The Intellectual Spoils of War? Defense R&D, Productivity, and International Spillovers

WHILE a large body of empirical research has argued that R&D is a key source of firm productivity growth, the question of exactly which policies governments should adopt to foster R&D investment is still largely an open question.¹ In this paper, we study the impact of government funding for R&D on privately conducted and financed R&D, and its ultimate effect on productivity growth. We use two complementary longitudinal datasets—a country-industry-year-level dataset for OECD countries and a firm-year-level dataset for France—to address two related questions. First, we estimate the effect of government-funded R&D on private R&D—namely, R&D conducted and financed by private businesses. We are interested in whether government-funded R&D in a given country and industry (or to a given firm) displaces or fosters private R&D in the same country and industry (or firm). Having found evidence of a positive effect (i.e., “crowd in” rather than “crowd out”), we next estimate how investment in R&D affects productivity. For both types of analysis, we assess whether the benefits of public R&D investment are limited to a single country or spill over across multiple countries.

To isolate the causal effect of government-funded R&D, we use quasi-exogenous variation in defense-related R&D. Defense-related R&D is an important but relatively understudied component of public policy on R&D. It represents a key channel through which governments seek to shape innovation (Lichtenberg, 1995, Draca, 2013). In the United States, annual government defense-related R&D expenditures amounted to about $78.1 billion in 2016, 57.2% of all government-funded R&D (Congressional Research Service, 2018). While defense-related R&D is motivated by goals that are not mainly economic, it is often the most important de facto industrial policy used by the federal government to affect the speed and direction of innovation in the economy. The amount of public money flowing into defense R&D dwarfs the amount spent on other prominent innovation policy tools in the US. For example, the total budget of the National Science Foundation or the overall value of the federal R&D tax credit in a typical year are less than one tenth of federal outlays for defense-related R&D (National Science Foundation, 2006). Defense R&D is the single most important component of government-funded R&D in the UK and France as well, and a major component of government-sponsored R&D in many other developed economies.

We begin our empirical analysis using a unique dataset that we constructed by linking detailed information on defense-related and nondefense related government-funded R&D to information on private R&D, output, employment, and salaries in 26 industries in all OECD countries over 23 years. We estimate models that relate privately funded R&D in a given country, industry, and year to government-funded R&D in the previous year, conditioning on a full set of country-industry and industry-year fixed effects.

We complement this industry-level analysis with a firm-level analysis based on a longitudinal sample of firms that engage in R&D collected by the French Ministry of Research from 1980 to 2015. This is the only available dataset we know of that disaggregates public defense R&D subsidies by firms across the whole economy. One advantage of using firm-level data is that we observe which firms within an industry actually receive public R&D funds and which do not. The longitudinal nature of the data allows us to control for firm fixed effects, absorbing all time invariant unobserved differences across firms that may be systematically correlated with the propensity to invest in R&D. We compare the same firm to itself in different moments of time, and identification stems from the exact timing of the public R&D award.

We use predicted defense R&D as an instrumental variable to isolate exogenous variation in public R&D. This instrument combines nationwide changes to defense R&D with fixed allocations across industries. Annual aggregate changes in defense spending reflect political and military priorities that are largely independent of productivity shocks in different domestic industries. Wars, changes of government, and terrorist attacks have had major influences on defense spending. In the United States, for example, military R&D spending ramped up under President Reagan; fell back after the end of the Cold War and rose again after 9/11. Importantly for our identification strategy, the impact that nationwide exogenous changes in military spending have on defense related R&D varies enormously across industries, because some industries (e.g., aerospace) rely more heavily on defense-funding than others (e.g., textiles).

The sign of the effect of government-funded R&D on privately funded R&D could be positive or negative, depending on whether government-funded R&D crowds out or crowds in privately-funded R&D. Crowding out may occur if the supply of inputs to the R&D process (specialized engineers, for example) is inelastic within an industry and country (Goolsbee, 1998). In this case, the only effect of an increase in government-funded R&D is to displace private R&D with no net gains for total R&D. Crowding in may occur if (i) R&D activity involves large fixed costs and, by covering some of the fixed costs, government-funded R&D makes some marginal private sector projects profitable; (ii) government-funded R&D in an industry generates technological spillovers that benefit other private firms in the same industry; and/or (iii) firms face credit constraints.

Empirically, we find strong evidence of crowding-in across both the OECD and French datasets. Increases in government-funded R&D generated by variation in defense R&D translate into significant increases in privately funded R&D expenditures, with our preferred estimates of the elasticity equal to about 0.5. Our estimate implies that defense-related R&D is responsible for an important part of private R&D investment in some industries. For example, in the United States “aerospace products and parts” industry, defense-related R&D amounted to $3,026 million in 2002 (nominal). Our estimates suggest that this public investment results in $1,948 million of additional private investment in R&D. Considering the total amount spent by the U.S. government, we estimate that private R&D investment in the United States is $85 billion higher than the counterfactual with no government-funded defense R&D. Using our estimates, we calculate that dollar-for dollar, publicly funded R&D generates twice as much overall R&D compared to R&D tax credits.

Our estimates also indicate that cross-country differences in defense R&D might play an important role in determining cross-country differences in overall private sector R&D investment. For example, we estimate that if France increased its defense R&D to the level of the United States as a fraction of its GDP (admittedly a large increase), private R&D in France would increase by 10.3%.

We also find evidence of spillovers between countries.² Increases in government funded R&D in one country appear to increase private R&D spending in the same industry in other countries. For example, an increase in government-funded R&D in the United States chemical industry induced by an increase in U.S. defense spending in the chemical industry raises the industry's private R&D in the United States, but it also raises private R&D in the German chemical industry. This type of cross-border spillover is consistent with the presence of industry-wide technological or human capital spillovers.

In the final part of the paper, we turn to the effect of R&D on productivity. We uncover a positive effect of private R&D on TFP. Our preferred model suggests that an increase in the defense R&D to value added ratio of one percentage point causes an 8.3% increase in the yearly growth rate of TFP (e.g., from 0.98 percent per annum to 1.06%). We view this as a significant but not overwhelming effect. It suggests that a small fraction of U.S. economic growth is accounted for by investment in defense R&D. For example, defense R&D in the United States increased by a third between 2001 and 2004 following the 9/11 attack. We estimate that, holding taxes constant, this translated into a 0.005 percentage point increase of the annual TFP growth rate, or a 1.5% increase.

Overall, our estimates suggest that cross-country differences in defense R&D play a role in explaining cross-country differences in private R&D investment, speed of innovation, and ultimately in productivity of private sector firms. We caution that our estimates do not necessarily imply that it is desirable for all countries to raise defense R&D across the board. Our finding that government-funded R&D results in increased private R&D does not necessarily imply that defense R&D is the most efficient way for a government to stimulate private sector innovation and productivity. There are other possible innovation policies available to governments (see Bloom et al., 2019, for a survey).

We focus on the effect of government-funded R&D on private R&D activity. Specifically, we are interested in the direct effect for or a firm of receiving government-funded R&D on the recipient's own private R&D investment.

The direction of such effect is unknown a priori. If increases in government-funded R&D crowd out private R&D, the effect will be negative. In the case of complete crowding out, the only effect of the policy is to displace private R&D, with no net gain in total R&D. This would be the case if the supply of inputs in the R&D process in any given industry was perfectly inelastic in the short run. A key input in this respect is likely to be specialized scientists and engineers and the elasticity of their supply to a country-industry depends on their mobility across industries and countries. With inelastic supply to a country-industry, increases in public funds for R&D come at the expense of declines in private R&D.

If, on the other hand, increases in government funded R&D crowd in private R&D, the effect will be positive. In this case, more public R&D stimulates even more private R&D. There are at least three possible reasons for why this might be the case.

First, in the presence of large fixed costs, public R&D may make marginal private projects feasible. In most industries, R&D activity is characterized by large fixed costs in the form of labs, research, human capital accumulation, set up costs, etc. It is realistic to think that some of these fixed costs can be used for multiple projects. For example, lab infrastructure set up for a specific project can, in some cases, be used for other projects as well. Similarly, a scientist's human capital acquired while working on a specific project—the intellectual understanding of a specific literature, for example, or her mastery of a scientific technique—can be helpful in other projects. By paying for some of the fixed costs, government-funded R&D may make profitable for private firms’ projects that otherwise would not have been profitable. Similarly, if government-funded R&D results in process innovation, it is conceivable that this innovation can indirectly benefit private R&D. Second, if firms are credit constrained, the public provision of R&D might relax these financial constraints.

Finally, government-financed R&D investment by one firm may make other firms in the same industry more productive because of technology or human capital spillovers (e.g., Moretti, 2004, 2021). In this case, an increase in government-financed R&D directly raises R&D in the firm that receives the government contract and may indirectly raise R&D in other firms in the same industry or same locality. Spillovers could also be negative in the case of strategic substitutability, as rival firms could free ride off the R&D of the supported firms (e.g., Bloom et al., 2013).

An implication that is relevant for our empirical analysis is that in the presence of R&D spillovers within an industry the estimated coefficient from industry-level data does not need to be identical to the coefficient from firm-level data in equation. Broadly, we expect industry coefficients should be larger if crowd-in induces rival firms to do more R&D (e.g., due to strategic complementarity) or smaller if rivals do less R&D (e.g., due to strategic substitutability).

We derive equations (1) and (2) in the context of a simple model in appendix A, where we also discuss the assumptions needed. The focus of our analysis is on estimating the coefficients $αOECD$ and $αFRA$ that relate changes in government-funded R&D in a given year to changes in private R&D in the following year.

To account for the possible correlation of residuals in each year across industries in a given country and across countries in a given industry, standard errors for OECD data are multiway clustered by country and industry pair and country by year pair. In the regressions based on the French data, we cluster at the two-digit industry for industry-level regressions and three-digit industry for firm-level regressions.

Government R&D policies are unlikely to be random and may be set endogenously as a function of shocks to firms in the private sector. Our models yield inconsistent estimates if the timing and amount of public R&D is correlated with unobserved time-varying determinants of private R&D. This may happen, for example, if governments tend to use public funds to help firms in sectors that are struggling and are experiencing declines in private R&D. In this case, changes in public R&D would be negatively correlated with unobserved determinants of private R&D, introducing a negative bias in our estimates of the coefficient $α$ in equations (1) and (2). The opposite bias arises if governments tend to use public funds to help firms in sectors that are thriving and are experiencing increases in R&D over and above those experienced by the same sector in other countries. If governments disproportionately help “winners”, the correlation between $Sik(t-1)$ and $υikt$ (and $Sfik(t-1)$ and $υfikt$⁠) is positive and OLS overestimates the true effect. If governments disproportionately help “losers” (compensatory policies), the correlation between $Sik(t-1)$ and $υikt$ (and $Sfik(t-1)$ and $υfikt$⁠) is negative and OLS overestimates the true effect.

A second possible reason why the OLS estimates of equations (1) and (2) may be biased is the presence of measurement error in our measure of public subsidies. In the presence of classic measurement error in $S$⁠, attenuation bias may arise.

To deal with these two issues, we use an instrumental variable that is a function of variation in defense R&D subsidies. Defense R&D is by far the largest component of government R&D in many countries, for example, United States, United Kingdom, and France. Defense R&D also causes the biggest variations in public R&D over time, and there is a large variation across countries, ranging from pacifist countries like Japan or neutral countries like Austria, to defense-heavy countries like the United States and South Korea. This ensures that our instrument has a strong first stage.

Defense R&D is usually motivated by geopolitical, not economic, considerations (Mowery, 2010), raising the possibility of using actual R&D defense subsidies as the instrument for government funded R&D. However, we are concerned that while most of the variation in defense R&D is motivated by geopolitical considerations, variation in defense R&D may also include an endogenous component. This would be the case if changes in the timing and amount of defense R&D allocated to some industries and firms respond at least in part to shocks to the supply or demand of private R&D in those industries or firms. While variation in R&D defense subsidies is almost certainly more exogenous than variation in overall public R&D, we cannot rule out the existence of an endogenous component.

For this reason, we use predicted defense R&D subsidies as instrumental variable instead of actual defense R&D subsidies. Predicted defense R&D subsidies isolate variation in defense R&D subsidies based on the combination of lagged defense R&D subsidies to a given industry and the overall total defense R&D spending. While the use of predicted instead of actual defense R&D subsidies may weaken the power of the instrument in the first stage, it strengthens its validity. In practice, our first stage has good power and is robust to various changes in the assumptions we use to construct the instrument.

The exact definition of predicted public defense R&D differs slightly for the OECD and the French dataset due to differences in level of aggregation and variable definitions. The details on how we construct the instrument are in appendix B.

Our identifying assumption is that variation over time in the amount of predicted defense-related R&D experienced by a given industry in a given country is driven by shocks that are orthogonal to private R&D shocks, such as wars, terrorism, geopolitical shocks like the end of the Cold War, and the ideological preferences of the political leaders in power.

It is possible that while the overall level of defense spending in a country is orthogonal to the residual $υikt$⁠, the industry composition of defense spending may still be correlated with $υikt$⁠. This would be the case if, for example, French defense spending declined after the end of the Cold War for exogenous reasons, but the decline was smaller in, say, aerospace, for endogenous reasons. Because we are using a weighted average of U.S. and French industry shares for all countries, this is a problem only to the extent that endogenous adjustments to the industry shares reflect unobserved industry-specific time-varying shocks that are shared by the United States, France and the relevant country. As tests of this we look at models that exclude the United States or France (or both) and find that they all yield similar estimates.

It is possible that increases in government-funded R&D in an industry in a given country affect private R&D investment by firms in the same industry located abroad. For example, an increase in government-funded R&D in the German chemical industry may increase private R&D in the French chemical industry. This would be the case if R&D is a strategic complement between countries, so French chemical firms decide to invest more to keep up in the race; or if there are significant cross-country technological or human capital externalities within the chemical industry. On the one hand, it is possible that the effect is negative. This may happen if the global supply of industry-specific R&D inputs (e.g., chemical engineers) is inelastic, so that their cost increases.

We combine data for OECD countries from the STructural ANalysis (STAN) dataset and the Main Science and Technology Indicators (MSTI) dataset. Our data include 26 countries, 26 industries, and 23 years, from 1987 to 2009. Appendix B describes in detail how we cleaned and merged the data and provides the exact definition of each variable with the corresponding source. Appendix figure A1 shows how employment is distributed across the industries in our sample.

The definitions of R&D are based on the internationally recognized “Frascati Manual” used by the OECD and national statistical agencies. Our main R&D variable measures industry-level R&D conducted by businesses (known as “Business Enterprise R&D” or “BERD”). We will generally refer to BERD as simply “R&D” for brevity. While all BERD is conducted by firms, some of its funding comes from private sector sources while other funding comes from the government. Hence, in the notation of our model, BERD = $R+S$. We refer to the part of BERD that is funded by private sources as “privately-funded R&D,” or “private R&D.” This is the variable $R$⁠, the main dependent variable in equations (1) and (2). We refer to the part of BERD that is funded by the government as “government-funded R&D” or “public R&D.” This is the variable $S$⁠. A subset of public R&D is defense-related, and we refer to it as “defense R&D.” Note that $S$ only includes government-funded R&D conducted by private firms and does not include R&D conducted by universities (and other nonprofits) and by the government itself (e.g., in government R&D labs). Appendix table A1 (panel A) summarizes the variable definition and presents summary statistics.

There is wide variation in private R&D, public R&D, and defense R&D across countries, industries, and years. Consider first aggregate R&D as a percent of GDP by country (appendix table A2). The most R&D-intensive country is South Korea at 2.7%, followed by Sweden at 2%. The United States also has a very high R&D/GDP ratio of 1.9%. At the other end of the spectrum, there are Southern European countries like Greece and Portugal, with ratios of approximately 0.2%.

R&D intensity also varies widely across industries. Appendix figure A2 shows how private R&D is distributed across the industries in our sample; the chemical industry spends the largest share of private R&D in our sample, followed by telecommunications, and automotive.

Public R&D also varies widely across countries and over time. Appendix table A3 shows that the United States and Eastern European nations such as Poland and Slovakia have the highest share of R&D funded by the government (over 15%), whereas the share is under 2% in Switzerland and Japan. In many countries, such as the United States, the UK, France, and Canada, the rate of public funding has decreased over time. Some of this is likely to be due to a shift from direct to indirect support to business R&D, such as tax breaks (see Guellec & van Pottelsberghe de la Potterie, 2001). In some of our models, we also control for tax incentives. Appendix table A4 shows the defense share of government-funded R&D by country. Not surprisingly, the United States has the highest proportion of defense-related R&D (57%), followed by Great Britain (35%), and then France (29%). In the data, we observe the defense-related part of the government's total R&D budget from the OECD MSTI. “Total government funded R&D” is all government budget appropriations or outlays of total R&D, that is, not just the government-funded part of R&D conducted by businesses, but also the part of R&D conducted by government agencies and labs.

Overall, the experiences of these four major economies with highly variable levels of defense R&D illustrate how the timing of changes in defense R&D often reflects factors that are largely exogenous to economic and technological conditions, being driven by geopolitical events that are heterogeneous across countries.³

Our instrumental variable strategy is predicated on the notion that defense R&D is an important driver of overall government-funded R&D. Appendix figure A3 presents the series of defense R&D and public R&D by country (summed across industries). Clearly, in most cases the two series tend to move together: the average correlation is 0.29 (standard error 0.11). The importance of defense R&D varies widely across industries: Aerospace tends to be the single most important beneficiary of defense R&D. In the OECD data the first stage of our IV relies on the relationship between public R&D and predicted defense R&D. The correlation at the industry level is visually strong (see appendix figure A4). In years when defense R&D is high (low), overall government funded R&D tends to be high (low).

We use firm-level data collected by the French Ministry of National Education, Higher Education and Research (“Ministry of Research”)¹ in their annual R&D survey from 1980 through 2015. Appendix B provides details on the survey that seeks to include all large firms that perform R&D and a rotating sample of smaller firms that perform R&D. We refer to all R&D subsidies originating from Ministry of the Armed Forces and its agencies as “defense R&D subsidies.” We refer to the sum of all R&D subsidies (including defense R&D subsidies) originating from any ministry or government agency as “total R&D subsidies” or just “R&D subsidies.” We refer to the firm's R&D budget less total R&D subsidies, other national funds, and international funds, as “privately funded R&D.”

The sample includes 12,539 firms appearing an average of 6.5 years each, 56% of which appear in more than 5 years.⁴ Summary statistics are in panel B of appendix table A1. Of the €833 billion in R&D conducted in our sample, €87 billion was publicly funded, and €57 billion of that was targeted at defense. In industries like aerospace/transport, the dominance of defense subsidies is even clearer, with the industry conducting €119 billion in R&D, of which €38 billion was publicly funded, almost €31 billion specifically for defense. The industries with the largest defense subsidies after aerospace/transport are electronics, technical instruments, machinery, and chemicals.

Table 1 presents estimates of the relationship between privately funded R&D and lagged public R&D in the OECD industry-country panel. The dependent variable is R&D conducted in the private sector (BERD) that is also financed by the private sector (recall that it excludes government financed R&D). As discussed in the Data section, “Public R&D” is government-financed R&D performed by private firms. All columns control for a full set of country by industry fixed effects, a full set of industry by year dummies and a set of country-specific linear trends. Standard errors are two-way clustered at the industry-country and country-year level. All models are weighted by the industry-country pair's initial share of employment in total country employment.

Panel A of table 1 reports OLS estimates. It shows that there is a statistically significant positive correlation between public R&D and private R&D, more consistent with crowding in rather than crowding out. In panel B, we report 2SLS estimates obtained by using predicted defense R&D as an instrument for public R&D. The first stages of our instrumental variable estimates are generally well identified. Weak instrument diagnostics are reported at the bottom and show that the instruments have good power: the F-Test (Kleibergen-Paap) ranges from 10.02 to 14.66 in our main specifications; and Anderson-Rubin Wald test rejects the null hypothesis of weak instruments in all columns.⁵

The entry in column 1 in panel B of table 1 indicates a positive effect of public R&D on private R&D. A 10% increase in public R&D subsidies is associated with a 5.6% increase in the industry's privately funded R&D spending in the following year. A comparison with panel A indicates that the point estimate is larger than the corresponding OLS estimate. This could indicate that subsidies are compensatory—targeted at “losers” and/or the presence of measurement error in public R&D.

One possible concern is that changes in defense R&D might be correlated with changes in other policies that affect firms’ private R&D spending. For example, our estimate would be biased if, say, right-wing governments tend to both increase defense spending for specific sectors and simultaneously adopt pro-business policies for those sectors. In the rest of the table, we probe the robustness of our estimates to additional controls intended to capture variation in public policies. Since our sample size declines from 5,026 to 4,459, in column 2 we replicate the model in column 1 using the smaller sample for comparison.

In column 3, we add controls for industry output and national GDP; the coefficient on public R&D increases slightly to 0.518 (0.204). Recall that our models condition on country-specific linear trends. Adding country-specific quadratic trends to absorb nonlinear drifts in each country results in significantly larger estimates of the effect of Public R&D. For example, the estimated IV coefficient from the model in column 3 is 0.780 (0.244).

In column 4, we add a measure of R&D tax credits based on data from Thomson (2012). R&D tax credits are an alternative form of government support for R&D used by a number of countries. Over the past 20 years, many governments have started to replace direct R&D subsidies with other fiscal policies such as R&D tax credits (Guellec & van Pottelsberghe de la Potterie, 2001; Moretti & Wilson, 2017). From the point of view of governments, publicly funded R&D and R&D tax credits are likely to be substitutes, making it possible that in practice the two types of public support are negatively correlated. In this case, our estimates might understate the true effect of government-funded R&D. In practice, the magnitude of this bias is unlikely to be large, since R&D tax credits are in most countries part of the national tax code, and unlike the direct R&D subsidies, they are not industry specific. Empirically, the coefficient on public R&D in column 4 appears to decrease to 0.476 (0.190).

Besides businesses, other institutions like universities and government-funded research labs receive subsidies for R&D, which might be correlated with business R&D subsidies. In column 5, we also include R&D subsidies to nonbusiness institutions. Empirically, nonbusiness R&D does not appear to affect private R&D undertaken by businesses significantly, and the coefficient on public R&D rises slightly. R&D subsidies might also be correlated with other business favoring policies, for example taxes on businesses, which might also affect private R&D directly (e.g., Akcigit et al., 2022). In column 6, we control for business tax revenues as a proportion of GDP (tax revenue data are from OECD and includes taxes on income, profits and capital gains of corporates). There is a weakly negative effect of taxes, but the point estimate on public R&D subsidies is robust to this addition.

Another concern is that increases in defense R&D spending might be correlated with increases in expected future demand for output, since the military is often the main customer of defense companies. Consider the example of the F-35—one of the largest single defense programs in the United States. It started with DARPA's ASTOVL program, which provided R&D subsidies to Lockheed Martin to do research on short/vertical takeoff and landing of aircraft. Ultimately, Lockheed Martin was the prime contractor for the production of the F-35. If after receiving the ASTOVL subsidy Lockheed Martin increased its private R&D investment not only as a function of the subsidy but also because it anticipated winning the contract for the production of the F-35, then our models would overestimate the effect of public R&D on private R&D. Intuitively, our model would attribute to public R&D an effect that is in part driven by an increase in future demand. Note that in order for this to be a failure of our identification assumption, it is not enough that defense R&D in a given industry and country at time $t$ is correlated with future procurement contracts. It also needs to be the case that firms in that industry and country invest in private R&D at time t not just as a function of the public subsidy but also because they expect to win future production contracts. While in the case of Lockheed Martin this may have been true, it is unclear how much current R&D expenditures firms may find optimal to incur for uncertain future contracts that may or may not materialize.

For our purposes, the question is how common cases like the F-35 are example. More precisely: how much of the changes in defense R&D funding observed in our data across industries-country pairs is correlated with changes in expectations of future procurement spending? Historically, large increases in government defense procurement have been typically targeted toward existing, rather than new technologies, while most R&D is likely to be directed at new technologies—see Milward (1977). This may suggest that the F-35 example is more the exception than the rule, at least historically.

Ultimately, this is an empirical question. To investigate the extent of the problem in our setting, in appendix table A5 we perform placebo tests based on components of defense spending that should be unrelated to R&D subsidies paid to businesses: defense procurement excluding R&D; and military wage bill excluding R&D. We use either using a narrow or a broad definition of R&D, so we end up with four placebo instruments. The idea is that changes in defense procurement excluding R&D in an industry are a direct measure of changes in product demand faced by firms in that industry. If our models are correctly specified, they should not result in changes in R&D. Similarly, changes in military wage bill excluding R&D are probably a good proxy for change in product demand, but should not directly result in changes in R&D. Thus, if our models are properly specified, the four placebo instruments should not be predictive of public or private R&D. Finding a significant correlation between the placebo instruments and public or private R&D would suggest that our IV estimates might be driven by demand effects coming from procurement spending, or by a correlation of defense spending with other policies that encourage economic growth and therefore R&D. The results in appendix table A5 indicate that the effect of non-R&D defense procurement and non-R&D military wage bill on public and private R&D is not statistically different from zero.

We also estimated versions of equation (1) that directly control for (i) current and future non-R&D military spending; or (ii) current and future output. The estimates are similar to the baseline estimates in table 1. (See appendix table A5 in Moretti et al., 2021.) Overall, we conclude that the weight of the evidence appears to be more consistent with the effects of public R&D on private R&D reflecting forces of supply rather than demand.

Table 2 contains the estimates for the French dataset. Compared to the estimates based on the OECD data, the firm-level French data allow for a much finer level of detail, since we observe which firms within an industry actually receive public R&D and which do not. In terms of identification, firm-level data allow us to estimate models that include firm fixed effects, therefore accounting for all time-invariant heterogeneity across firms. Identification comes from comparing the level of private R&D in the same firm observed before it receives a government R&D subsidy and after it receives a government R&D subsidy.

Panel A presents the industry-level results for France and panel B presents the firm-level results. We present industry-level results for comparison to the OECD industry-country data in table 1, although it should be noted that the French data allow for a finer degree of industry disaggregation (169 sectors). Column 1 of panel A shows the OLS estimates. The coefficient suggests a positive correlation between privately funded business R&D and lagged government subsidies but is smaller in magnitude than the OECD results in table 1. Column 2 reports the corresponding IV estimate using defense spending predicted from more aggregate industry trends as an instrument for defense R&D subsidies. The first stage F-statistic is F = 11.56. (First stage coefficients are reported in appendix table A7 in Moretti et al., 2021.) The IV estimate is significant and much larger than the OLS estimate, just like the OECD results. The IV coefficient of 0.346 is not significantly different from the comparable OECD coefficient of 0.511 in column 2 of table 1 panel B (⁠$p$-value of difference = 0.20).

Recall that defense spending at the industry level is not available in OECD industry data for most countries, but we do have it in France. Consequently, we include it directly on the right-hand side of the private R&D equation in columns 3 and 4 of table 2. The coefficient on defense subsidies is positive and significant for the OLS and IV specifications, although again the IV coefficient is larger: 0.150 (0.041). Note that a 10% increase in total subsidies is obviously a larger amount of money than a 10% increase in defense subsidies alone, which explains the smaller elasticity in column 4 compared to 2.

The firm-level analysis in panel B is based on a longitudinal sample of 12,586 firms observed for several years, for a total sample size of 81,201 firm-years. Panel B shows similar patterns to the results in panel A. In column 2, the IV coefficient is 0.119 (0.069), while in column 4, it is 0.374 (0.215). The IV estimates again lead us to reject the null of crowd-out: increases in public R&D result in more investment in private R&D, not less. Based on entries in column 2, a 10% increase in R&D subsidies is associated with a 1.2% increase in the firm's privately funded R&D spending in the following year. This confirms that even after controlling for firm fixed effects, defense R&D subsidies appear to be crowding in private R&D spending.

A comparison with panel A of table 2 indicates that industry-level coefficients are smaller than firm-level coefficients when we use defense R&D subsidies (columns 3 and 4), but the reverse is true for total R&D subsidies (columns 1 and 2). Coefficients from industry-level data do not need to be identical to coefficients from firm-level data in the presence of technology spillovers from R&D within an industry. Industry coefficients should be larger if crowd-in induces rival firms to do more R&D (strategic complementarity). However, it might be that rivals do less R&D if there is strategic substitutability (e.g., free riding), for example, meaning that industry coefficients would be less than their firm-level counterparts (Bloom et al., 2013). We will investigate spillover effects at the international level in more detail below.

Overall, there is little evidence of upward bias in the OLS estimates in tables 1 and 2. In fact, the OLS estimates are consistently below the IV estimates. In the context of our discussion in section II, there are three possible nonmutually exclusive explanations. First, this finding is consistent with compensatory government policies, whereby governments tend to subsidize industries that are underperforming in terms on R&D investment. For example, Criscuolo et al. (2019) find evidence of compensatory policies in the case of UK investment subsidies. In our data, there is some evidence that public R&D policies tend to be compensatory in OECD countries. To see whether public R&D subsidies tend to be directed toward industries that are struggling or thriving, we used our OECD data to estimate simple VAR models that relate changes in public R&D to changes in industry output in a given country and year (controlling for changes in country GDP). Results for models with ten lags are in appendix figure A5. Panel A indicates that public R&D subsidies increase after a negative industry output shock. While this evidence needs to be interpreted merely as suggestive, it appears more consistent with compensatory government policies. By contrast, panel B shows that industry output reacts positively to lagged public R&D subsidies, as we would expect.

Alternatively, the finding of IV estimates being larger than OLS estimates may reflect attenuation bias from measurement error. Or it may reflect local average treatment effects. If the effect of public R&D is heterogeneous and it varies across firms and sectors, our IV estimates identify the effect for compliers. If the effect on private R&D for sectors and firms that experience an increase in government R&D due to an increase in defense R&D subsidies is larger than the effect for sectors and firms that experience an increase in government R&D due to an increase in nondefense R&D subsidies, then our IV estimates may be larger than our OLS estimates even if OLS estimates are unbiased.

Taken together, the estimates in tables 1 and 2 indicate that increases in public R&D translate into increases in private R&D expenditures. This is true both when we focus on industry changes across the whole OECD or within France and when we focus on within-firm changes in France. This crowd-in is consistent with the existence of agglomeration economies—whereby increases in government R&D raise the returns for private companies in the same country and industry—or large fixed costs or credit constraints.

Our preferred elasticity for the OECD dataset is 0.518 (table 1, panel B, column 3), suggesting that a 10% increase in government subsidies in a given year is expected to result in a 5% increase in private sector R&D the following year. Our preferred elasticity at the firm level in the French dataset is 0.119 (table 2, panel B, column 2). At the mean values of public and private R&D in France, this implies that €1 of additional public funds for R&D translates into €0.85 of extra R&D funded by the private sector. As noted above, the smaller firm level effects compared to industry level effects could be due to positive within industry spillovers.

Our findings imply that in some industries, defense-related R&D is responsible for a significant portion of private R&D investment. For example, in the United States “aerospace products and parts” industry, defense-related R&D amounted to $3,027 million in 2002 (nominal). Our estimates suggest that this public investment results in $1,948 million of additional investment in private R&D. If we take the total amount spent by the U.S. government, we estimate that private R&D investment is $85 billion higher than the counterfactual with no government-funded defense R&D.

Interestingly, differences in defense-related R&D can account for some of the differences in private R&D across countries. For example, our estimates indicate that if France increased its defense R&D to the level of the United States as a fraction of GDP (admittedly a very large increase: roughly a factor of 2.2), private R&D investment would increase by 10.3%. Our estimates also indicate that if Germany increased its defense R&D to the level of the United States as a fraction of GDP (an even larger increase), private R&D investment would increase by 72%.

In order to understand how the estimated effect of public R&D subsidies compares to the effect of alternative innovation policies, we compare public R&D subsidies to R&D tax credit policies. We consider the impact on total R&D of abolishing the U.S. tax credit and reallocating the saved public funds to direct government grants.⁶ On the most recent data, the federal tax credit costs $11.3 billion. Using the user-cost elasticity of around unity in table 1, we estimate that the credit raises R&D by $14.2 billion. By comparison, the crowd-in elasticities of table 1 imply that spending the $11.3 billion saved from abolishing tax credits on grants would raise total R&D by $30.7 billion. This is over twice as much as the effect generated by R&D tax credits. Appendix C provides the details of these calculations, considers a range of robustness tests and concludes that direct grants are likely no worse value for money than tax incentives and generally seem to perform better.

We now examine the effect of increases in public R&D investment on employment and wages. This is important because an increase in private R&D expenditures does not necessarily equal an increase in R&D activity. If the supply of R&D workers is completely inelastic in the short run, increased R&D spending could simply result in higher wages, with little or no effect on employment and innovation (Goolsbee, 1998). On the other hand, if R&D workers can move across industries or across countries so that supply to a specific country and industry is fairly elastic, we might find significant increases in R&D personnel and limited increases in their wages. The effects on demand for non-R&D personnel in the industry depend on whether R&D generates technologies that substitute for or complement such labor.

Appendix table A6 reports estimates of models where the dependent variable is employment or wages. Specifically: in column 3, the dependent variable is the number of workers directly engaged in R&D activities; in column 4 it is the number of workers not engaged in R&D activities; and in column 5 it is the average salary of R&D workers—measured as the cost of R&D personnel over divided by R&D personnel. OLS estimates using the OECD data uncover significant elasticities of employment of R&D workers and the average salary of R&D workers and significant positive but much smaller elasticities on the employment of non-R&D workers. The large employment effects and smaller wage effects for R&D workers are consistent with an elastic labor supply, possibly indicating that it might be easy for R&D workers to relocate to the affected industry from other industries or countries.

For France, the estimated elasticities on employment of R&D workers in column 3 are similar to those for R&D expenditures in column 2, indicating that employment of French scientists increases proportionally to increases in R&D expenditures. At the same time, the employment effects are much larger than the wage effects, indicating a more elastic labor supply of researchers from possibly abroad compared to the average OECD country. IV estimates for French three-digit industries have a similar pattern as OLS estimates, but estimates based on OECD data and French firm level data are too imprecise to draw firm conclusions.

So far, we have estimated the direct effect of government-funded R&D in an industry and country on private R&D activity in the same industry and country. We now consider the possibility that government-funded R&D in an industry and country may have an additional, indirect effect on private R&D investment in other countries.

In panel A of appendix table A7, we regress private R&D on lagged domestic public R&D and lagged neighbors’ public R&D, measured as a weighted average of public R&D in other countries in the same industry and year, with weights reflecting various measures of geographic and economic proximity (equation (3)). Column 2 uses the difference in GDP per capita as a distance measure, column 3 the geographic distance in kilometers between the capital cities, column 4 the difference in skill intensity as measured by the share of the population with tertiary education, column 5 the similarity of patent technology classes (out of 15 different technology classes), column 6 the difference in R&D intensity as measured by R&D/GDP. We instrument domestic public R&D but not neighbors’ public R&D, which we assume to be exogenous to domestic firms. (The OLS coefficients are in appendix table A8.)

The coefficient of interest is the one on neighbors’ public R&D. It is positive and statistically significant in all columns but column 4, which uses skill intensity, indicating that if one country increases its public R&D, firms in nearby countries in the same industry increase their investment in private R&D after controlling for public R&D received from their own government. The positive effect is consistent with significant crowd-in between close countries when proximity is defined by income, geography, technology, FDI flows, and R&D intensity.

Panel B uses business R&D (not government-funded R&D) to compute the international spillover pool to test whether private R&D undertaken in a foreign country can also generate spillover effects. Here the coefficients in columns 5 and 6 are negative, providing evidence of international displacement between firms that are technological close or have similar R&D intensity. The coefficients in the other columns are not statistically different from zero. Thus private R&D investment by firms in an industry and country appear to have either no effect, or in some cases to discourage competitors in the same industry in other countries from undertaking their own R&D.

In panel C, we include both international public R&D and international business R&D simultaneously. In all but one specification, elasticities on international public R&D are positive while elasticity on international private R&D are negative and significant. The elasticities on the international public R&D and international private R&D appear of the same order of magnitude in absolute value, indicating that they have a quantitatively similar percentage effect, although of opposite³ sign.

Overall, we conclude that private and public R&D generate rather different spillover effects on R&D behavior. While there are positive spillover effects from public R&D subsidies, private R&D leads to either no spillover effects or crowding out. One possible explanation could be the fact that governmental subsidies may be associated with requirements to make research findings public; or that research supported by the government tends to be more basic research.

We derive equations (4) and (5) in appendix A.

In practice, variation in value added and output per worker reflect both variation in physical productivity as well as variation in the prices of output. This is a common issue in the estimation of production functions. In our context, this problem is likely to be serious because shocks to the demand for defense products (geopolitical shocks, leadership changes, etc.) are likely to results in shocks to the price of defense-related products. The defense industry is highly concentrated and has significant barriers to entry, at least in the short run. This means that the supply curve is almost certainly not infinitely elastic in the short run. An upward sloping supply curve implies that when product demand increases, our measure of TFP increases even if productivity does not change. As standard in this literature, we deal with this problem by using industry-year specific price deflators.

In table 3, we estimate equations (4) and (5) by regressing changes in productivity on lagged total R&D intensity. Total R&D is measured as the sum of private R&D (⁠$R$⁠), public R&D (⁠$S$⁠) and R&D from any other source. The OLS coefficient on R&D of column 1 indicates a positive correlation between lagged R&D intensity and subsequent TFP growth. Column 2 adds country dummies and shows that the coefficient is essentially the same as in column 1. We find a similar coefficient of 0.097 (0.031) for the IV estimate in column 3, which is very similar to the OLS estimate. Column 4 reports the reduced form estimate. In this model the independent variable is defense R&D divided by value added, which has a both positive and statistically significant effect. We conduct a similar exercise for French three-digit industries in column 5. The OLS estimate is positive, just like the one for the OECD industry-country panel, but of smaller magnitude—0.026 (0.004). In column 6, we repeat this exercise on the French firm-level data. We uncover a coefficient of 0.040 (0.004), slightly larger than the corresponding industry-level elasticity. Unfortunately, the IV estimates corresponding to columns 5 and 6 are unidentified as the first stages have insufficient power (the F-statistics at the industry and firm level are 0.96 and 0.10, respectively).

The magnitude of the estimated effects in table 3 is economically significant. Using the estimate for the OECD industry-country panel in column 4, for example, a permanent increase in the predicted defense R&D to value added ratio of one percentage point is associated with an increase in the annual growth rate of TFP of 0.08 percentage points. Since average annual TFP growth in our sample is around 0.98%, this represents an increase from 0.98% to 1.06% a year (i.e., an increase by 8.3%). Using the OLS estimate in column 5, a similar calculation suggests an increase from an average annual labor productivity growth rate of 0.05% to 0.076% a year in France.

To put this in perspective, consider that our estimates indicate that if France and Germany were to raise their defense spending to the level of the United States as a percentage of value added—holding constant everything else and ignoring the additional tax revenues needed—they would experience an increase in the productivity growth rate by 3% and 5%, respectively.

We also note that our estimates quantify the TFP gains occurring within a relatively short horizon. It is likely that the effects are larger when looking at a longer time horizon.

We end with an illustration of the magnitudes of various effects arising from our analysis based on a concrete example: the increase in military R&D that occurred in the United States after the 9/11 attacks. Using all the linkages in the results above, we calculate that the 9/11 shock induced an increase of the TFP growth rate by 0.005 percentage points, holding taxes constant—a 1.5% increase. We view this effect as significant but not exceedingly large. In addition, TFP growth in other OECD countries is estimated to rise by 0.028% on average. We provide a detailed explanation of how we quantified these effects in appendix D.

Our results suggest that government R&D “crowds in” rather than “crowds out” private R&D. In addition, we find evidence that an increase in public R&D in one industry and country raises private R&D in the same industry in other countries through a positive spillover effect. Finally, we uncover significant but not overwhelming effects of private R&D investment on TFP growth and therefore economic growth.

In terms of policy implications, our estimates point to a specific tool that governments can use to raise private R&D investment in their jurisdiction. Our estimates indicate that government-funded R&D in general—and defense R&D in particular—are effective at raising a country's total expenditures on innovation in a given industry. The ultimate effect of government-funded R&D on overall R&D significantly exceeds its dollar value because government-funded R&D stimulates additional R&D investment on the part of the private sector. This positive effect of government-funded R&D on private R&D is important not just in itself, but because it generates higher productivity.

This of course does not imply that it is efficient to raise defense R&D or government-funded R&D across the board, since government-funded R&D clearly has an opportunity cost in the form of taxpayer money used plus any welfare loss that inevitably comes from taxation. Our paper does not compare the benefits of government-funded R&D to its costs.⁷

Our findings also indicate that the benefits of public R&D investment do not stop at a country's borders but spill over to other countries. This implies that countries that spend aggressively on government funded R&D—like the United States—indirectly support the productivity of countries with less government-funded R&D. This externality indicates the desirability of more international cooperation in government-funded R&D.