The effects of unification: markets, policy, and cyclical convergence in Italy, 1861–1913

Abstract

This paper uses time-series evidence on construction movements to examine the convergence of regional business cycles in the decades that followed Italy’s unification. The aggregate series point to cyclical convergence, but a sector-level analysis traces this result to the decline in differentiated “regional-policy” shocks. The regional market cycles diverged, as regions specialized in different sectors of production; market-cycle convergence is observed only within the “industrial triangle,” the regions of which also developed different specializations. This suggests that the balance between growing interdependence and growing differentiation is not general, as the current literature presumes, but specialization-specific.

Appendices

Appendix 1

The dynamic correlations in Figs. 1, 2, 3, 4 and 5 are based on a decomposition of the regional series y _it , t = 1, …, T, i = 1, …, N, into a (flexible) trend μ _it , and a deviation cycle ψ _it :

$$ y_{it} = \mu_{it} + \psi_{it} $$

(1)

These components are here estimated by the Leser-Hodrick-Prescott (LHP) filter with a smoothness parameter set equal to the value suggested by Ravn and Uhlig for annual data, so that the corresponding trend filter can be interpreted as a low-pass filter with a cut-off period of 10–12 years. The component ψ _it thus retains to a great extent the fluctuations in the series that have a periodicity smaller than 12 years.¹⁷

As is well known, at the end of the sample the LHP-filtered components are of questionable reliability (Orphanides and Van Norden 2002). In principle, the LHP estimates could be adapted to the characteristics of the present series using appropriate techniques (Proietti 2009). In fact, the dynamic relationship between filtered time series is least distorted if the same (possibly suboptimal) filter is applied to all the series (Wallis 1974).

The LHP filter, like the Baxter and King (1999) or Christiano-Fitzgerald (2003) filters, is invariant to the properties of the time series under investigation. Such algorithms may yield filtered series that display spurious cycles, that is, cycles not actually present in the original series; this is known in the time-series literature as the Slutsky-Yule effect.

The distortions that may be induced by the LHP filter have been discussed by King and Rebelo (1993), Harvey and Jaeger (1993), and Cogley and Nason (1995). These authors document that, when the series to which the filter is applied is difference stationary (e.g., a random walk, or an integrated random walk), the detrended series can display spurious cyclical behavior. As a matter of fact, the transfer function will display a distinctive peak at business-cycle frequencies which is only due to the leakage from the non-stationary component.

While the problem is thus in ipsis rebus, its seriousness depends on one’s objective, and the corresponding characterization of the cyclical component in economic time series. No attempt is made in this paper to identify particular shocks and dynamic transmission mechanisms; the filter’s purpose is here essentially pragmatic, descriptive, and in keeping with the band-pass paradigm the cycle corresponds simply to the fluctuations within a prescribed range of periodicities. In such a context, the possible incidence of spurious components is not of compelling concern.

The overall evidence arising from unit roots tests (not reported for brevity) is that the levels of the series are integrated of order one; the null of integration is strongly rejected for the changes of the series. Under these circumstances, when the LHP filter is applied to the series y _it , both the estimated cycle and the trend changes are stationary.

The short-term comovements (see e.g., Fig. 1, graph 1) are evaluated by considering the deviations ψ _it ; the long-term comovements (e.g., Fig. 1, graph 3), by considering the trend growth rates g _it  = (μ _it  − μ _it−1 )/μ _it−1 . The latter may be considered as a smoothed version of the original series’ growth rate (the low-pass component thereof).

The concordance of the regional cycles is evaluated by the average ($\bar{r}_{t}$) of the N(N − 1)/2 pairwise dynamic correlation coefficients r _{ij, t} between the cyclical variables. With i and j denoting the regions and t time,

$$ \bar{r}_{t} = {\frac{2}{N(N - 1)}}\sum\limits_{i = 1}^{N} {\sum\limits_{j < i} {r_{ij,t} } } $$

(2)

The dynamic correlation coefficient between two time series z _i and z _j (where z equals ψ in the one case and g in the other) at time t is defined as

$$ r_{{ij,t}} = {\frac{{m_{t} (z_{{it}} z_{{jt}} ) - m_{t} (z_{{it}} )m_{t} (z_{{jt}} )}}{{\sqrt {m_{t} (z_{{it}}^{2} ) - (m_{t} (z_{{it}} ))^{2} } \sqrt {m_{t} (z_{{jt}}^{2} ) - (m_{t} (z_{{jt}} ))^{2} } }}} $$

(3)

where m _t (·) denotes a kernel function, i.e., a set of non-negative weights symmetric around time t non-increasing in the distance from time t, and summing up to one. Expression (3) computes a local correlation coefficient with a greater weight on the observations in the neighborhood of time t, as defined by the bandwidth of the kernel.¹⁸

In practice, this non-parametric concordance statistic requires selecting a kernel m _t (·) and a bandwidth. The recent literature proposes a family of estimators, with varying weights on the observations (Proietti 2009). Here, the kernel is allowed to adapt automatically at the boundaries of the sample space, and the bandwidth is related to the time horizon at which the correlation is computed. Specifically, the running means are estimated using a two-sided exponentially weighted moving average (EWMA) with weights determined by a smoothing parameter (λ) related to the cut-off period p and the signal-to-noise ratio. The actual computation of m _t (q _t ), where q _t is alternatively z _it , z _jt , $z_{it}^{2}$, $z_{jt}^{2}$ and z _it z _jt , is performed by the Kalman filter and smoother (Koopman 2001). This tool is applied to the local level model $q_{t} = q_{t}^{ * } + \varepsilon_{t}$ and $q_{t}^{*} = q_{{t - 1}}^{*} + \eta _{t},$ where ε and η are both white noise, and λ is related to $\sigma_{\eta }^{2} /\sigma_{\varepsilon }^{2}$. The filter m _t (q _t ) emerges as the estimate of the underlying component $q_{t}^{ * }$. The choice of the λ parameter entails a bandwidth of 12 years.

RiskMetrics follows a semiparametric approach, computing m _t (q _t ) with the one-sided EWMA

$$ m_{t} (q_{t} ) = \lambda_{qt} + \left( { 1 - \lambda } \right)m_{t - {\it 1}} (q _{t - {\it 1}}) = \lambda \sum\limits_{k \ge 0} {(1 - } \lambda )^{t - k} q_{t - k} $$

(4)

where λ is a smoothing constant between 0 and 1; in practice, λ is set ad hoc at 0.04 and 0.06 (RiskMetrics Group 1996). The two-sided EWMA used here is a smoother as well as a filter, and it eliminates the phase shift originating from the use of a one-sided filter. Moreover, the value of the smoothing constant is here related to a particular time horizon, and not simply assumed.

Estimates of $\bar{r}_{t}$ were also computed constraining the true dynamic correlations to zero. The simulations generated 10,000 replicate sets of 16 independent series of 53 observations under a range of assumptions as to their serial correlation. The mean dynamic correlations of the simulated cycles averaged very close to zero, with 95% of the results falling between approximately −0.05 and 0.10. This narrow simulation envelope suggests that the correlations generated by the present procedure are not induced by the procedure itself.

The computations were carried out in Ox, and the programs are available on request.

Appendix 2

The statistics in Table 1 are obtained from the benchmark estimates transcribed in Table 2. The latter replicate those in Fenoaltea (2003b), Table 2 and Appendix Table 2, with updated figures for textiles, clothing, metalmaking, non-metallic mineral products, and chemicals.¹⁹ The measures of structural dissimilarity in Table 1, panel A are, in each benchmark year, the simple average

$$ \bar{d} = {\frac{1}{N}}\sum\limits_{i} {\sum\limits_{j} {d_{i,j} } } \quad {\text{for }}i \ne j $$

(5)

where i and j index the regions ordered as in Table 2, and N is the number of differences d _ij for i ≠ j. In turn,

$$ d_{i,j} = \sum\limits_{s = 1}^{12} {\left| {v_{s,i} - v_{s,j} } \right|} $$

(6)

where s is the manufacturing sector index (s = 1,…,12) and

$$ v_{s,i} = {\frac{{VA_{s,i} }}{{L_{i} }}} $$

(7)

Table 2 Regional estimates, census years

The elements VA _s,i and L _i for each year appear in the corresponding panel of Table 2, cols. 1–12 and col. 13, respectively.

The measures for Italy in col. 1 are obtained with i = j = 1,…,16 (N = 120); those for the North-West in col. 2, with i = j = 1, 2, 3 (N = 3); those for the Center/North-East in col. 3, with i = j = 4,…,9 (N = 15); and those for the South in col. 4, with i = j = 10,…,16 (N = 21).

The estimates in Table 1, panel B are themselves, in each year,

$$ m = {\frac{1}{{\sum\nolimits_{i} {L_{i} } }}}\left( {\sum\limits_{i} {\sum\limits_{s} {VA_{s,i} } } } \right) $$

(8)

with i and s defined as above, s = 1,…,12, and, again, i = 1,…,16 for Italy (col. 1), i = 1, 2, 3 for the North-West (col. 2), i = 4,…,9 for the Center/North-East (col. 3), and i = 10,…,16 for the South (col. 4).