect this empirical result from this model as the cross-sectional dispersion in relative per capita income was larger during the 1911-1946 period than it was during the post-war period. An alternative explanation for the observed convergence is redistribution from rich to poor counties through central government policies. The central government can spur convergence by spending and hiring in the poor regions. This paper however partially controls for interregional redistribution, through the central government, by using an income measure that is net of taxable government transfers. Moreover, it is noteworthy that during the period 1911-1945, the size of the government sector was small relative to its current size, which limits the amount of interregional redistribution that could potentially be obtained during this period. For example, government tax revenues as a percentage of GDP was 16 percent in 1941 (Central Bureau of Statistics, 1960; Johansson, 1967), whereas in 2003 the ratio was 51 percent (Statistics Sweden, 2007). The relatively small public sector, during this early era therefore makes it unlikely that interregional government redistribution is the main source behind the results on convergence of the Swedish counties for the 1911-1945 period. During the 1946-2003 time period, when regional income inequality continues to decrease as indicated by a decreasing cross-county dispersion of relative per capita income and by the results on β-convergence, the size of the government greatly expands. For example, government tax revenue as a percentage of GDP is only 27 percent in 1960 but expands to 53 percent by 2000 (Statistics Sweden, 2007). 5 Persson (1995) however finds no statistically significant relationship between the per capita expenditures of the central government across counties and the counties’ per capita incomes (net of taxable transfers) for the fiscal year 1985-86. This suggests that central government expenditures are not redistributive across counties for this particular year. In a related study, Bergstrom (1998) reports that central government expenditures do not increase regional growth rates of per capita income in Sweden for the period 1970-1990. These results do not support a hypothesis that interregional redistribution, through the central government, is a leading force for the observed regional income convergence in Sweden. In a related study, Sala-i-Martin (1996) reports similar results to those of Persson (1995) for federal spending across states in the U.S., and finds that government expenditures play a very small role in the overall process of regional income convergence in both the U.S. and Europe.

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To check the robustness of our results to highly persistent errors, we calculated the t-PST statistics with JT correction, and the T-½ ty statistics based on the y regression. Columns 1-4 of Table 3 summarize the results reported in Table 2 whereas columns 5-12 of Table 3 summarize the results of these alternative model specifications. A C denotes point estimates consistent with β-convergence with both coefficients statistically significant at the 10 percent level. A c denotes point estimates consistent with βconvergence but with only one coefficient statistically significant at the 10 percent level. A D denotes point estimates consistent with divergence, with both coefficients statistically significant at the 10 percent level. A d denotes point estimates consistent with divergence but with only one coefficient statistically significant at the 10 percent level. Finally, an E denotes point estimates that are small in magnitude and not statistically different from zero, suggesting that β-convergence has been achieved. Table 3 indicates that the t-PST statistics with JT correction and the T-½ ty statistics tend to be smaller in magnitude than the t-PST statistics with no JT correction. For example, it is evident that some of the Cs in columns 1-4 changed to either c or E in columns 5-12. The results reported in Table 3, nonetheless, reveal that per capita income levels for majority of the Swedish counties have been converging since 1911 with most of the convergence occurring before the pre-break date. Finally, Table 4 shows that the results on β-convergence for the pre-break period are stronger when using the cost-of-livingadjusted income measure. Most of the c’s and d’s for the unadjusted income measure turn into C’s and D’s when using the adjusted income measure. For the post-war period it is not clear whether the results on β-convergence are stronger for the cost-of-livingadjusted income measure. 5. Summary and Conclusion This paper employs time series econometric techniques to examine whether the characteristics of per capita income across 24 Swedish counties during the period 19112003 are consistent with convergence. Our empirical results provide evidence of both stochastic convergence and β–convergence over the 92 years since 1911 when allowing for a trend break. These results indicate that the effects of shocks to per capita income tend to dissipate over time and that initially poor counties are growing faster and catching up with rich counties in Sweden. Moreover, the results are robust to alternate model specifications and assumptions regarding both unit roots and the choice of break date. The estimated rates of convergence are in general larger in the first half when regional differences in per capita income were greater than in the second half of the twentieth century. As for factors potentially influencing the convergence of per-capita county incomes, the small size of government sector in Sweden makes it likely that market forces are the driving force behind the results on convergence during the prebreak period, and that interregional government redistribution played a relatively minor role. Overall, the time series tests support the neoclassical growth model’s prediction of conditional per capita income convergence, and thus complement and extend the results from the cross-sectional study on the Swedish counties by Persson (1997). A natural

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extension is to determine the extent to which, if at all, government policies designed to help reduce regional income inequalities impacted convergence paths for the Swedish counties, and compare these results to the government roles in other Scandinavian countries. Another extension involves integrating spatial econometric techniques in cross section or panel regressions (see, for example, Rey and Montouri, 1999; Coughlin, Garrett and Hernandez-Murillo, 2007) to determine to what extent common borders or regional characteristics help to link growth trajectories within Swedish counties. 6. Notes 1. Joseph DeJuan is Associate Professor of Economics at the University of Waterloo, Ontario Canada, jdejuan@uwaterloo,ca; Joakim Persson is Associate Professor of Economics and Statistics at Karlstad University, Karlstad Sweden, [email protected]; Marc Tomljanovich is Associate Professor of Economics at Drew University, New Jersey USA, [email protected]. 2. Sweden was divided into 24 counties between 1911 and 1997. In 1997-1998, two counties in the south (Kristianstad and Malmohus) and three counties in the west (Gothenburg, Alvsborg and Skaraborg) were merged to form into two counties, giving rise to 21 counties in the current regional division. This paper uses the pre-1997 regional division of Sweden that assumes 24 counties in order to have a long and consistent time series data spanning the period 1911-2003. Post-2003 per-capita income data for the 24 counties are not freely available. 3. Per capita income is defined as gross per capita income net of taxable government transfers, an income measure available consistently across 24 Swedish counties and time periods. Data for the years 1911 and 1912 were collected from the Royal Ministry of Finance (1914, 1915), and for the years 1916 and 1919-1993 from Statistics Sweden, Tax Assessments and Income Statistics, various issues. No data are available for the years 1913-1915 and 1917-1918. We use interpolated values for these years. Population data are collected from Statistics Sweden, Vital Statistics, various issues (for details, see Persson, 1997). 4. If xi ,1911 is per capita income of county i in 1911, and x1911 is average per capita



 



income, then yi ,1911  ln xi ,1911 / xi ,1911  ln 1  ( xi ,1911  xi ,1911 ) / xi ,1911  ( xi ,1911  xi ,1911 ) / xi ,1911 when

( xi ,1911  xi ,1911 ) / xi ,1911 is small.

5. OECD data for the period 1960-2004 (Statistics Sweden, 2007) indicates that Sweden has a relatively high tax ratio among the OECD countries. For Norway the tax ratio is 31 percent in 1960 and 43 percent in 2000, for Finland it is 28 percent and 48 percent, for Denmark it is 25 percent and 49 percent, for Germany it is 31 percent and 37 percent, for the U.S. it is 27 percent and 30 percent, and for the U.K. it is 29 percent and 37 percent.

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7. References Aronsson, T., Lundberg, J., and Wikström, M., (2001), “Regional Income Growth and Net Migration in Sweden, 1970-1995”, Regional Studies, 35, 823-830. Barro, R.J. and Sala-i-Martin, X., (1991), “Convergence across States and Regions”,Brookings Papers on Economic Activity, 1, 107-182. Barro, R.J. and Sala-i-Martin, X., (1992), “Convergence”, Journal of Political Economy, 100, 223-251. Bergstrom, F., (1998), “Regional Policy and Convergence of Real Per Capita Income among Swedish Counties”, SSE/EFI Working Paper Series in Economics and Finance No. 284, Stockholm School of Economics, Sweden. Central Bureau of Statistics, (1960), Historical Statistics of Sweden, Stockholm, Sweden. Carlino, G.A., and Mills. L.O., (1993), “Are US Regional Incomes Converging?”, Journal of Monetary Economics, 32, 335–346. Carlino, G.A., and Mills, L.O., (1996), “Testing Neoclassical Convergence in Regional Incomes and Earnings”, Regional Science and Urban Economics, 26, 565-590. Couglin, C.C., Garrett, T.A., and Hernandez-Murillo, R., (2007), “Spatial Dependence in Models of State Fiscal Policy Convergence”, Public Finance Review, 35, 361-384. Grenander, U. and Rosenblatt, M., (1957), Statistical Analysis of Stationary Time Series, New York: John Wiley & Sons. Johansson, Ö., (1967), The gross domestic product of Sweden and its composition, Stockholm: Almqvist & Wiksell. Kwiatowski, D., Phillips, P., Schmidt, P., and Shin, Y., (1992), “Testing the Null Hypothesis of Stationary against the Alternative of a Unit Root”, Journal of Econometrics, 54, 159-178. Liew, V.K. and Ahmad, Y., (2009), “Income Convergence: Fresh Evidence from the Nordic Countries”, Applied Economic Letters, 16, 1245–48. Mankiw, N.G., Romer, D., and Weil, D., (1992), “A Contribution to the Empirics of Economic Growth”, Quarterly Journal of Economics, 107, 407–437. Myrdal, G., (1930), The Cost of Living in Sweden, London: P.S. King & Son. Persson, J., (1997), “Convergence across the Swedish Counties, 1911-1993”, European Economic Review, 41, 1835-1852. Persson, J., (1995), “Convergence in Per Capita Income and Migration Across the Swedish Counties 1906-1990”, Seminar Paper No. 601, Institute for International Economics Studies, Stockholm University, Sweden. Rey, S. and Montouri, B., (1999), “U.S. Regional Income Convergence: A Spatial Econometric Perspective”, Regional Studies, 33, 143-156. Sala-i-Martin, X., (1995), “The Classical Approach to Convergence Analysis”, Economic Journal, 106, 1019-1036. Sala-i-Martin, X., (1996), “Regional Cohesion: Evidence and Theories of Regional

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Growth and Convergence”, European Economic Review, 40, 1325-1352. Solow, R.M., (1956), “A Contribution to the Theory of Economic Growth”, Quarterly Journal of Economics, 70, 65–94. Statistics Sweden, (2007), “The Swedish Economy: Statistical Perspective”, No. 2, Gunnel Bengtsson Publisher, Sweden. Tomljanovich, M. and Vogelsang, T.J., (2002), “Are U.S. Regions Converging? Using New Econometric Methods to Examine Old Issues”, Empirical Economics, 27, 49–62. Vogelsang, T.J., (1997), “Testing for a Shift in Trend when Serial Correlation Is of Unknown Form”, CAE Working Paper 97-11, Cornell University, Ithaca, NY. Vogelsang, T.J., (1998), “Trend Function Hypothesis Testing in the Presence of Serial Correlation”, Econometrica, 66, 123–148.

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Figure 1: Relative Per Capita Income, 1911-2003

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Figure 2: Cross-section Dispersion of Relative Per Capita Income 0.45 0.4 0.35

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1967

1964

1961

1958

1955

1952

1949

1946

1943

1940

1937

1934

1931

1928

1925

1922

1919

0 1911

Std. Dev.

0.3

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DEJUAN, PERSSON, TOMLJANOVICH: REGIONAL INCOME

81

Table 1: Summary of KPSS Unit Root Tests Data Series: Natural logarithm of relative per-capita personal income. County County Name 1911-2003 1946-2003 No. 1 Stockholm 0.133 0.132 2 Uppsala 0.105 0.096 3 Sodermanland 0.183* 0.052 4 Ostergotland 0.152* 0.093 5 Jonkoping 0.134 0.106 6 Kronoberg 0.116 0.137 7 Kalmar 0.152* 0.120 8 Gotland 0.150* 0.118 9 Blekinge 0.132 0.145 10 Kristianstad 0.390‡ 0.148* 11 Malmohus 0.074 0.103 12 Halland 0.155* 0.095 13 Gothenburg 0.145 0.120 14 Alvsborg 0.146* 0.086 15 Skaraborg 0.145 0.173* 16 Varmland 0.138 0.075 17 Orebro 0.149* 0.092 18 Vastmanland 0.148 0.071 19 Kopparberg 0.127 0.074 20 Gavleborg 0.086 0.122 21 Jamtland 0.108 0.103 22 Vasternorrland 0.088 0.093 23 Vasterbotten 0.178* 0.159* 24 Norrbotten 0.106 0.156* * ‡ Notes: and indicate significance at the 1 percent and 5 percent level, respectively. The asymptotic critical values for KPSS (with trend) are 0.216 at 1 percent level, 0.146 at 5 percent level, and 0.119 at 10 percent level.

14

13

12

11

10

9

8

7

6

5

4

3

2

1

County

μ1 0.911** (16.512) -0.022 (-0.636) -0.153** (-7.813) -0.170** (-7.838) -0.435** (-13.482) -0.573** (-11.357) -0.560** (-10.382) -0.763** (-14.201) -0.399** (-10.182) -0.473** (-14.164) 0.237** (18.840) -0.441** (-18.511) 0.373** (17.337) -0.351** (-11.510)

Known Break Date: Tb = 1946 β1 μ2 -1.114** 0.350** (-2.803) (8.632) 0.070 -0.112** (0.273) (-4.358) 0.445** -0.011 (3.080) (-0.770) 0.289** -0.073** (1.806) (-4.598) 0.818** -0.097** (3.430) (-4.067) 0.134 -0.189** (0.357) (-5.082) 0.728** -0.260** (1.823) (-6.543) 1.255** -0.283** (3.156) (-7.159) 0.360** -0.204** (1.246) (-7.405) 0.457** -0.142** (1.850) (-5.765) -0.302** 0.095** (-3.250) (10.246) 0.784** -0.216** (4.444) (-12.308) -0.564** 0.121** (-3.547) (7.620) 0.781** -0.076** (3.463) (-3.400)

β2 -0.398** (-2.773) 0.196** (2.164) -0.094** (-1.848) 0.072** (1.284) 0.091* (1.087) 0.273** (2.077) 0.356** (2.537) 0.272** (1.941) 0.293** (3.116) 0.118** (1.360) -0.254** (-7.769) 0.377** (6.075) -0.241** (-4.302) 0.041 (0.521)

μ1 0.919** (16.868) -0.012 (-0.490) -0.130** (-3.161) -0.159** (-5.492) -0.420** (-13.807) -0.532** (-10.022) -0.555** (-25.994) -0.735** (-14.653) -0.420** (-48.880) -0.452** (-9.766) 0.244** (20.130) -0.441** (-23.337) 0.356** (10.318) -0.352** (-14.444)

Unknown Break Date β1 μ2 -1.218** 0.341** (-3.112) (7.962) -0.033 -0.117** (-0.204) (-4.919) 0.115 -0.011* (0.254) (-0.910) 0.168 -0.080** (0.624) (-6.319) 0.662** -0.106** (2.682) (-5.856) -0.319 -0.225** (-0.741) (-7.136) 0.750** -0.117 (9.182) (-0.810) 0.949** -0.303** (2.259) (-10.942) 0.556** -0.103** (17.130) (-1.826) 0.220 -0.163** (0.587) (-5.917) -0.373** 0.077** (-4.754) (6.188) 0.774** -0.205** (6.182) (-11.289) -0.362 0.146** (-1.212) (8.299) 0.793** -0.071** (4.909) (-3.022)

Table 2: Empirical Results Using the zt Regression and t - PST Statistics without JT Correction. β2 -0.383** (-2.479) 0.239** (2.618) -0.069** (-1.877) 0.076** (1.928) 0.109** (1.804) 0.349** (3.312) -0.063** (-0.046) 0.294** (3.240) 0.155 (0.302) 0.166** (1.810) -0.238** (-4.880) 0.390** (5.609) -0.277** (-4.872) 0.028 (0.313) 1949

1940

1949

1950

1942

1980

1941

1979

1942

1942

1938

1934

1949

1946

Tb

82 THE JOURNAL OF ECONOMIC ASYMMETRIES JUNE 2012

±1.120

μ1 -0.619** (-18.255) -0.434** (-12.211) -0.130** (-4.596) -0.196** (-6.686) -0.305** (-6.659) -0.155** (-4.526) -0.176** (-4.817) -0.489** (-4.819) -0.709** (-11.662) -0.324** (-5.058) ±0.854 ±0.883

±1.350

±1.200

Known Break Date: Tb = 1946 β1 μ2 β2 1.089** -0.186** 0.212** (4.340) (-7.443) (2.399) 0.516** -0.108** 0.091* (1.963) (-4.133) (0.985) 0.387** -0.018 -0.045 (1.855) (-0.885) (-0.607) 0.608** -0.010 -0.048 (2.803) (-0.443) (-0.627) 0.453** -0.132** 0.112* (1.317) (-3.860) (0.922) -0.310** -0.143** 0.180** (-1.226) (-5.664) (2.024) -0.673** -0.142** 0.236** (-2.491) (-5.296) (2.483) 0.233 -0.293** 0.398** (0.311) (-3.918) (1.505) 1.143** -0.282** 0.495** (2.541) (-6.311) (3.126) -0.379* -0.200** 0.326** (-0.799) (-4.252) (1.957) ±0.683 ±1.030 ±0.908

±2.190

μ1 -0.591** (-14.444) -0.447** (-11.338) -0.092** (-2.473) -0.148** (-4.687) -0.254** (-4.865) -0.136** (-3.780) -0.167** (-4.789) -0.432** (-4.399) -0.688** (-23.786) -0.358** (-7.140) ±1.570 ±1.760

±1.500

Unknown Break Date β1 μ2 0.763** -0.213** (2.111) (-10.013) 0.637** -0.100** (2.313) (-3.014) -0.085 -0.013 (-0.208) (-1.137) -0.016 -0.011 (-0.046) (-1.121) -0.153 -0.149** (-0.290) (-7.755) -0.518** -0.160** (-1.718) (-8.039) -0.767** -0.150** (-2.888) (-6.294) -0.367 -0.317** (-0.431) (-6.320) 1.056** -0.112 (9.151) (-0.720) -0.050 -0.151** (-0.156) (-2.941) ±1.330 ±1.140 ±1.270

β2 0.256** (3.729) 0.072 (0.593) -0.046 (-1.386) -0.033 (-1.164) 0.127** (2.199) 0.206** (3.163) 0.252** (3.044) 0.407** (2.516) 0.169 (0.130) 0.217* (1.079) ±0.936 1950

1976

1940

1944

1941

1936

1934

1934

1947

1940

Tb

Notes: Data Series: Natural logarithm of relative per-capita personal income. ** and * denote significance at the 5 percent and 10 percent level using a one-tailed test. Values in parentheses are the t – PST statistics using b = 0. The last two rows report the 10 percent and 5 percent asymptotic critical values.

I(0) 10% cv I(0) 5% cv

24

23

22

21

20

19

18

17

16

15

County

Table 2 (continued): Empirical Results Using the zt Regression and t - PST Statistics without JT Correction.

VOL. 9 NO. 1 DEJUAN, PERSSON, TOMLJANOVICH: REGIONAL INCOME 83

Table 3: Summary of Empirical Results for Relative Per Capita Personal Income (unadjusted data) County t – PST: I(0) Errors Assumed t – PST: Robust to I(1) Errors T-1/2ty : Robust to I(1) Errors Tb = 1946 Tb Unknown Tb = 1946 Tb Unknown Tb = 1946 Tb Unknown PrePostPrePostPrePostPrePostPrePostPrePostbreak break break break break break break break break break break break County 1 C C C C C c C c County 2 E C E C E E C E E E E County 3 C d c D C E c E C E c E County 4 C C c C c E c E C E c E County 5 C C C C C E c E C E c E County 6 c C d C c d C c County 7 C C C d c c E C c C County 8 C C C C c c C C c c c County 9 C C C c c c E C c C County 10 C C c C c E c E C c c c County 11 C C C C C C C C C C c c County 12 C C C C C C C C C C C c County 13 C C c C C c C C c c C County 14 C c C c c E c E C E C E County 15 C C C C c E c C c c c

. 84 THE JOURNAL OF ECONOMIC ASYMMETRIES JUNE 2012

Table 3: (continued) Summary of Empirical Results for Relative Per Capita Personal Income (unadjusted data) County t – PST: I(0) Errors Assumed t – PST: Robust to I(1) Errors T-1/2ty : Robust to I(1) Errors Tb = 1946 Tb Unknown Tb = 1946 Tb Unknown Tb = 1946 Tb Unknown PrePostPrePostPrePostPrePostPrePostPrePostbreak break break break break break break break break break break break County 16 C C C c c E c E C E c E County 17 C E d E E E E C E d E County 18 C E d E c E d E C E c E County 19 C C d C c E d C c E d E County 20 D C D C d E d E d c d c County 21 D C D C d d E d County 22 c C d C c d County 23 C C C E c c E C c C County 24 D C d C d d d c E Notes: C denotes point estimates consistent with -convergence that are statistically significant at least at the 10 percent level. c denotes point estimates consistent with  -convergence with only one estimate statistically significant at least at the 10 percent level. D denotes point estimates consistent with divergence that are statistically significant at least at the 10 percent level. d denotes point estimates consistent with divergence with only one estimate statistically significant at least at the 10 percent level. E denotes point estimates very small in magnitude (<|0.200|) and statistically insignificant, which suggests that -convergence has occurred. No symbol signifies point estimates that are statistically insignificant and larger in magnitude (>|0.200|), making inference about convergence or divergence difficult.

VOL. 9 NO. 1 DEJUAN, PERSSON, TOMLJANOVICH: REGIONAL INCOME 85

Table 4: Comparison of Empirical Results for Relative Per Capita Personal Income All Results are for t - PST: Robust to I(1) Errors All Results are Tb Unknown County Unadjusted Data Adjusted Data Pre-break Post-break Est. Tb Pre-break Post-break County 1 1946 C County 2 C 1949 C County 3 c E 1934 C c County 4 c E 1938 C E County 5 c E 1942 C E County 6 d 1942 D County 7 c E 1979 C E County 8 c C 1941 C C County 9 c E 1980 C E County 10 c E 1942 E County 11 C C 1950 C County 12 C C 1949 C c County 13 c C 1940 C E County 14 c E 1949 C c County 15 c 1940 C County 16 c E 1947 C E County 17 E E 1934 E County 18 d E 1934 D d County 19 d C 1936 D C Est. Tb 1946 1949 1938 1954 1942 1942 1980 1940 1978 1942 1979 1949 1969 1959 1939 1945 1934 1934 1936

86 THE JOURNAL OF ECONOMIC ASYMMETRIES JUNE 2012

Table 4: Comparison of Empirical Results for Relative Per Capita Personal Income All Results are for t - PST: Robust to I(1) Errors All Results are Tb Unknown County Unadjusted Data Adjusted Data Pre-break Post-break Est. Tb Pre-break Post-break Est. Tb County 20 d E 1941 D C 1941 County 21 1944 1944 County 22 1940 D 1940 County 23 c E 1976 C 1974 County 24 d 1950 C 1950 Notes: C denotes point estimates consistent with -convergence that are statistically significant at least at the 10 percent level. c denotes point estimates consistent with  -convergence with only one estimate statistically significant at least at the 10 percent level. D denotes point estimates consistent with divergence that are statistically significant at least at the 10 percent level. d denotes point estimates consistent with divergence with only one estimate statistically significant at least at the 10 percent level. E denotes point estimates very small in magnitude (<|0.200|) and statistically insignificant which suggests that  -convergence has occurred. No symbol signifies point estimates that are statistically insignificant and larger in magnitude (>|0.200|), making inference about convergence or divergence difficult.

VOL. 9 NO. 1 DEJUAN, PERSSON, TOMLJANOVICH: REGIONAL INCOME 87