CROSS-COUNTRY STOCK MARKET COMOVEMENT: A MACRO PERSPECTIVE (cid:3)

. Since the 1990s, there has been a simultaneous rise in cross-country stock market correlations and FDI positions. We establish an empirical relationship between these two, for pairs of developed economies that survives controlling for relevant factors. At (cid:133)rm level, we (cid:133)nd that stock returns of multinationals that invest in technology capital are more correlated with world stock markets. Using a calibrated two-country asset pricing model with multinationals, we (cid:133)nd that the increase in FDI accounts for one third of the rise in the observed stock market correlations. When allowing for increases in trade and portfolio diversi(cid:133)cation, we (cid:133)nd that these two factors do not generate an increase in stock market correlations.


Introduction
In the post WW2 period, the cross-country correlations between the stock markets in developed economies were fairly low, implying signi…cant potential bene…ts from diversi…cation. Beginning in the mid 1990s, stock market correlations started increasing and continued to do so up until the aftermath of the Great Recession. These increases have been quantitatively large; for example the correlation of US equity returns with the equity returns in an aggregate index of other developed economies has risen from below 0:4 in the 1980s to above 0:8 in the 2010s and a similar pattern emerges when looking at bilateral developed country pairs (see Figure 1). The increase in stock market correlations has coincided with a concurrent strengthening in foreign direct investment (FDI) linkages between the largest economies with developed equity markets. The aim of this paper is to explore the relationship between these two phenomena.
We propose an intuitive mechanism through which increases in bilateral FDI positions can lead to higher stock market correlations between two countries. Because multinational corporations engage in FDI abroad, they become exposed to country speci…c TFP shocks in the foreign country. In an environment with increased FDI, …rms generate a larger fraction of their earnings abroad. This implies stronger incentives to increase investment in response to shocks in the foreign country. In the presence of intangible technology capital, increased investment abroad can also spill over to investment at home, due to the complementarity between tangible and intangible capital. Investment and capital are therefore more synchronized across multinationals and this implies their equity values are also more correlated. 1 We …rst establish an empirical link between the comovement of stock returns with international stock markets and FDI. We provide evidence that the returns of multinational …rms comove with foreign stock markets more than the returns of non-multinational …rms; this is more so when multinational …rms have more intangible assets, or have high R&D expenditure, which is consistent with our theoretical mechanism. Additionally, using a panel of 21 developed economies, we also …nd that increases in FDI of the order of magnitude observed across these countries, are associated with increases in their bilateral stock market comovement that are sizeable, positive and highly signi…cant, even when controlling for trade.
With this empirical evidence in place, we propose a production-based asset pricing model (see Jermann, 1998) extended to two countries and, crucially, incorporating multinational …rms investing in technology capital as in McGrattan and Prescott (2010). To quantify the importance of the mechanism, we add country-speci…c shocks, introduce incomplete international asset markets and calibrate the model to two regions, the US and the rest of the world. We …nd that the observed increase in FDI positions leads to a rise in stock market correlation from 0:380 to 0:520, accounting for one third of the overall observed increase.
When markets are incomplete, a …rm's FDI operations provide access to foreign markets and, at the same time, o¤er diversi…cation bene…ts for its shareholders. The model assigns FDI an important role in explaining stock market comovements, even when abstracting from the diversi…cation channel.
To show this, we recompute our experiments assuming a complete set of contingent claims available to shareholders. In that case, …rms'investment decisions are decoupled from portfolio diversi…cation considerations. We …nd that the level of stock market correlation increases as markets become more complete, as expected. However, the increase in stock market correlation when FDI linkages are strengthened is present for all asset market structures, including the two extremes of complete markets and …nancial autarky. This is despite the fact that the correlation of dividends can be quite di¤erent across market structures and can go up or down in response to the FDI increase, depending on the degree of market incompleteness. Thus, the divergence between the comovement of dividends and the comovement of equity prices, highlighted in Jordà, Schularick, Taylor and Ward (2019), can be rationalized in our model by incomplete markets. The key insight from the production asset pricing model is that equity price comovements must re ‡ect comovement in investment and capital across multinationals, but can be entirely independent of dividend comovements.
Concurrently with the increase in FDI, the US experienced moderate increases in cross-border equity holdings, as well as in goods trade with other developed economies. Our work also sheds light 1 Key for this mechanism is that intangible capital of the parent …rm of the multinational is utilized by both the parent and foreign a¢ liates. Bilir and Morales (2020) o¤er direct evidence in support of this. on the contribution of those two changes to the stock market comovement. Consider …rst cross-border equity holdings. In contrast to standard models of diversi…cation as in Perri (2004, 2013) where FDI and portfolio diversi…cation are treated as interchangeable, our model allows for a distinction and thus a non-trivial interaction between the two. When we introduce cross-border equity holdings to the model, and allow them to rise exogenously at the same time as FDI and in line with the data, this does not generate additional increases in the stock market correlation. We also extend our model to allow for trade as in McGrattan and Waddle (2020). In our setup, trade and FDI are substitutes re ‡ecting the focus of the model on horizontal FDI between developed economies. 2 As a result, an increase in trade tends to decrease FDI and hence stock market correlation. Thus, in our experiments, increased trade does not contribute to stock market comovement either.
The mechanism we propose highlights a key role for FDI in explaining stock market correlation over and above any indirect e¤ects it might have through inducing GDP synchronization. Our calibration exercise suggests that increased GDP synchronization could have also played a role. To the extent that this synchronization is itself a result of higher FDI, the role of FDI could potentially have been larger than captured by our model. A small but signi…cant e¤ect of FDI on GDP correlations is found in Cravino and Levchenko (2017) and in Menno (2017). 3 Cravino and Levchenko (2017) show this using …rm-level data and rationalize their …nding in a model based on Melitz (2003). Their model includes labor supply ‡uctuations and a rich structure of shocks, but abstracts from investment and capital dynamics. In contrast, we abstract from some of those features, but incorporate investment and capital dynamics and argue these are crucial for understanding equity price comovement. Such dynamics are also included in Menno (2017) but, like Cravino and Levchenko (2017), his focus is on business cycles synchronization and not equity prices. Following a similar logic, trade could also have had an indirect e¤ect on stock market correlation through more synchronized business cycles. Baxter and Kouparitsas (2005) argued that trade can indeed drive business cycle synchronization. is on horizontal FDI, but in contrast to that paper it also incorporates the dynamics of investment and capital which are crucial for understanding equity price comovements. 4 The novel contribution of our paper is that we use this dynamic FDI model to study cross-country stock market comovement.
On the empirical side, the observation that cross-country stock market correlations increased since the mid 1990s has been documented in a number of papers. Goetzmann, Li and Rouwenhorst (2005) were amongst the …rst showing that there has been a dramatic increase in global stock market cor-relations starting early 1990s. Along the same lines, Quinn and Voth (2008) argue that the observed increase is attributed to greater capital market openness. Claessens, Kose and Terrones (2011) document the same fact and contrast this …nding to the fact that there has been no notable change in the cross-country correlations of credit and house prices. Viceira and Wang (2018) attribute the increase in stock market correlations to …nancial globalization, which has made discount rate shocks signi…cantly more correlated across markets, while they argue that trade globalization does not seem to play a role. Jordà et al. (2019) also document the increase in global equity price synchronization since the 1990s. Interestingly, they …nd that investment comovement also reached a peak in the mid 2000s, a result consistent with the prediction of our model, namely that higher FDI openness leads to an increase in both investment and stock market correlations. They focus on the role of US monetary policy in coordinating the global appetite for risk as an additional explanation of stock market comovement going beyond the synchronization of investment whereas, our focus is on quantifying the e¤ect of FDI and the resulting investment synchronization. More recently, Gavazzoni and Santacreu (2020) highlight the importance of R&D spillovers as a potential driver for increased international stock market comovement.

Stock market comovement and FDI: Empirical evidence
We …rst provide descriptive evidence on the evolution of global stock market correlations and FDI linkages over the past four decades. We then formally establish the empirical relationship between FDI and stock market comovements in two ways, …rst using a panel of bilateral country pairs, and second using a cross-section of …rms. The former analysis o¤ers evidence of a positive association of FDI and stock market comovement over and above what can be attributed to increased trade and business cycle synchronization. The latter rea¢ rms the country level results at a disaggregated level and con…rms that intangible capital is key for our proposed mechanism by allowing us to test whether the comovement of stock returns is stronger for multinationals that rely more on R&D and intangible capital.
Starting with stock markets, our data consists of MSCI Indices for the developed economies that are included in MSCI World. 5 We …rst look at the stock markets in the US, and compare to the rest of the world, using MSCI US and MSCI World excl. US, then look at all bilateral correlations using MSCI indices for 21 countries included in MSCI World. We use the MSCI indices to …rst calculate week-on-week returns for a country i at the end of week t as r it = (M SCI it M SCI i;t 1 ) =M SCI i;t 1 and then calculate a measure of comovement SM C ij;t between the stock markets of countries i and j at time t, using the de…nition SM C ij;t = corr r i t ; r j t ; where r i t = (r i t w=2 ; :::; r i t+w=2 ), with w a pre-speci…ed time 'window'. Using a rolling window of w = 208 weeks (four years), the left panel of Figure 1 shows correlations between the US and the rest of the world, and the right panel shows the average bilateral correlations of all bilateral country pairs, for data that ranges from 1984 to 2021.
Each point reported in this graph shows the middle of the rolling window used for calculating the reported correlation. The left panel of Figure 1 shows that there has been a substantial upshift in the correlation between US and the rest of the world, starting in the mid 1990s. The average correlation of weekly returns for the decade 1986 to 1995 is 0:368 and the one for 2006 to 2015 is 0:825. The right 5 The MSCI World consists of the following 23 countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, UK and USA. For our empirical analysis and calibration, we exclude Singapore and Hong Kong. Data sources: Bloomberg and Re…nitiv Eikon. panel of Figure 1 con…rms that the substantial increase in correlations is not only a US phenomenon but can be seen at the bilateral level too.
We de…ne a measure of FDI linkages between two countries i and j at the start of year t relative to the size of the two economies, as in : where F DI j i;t is the FDI position of country j in country i, F DI i j;t is the FDI position of country i in country j, and GDP i;t and GDP j;t denote the country GDPs, all in million USD. In Figure 2, the left panel shows the measure of relative FDI, RF between the US and the rest of the world, and the right panel shows the average relative FDI from all bilateral pairs of the 21 countries, all in %.
During the 1980s and well into the 1990s, the FDI between the US and the rest of the world was stable and around 5% of world GDP. Starting in the mid-90s, the FDI measure increases steadily reaching double the size by 2015 at approximately 10% and increasing further to about 13% more recently.
The right panel of Figure 2 shows a similar trend for the average relative FDI positions between the 21 countries, which has more than doubled over the same time period. Comparing Figures 1 and 2 suggests that these increases in FDI have coincided with the period of increased average correlation of returns.
Panel evidence at the country-pair level. Our panel consists of variables of interest for country pairs, at yearly frequency, for the period 1985 to 2019. We construct a yearly measure of stock market comovement between two countries i and j in year t, denoted by smc ij;t , by calculating the correlations of 52 week-on-week returns between the MSCI indices of the two countries in the given year t. Our remaining data consists of yearly bilateral FDI positions and ‡ows, and GDPs from OECD, and bilateral trade ‡ows from the database of the Center for International Data from UC Davies and ComTrade. We construct the measure of relative FDI as in equation (1), and a measure of relative trade de…ned as RT ij;t IM j i;t + EX j i;t = (GDP i;t + GDP j;t ) ; where IM j i;t and EX j i;t denote imports and exports respectively from country j to country i. Table 1 presents the main estimation results. Columns (1) -(5) report results from the following empirical speci…cation: smc n;t = n + t + F ln RF n;t + T ln RT n;t + " n;t ; ( where n indexes a country pair (we have data for N = 189 country pairs). We allow for country-pair …xed e¤ects n , as well as time …xed e¤ects t , or a time trend. The reported Driscoll-Kraay standard errors with four lags take into account potential cross country pair correlation, heteroskedasticity and serial autocorrelation. 6 The coe¢ cient on FDI remains positive and highly signi…cant across speci…cations, including controlling for trade, allowing for a trend, controlling for time …xed e¤ects and using FDI ‡ows instead of stocks. In addition, it remains signi…cant when we allow for slope heterogeneity across bilateral pairs using Pesaran and Smith's (1995) mean group (MG) estimator as well as accounting for common factors using Pesaran's (2006) common correlated e¤ects mean group (CCEMG) estimator. 7 In our benchmark estimation in column (2), we …nd that doubling RF is associated with an increase of 0.157 in stock market correlation even after controlling for trade. In light of our model in the next section, we view this as an association that is likely to be driven, at least to some extent, by an underlying common factor relating to globalization and …nancial liberalization. This is indeed con…rmed when we include a trend or a time …xed e¤ect or account for common correlated e¤ects, all of which reduce the size of the estimated direct e¤ect of FDI. In the model section we argue that globalization drives up stock market correlations speci…cally through increasing FDI linkages and that other aspects of globalization pertaining to increases in trade and portfolio diversi…cation have less of an e¤ect. 8 Firm level data can provide more direct evidence on causality.
Cross-sectional evidence at the …rm level. We now investigate the relationship between stock price correlations and FDI using cross-sectional, …rm-level data. Our main hypothesis is that stock prices and returns of publicly quoted companies with no foreign subsidiaries will correlate less with foreign stock markets than those of companies with foreign subsidiaries. Our model in the next section provides a mechanism through which this can work and the mechanism assigns a key role to intangible technology capital used by multinationals. To investigate this mechanism more closely, we also consider a second hypothesis, namely that multinational …rms that engage in more R&D and/or intangible capital investment should have stock returns that correlate more with international stock markets.
Our data is from Orbis and consists of 2,296 currently active …rms in the US corporate sector that are listed in the main US stock exchanges, i.e. NYSE and NASDAQ, with ordinary and registered shares for a four-year period of Jan 2016 to Dec 2019. We consider …rms from this dataset to be multinational, if they have any foreign subsidiaries. Table 2 provides summary statistics for the …rms in our sample, grouped by whether they are multinationals (f sub = 1) or not (f sub = 0). The top rows of the table show summary statistics for the variables we use in our regression analysis. The …rst variable, denoted by correl, is the correlation of a …rm's weekly returns with MSCI World ex.
US. On average, this correlation is almost 50% higher for …rms with foreign subsidiaries than those without. Next, we consider three measures of intangible investment of a …rm, namely (i) intangible …xed assets over total assets (if a_ta), average of yearly data over 2016-19; (ii) intangible …xed assets over total …xed assets (if a_tf a), average of yearly data over 2016-19; and (iii) a dummy variable that takes the value 1 if the …rm belongs to the R&D Scoreboard 2019, published by the European Commission (rdsb). All these measures are higher for …rms with foreign subsidiaries than those without. Additionally, our controls include (iv) the …rms' betas for the same period, in order to capture comovement of …rms' returns with international stock markets that is potentially over and above any comovement of the US market with the rest of the world markets, (v) the …rms'average revenues over 2016-19, to control for …rm size and (vi) industry dummies based on the NAICS 2 digit classi…cation. 9 The last few rows of Table 2 give additional summary statistics pertaining to the size of …rms in the sample including the number of employees, tangible and intangible assets, and earnings. In our dataset, …rms with foreign subsidiaries, i.e. multinationals, are larger (higher revenues, higher earnings and larger number of employees) than …rms without foreign subsidiaries. 8 Among other robustness checks, we control for relative trade in intermediate goods, and …nd that the e¤ects of They also tend to have returns that are more volatile than the market returns (beta > 1), while …rms without foreign subsidiaries have returns that are less volatile than the market (beta < 1). Figure 3 shows the breakdown of …rms by industry.
Our empirical speci…cation is where intang stands in for one of the three measures of intangible investment described above, i.e.
if a_ta, if a_tf a or rdsb. In Table 3 we report results for several versions of the above speci…cation.
For each speci…cation (see columns 1, 2, 3, 4), we report a version of the regression where we control for industry and cluster standard errors by industry in columns marked with (b). First, we note that betas and revenues have signi…cant e¤ects on correlations and these are quite stable across speci…cations.
Also, industry dummies improve the model's explanatory power. Even controlling for these, columns (1a) and (1b) show, as a …rst pass, that multinational …rms have signi…cantly higher correlations with MSCI World ex. US than …rms with no foreign subsidiaries.
Our main focus is on results in columns (2)-(4) where a measure of intangibles is included. With these speci…cations, we can gauge the e¤ect of being a multinational ( + intang i ), as well as the additional e¤ect that intangible capital has on correlations conditional on a …rm being a multinational ( ). In those, the interaction term is always signi…cant. Interestingly, having a lot of intangibles alone does not seem to increase correlations unless this is combined with being a multinational. This is exactly what our theoretical model captures. In terms of the size of the e¤ects, even though the coe¢ cients on f sub and on the interaction term vary somewhat across speci…cations, we note that the combined e¤ect is stable across speci…cations. For example, looking at column 4, a multinational (f sub = 1) that is also part of the R&D Scoreboard (rdsb = 1) has on average a correlation with world stock markets that is 0.10 -0.11 larger than a non-multinational that is not part of the R&D Scoreboard. This size remains similar whether one controls for industry or not. Similar e¤ects are implied by the speci…cations in columns (2) and (3), for which the intang variables are continuous.

A two-country asset pricing model with multinational firms
Our model extends McGrattan and Prescott (2010), by adding country-speci…c productivity shocks and capital adjustment costs, and allowing for incomplete international asset markets. Time is discrete and in…nite, indexed by t = 0; 1; 2; : : :. There are two countries, each populated by a representative household, and two multinational …rms. Each multinational …rm operates two productive units (plants), one located within the country where the multinational is incorporated and one located abroad, i.e. there are four plants overall. Superscripts h = 1; 2 denote the multinational that owns the plant and subscripts i = 1; 2 denote the country in which the plant is located. We assume that …rm h is incorporated in country h.
Firms. Consider the plant located in country i and owned by multinational …rm h. Its output at time t is denoted by Y h it ; and the tangible capital stock and labour used for this production are denoted by K h it and N h it respectively. Each multinational also has technology (intangible) capital M h t which is used as an additional input to production in both of its plants, hence no i subscript. The production technology of multinational h in country i is given by where K ; M and N denote, respectively, the income shares of tangible capital, intangible capital and labor, 0 < K ; M ; N < 1 and K + M + N = 1: A i is a productivity level parameter, Z it is a country-speci…c productivity (TFP) shock and h i are parameters governing the degree of FDI openness of each country i. We normalize 1 1 = 2 2 = 1 and assume that 0 < 2 1 ; 1 2 < 1. As in McGrattan and Prescott (2010), h i < 1 re ‡ects exogenous barriers preventing …rm h from taking full advantage of FDI opportunities in country i. In the calibration, these are used to capture the amount of production by the foreign a¢ liate relative to the home …rm in country i. The term i captures the number of locations available for setting up plants in country i and will be proxied by population size in country i in our calibrations. Capital accumulations are described by where X h K;it and X h M;t are investment in tangible and technology capital respectively, K and M are depreciation rates and is the capital adjustment cost function, in line with Hayashi (1982).
t is the stochastic discount factor used by the …rm. Dividends D h t are given by Households. The representative household in each country i maximizes E 0 P 1 t=0 t ln c it ; where c it is the consumption of household i. 10 Each country i is populated by i identical individuals so that aggregate consumption in country i is C it i c it and aggregate supply of labour to the plants that operate domestically is N it i n it , where n it is the labor supply of household i, which we assume to be inelastic. Households earn a wage W it and can trade shares of the domestically incorporated …rm only. 11 The number of shares bought by each household at time t and the price at which they are bought are denoted by it+1 and Q i t respectively. The total number of shares bought at time t in country i is i it+1 . As a benchmark, we assume that markets are incomplete (IM) and allow households to only trade a non-contingent bond b it across countries. The budget constraint is then where Q b;t is the bond price at t and bond holdings are subject to a quadratic adjustment cost. We also consider two extreme international asset market structures, namely …nancial autarky (FA) and complete markets (CM). In the FA economy, we do not allow cross-country trade in …nancial assets by households, as in Heathcote and Perri (2002). 12 The budget constraint is 1 0 The choice of log utility is not crucial for our results, see the Online Appendix for alternative preference speci…cations. 1 1 This assumption of perfect home bias is relaxed in Section 5. 1 2 Notice, however, that this is not strict …nancial autarky since …rms can still engage in FDI and expose their shareholders to the economic conditions of the foreign country.
In the CM economy, households can trade a full set of state contingent claims. The budget is where s t denotes the history of shocks Z t 1 ; Z t 2 , b it s t 1 ; s t is the number of contingent claims bought in the previous period at state s t 1 and promising to pay at state s t = s t 1 ; s t today and q t 1 s t 1 ; s t is the corresponding price. When markets are complete, the intertemporal marginal rates of substitution are equalized across all households (of both countries), and this de…nes the stochastic discount factors for both …rms. When markets are not complete, since we have assumed perfect home bias, the stochastic discount factor of …rm h corresponds to the intertemporal marginal rate of substitution of the representative household in country h.
Market clearing. Labour markets clear in each country, so that N it The aggregate supply of shares of each …rm is normalized to one and the stock market clears in each country, i it = 1, i = 1; 2. Additionally, under incomplete markets, we assume that bonds are in zero net supply and the world bond market clears, i.e. 1 b 1t+1 + 2 b 2t+1 = 0: Finally, under complete markets, the contingent claims markets clear, that is 1 b 1t+1 s t ; s + 2 b 2t+1 s t ; s = 0 for all s and all s t : The following world aggregate resource constraint holds Under IM the left hand side of the resource constraint also includes aggregate bond holding costs

Quantitative results
Calibration. We calibrate the model in quarterly frequency, to match long run ratios based on US data and only make countries asymmetric with respect to the levels of GDP, population sizes and the fraction of …rm tangible capital installed in the foreign plant (FDI). 13 The income shares K ; M and N along with the depreciation rates K , M and the discount factor are calibrated as follows. and productivity to one, i.e. 1 = A 1 = 1. We then take country 2 to be the rest of the world, as de…ned by the set of 21 countries used in section 2. Using OECD data for 1991-1995 we …nd that the population of these countries is 2:160 times the US population and thus set 2 = 2:160. We also …nd the sum of the GDPs of these countries to be 1:75 times that of the GDP of US, and therefore 1 3 As pointed out by McGrattan and Prescott (2010) domestic production in the model has to be adjusted by subtracting technology investment to match to measured GDP in the BEA data GDPit Y 1 it + Y 2 it X i M t . We do so in our calibration and denote measured GDP in the Tables as GDPi.
Capital adjustment costs are commonly used in international macro models to avoid excessive investment volatility. Accordingly, in our model, tangible and intangible capital are subject to adjustment costs and we assume that (x) = (x ) 2 =2; where the adjustment cost parameter is calibrated to match the observed standard deviation of tangible capital investment relative to the standard deviation of output for the US economy. We target the value of 2:390 for this ratio, reported by Boldrin, Christiano and Fisher (2001). 14 Turning to the productivity shocks, we follow Backus et al. (1992), Baxter and Crucini (1995) and Kehoe and Perri (2002), and assume that the shocks Z t = (Z 1t ; Z 2t ) T follow a vector autoregressive (VAR) process of the form Z t+1 = Z t + " t+1 ; where 11 = 22 1 is a common persistence parameter and 21 = 12 2 is a spillover parameter. The innovations " t = (" 1t ; " 2t ) T are serially independent, multivariate normal random variables. We set 1 = 0:95 and 2 = 0, using the estimates Results. Our baseline experiment involves exogenously increasing the FDI openness parameters h i to match the increase in FDI positions observed in the data and using the model to obtain the implied increase in the stock market correlation. Table 4 presents correlations of returns, stock prices and other key variables in the stationary distribution of the economy before and after the changes in h i . 15 Under the benchmark calibration with incomplete markets, the correlation of quarterly stock returns is 0:380 before the FDI openness increase and it increases to 0:520 after the increase.
In the data, the correlation increases from 0:387 to 0:809. Thus the FDI channel alone explains approximately one third of the increase in stock market correlation.
To understand stock price comovement, it is helpful to relate the stock price of a …rm to its capital and investment. In the Online Appendix, we derive the following equilibrium condition which expresses the ex-dividend value of …rm h as a weighted sum of its capital stocks. In a standard RBC model with no FDI and no intangible capital, there is only one capital stock and it is valued at a price q arising from the presence of adjustment costs just like in this model. This is commonly referred to as Tobin's q. Here, similar capital stock valuations arising from adjustment costs are derived, but they can potentially be di¤erent for the di¤erent types of capital. As is standard, these capital stock valuations arise due to adjustment costs and are increasing in the investment rates of the corresponding capitals. Using this equilibrium relation, and noting that to a …rst order approximation, the stock price of a …rm is the weighted average of the total capital stock and the total investment of the …rm, we can relate the correlation of stock prices to the comovement of the total capital stocks as well as the comovement of the similarly de…ned total investments X h t of the two …rms. Table 4 illustrates that the correlation of investment is very similar to the correlation of the capital stocks and both are very similar to the correlation of stock prices. Therefore, stock price comovement can be attributed to synchronization of investment across the two multinationals.
Guided by this observation, we can see how stock prices tend to comove when foreign …rms are exposed to domestic shocks through FDI. A persistent increase in home TFP induces the foreign multinational to increase its investment at the same time as the home multinational, because its foreign plant is now expected to be temporarily more productive. This increased investment has a positive e¤ect on the accumulation of both the tangible capital of the foreign …rm in the home country and the intangible capital of the foreign …rm. Depending on the level of exposure and the size of the shock, the increased investment may also induce an increase in tangible capital of the foreign …rm in the foreign country, due to the complementarity with intangible capital. Therefore, the higher the FDI exposure is, the larger the stock price correlation is. Key to this channel is the presence of intangible technology capital, without which the e¤ect on the foreign capital of the foreign …rm is absent. 16 To analyze the interaction between investment and stock prices for the two multinational …rms, we consider impulse responses to a one standard deviation increase in the TFP of the home country, Z 1 , under the assumption that corr(" 1t ; " 2t ) = 0. Impulse responses of the stock prices, investment and dividends of the two …rms are shown in Figure 4. Solid lines represent responses in the low FDI environment (Before) and dotted lines responses in the high FDI environment (After ). The initial impact of the TFP increase is to increase overall production in country 1, i.e. both Y 1 1 and Y 2 1 . The e¤ect is exactly symmetric on the two plants located in country 1, which implies a symmetric increase in labor demand by the two plants. Because labour supply is inelastic at the country level, wages in the home country increase and there is no re-allocation of labor across the two plants on impact.
The e¤ect is to increase the current operating pro…ts for …rm h, i.e. the right hand side of the …rm The e¤ect is larger for the home (country 1) …rm, since most of its production and cash ‡ow comes from the home plant and smaller for the foreign (country 2) …rm since its plant abroad (in country 1) is small relative to its plant in its own country. Importantly, this asymmetry in the size of the cash ‡ow e¤ect on the two …rms becomes smaller as FDI increases.
Firm investment responds for two reasons: the direct e¤ect is due to the TFP shock persistence, which implies higher expected TFP for the corresponding plants and increases the return to investment. This prompts both …rms to increase investment generating the positive investment correlation.
A second e¤ect arises due to a smoothing motive and operates via the …rm's stochastic discount factor which, in equilibrium, is equalized to the marginal rate of substitution of households owning the …rm. Speci…cally, depending on the availability of other risk sharing opportunities for the …rms' owners, the foreign …rm might adjust its investment and dividend choice to provide some smoothing for its owners. Thus the comovement of investment and of dividends will depend on the underlying asset market structure and, in particular, dividends may be negatively correlated across …rms, as the numerical results in Table 4 indicate.
To further understand how these two channels a¤ecting the stock price comovements operate, it is instructive to consider the two extreme cases of …nancial autarky and complete markets using the results from Table 4. First, we note that when markets are complete, stock prices comove more closely both before and after the change, but there is still a sizeable increase from 0:644 to 0:824 as a result of the increase in FDI openness. Under …nancial autarky, stock prices comove less overall, but the increase is still present and of similar magnitude going from 0:340 to 0:478. Investment responds to a positive shock Z 1 more symmetrically across …rms when markets are complete, because perfect insurance ensures marginal rates of substitution, and hence …rms'discount factors, are perfectly synchronized across countries. In the absence of insurance possibilities (FA), because the stochastic discount factors of the two …rms are not synchronized, the stock price correlation is lower. Nevertheless, these numerical results suggest that the e¤ect of increased expected returns to investment dominates, and therefore investment and hence stock market correlation are positive and increasing in FDI openness, irrespective of the comovement of dividends.
An alternative way to look at stock prices is by reference to the usual asset pricing equation, which relates the stock price to the expected discounted sum of dividends, where the …rm's discount factor re ‡ects shareholders'marginal rate of substitutions. It is tempting to infer stock price comovement by looking at the correlation of dividends and the correlation of stochastic discount factors, but this can be misleading. Both the covariance of the marginal rate of substitution with foreign …rm dividends and the serial correlation of both these variables would need to be taken into account, and this makes it harder to obtain a simple intuitive explanation using this approach. It is nevertheless interesting to highlight the behavior of dividends in our model, as this is an observable that is often used to analyze the sources of equity price comovements (see, for example, Viceira  In summary, a production based asset pricing model ties stock prices to investment and, with more FDI exposure, multinationals respond positively and by more to foreign shocks. This implies an increase in the stock market correlation. Looking at the correlation of dividends can be misleading as a means of inferring stock price comovement. If anything, the level and change in the correlation of dividends are more relevant for inferring the level of international asset market completeness, and could potentially be used as a test of market completeness. 17

A model extension with portfolio diversification and trade
We now introduce portfolio diversi…cation and trade to the model and show that, at least in this context, these two candidates have limited ability to explain increases in cross-country stock market correlations. Even though the home bias in stock holdings is a well-documented fact, assuming perfect home bias, is somewhat extreme. In practice, there were some cross border holdings of equities in the beginning of the 1990s and, more importantly, there was an increase in cross-border holdings from the 1990s to the 2010s.
In addition to the consumption price P it , the budget also di¤ers from our benchmark model in that households in country i hold shares h it in both h = 1 and h = 2 …rms. That is, we allow households to hold a diversi…ed portfolio. Stock market clearing requires now that 1 h 1t+1 + 2 h 2t+1 = 1, h = 1; 2: Solving the model with a portfolio choice for households is beyond the scope of our paper. We instead aim to obtain a sense of the e¤ects of diversi…cation by making a simplifying assumption: households can only trade shares of their home …rm. As a result, shares of …rm h are priced in the market using the country h marginal rate of substitution. We use this market value as the objective of the …rm, which is consistent with the notion that portfolio investment, as opposed to FDI, does not endow the investor with signi…cant in ‡uence over …rm decisions. 18 An important implication of our simplifying assumption is that, in equilibrium, the fraction of each …rm held by home (and foreign) households is …xed as in Fogli and Perri (2015). To be concrete, let h i be the total number of shares of …rm h held by households in country i so that 2 Households hold a diversi…ed portfolio and their dividend payments are a weighted sum of the two …rms' dividends. Furthermore, increases in h6 =i i can capture the increased reliance on foreign dividends arising from increased cross-border equity holdings.
We maintain the same benchmark calibrated targets as in the previous section. 19 We follow McGrattan and Waddle (2020) in choosing = 10 and % = 100, the latter intended to capture a high substitutability between the FDI and trade goods produced by the same …rm. We choose a symmetric transport cost = 0:186 to match a ratio of exports plus imports over measured GDP of 0:206 for the US. We also assume that the equity home bias is symmetric across the two countries 2 1 = 1 2 .
We set the fraction of shares held by foreigners = 0:051 in the benchmark case so the fraction held at home is = 1 . In the experiments we consider, we incorporate simultaneous increases in FDI, trade and cross-border equity holdings, as well as changes in the relative size of the two economies.
Speci…cally, we set 2 1 = 0:868 and 1 2 = 0:891 to match the same FDI increases as in the original experiment, we set = 0:136 and = 0:052 to capture the documented increases in cross-border equity holdings and in trade between the US and the rest of world and we also let 2 = 1 drop to 1:950 and A 2 =A 1 drop to 0:795 to match the changes in relative population and GDP observed in OECD data in the periods of interest. Table 5  It is noteworthy that the correlation of stock prices when all changes are included increases from 1 8 With incomplete markets and heterogeneous shareholders, unanimity on the …rm's objective cannot be guaranteed (Carceles-Poveda and Coen-Pirani, 2009). Our choice is also consistent with a majority rule since in our calibrations the home households are indeed a large majority of the shareholders. 1 9 Parameters remain the same as for the baseline model except for minor adjustments due to the the presence of trade, see the Online Appendix for more details. 0:385 to 0:527, which is very close to the result we obtained in Table 4 where only FDI changes were included. To understand why, note …rst that changes in the relative size of the economies via i and A i do not a¤ect stock market correlations. This is not entirely surprising given that these parameters mostly a¤ect steady states and the level changes are not dramatic. However, when we switch o¤ the increase in cross-border equity holdings , the correlation actually increases even more to 0:556. That is, increased cross-border holdings have a negative e¤ect on the stock market correlation. This is because with incomplete markets, …rms' investment behavior is to some extent driven by a desire to provide insurance to their owners. In response to a positive TFP shock in country 1, the insurance e¤ect pushes …rms to adjust their dividend responses in opposite directions in order to provide some smoothing, and that induces lower investment correlations. To provide the same level of smoothing through negatively correlated dividend payments, …rms have to adjust their dividends more aggressively the closer is to 1=2. In turn, this leads to even lower correlation of investment. As a result, when is higher, the correlation of …rm investment and stock prices is lower. If households had a full set of contingent claims available for trade, i.e. under complete markets, the introduction of portfolio diversi…cation would be moot. In that case, …rm decisions on dividends and investment are decoupled from cross-country risk sharing considerations. Marginal rates of substitution are equalized across countries state-by-state, and the portfolio composition is indeterminate and irrelevant for stock price comovement. However, as we saw in the previous section, it is still the case that FDI plays a signi…cant role, since it directly a¤ects the synchronization of investment across …rms. We view this as an important takeaway, namely that FDI can matter over and above any risk sharing role that it might play, and this clearly distinguishes FDI from household portfolio diversi…cation in this model in contrast to standard models of diversi…cation as in Perri (2004, 2013).
Increased goods trade is also found to have a negative e¤ect on the stock market correlation, albeit for a di¤erent reason. To understand why, we …rst note that there is an important interaction between the trade cost parameter and the FDI openness parameters, since there is high substitutability between the two corresponding goods. This is intended to capture the idea that a …rm can access foreign markets for its good either by exporting more or by producing more in their FDI plant. When transport costs decrease, …rms substitute away from FDI production and increase exports. As a result, to rationalize the observed increase in FDI, the underlying reduction in barriers to FDI must be larger in the presence of falling transport costs than in the absence thereof. Thus, our calibration in this extended model features an even larger increase in the FDI openness parameters h i compared to our benchmark model. When we shut down the transport cost change, FDI increases by more than in the data and, as a result, the stock market correlation increases by more to 0:571.
An alternative way to compare quantitatively our model mechanism to the data is to run similar regressions in the model and data. To this end, we consider detrended time series data for the US versus the RoW for the period 1970Q1 to 2017Q2 and regress correlations of quarterly returns of MSCI US and MSCI World ex. US on relative FDI ‡ows (RF L t ) and relative trade (RT t ). For the model regressions, we …rst generate 190 steady states after calibrating 12 , 21 and to match the data time series of FDIs and trade for each of the quarters in the same period. Keeping all our other parameters constant at the values calibrated to the 'Before'scenario, we simulate our model for 10,000 periods for each of the 190 calibrations and we calculate the correlation of quarterly stock returns over the long simulation. We then run the same regressions with detrended model generated data as we did with the data, and compare the outcomes in Table 6. 20 The coe¢ cients on FDI are remarkably similar in model and data, meaning the extended model is capturing the quantitative relationship well.
To summarize, the e¤ect on stock market comovement of the shift in FDI survives the addition of all the additional factors; even though globalization has brought about increases in trade and crossborder equity holdings concurrently with the increase in FDI, in the model these additional factors do not seem to explain the remaining increase in the stock market correlation, after the increase in FDI has been taken into account. Globalization has arguably also brought about increased business cycle synchronization, which could be another factor explaining the stock market comovement increase.
To investigate this, as a …nal experiment, we mechanically increase the correlation of TFP shocks to gauge the extent to which business cycle synchronization could explain the remaining di¤erence.
For the years 1996-2015, we compute the average correlation between US real GDP and real GDP of each of the countries in the MSCI index to be 0:610 (compare to 0:256 in our benchmark calibration).
Starting from our full model, we increase corr(" 1t ; " 2t ) to match this increase in GDP correlations and …nd the stock price correlation increases further from 0:527 and up to 0:787. We conclude that increased business cycles synchronization is likely to have played an important role too, but we note that part of the observed increased business cycle synchronization could also be due to the increase in FDI. 21 Our model however abstracts from this additional indirect channel, in order to focus on the direct e¤ects of FDI on stock market correlation, over and above any e¤ects through business cycles synchronization.

Closing comments
Cross-country stock market correlations have seen a sharp rise in the past 30 years. This paper establishes a relationship between this rise and the increase in FDI positions in the last thirty years, both empirically and theoretically. The timing of the observed increase in stock market correlations coincides with the sharp increase in FDI positions among large developed economies that has taken place from the mid 1990s onwards. A positive relationship between stock market correlation and FDI is found to be present even when controlling for other potentially contributing factors.
Our theoretical framework is rich enough to provide a meaningful calibrated asset pricing model of the US economy versus the rest of the world, yet parsimonious enough to be able to disentangle the channels that matter for the comovements of the two stock markets. There are two key elements of the model that are important for establishing the link between FDI and stock markets: …rst the multinational …rms, that engage in foreign direct investment, and second the presence of intangible technology capital in the production functions of the …rms. With these two in place, we show that the comovement of investment can drive to a signi…cant extent the comovement in stock prices. In our benchmark calibration, FDI was found to generate approximately one third of the observed rise in stock market comovement. We have argued that in the context of our model, neither increased trade nor increased portfolio diversi…cation alone can help explain the stock market correlation increase.   (7) and (8). Pesaran-Smith standard errors reported in parentheses. *** , ** and * denote signi…cance at 1%, 5% and 10% level respectively. Data sources: Eikon, Bloomberg, OECD Statistics and ComTrade.  Notes: Cross sectional data based on averages from years 2016-2019. Sample size = 2,296 …rms incorporated in the US. correl is the correlation of a …rm's weekly returns with MSCI World ex. US; f sub is 0 for …rms without foreign subsidiaries and 1 with …rms with foreign subsidiaries, i.e. multinationals. The third line, intang var, speci…es which control variable was used as a proxy for investment in intangible technology capital: ifa_ta is intangible …xed assets over total assets; ifa_tfa is intangible …xed assets over total …xed assets; rdsb is a dummy variable that takes the value 1 if the …rm belongs to the European Commission R&D Scoreboard 2019 and 0 otherwise. beta is the …rm's beta, calculated as covar(r i ; r U S )=var(r U S ), where r i and r U S are are weekly returns for …rm i and MSCI US respectively, for the period 2016-19; rev is …rm's revenues in billion USD. NAICS-2 = yes indicates that two digit NAICS industry dummies were included in the speci…cation. Robust standard errors reported in parentheses in columns (1a), (2a), (3a) and (4a). Standard errrors are clustered by two digit NAICS industry in columns (1b), (2b), (3b), (4b). ***, ** and * denote signi…cance at 1%, 5% and 10% level. Data sources: Eikon, Bloomberg, Orbis and European Commision R&D Scoreboard.   Notes: Correlations of stock returns r, stock returns prices Q, total …rm investment X, total …rm capital K, …rm dividends D, country consumptions C, GDP and country tangible capital investment XK , when the model is calibrated to 1990s (Before) and to 2010s (After, all incl ), under Incomplete Markets. Cols (3) -(6) report correlations from counterfactual experiments where the corresponding parameter is at its Before level.    Notes: Shock is one standard deviation increase in the TFP of country 1, assuming correl (" 1t ; " 2t ) = 0. Q h , D h and X h denote stock price, dividends total investment respectively for …rm h = 1; 2. Blue solid line is the economy Before; red dotted line is the economy After.