Informational frictions and misallocation

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Informational Frictions and

Misallocation

The Italian Case

Luca Gius

Ch.mo Prof. Davide Fiaschi

Master of Science in Economics,

University of Pisa

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Abstract

This thesis builds on the seminal contribution by David et al. [2016] to analyze the impact of uncertainty and misinvestment on resource misallocation. To begin with, we augment the original model by adding aggregate shocks and investigating the feasibility of firm–specific reactions. Moreover, we take advantage of the clever empirical strategy developed in the original paper to unveil the information structure in the Italian economy: using data on Italian listed firms, we estimate that a 7% aggregate output loss among big firms may be traced back to informational misallocation. Moreover, we highlight the limited contribution of financial markets to informational efficiency.

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1 Introduction

The central theme of this thesis is uncertainty and learning. The world we live in, in which companies are born, operate and struggle to survive, is incredibly complex. The decision to invest in a new project, to hire new personnel, to open a new branch tremendously depend on a set of future conditions extremely difficult to predict. Do firm–level forecast errors accumulate and impact on aggregate outcomes? Or do they cancel each other out?

David et al.[2016] offer a clever structural model to measure uncertainty at firm level and summarize its impact on aggregate output and TFP. In this work, we augment the model with aggregate shocks and then estimate it using Italian data.

In section 2, we provide a brief literature review on misallocation studies, ranging from the earliest structured works to the more recent “wedge” approach. In section3, we analyze the literature on Italy’s productivity conundrum. A rich set of economic and institutional factors have been from time to time pointed out as the culprits: a common theme is the “curse of smallness”, and big firms typically play the convenient role of a godly panacea. Nonetheless, as we will see, misallocation and uncertainty among bigger firms is substantial and should not be overlooked.

In section4, we present the original model: it is a standard general equilibrium model of firm dynamics with uncertainty. The stock market part provides an elegant representation of the stock market price as an aggregated signal, which will come in handy in the identification part. In the following section 5, we augment the model with aggregate shocks, underlining the substantial complications suffered by the original model if we add firm–specific shock reactions.

Section6describes the quantitative analysis: we estimate by means of a simulated method of moments methodology the impact of informational frictions on Italian listed companies. Data and results are described in section 7. The conclusions follow in the last section8.

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2 A brief history of misallocation studies

Cross–country differences in output per worker and TFP are ubiquitous and surprisingly resilient (Caselli [2005]). The literature on the so-called “development gap” has offered a vast and diverse array of factors explaining such differences, ranging from slow technology diffusion to structural differences in unit labor costs (seeHowitt[2000] andManasse [2013] on the Italian case).

A growingly important strand of literature has concentrated, rather than on quality or quantity differences in production inputs, on the countries’ effectiveness in allocating inputs across heterogeneous firms1. The results, as will be highlighted in the forthcoming sections, suggest that higher inefficiency translates into lower levels of development: bad institutions, uncertainty and corruption seem to be the worst enemies of laggard countries.

The present work concentrates on (mis)allocation of resources across Italian public companies – in particular, on how aggregate uncertainty may lead to an inefficient cross–sectional distribution of capital and labor. The following sections will provide a tentative introduction to the diverse literature on misallocation.

2.1 The “structured” approach

As highlighted byRestuccia and Rogerson[2013] and as epitomized in the seminal paper byHopenhayn and Rogerson[1993], the earliest approach to study misallocation involved choosing a specific factor (e.g.: firing taxes or size-dependent policies), empirically measuring such factor and then calibrating a model of heterogeneous firms to quantitatively assess its distortive impact on aggregate Total Factor Productivity. Most works in this area typically modelize J firms with a common production function and firm–specific TFP or demand conditions:

yj = Ajf (lj, kj)

Given a fixed aggregate amount of labor L and capital K, maximization of aggregate output typically allows for an “optimal” cross–sectional distribution of capital and labor across the J firms. Various factors may distort the distribution of inputs thus lowering aggregate output: Restuccia and Rogerson [2013] distinguish between statutory provisions (e.g: size–specific taxes or labor market regulations), subsidies, “crony” capitalism (seePellegrino and Zingales[2017] on the italian case) and market imperfections. Whatever the specific cause, the structural approach allows to measure the distortion and elaborate on counterfactuals, though the analysis may be severely influenced by the choice of deep parameters (e.g: Cobb–Douglas coefficients in the production function). Once again,Restuccia and Rogerson[2013] recall

1_{To avoid any confusion: in this framework, misallocation does not refer to those factors (e.g: search costs) affecting the}

quantity of labor and capital in equilibrium, rather to those elements affecting the distribution of labor and capital across firms.

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that such an approach may be more feasible in some contexts than in others.2

As an example, credit market imperfections have been quite a beaten path and authors have concentrated on the deleterious effects of both selection and misallocation: credit–constraints either prevent entry of productive businesses, thus lowering the overall quality of the entrepreneurial pool, or limit access to capital to existing firms, thus impeding the flow of resources towards the most productive establishments. For example, Banerjee et al.[2003] analyzed the relationship between marginal productivity of capital and market interest rate in India, concluding that the neoclassical prediction of equality failed by a wide margin. These models necessarily rely on a “naive” measure of credit constraintness (e.g: size) which provides a mere first order approximation to the difficulties faced by, e.g., innovative firms.

A further example, this time on the labor side, is provided byCaggese and Cu˜nat[2013]: the authors elaborate on a standard firing model. Other that firing and hiring costs, a firm’s decision to disimiss a worker depends on wages and expected productivity – financing constraints may interfere with the intertemporal decision and induce entrepreneurs to fire the “wrong” workers3_{so as to maximize available}

cashflow. AlsoGuiso et al.[2013] depict the employee–employer bargaining process in an internal credit market framework, whereby credit–constraint firms implicitly borrow from their workers by offering lower entry wages and a steeper wage growth than their competitors.

2.2 The “wedge” approach

A second, more ecumenical approach emerged from the seminal contributions of Restuccia and Rogerson [2008] and Hsieh and Klenow[2009]: these authors started to shift focus from a specific list of potential sources of misallocation to the wedges themselves. As already highlighted, many underlying factors are difficult to measure (corruption, tax-avoidance, crony capitalism). It is easier to gauge the macroeconomic effect of the phenomenon by analyzing the ex post effect of all these factors on the static FOCs of firms’ optimization problems. In other words, the latter strand has especially concentrated on the cross–sectional dispersion of marginal productivity of factors across firms in a given industry: in a frictionless environment, optimality should lead to equalization of marginal products; conversely, positive dispersion points towards suboptimal allocation – the higher, the worse.

The latter approach, which required much less formalism than the “structured” one, revived a struggling literature and provided a readily available methodology to calculate misallocation loss: for instance,Hsieh and Klenow[2009] adopt a rather standard model (Cobb–Douglas with constant return to scale, monopolistic competition with constant demand elasticity) which renders the problem of distortions analytically tractable and allows to quantify the losses in productivity.

The basic intuition is that if firms face the same input costs, efficient allocation of capital and labour

2_{For example, statutory provisions readily provide a framework for the varying impact of different regulations on different}

firms. Conversely, specifying a model which precisely identifies those firms advantaged by corruption may prove challenging.

3_{E.g: workers with a higher learning curve (representing a long–term, illiquid investment) or productive workers with}

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yields an equalization of marginal revenue product of capital and labour across firms. So the magnitude of resource misallocation is directly proportional to the within-industry dispersion of MRPK and MRPL. Additionally, the aggregate effect of these distortions may be gauged by looking at the distribution of the revenue TFP(TFPR) even if the “physical productivity”(TFPQ) is unobserved4_{: in the HK model,}

the peculiar market structure and the assumption of joint lognormality between TFPR and TFPQ leads to a simple closed-form expression for aggregate TFPQ. In this case, vars(logT F P Rsi) is a sufficient

statistics to sum up the negative effect of distortions on aggregate TFPQ:

logT F P Qs= 1 σ − 1log Ms X i T F P Qσ−1_si ! −σ 2vars(logT F P Rsi) (1) where s is the industry or geographical group under analysis and Ms the number of firms in such

group.

The authors apply such framework to quantify the potential extent of misallocation in China and India compared to the U.S. (the “benchmark economy”). They find much bigger gaps in the former two countries; a counterfactual exercise which moved China and India to the U.S. dispersion in marginal products would boost TFP in China by 30–50% and by 40–60% in India.

A second cornerstone of this influential approach is represented by the work ofPetrin and Sivadasan [2013]: misallocation is to them the “gap among the value of the marginal product and marginal input price”; in this framework, gaps are first computed at the firm-level and then aggregated at sector or spatial level. The intuition is that perfect competition requires an equalization between marginal return and marginal cost, so high wedges are inefficient and signal misallocation. For example, the capital wedge is defined as follows: Gk_it= |M P Kit− rit| where M P Kit= Pit ∂Qit ∂K = Pitβk Qit Kit (2)

M P Kit is the value of the marginal product of capital5 while rit is the capital input marginal price,

typically proxied through the user cost of capital.

To sum up, both these papers and numerous others (see, e.g,Bartelsman et al. [2013] and its focus on the covariance between size and productivity) build on specific production moments to identify misallocation. The approach is far from perfect (seeBrown et al.[2016] for a thorough critique), but the following merit of this line of work is indisputable: these papers have ignited a final, brand-new branch of literature focused once again on investigating specific causes of dispersion in marginal productivity of factors.

4_{Study of TFPQ requires plant-specific prices or physical output, which are rarely at disposal: see}_{Foster et al.}_[₂₀₀₈_]. 5_{Obtained using a Cobb-Douglas production function specification.}

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2.3 The third way: specific factors and uncertainty

The simplistic methods aptly developed byHsieh and Klenow[2009] and numerous others faced fierce criticism regarding the definition of misallocation, the factors behind dispersion in marginal productivity and the reliability of the estimates of aggregate effects. The criticism proved quite constructive and allowed to unveil an array of factors contributing both to dispersion in productivity and to misallocation stricto sensu.

To begin with,Bils et al.[2017] highlighted how mismeasurement of capital and revenues may account for a substantial part of the dispersion in the marginal revenue products found in the original paper by Hsieh and Klenow [2009]. Restuccia and Rogerson [2013], on a cautionary note, showed how the assumption of common technology also crucially influenced the results: with such an assumption “any variation in capital-to-labor ratios will be interpreted as misallocation”.

A primary source of criticism regarded the static nature of the model `a la HK. Asker et al. [2014] were among the first to challenge the usefulness of deriving policy implications from static misallocation models: they showed how adjustment costs in a dynamic optimization setting naturally lead to dispersion in marginal productivity of factors. Nevertheless, they argue, “resource allocation, while appearing inefficient in a static setting, may well be efficient in a dynamic sense”. They highlighted the importance of aggregate effects of an ex–post inefficient dynamic optimization which is also central to two fundamental works in the area (Bloom[2009] andDavid et al.[2016], on which the present work largely relies).

Bloom [2009], in this last wave of papers, best identifies the mechanisms linking uncertainty and aggregate outcomes. The author extends previous models by Bernanke [1983] and Pindyck [1988] to simulate the effect of a macro uncertainty shock: the “wait and see” phenomenon leads to a stop in hiring and investments, with negative repercussions on aggregate output and productivity. But there’s more: reallocation among units freezes due to the declined variability in capital and labor changes, thus misallocation rises. A prominent role in this real option framework is played by adjustment costs.

Uncertainty may influence hiring decisions as well: Lotti and Viviano[2012] specify a model where workers on long–term contracts are more productive but comparably more difficult to fire. In uncertainty, the trade–off of investing in efficient but irreversible inputs of production may induce firms to rely more on short–term workers.

David et al.[2018] developed a theory linking firm–specific propensity and risk exposure to wedges in capital productivity: they argue that previous works on misallocation in a dynamic optimization context (e.g.: with adjustment costs/irreversibility), while allowing for ex–post wedges still led to an ex-ante equalization of expected marginal product of capital. Instead their theory allows for firm-specific discounting factors providing a sharp link with cross-sectional dispersion in marginal productivity of capital.

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of the impact of uncertainty on misallocation. Firm–specific demand (or productivity) shocks undermine an equalization of marginal products on an ex-post basis and translate into lower levels of TFP and output. The identification strategy represents the core of the work and allows to peek into the firm’s information set using stock prices. The authors find that informational frictions account for a 20%–50% of observed dispersion in MRPK, with a 7–10 % TFP losses in India and China (4% for U.S.).

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3 The Italian productivity conundrum

The present work focuses on Italy and its worrying productivity trend, seeking a link between misallocation and uncertainty among big firms. Especially recently, economical and political uncertainty has reached a climax: what is the effect of the current turbulent environment on the firms’ strategic decisions?

The literature on the Italian conundrum has flourished lately, mostly because the 2008 crisis has provided a pitiless spotlight. How underscored byManasse[2013], the “lost decade” of missed reforms is greatly responsible for the inability to weather the economic storm. This, however, represented only the climax of a slowdown started in the 1990s and aggravated in the 2000s when TFP turned negative (see Lusinyan[2013]). Figure1represents an accurate account of the Italian weak productivity dynamics: the depressive performance in real GDP and TFP (both decreasing for a great part of the last twenty years) is especially apparent when compared with the quicker recovery of the rest of the EU countries.

Manasse [2013] blames Italy’s high unit labour costs and rigid wages, reportedly responsible for the huge competitiveness gap with foreign competitors: after the introduction of the Euro, no devaluation could mitigate the abysmal gap between Italian and Chinese relative wages. This contrasts with the view of Bugamelli et al. [2012], who maintain that precarious job positions discourage workers and firms to invest in firm-specific training activities. This, coupled with a preponderance of SMEs and risk-averse managers, curbs innovative activities (especially radical ones). Moreover, Hassan and Ottaviano[2013] maintain that, according to OECD data, labour market rigidity has been falling steadily in Italy since the 1990s and is now comparable to that of France and Germany.

At the very least, inputs can be struck out our suspect list. How underscored by Gros [2011], the percentage of those with a tertiary degree has steadily increased over the last decade to approximately 20%, a growth which has reduced the gap with partner countries. Figure1shows that Italy’s performance in terms of “capital deepening”6 _{has only recently began to suffering, and the labour input indicators}

show no remarkable difference between Italy and the rest of EU.

Italy’s R&D share over GDP, though low, has increased by one fourth over the first decade of the 2000s.7 In the same period Italy has invested, on average, 9% of its GDP in plant and equipment (against ca. 8% in Germany). The Euro convergence process has contributed to maintain low real interest rates since the early 1990s, leading to huge capital inflows to the southern Europe countries (a recent, influential paper,Gopinath et al.[2017], analyzes the link between these low rates and misallocation ensued in Italy and Portugal).

Another controversial line of interpretation (see Faini and Sapir [2005]) maintains that the Italian model of specialization tendentially curbs innovation and suffers China’s low-cost competition. Thus, a

6_{Measured as rate of change in capital stock per labour hour.}

7_{This does not contrast with the views expressed in}_{EU-Commission}_[₂₀₁₇_{] – low investments and underutilized female}

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way out could be provided by a variation in the sectoral composition. The stylized fact is confirmed by Bugamelli et al. [2012], who recall that, in Italy, textiles, wearings, leather and wood products reach a value-added share of the total economy of almost 15%, three to four times that of Germany or France. But while this matters in terms of foreign competitors8_{, the authors maintain that a lower innovation}

activity is typical of all sectors of the Italian economy and could not be solved by a simple sectoral redistribution of value added shares.

If the problem does not lie in the dearth of inputs, it may lie in the allocation of such inputs among firms. Gopinath et al.[2017] confirm the misallocation problem characterizing Italy (paralleled by Spain and Portugal): they find evidence of trends in TFP loss due to misallocation in the 1999-2012 period and an increase in the marginal product of capital dispersion after the crisis.9 Hassan and Ottaviano[2013], applying an Olley–Pakes (Olley and Pakes [1996]) decomposition of Italian manufacturing data, show that in the early 2000s “the TFP index in manufacturing is 5.77% lower than if productive resources were randomly allocated across firms”. Moreover,Bugamelli et al. [2012] cite lack of finance as a crucial barrier against innovation: risk-averse banks and a nearly non-existent venture capital system discourage innovation investments of R&D intensive SMEs and redirect capital towards bigger or politically-tied firms. Deterioration in corruption and government effectiveness indicators (see once again Gros [2011]) may have exacerbated these adverse selection issues.

As a final note, there are relatively few studies concentrating on misallocation in the Italian framework and none on the role of uncertainty. An important exception to this are Calligaris[2015] and Calligaris et al. [2016]: they have exposed a thickening of the left tail of the Italian productivity distribution after the crisis, which has contributed to increasing its dispersion and lowering its mean. Moreover, they have investigated the evolution of misallocation both within and between various categories of firms (based on geographic areas, industries and firm size), highlighting how misallocation has all but spared Northern industries and bigger firms. This is interesting, because it contrasts with a long–standing literature on the curse of small firms: how important is misallocation amongst bigger firms?

8_{The French and German economies suffered less the Chinese competition and the devaluation restrictions linked to the}

Euro convergence process, seeWorld-Bank[2016].

9_{Intuitively, dispersion is higher in the presence of some market imperfections which impede the flow of capital from}

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4 David et al.

[

2016

]: measuring the impact of uncertainty

The greatest challenge in analyzing the aggregate impact of uncertainty is measuring uncertainty itself: firm–level information sets and forecast errors are typically unknown to the econometrician and hardly measurable. An elegant solution to this conundrum is provided byDavid et al.[2016].

In their model, firms choose inputs under imperfect knowledge of their own fundamentals and demand conditions, and their forecast error results in aggregate productivity and output losses. The authors devise a peculiar empirical strategy to pin down the economy’s information structure, by exploiting the informational content of observed market prices: intuitively, the better the signal in the market price and the worse the firms’ own signals, the more the firms will rely on the information of past prices, and investment will comove with stock returns.

Hereby follows a brief recap of the model’s main conclusions – the augmentation with common shocks is in the forthcoming sections. I tried to retain the authors’ original notation wherever feasible.

4.1 The Production Side

The authors consider a discrete–time, infinite–horizon economy where a single family provides inelastically a fixed quantity of labor N, rents capital to intermediate firms and consumes the final good.

4.1.1 Technology

A continuum of firms indexed by i produce intermediate goods according to

Yit= Kαb1 it Nb

α2

it , αb1+αb2≤ 1 (3)

These goods are aggregated in CES style into the single final good:

Yt= Z AitY θ−1 θ it di θ−1θ (4)

with θ as the usual elasticity of substitution and Aitwhich may be interpreted as demand– or productivity–specific.

They specify a simple AR(1) process governing logAit:

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4.1.2 Market structure and imperfect information

The final good is produced under perfect competition and information– this implies a demand function for intermediate good i as follows10_:

Pit=

Yit

Yt

−1θ

Ait (6)

Unfortunately for the intermediate firm, capital and labor have to be chosen at t-1 under uncertainty.11 The firm’s profit maximization can then be expressed as12:

max Kit,Nit Y1θ t Eit[Ait]Kitα1N α2 it − WtNit− RtKit (7) where αj= 1 −1 θ b αj, j = 1, 2 (8)

Standard optimality and market clearing allow for a recharacterization of eq.7 as a capital input choice problem: max Kit N Kt α2 Y 1 θ t Eit[Ait]Kitα− 1 +α2 α1 RtKit (9) where α = α1+ α2 (10)

Imposing capital market clearing and noting that aggregate revenue must equal aggregate output leads to the following simple expression13_:

yt= 1 θyt+ α1kt+ α2n + log Z Ait(Eit[Ait]) α 1−α_{di − αlog} Z (Eit[Ait]) α 1−α_di ₍₁₁₎

This result hints towards an impact of the firms’ forecast errors on aggregate productivity and output. As will be shown, David et al. [2016]’s clever structure will allow for a more straightforward representation of such impact.

4.1.3 Information Set

Studying Eit[Ait] requires outlining the firm’s information set prior to the input choice. The authors

fill it with three elements.

The first, common knowledge of all the actors, is the entire history of the firm’s past fundamental

10_{Intuitively: perfect competition implies that the final producer’s marginal cost of input i at time t is equal to P} it.

Maximization of profit of the final producer leads to equalization of marginal product from input i at time t (obtained from derivation of eq.4) and marginal cost.

11_{The authors specify two versions of their model: in the first, both inputs are subject to the same imperfect information}

set. In the second, labor is freely adjustable at time t after the contemporaneous demand shock has been observed.

12_W

t, Ntare known at time t-1: either because they are fixed, or because we allow for a frictionless spot market where

firms may buy future inputs.

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realizations {ait−s}∞s=1. Due to the Markovian process of the AR(1) evolutionary process, ait−1 is

sufficient to sum up the whole past process.

Second, each firm is endowed with a private signal of its contemporaneous fundamental:

sit= ait+ eit, sit∼ N (0, σe2) (12)

Here, realizations of eitare assumed to be iid both in cross–section and in time.

Finally, the authors conveniently specify the financial markets structure and show that the firm i’s stock price is informationally equivalent to a signal of the following form:

ˆ

sit= ait+ σvzit, zit∼ N (0, σz2) (13)

In their baseline model Pitmay be interpreted as a conditionally independent, normally distributed signal

of firm fundamentals of precision _σ21 vσ2z

. As put in the original paper, “firms also observe movements in their own stock prices, which aggregate the information of financial market participants about the firm’s future prospects”. This is crucial for the identification strategy, since it allows the econometrician to observe an (albeit limited) portion of the firm’s information set. Moreover, it proxies the degree to which financial markets facilitate efficiency and firm–level learning. To conclude, the authors apply Bayes’ rule and verify that the conditional distribution of the fundamental is lognormal:

ait|Iit∼ N (Eit[ait], V) (14) where            Eit[ait] = _σV2 µ[(1 − ρ)¯a + ρait−1] + V σ2 esit+ V σ2 vσz2sˆit V = 1 σ2 µ +_σ12 e +_σ21 vσz2 −1 (15)

V (the variance of the firm’s forecast error) oscillates between 0 (perfect information) and σµ2 (absence

of any learning, only the common knowledge is employed to forecast Ait). Reformulating in terms of the

forecast error yields:

ait− Eitait= V µit σ2 µ −eit σ2 e −σvzit σ2 vσz2 (16)

4.2 The stock market

David et al.[2016] build on the recent contribution byElias et al.[2011] to model the stock market side. Two group of agents (noise and imperfectly informed ones) trade up to one unit measure of outstanding equity.

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Each period, the noise traders buy a quantity Φ(zit) of stock i.14 The rest of the supply 1 − Φ(zit) is

bought by informed traders who put limit orders conditional on Pit and are endowed with independent

noisy signals on the firms’ fundamentals ait. Agent j’s signal on the fundamental of firm i is as follows:

sijt= ait+ vijt, vijt∼ N (0, σ2v) (17)

Aggregating stock i’s demand of both type of traders yields: Z

d (ait−1, sijt, Pit) dF (sijt|ait) + Φ(zit) = 1 (18)

Here d (ait−1, sijt, Pit) is the demand of investor j and F is the conditional distribution of the private

signals: by the law of large numbers and independence of signals among different investors, the latter coincides with the cross-sectional distribution of sijt across the investors. The informed investor j

purchases the stock only if his expected payoff (specified below) is greater than the purchase price.

Eijt[Πit] =

Z

[π(ait−1, ait, Pit) + βP (ait)]dH(ait|ait−1, sijt, Pit) (19)

π(ait−1, ait, Pit) represents the firm’s expected profit which accrues to the investor as a dividend. The

problem is complicated by the endogeneity of Pit which insinuates into the firm’s information set,

influences its decisions and therefore the expected profits. H(|.) denotes investor j’s posterior over ait.

Elias et al.[2011] show that a rational expectations equilibrium displays the following rather convenient properties: (i) investors buy only if their signal is higher than a fixed threshold ˆsit(ii) the market price

Pitis an invertible function of ˆsit.

We apply property (i) to eq18: aggregating demand and imposing market clearing yields:

1 − Φ ˆsit− ait σv

+ Φ(zit) = 1 (20)

which allows for a simple yet elegant characterization of the threshold signal (informationally equivalent to Pit):

ˆ

sit= ait+ σvzit (21)

Finally, and crucially for the identification strategy, notice that the marginal investor (the one who observes sijt= ˆsit) is necessarily indifferent between buying or not buying stock i. This means that Pit

must equal his expected payoff from buying the stock:

14_z

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Pit=

Z

[π(ait−1, ait, Pit) + βP (ait)]dH(ait|ait−1, ˆsit, Pit)

= Z

[π(ait−1, ait, ˆsit) + βP (ait)]dH(ait|ait−1, ˆsit, ˆsit)

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Writing this equation in recursive form yields the model–implicit price Pit of firm i at time t, which

only depends on [ait−1, ait] (given by the data) and zit (drawn from the distribution), while H(|.) and

G(|.)15 _{are easily derivable normal distributions.}

The identification strategy will basically consist in randomly drawing the triad (σ2

e, σv2, σzv), using past

data on aitand ait−1to generate the market–implied prices and the price moments. Then we compare the

model–implied moments to the real moments: we select the triad which minimizes the distance between the two set of moments.

4.3 Aggregation

Two elements greatly simplify the analysis:

(i) the log–normal nature of the conditional distribution of Ait (outlined in eq.14);

(ii) the fact that the variance of the forecast error V is common to all the firms.

The authors show that ait and its conditional expectation Eitaitare jointly normal.16 In fact, given

two independent normal random variables U,V we know that X = aU + bV and Y = cU + dV are jointly normal. So

(i) cross–sectional and time–series distribution of aitare equivalent because no element of the stochastic

process is firm–specific. Hence the cross–sectional distribution of ait is normal; (ii) Eitait− ait (the

forecast error) is normal because sum of 4 normal RVs, none of which have firm–specific components; (iii) the forecast error and aitare by definition independent. So it suffices to take Eitait− aitas U, aitas

V: Eitaitis X = −U + V , aitis Y = 0 + 1 ∗ V and the two RVs are shown to be jointly normal. Applying

the conditional variance identity results in the covariance matrix.    ait Eit[ait]   ∼ N       ¯ a ¯ a   ,    σ2 a σ2a− V σ2 a− V σ2a− V       (23)

15_{The future stock price P (a}

it)’s distribution, conditional on ait.

16_{For the results to hold, they have to be “cross–sectionally” jointly normal (conditional on t). Given that the original}

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This allows for a closed–form solution of the integrals in eq 11_{which reflects the influence of V:} yt= ˆα1kt+ ˆα2n + θ θ − 1¯a + 1 2 _θ θ − 1 _σ2 a 1 − α− 1 2θV | {z } a (24)

Where a is aggregate TFP and y is aggregate output (in logs). Uncertainty affects both a and the steady–state stock of capital.17 _{The authors show that:}

dy dV= da dV 1 1 − ˆα1 = −1 2θ 1 1 − ˆα1 (25)

4.4 Identification

The econometric hurdle lies in the impossibility to observe the agents’ signals. David et al. [2016] offer a first, simplistic solution by noting that in their baseline version without other frictions, the firms’ forecast errors are identically and independently distributed in the economy. Thus, dispersion in the marginal productivity of the inputs (e.g: σ2

mrpk) reflects the ex–post dispersion of the forecast error

which, by the law of large numbers, is reconducible to the ex–ante dispersion of the forecast error (thus, V). In short,

V = σmrpk2 (26)

Nevertheless, a pressing issue frustrates the efforts to identify V by means of observable moments in production–side variables (σ2

mrpk, but also σ 2

ak, for example): the presence of other frictions, ranging

from adjustment costs to financial frictions and many others.

To tackle this, the authors combine moments from the production–side with moments from the stock market data: in particular, they mingle the correlations of stock returns with both productivity growth and investment, and the volatility of stock returns. They take full advantage of the gaussian nature of the observables, analytically demonstrating their results in two “easy” cases: when ρ = 0 and ρ = 1. In the general scenario they are unable to derive a closed form relationship between these three moments and V, but use a simulated method of moments approach to derive the “best” combination of (σe2, σv2, σ2z)

that minimizes the sum of squared deviations of the model–implied moments from the target moments.

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5 David et al.

[

2016

] with common shocks

A first, albeit simple augmentation of the model proposed byDavid et al. [2016] consists in adding aggregate demand shocks which similarly affect all firms in the economy:

∂ait

∂ft

= γ (27)

The main results of the original paper are retained, with the notable exception of the identification strategy: the ex–ante distribution of the forecast error cannot be surmised solely by the cross–sectional moments since all firms are subject to a same shock.18 A second, less straightforward extension adds firm–specific effects of the aggregate shock:

∂ait

∂ft

= γi (28)

The model is greatly complicated because the forecast error’s variance Vi becomes firm–specific and

dependent on the cross–sectional distribution of γ2

i which may be non–standard. A simple enough

cross–sectional distribution of the γis will return a manageable model.

As usual, I tried to retain the authors’ original notation wherever feasible.

5.1 The Production Side

The authors consider a discrete–time, infinite–horizon economy where a single family provides inelastically a fixed quantity of labor N, rents capital to intermediate firms and consumes the final good.

5.1.1 Technology

A continuum of firms indexed by i produce intermediate goods according to

Yit= Kitαb1Nb α2

it , αb1+αb2≤ 1 (29)

These goods are aggregated in CES style into the single final good:

Yt= Z AitY θ−1 θ it di θ−1θ (30) with θ as the usual elasticity of substitution and Aitwhich may be interpreted as demand– or

productivity–specific. The original AR(1) process governing ait is augmented with a common shock

independent to the firm–specific shock:

18_{In other words, forecast errors of the various firms in a given year are not necessarily iid anymore: the moment}

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• γi = γ ∀i

logAit= ait= (1 − ρ)¯a + ρait−1+ γft+ µit, µit∼ N (0, σµ2) ft∼ N (0, σ2f) (31)

• firm–specific γi:

logAit= ait= (1 − ρ)¯a + ρait−1+ γift+ µit, µit∼ N (0, σ2µ) ft∼ N (0, σ2f) (32)

An easy way to introduce firm–specific γs is as follows:

γi∼ Bern            γ with p = 1₂ −γ with 1 − p = 1₂ (33)

This allows to maintain a normal distribution of the RV γi∗ ftand an easy (degenerate) distribution

of γ2

i. Why this is so important will become apparent in the next sections.

5.1.2 Market structure and imperfect information

The final good is produced under perfect competition and information– this implies a demand function for intermediate good i as follows:

Pit=

Yit

Yt

−1θ

Ait (34)

A key assumption is that the intermediate firm chooses capital and labor at t-1 under uncertainty.19

The firm’s profit maximization can then be expressed as20_:

max Kit,Nit Y 1 θ t Eit[Ait]Kitα1N α2 it − WtNit− RtKit (35) where αj= 1 −1 θ b αj, j = 1, 2 (36)

Standard optimality and labor market clearing allow for a recharacterization of eq. 7 as a capital input choice problem: max Kit N Kt α2 Y1θ t Eit[Ait]Kitα− 1 +α2 α1 RtKit (37)

19_{Once again, the authors of the original paper had envisaged two versions of their model: in the first (here depicted),}

both inputs are chosen under uncertainty at t-1, in the second, labor is freely adjustable. Reality is likely to fall inbetween these extreme cases.

20_{An underlying assumption is that each firm is risk–neutral: otherwise the discount factor would be firm–specific and}

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where

α = α1+ α2 (38)

Imposing capital market clearing and noting that aggregate revenue must equal aggregate output leads to the following simple expression21_:

Kit= (E it[Ait]) 1 1−α R (Eit[Ait]) 1 1−α_di Kt (39) yt= 1 θyt+ α1kt+ α2n + log Z Ait(Eit[Ait]) α 1−α_{di − αlog} Z (Eit[Ait]) α 1−α_di ₍₄₀₎

This part is analogous to the one in the original paper: the common shock will nevertheless be reflected in the capital choice given its influence on the forecast of future demand conditions. Notice however that the two integrals require variation on the cross–sectional dimension only: they will be solved exploiting the simple structure of the joint distribution (conditional on t) of Aitand Eit[Ait]. The solution is much

more complicated in case γi 6= γ, which adds variation on the cross–sectional dimension with Vi now

dependent on the distribution of γ2 i.

5.2 Information Set

Studying Eit[Ait] requires outlining the firm’s information set prior to the input choice. As in the

original paper, this is filled with three elements22.

The first building block, common knowledge to all the actors, is the entire history of the firm’s past fundamental realizations {ait−s}

∞

s=1. Notice that the addition of the common shock does not interfere

with the stationarity or the Markovian nature of the AR(1) original process, so that ait−1is sufficient to

sum up the whole past process. In other words: 

   

ait|ait−1∼ N (1 − ρ)¯a + ρait−1, σ2µ∗

σ_µ∗2 = γ2σ_f2+ σ2_µ

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This is true in both our baseline cases.

Second, each firm is endowed with a private signal on the true realization of ftand µit:

     µaz_it ∼ N (µit, σaz,µ2 ) ftaz∼ N (ft, σaz,f2 ) (42)

Importantly, these two signals are independent of each other. Moreover, the signals on the common shock in a same year are independently distributed across different firms. It is straightforward to recover the

21_{Lower case for logs.}

22_{All parameters, included the γ}

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paper’s original notation:

sit= (1 − ρ)¯a + ρait−1+ γftaz+ µ az it

= (1 − ρ)¯a + ρait−1+ γ(ft+ erraz,f) + (µit+ erraz,µ)

= ait+ γerraz,f+ erraz,µ = ait+ erraz,f −µ, erraz,f −µ∼ N (0, σe∗2 )

where σ2

e∗= γ2σaz,f2 + σaz,µ2 .

In the case of firm–specific γis, erraz,f may show a negative sign; this does not influence the distribution

of erraz,f −µ.

Finally, also the financial markets structure has to be tweaked accordingly to fit the common shock: each (partially) informed agent observes two independent signals on common shocks and on the fundamental of the unique firm he is stockholder of.23 _{In other words:}

     vµ_ijt∼ N (µit, σ2v,µ) vf_ijt∼ N (ft, σv,f2 )

⇒ sijt= ait+ γerrv,fijt + err v,µ

ijt = ait+ errv,f −µijt (43)

These signals are independent across each dimension indexed in [i, j, t]. The result in David et al.[2016] can be recovered as follows (the procedure is the same):

     errv,f −µ_ijt ∼ N (0, γ2_σ2 v,f+ σ 2 v,µ) σ2 v∗= γ2σ2v,f+ σ 2 v,µ ⇒ ˆsit= ait+ σv∗zit, zit∼ N (0, σ2z) (44)

where ˆsit is the signal of precision _σ21

v∗σz2 informationally equivalent to the firm’s stock price Pit. To

conclude, we can apply Bayes’ rule and verify that the conditional distribution of the fundamental is lognormal as in the original model:

ait|Iit∼ N (Eit[ait], V) (45) where Eit[ait] = V σ2 µ∗ [(1 − ρ)¯a + ρait−1] + V σ2 e∗ sit+ V σ2 v∗σz2 ˆ sit (46) and V = ₁ σ2 µ∗ + 1 σ2 e∗ + 1 σ2 v∗σz2 −1 (47)

23_{Differently from the baseline model, here each agent trades stocks of at most one firm. The assumption is quite}

harmless, and guarantees that one agent’s signal of the common shock cannot be used in determining demand of different stocks – otherwise, Pitwould concur in influencing demand of stock j and this would substantially complicate the model.

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V oscillates between 0 (perfect information) and σ2µ∗ (absence of any learning, only common knowledge

is employed to forecast Ait).

If the γis follow our simple Bernoulli distribution, all of this structure is mantained. If, however, the

distribution was slightly more complicated (e.g: γi ∼ N 0, σγ2, we would (i) witness a firm–specific

forecast error Vi dependent on γi2 (ii) the cross–sectional distribution of the forecast error would be the

same, non–standard distribution of the square of a normal RV.

5.3 _{Disentanglement of V}

The relation between V and the correlations employed in the identification strategy inDavid et al. [2016]24 _{is very similar. Hereby follows an exemplificative analysis in which shocks are purely transitory:}

we show that the relations identified in the original paper are recovered. 5.3.1 Transitory shocks: ρ = 0

Loglinearization of prices around the equilibrium is akin to what is found in the original paper25:

Pit= P epit = Z _N Kt α2 Yθ1 t AitKitα− 1 +α2 α1 RKit dH(a|a−1, a + σvz) + β Z [Pit+1] dH(a|.) = eEit N Kt α2 Y 1 θ t AitKitα− 1 +α2 α1 RKit + β eEitPit+1 = N Kt α2 Y1θ t e_EitAKαeait+αkit− eEit 1 + α2 α1 RKekit_{+ β e} EitPit+1+ Const.

Now, we normalize the constant multiplying revenues and capital costs to 1. Furthermore, we log–linearize by means of exet' 1 + e xt. ⇒ P epit _{' P (1 + p} it) = AKα− RK + βP + eEitAKαeait+αkit− eEitRKekit + β e_EitPit+1+ Const.

24_{Correlations of stock returns with both ∆a}

itand investment, and the volatility of stock returns. 25

e

Eit denotes the expectation for the marginal investor, the one who observes the threshold signal ˆsit. In other words,

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⇒ P pit= AKαe_Eitait+ αAKα_{− RK} 1 − α e Eit[Eitait] + β eEitP pit+1+ C. = AKαeEitait+ β eEitP pit+1+ C.

Now, given our assumption of transitory shocks, this translates into: ⇒ pit=

AKα

P eEitait+ β eEitP pit+1+ C. (48) It is then straightforward to guess and verify pit= ξ ˜Eitait+ Const. To sum up:

                         pit= log(_PP_eqit) = ξ ˜Eitait+ Const. ˜ Eitait= ˜Eitµit= ψ(µit+ γft+ σv∗zit) + Const. ψ = 1 σ2_v∗+ 1 σ2_{v∗ σ}2 z 1 σ2_µ∗+ 1 σ2_v∗+ 1 σ2_{v∗ σ}2 z                          (49)

We also need a characterization for the other two variables whose moments will be recovered in the data, namely ait and kit. Their derivation is the same as in the original paper (though the expectations are

taken on a different information set). aitis specified as in eq.5; kit, following eq.39:26

                       kit=E_(1−α)it[ait]+ Const. = Eit [µ∗_it] (1−α) + Const. Eit[µ∗it] = ϕ1(µ∗it+ erraz,f −µ) + ϕ2(µ∗it+ σv∗zit) + (ϕ3∗ 0) µ∗_it= µit+ γft, ϕ1= σV2 e∗ , ϕ2= σ2V v∗σ2z                        (50)

Finally, we’ll seek to disentangle ρ∆p∆a and ρ∆p∆k:

     ρ∆p∆a= Cov(∆p,∆a) σ∆pσ∆a ρ∆p∆k= Cov(∆p,∆k) σ∆pσ∆k where            σ_∆p2 = V ar(pit− pit−1)

σ2_∆a= V ar(ait− ait−1)

σ2

∆k= V ar(kit− kit−1)

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Direct computation of the moments leads to the following results:

ρ∆p∆a= 2ξψσ2 µ∗ q 4ψ2_ξ2_(σ2 µ∗+ σv∗2 σz2)σ2µ∗ =_q 1 1 + σ2v∗σ2z σ2 µ∗ (52)

26_{Notice that a common V greatly simplifies the relation between a}

itand kit, allowing the dispersion component to be

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ρ∆p∆k= 2ξψσ2_µ∗ q 4ψ2_ξ2_(σ2 µ∗+ σv∗2 σ2z)(σµ∗2 − V) = _q 1 (1 +σ2v∗σ2z σ2 µ∗ )(1 − V σ2 µ∗ ) (53)

So that V can be recovered once σµ∗2 is obtained from estimation of eq.5:

V σ2 µ∗ = 1 − ρ∆p∆a ρ∆p∆k 2 (54) An important difference fromDavid et al.[2016] is that ρ∆p∆aand ρ∆p∆k are functions of ∆ft. Given

the simplified nature of this common shock (modelled with no memory), this parameter does not affect the iid nature of the observed ∆aitand ∆pit, so that ex ante correlations still coincide with the cross–sectional

ex post correlations. A persistent common shock would nevertheless require either detrendization of data or exploitation of the panel dimension so as to capture the shock–implied variation. Failure to do so would entail substantial bias in the estimate of V.

Finally, these simple, closed–form relationships are no longer attainable if 0 < ρ < 1: this is the reason for which we will resort to computational techniques in the empirical analysis.

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6 Quantitative analysis

The analytic results in the previous sections highlighted the link between the moments (ρ∆p∆k, ρ∆p∆a,

σ2

∆p) and the unknown subcomponents of V: (σ2e, σv2, σ2z). David et al.[2016] moreover demonstrate how

their empirical strategy, here adopted, is robust to the presence of other factors which may affect input choices.27 _{Complementarily to the original paper, we infer the parameters for the Italian case and compare}

the results with the U.S. and Indian baseline cases. The results unveil the extent of informational frictions, the effect on aggregate productivity and the impact on aggregate output. Following David et al.[2016], we investigate the role of learning, highlighting the uselessness of financial markets in improving allocative efficiency by conveying information.

6.1 Parametrization

To begin with, we restrict our analysis to listed firms (for which stock price data is available): we depart from the traditional literature on the “curse of smallness”28 to document the misallocation of big–sized firms.

The first step is to assign values to the parameters governing the preference and production structure of the model, as reported in table1.

A first issue lies in the period length: though agreeing on principle with the necessity to push towards longer time horizons, we stick with a one–year time period largely for data availability. As suggested by David et al. [2016], this may be not entirely reflect the “long lags in planning and implementing investment projects” which suggest that firms may be called to forecast fundamentals and put aside resources 2–3 years in advance. Moreover, since we omit adjustment costs and irreversibilities from the analysis29, choosing only one year may exacerbate such biases.

To maintain comparability to the original paper, the discount rate β is set to 0.9. Capital and labor shares are set to 0.33 and 0.67; of course, this is a strong assumption which neglects the heterogeneity characterizing our small but diverse sample of listed firms. We stick with the literature consensus and set θ to a baseline value of 6.

Regarding the parameters governing the AR(1) process of firm fundamentals ait, we perform an

Arellano–Bond estimation with 2000–2010 data on the selected listed firms30_{, identifying ρ and the}

variance of innovations. Following the original paper, we directly construct the fundamental aitfor each

firm (up to a constant) as vait− αkit, where va denotes the log of value added. Differently fromDavid

et al.[2016], we have data on materials and avoid to generate va as a fixed proportion of revenues.

27_{Intuitively, the authors show how wedges `}_{a la}_{Hsieh and Klenow} _[₂₀₀₉_{] are linear in correlations, so that ratios of}

correlations such as in eq.52still yield the true V. The demonstration is here omitted for brevity.

28_{As will be shown, a skewed size distribution is not the root of all Italian evil.} 29_{Notice that firms in the model target Ea}

itwithout taking into account the option value of waiting or dynamic investment

costs.

30_{Following the second part of our theoretical analysis, we add time fixed effects and set σ}2

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What is left is the triad of parameters (σe2, σ2z, σv2). As already described, we target cross–sectional

correlations of stock returns with investment31_{and changes in fundamental, plus the variance of returns.}

We lag stock returns by one period to avoid feedback effects of input choices on returns.

Basically, we exploit the recursive nature of the functional equation22to solve iteratively with a grid of shocks zit the price equation Pit(ait−1, ait, zit). From the Orbis dataset, we have data on roughly 120

firms for 2009, 2010 and 2011. We use data on aitfrom 2009 and 2010 (plus a random draw of zitfrom its

known distribution) to unveil the 2011 model–implied stock prices. Next, we compute the model–implied moments and compare them to the actual moments: using a simulated method of moments (SMM) approach, we search over the parameter vector space [σ2_e, σ2_z, σ_v2] and select the triad which minimizes the unweighted sum of squared deviations of the model moments from the real moments.

31_{Curiously, in the original paper the authors do not follow the methodology outlined, but prefer to target the correlation}

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7 Data and Results

To construct firms’ fundamentals and obtain the target moments, we use firm–level data on 122 Italian firms. The dataset is Orbis and we choose our baseline year (2011) so as to maximize the number of observations given the requirement for availability of capital, output and materials and stock price for 2009, 2010 and 2011 and 2012. We trim the 1% tails of each distribution to take care of outliers.

The firm’s capital stock kit is obtained as the log of the sum of tangible and intangible fixed assets,

while investment is the change in the capital measure between two periods. ait is computed as outlined

above, and first–differencing gives us the changes in fundamentals between the two periods. Similarly to the original paper, the firm’s stock price is adjusted for splits, dividend distributions and financial leverage.32 _{We need data on a}

it for 2009, 2010 and 2011 to build the model–implied stock price of 2010

and 2011 and the model–implied stock returns for 2011. We then build the model–implied moments using the model–implied stock return for 2011 and the real growth in capital and fundamental in 2012 (to avoid simultaneity problems). Finally, we compare the model–implied moments and the target moments to derive the best triad of parameters.

The elegance of the original model lies in the possibility to disentangle the triad and isolate V even in the presence of other distortions: none of these moments alone would be sufficient to this aim, nor would a different modeling of the production and financial market activity guarantee such a result. In particular, the comovement of price and firm’s future fundamental changes reveals how “good” is the investors’ information on firm i. But this is not sufficient to understand how reliable is the information of firm i: we also need to know to what extent input decisions correlate with past price movement – intuitively, in this way we can understand (i) whether the stock market has sharp knowledge on the stocks it trades; (ii) whether a firm’s decisions follow the indications of the stock market (the more this happens, the less informed is the firm given its baseline signal). Little would be gained by considering these moments in isolation: as put in the original paper, “the correlation between returns and investment can be high either because firms and investors are both perfectly informed [...] or because firms are poorly informed and therefore learn much from market prices”.

In table1 we have the starting parameters. Target moments and the model–implied triad (σv2, σe2,

σ2z) are reported in table2.

32_{As a simplifying assumption, we follow}_{David et al.}_[₂₀₁₆_{] in pretending that “claims to firm profits are sold to investors}

in the form of debt and equity in a constant proportion”. This implies that unlevered return variance may be obtained by multiplying the observed return variance by (1 − d)2where d is the debt–asset ratio.

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7.1 Results: the impact of frictions

The final outcomes are reported in table 3. Results for U.S. and India are from the original paper by David et al. [2016], while results for Italy are from own calculations. On the left, we have the model–implied value for firm–level uncertainty V: it is comparable to the “efficient” baseline provided by the U.S. case, representing about one half of the underlying fundamental uncertainty σ2_µ∗: learning washes away half of it, decisively more than in the Indian case. U.S. firms remain the most informed.

We retain σ2_mrpk∗ as a rough proxy for ex–post misallocation, showing that informational frictions represent approximately one–fifth of total misallocation affecting big, listed firms. Once again, this is very near to the U.S. case and noticeably smaller than in the Indian case, a sign that other reasons behind uncertainty need to be investigated to precisely catalogue the Italian inefficiencies.

In the last two columns, we compute aggregate outcomes as percentage deviation from the theoretically optimal case in terms of aggregate TFP and aggregate output (see eq. 24and25: in the “optimal” case we assume V = 0)33_{; Italy is somewhat midway between the Indian and the U.S. case, with aggregate}

TFP losses around 5% and output losses of no more than 7%; there is a caveat: as highlighted in the original paper, this is the more conservative case given that we assume only capital to be subject to uncertainty at decision time.

33_{Implied losses are for the baseline case in which only capital is chosen under imperfect information. Results for the}

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7.2 Results: the sources of learning

As displayed in table4, firm learning is effective in reducing the ex–ante forecast error, maximizing information spillovers and moving the equilibrium closer to the efficient case. Learning, both from private and market sources, results in absolute and percentage reductions in V of up to 46%, where ∆V = V−σ2

µ∗.

This has sizable effects on aggregate outcome: if no learning took place, aggregate TFP would be 8% lower and aggregate output up to 10% lower. This is probably due to the high fundamental uncertainty of the Italian baseline case (which probably capture some undue heterogeneity, a necessary evil of aggregation), but also due to the dramatically low σ2

e.

In fact, if we analyze the relative contribution of private and market sources we can conclude that the financial markets play no decisive role in lowering informational frictions. Focusing on the relative contribution of, respectively, private signals

1 σ2_e 1 σ2e + 1 σ2z σ2v

and market signals 1 σ2_{z σ}2 v 1 σ2e + 1 σ2z σ2v , we find that almost 98% of the reduction in V due to learing is ascribable to private sources. The foremost reason for this is the high level of noise σ2

z which pervades the financial markets.

Importantly, the little role for market informativeness is also found in the U.S. and Indian dataset, though to a lesser extent. David et al. [2016] notice that one reason for the limited informational role of financial markets is that, in the exercise, we focus on a short–to medium horizon: if stock prices movements reflect deeper firm’s fundamentals which are tied to longer time prospects, this would generate a confounding effect that would weaken the link between firm investment and stock price returns34_{. The}

identification strategy would not necessarily be affected, but any conclusion on the efficiency of the stock market would have to take this caveat into account.

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8 Conclusions

In this work, we built on the seminal contribution ofDavid et al.[2016] on the role of informational frictions: we analytically explored the implementation of aggregate shocks (somewhat ignored in the original paper), highlighting the rapidly growing difficulties in maintaining the original paper’s elegant results once firm–specific reactions to aggregate shocks are added to the model.

We also solved the financial side of the model through an iterative procedure to obtain the model–implied stock prices, then resorted to a simulated method of moments methodology to unveil the “most likely” triad of parameters (σ2e, σv2, σz2) which form the ex–ante uncertainty V. We then calculated the impact

of informational frictions on aggregate TFP and output with data on Italian public firms for 2011–2012, finding a somewhat midway case between the U.S. “efficient” baseline and India: a conservative estimate of 7% of aggregate output loss may be traced back to uncertainty and misinvestment.

Finally, we have assessed a somewhat limited role for the financial markets: only up to 3% of firm–level information would be lost if financial markets were to be wiped away. Most of the learning is internal: how the firm–specific forecasting ability may be linked to heterogeneity in managerial quality and different information processing systems, as well as how technological improvements may improve forecasting ability, could be subject for future work.

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A

Figures

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B

Tables

Table 1: Parametrization – Summary

Parameter

Description

Target/Value

Time period

1 year

β

Discount rate

0.90 ˆ

α

1

Capital share

0.33 ˆ

α

2

Labor share

0.67 θ

Elasticity of substitution

6 ρ

Persistence of fundamentals

Estimates of eq.

31 σ

_µ∗2

Shocks to fundamentals

Estimates of eq.

31 σ

_e2

Precision of firm’s private signal

ρ

∆p,i

ρ

∆p,∆a

σ

∆p2

σ

v2

Precision of investor’s private signal

ρ

∆p,i

ρ

∆p,∆a

σ

∆p2

σ

_z2

Noise trading variance

ρ

∆p,i

ρ

∆p,∆a

σ

∆p2

Table 2: Target moments and parameter estimates

Target Moments Parameters

ρ∆p,i ρ∆p,∆a σ∆p2 ρ σ 2 µ∗ σ 2 v σ 2 e σ 2 z -.0003 -.0181 .1589 0.81 0.2025 1.08 0.24 9.5

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Table 3: The impact of informational frictions

V

_σV2 µ

σ

2 mrpk _σ2V mrpk

a

∗

− a

y

∗

− y

Italy

0.11 53.6%

0.52 21%

5.1%

7.0%

United States

0.08 41%

0.38 22%

4%

5%

India

0.22 77%

0.46 48%

10%

14%

Data for U.S. and India is fromDavid et al.[2016].

Table 4: The importance and sources of learning

Share from source ∆V ∆ V

σ2

µ ∆a ∆y Private Market

Italy -0.09 -46.4% 7.9% 10.1% 97.5% 2.5% United States -0.12 -59% 5% 8% 92% 8% India -0.06 -23% 3% 4% 89% 11%

Informational frictions and misallocation