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Sectoral sources of metropolitan growth
Regional Science and Urban Economics 29 (1999) 723–743 www.elsevier.nl / locate / econbase
Sectoral sources of metropolitan growth N. Edward Coulson* Department of Economics, Penn State University, University Park, PA 16802, USA Received 15 June 1997; received in revised form 8 March 1999; accepted 27 April 1999
Abstract The paper proposes a method for identifying sectoral sources of metropolitan employment growth The key feature of the VAR is the set of (over)identifying restrictions which do not require a causal ordering to be developed among industries to create orthogonal sectoral shocks. The simulations for four cities indicate that local sectoral shocks are more important than national counterparts, and that among local shocks, the overall evidence indicates that manufacturing, service and public sector employment shocks account for a substantial portion of employment growth variation, a conclusion that seems roughly consistent with export-oriented models of metropolitan growth. 1999 Elsevier Science B.V. All rights reserved. Keywords: Metropolitan employment growth; Export-oriented models
1. Introduction There is an intense practical interest in knowing which industrial sectors are responsible for growth in cities. The growth or decline of employment in a metropolitan area must by definition be the result (indeed, is the sum) of employment growth or decline in its various industries. But to the extent that sectors move in the same direction at roughly the same time, it is difficult to discover which sectors are responsible (or causally prior) for that growth. Theory is of little help. The only widely recognized theory that addresses the causal *Tel.: 11-814-863-0625; fax: 11-814-863-4775. E-mail address: [email protected] (E. Coulson) 0166-0462 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0166-0462( 99 )00017-4
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ordering of sectoral growth is the export base model, in which ‘export’ industries create exogenous (export) demand and through backward linkages and factor earnings, generate demand for the output of other (local-serving) sectors. Empirical implementation of this theory then requires a bifurcation of employment into export and local sources, and this is often done at the sectoral level. But this is very difficult. Theories of agglomeration are even worse at identifying sectorspecific shocks, since such theories can imply two-way causality between suppliers’ and demanders’ employment. As an example of the difficulties, Browne (1988) examines the role of business services in the Massachusetts Miracle, the explosive employment surge which took place in Massachusetts and surrounding areas during the late 1970s and early 1980s. Consider the dilemma faced by this author when trying to analyze this issue: ‘‘High tech manufacturing has not been the sole source of new jobs in the region. Growth has been very rapid in the service industries . . . But while it would be a mistake to look upon high technology as the only reason for New England’s prosperity, it would also be a mistake to view these other developments as entirely independent of the developments in high tech manufacturing. In particular, the growth in some of the most rapidly expanding business services is, to some extent, a reflection of the growth in high tech manufacturing’’ (p. 202). Thus, it is clear that a technology for isolating the separate contributions over time of the various metropolitan industries is imperative. Neither input–output models nor previous time series models have successfully grappled with this issue.1 In this paper, the aim is to provide such a framework. VARs are a convenient tool for this purpose because they provide a mechanism for constructing innovations in various sectors that are orthogonal to each other, and allow the implementation of a technology for assessing the dynamic impact of these separate shocks. However, the conventional method for orthogonalization (Choleski decomposition of the VAR’s residual covariance matrix) is inappropriate for this problem, for reasons which are discussed below, so instead a new (overidentified) method of constructing the sectoral shocks is proposed. This method is related to shift-share analysis, in that it precludes inter-industry effects except through their impact on aggregate totals. The vector autoregression model is estimated for four US cities. Results indicate that local shocks are more potent than national shocks and that among local shocks, those to the manufacturing, public and service sectors predominate.
1 Studies most similar in spirit to this one, as ably surveyed in Clark and Shin (1998) have concentrated on effect of various types of shocks on regional sectors (Norrbin and Schlagenhauf, 1988; Altonji and Ham, 1990; Clark, 1998) as opposed to the metropolitan focus of this paper (and of Coulson, 1993; Coulson and Rushen, 1995; McCarthy and Steindel, 1997). The methods followed here also differ slightly from the above papers (see footnote 6).
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2. The econometric framework The shift-share model is built on the premise that national, sectoral and, in some models, metropolitan fluctuations are reflected proportionally in local sectoral movements. This then encompasses (respectively) aggregate demand and supply shocks, sectoral supply and demand shocks and metropolitan demand shocks, so that deviations from proportionality are then attributed to supply side factors at the local-sectoral level. Some of the econometric implications of this model have been discussed in Coulson (1993). In the more highly parameterized context of vector autoregressions, it is straightforward to extend this idea. Consider the following regression model which (ignoring deterministic components) determines sector i employment, e it , in an (unindexed) metropolitan area at time t: e it 5 c i (B)n t 1 d i (B)s it 1 fi (B)m t 1 gi (B)e it 1 u it . Each right-hand side term x i (B)z it term represents a lag polynomial, i.e. a collection of coefficients and associated regressors that are lagged values of the various z terms. These regressors are: n, (aggregate) employment in the nation; s, sectoral employment in the nation; m, (aggregate) metropolitan employment; and e, sectoral employment in the metropolitan area. The idea here is that these four sets of lagged variables represent the four kinds of stimuli identified in the shift-share framework, albeit in a more dynamic framework, and without the restriction of proportionality. The u it term is a residual for this sectoral equation which represents the exogenous shocks to industry employment. Now consider a set of such equations, one for each of the k sectors in the metropolitan area: e 1t 5 c 1 (B)n t 1 d 1 (B)s 1t 1 f1 (B)m t 1 g1 (B)e 1t 1 u 1t . . . e kt 5 c k (B)n t 1 d k (B)s kt 1 fk (B)m t 1 gk (B)e kt 1 u kt This set of k equations can be augmented with an identity which links m and the various e i values with the obvious aggregation identity: m t 5 e 1t 1 ? ? ? 1 e kt . We can similarly write k equations that model each national sector. Each of these will be modeled as a function of its own past, and lags of n t . We, therefore, have k equations of the form s it 5 h i (B)n it 1 j i (B)s it 1 vit for i51 to k, so that each national industry’s employment is dependent on national aggregate employment lags, and its own past. Similarly, an aggregation condition is added of the form
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n t 5 s 1t 1 ? ? ? 1 s kt . The above equations comprise a (2k12)-dimensional vector autoregression whose principal task is to model the short run fluctuations of each metropolitan sector and the metropolitan aggregate as a function of those sectors. Imagine an exogenous increase in the ith sector’s employment as manifested by an increase in u it . This shock immediately increases both e it and m t . The remaining sectors are then affected with a lag by the increase in m t , which then causes further increases in m t and yet further increases in each sectors’ employment, and so on.2 At the national level, a similar mechanism applies. An increase in vit immediately increases s it and n it , the latter through the aggregation equation, and then s it as well as e it with a lag. This causes an increase in m it and all of these changes set further changes in motion. This description of the short run process of employment growth in a metropolitan area is roughly congruent with the base multiplier model in that short run growth is generated by an exogenous increase in one sector’s employment, perhaps due to an export shock, which in turn stimulates and restimulates aggregate employment through standard multiplier analytics,3 and like the base multiplier it restricts the kinds of interaction that sectors can have with one another. In the case of the multiplier model sectors are bifurcated into basic and local sectors, and basic sector employment is determined exogenously. In turn, these exogenous movements influence local sectors, and this influence is remanifested in further increases in local employment. In the present VAR model, each sector has an exogenous component, which arises from the residual, and from national influences and an induced (local) component, so that there is no necessity of providing the often arbitrary distinction between exporting and non-exporting sectors. But neither is there an allowance for the possibility that the relationship between two particular sectors might be different (as that of supplier and demander, say). This would be the case in more highly parameterized models such as input–output, but is not allowed here.4 A major issue remains, which is the contemporaneous correlation of the residuals. Under the interpretation of each of the u i as shocks to employment in the ith sector, we can putatively trace the sources of metropolitan growth to individual sectors, but only if the u i are uncorrelated. They of course do not have this property in practice, and this prevents us so far from assigning variation in 2
This description of the process assumes that the lag coefficients are positive, and that the system is such that the impacts die out after a sufficient number of iterations. 3 A version of those analytics is contained in Brown et al. (1992) or Richardson (1985). 4 In fact it is possible to allow this in the VAR itself, but I do not allow it for reasons of parsimony, and to maintain congruency with the orthogonalization procedure below, where such a parameterization is not possible. Models that partially relax some of these restrictions are discussed later on in the paper.
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aggregate metropolitan employment to particular sectors. If say, construction and manufacturing employment shocks move together, which of them is ultimately responsible? It is necessary to extract components of the u i that are orthogonal to each other in order to accomplish this task. The problem of orthogonalization is as old as the method of vector autoregression itself. We wish to find an identifiable matrix of parameters, W such that
SuvD 5 WSufD where u and v are the obvious vectorizations of the VAR residuals above and u and f are k-dimensional vectors which contain orthogonal innovations to national and local employment series. By orthogonal it is meant that
SD
u Cov f 5 D where D is a diagonal matrix. Under such circumstances we can identify the orthogonalized residuals as those representing exogenous shocks to each of the sectors, with which the sectoral origin of metropolitan growth and decline are delineated. The discussion now centers on the identifiability of the parameters in W. A standard tack is to make W lower triangular, with ones along the main diagonal. This automatically ensures the identifiability of W through recursion; there are k(k21) parameters in the matrix, which along with the 2k variances in D equals to the number of parameters in the residual covariance matrix of u and v. However, the lower triangularity of W implies a particular relationship among the residuals. The first element of u is a function of only the first element of u, indeed is identical with it. The second element is a function of the first and second elements of u, and so on through all of the elements of u and v. Thus, there is a hierarchical relationship implied among the innovations – what is sometimes called a (contemporaneous) causal ordering among them. This causal ordering must be inferred from a priori reasoning, such as economic theory, and can never be completely dictated by sample properties, and as such can be the source of controversy. This is especially true when the inferences drawn from a VAR vary with the ordering chosen. In the present application the problem is exacerbated, since (unlike many macroeconomic applications) there is almost no theoretical guide to aid in choosing an appropriate ordering. The only such theories arise (as noted above) from variants of the base multiplier model which imply that local growth is a function of exports, and that exports depend on national (and international) conditions. For this model the implication would be that national sectoral employment ought to be placed causally prior to local sectors, and that within the set of local equations, that export sectors are causally prior to local-serving sectors.
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The first of these statements seems reasonable. Indeed it informs the construction of the VAR model itself, in that Ei does not appear in the equations determining Si . However the second assumption is fraught with difficulty, because it requires identifying export industries among the group of local sectors, and moreover it requires identifying any sector as either entirely local or entirely export. The base multiplier literature (Richardson, 1985; Brown et al., 1992) is fairly convincing that the latter bifurcation is impractical, even at high levels of disaggregation. Even if these last difficulties could be overcome, the standard approach still requires a causal ordering within the export and local-serving groups and within the national sectors as well. This seems an insurmountable difficulty, and compels one to search for alternative means of identifying W, one that is neutral among the various sectors. To do so again consider the principles underlying the VAR itself and decompose the local sectoral residual into functions of a national shock, industry shock, metropolitan shock and a shock idiosyncratic to the city-industry. In doing so, it is necessary to recognize that there is no national shock and no metropolitan shock per se, but that we can in some sense create one by adding together the sectoral shocks at the national and local levels, respectively. In so doing we have: u it 5 bi fit 1 gi Sfj 1 cit 1 dj Scjt where as notated above fj and cj are the orthogonal shocks to the jth national and local sector, respectively. The b, g, and d parameters are to be estimated. It can be seen that the pattern of relationships is congruent with the description above. The residual u it is a linear combination of its own sectoral shock fj , the ‘national’ shock – i.e. the sum of national sectoral shocks – Sfj the ‘metropolitan’ shock Scj and the idiosyncratic shock ci . The parameter b then represents the local share of sectoral movements, g represents the local industry’s share of aggregate movement,5 and d is the local sector’s share of the metropolitan shock. The unit coefficient on the own shock is then an appropriate normalization. We employ a similar but simpler scheme for the aggregate sectoral shocks: u 1 5 f1 1 a1 Sfi that is, the first residual is the sum of the first innovation (which is now identified as the first national industry’s shock) plus a fraction (a1 ) of the shock to national output, which by definition is the sum of all national sectoral shocks. Note that the unit coefficient on the first term above also serves as the appropriate normalization. 5
There is obviously an implicit normalization here, in that one could alternatively write the sectoral weight as zi 5 bi 1gi and let the national shock omit the ith sector.
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The remaining national sectors have their innovations described in an analogous way.6 Thus, local and national innovations from the same sector are correlated through the national sectoral effect, all national sectoral innovations are correlated with every sector’s local and national innovation through the respective aggregates, and every local innovation is allowed to be correlated with every other local innovation through the metropolitan aggregate. Nevertheless, the parameters are identified. The identification of the parameters of this decomposition arises from the constraints placed on the way in which sectors can respond to movements in one another. Were we to allow each sector to respond to others in an unrestricted fashion, the resulting number of parameters would eliminate the possibility of identifying any of them. The method proposed here is a plausible way of limiting the number of parameters in order to achieve identification while remaining neutral in its treatment of each of the sectors (i.e. not imposing a causal hierarchy). The drawback is that in a sense it goes too far – it is highly overidentified.7 6
Previous literature (as cited in footnote 1) has grappled with this identification problem in various ways. A common tack is to assume the industry (or regional, as the case may be) shocks are independent of each other. Typically the models then contain a separate national employment shock. Separate identification of national and industry shocks can then be achieved through (a) omission of an industry; (b) use of a logarithmic functional form (in which case aggregation fails); or (c) measurement error, since in published BLS data the sum of industry employments is never equal to aggregate employment at the local level. Here, the national (and metro) shocks are omitted from the decomposition of the shocks (to achieve both perfect aggregation and identification), but to the extent that propagation of shocks is common across sectors this is effectively viewed as a ‘national shock’. Given the emphasis here on the differences in sectoral impacts on metropolitan aggregates, this view seems appropriate. See Clark and Shin (1998) for a full discussion of these issues. 7 While method of moments estimation is available for overidentified models such as this, the ease of computing the likelihood ratio tests makes maximum likelihood estimation attractive as long as normality is assumed. Consider the log-likelihood function, written in this case (without constants) as
S D log(WDW9)2]12 S suvd (WDW9)
T 2 ] 2
t
t
21
suvd
t
with T as the sample size, so that the covariance matrix of the residuals is replaced by its decomposition. The value of this likelihood function is invariant to the decomposition as long as the parameters are just-identified. As with standard likelihood ratio tests, the imposition of constraints lowers the value of the log-likelihood and twice the difference of the overidentified and just-identified versions of the model will be distributed under the null that the constraints are satisfied will be distributed in the usual way as a x 2 with degrees of freedom equal to the number of constraints. Thus, the comparison of the Choleski decomposition (with any causal ordering) to the overidentified model will yield the appropriate test statistic. It will happen in the empirical application that k57 or 8, which regrettably leads to 70 or more overidentifying restrictions. This is problematic in that with so large a number of restrictions it will be almost impossible to satisfy them all, and the overidentifying restrictions will be rejected. As it happens, this turns out to be the case in the estimates below. Nevertheless the model’s relative simplicity and neutrality with respect to sectoral prominence provide sufficient tradeoff against the large degree of overidentification.
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3. Implementation The parameters of the model are to be estimated using data from four US cities: Baltimore, Denver, Houston, and New York City. The sample frames are as follows: before lags are introduced the beginning date is January 1949 for Baltimore and January 1950 for New York City, with January 1970 being the starting date for the other two. The ending date is April 1996 in all four samples.8 Other dimensions of the model specification are now taken up. One difficult decision deals inevitably with whether to specify the variables in level or first differences, a decision not informed by the importance placed here on aggregation. In the end, first differences are used exclusively. The maintained assumption is, therefore, that the data are difference-stationary with no cointegrating relationship among them, an assumption which coincides with the results in the literature (Brown et al., 1991; Coulson, 1993) which in particular examined the most natural cointegrating possibility, that of local and national employment within the same sector.9 Another important aspect of model specification is the lag length. Under the convenient assumption that all of the lag polynomials in the VAR are the same length, model selection criteria indicated that the optimal lag length should be one. This is undoubtedly due to the large number of parameters added for each increase in the polynomial order, which incurs a heavy penalty in, e.g. the Schwarz information criterion. The estimation then proceeds with the following steps. The VAR is estimated using the method of Seemingly Unrelated Regressions. The residuals from this estimate are then used to maximize the likelihood function (see Section 2), and this provides the estimates of the parameters of the W and D matrices. The constrained covariance matrix is then used to re-estimate the VAR parameters using Seemingly Unrelated Regressions once more.10 The parameters of the W matrix are accordingly estimated in this way, but not 8
The data is taken from the Bureau of Labor Statistics World Wide Web site for retrieval of information from Employment and Earnings, and Employment and Earnings: States and Areas. The starting point for such retrieval is at URL http: / / stats.bls.gov:80 / sahome.html. 9 It must be admitted, nevertheless that with 2n equations, cointegration tests will only rarely fail to reject the null hypothesis of no cointegration. Unfortunately such ‘random’ cointegration which was found in this case appeared to have little meaningful interpretation. Furthermore the shift-share model from which the present construction draws some of its inspiration is a decomposition based on changes. Since the data are in differences rather than growth rates, it is necessary to add a deterministic trend to the model, since absolute changes grow resolutely over time. This time trend is not reported below (for space considerations) but is uniformly significant. Finally, a full set of seasonal dummies is used in all equations to account for seasonal variation in employment cycles. These are suppressed in the presentation of the results as well. 10 Two more details: OLS is often used to estimate the equations of the VAR, since no efficiency gains are available to SUR if the data matrix on the right-hand side is identical across equations. This is not the case here, so SUR is required in the second step. It is not strictly necessary in the first step, since all that is required is a consistent estimate of the lag polynomial and other parameters in the VAR.
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presented here to save space.11 To summarize, they are nearly always positive and of intuitive size; a few are negative and this may be due to some cross-sectoral substitution as growth or decline occurs. Given these W parameters (and the estimated standard errors of the shocks themselves) the constrained covariance matrix can be constructed and the parameters of the VAR estimated. The key coefficients are displayed in Table 1a–d. The overall fits, as measured by the adjusted R 2 are weakest for the New York City estimates although in general, they are reasonable for differenced data. The sizes of the coefficients are roughly of the same orders of magnitude as the parameters in W and while there are a number of unexpected negative coefficients, most of these are small and statistically insignificant.12 The t-statistics in Table 1 can be looked upon as Granger-causality results. Recalling that Granger-causality tests are always conditional on the specific information set, the information set here is quite extensive, compared to the oft-used two-variable Granger test. In any case the pattern of causal relationship varies quite a bit across cities and sectors. In Baltimore, for example, there would seem to be a relatively strong causal relationship between national economic factors and local sectoral employment since five of the seven sectors are Granger caused by national employment. Five sectors (a different five) are Granger caused by their national sectoral counterparts, whereas none of Baltimore’s local sectors have aggregate metropolitan employment as a significant determinant. A similar, though weaker, set of relationships holds for Denver, wherein three of the eight local sectors have significant coefficients for national aggregate employment, and four of them are significantly related to national sectoral employment (and two of those are negative). But like Baltimore, the relationship between M and local sectoral employment is surprisingly weak. In Houston the pattern of coefficients and t-statistics is rather different. Aggregate national employment is insignificant in all eight sectoral equations, while sectoral employment is significant in but two cases. In addition, aggregate metropolitan employment does Granger cause sectoral employment in four of the eight Houston sectors, and a fifth (services) has a t-statistic of 1.8. This would seem to indicate a relatively insular Houston economy, but another explanation is that Houston’s economy is counter-cyclical given its dependence on the oil market for its strength. Certainly this has been true in the latter part of the sample period. New York City sectoral employment has a wide range of determinants. National aggregate employment is Granger-causal for five sectors (though two are negative) and national sectoral employment is a significant determinant in five cases as well 11
They, and the full set of coefficients of the VAR, are available from the author. There are a large number of negative own-coefficients, especially in the slower growing cities of Baltimore and New York. This may indicate overdifferencing, i.e. stationarity in the levels, despite the results of Dickey–Fuller tests indicating nonstationarity. 12
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Table 1 Lag coefficients and summary statistics Dependent variable Constr.
Manuf.
TPU
Trade
FIRE
Service
Govt.
(a) Baltimore Nt 21 0.0008 (4.56) It 21 0.0001 (0.12) Mt 21 20.0120 (21.69) Et 21 0.0175 (0.39) Mean E 0.04 ˆ s 1.04 2 Adj. R 0.784
0.0005 (0.81) 0.0065 (4.52) 20.0046 (20.17) 20.2696 (26.37) 20.096 2.99 0.176
0.0003 (2.02) 0.0008 (0.83) 0.0176 (2.51) 20.2939 (27.11) 0.0066 0.988 0.321
0.0006 (2.44) 0.0023 (2.39) 0.01145 (1.29) 20.1150 (22.45) 0.281 1.599 0.866
0.0001 (2.25) 0.0043 (3.49) 0.0021 (0.85) 20.0909 (22.14) 0.084 0.351 0.432
0.0011 (2.20) 0.0040 (2.21) 0.0352 (1.50) 20.0994 (21.91) 0.841 2.83 0.779
0.0006 (1.21) 0.0053 (5.92) 20.0222 (21.12) 20.2459 (5.64) 0.265 2.32 0.501
(b) Denver Nt 21 0.00003 (0.58) It 21 0.0013 (2.18) Mt 21 20.0004 (21.8) Et 21 0.4671 (9.19) Mean E 0.0029 ˆ s 0.237 Adj. R 2 0.377
20.0001 (20.32) 0.0011 (0.76) 20.0015 (20.14) 0.1918 (3.25) 0.08 0.97 0.660
0.0007 (1.58) 0.0015 (2.11) 20.009 (20.41) 0.056 (0.77) 20.006 1.67 0.177
0.0003 (1.98) 20.004 (24.6) 0.0006 (0.122) 0.1030 (1.76) 0.163 0.74 0.149
0.0017 (4.35) 0.0033 (22.9) 20.0105 (20.56) 0.0009 (0.014) 0.402 1.49 0.797
0.0003 (3.03) 20.0011 (20.07) 20.0020 (20.45) 0.0608 (1.03) 0.162 0.411 0.339
0.0003 (0.81) 0.0025 (1.84) 0.0268 (1.43) 20.1210 (21.7) 0.683 1.54 0.483
(c) Houston Nt 21 20.0003 (21.4) It 21 0.0032 (1.63) Mt 21 0.0343 (4.11) Et 21 0.3427 (6.02) Mean E 0.113 ˆ s 0.786 2 Adj. R 0.421
20.0006 (21.2) 0.0014 (0.53) 0.0546 (3.14) 0.044 (0.70) 0.179 1.79 0.390
20.0000 (20.1) 0.0025 (2.90) 0.158 (1.10) 0.5461 (9.99) 0.132 1.29 0.541
0.0004 (1.23) 20.004 (22.7) 0.033 (3.56) 20.284 (25.1) 0.199 1.22 0.289
0.0004 (0.87) 0.0011 (0.65) 0.085 (4.16) 20.001 (20.02) 0.763 1.84 0.764
(d) New York City Nt 21 20.0000 (22.5) It 21 20.0001 (21.3) Mt 21 0.0000 (2.06) Et 21 20.142 (23.5) Mean E 20.000 ˆ s 0.047 Adj. R 2 0.092
20.0003 (20.8) 20.0001 (20.2) 20.0034 (22.1) 0.0681 (1.57) 20.051 2.65 0.596
0.0171 (8.86) 20.0208 (24.3) 20.0757 (25.3) 0.268 (5.54) 21.45 10.10 0.702
0.0013 (2.02) 20.0117 (22.5) 0.0222 (5.58) 20.2426 (25.9) 20.216 4.20 0.252
20.0018 (22.4) 0.0003 (0.10) 0.04011 (4.58) 20.182 (24.7) 20.333 4.49 0.899
0.00001 (0.08) 0.0044 (1.71) 0.004 (0.78) 0.0325 (0.55) 0.170 0.57 0.412
20.0004 (1.53) 0.0162 (2.51) 20.0071 (22.5) 0.0782 (2.66) 0.248 1.93 0.525
0.0011 (1.58) 20.0004 (20.1) 0.0411 (1.82) 0.0082 (0.11) 1.28 2.47 0.416
0.0056 (6.41) 20.0013 (3.14) 0.0061 (1.00) 20.041 (1.00) 1.28 5.25 0.617
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(again with two negative cases). Aggregate metropolitan employment is significant in seven of the eight aggregate sectors, which is substantive evidence of New York’s ability to support and determine the employment cycles of its own sectors. The examination of individual coefficients in a VAR is, however, an inappropriate method of drawing conclusions about the behavior of variables, precisely because of the dynamic, interlocking nature of the equations, and collinearity among the regressors. The whole point of creating conditions that identify orthogonal shocks is to examine these exogenous component’s effects on the jointly determined variables through simulation exercises. The standard, which is followed here, is to increase each of the shocks – that is, the various components of f, the national sectoral shocks, and c, the local sectoral shocks by one standard deviation and observe their impact on other variables in the system. These impulse response functions, will be presented in Figs. 1 through 4 only for the impact of each shock on the aggregate employment of each of the four cities. It is then possible to assess the importance of each sectoral shock to the determination of metropolitan employment through the variance decomposition which asks, for various forecast horizons, how much of the forecast variance is due to each of the unobservable shocks. The results are presented in Table 2 and are discussed for each city are discussed in turn. In Baltimore, the results are reasonably congruent with the causality results previously discussed, in that the influence of national shocks is relatively stronger than those for other cities. The shocks with the largest impacts on aggregate Baltimore employment are shocks to employment in the national public sector and the national manufacturing sector. Among local shocks the service, manufacturing and public sectors have the largest impacts, and according to Table 2 these three shocks account for well more than half of the variation in Baltimore employment. Nevertheless, and unlike the other example cities, national effects play a major role with national manufacturing and government employment shocks accounting for almost a quarter of the long run variation in metropolitan employment. In Denver, by contrast, no national shock invokes a larger response than the sixth most powerful among the local shocks (TPU) as displayed in Fig. 3. Among the local shocks, the public sector again seems to invoke a large response along with construction, trade, manufacturing and services. The variance decomposition of Table 2 confirms this result – the national sectoral shocks added together account for less than 5% of Denver employment variation, while the five local sectors mentioned account for the vast majority of movement in Denver employment. For Houston, the results are similar to Denver, in that responses to national shocks are small, but with one exception – as in Baltimore the impact of a national increase in public sector employment is large and account for more than 8% of employment variation in Houston. An interesting contrast is the trade sector, which invokes a large impulse response, but evidently does not have much explanatory effect. Table 2 shows that only 1.66% of Houston employment is explained by national trade employment shocks.
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Fig. 1. Response of Baltimore employment to local and national shocks.
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Fig. 2. Response of Denver employment to local and national shocks.
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736
Baltimore
US Mining US Constr. US Manuf. US TPU US Trade US Fire US Serv. US Govt. Local Mining Local Constr. Local Manuf. Local TPU Local Trade Local Fire Local Serv. Local Govt.
Denver
Houston
NYC
1 month
36 months
1 month
36 months
1 month
36 months
1 month
36 months
– 1.46 12.53 0.52 4.33 0.07 5.44 4.53 – 2.65 24.62 3.51 3.68 0.36 21.00 15.26
– 1.51 13.13 0.61 4.56 0.09 5.61 10.25 – 2.33 25.56 3.24 3.26 0.32 18.54 13.96
0.00 0.10 0.01 0.39 0.20 0.01 0.42 0.32 0.91 14.77 14.37 5.46 16.97 1.92 14.80 29.31
0.04 0.24 0.77 0.39 0.21 0.01 0.63 0.98 0.93 14.55 14.09 5.36 16.63 1.88 14.53 28.73
0.060 0.063 2.04 2.27 1.78 0.06 4.01 7.34 2.94 16.96 8.07 7.11 10.54 1.62 17.70 16.82
0.07 0.61 3.05 1.99 1.66 0.07 3.58 8.54 3.39 16.32 11.44 6.20 9.95 1.56 16.75 14.76
0.00 0.197 4.82 1.64 1.52 0.137 1.77 0.32 0.00 1.84 28.52 3.64 3.32 0.96 6.48 44.77
0.04 0.307 4.47 1.52 1.54 0.172 0.52 6.20 0.00 1.66 27.35 3.42 3.05 0.87 5.83 41.92
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Table 2 Variance decomposition of employment
Fig. 3. Response of Houston employment to local and national shocks.
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Fig. 4. Response of NYC employment to local and national shocks.
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A large number of local shocks are seen to be important to Houston’s economy: manufacturing, services, construction, government and trade all have substantial impulse responses emanating from them, and all have roughly equal shares in explaining metropolitan employment. The results for New York are different yet again. As befitting its size the impact of the shocks is larger here overall than those from the other cities, as can be seen from the vertical scale of the figures. The comparison of scales also reveals that the local shocks are far more substantial in their impact than national shocks. Two national shocks appear to have more than a trivial impact on New York’s economy: government employment and manufacturing employment. Interestingly, the national public sector only has minimal impact in the short run but a much more substantial importance in the long, a phenomenon that is also visible in Baltimore. Just as interesting is the fact that the same two sectors have dominant impacts from the set of local shocks. Manufacturing shocks have a huge impact on New York aggregate employment as do public sector employment shocks. The impact of these two sectors is also obvious from the variance decomposition where the local public sector accounts for nearly half of the employment variation all by itself. This plus the local manufacturing shock more or less dwarf the remaining sources of fluctuations. It would, therefore, seem fairly straightforward to summarize the results from this exercise, since there are some strong commonalities in these results across the four cities. First, local shocks play a more important role in the determination of aggregate local employment than do national shocks, thus corroborating the results for local sectoral employment contained in Coulson (1993). Second, for most cities a broad array of local sectors is important in local employment. In various instances, manufacturing, government, services, construction and trade all can have substantial impact on local employment movements. But, third, the importance of the manufacturing, public, and (with New York as an exception) the service sector seem significantly greater overall than other local sectors. This seems congruent with long standing export-oriented models of cities, such as the base multiplier model. Manufacturing is traditionally thought of as an important source of export earnings that are in turn thought to be the engines of urban growth. Similarly, government expenditure is also thought to be an important source of export earnings. It is important to recall that local government employment includes federal and state employment within the metropolitan area and, therefore, to that extent consists of injections into the local economy and are not (at least directly) paid for with local tax dollars. Services, on the other hand have only recently been regarded as having any kind of export orientation. There are some limitations that should be recognized. The most important of these is the potential limitation of the neutrality restriction. To test the limitations of this set of assumptions, the model is expanded to allow for increased influence
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(for better or worse) by a particular sector in both the residual decomposition and the VAR itself. This is done for four city-industry pairs: the service sector in Baltimore, the TPU sector in Denver; the construction sector in Houston; and the FIRE sector in New York City. In each case a lag of that local sector was added to each of the local sector equations, and a parameter was added to the orthogonalization specification which allowed that sector’s orthogonal shock to have a separate influence each local sector’s residual. The results are striking in that in three of the four cases the change in specification had only a minuscule impact on the results. For example the expanded role of the financial sector in New York City model leads to a change in the contribution of that sector from 0.96% in the short run and 0.87% in the long run to 0.97 and 1.5%, respectively. The added scope for the Baltimore service sector yields similarly small increases in that sector’s contribution from 21 and 19.5 to 21.8 and 19.8%. In the Denver case, the changes are from 5.5 and 5.4 to 7.5 and 7.7%. There was, however, a substantive change in the Houston results when the construction sector was allowed to have extra explanatory power, which was to reduce that sector’s contribution from roughly 16–17% to around 10–11%. (The slack was mostly taken up by the local service sector.) Thus, the additional parameters served to move the Houston results closer to the norm, in light of the reduced importance of construction. Other caveats apply. The first is that it should be recalled that all of the data is in absolute thousands of employees, and not (say) in logarithmic form. This is required given the emphasis on aggregation in the empirical model but it creates a size effect in the results that would perhaps not be as pronounced in the logarithmic case.13 The size of the shocks, as noted, is the standard deviation of the shock, and this depends on the size of the sector, but this ‘magnitude effect’ is part of what creates employment; big sectors create more jobs, other things equal, than small sectors. Moreover this effect is not all-encompassing. While it might account for the lack of influence of certain local sectors, particularly mining, and the finance industry,14 the trade sector is quite large in these metropolitan areas, and
13 A logarithmic model was created in order to try and judge the extent of the effect discussed here. This model used log differences of sectors and aggregate metropolitan employment and identified sector-specific shocks by assuming that the local vi values were mutually orthogonal to each other but not to an aggregate (log) citywide employment shock. The first restriction is necessitated by the desire for sector-neutral treatment coupled with an inability to aggregate the sectoral shocks in any meaningful way. (Carlino and Defina (1995) inter alia take this approach in a study of the impact of regional employment shocks.) Applying the results to each of the sample MSAs in turn entailed some surprise in that size actually appears to play more of a role here than in the levels model. In three of the four cities the most significant sector was the service sector, the largest of the one-digit sectors. In the fourth case of Houston, the manufacturing sector was the most powerful determinant. The conclusion is that the size of sectors does not completely drive the results above. 14 Indeed the lack of explanatory power for this industry in New York City given its putative role in New York’s growth (as outlined in Sassen, 1991) is notable.
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yet is not the origin of important movements in aggregate employment. It is evidently a follower, rather than a leader, and what is important, the method proposed here identifies it as such. Moreover, some sectors have lots of explanatory power despite their small size. In this vein the role of the construction sector in the Denver and Houston cases is interesting. Both are fast-growing cities, so the construction sector might be more active here than in our other example areas. Nevertheless the role of construction as a causal factor in growth might be questionable, since it is among the most local-serving of sectors and, therefore, presumably lagging growth rather than leading it. Case (1992), for example, details how the construction sector had a role in perpetuating, rather than initiating, the 1980s expansion of Boston area employment. This, then, brings us to the second caveat which is that many of the effects being discussed here are, over the sample frame, of the opposite sign of the discussion presented. That is, the employment shocks which actually occur (rather than simulated for presentation purposes) might be negative, leading to negative impacts on employment. One might speculate that this explains the power of manufacturing shocks in New York in particular. Recall that the data for New York is for the city itself rather than the metropolitan area, and that central city job loss in manufacturing is ongoing for New York over the sample period (Table 1d). The response of the aggregate economy to these manufacturing shocks can be large. Third, the analysis is entirely positive in orientation. Nothing in this is meant to suggest that policy options designed to favor manufacturing or public sector employment are superior, on the grounds of having larger multipliers, to a policy which is neutral across sectors. Recalling the first of the caveats above, the simulations here are not ceterus paribus experiments, since the initial stimulus is not identical across regions. Even if they were, the existence of differential multipliers is not necessarily grounds for such industry specific policy initiatives.
4. Summary and conclusions This paper has delineated a new method for using vector autoregression models to measure the contribution of industrial sectors to metropolitan growth. By using an orthogonalization scheme based on shift-share principles, industry shocks at the national and local levels are identified, without assuming any causal ordering among the industries. In the four example cities, local shocks are generally more important than national shocks in the determination of metropolitan employment. Among local shocks, public sector employment shocks and manufacturing employment shocks and sometimes service sector shocks have the most explanatory power overall, a result which is congruent with export-based models of metropolitan growth and decline.
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There are of course extensions which are available. Despite commonalities across the various cities, there is sufficient heterogeneity to warrant a broader cross-section of examples. There is also the potential for finer disaggregation of sectors, particularly within manufacturing, and this may be important in the analysis of particular areas. It is also possible to include other types of shocks in the framework provided here. As one example, there has been work on the differential effects of monetary policy across industries (Carlino and Defina, 1996) and across regions. The framework here can naturally include money shocks which would then have differential effects across both disaggregate dimensions. Further extensions along these lines may include the reaction to oil prices, or defense spending shocks (Coulson and Rushen, 1995).
Acknowledgements I am grateful to Todd Clark, Jim Kurre, John Quigley, Norm Swanson, and an anonymous referee for helpful comments.
References Altonji, J., Ham, J., 1990. Variation in employment growth in Canada. Journal of Labor Economics 8, 198–236. Brown, S., Coulson E., Engle R., 1991. Noncointegration Econometric Evaluation of Models of Regional Shift and Share. NBER Working Paper 3291. Brown, S., Coulson, E., Engle, R., 1992. On the determination of regional base and regional base multipliers. Regional Science and Urban Economics 22, 619–635. Browne, L., 1988. High technology and business services. In: Lampe, D. (Ed.), The Massachusetts Miracle, MIT Press, Cambridge. Carlino, G., Defina, R., 1996. Does US Monetary Policy have Differential Regional Effects. Working Paper, Federal Reserve Bank of Philadelphia. Case, K., 1992. The real estate cycle and the regional economy: the consequences of the Massachusetts Miracle of 1984–87. Urban Studies 92, 171–183. Clark, T., 1998. Employment Fluctuations in US Regions and Industries. Journal of Labor Economics 16, 202–229. Clark, T., Shin, K., 1998. Sources of Fluctuations within and across Countries. Working paper, Federal Reserve Bank of Kansas City. Coulson, E., 1993. The sources of sectoral fluctuations in Metropolitan areas. Journal of Urban Economics 33, 76–94. Coulson, E., Rushen, S., 1995. Sources of fluctuations in the Boston Economy. Journal of Urban Economics 38, 74–93. McCarthy, J., Steindel, C., 1997. National and regional factors in the New York Metropolitan Economy. Economic Policy Review 3, 5–20.
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Norrbin, S., Schlagenhauf, D., 1988. An inquiry into the sources of macroeconomic fluctuations. Journal of Monetary Economics 22, 43–70. Richardson, H., 1985. Economic base and input–output models. Journal of Regional Science 25, 607–622. Sassen, S., 1991. In: The Global City, Princeton University Press, Princeton.
Sectoral sources of metropolitan growth N. Edward Coulson* Department of Economics, Penn State University, University Park, PA 16802, USA Received 15 June 1997; received in revised form 8 March 1999; accepted 27 April 1999
Abstract The paper proposes a method for identifying sectoral sources of metropolitan employment growth The key feature of the VAR is the set of (over)identifying restrictions which do not require a causal ordering to be developed among industries to create orthogonal sectoral shocks. The simulations for four cities indicate that local sectoral shocks are more important than national counterparts, and that among local shocks, the overall evidence indicates that manufacturing, service and public sector employment shocks account for a substantial portion of employment growth variation, a conclusion that seems roughly consistent with export-oriented models of metropolitan growth. 1999 Elsevier Science B.V. All rights reserved. Keywords: Metropolitan employment growth; Export-oriented models
1. Introduction There is an intense practical interest in knowing which industrial sectors are responsible for growth in cities. The growth or decline of employment in a metropolitan area must by definition be the result (indeed, is the sum) of employment growth or decline in its various industries. But to the extent that sectors move in the same direction at roughly the same time, it is difficult to discover which sectors are responsible (or causally prior) for that growth. Theory is of little help. The only widely recognized theory that addresses the causal *Tel.: 11-814-863-0625; fax: 11-814-863-4775. E-mail address: [email protected] (E. Coulson) 0166-0462 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0166-0462( 99 )00017-4
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ordering of sectoral growth is the export base model, in which ‘export’ industries create exogenous (export) demand and through backward linkages and factor earnings, generate demand for the output of other (local-serving) sectors. Empirical implementation of this theory then requires a bifurcation of employment into export and local sources, and this is often done at the sectoral level. But this is very difficult. Theories of agglomeration are even worse at identifying sectorspecific shocks, since such theories can imply two-way causality between suppliers’ and demanders’ employment. As an example of the difficulties, Browne (1988) examines the role of business services in the Massachusetts Miracle, the explosive employment surge which took place in Massachusetts and surrounding areas during the late 1970s and early 1980s. Consider the dilemma faced by this author when trying to analyze this issue: ‘‘High tech manufacturing has not been the sole source of new jobs in the region. Growth has been very rapid in the service industries . . . But while it would be a mistake to look upon high technology as the only reason for New England’s prosperity, it would also be a mistake to view these other developments as entirely independent of the developments in high tech manufacturing. In particular, the growth in some of the most rapidly expanding business services is, to some extent, a reflection of the growth in high tech manufacturing’’ (p. 202). Thus, it is clear that a technology for isolating the separate contributions over time of the various metropolitan industries is imperative. Neither input–output models nor previous time series models have successfully grappled with this issue.1 In this paper, the aim is to provide such a framework. VARs are a convenient tool for this purpose because they provide a mechanism for constructing innovations in various sectors that are orthogonal to each other, and allow the implementation of a technology for assessing the dynamic impact of these separate shocks. However, the conventional method for orthogonalization (Choleski decomposition of the VAR’s residual covariance matrix) is inappropriate for this problem, for reasons which are discussed below, so instead a new (overidentified) method of constructing the sectoral shocks is proposed. This method is related to shift-share analysis, in that it precludes inter-industry effects except through their impact on aggregate totals. The vector autoregression model is estimated for four US cities. Results indicate that local shocks are more potent than national shocks and that among local shocks, those to the manufacturing, public and service sectors predominate.
1 Studies most similar in spirit to this one, as ably surveyed in Clark and Shin (1998) have concentrated on effect of various types of shocks on regional sectors (Norrbin and Schlagenhauf, 1988; Altonji and Ham, 1990; Clark, 1998) as opposed to the metropolitan focus of this paper (and of Coulson, 1993; Coulson and Rushen, 1995; McCarthy and Steindel, 1997). The methods followed here also differ slightly from the above papers (see footnote 6).
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2. The econometric framework The shift-share model is built on the premise that national, sectoral and, in some models, metropolitan fluctuations are reflected proportionally in local sectoral movements. This then encompasses (respectively) aggregate demand and supply shocks, sectoral supply and demand shocks and metropolitan demand shocks, so that deviations from proportionality are then attributed to supply side factors at the local-sectoral level. Some of the econometric implications of this model have been discussed in Coulson (1993). In the more highly parameterized context of vector autoregressions, it is straightforward to extend this idea. Consider the following regression model which (ignoring deterministic components) determines sector i employment, e it , in an (unindexed) metropolitan area at time t: e it 5 c i (B)n t 1 d i (B)s it 1 fi (B)m t 1 gi (B)e it 1 u it . Each right-hand side term x i (B)z it term represents a lag polynomial, i.e. a collection of coefficients and associated regressors that are lagged values of the various z terms. These regressors are: n, (aggregate) employment in the nation; s, sectoral employment in the nation; m, (aggregate) metropolitan employment; and e, sectoral employment in the metropolitan area. The idea here is that these four sets of lagged variables represent the four kinds of stimuli identified in the shift-share framework, albeit in a more dynamic framework, and without the restriction of proportionality. The u it term is a residual for this sectoral equation which represents the exogenous shocks to industry employment. Now consider a set of such equations, one for each of the k sectors in the metropolitan area: e 1t 5 c 1 (B)n t 1 d 1 (B)s 1t 1 f1 (B)m t 1 g1 (B)e 1t 1 u 1t . . . e kt 5 c k (B)n t 1 d k (B)s kt 1 fk (B)m t 1 gk (B)e kt 1 u kt This set of k equations can be augmented with an identity which links m and the various e i values with the obvious aggregation identity: m t 5 e 1t 1 ? ? ? 1 e kt . We can similarly write k equations that model each national sector. Each of these will be modeled as a function of its own past, and lags of n t . We, therefore, have k equations of the form s it 5 h i (B)n it 1 j i (B)s it 1 vit for i51 to k, so that each national industry’s employment is dependent on national aggregate employment lags, and its own past. Similarly, an aggregation condition is added of the form
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n t 5 s 1t 1 ? ? ? 1 s kt . The above equations comprise a (2k12)-dimensional vector autoregression whose principal task is to model the short run fluctuations of each metropolitan sector and the metropolitan aggregate as a function of those sectors. Imagine an exogenous increase in the ith sector’s employment as manifested by an increase in u it . This shock immediately increases both e it and m t . The remaining sectors are then affected with a lag by the increase in m t , which then causes further increases in m t and yet further increases in each sectors’ employment, and so on.2 At the national level, a similar mechanism applies. An increase in vit immediately increases s it and n it , the latter through the aggregation equation, and then s it as well as e it with a lag. This causes an increase in m it and all of these changes set further changes in motion. This description of the short run process of employment growth in a metropolitan area is roughly congruent with the base multiplier model in that short run growth is generated by an exogenous increase in one sector’s employment, perhaps due to an export shock, which in turn stimulates and restimulates aggregate employment through standard multiplier analytics,3 and like the base multiplier it restricts the kinds of interaction that sectors can have with one another. In the case of the multiplier model sectors are bifurcated into basic and local sectors, and basic sector employment is determined exogenously. In turn, these exogenous movements influence local sectors, and this influence is remanifested in further increases in local employment. In the present VAR model, each sector has an exogenous component, which arises from the residual, and from national influences and an induced (local) component, so that there is no necessity of providing the often arbitrary distinction between exporting and non-exporting sectors. But neither is there an allowance for the possibility that the relationship between two particular sectors might be different (as that of supplier and demander, say). This would be the case in more highly parameterized models such as input–output, but is not allowed here.4 A major issue remains, which is the contemporaneous correlation of the residuals. Under the interpretation of each of the u i as shocks to employment in the ith sector, we can putatively trace the sources of metropolitan growth to individual sectors, but only if the u i are uncorrelated. They of course do not have this property in practice, and this prevents us so far from assigning variation in 2
This description of the process assumes that the lag coefficients are positive, and that the system is such that the impacts die out after a sufficient number of iterations. 3 A version of those analytics is contained in Brown et al. (1992) or Richardson (1985). 4 In fact it is possible to allow this in the VAR itself, but I do not allow it for reasons of parsimony, and to maintain congruency with the orthogonalization procedure below, where such a parameterization is not possible. Models that partially relax some of these restrictions are discussed later on in the paper.
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aggregate metropolitan employment to particular sectors. If say, construction and manufacturing employment shocks move together, which of them is ultimately responsible? It is necessary to extract components of the u i that are orthogonal to each other in order to accomplish this task. The problem of orthogonalization is as old as the method of vector autoregression itself. We wish to find an identifiable matrix of parameters, W such that
SuvD 5 WSufD where u and v are the obvious vectorizations of the VAR residuals above and u and f are k-dimensional vectors which contain orthogonal innovations to national and local employment series. By orthogonal it is meant that
SD
u Cov f 5 D where D is a diagonal matrix. Under such circumstances we can identify the orthogonalized residuals as those representing exogenous shocks to each of the sectors, with which the sectoral origin of metropolitan growth and decline are delineated. The discussion now centers on the identifiability of the parameters in W. A standard tack is to make W lower triangular, with ones along the main diagonal. This automatically ensures the identifiability of W through recursion; there are k(k21) parameters in the matrix, which along with the 2k variances in D equals to the number of parameters in the residual covariance matrix of u and v. However, the lower triangularity of W implies a particular relationship among the residuals. The first element of u is a function of only the first element of u, indeed is identical with it. The second element is a function of the first and second elements of u, and so on through all of the elements of u and v. Thus, there is a hierarchical relationship implied among the innovations – what is sometimes called a (contemporaneous) causal ordering among them. This causal ordering must be inferred from a priori reasoning, such as economic theory, and can never be completely dictated by sample properties, and as such can be the source of controversy. This is especially true when the inferences drawn from a VAR vary with the ordering chosen. In the present application the problem is exacerbated, since (unlike many macroeconomic applications) there is almost no theoretical guide to aid in choosing an appropriate ordering. The only such theories arise (as noted above) from variants of the base multiplier model which imply that local growth is a function of exports, and that exports depend on national (and international) conditions. For this model the implication would be that national sectoral employment ought to be placed causally prior to local sectors, and that within the set of local equations, that export sectors are causally prior to local-serving sectors.
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The first of these statements seems reasonable. Indeed it informs the construction of the VAR model itself, in that Ei does not appear in the equations determining Si . However the second assumption is fraught with difficulty, because it requires identifying export industries among the group of local sectors, and moreover it requires identifying any sector as either entirely local or entirely export. The base multiplier literature (Richardson, 1985; Brown et al., 1992) is fairly convincing that the latter bifurcation is impractical, even at high levels of disaggregation. Even if these last difficulties could be overcome, the standard approach still requires a causal ordering within the export and local-serving groups and within the national sectors as well. This seems an insurmountable difficulty, and compels one to search for alternative means of identifying W, one that is neutral among the various sectors. To do so again consider the principles underlying the VAR itself and decompose the local sectoral residual into functions of a national shock, industry shock, metropolitan shock and a shock idiosyncratic to the city-industry. In doing so, it is necessary to recognize that there is no national shock and no metropolitan shock per se, but that we can in some sense create one by adding together the sectoral shocks at the national and local levels, respectively. In so doing we have: u it 5 bi fit 1 gi Sfj 1 cit 1 dj Scjt where as notated above fj and cj are the orthogonal shocks to the jth national and local sector, respectively. The b, g, and d parameters are to be estimated. It can be seen that the pattern of relationships is congruent with the description above. The residual u it is a linear combination of its own sectoral shock fj , the ‘national’ shock – i.e. the sum of national sectoral shocks – Sfj the ‘metropolitan’ shock Scj and the idiosyncratic shock ci . The parameter b then represents the local share of sectoral movements, g represents the local industry’s share of aggregate movement,5 and d is the local sector’s share of the metropolitan shock. The unit coefficient on the own shock is then an appropriate normalization. We employ a similar but simpler scheme for the aggregate sectoral shocks: u 1 5 f1 1 a1 Sfi that is, the first residual is the sum of the first innovation (which is now identified as the first national industry’s shock) plus a fraction (a1 ) of the shock to national output, which by definition is the sum of all national sectoral shocks. Note that the unit coefficient on the first term above also serves as the appropriate normalization. 5
There is obviously an implicit normalization here, in that one could alternatively write the sectoral weight as zi 5 bi 1gi and let the national shock omit the ith sector.
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The remaining national sectors have their innovations described in an analogous way.6 Thus, local and national innovations from the same sector are correlated through the national sectoral effect, all national sectoral innovations are correlated with every sector’s local and national innovation through the respective aggregates, and every local innovation is allowed to be correlated with every other local innovation through the metropolitan aggregate. Nevertheless, the parameters are identified. The identification of the parameters of this decomposition arises from the constraints placed on the way in which sectors can respond to movements in one another. Were we to allow each sector to respond to others in an unrestricted fashion, the resulting number of parameters would eliminate the possibility of identifying any of them. The method proposed here is a plausible way of limiting the number of parameters in order to achieve identification while remaining neutral in its treatment of each of the sectors (i.e. not imposing a causal hierarchy). The drawback is that in a sense it goes too far – it is highly overidentified.7 6
Previous literature (as cited in footnote 1) has grappled with this identification problem in various ways. A common tack is to assume the industry (or regional, as the case may be) shocks are independent of each other. Typically the models then contain a separate national employment shock. Separate identification of national and industry shocks can then be achieved through (a) omission of an industry; (b) use of a logarithmic functional form (in which case aggregation fails); or (c) measurement error, since in published BLS data the sum of industry employments is never equal to aggregate employment at the local level. Here, the national (and metro) shocks are omitted from the decomposition of the shocks (to achieve both perfect aggregation and identification), but to the extent that propagation of shocks is common across sectors this is effectively viewed as a ‘national shock’. Given the emphasis here on the differences in sectoral impacts on metropolitan aggregates, this view seems appropriate. See Clark and Shin (1998) for a full discussion of these issues. 7 While method of moments estimation is available for overidentified models such as this, the ease of computing the likelihood ratio tests makes maximum likelihood estimation attractive as long as normality is assumed. Consider the log-likelihood function, written in this case (without constants) as
S D log(WDW9)2]12 S suvd (WDW9)
T 2 ] 2
t
t
21
suvd
t
with T as the sample size, so that the covariance matrix of the residuals is replaced by its decomposition. The value of this likelihood function is invariant to the decomposition as long as the parameters are just-identified. As with standard likelihood ratio tests, the imposition of constraints lowers the value of the log-likelihood and twice the difference of the overidentified and just-identified versions of the model will be distributed under the null that the constraints are satisfied will be distributed in the usual way as a x 2 with degrees of freedom equal to the number of constraints. Thus, the comparison of the Choleski decomposition (with any causal ordering) to the overidentified model will yield the appropriate test statistic. It will happen in the empirical application that k57 or 8, which regrettably leads to 70 or more overidentifying restrictions. This is problematic in that with so large a number of restrictions it will be almost impossible to satisfy them all, and the overidentifying restrictions will be rejected. As it happens, this turns out to be the case in the estimates below. Nevertheless the model’s relative simplicity and neutrality with respect to sectoral prominence provide sufficient tradeoff against the large degree of overidentification.
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3. Implementation The parameters of the model are to be estimated using data from four US cities: Baltimore, Denver, Houston, and New York City. The sample frames are as follows: before lags are introduced the beginning date is January 1949 for Baltimore and January 1950 for New York City, with January 1970 being the starting date for the other two. The ending date is April 1996 in all four samples.8 Other dimensions of the model specification are now taken up. One difficult decision deals inevitably with whether to specify the variables in level or first differences, a decision not informed by the importance placed here on aggregation. In the end, first differences are used exclusively. The maintained assumption is, therefore, that the data are difference-stationary with no cointegrating relationship among them, an assumption which coincides with the results in the literature (Brown et al., 1991; Coulson, 1993) which in particular examined the most natural cointegrating possibility, that of local and national employment within the same sector.9 Another important aspect of model specification is the lag length. Under the convenient assumption that all of the lag polynomials in the VAR are the same length, model selection criteria indicated that the optimal lag length should be one. This is undoubtedly due to the large number of parameters added for each increase in the polynomial order, which incurs a heavy penalty in, e.g. the Schwarz information criterion. The estimation then proceeds with the following steps. The VAR is estimated using the method of Seemingly Unrelated Regressions. The residuals from this estimate are then used to maximize the likelihood function (see Section 2), and this provides the estimates of the parameters of the W and D matrices. The constrained covariance matrix is then used to re-estimate the VAR parameters using Seemingly Unrelated Regressions once more.10 The parameters of the W matrix are accordingly estimated in this way, but not 8
The data is taken from the Bureau of Labor Statistics World Wide Web site for retrieval of information from Employment and Earnings, and Employment and Earnings: States and Areas. The starting point for such retrieval is at URL http: / / stats.bls.gov:80 / sahome.html. 9 It must be admitted, nevertheless that with 2n equations, cointegration tests will only rarely fail to reject the null hypothesis of no cointegration. Unfortunately such ‘random’ cointegration which was found in this case appeared to have little meaningful interpretation. Furthermore the shift-share model from which the present construction draws some of its inspiration is a decomposition based on changes. Since the data are in differences rather than growth rates, it is necessary to add a deterministic trend to the model, since absolute changes grow resolutely over time. This time trend is not reported below (for space considerations) but is uniformly significant. Finally, a full set of seasonal dummies is used in all equations to account for seasonal variation in employment cycles. These are suppressed in the presentation of the results as well. 10 Two more details: OLS is often used to estimate the equations of the VAR, since no efficiency gains are available to SUR if the data matrix on the right-hand side is identical across equations. This is not the case here, so SUR is required in the second step. It is not strictly necessary in the first step, since all that is required is a consistent estimate of the lag polynomial and other parameters in the VAR.
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presented here to save space.11 To summarize, they are nearly always positive and of intuitive size; a few are negative and this may be due to some cross-sectoral substitution as growth or decline occurs. Given these W parameters (and the estimated standard errors of the shocks themselves) the constrained covariance matrix can be constructed and the parameters of the VAR estimated. The key coefficients are displayed in Table 1a–d. The overall fits, as measured by the adjusted R 2 are weakest for the New York City estimates although in general, they are reasonable for differenced data. The sizes of the coefficients are roughly of the same orders of magnitude as the parameters in W and while there are a number of unexpected negative coefficients, most of these are small and statistically insignificant.12 The t-statistics in Table 1 can be looked upon as Granger-causality results. Recalling that Granger-causality tests are always conditional on the specific information set, the information set here is quite extensive, compared to the oft-used two-variable Granger test. In any case the pattern of causal relationship varies quite a bit across cities and sectors. In Baltimore, for example, there would seem to be a relatively strong causal relationship between national economic factors and local sectoral employment since five of the seven sectors are Granger caused by national employment. Five sectors (a different five) are Granger caused by their national sectoral counterparts, whereas none of Baltimore’s local sectors have aggregate metropolitan employment as a significant determinant. A similar, though weaker, set of relationships holds for Denver, wherein three of the eight local sectors have significant coefficients for national aggregate employment, and four of them are significantly related to national sectoral employment (and two of those are negative). But like Baltimore, the relationship between M and local sectoral employment is surprisingly weak. In Houston the pattern of coefficients and t-statistics is rather different. Aggregate national employment is insignificant in all eight sectoral equations, while sectoral employment is significant in but two cases. In addition, aggregate metropolitan employment does Granger cause sectoral employment in four of the eight Houston sectors, and a fifth (services) has a t-statistic of 1.8. This would seem to indicate a relatively insular Houston economy, but another explanation is that Houston’s economy is counter-cyclical given its dependence on the oil market for its strength. Certainly this has been true in the latter part of the sample period. New York City sectoral employment has a wide range of determinants. National aggregate employment is Granger-causal for five sectors (though two are negative) and national sectoral employment is a significant determinant in five cases as well 11
They, and the full set of coefficients of the VAR, are available from the author. There are a large number of negative own-coefficients, especially in the slower growing cities of Baltimore and New York. This may indicate overdifferencing, i.e. stationarity in the levels, despite the results of Dickey–Fuller tests indicating nonstationarity. 12
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Table 1 Lag coefficients and summary statistics Dependent variable Constr.
Manuf.
TPU
Trade
FIRE
Service
Govt.
(a) Baltimore Nt 21 0.0008 (4.56) It 21 0.0001 (0.12) Mt 21 20.0120 (21.69) Et 21 0.0175 (0.39) Mean E 0.04 ˆ s 1.04 2 Adj. R 0.784
0.0005 (0.81) 0.0065 (4.52) 20.0046 (20.17) 20.2696 (26.37) 20.096 2.99 0.176
0.0003 (2.02) 0.0008 (0.83) 0.0176 (2.51) 20.2939 (27.11) 0.0066 0.988 0.321
0.0006 (2.44) 0.0023 (2.39) 0.01145 (1.29) 20.1150 (22.45) 0.281 1.599 0.866
0.0001 (2.25) 0.0043 (3.49) 0.0021 (0.85) 20.0909 (22.14) 0.084 0.351 0.432
0.0011 (2.20) 0.0040 (2.21) 0.0352 (1.50) 20.0994 (21.91) 0.841 2.83 0.779
0.0006 (1.21) 0.0053 (5.92) 20.0222 (21.12) 20.2459 (5.64) 0.265 2.32 0.501
(b) Denver Nt 21 0.00003 (0.58) It 21 0.0013 (2.18) Mt 21 20.0004 (21.8) Et 21 0.4671 (9.19) Mean E 0.0029 ˆ s 0.237 Adj. R 2 0.377
20.0001 (20.32) 0.0011 (0.76) 20.0015 (20.14) 0.1918 (3.25) 0.08 0.97 0.660
0.0007 (1.58) 0.0015 (2.11) 20.009 (20.41) 0.056 (0.77) 20.006 1.67 0.177
0.0003 (1.98) 20.004 (24.6) 0.0006 (0.122) 0.1030 (1.76) 0.163 0.74 0.149
0.0017 (4.35) 0.0033 (22.9) 20.0105 (20.56) 0.0009 (0.014) 0.402 1.49 0.797
0.0003 (3.03) 20.0011 (20.07) 20.0020 (20.45) 0.0608 (1.03) 0.162 0.411 0.339
0.0003 (0.81) 0.0025 (1.84) 0.0268 (1.43) 20.1210 (21.7) 0.683 1.54 0.483
(c) Houston Nt 21 20.0003 (21.4) It 21 0.0032 (1.63) Mt 21 0.0343 (4.11) Et 21 0.3427 (6.02) Mean E 0.113 ˆ s 0.786 2 Adj. R 0.421
20.0006 (21.2) 0.0014 (0.53) 0.0546 (3.14) 0.044 (0.70) 0.179 1.79 0.390
20.0000 (20.1) 0.0025 (2.90) 0.158 (1.10) 0.5461 (9.99) 0.132 1.29 0.541
0.0004 (1.23) 20.004 (22.7) 0.033 (3.56) 20.284 (25.1) 0.199 1.22 0.289
0.0004 (0.87) 0.0011 (0.65) 0.085 (4.16) 20.001 (20.02) 0.763 1.84 0.764
(d) New York City Nt 21 20.0000 (22.5) It 21 20.0001 (21.3) Mt 21 0.0000 (2.06) Et 21 20.142 (23.5) Mean E 20.000 ˆ s 0.047 Adj. R 2 0.092
20.0003 (20.8) 20.0001 (20.2) 20.0034 (22.1) 0.0681 (1.57) 20.051 2.65 0.596
0.0171 (8.86) 20.0208 (24.3) 20.0757 (25.3) 0.268 (5.54) 21.45 10.10 0.702
0.0013 (2.02) 20.0117 (22.5) 0.0222 (5.58) 20.2426 (25.9) 20.216 4.20 0.252
20.0018 (22.4) 0.0003 (0.10) 0.04011 (4.58) 20.182 (24.7) 20.333 4.49 0.899
0.00001 (0.08) 0.0044 (1.71) 0.004 (0.78) 0.0325 (0.55) 0.170 0.57 0.412
20.0004 (1.53) 0.0162 (2.51) 20.0071 (22.5) 0.0782 (2.66) 0.248 1.93 0.525
0.0011 (1.58) 20.0004 (20.1) 0.0411 (1.82) 0.0082 (0.11) 1.28 2.47 0.416
0.0056 (6.41) 20.0013 (3.14) 0.0061 (1.00) 20.041 (1.00) 1.28 5.25 0.617
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(again with two negative cases). Aggregate metropolitan employment is significant in seven of the eight aggregate sectors, which is substantive evidence of New York’s ability to support and determine the employment cycles of its own sectors. The examination of individual coefficients in a VAR is, however, an inappropriate method of drawing conclusions about the behavior of variables, precisely because of the dynamic, interlocking nature of the equations, and collinearity among the regressors. The whole point of creating conditions that identify orthogonal shocks is to examine these exogenous component’s effects on the jointly determined variables through simulation exercises. The standard, which is followed here, is to increase each of the shocks – that is, the various components of f, the national sectoral shocks, and c, the local sectoral shocks by one standard deviation and observe their impact on other variables in the system. These impulse response functions, will be presented in Figs. 1 through 4 only for the impact of each shock on the aggregate employment of each of the four cities. It is then possible to assess the importance of each sectoral shock to the determination of metropolitan employment through the variance decomposition which asks, for various forecast horizons, how much of the forecast variance is due to each of the unobservable shocks. The results are presented in Table 2 and are discussed for each city are discussed in turn. In Baltimore, the results are reasonably congruent with the causality results previously discussed, in that the influence of national shocks is relatively stronger than those for other cities. The shocks with the largest impacts on aggregate Baltimore employment are shocks to employment in the national public sector and the national manufacturing sector. Among local shocks the service, manufacturing and public sectors have the largest impacts, and according to Table 2 these three shocks account for well more than half of the variation in Baltimore employment. Nevertheless, and unlike the other example cities, national effects play a major role with national manufacturing and government employment shocks accounting for almost a quarter of the long run variation in metropolitan employment. In Denver, by contrast, no national shock invokes a larger response than the sixth most powerful among the local shocks (TPU) as displayed in Fig. 3. Among the local shocks, the public sector again seems to invoke a large response along with construction, trade, manufacturing and services. The variance decomposition of Table 2 confirms this result – the national sectoral shocks added together account for less than 5% of Denver employment variation, while the five local sectors mentioned account for the vast majority of movement in Denver employment. For Houston, the results are similar to Denver, in that responses to national shocks are small, but with one exception – as in Baltimore the impact of a national increase in public sector employment is large and account for more than 8% of employment variation in Houston. An interesting contrast is the trade sector, which invokes a large impulse response, but evidently does not have much explanatory effect. Table 2 shows that only 1.66% of Houston employment is explained by national trade employment shocks.
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Fig. 1. Response of Baltimore employment to local and national shocks.
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Fig. 2. Response of Denver employment to local and national shocks.
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Baltimore
US Mining US Constr. US Manuf. US TPU US Trade US Fire US Serv. US Govt. Local Mining Local Constr. Local Manuf. Local TPU Local Trade Local Fire Local Serv. Local Govt.
Denver
Houston
NYC
1 month
36 months
1 month
36 months
1 month
36 months
1 month
36 months
– 1.46 12.53 0.52 4.33 0.07 5.44 4.53 – 2.65 24.62 3.51 3.68 0.36 21.00 15.26
– 1.51 13.13 0.61 4.56 0.09 5.61 10.25 – 2.33 25.56 3.24 3.26 0.32 18.54 13.96
0.00 0.10 0.01 0.39 0.20 0.01 0.42 0.32 0.91 14.77 14.37 5.46 16.97 1.92 14.80 29.31
0.04 0.24 0.77 0.39 0.21 0.01 0.63 0.98 0.93 14.55 14.09 5.36 16.63 1.88 14.53 28.73
0.060 0.063 2.04 2.27 1.78 0.06 4.01 7.34 2.94 16.96 8.07 7.11 10.54 1.62 17.70 16.82
0.07 0.61 3.05 1.99 1.66 0.07 3.58 8.54 3.39 16.32 11.44 6.20 9.95 1.56 16.75 14.76
0.00 0.197 4.82 1.64 1.52 0.137 1.77 0.32 0.00 1.84 28.52 3.64 3.32 0.96 6.48 44.77
0.04 0.307 4.47 1.52 1.54 0.172 0.52 6.20 0.00 1.66 27.35 3.42 3.05 0.87 5.83 41.92
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Table 2 Variance decomposition of employment
Fig. 3. Response of Houston employment to local and national shocks.
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Fig. 4. Response of NYC employment to local and national shocks.
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A large number of local shocks are seen to be important to Houston’s economy: manufacturing, services, construction, government and trade all have substantial impulse responses emanating from them, and all have roughly equal shares in explaining metropolitan employment. The results for New York are different yet again. As befitting its size the impact of the shocks is larger here overall than those from the other cities, as can be seen from the vertical scale of the figures. The comparison of scales also reveals that the local shocks are far more substantial in their impact than national shocks. Two national shocks appear to have more than a trivial impact on New York’s economy: government employment and manufacturing employment. Interestingly, the national public sector only has minimal impact in the short run but a much more substantial importance in the long, a phenomenon that is also visible in Baltimore. Just as interesting is the fact that the same two sectors have dominant impacts from the set of local shocks. Manufacturing shocks have a huge impact on New York aggregate employment as do public sector employment shocks. The impact of these two sectors is also obvious from the variance decomposition where the local public sector accounts for nearly half of the employment variation all by itself. This plus the local manufacturing shock more or less dwarf the remaining sources of fluctuations. It would, therefore, seem fairly straightforward to summarize the results from this exercise, since there are some strong commonalities in these results across the four cities. First, local shocks play a more important role in the determination of aggregate local employment than do national shocks, thus corroborating the results for local sectoral employment contained in Coulson (1993). Second, for most cities a broad array of local sectors is important in local employment. In various instances, manufacturing, government, services, construction and trade all can have substantial impact on local employment movements. But, third, the importance of the manufacturing, public, and (with New York as an exception) the service sector seem significantly greater overall than other local sectors. This seems congruent with long standing export-oriented models of cities, such as the base multiplier model. Manufacturing is traditionally thought of as an important source of export earnings that are in turn thought to be the engines of urban growth. Similarly, government expenditure is also thought to be an important source of export earnings. It is important to recall that local government employment includes federal and state employment within the metropolitan area and, therefore, to that extent consists of injections into the local economy and are not (at least directly) paid for with local tax dollars. Services, on the other hand have only recently been regarded as having any kind of export orientation. There are some limitations that should be recognized. The most important of these is the potential limitation of the neutrality restriction. To test the limitations of this set of assumptions, the model is expanded to allow for increased influence
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(for better or worse) by a particular sector in both the residual decomposition and the VAR itself. This is done for four city-industry pairs: the service sector in Baltimore, the TPU sector in Denver; the construction sector in Houston; and the FIRE sector in New York City. In each case a lag of that local sector was added to each of the local sector equations, and a parameter was added to the orthogonalization specification which allowed that sector’s orthogonal shock to have a separate influence each local sector’s residual. The results are striking in that in three of the four cases the change in specification had only a minuscule impact on the results. For example the expanded role of the financial sector in New York City model leads to a change in the contribution of that sector from 0.96% in the short run and 0.87% in the long run to 0.97 and 1.5%, respectively. The added scope for the Baltimore service sector yields similarly small increases in that sector’s contribution from 21 and 19.5 to 21.8 and 19.8%. In the Denver case, the changes are from 5.5 and 5.4 to 7.5 and 7.7%. There was, however, a substantive change in the Houston results when the construction sector was allowed to have extra explanatory power, which was to reduce that sector’s contribution from roughly 16–17% to around 10–11%. (The slack was mostly taken up by the local service sector.) Thus, the additional parameters served to move the Houston results closer to the norm, in light of the reduced importance of construction. Other caveats apply. The first is that it should be recalled that all of the data is in absolute thousands of employees, and not (say) in logarithmic form. This is required given the emphasis on aggregation in the empirical model but it creates a size effect in the results that would perhaps not be as pronounced in the logarithmic case.13 The size of the shocks, as noted, is the standard deviation of the shock, and this depends on the size of the sector, but this ‘magnitude effect’ is part of what creates employment; big sectors create more jobs, other things equal, than small sectors. Moreover this effect is not all-encompassing. While it might account for the lack of influence of certain local sectors, particularly mining, and the finance industry,14 the trade sector is quite large in these metropolitan areas, and
13 A logarithmic model was created in order to try and judge the extent of the effect discussed here. This model used log differences of sectors and aggregate metropolitan employment and identified sector-specific shocks by assuming that the local vi values were mutually orthogonal to each other but not to an aggregate (log) citywide employment shock. The first restriction is necessitated by the desire for sector-neutral treatment coupled with an inability to aggregate the sectoral shocks in any meaningful way. (Carlino and Defina (1995) inter alia take this approach in a study of the impact of regional employment shocks.) Applying the results to each of the sample MSAs in turn entailed some surprise in that size actually appears to play more of a role here than in the levels model. In three of the four cities the most significant sector was the service sector, the largest of the one-digit sectors. In the fourth case of Houston, the manufacturing sector was the most powerful determinant. The conclusion is that the size of sectors does not completely drive the results above. 14 Indeed the lack of explanatory power for this industry in New York City given its putative role in New York’s growth (as outlined in Sassen, 1991) is notable.
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yet is not the origin of important movements in aggregate employment. It is evidently a follower, rather than a leader, and what is important, the method proposed here identifies it as such. Moreover, some sectors have lots of explanatory power despite their small size. In this vein the role of the construction sector in the Denver and Houston cases is interesting. Both are fast-growing cities, so the construction sector might be more active here than in our other example areas. Nevertheless the role of construction as a causal factor in growth might be questionable, since it is among the most local-serving of sectors and, therefore, presumably lagging growth rather than leading it. Case (1992), for example, details how the construction sector had a role in perpetuating, rather than initiating, the 1980s expansion of Boston area employment. This, then, brings us to the second caveat which is that many of the effects being discussed here are, over the sample frame, of the opposite sign of the discussion presented. That is, the employment shocks which actually occur (rather than simulated for presentation purposes) might be negative, leading to negative impacts on employment. One might speculate that this explains the power of manufacturing shocks in New York in particular. Recall that the data for New York is for the city itself rather than the metropolitan area, and that central city job loss in manufacturing is ongoing for New York over the sample period (Table 1d). The response of the aggregate economy to these manufacturing shocks can be large. Third, the analysis is entirely positive in orientation. Nothing in this is meant to suggest that policy options designed to favor manufacturing or public sector employment are superior, on the grounds of having larger multipliers, to a policy which is neutral across sectors. Recalling the first of the caveats above, the simulations here are not ceterus paribus experiments, since the initial stimulus is not identical across regions. Even if they were, the existence of differential multipliers is not necessarily grounds for such industry specific policy initiatives.
4. Summary and conclusions This paper has delineated a new method for using vector autoregression models to measure the contribution of industrial sectors to metropolitan growth. By using an orthogonalization scheme based on shift-share principles, industry shocks at the national and local levels are identified, without assuming any causal ordering among the industries. In the four example cities, local shocks are generally more important than national shocks in the determination of metropolitan employment. Among local shocks, public sector employment shocks and manufacturing employment shocks and sometimes service sector shocks have the most explanatory power overall, a result which is congruent with export-based models of metropolitan growth and decline.
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There are of course extensions which are available. Despite commonalities across the various cities, there is sufficient heterogeneity to warrant a broader cross-section of examples. There is also the potential for finer disaggregation of sectors, particularly within manufacturing, and this may be important in the analysis of particular areas. It is also possible to include other types of shocks in the framework provided here. As one example, there has been work on the differential effects of monetary policy across industries (Carlino and Defina, 1996) and across regions. The framework here can naturally include money shocks which would then have differential effects across both disaggregate dimensions. Further extensions along these lines may include the reaction to oil prices, or defense spending shocks (Coulson and Rushen, 1995).
Acknowledgements I am grateful to Todd Clark, Jim Kurre, John Quigley, Norm Swanson, and an anonymous referee for helpful comments.
References Altonji, J., Ham, J., 1990. Variation in employment growth in Canada. Journal of Labor Economics 8, 198–236. Brown, S., Coulson E., Engle R., 1991. Noncointegration Econometric Evaluation of Models of Regional Shift and Share. NBER Working Paper 3291. Brown, S., Coulson, E., Engle, R., 1992. On the determination of regional base and regional base multipliers. Regional Science and Urban Economics 22, 619–635. Browne, L., 1988. High technology and business services. In: Lampe, D. (Ed.), The Massachusetts Miracle, MIT Press, Cambridge. Carlino, G., Defina, R., 1996. Does US Monetary Policy have Differential Regional Effects. Working Paper, Federal Reserve Bank of Philadelphia. Case, K., 1992. The real estate cycle and the regional economy: the consequences of the Massachusetts Miracle of 1984–87. Urban Studies 92, 171–183. Clark, T., 1998. Employment Fluctuations in US Regions and Industries. Journal of Labor Economics 16, 202–229. Clark, T., Shin, K., 1998. Sources of Fluctuations within and across Countries. Working paper, Federal Reserve Bank of Kansas City. Coulson, E., 1993. The sources of sectoral fluctuations in Metropolitan areas. Journal of Urban Economics 33, 76–94. Coulson, E., Rushen, S., 1995. Sources of fluctuations in the Boston Economy. Journal of Urban Economics 38, 74–93. McCarthy, J., Steindel, C., 1997. National and regional factors in the New York Metropolitan Economy. Economic Policy Review 3, 5–20.
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Norrbin, S., Schlagenhauf, D., 1988. An inquiry into the sources of macroeconomic fluctuations. Journal of Monetary Economics 22, 43–70. Richardson, H., 1985. Economic base and input–output models. Journal of Regional Science 25, 607–622. Sassen, S., 1991. In: The Global City, Princeton University Press, Princeton.