3.1. The data

Our baseline analysis relies on Fernald’s (Reference Fernald2014) quarterly utilization-adjusted TFP for the US business sector, which we label PTFP. Fernald’s (Reference Fernald2014) PTFP is closely related to the annual technology measure derived in Basu et al. (Reference Basu, Fernald and Kimball2006). Using disaggregate information at the industry level, Fernald (Reference Fernald2014) obtains PTFP from a growth-accounting exercise that controls for varying utilization of labor and capital. Thus, our SVAR identification does not require an explicit control for non-technological factors, which in our view is an advantage compared to other approaches, like the long-run identification approach proposed by Galí (Reference Galí1999).Footnote 2

Notably, Fernald’s (Reference Fernald2014) PTFP is prone to measurement errors (Kurmann and Sims (2020)). Particularly, the detrending (filtering) method in the estimation of factor utilization affects the PTFP estimate. However, identification approaches of US technology shocks in SVARs encounter similar and other issues. They are vulnerable to lower-frequency movements in the considered variables, are unreliable in small samples, depend on the proxy for factor utilization, and do not account for composition effects contained in the disaggregated data.

The lack of comparable quarterly PTFPs across countries challenges our analysis.Footnote 3 Therefore, we rely on quarterly unadjusted TFP estimates for the countries under consideration. To this end, we interpolate annual Solow residuals provided in the PWT (Feenstra et al. (Reference Feenstra, Inklaar and Timmer2015)) using our own estimates of “auxiliary” quarterly TFPs. An appealing feature of this approach is that when converted to annual frequency, our final TFP estimates match the respective PWT measures. The latter are, in turn, highly correlated with the TFP series provided by the EU KLEMS Growth and Productivity Accounts database, the annual macroeconomic (AMECO) database of the European Commission, and the OECD, respectively.

Specifically, we employ the following two-step procedure. First, we compute “auxiliary” quarterly TFP series assuming a Cobb–Douglas production function with constant returns to scale. The production elasticities for labor input are from the PWT. We use quarterly data for real GDP and investment from the OECD. Ohanian and Raffo (Reference Ohanian and Raffo2012) provide internationally consistent hours worked series. To obtain a quarterly capital stock series, we use the perpetual inventory approach (Appendix B gives the details). The annual averages of our “auxiliary” TFPs are highly correlated with TFPs from the PWT, as reported in Table 2.

Table 2. Correlations of annual unadjusted TFP series from different sources

Notes: This table reports the correlations between the annual growth rates of our estimated TFP measures from the two steps as described in Section 3 and the corresponding TFPs from the Penn World Table (PWT), the EU KLEMS Growth and Productivity Accounts database, the annual macroeconomic (AMECO) database of the European Commission, and the OECD, respectively. The sample period varies due to data availability. N/A: values are not available.

Second, we use the “auxiliary” quarterly TFPs to convert annual PWT data into quarterly TFP series employing the Chow–Lin interpolation method (Chow and Lin (Reference Chow and Lin1971)). In addition, using the final TFP series for the 13 countries in the sample, we construct a weighted average TFP measure for the RW. The weights are obtained from the country-specific shares of world GDP based on purchasing power parities (PPPs), provided by the IMF.Footnote 4

3.2. VAR specification

We estimate for each individual country a three-variable VAR that includes PTFP, the RW TFP, and the TFP measure for the country under consideration. We include RW TFP to capture fluctuations in global technology outside the US. All models include a constant and four lags. We use seasonally adjusted quarterly data that cover 13 advanced economies over the sample period 1970:1–2016:4, unless otherwise indicated. Determined by the availability of quarterly total hours series in the Ohanian–Raffo dataset (Ohanian and Raffo (Reference Ohanian and Raffo2012)), which we use to compute TFP measures, we consider the following countries: Australia, Austria, Canada, Finland, France, Germany, Ireland (1970:1–2014:4), Italy, Japan, Norway, South Korea, Sweden (1974:1–2016:4), and the UK (1971:1–2016:4).Footnote 5

The VARs do not include country-specific TFPs in the estimation equations for PTFP and RW TFP. We estimate each model as a subset system of equations using the method of seemingly unrelated regressions, which guarantees that the sequence of US technology shocks is the same for each country.

All variables enter the model in first log-differences as cointegration tests for PTFP and RW TFP do not provide evidence that both series are cointegrated, which would warrant the estimation of the model in log-levels. Moreover, we find for almost all country-specific TFPs no cointegration relationships with PTFP. Exceptions are Canada and to a lesser extent Sweden. Table 3 summarizes the results of the cointegration tests. The Engle–Granger test statistics (columns 1–2) and the trace and maximum eigenvalue statistics for the Johansen test (columns 3–4).Footnote 6 The test results are not sensitive with respect to the number of lags.

Table 3. Cointegration tests

Notes: This table reports the results of the cointegration tests. For the Engle–Granger test, we use the residuals from the regression of the country-specific TFP series on Fernald’s (Reference Fernald2014) PTFP (in log-levels). For the Johansen test, we specify a bivariate VAR with Fernald’s (Reference Fernald2014) PTFP and a country-specific TFP. The Johansen’ s trace and maximum eigenvalue tests include an intercept in the cointegration equation and the dynamic part of the system. For the dynamic part, we assume four lags. The null hypothesis of each test assumes no cointegration relationship between the variables under consideration. Sample period is 1970:1–2016:4, except for Ireland (1970:1–2014:4), Sweden (1974:1–2016:4), and the UK (1971:1–2016:4). *** $p<0.01$ , ** $p<0.05$ , * $p<0.1$ .

3.3. Identification of US technology shocks

Changes in PTFP capture a domestic (idiosyncratic) and a global (common) component. Therefore, to isolate the idiosyncratic US technology shocks, we use the medium-run identification approach introduced by Uhlig (Reference Uhlig2004a,b), which extracts the shock series explaining the largest share of fluctuations in PTFP over the medium to the long horizon as follows.Footnote 7

The reduced-form moving average (MA) representation of $Y_t$ , a $k\times1$ vector of endogenous variables at time t, with PTFP ordered first is:

(1) \begin{equation} Y_t = C(L)u_t,\end{equation}

where $u_t$ is a vector of prediction errors with covariance matrix $\Sigma_u$ .Footnote 8 The vector of structural shocks $\varepsilon_t$ can be represented as a linear combination of prediction errors $u_t = A\varepsilon_t$ . To obtain $\varepsilon_t$ , the impact matrix A must satisfy $\Sigma_u = AA^{\prime}$ , which given the symmetry of $\Sigma_u$ is not unique. The Cholesky decomposition of $\Sigma_u$ gives such a matrix $\tilde{A}$ , which allows to summarize the entire space of acceptable impact matrices as $A =\tilde{A}Q$ , where Q is a $k \times k$ orthonormal matrix ( $QQ^{\prime} =I$ ). Thus, the structural MA representation of $Y_t$ takes the form:

(2) \begin{equation} Y_t = C(L)\tilde{A}Q\varepsilon_t.\end{equation}

The medium-run identification approach by Uhlig (Reference Uhlig2004b) isolates the structural shock that accounts for the largest forecast error variance (FEV) share of the target variable $y_{i,t}$ in $Y_t$ over the forecast horizon $h = \underline{h} \leq \overline{h}$ .Footnote 9 The h-step ahead forecast error of $y_{i,t}$ is:

(3) \begin{equation} y_{i,t+h} - E_{t}y_{i,t+h} = e_i^{\prime}\Bigg[\sum\limits_{l=0}^{h-1}C_l\tilde{A}Q\varepsilon_{t+h-l}\Bigg],\end{equation}

where $e_i$ is a column vector with 1 in the i-th position and 0’s elsewhere. The shock explaining most of the FEV of the i-th variable in $Y_t$ results from the maximization problem:Footnote 10

(4) \begin{equation} q_{1}^* = \arg\phantom{{\tiny x}}\underset{q_1}{\max}\phantom{{\tiny x}} e_i^{\prime}\Bigg[\sum\limits_{h=\underline{h}}^{\overline{h}}\sum\limits_{l=0}^{h-1}C_l\tilde{A}q_1q_1^{\prime}\tilde{A}^{\prime}C_l^{\prime}\Bigg]e_i, \quad \text{s.t.} \quad q_1^{\prime}q_1 = 1,\end{equation}

where $q_1$ is a vector of unit length that represents a column of Q. Uhlig (Reference Uhlig2004b) shows that the maximization problem in (4) can be expressed as $Sq_1 = \lambda q_1$ , where $S = \sum\limits_{h=\underline{h}}^{\overline{h}}\sum\limits_{l=0}^{h-1}(C_l\tilde{A})^{\prime}(e_ie_i^{\prime})(C_l\tilde{A})$ . To find the structural shock associated with the largest FEV of $y_{i,t}$ over $h = \underline{h} \leq \overline{h}$ , we need to find the eigenvector $q_1$ with the maximal eigenvalue $\lambda$ of the matrix S. Following Uhlig (Reference Uhlig2004b), we specify the forecast horizon between $\underline{h} = 12$ and $\overline{h} = 40$ quarters.

5.1. Indicators of institutional characteristics

While our baseline results do not reveal significant cross-country heterogeneity in the spillovers of US technology gains, the IRFs after 5 years vary to some degree, which warrants further analysis. Following Acemoglu (Reference Acemoglu2009), differences in institutional environments can explain the gaps in technology and income across countries. Thus, to analyze the role of institutions for our key results, we estimate the spillover effects of the US technology shock on TFPs for the groups of countries with contrasting institutional environments. We group the countries along various institutional dimensions using indicators of non-price competitiveness.

First, we scrutinize the statements in Cette et al. (Reference Cette, Fernald and Mojon2016) on the importance of labor and product market regulations for the transmission of US technology gains.Footnote 12 Following Gnocchi et al. (Reference Gnocchi, Lagerborg and Pappa2015), regulations that influence job and worker flows (employment rigidities) are key determinants of labor market adjustments.Footnote 13 Therefore, we use the OECD indicator of the strictness of employment protection legislation (EPL) against individual dismissal (based on regular contracts). Further, we use the OECD index of product market regulation for the total economy that measures the degree to which policies promote or inhibit competition in product markets (Koske et al. (Reference Koske, Wanner, Bitetti and Barbiero2015)).

Second, the literature shows that financial development and an overall high quality of institutions enhance productivity growth (Kose et al. (Reference Kose, Prasad and Terrones2009); Bekaert et al. (Reference Bekaert, Harvey and Lundblad2011)). Svirydzenka (Reference Svirydzenka2016) argues that the degree of a country’ s financial development influences saving and investment decisions, which affect the accumulation of physical and human capital and thus TFP growth. Masuch et al. (Reference Masuch, Moshammer and Pierluigi2016) find that good institutions promote the catching-up process in terms of economic performance.Footnote 14

The diversity of financial and institutional systems across countries requires a broad and multidimensional approach to computing an encompassing index. We use the IMF broad-based index of financial development (Svirydzenka (Reference Svirydzenka2016)) that summarizes important dimensions, like depth (size and liquidity of markets), access (ability of individuals and companies to access financial services), and efficiency (ability of institutions to provide financial services at low cost and with sustainable revenues, and the level of activity of capital markets). To capture the quality of institutions across countries, we use the Global Competitiveness Index (GCI) reflecting the overall efficiency of public and private sectors, that is legal and administrative framework within which individuals, firms, and governments interact.

Figure 3 shows the time series averages of the institutional characteristics for each country. Based on these cross-country averages, we compute the median for each indicator, excluding the US (dashed lines). Using each median value as a threshold, the countries with a score above (below) the respective median are clustered into “high” (“low”) regime groups, excluding the median country (dark bars) and the US (see Table E.1 in Appendix E). Thus, each regime-grouping includes an equal number of countries. Note that high (low) scores for the strictness of employment protection and product market regulation point to rigid (flexible) institutions. By contrast, high scores for the financial development and the quality of institutions point to a favorable institutional environment.

Figure 3. Cross-country institutional characteristics. Notes: The bars show for each country the time series averages of indicators and the highlighted bars correspond to the respective median country. The dashed lines show the cross-country median value of each indicator (excluding the US). The OECD indicator of the strictness of employment protection legislation refers to individual dismissals (regular contracts) and covers the period from 1985 to 2013. The OECD indicator of product market regulation reflects the degree to which policies promote or inhibit competition and is available for the years 1998, 2003, 2008, and 2013 (Koske et al. (Reference Koske, Wanner, Bitetti and Barbiero2015)). The IMF index of financial development summarizes factors like depth, access, and efficiency of financial markets (Svirydzenka (Reference Svirydzenka2016)) and is available from 1980 to 2016. The Global Competitiveness Index (GCI) of quality of institutions reflects the efficiency of public (with a weight of 75% in the index) and private (25%) sectors and is available from 2006 to 2016. Data Appendix A provides further details and definitions.

While labor and product markets in major European economies (Germany, France, and Italy) are highly regulated, the opposite applies to Anglo-American countries (Australia, the UK, and the USA) and Japan. Interestingly, the qualitative institutional differences between these groups of countries also hold for financial development, which is below average in European economies and high in Anglo-American countries and Japan. In Canada, loose labor market institutions stand in contrast to strict product market regulation. Regarding the quality of institutions, France, Italy, Japan, South Korea, and the USA display scores well below average. By contrast, the Scandinavian countries (Finland, Norway, and Sweden) have the highest quality of institutions.

5.2. The role of institutions

To analyze the differences in TFP spillovers across countries after the US technology shock, we adopt the approach by Calza et al. (Reference Calza, Monacelli and Stracca2013). We first estimate our baseline model country by country and then compute the average impulse responses of TFPs for “high” and “low” regime groupings as defined in the previous section. The computation of mean IRFs based on country-specific SVARs (mean group estimator) results in efficiency gains versus panel estimation methods, like pooled ordinary least squares or fixed effect VAR approaches. Estimating subset SVARs country by country does not only take into account country-specific fixed effects (intercepts) but also results in country-specific estimates of the slope parameters.Footnote 15

Figure 4 shows the mean IRFs and the 95% confidence intervals. We normalize the US technology shock to induce a 1% increase in PTFP after 20 quarters. We find that differences in TFP spillovers are negligible between the two regimes and along the four institutional dimensions. However, the difference between two regimes is more pronounced for the quality of institutions, with a surprisingly stronger TFP response in the “low” regime.

Figure 4. Mean impulse responses to a US technology shock. Notes: The average IRFs of TFPs to a US technology shock are computed over the groups of six countries, respectively. The IRFs were obtained from the estimation of the baseline model on a country-by-country basis (see Figures 1 and 2). The classification of countries into “high” and “low” regime groupings is done according to their respective institutional characteristics, which can be found in Table E.1. We standardize the US technology shock such that the structural shock induces a 1% increase in Fernald’s (Reference Fernald2014) PTFP after 20 quarters ( $h=20$ ). Shaded areas are the corresponding cross-sectional averages of the 68% and 95% confidence intervals computed using a recursive design wild bootstrap procedure proposed by Gonçalves and Kilian (Reference Gonçalves and Kilian2004). All details concerning the model estimation, specification, and data sources are provided in Section 3 and in the notes to Figure 1.

Following Gnocchi et al. (Reference Gnocchi, Lagerborg and Pappa2015), we further examine the link between TFP spillovers and institutional characteristics based on Spearman’s rank correlation coefficients.Footnote 16 Table 4 reports the correlations between the cumulated TFP responses at a 1- and 5-year horizon for 13 countries and indicators of institutional characteristics. The results broadly support our findings in Figure 4 and Section 4. Thus, labor, product, and financial market characteristics do not seem to be able to explain the cross-country differences in the size of the spillover effects. This evidence is at odds with the statements made by Cette et al. (Reference Cette, Fernald and Mojon2016).

Table 4. Evidence from Spearman’s correlation coefficients

Notes: This table reports the Spearman’s rank correlation coefficients between the cumulated IRFs of TFPs at a 1- and 5-year horizon for 13 countries and indicators on institutional characteristics. ^*** $p<0.01$ , ^** $p<0.05$ , ^* $p<0.1$ .

While isolated institutional characteristics do not seem to affect the transmission of US technology shocks across countries, the results in the last column of Table 4 suggest that in the short run, the overall quality of institutions is negatively associated with the size of TFP spillovers. A possible explanation for this puzzling result is that countries with a lower quality of institutions provide a worse environment for innovation and instead rely more on imitation, at least in the short run (Benhabib et al. (Reference Benhabib, Perla and Tonetti2014)). However, this relationship is only short-lived and the correlation becomes insignificant after 5 years.

6.1. Identification approach

We check the robustness of our baseline results with respect to alternative identification schemes that rely on US labor productivity by employing Uhlig’s (Reference Uhlig2004a) medium-run identification approach and a modified version of a Proxy-SVAR model proposed by Mertens and Ravn (Reference Mertens and Ravn2013, Reference Mertens and Ravn2014). Following Kurmann and Sims (2020), Fernald’s (Reference Fernald2014) PTFP is subject to measurement errors and changes due to methodological refinements.

While the medium-run and Proxy-VAR approaches rely on different identification assumptions, both models use US labor productivity as target technology measure to recover structural shocks. Notably, labor productivity is defined as the ratio of real GDP to total hours worked and is not corrected for cyclical variations in factor utilization. We address this issue by controlling for fluctuations in US total hours worked in the nonfarm business sector adjusted by the working-age population in the VAR specification. To control for global productivity developments, we compute a weighted average labor productivity measure for the the RW. Similar to RW TFP measure, the weights are obtained from the country-specific shares of world GDP based on PPPs, provided by the IMF.

Since RW labor productivity is also not corrected for variations in factor utilization, we include an aggregate measure of total hours worked adjusted by the working-age population for the RW. Both RW variables are based on data for 13 countries. Finally, we include country-specific labor productivity as subset variable one at a time. Thus, we exclude country-specific labor productivity from the equations for the US and RW variables and estimate the models as a subset system of equations. All variables are in first log-differences. The VAR models include a constant and four lags.

In contrast to our baseline model, this section employs both a different target technology measure for the US and a different instrument series to isolate variations in factor utilization. Figure 5 illustrates the time series used in our SVARs. Therefore, in addition to alternative identification schemes of US technology shocks, we also test the robustness of our baseline results with respect to an alternative specification of the empirical model.

Figure 5. Time series used in VARs. Notes: The figure shows the growth rates of the US time series used in SVAR models for the sample period 1970:1–2016:4. The shaded areas are NBER recession periods. Data sources: Fernald (Reference Fernald2014) and the Federal Reserve Economic Data (FRED).

While being mainly driven by technology shocks, labor productivity can also be shifted in the long run by changes in dividend taxation and/or social attitude toward workplace. Thus, we employ the medium-run identification approach by Uhlig (Reference Uhlig2004a), which maximizes the contribution of technology shocks to the FEV of labor productivity at intermediate horizons while letting other shocks play a role. Similar to our baseline model, we use $\underline{h} = 12$ and $\overline{h} = 40$ and obtain a shock series that is highly correlated with our baseline technology shocks (0.70).Footnote 17

Next, we estimate a Proxy-SVAR model that uses PTFP as instrument to isolate technology shocks from US labor productivity. The shock series is defined as unexpected changes in US labor productivity that have the highest correlation with the instrument series. The shock series from the Proxy-SVAR model is highly correlated with our baseline US technology shocks (0.74) and with the shock series from the model described above (0.97).

Figure 6 shows the cumulated IRFs of labor productivity for the major six economies and the IRFs of US capacity utilization (Fernald (Reference Fernald2014)) and hours to the US technology shock. Figure 7 summarizes the results for 13 countries and the RW at a 1- and 5-year horizon. The results in Figure 6 are very close to the baseline IRFs, with the exception of Canada, where the labor productivity effect of the US technology shock is higher than the baseline TFP response. The results in the upper row of Figure 7 are broadly in line with the baseline outcomes. The US capacity utilization and hours decline significantly following the US technology shock, which is in line with other studies (see, e.g., Basu et al. (Reference Basu, Fernald and Kimball2006)).

Figure 6. Impulse responses to a US technology shock from different models. Notes: Cumulated IRFs of country-specific labor productivity, the US capacity utilization, and hours following the US technology shock from five-variable SVARs identified using Uhlig’s (Reference Uhlig2004) approach with $\underline{h}=12$ and $\overline{h}=40$ and Proxy-SVAR model proposed by Mertens and Ravn (Reference Mertens and Ravn2013, Reference Mertens and Ravn2014) that uses PTFP as instrument. All models are estimated as subset SVARs using data for the sample period 1970:1–2016:4. The US capacity utilization enters these models as a subset variable. We normalize the scale of shocks to induces a 1% increase in Fernald’s (Reference Fernald2014) PTFP after 20 quarters ( $h=20$ ). All models include four lags and all variables are in first log-differences. Shaded areas are the 68% and 95% confidence intervals based on a recursive design wild bootstrap procedure proposed by Gonçalves and Kilian (Reference Gonçalves and Kilian2004). Data sources and definitions are provided in the Data Appendix A.

Figure 7. Robustness checks of the US productivity spillovers. Notes: This figure shows the cumulated IRFs of TFPs and labor productivity following the US technology shock over a 1- and 5-year horizon for 13 advanced economies and the aggregate for the rest of the world (RW) from alternative model specifications and identification schemes. The graphs in the first row show the results from the baseline model (bars) and the markers denote the point estimates from the Uhlig’s (Reference Uhlig2004) medium-run identification approach with $\underline{h}=12$ and $\overline{h}=40$ and Proxy-SVAR model proposed by Mertens and Ravn (Reference Mertens and Ravn2013, Reference Mertens and Ravn2014) that uses PTFP as instrument. The graphs in the second row show the results from the baseline model (bars) and the markers denote the point estimates from the baseline model that uses data for the post-1985 sample period, the detrended PTFP and TFP series, respectively. We normalize the scale of shocks to induces a 1% increase in Fernald’s (Reference Fernald2014) PTFP after 20 quarters ( $h=20$ ). All models include four lags and all variables are in first log-differences.

Consequently, using labor productivity as target and outcome variables and applying alternative identification approaches does not change our baseline statements. Thus, the results from the two alternative models support our main conclusions related to an overall low elasticity of cross-country productivity with respect to the US technology shock, as well as heterogeneous productivity spillovers across the major advanced economies.

6.2. Specification of the empirical model

Next, we test the robustness of our baseline results with respect to alternative sample period and transformations of variables included in our baseline VAR model. First, we follow Canova et al. (Reference Canova, Lopez-Salido and Michelacci2010) and restrict our estimation sample to start in the first quarter of 1985.Footnote 18 Second, we detrend PTFP to account for breaks in the mean growth rate of the series. For this purpose, we use the break dates documented in Fernald (Reference Fernald2015): 1973:2, 1995:4, and 2003:4. In a final check, we use detrended growth rates of TFPs for 13 advanced economies while leaving PTFP unchanged.Footnote 19

The second row of Figure 7 shows the results. Overall, these robustness checks confirm our finding of broadly positive but quantitatively limited spillovers of US technology shocks across countries. Thus, our key outcome that the elasticity of foreign TFP with respect to a 1% increase in the US technology level is significantly lower than one remains unaffected. Furthermore, we again find some heterogeneity in the magnitudes of the IRFs across countries.

Notably, concerning the model specification with detrended PTFP, an interesting pattern emerges. While the key conclusions related to limited spillover effects and thus low elasticity of foreign TFP with respect to changes in US technology level hold, responses in some countries flip signs. However, we still find positive effects in France, Italy, Japan, and South Korea.

In sum, our main statements are unaffected by these modifications in the empirical model.