Statistical capacity and corrupt bureaucracies

We start by presenting motivating evidence on the relationship between the quality of economic statistics and economic performance. We also consider the moderating role of corruption. To capture the quality of economic statistics, we use the World Bank’s Statistical Capacity Index (SCI). The SCI is available for 153 developing and emerging economies at yearly frequency. We have recoded the index so that it ranges from 0 to 1, where 1 indicates maximum statistical capacity (the original range is 0 to 100). The index measures the extent to which a country’s statistical system adheres to international technical standards deemed essential for the quality of economic data. We use the growth rate of real GDP p.c. (PPP, constant 2011 I$) to capture economic performance and the World Bank’s Control of Corruption Index (CCI) as a measure for (the absence of) corruption. The CCI is a corruption perception index that is concerned with the exercise of public power for private gain and is constructed from a broad range of sources.⁴ Our dataset includes 146 countries and covers the period from 2005 to 2016. The figures in this section rely on observations averaged over periods of three years (2005-07, 2008-10, 2011-2013, 2014-16). The full sample includes 556 observations.

Figure 1 shows a partial residual plot that illustrates the correlation between the residual growth rate of real GDP p.c. and statistical capacity.⁵ We see a significant positive relationship: an increase in the SCI of one standard deviation (0.16) is associated with a rise in real GDP p.c. growth of 0.6 percentage points. Figure 1 is based on the full sample and does not account for cross-country differences in corruption. The role of corruption is highlighted in Fig. 2, which again shows partial residual plots. Each subfigure considers two disjunct subsamples of the full sample. One of the subsamples contains all countries with an average CCI score belonging to the top 25% of the distribution (“low corruption”) and the other one all countries with an average CCI score belonging to the bottom quartile (“high corruption”). Examples of low-corruption countries are Uruguay and Chile (both high SCI), but also Botswana and Namibia (both low SCI). High-corruption countries are, among others, Libya and Equatorial Guniea (both low SCI), but also Russia and Ukraine (both high SCI). Subfigure (a) of Fig. 2 replicates the regression from Fig. 1 for the two subsamples. The plot suggests that the positive correlation found in Fig. 1 is driven by observations from low-corruption countries. While there is a positive relationship between the growth rate of real GDP p.c. and statistical capacity in the low-corruption subsample, no such relationship emerges among high-corruption countries.⁶ In Subfigure (b), the underlying regression additionally includes country fixed effects. The moderating role of corruption seems to be even stronger. However, in statistical terms, the difference becomes less significant.

The basic pattern shown in Fig. 2 is fairly robust to a number of modifications. It remains mostly unaffected when we use larger subsamples of low- and high-corruption countries,⁷ or when we split the full sample into disjunct subsamples according to the World Bank’s Rule of Law Index (instead of the CCI). Moreover, given the concerns regarding GDP data quality, we were also using the (log) change in nighttime light intensity as a proxy for economic performance (Henderson et al. 2012). The source of the light data is Hodler and Raschky (2014), who aggregated the georeferenced raw data to ADM2 administrative levels (from where we aggregated it to the country level).⁸ The data are scaled from 0 to 63, with a larger number reflecting more intense nighttime lights. The data are available up to 2013, which leaves us with 399 observations from 134 countries. While the differences between low- and high-corruption countries are smaller and more sensitive to the threshold applied, Fig. 3 shows that the swap of GDP for light data does not change the basic pattern documented in Fig. 2.

Overall, we find a positive relationship between economic performance and statistical capacity among low-corruption countries, while no such relationship appears among high-corruption countries. This pattern is consistent with our model, which predicts improvements in technical statistical capacity to lift economic growth in low-corruption places but warns that such a positive relationship should not be expected in places where corruption is higher.

At a more general level, the mechanism we explore emphasizes that increased data gathering by the government makes people adjust their behavior in anticipation of the possibility that the data, when leaked, is used to their disadvantage. In turn, these adjustments in behavior may well undermine the very purpose of data gathering. There is anecdotal evidence that broadly supports the relevance of this mechanism in developing countries. First of all, fear of data leaks is clearly well-founded. One reason is the prevalence of IT security holes. In a recent focus on Africa, the Brookings Institution (2018) warns that throughout the continent and across sectors, including government, the commitment to cybersecurity is weak. Again relating to Africa, Serianu (2017) reports that the government sector is among the most frequent victims of cybercriminal activity. This aggregate perspective meshes well with country-level accounts. As an example, consider Kenya, a country where reports about data leaks abound. For instance, in April 2016 servers of the Kenyan Ministry of Foreign Affairs were breached and one terabyte of (partly confidential) information stolen (Privacy International 2019b). This should not come as a surprise, considering that according to an estimate from 2017 more than 80% of public sector institutions in Kenya do not even have the means to detect network intruders. The frequent leaking of data held by public institutions does not go unnoticed and leads to reactions in the business community: in 2016, a newspaper headline ran “Hoteliers withhold data from KNBS [Kenya National Bureau of Statistics] citing fears of leaked business secrets”.⁹

Besides IT security holes, the expansive use of data gathered by the government is another reason for why fear of leaks is often warranted. A particular ostensive illustration of this problem is India’s Aadhaar biometric database. According to Privacy International (2019a) the breaches and leaks of personal data have been enormous. At some point in 2018, personal details of hundreds of millions of Indians apparently could be purchased online for as little as 500 (see Fig. 4). The leaks did not seem to be driven by weak IT security (Privacy International 2019a); they rather appeared to be a result of the fact that the data are shared across the public sector to an extent way beyond what was originally imagined. In this context, an article in the https://​www.​economist.​com/​christmas-specials/​2018/​12/​18/​establishing-identity-is-a-vital-risky-and-changing-business (Dec 18, 2018) noted that “No one knows for certain how much Aadhaar-associated data have been shared with whom, (...).” It is obvious that the wide sharing of data, in combination with weak governance, increases the risk of someone making illicit use of them. The consequences for Aadhaar are severe: “A system designed to prevent fraud has given rise to a whole new economy of fraudulent activity (...).” As in Kenya, there is evidence that people respond to the danger of data breaches. For instance, reports suggest that HIV patients preferred to abandon essential treatment programs when they had their Aadhaar numbers linked to their patient identity cards (Privacy International 2019a).

The general pattern of anticipation and response that arises in the examples from Kenya and India can be found in many places. In the model below, it emerges in a generic setting that considers data gathering for the purpose of evaluating uncertain policies.

We consider a two-period economy with N > 0 firms. Each firm i ∈{1,⋅⋅⋅,N} is equipped with a technology to produce a homogeneous good whose price is normalized to 1. The technology is uniform across firms and represented by the production function where t ∈{1,2} denotes time and 0 < α < 1. A_t is a productivity parameter and x_it refers to a firm-specific investment. For simplicity, the per-unit cost of investment is normalized to 1, too. Following Barro (1990) and the subsequent literature, we assume that economic policy plays a productive role in output generation; it offers complementary inputs to private production (such as reliable power supply) and so potentially creates a positive link between government, investment, and economic performance. However, unlike much of the literature, our setup includes a status-quo policy and assumes that any deviation from the status quo has an uncertain effect on production. For concreteness, suppose that economic policy, P_t, enters production function (1) via the productivity parameter. Following Binswanger and Oechslin (2020), we assume P_t ∈{− 1,0,1}, where 0 is the status-quo policy and − 1 and 1 refer to two alternative reform policies. Policy affects productivity according to where 0 < γ < 1 reflects the economic significance of the reform and S ∈{− 1,1} captures the unobserved and invariable “state of the world” that materializes prior to the start of the economy.¹⁰ In Eq. (2), we use the square root of γ to simplify the formal presentation of the main results below. Together, Eqs. (1) and (2) imply that a reform policy is beneficial (harmful) if its sign is the same as (is different from) the sign of the state. S takes each of its two possible values with probability 1/2. This specific value is chosen for analytical convenience and not important for our argument. What matters is that there is some uncertainty as to whether a particular reform alternative has a positive or a negative effect on productivity. For the policy maker, the only way to gain information is “policy experimentation”: implement one of the alternatives, monitor the result—and then adjust if necessary. We note that in terms of key results our analysis would be unchanged if there were no status-quo policy. The difference would be that in such a simplified setup the government would be forced to try an uncertain policy while in the present framework this will be an endogenous decision.

While producing the homogeneous good is the core activity, each firm additionally runs its individual side business. There are many possibilities: wholesale trade in a different good, property dealing, services such as repairs, etc. The side business is volatile and enters the analysis as an exogenous net contribution ζ_it to the total firm revenue z_it: To capture the volatile nature of individual side businesses, we assume that ζ_it is a continuous i.i.d. random variable with support on \([0,\infty )\), mean χ > 0, and variance σ. In combination with the informational frictions introduced in Section 3.2 below, the plausible consequence of firms running side businesses will be that the impact of any reform cannot be immediately inferred from the data of a single or a handful of firms. Hence the case for systematic data gathering. To keep the analysis tractable, the modeling of side businesses is parsimonious. Among other things, a side business is unaffected by policy and its contribution to total firm revenue is independent of the scale of the firm’s core activity. The latter assumption, a measure of independence from core activities, is important for some of our findings.¹¹

It is worthwhile to note that there is no need to impose a specific distribution function for the ζ_its. But it is helpful to make two “technical” assumptions in this regard. First, to secure that the model is scale invariant regarding the number of firms, we assume where 𝜃 > 0. The parameter 𝜃 will govern the volatility of the average side business contribution. Second, for a reason that will become clear below, we assume that the distribution of the ζ_its has a light left tail. Finally, we will use an asterisk (^∗) to mark values reflecting optimal firm choices: \(x_{it}^{\ast }\) denotes firm i’s optimal investment level, while \(y_{it}^{\ast }\) and \(z_{it}^{\ast }\) refer to, respectively, the resulting output of the homogeneous good and the resulting total firm revenue.

The government runs a statistical office that is tasked with the timely collection of firm-level data with the sole purpose of producing economic statistics at the end of each period.¹² Yet there are practical problems placing constraints on the level of detail with which firm-level data can be collected: within the limited time frame for completing statistical questionnaires, firms can only just identify total firm revenue; they do not have more detailed information on individual components yet. In brief, firm i observes \(z_{it}^{\ast }\) but does not individually observe \(y_{it}^{\ast }\) or ζ_it before period t ends. So firms can only report data on total firm revenue. Naturally, with time, the informational constraints ease and firms become able to separately identify the components of \(z_{it}^{\ast }\). Specifically, firm i learns \((y_{i1}^{\ast },\zeta _{i1})\) in period 2 just before it is set to choose its level of investment. Provided that P₁≠ 0, learning \((y_{i1}^{\ast },\zeta _{i1})\) permits the identification of A₁ and hence state S. Assuming that firms (possibly) identify S before they decide on their second-period investment simplifies the analysis without changing its substance.

Firms provide the statistical office with accurate revenue data (e.g., because misreporting, if detected, carries a prohibitive fine). The office uses the data to compute estimates of average total firm revenue, which are then published at the end of each period and become valuable in the case of reforms. All activities of the statistical office are costless. The office’s estimates are based on a random sample of n ≤ N firms, where n is determined before the start of the economy. The ratio p ≡ n/N is an obvious measure of technical statistical capacity. With this, the office’s estimate of average total firm revenue in period t can be written as where Assuming that pN is sufficiently large, the Lindeberg-Lévy CLT implies that the distribution of \(\sqrt {pN}\left ({\zeta _{t}^{p}}-\chi \right )\) is closely approximated by N(0,𝜃N). We therefore work with

If the government has implemented a reform policy in period 1 (P₁≠ 0), it has to rely on \({Z_{1}^{p}}\) as the only available source of information when it determines its second-period policy at the very beginning of that period.¹³ The government understands the firms’ decision problem (and hence can infer their first-period investments, \(x_{i1}^{\ast }\)) as well as the parameters of the side businesses. Based on this, and with the help of \({Z_{1}^{p}}\), it uses Bayes’ rule to compute the ex-post probability that the implemented first-period reform policy is the beneficial one:

In Section 6, we sketch a modified version of the model in which the data firms report to the statistical office is not necessarily fully accurate. Misreporting becomes an option as firms can shift parts of their core business into informal operations whose output cannot be detected.

While officially firm-level data collected by the statistical office may not be used for any purpose other than output estimation, there is a potential for data misuse: in both periods, there is a probability π > 0 of a confidentiality breach that puts the data into the hands of a “corrupt” government official. Following Svensson (2003) and Fisman and Svensson (2007), we may think of an official outside the statistical office whose power to collect bribes derives from his discretion in the application and enforcement of complex regulations. In practice, there is more than one way by which the official can get hold of confidential firm data (Section 2.2). Just like any hacker from outside the government bureaucracy, the official may take advantage of insufficient cyber defenses. Alternatively, the official may obtain access to the firm data due to an illicit practice of expansive data sharing within the government bureaucracy.

In many instances, corruption is governed by norms (see, e.g., Malesky and Samphantharak 2008, della Porta and Vannucci 2012, World Bank 2015). While authorizing corruption, these norms sometimes include restrictions, a sense of what would be an official’s customary share and what would amount to excessive, “intolerable” extortion. For the model, assume a norm that tolerates bribe collection as long as it is not out of proportion with a target’s economic capacity. Such a norm may be rooted in the experience that the economic damage associated with bribe collection beyond a certain relative limit causes civil unrest, putting in danger the government bureaucracy as a whole. For concreteness, assume that the corrupt official is protected by the responsible superior (e.g., a high-ranking bureaucrat) as long as a collected bribe does not exceed a share \(0<\hat {\beta }<1\) of the target firm’s total revenue; for bribes in excess of this limit, if credibly reported to the superior, the norm demands that the corrupt official face a severe penalty (i.e., one that is large relative to the bribe collected). Further assume that firms can, and also do, credibly report excessive bribe collection.

In the model, \(\hat {\beta }\) is one of two parameters that determine the scope for corruption. The second parameter is the probability of a confidentiality breach, π. In what follows, we use \(\beta \equiv \pi \hat {\beta }\in (0,1)\) as an overall measure of corruption and refer to it as the bureaucracy’s vulnerability to corruption. With the help of β, the model is able to capture a broad spectrum of institutional realities. If β takes a relatively low value, we have a bureaucracy whose integrity is merely compromised. By contrast, a value close to 1 may capture a setting in which an illicit practice of data sharing, combined with a norm authorizing vast bribe collection, enables an extractive bureaucracy that is hardly bound to the rule of law at all.

Regardless of the concrete level of β, leaked firm data offer valuable information to the corrupt official. Eliminating the informational asymmetry between the official and the firms in the sample, the data permit bribe discrimination—i.e., tailored bribes that extract the maximum possible without any risk of sanctions. By contrast, collecting bribes from firms that are not part of the sample is risky. Without information on firm revenue, collecting a bribe entails the possibility of a penalty. The official considers collecting a uniform bribe from those firms, weighing the penalty to be expected as a function of the bribe level. Since a uniform (“lump-sum”) bribe does not affect firms’ incentives, we assume without loss of generality that the outcome of this optimization process is a bribe of zero. In summary, in the case of a confidentiality breach in period t, the official collects \(\hat {\beta }z_{kt}\) from all firms k that are part of that period’s sample and leaves the remaining firms alone.¹⁴ Without a confidentiality breach in t, the official abstains from collecting bribes in that period.

The government determines statistical capacity, p, and is in charge of economic policy, P_t, t ∈{1,2} (mind the difference between lower- and upper-case letters). We consider a benevolent government that, however, has inherited a bureaucracy whose vulnerability to corruption is deep-rooted and thus cannot be reduced within the time horizon of the model (i.e., must be taken as exogenous). Naturally, this assumption entails that β is unaffected by both p and P_t. Put differently, a possible improvement in statistical capacity, or a deviation from the status-quo economic policy, would not help in addressing problems with data confidentiality or corruption.¹⁵ The government’s objective is to maximize the expected lifetime total revenue of the representative firm i and its objective function reads where the expectation in Eq. (9) is formed at the beginning of period 1. So our analysis of optimal technical statistical capacity assumes a relatively “favorable” environment in which the government does not pursue special interests but aims at maximizing economic performance and in which running the statistical office is free of charge.

The timing of actions is as follows. Prior to the start of the economy, Nature determines the unobserved state of the world S and the government chooses statistical capacity p.

In the first period, the government sets P₁; observing the government’s decision, all firms i choose x_i1; the statistical office draws the random firm sample, thereby complying with the government’s choice of p; Nature determines \(\{\zeta _{i1}\}_{i=1}^{N}\); the statistical office collects the data and—if there is a confidentiality breach—the official collects bribes from the sampled firms; the statistical office publishes \({Z_{1}^{p}}\) and—if P₁≠ 0—the government computes \(r({Z_{1}^{p}})\).

In the second period, the government sets P₂; all firms learn \( (y_{i1}^{\ast },\zeta _{i1})\) and—if P₁≠ 0—infer state S; taking P₂ and the available information on S into account, all firms i choose x_i2. From this point onwards, the sequence of actions is identical to that in the first period.

Before going backwards through the sequence of policy choices, we consider the firms’ investment decisions. In period t ∈{1,2}, firm i solves the maximization problem where \({E_{t}^{i}}\{\cdot \}\) refers to the expectation formed by the firm just before it chooses x_it. The objective function in problem (10) reflects that, with probability p, firm i is sampled by the statistical office, in which case there is a chance π that it will be approached by a bribe-collecting official who would take a share \(\hat {\beta } \) of total revenue. Problem (10) can be simplified to Since 0 < α < 1, the objective function in maximization problem (11) is a strictly concave function of \( x_{it}\in [0,\infty )\). The function’s maximizer is given by Using production function (1), one can calculate firm i’s output of the homogeneous good as

The final decisions of interest to be taken in period 2 are those by the firms on second-period investment. Those decisions are mostly analyzed in Section 4.1. What remains to be done here is to determine \({E_{2}^{i}}\left \{ A_{2}\right \}\). When deciding on x_i2, firm i has just learned about \((y_{i1}^{\ast },\zeta _{i1})\). As a result, if P₁≠ 0, the firm can infer S ∈{− 1,1} from \((y_{i1}^{\ast },\zeta _{i1})\); moreover, having observed P₂, it can identify A₂ with certainty (Eq. 2). Otherwise, if P₁ = 0, firms still reckon that S has taken the value − 1 with probability 1/2 and the value 1 with the same probability; thus, \({E_{2}^{i}}\left \{ A_{2}\right \} =1\) irrespective of the choice of P₂. To summarize:

The first decision to be taken in period 2 is that by the government on second-period policy, P₂ ∈{− 1,0,1}. Objective function (9) implies that, at this point in time, the government wants to maximize \(E_{2}\left \{ z_{i2}^{\ast }\right \}\), where the expectation is formed at the beginning of period 2. First assume that the status-quo policy has been implemented in period 1 (P₁ = 0). For this case, Eq. (14) implies \({E_{2}^{i}}\left \{ A_{2}\right \} =1\). We therefore obtain Again, since there is no information on the realization of S in this case, we have \(E_{2}\left \{ A_{2}(P_{2})\right \} =1\) for all P₂ ∈{− 1,0,1}. So the government is indifferent between the three options. Without loss of generality, we henceforth assume that it decides to keep the status-quo policy in place:

Now suppose that a reform policy has been implemented in period 1 (P₁≠ 0). In this case, taking into account Eq. (13) and Eq. (14), we obtain The expectation in Eq. (17) is now based on \(r({Z_{1}^{p}})\), the ex-post probability that the first-period reform alternative is the beneficial one. Therefore:

If a reform policy has been implemented, the final activity in period 1 is the computation of the ex-post probability \(r({Z_{1}^{p}})\equiv \Pr \left [ \left .P_{1}=S\right \vert {Z_{1}^{p}}\right ]\). When doing this computation, the government considers the firms’ investments earlier in the period and the resulting implications for the output of the homogeneous good. The government knows that the firms have solved the maximization problem stated in Section 4.1 and accordingly that the level of output is as specified in Eq. (13). Moreover, it follows that \({E_{1}^{i}}\left \{ A_{1}\right \} =1\) since state S takes each of its two possible values with probability 1/2. So it is clear that Given this, and considering Eq. (5) and Eq. (7), the government understands that \({Z_{1}^{p}}\) follows a normal distribution with a mean that depends on S and P₁: where \(A_{1}=1+\sqrt {\gamma } \) if P₁ = S and \(A_{1}=1-\sqrt {\gamma } \) if P₁ = −S. Since each of these two possibilities materializes with probability 1/2, Bayes’ rule implies where \(f \left (\left . {Z_{1}^{p}}\right \vert \cdot \right ) \) denotes the corresponding normal density. Using functional forms, we obtain where According to Eq. (22), \(r({Z_{1}^{p}})\) is a strictly increasing function of \({Z_{1}^{p}}\), rising from 0 (if \( {Z_{1}^{p}}\longrightarrow -\infty \)) to 1/2 (if \({Z_{1}^{p}}=\hat {Z}_{1}^{p}\)) to 1 (if \({Z_{1}^{p}}\longrightarrow \infty \)). In combination with Proposition 1, this implies that P₂ = P₁ if \({Z_{1}^{p}}\geq \hat {Z}_{1}^{p}\) and P₂ = −P₁ otherwise.

Moving backwards to the firms’ actual investment decisions, it is sufficient to refer to the above discussion and repeat that \(x_{i1}^{\ast }\) and \(y_{i1}^{\ast }\) are given by Eqs. (12) and (13), respectively, with \({E_{1}^{i}}\left \{ A_{1}\right \} =1\) irrespective of the actual policy decision.

The first decision to be taken in period 1 is that by the government on first-period policy. To inform this decision, the government compares the value of its objective function, \(V=E_{1}\left \{ z_{i1}^{\ast }+z_{i2}^{\ast }\right \}\), under the status quo to the value under any of the two reform alternatives. According to Eq. (16), P₁ = 0 implies P₂ = 0. So, if the government opts for the status quo in period 1 (P₁ = 0), we obtain A₁ = A₂ = 1. From this, it follows that the expected lifetime total revenue by the representative firm i is given by

Due to the symmetric setup, the government is indifferent between the two reform alternatives. Without loss of generality, we henceforth assume that P₁ = 1 if the government decides to abandon the status quo. In this case, P₂ is specified by Eq. (18) and the expected lifetime total revenue by the representative firm i is given by Moreover:

The results derived so far lead to the following conclusion:

In period 1, there are two factors that make the government prefer a reform policy to the status quo. First, if a reform policy is implemented, the government gains information about “what works”; this, in turn, allows for a better informed policy decision in period 2. Second, \(y_{i2}^{\ast }\) is convex in A₂ (see Eqs. 13 and 14). For this reason, the government prefers taking a “symmetric risk” to obtaining the expected value with certainty.

Besides economic policy, the government determines technical statistical capacity, p, with a view to maximizing V. The key magnitude in its decision problem is the probability with which the beneficial reform will be implemented eventually (Eqs. 25) and (26).

In what follows, we will call I the “informativeness of policy experimentation”.¹⁶ As can be seen from Eq. (28), informativeness depends on five parameters, some of them unrelated to the statistical office: other things equal, if a reform is more significant (higher γ), or if the side businesses are less volatile (lower 𝜃), informativeness is higher. On the other hand, informativeness is influenced by the statistical office. In Eq. (28), C(p;α,β) captures the entirety of channels by which the statistical office affects informativeness. For this reason, we will call C(p;α,β) a measure of “comprehensive statistical capacity”. It is immediately apparent that the effect of technical statistical capacity on comprehensive statistical capacity is ambiguous if the bureaucracy’s vulnerability to corruption is not equal to zero (β > 0). This reflects that firms—observing a positive relationship between p and expected bribe demands—reduce investment in response to a rise in p (Eq. 12). Note that α affects C(p;α,β) because this parameter governs the elasticity of investment with respect to expected bribe demands. C(p;α,β) has the following important properties:

What level of technical statistical capacity maximizes comprehensive capacity? The answer depends on the bureaucracy’s vulnerability to corruption:

A rise in technical statistical capacity has two opposing effects on comprehensive statistical capacity and hence on the extent to which the estimate of average total firm revenue, \({Z_{1}^{p}}\), is informative for the policy decision in period 2. On the positive side, a rise in technical statistical capacity reduces the variance of the exogenous component of \( {Z_{1}^{p}}\) (Eq. 7); all else equal, this helps informativeness. On the negative side, for any individual firm, a rise in technical statistical capacity implies a higher chance of being subjected to bribe collection. As a result, firms respond by reducing investment (Eq. 12)—which dampens the impact of reforms on production; all else equal, this harms informativeness. The strength of the negative effect rises in the bureaucracy’s vulnerability to corruption. If β is sufficiently large, the negative effect starts to dominate at a strictly interior level of technical statistical capacity.

Figure 5 illustrates the ambiguous role of technical statistical capacity. In both subfigures, the underlying assumption is that the implemented first-period reform is the beneficial one (P₁ = S); moreover, in both subfigures, the shaded areas correspond to the probabilities of committing a type-I error (P₁ = S rejected although true) under low (blue) and high (red) technical statistical capacity, respectively. Subfigure (a) shows a case in which higher technical statistical capacity (red line) improves informativeness: an increase in p from p_l to p_h reduces the probability of a type-I error. In other words, the reduction in the variance of the exogenous component of \({Z_{1}^{p}}\) outweighs the reduction in the beneficial effect of the reform (leftward shift of the entire distribution). By contrast, Subfigure (b) shows a situation in which an increase in technical statistical capacity leads to a higher probability of a type-I error: the reduction in the variance of the distribution is dominated by its shift to the left.

However, informativeness—and the associated probability of choosing the beneficial reform alternative in period 2—is not the only variable the government has to consider when determining the level of p that maximizes V, the expected lifetime total firm revenue. The negative static effect of technical statistical capacity on firm investment (and hence production) must be taken into account, too. We therefore obtain the following result:

Figure 6 illustrates how I(C;γ,𝜃) and \( V=E_{1}\left \{ z_{i1}^{\ast }+z_{i2}^{\ast }\right \}\) depend on technical statistical capacity, assuming that condition (R1) holds. Both curves are hump-shaped. Proposition 5 predicts that V peaks at a strictly lower level of technical statistical capacity than C does. As a result, the peak of I must lie to the right of the peak of V.

In Fig. 6, p^∗∗ takes a particularly low value. So technical statistical capacity is weak, as is the case in many developing countries. The figure thus conveys the message that real-world instances of low technical statistical capacity should be interpreted with care. They are compatible with completely different versions of reality. Clearly, “poor numbers” may be an expression of neglect and/or a lack of resources and expertise. However, keeping technical statistical capacity weak may also be the best response by a capable government that is mindful of facing a corrupt bureaucracy and problems with data confidentiality like those illustrated in Section 2.2. “Flying blind” may be a well-considered choice.

An increase in the bureaucracy’s vulnerability to corruption amplifies the negative effect of statistical capacity on firm investment. As a result, the level of technical statistical capacity that maximizes comprehensive statistical capacity and informativeness, p^∗, is a decreasing function of β (Eq. 30). Simulations suggest that a similar result holds for the level of statistical capacity that maximizes the expected lifetime total firm revenue, p^∗∗. Figure 7 illustrates that p^∗∗ shifts to the left as β increases. Consistent with this, we find that a rise in β has negative consequences for the two outcomes of interest:

There is a large literature on the channels by which corruption affects economic performance. Proposition 6 puts the spotlight on a novel one. An increase in the bureaucracy’s vulnerability to corruption reduces the informativeness of policy experiments (a process that is understood to involve the implementation, evaluation, and adjustment of reform policies). Two mechanisms are simultaneously at work. On the one hand, an increase in corruption dampens the economy’s response to policy changes (Eq. 13). On the other hand, as can be inferred from Fig. 7, higher corruption induces the government to lower the level of technical statistical capacity—which makes navigating among the different reform alternatives even more challenging. This is also reflected in the economy’s growth rate:

So the consequences of an increase in corruption are not limited to a mere level effect; higher corruption also flattens the path of production over time.