metadata: authors: 0: author: Buera,Francisco J.
1: author: Fattal Jaef,Roberto N.
count: Chile
docna: 0: docna: The dynamics of development : innovation and reallocation
docty: Policy Research Working Paper
subtopic: Democratic Government,Public Sector Administrative & Civil
            Service Reform,State Owned Enterprise Reform,Economics and Finance of Public
            Institution Development,De Facto Governments,Public Sector Administrative and Civil
            Service Reform,Private Sector Economics,Marketing,Private Sector Development Law,Labor Markets
teratopic: Public Sector Development,Governance,Private Sector Development,Law and Development,Social Protections and Labor
abstracts: cdata!: This paper proposes a quantitative model
            of endogenous firm dynamics to study growth acceleration
            episodes triggered by reforms. It finds that reversals of
            entry distortions lead to persistent growth in TFP and
            declining average firm size, as in the experience of
            successful post-communist transitions. Removing
            idiosyncratic distortions results in a more protracted path
            of TFP and a rising average firm size, as in non-communist
            growth accelerations. When calibrating the reforms to
            China’s liberalization, the model accounts for one-third of
            the observed growth in TFP, while matching the dynamics of
            average firm size and income inequality.
geo_reg_key: 119228,517191
repnme: repnme: The dynamics of development : innovation
            and reallocation
display_title: The dynamics of development :
            innovation and reallocation
listing_relative_url: /research/2018/06/30224452/dynamics-development-innovation-reallocation
topicv3: Private Sector Development m1326060 1921,State Owned Enterprises m1326323 721,Jobs m1503931 2670,Entrepreneurship m1582903 4424,Labor Demand m1583073 4422
publishtoextweb_dt: 2018-06-29T00:00:00Z
historic_topic: Public Sector Development,Governance,Private Sector Development,Law and Development,Social Protections and Labor
no_of_pages: 58
author_keys: 0: author_key: 1253388
model_extractions: Policy Research Working Paper 8505 The Dynamics of Development Innovation and Reallocation _Francisco J. Buera Roberto N. Fattal-Jaef_ Development Economics Development Research Group June 2018
Policy Research Working Paper 8505

# **Abstract**

This paper proposes a quantitative model of endogenous firm dynamics to study growth acceleration episodes triggered by reforms. It finds that reversals of entry distortions lead to persistent growth in TFP and declining average firm size, as in the experience of successful post-communist transitions. Removing idiosyncratic distortions results in a more protracted path of TFP and a rising average firm size, as in non-communist growth accelerations. When calibrating the reforms to China’s liberalization, the model accounts for one-third of the observed growth in TFP, while matching the dynamics of average firm size and income inequality..

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at rfattaljaef@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# The Dynamics of Development: Innovation and Reallocation<sup>*</sup>

Francisco J. Buera<sup></sup> Roberto N. Fattal-Jaef<sup></sup> Originally published in the Policy Research Working Paper Series on _June, 2018._ This version is updated on _January, 2022._ To obtain the originally published version, please email <u>prwp@worldbank.org.</u> Keywords: Transition dynamics, misallocation, innovation

> *We are grateful to Richard Rogerson and Michael Peters for insightful discussions of our paper. We also thank seminar participatns a the NBER Summer Institute, the Research Institute for Development, Growth, and Economics (RIDGE), the University of Toronto, and the World Bank Development Research Group. The views expressed here do not necessarily represent the views of the World Bank Group, its aliated organizations, or any of its member countries.

> Washington University at Saint Louis, Department of Economics; fjbuera@gmail.com.

> World Bank Research Group; rfattaljaef@gmail.com.
# 1 Introduction

A large body of literature documents the pervasiveness of allocative distortions (e.g. idiosyncratic taxes and subsidies, entry frictions) in developing countries and establishes their quantitative signicance in accounting for cross-country dierences in the level of _TFP_ (Hsieh and Klenow, 2009; Bartelsman et al., 2013; Restuccia and Rogerson, 2008; Brandt et al., 2020). While their long-run implications are well understood, the role that reforms reversing these distortions play in understanding episodes of sustained growth accelerations remains relatively unexplored. The goal of this paper is to ll this gap, proposing a quantitative model of endogenous rm dynamics, characterizing its transitional dynamics in response to reforms that remove allocative distortions, and assessing its ability to account for the aggregate and micro-level properties of a concrete reform-driven growth acceleration episode: China since 1998.

In the rst part of the paper, we revisit the evidence on sustained growth accelerations to motivate the consideration of two types of reforms: those that alleviate idiosyncratic distortions (Hsieh and Klenow 2009, Restuccia and Rogerson, 2008) and those that remove obstacles to rm entry (Brandt et al. 2020). The motivation for these reforms stems from the observation of divergent dynamics of the average rm size between successful post-communist transitions and the rest of the growth accelerations. While the former is characterized by a strong decline in the average rm size, consistent with a predominance of entry distortions in the initial allocation, the opposite occurs in the latter, consistent with a prevalence of idiosyncratic distortions.

We then characterize the transitional dynamics implied by our model in response to reforms that withdraw each of these distortions. We show that the endogenous nature of rm-level dynamics allows for a protracted convergence in _TFP_ and a hump-shaped behavior of the investment rate, observations that are consistent with the data. Moreover, while the _TFP_ dynamics are protracted in both reforms, there is a decline in measured _TFP_ on impact when removing entry distortions followed by a faster recovery thereafter. At the micro-level, we nd a declining average rm size following the reversal of entry distortions, as in the experience of postcommunist transitions, and an increasing average rm size in response to the removal of idiosyncratic distortions, as in the rest of the growth accelerations.

Our quantitative contribution involves evaluating the ability of the model to ac2
count for the aggregate productivity dynamics during China's growth acceleration since 1998, episode for which we tightly calibrate the pace of reforms. We nd that when feeding the model with the calibrated path of reversal of distortions, it can account for one-third of the observed aggregate productivity gain between 1998 and 2011 while tracking closely the dynamics of rm size and earnings inequality in the transition. We further show that alleviating both distortions is crucial for replicating the micro-level features of the acceleration. Considering a partial reform that preserves the entry distortions leads to transitional dynamics that account for half as much of the aggregate productivity growth and delivers counterfactual behaviors of the average rm size and the earnings inequality.

Our baseline economy builds on Lucas (1978), which we extend to incorporate a theory of innovation along the lines of Atkeson and Burstein (2010).<sup>1</sup> There is a large household populated by a continuum of individuals, who are heterogeneous with respect to the ability to operate a rm. Entrepreneurial ability evolves endogenously as a result of entrepreneurs' investments in innovation, and exogenously as a result of productivity shocks. Individuals have a choice between working for a wage or running a rm. We consider an environment with perfect insurance, but with allocative distortions. Growth accelerations are triggered by reforms that dismantle a combination of two types of allocative distortions: i) distortions to occupational choices, modeled as taxes to the rm's prots gross of innovation expenses, and ii) distortions to the allocation of resources across rms, modeled as idiosyncratic wedges in the spirit of Restuccia and Rogerson (2008) and Hsieh and Klenow (2009).

Our exploration of reforms shows that the model can capture the qualitative features of growth accelerations in the data. In particular, the model delivers a protracted path for _TFP_ and a hump-shaped behavior of the investment rate. In reforms lifting idiosyncratic distortions, the main driver of these two features is the innovation decisions of rms. Absent any reallocation friction, the allocative eciency gains accrue immediately. Moreover, the removal of distortions encourages the most productive rms to innovate, accelerating the convergence. However, the enhanced incentives to innovate by the most productive rms coexist with the disincentive to innovate among the least productive ones, who beneted from the distorted environment. Given the stochastic nature of entrepreneurial ability, it takes time for these rms to exit the market, a force that protracts the transition. When

> 1The framework also shares elements with the work by Acemoglu et al. (2013), who emphasize the interaction between innovation and reallocation in the US Economy.

3
lifting entry distortions, on the other hand, the most relevant protracting force in the transition is given by the dierence in the distribution of entrepreneurial talent between entering rms and incumbents. The distribution of entrepreneurial ability at entry is calibrated to match the life-cycle growth of rms in the U.S. which requires a substantial gap between the average productivity of entrants and incumbents. When entry distortions are lifted, a burst of new entrepreneurs enters the market, increasing the density on the left tail of the productivity distribution. As these entrepreneurs innovate and their abilities follow their stochastic course, the distribution converges sluggishly to the stationary one, protracting the dynamics of productivity in the aggregate.

We then evaluate the quantitative implications of the model in the context of China's growth acceleration since 1998, for which we can tightly discipline the initial level and subsequent reversal of distortions. In terms of the idiosyncratic distortions, we follow Hsieh and Klenow (2009) in measuring these as wedges from the rms' optimal conditions. In particular, we compute the regression coecient between the logarithm of distortions, log ( _TFPR_ ) , and the logarithm of rm-level productivity, log ( _TFPQ_ ) , from the Annual Survey of Industries between 1998 and 2005. We consider the value for 1998 as part of China's initial stationary allocation and consider the values thereafter as dictating the speed of reforms. In terms of entry distortions, we model these as a combination of overhead production costs and taxes to entrepreneurial prots. To calibrate their values, we appeal to moments in the data on which these distortions exert a rst-order eect. Concretely, we set the prot tax and the xed cost in the distorted stationary allocation to match the average rm size and the earnings share accounted for by the richest 1% of households in China in 1998. Then, we discipline the path of reversal of prot taxes to match the average rm size dynamics during the acceleration and let the dynamics of earnings inequality be used as validation of the model's quantitative t. Starting from the distorted stationary allocation and feeding the path of reversal of both types of distortions, we nd that the model can account for one-third of the productivity growth evidence by China between 1998 and 2011, and matches the dynamics of inequality remarkably closely.

The rest of the paper is organized as follows. Section 2 relates our work to the literature, in section 3 we provide the macro and micro facts that motivate our analysis, and section 4 presents the model with and without distortions. The calibration and quantitative explorations of the benchmark reforms and the case 4
study are in section 5. Lastly, we conclude.

# 2 Related Literature

Our study provides a unied framework for thinking about the short-run and longrun implications of various types of allocative distortions, spelling out the micro and macro behavior of the economy along development paths. It is therefore related to the large body of studies that have made contributions to each of these areas.

Our work is related to the burgeoning empirical and quantitative literature on misallocation and productivity, of which Hsieh and Klenow (2009), Bartelsman et al. (2013), and Restuccia and Rogerson (2008) are salient examples. We connect to this literature from two dimensions. First, we appeal to it as motivation for assigning a prominent role to resource misallocation in the construction of an initial allocation with low productivity and income per capita in the model. We follow their methodology to measure the extent of misallocation before the onset of our transition experiments, and their dynamics afterward. Secondly, we connect with the series of papers investigating the extent to which the dynamic responses from rms, such as innovation, entry, and exit, complement the static allocative responses in shaping long-run losses in productivity. Salient works in this area are Bhattacharya et al. (2013), Da-Rocha et al. (2017), Hsieh and Klenow (2014), and Akcigit et al. (2014). Our contribution is to characterize the importance of these mechanisms in the context of a relatively unexplored phenomenon: reform-driven growth accelerations.

Our focus on growth accelerations is also related to the literature evaluating the quantitative implications of growth theories for transition dynamics. Christiano (1989), King and Rebelo (1993), and Imrohoroglu et al. (2006) emphasize the shortcomings of the frictionless neoclassical model in accounting for features of transition dynamics in post-war growth accelerations. In particular, the neoclassical model failed at capturing the protracted rise of the rate of return to capital and the humpshaped dynamics of the rate of investment. As shown by the authors, considering exogenous _TFP_ growth and adjustment costs to the capital stock proved successful in reconciling the neoclassical model with the Japanese data. Our contribution is to develop a model that can account endogenously for the joint dynamics of _TFP_ and investment rates while delivering rich rm-level implications to be validated against rm-level data. In our model, the protractedness of the _TFP_ dynamics arises from 5
convex innovation costs and stochastic innovation returns, which translate into a hump-shaped behavior of the investment rate without any friction in the accumulation of physical capital.

Our work is also close to the study of growth accelerations in Buera and Shin (2013). The authors develop a theory of transitions featuring heterogeneous entrepreneurs, entry and exit to production, and credit market imperfections. Motivated by the experience of seven Asian economies, the authors show that in the presence of nancial frictions that delay capital reallocation, transition paths triggered by the removal of idiosyncratic distortions are characterized by paths of investment and interest rates that resemble the data. The model also yields an endogenous path for _TFP,_ although on this front the model's convergence is substantially faster than in the data. Our relationship to this paper is twofold. Firstly, we update and extend the characterization of growth acceleration episodes, highlighting the divergent patterns between average rm size dynamics in post-communist transitions and the remaining cases. This distinction plays a critical role in motivating our consideration of entry and idiosyncratic distortions. Secondly, our model provides a complementary mechanism through which macroeconomic dynamics can depart from those of the standard neoclassical model. Rather than emphasizing barriers to factor reallocation, we show that the interaction between the economy's incentives to accumulate tangible capital, through household's investment decisions, and intangible capital, from rms' innovation eorts, can generate transition paths for output, investment, and _TFP_ similar to those in the data in a frictionless setup.

The consideration of tangible and intangible forms of capital relates our paper to the work of Atkeson and Kehoe (2007). The authors develop a theory of development in which life-cycle dynamics are driven by age-dependent, exogenous stochastic accumulation of organizational capital and in which entering rms embody the best available technology. The trigger of development in their model stems from a sudden permanent improvement in the technologies embodied in new plants. Despite the resemblance of our model to theirs, there are several points of departure. First, as in the data, the life-cycle dynamics of rms in the frictionless steady state of our model are dierent from those of the distorted equilibrium. In turn, these dierences are generated endogenously, from a theory of innovation that connects rm growth to allocative frictions. Secondly, the predictions about entry along the transition path in our model dier from those in Atkeson and Kehoe (2007). In the case of idiosyncratic distortions, entry is ineciently encouraged by subsidies in the pre-reform 6
steady state of our economy, which implies that our development paths are characterized by reductions in entrepreneurship, and increases in the average rm size. Lastly, because of our focus on growth accelerations, we follow a dierent strategy for parameterizing the pre-reform stationary equilibrium, appealing to rm-level data in low-income countries to discipline the choice of distortions that hinder output and productivity.

Lastly, our consideration of China's growth acceleration as a case study merits a discussion of the closely related work of Song et al. (2011). The authors propose a model with a private entrepreneurial sector and state-owned enterprises to understand the behavior of the savings rate, the rate of return on capital, and capital ows, during China's economic transition. As in Buera and Shin (2017), their emphasis is on nancial frictions, which limit the access to credit by private entrepreneurs and encourage the accumulation of internal sources of nancing for investment. Credit is mostly devoted to state-owned enterprises. In a context of heterogeneous but exogenous rm-level productivity, the authors show that the downsizing of the public sector leads to excess demand for nancial assets that result in capital outows. In our paper, we approach the Chinese acceleration from a dierent angle. While we propose a more reduced-form specication of entry distortions to implement features of a communist regime, we leverage this tractability to characterize more sharply the interaction between the underlying distortions and the innovation incentives of rms in a context of costless reallocation.

# 3 Motivating Facts

We set the stage for the quantitative model presenting some evidence characterizing aggregate and micro-level features of economic transitions. We consider separately two types of convergence episodes: sustained growth accelerations in the post-war period, identied appealing to the methodology of Hausmann et al. (2005), and postcommunist transitions.<sup>2</sup> As we shall explain in greater detail below, we proceed in

> 2In Hausmann et al. (2005) a growth acceleration starts in year _t_ only if the following three conditions are met: (1) the average growth rate in the seven ensuing years (years _t_ through _t_ +6 ) is above 3.5 percent; (2) the average growth rate in the seven ensuing years is at least two percentage points higher than in the preceding seven years (years _t −_ 7 to _t −_ 1 ); and (3) the output per-capita in the ensuing seven years is above the previous peak. If more than one contiguous years satisfy all three conditions, the start of the growth acceleration is chosen to be the one for which a trend regression with a break in that year provides the best t among all eligible years, in terms of the F-statistic. A sustained growth acceleration is one for which the average growth rate in the decade

7
this way because of the fundamental dierences in the adjustments occurring at the micro-level between these episodes, dierences that we want to carefully account for in the theory that we develop later.

# 3.1 Aggregate and Firm-Level Features of Accelerations and PostCommunist Transitions

Consider rst the dynamics of aggregate variables. Figure 3.1 shows the average behavior of TFP and investment rates in our selection of growth accelerations and post-communist transitions. The left panel plots the average dynamics of TFP. In the vertical axis, units are measured relative to the average value of TFP in the 5 years preceding the take-o.<sup>3</sup> For post-communist countries, we assume that all transitions start in 1990, so the corresponding line illustrates the ratio between the average of TFP across countries relative to the average value between 1985 and 1990.

Despite the initial slump in the case of post-communist transitions, both TFP and investment rate increase over time. This pattern of behavior has been noted before in the literature as a limitation of the standard neoclassical growth model, which is silent about TFP dynamics and predicts a decreasing path in the investment rate when converging towards an equilibrium with higher capital stock. In this context, one of the goals of our paper is to attempt to reconcile theory and data, by developing a quantitative model of transitions with endogenous TFP and investment rate dynamics.<sup>4</sup> While exhibiting similar characteristics in the aggregate, acceleration episodes and post-communist transitions dier notably in the adjustments taking place at the micro-level, in particular regarding the size distribution of rms. To see this, gure 3.2 reproduces the dynamics of the average size of manufacturing rms, in following a growth acceleration (years _t_ + 7 through _t_ + 16 ) is above 2 percent. We update the identication of growth accelerations applying the methodology to the most recent data in Penn World Tables 10.0 Zeileis (2021). The complete list of post-communist countries and the list of acceleration episodes picked up by the methodology is presented in Appendix A.

> 3Since accelerations occur at dierent dates in each country, we construct a measure of average TFP dynamics as follows. For each country, we construct the time series of TFP during the acceleration years and we express them relative to the average value of TFP in the 5 years preceding the start of the acceleration; and then we average across countries.

> 4Christiano (1989), King and Rebelo (1993), Chen et.al. (2006), and Buera and Shin (2013) are salient examples of papers that have noted the conict between the neoclassical growth model and macroeconomic data on transitions and developed extensions of the neoclassical model to bridge the gap between the two. See the literature review for a more thorough explanation of how our paper relates to this literature.

8
Figure 3.1: Macroeconomic Features of Acceleration Episodes and Post-Communist Transitions <!-- Start of picture text --> TFP Investment Rate<br>Sustained Acceleration<br>Post−Communist Acceleration<br>All Post−Communist<br>−5 0 5 10 15 20 25 30 −5 0 5 10 15 20 25 30<br>Period Period<br>0.20<br>2.0 0.15<br>0.10<br>1.5<br>0.05<br>Relative To Pre−Reform 0.00<br>Difference from Pre−Reform<br>1.0<br>−0.05<br>−0.10<br><!-- End of picture text --> The left panel plots _TFP_ dynamics for the simple average of post-communist transitions and acceleration episodes. The right panel illustrates the average of investment rates. The horizontal axis measures years with respect to the beginning of each episode, which we label period. For post-communist transitions we date such period to be 1990, while for growth accelerations, period is given by the country's specic date which we identify, using the methodology, as the start of the growth take-o. _TFP_ dynamics are measured relative to the _TFP_ level in period while the investment rates are expressed as absolute deviations from the period levels. A complete list of countries in each group is presented in Appendix A.

terms of employment, for the subset of countries for which we were able to gather time-series average size data. We consider three post-communist cases, Hungary, Romania, and China, and four acceleration episodes, Singapore, Japan, Chile, and Korea. The former group of countries is plotted in the left panel and the latter group in the right one.

Figure 3.2 shows a divergence in the behavior of average rm size across episodes. While the average size increases by a factor of two 20 years into the acceleration, the typical rm shrinks by almost 70% in the post-communist case.

Several authors studied the behavior of the industrial sector in post-communist economies and emphasized the declining role played by large state-owned enterprises in favor of small privately-owned businesses. Maddison (1998) is perhaps the most eloquent of these explorations, showing data about the re-organization of production in China and the economies of former Soviet Union countries.<sup>5</sup> Our contribution is

> 5The following quote from Maddison (1998), referred to China, illustrates this point: There has been a huge expansion in industrial activity outside the state sector. In 1978 there were 265 000 collectives. By 1996 there were l.6 million. The number of private enterprises rose from zero to

9
Figure 3.2: Average Size Dynamics during Acceleration Episodes and Post-Communist Transitions <!-- Start of picture text --> Hungary (1992) Singapore (1967)<br>Romania (1992) Japan (1949)<br>China (1992) S. Korea (1961)<br>Chile (1980)<br>Average<br>0 5 10 15 0 5 10 15 20<br>Periods After Liberalization Periods After Liberalization<br>1.0 5<br>0.8 4<br>0.6 3<br>0.4 2<br>Relative to Time Zero (T0) Relative to Reform Date<br>0.2 1<br><!-- End of picture text --> Left panel illustrates average size dynamics for post-communist countries. Acceleration episodes are plotted on the right. Horizontal axes measure years after period 0, which corresponds to the year of reforms in the case of accelerations, and the rst available year with rm level data in the case of post-communist transitions. Given the substantial dierences in average size dynamics across growth accelerations, we also plot the behavior of the simple average of average size dynamics across these episodes. In all cases, the vertical axes measure the ratio of the average size relative to period 0.

to extend this analysis to a more recent period and to revisit the previous ndings through the lens of newer datasets.

Similarly, the fact that average rm size tends to increase with development has also been noted before in the literature. In fact, our data for average size dynamics during accelerations draw exactly from that in Buera and Shin (2013). What has not been equally emphasized before is that divergences from this average behavior can be driven by the nature of the underlying transformations taking place in the economy and that one such transformation that diers from the average is a post-communist liberalization.

# 3.2 From the Data to a Theory of Transitions

Growth accelerations tend to be highly unpredictable. However, large-scale economic reforms constitute one of the few successful predictors of growth acceleration, as shown by Hausmann et al. (2005) in the context of reduced-form regressions and by 6.2 million. The bulk of these are small-scale operations, most of them in rural areas, and run by individuals, townships, and village level governments. A major reason for the success of these new rms is that their labor costs are much lower than in state-owned enterprises, their capitalization is much more modest, and they are freer to respond to market demand. Many benet from special tax privileges granted by local authorities. 10
Buera and Shin (2013)'s narrative of the wave of reforms that preceded the growth accelerations in the so-called miracle economies. Supported by this evidence, this paper characterizes development dynamics that are triggered by economic reforms, dened as the removal of distortions in the economy.

The patterns of development described above, particularly the divergent dynamics in the average rm size, guide the identication of the family of distortions that are adequate for thinking about the allocations before each type of acceleration episode. For average growth accelerations, we interpret the data as suggestive of the predominance of allocative distortions and their dismantlement in understanding their growth dynamics.<sup>6</sup> The evidence shows that allocative distortions, identied as reduced form idiosyncratic wedges, tend to tax productive rms more heavily than unproductive ones, a feature that facilitates the survival of low productivity rms, discourages innovation, and, ultimately, reduces the scale of operations of the rms.<sup>7</sup> When dismantled, these types of distortions deliver dynamics of the average rm size that are consistent with what we observed for the average acceleration. For post-communist transitions, on the other hand, the dynamics of the average rm size suggest that barriers to the creation and operation of rms constitute a more prevalent source of distortion.<sup>8</sup> Distortions to entry concentrate production in fewer and larger rms and increase the average rm size, as in the allocation of centrally planned economies. Their dismantlement, then, is consistent with a spreading of production into more and smaller rms, which is what we found in the data. While the ability to replicate the patterns of micro-dynamics in the data will emerge by construction from the choice of distortions, it is the quantitative t of this and other predictions of the theory as well as the relative contribution of the innovation and reallocation channels, that we seek to validate and uncover in the quantitative analysis.

> 6Throughout the paper, with average growth acceleration, we refer to all the sustained growth episodes that we identify from the data that are not originated by the dismantlement of a communist regime.

> 7The correlated nature of idiosyncratic distortions with respect to the distribution of rms' productivity is a pervasive property of resource misallocation around the world. Hsieh and Klenow (2007) rst established this fact in the context of China, India, and the United States. Subsequent applications of this methodology in Latin America (Neumeyer and Sandleris, 2009 for Argentina; Casacuberta and Gandelman, 2009 for Uruguay, Camacho and Conover, 2010 for Colombia and Chen and Irarrazabal, 2015 for Chile) and Sub-Saharan Africa (Cirera et al., 2017) verify the generality of this feature of the data.

> 8More direct evidence is provided by Brandt et al. (2020), who show that entry barriers are the salient friction for explaining cross-regional growth disparities in China.

11
# 4 Model

We study an economy populated by a single household composed of a continuum of agents. These agents are heterogeneous with respect to their ability to operate a production technology and run a business. The head of the household makes an occupational choice on behalf of each agent, choosing either to assign her to entrepreneurship and earn a risky prot or make her participate in the labor force, in exchange for a xed wage. Each individual commits to participate in a risk-sharing agreement that insulates individual consumption from uctuations in idiosyncratic income. In addition to occupational choices, the head of household chooses aggregate consumption and investment to maximize lifetime utility.

There are endogenous and exogenous forces for rm dynamics and resource reallocation. The endogenous component stems from entrepreneurs' investments in a risky innovation technology that controls the expected evolution of entrepreneurial ability over time, and their entry and exit decisions. The exogenous element results from idiosyncratic productivity shocks around the expected path. It is the endogenous decision of entrepreneurs to innovate together with the decision to enter and exit entrepreneurship that connects the life cycle and the size distribution of rms with policies and distortions to factor allocation.

We rst present the details of the frictionless economy, which we take as a reference for the calibration of preferences and technological parameter values which are kept constants across countries. These parameters are calibrated to match data on the dynamics of rms and income inequality in the US, a relatively undistorted economy. Then we introduce an extension with distortions and calibrate it using information from growth accelerations.

## 4.1 Consumption and Savings Problem

The assumption of perfect sharing of idiosyncratic risk allows us to separate the consumption/investment decision from the occupational choices.

Taking wages and occupational choices as given, the household chooses consumption and investment in order to solve the following problem: 12
subject to Aggregate labor supply and aggregate prots, _L_<sup>_s_</sup> _t_<sup>andΠ</sup><sup>_t_respectively, are dened</sup> as follows: and where _ot_ ( _z_ ) is the outcome of the occupational choice of a household member with productivity _z_ , being equal to 0 if she is a worker, and 1 is she is an entrepreneur; and _Mt_ ( _z_ ) denotes the endogenous distribution of agents over productivity levels. All these objects will be characterized in detail below.

# 4.2 Occupational Choice

We assume that the head of the household chooses occupations for its members every period. Furthermore, we assume that movements in and out of entrepreneurship are costless. Therefore, the decision to allocate an individual into working for a wage or becoming an entrepreneur amounts to comparing the values associated with each activity.

When selected into entrepreneurship, agents produce the nal good combining their idiosyncratic productivity, _z_ , together with capital and labor into a CobbDouglas production function with decreasing returns to scale:<sup>9</sup> We assume that there are perfectly exible labor and capital rental markets every period, so that both capital and labor can be adjusted freely in response to changes in aggregate or idiosyncratic conditions. It follows that capital and labor choices are determined by the following static maximization problem:

> 9 The introduction of the productivity term raised to the (1 _− α − θ_ ) power is a normalization that simplies the description of the stochastic process for productivity. As we will show below, rms' capital and labor demands become proportional to _z_ when productivity is introduced in this way in the production function. This allows us to map the space of productivity levels _z_ directly into the space of labor and capital demands.

13
which yields the following expressions for optimal capital and labor demands: and The indirect prot function associated with optimal capital and labor demands is given by: Besides production decisions, entrepreneurs make investments in innovation. We adopt a process of technology upgrading and downgrading similar to that in Atkeson and Burstein (2010). Specically, we assume that the growth rate of idiosyncratic productivity follows a simple binomial process, with an expected rate of growth that is determined by the rm's investments in innovation, and an exogenous standard deviation.

Let ∆ denote the change in the logarithm of productivity that a rm can experience from one period to the other. Entrepreneurs use a research technology that yields a probability _p_ of a technological upgrade (and probability 1 _− p_ of a downgrade) in return to investing _χ_ ( _p, z_ ) units of labor. We assume a convex function for the cost of innovation of the following form: Notice that the innovation cost is scaled by the current productivity of the entrepreneur. As we will explain below, this is an important assumption that allows the model to be consistent with innovation patterns of large rms in the U.S, which is our target economy for the calibration of parameters that are kept constant across economies. We will also explain the relevance of the scale parameter _μ_ and the elasticity parameter _φ_ to replicate properties of the size distribution and rm life-cycle dynamics in the U.S.<sup>10</sup> Taking capital and labor demands from the static prot maximization problem,

> 10The process for idiosyncratic productivity can be interpreted as a binomial approximation to a geometric Brownian motion, with an exogenous standard deviation ∆ , and endogenous drift (2 _pt_ ( _z_ ) _−_ 1) ∆ .

14
entrepreneurs' innovation-decision solves the following optimization problem: with _vt_<sup>_E_(</sup><sup>_z_)standing for the value of an entrepreneur with productivity</sup><sup>_z_in period</sup><sup>_t,_</sup> and _vt_ ( _z_ ) denoting the value of an individual in period _t_ with productivity _z_ , facing the decision to become an entrepreneur or working for a wage. We will come back to this value below, once we characterize the value of a worker.

Unlike entrepreneurs, we abstract from modeling workers' eorts in developing entrepreneurial ability. We assume that while working for a wage, agents get a random draw of entrepreneurial ability from a known stationary distribution _F_ ( _z_ ) that they can exploit the following period if they nd it protable to do so. In particular, we assume that an individual in the labor force with current entrepreneurial ability _z_ gets to keep it for the following period with probability _ψ_ , and gets a random draw from the distribution _F_ ( _z_ ) with probability (1 _− ψ_ ) . The same process governs the evolution of the entrepreneurial ability of agents that join the labor force after having exited from operating a business. These agents will keep their accumulated stock of knowledge with probability _ψ,_ and will get random draws with probability (1 _− ψ_ ) .

Our probabilistic representation of the arrival of entrepreneurial ideas among workers allows us to be consistent with two key properties about the behavior of entrants in the data: 1) the rate of establishment entry and exit, and 2) the average size of entrants relative to incumbents. We will see below that consistency with these facts is important for the properties of a rm's life-cycle dynamics, and for shaping the responses to reforms.

It follows from the above that the value of a worker is simply dened by the wage rate in the period, plus the discounted expected value of resetting occupations in the following period: 15
with the value of an agent before making an occupational choice given by

# 4.2.1 Aggregation and Denition of Equilibrium

At any given point in time, all individuals in the economy will be distributed over the space of entrepreneurial productivity. We denote the fraction of individuals with productivity less than or equal to _z_ with _Mt_ ( _z_ ) _._ We need to characterize the evolution of this distribution to be able to aggregate individual decisions and compute equilibrium prices.

Say we start with a given distribution _Mt_ ( _z_ ) at the beginning of period _t._ Entrepreneurs move across productivity levels in accordance to their innovationdecisions, while workers do so in response to the stochastic process of productivity. Combining these processes leads to the following law of motion for the distribution of agents across productivity levels: The rst two terms refer to the individuals that worked as entrepreneurs in period _t_ and transition to (remain in) the set with productivity in [0 _, z_ ] after a period. Those with productivity level _x ∈_ � _z, ze_<sup>∆�</sup> downgrade to _xe_<sup>_−_∆</sup> _< z_ with probability 1 _− pt_ ( _x_ ) , and those with productivity level _x ∈_ � _ze_<sup>_−_∆</sup> _, z_ � upgrade to _xe_<sup>∆</sup> _> z_ with probability _pt_ ( _x_ ) . The last two terms refer to workers. A fraction 1 _− ψ_ of workers with ability less than _z_ get a new productivity. Among all the workers that get a new productivity, a fraction (1 _− ψ_ ) _F_ ( _z_ ) have a new draw less than or equal to _z_ .

A competitive equilibrium in this economy is given by sequences of choices by the head of the household _{ct, kt_ +1 _, ot_ ( _z_ ) _}_<sup>_∞_</sup> _t_ =0<sup>;sequencesofentrepreneurs'decisions</sup> _{lt_ ( _z_ ) _, kt_ ( _z_ ) _, pt_ ( _z_ ) _}_ ; sequences of interest rates and wage rates _{rt, wt}_ ; and a distribution of agents over productivity _{Mt_ ( _z_ ) _}_ ; such that given an initial capital stock _K_ 0 and a given distribution of talent draws for workers _F_ ( _z_ ) , household's and rm's decision solve their dynamic optimization problems and capital and labor markets 16
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# 4.3 Introducing Distortions

As mentioned earlier, our approach for characterizing transitions is to emphasize the role of distortions. The exploration of growth acceleration episodes and postcommunist transitions suggested that we investigate idiosyncratic distortions that misallocate resources across rms and entry distortions that distort the occupational choices and increase the average rm size.

Idiosyncratic distortions are modeled as productivity-dependent taxes to the rms' revenues, while entry distortions are implemented through taxes to the profits of the rms gross of innovation expenses and overhead production costs.<sup>11</sup> The productivity dependence of idiosyncratic distortions is a pervasive feature of misallocation in developing countries and has been used to characterize distortions in many studies<sup>12</sup> . The prot taxes, on the other hand, are less standard. We appeal to taxes to the prots of rms, gross of innovation expenses, to capture the barriers to the creation of private enterprises that characterize the functioning of centrally planned economies. In the model, this type of taxation discourages entrepreneurship, hinders private innovation, and concentrates production into fewer and bigger rms. In addition, a prot tax is a natural instrument to capture the nature of a communist regime, where prots are ultimately collectivized, or captured by the party elite. Fixed production costs are a complementary instrument to prot taxes that help the model replicate the micro-level features of China's economy at the onset of its economic liberalization. In particular, these instruments allow us to jointly capture the average rm size and the concentration of earnings among the richest households prior to the reforms.

Formally, let _τt_ ( _z_ ) and _τt_<sup>_π_denotetherevenueandprottaxratescorresponding</sup> to a rm with productivity _z_ in period _t_ . Notice that the prot tax is identical across rms, while revenue taxes are idiosyncratic to the rm's productivity, according to the following function:

> 11Notice that our analysis seeks to capture the degree of misallocation stemming from the correlation of distortions with productivity only, without consideration of uncorrelated dispersion. Uncorrelated dispersion would further misallocate resources and drag TFP, and their removal help account for the dynamics of TFP. In this sense, our result should be interpreted as a lower bound on the contribution of idiosyncratic distortions.

> 12See, for instance, Bento and Restuccia (2017) and Fattal Jaef (2019)

18
The productivity-elasticity of the distortion prole _υt_ controls the degree of a linear relationship between the logarithm of the marginal revenue product of the rm ( _TFPR_ ) and the logarithm of physical productivity ( _TFPQ_ ) . As explained in greater detail in the calibration section, we appeal to China's rm-level data to estimate the regression coecient between these variables to discipline its parameterization. The productivity index _zI,t_<sup>(1</sup><sup>_−α−θ_)</sup> separates rms into those that get a revenue subsidy from those that get a revenue tax and hence determines the average distortion in the economy. This parameter is neutral for the resource misallocation that the distortions induce, but shapes the rate of return to capital in the distorted allocation, and therefore the investment rate. We explain later how we calibrate this parameter in the context of the benchmark reforms and in China's case study.

In terms of the prot tax, it can be shown that a at prot tax has a direct eect on occupational choices, innovation, and, thereby, the average rm size and inequality. We appeal to data on average size and inequality statistics to calibrate the prot tax in the quantitative analysis.

We now turn to incorporating the prot and revenue taxes into the optimization problems of the agents. Consider rst the value of an entrepreneur with productivity _z_ and associated revenue and prot taxes _τt_ ( _z_ ) and _τt_<sup>_π_.This is given by the following</sup> expression: which in addition to the tax distortions, also reects the xed cost of production _fc_ Prot taxes have a direct eect on the rm's incentives to innovate but have no implication for the entrepreneur's choice of labor and capital demands. Revenue taxes, on the other hand, do interfere with factor demand and protability, as reected in the rm's static prot maximization problem: with optimal policies 19
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The misallocation eect of revenue taxes is manifested in the aggregation of individual productivity, which now reects the ineciency in the distribution of capital and labor across producers. The dynamic eects of revenue and prot taxes, which operate through distortions to innovation, are captured in the distribution of rms across productivity levels _Mt_ ( _z_ ) .

# 5 Quantitative Exploration

We organize the presentation of the quantitative analysis as follows. We rst characterize the response of the economy to reforms that dismantle idiosyncratic distortions or entry distortions in isolation. We refer to these as the benchmark reforms. The distinguishing features of these reforms are that they are implemented abruptly (as opposed to through a smooth pace of reversal as in the case study below) and that their magnitude is not calibrated to match any specic episode but are rather disciplined to replicate broad features of the average growth acceleration. We appeal to the benchmark reforms to validate our choice of entry and idiosyncratic distortions as instruments to characterize the heterogeneous behavior of the rm size distribution across types of growth accelerations, and to more clearly illustrate the mechanisms driving the transition depending on the type of reform.

We then evaluate the quantitative merit of the theory in the context of China's economic liberalization since 1998. This case study presents an opportunity to adequately evaluate our theory since we count with data to tightly calibrate the degree of distortions at the initial conditions and to discipline the rate of reversal of the distortions along the transition paths. Using our quantitative theory as measurement device, we assess how much of the observed _TFP_ growth since China's liberalization can be accounted for by the calibrated reversal of the distortions.

## 5.1 Calibration

We split the presentation of the parameter values into those that remain unchanged throughout all our quantitative explorations, and those that vary depending on us considering the benchmark reforms or China's case study.

21
# 5.1.1 Parameters Common Across Economies

There are 8 parameters that remain invariant across the types of economies that we consider: the coecient of relative risk aversion _σ,_ the labor and capital shares in production _α_ and _θ,_ the subjective discount factor _β_ , the scale and the convexity parameters in the innovation cost function _μ_ and _φ_ , the capital depreciation rate _δ_ , and the arrival rate of entrepreneurial ability among worker _ψ_ . In addition, we must specify and parameterize the distribution of entrepreneurial ability types among workers. Parameters are calibrated within the stationary equilibrium of the undistorted economy targeting moments in the U.S. economy.<sup>13</sup> For the coecient of relative risk aversion, we set _σ_ = 1 _._ 5 , which is standard in the macroeconomics literature. We set _β_ = 1 _/_ (1 + 0 _._ 04) , to target a 4% yearly interest rate, and set the annual capital depreciation rate at _δ_ = 0 _._ 06 . In terms of factor shares in the production technologies, given a value of the span of control 1 _− α − θ_ , we calibrate _α/_ ( _α_ + _θ_ ) = 1 _/_ 3 , so that 1 _/_ 3 of the income going to nonentrepreneurial factors is paid to to capital. For the probability that workers get a new draw of entrepreneurial ability, (1 _− ψ_ ) , we set _ψ_ = 0 so that workers update their entrepreneurial talent every period.

The span of control _α_ + _θ_ is calibrated jointly with the parameters of the innovation cost function, _μ_ and _φ_ , and the innovation step ∆ , to match the concentration of earnings in the top 1% of the population, the employment share in the top 10% of the rm size distribution, the average employment ratio between rms aged 21-25 to 1 year old, and the log dispersion of the distribution of employment growth rates for large rms. Finally, we assume that the distribution of entrepreneurial abilities is Pareto, with a productivity lower bound equal to one and a tail parameter _η_ that we calibrate to match the ratio between the average employment of entrants relative to the average employment of incumbents.<sup>14</sup> The parameter values resulting from this strategy are reported in table 1

> 13As a robustness check, we solved for a distorted version of the U.S. economy, keeping parameters values xed at the baseline calibration, but feeding an estimate of the productivity-elasticity of idiosyncratic distortions for the U.S., which Hsieh and Klenow (2007) report to be equal to _ν_ = 0 _._ 138 _._ We nd that these mild distortions generate a weak contraction in the _TFP_ relative to an undistorted benchmark, in the order of 5%

> 14In appendix F, we further explore the goodness of t of the Pareto assumption comparing the size distribution of rms at entry with the data

22
Table 1: Calibration of Common Parameters across Economies

||US data|Model|Parameter|
|---|---|---|---|
|Top 1 % Earnings Share|18.5%|18.5%|_α_+_θ_ = 0_._71|
|Top 10% Employment Share|0.76|0.77|_μ_= 4_._8_e −_05|
|Employment Age 21-25 relative to Age 1|3.95|3.83|_φ_= 10|
|Std Dev. Employment Growth rate|0.25|0.25|∆= 0_._25|
|Empl. Ratio Entrants to Incumbents|18.9%|18.9%|_η_ = 4_._46|

The top 1% earnings share for the US is taken from Khun and RÃos-Rull (2015). We report the average of the top 1% share between 2007 and 2013. The top 10% employment share, the average employment ratio between 21-25 and 1 year old rms, and the average employment ratio between entrants and incumbents were computed from Business Dynamics Statistics database for the year 2007. Numbers are for the manufacturing sector. Standard deviation of employment growth rates for large rms are reported in Atkeson and Burstein (2010).

# 5.2 Reforms

We now turn to discuss the strategy for calibrating the parameter values governing the distortions in the model and their paths of reversal in the reforms. These are given by a sequence of slopes and scale parameters of the revenue tax prole, _υt_ and _ZI,t_ , a sequence of prot taxes, _τt_<sup>_π_,andavalueforthexedcostsofproduction</sup> _fc_ . We rst specify the calibration strategy of these objects in the context of the benchmark reforms, and later describe their connection with the data for the case study.

## 5.2.1 Calibration of Benchmark Reforms

We consider two types of benchmark reforms, one that dismantles idiosyncratic distortions, which we found pertinent for thinking about average acceleration episodes, and one that reverses taxes to the prots of the rms, with which we characterize the barriers to rm entry of communist regimes. The idiosyncratic distortions and the prot tax rate are calibrated to match the observed growth in _TFP_ that occurs between the starting and the ending point of the average acceleration in the data. Specically, we construct the target by subtracting a linear trend to the solid black line in the left panel of gure 3.1. The linear trend is a 0.85% annual growth rate, which corresponds to the average growth of _TFP_ in the United States since 1980, as measured from the Penn World Tables 10.1. The resulting target is a _TFP_ growth of 20%. Then, we identify the slope of the idiosyncratic distortion prole and the prot tax rate that generates, between the distorted and undistorted steady states, a productivity growth of 20% as in the data. The scale parameter _ZI_ in the idiosyn23
cratic distortion prole is calibrated to keep the capital-output ratio xed across the stationary allocations. The idea is to evaluate the dynamics of investment without the interference of distortions in the rate of return to capital<sup>15</sup> . We dispense from xed production costs in the benchmark reforms, setting _fc_ = 0 _._ The reform consists of a once and for all withdrawal of each distortion. The resulting parameter values of the distortions are reproduced in table 2 Table 2: Calibration of Distortions in Benchmark Experiments

|Parameter Value<br>Target|
|---|
|Productivity-elasticity of distortions _υ_<br>0.35<br>_TFP_(_undistorted_)<br>_TFP_(_idiosyncratic−distortions_) <sup>= 1</sup><sup>_._2</sup>|
|Prot tax _τ _<sup>_π_</sup><br>0.74<br>_T F P_ (_undistorted_)<br>_T F P_(_profit−taxes_) <sup>= 1</sup><sup>_._2</sup>|
|Scale parameter _ZI_<br>5.47<br>_K_<br>_Y_ <sup>= 2</sup><sup>_._36</sup>|
|Fixed cost _fc_<br>0|

Parameter values apply to model economies with one type of distortion at a time. Values are set so that model's long run growth in _TFP_ from achieving the undistorted steady state allocation matches the 20% detrended _TFP_ growth observed in the data for an average acceleration.

# 5.2.2 Calibration of the Case Study

For the case study, we pursue a richer calibration that enables us to pin down parameter values for the combination of distortions at the onset of China's acceleration and their rate of reversal throughout the transition. As a reminder, we are modeling China's communist regime as a combination of taxes to the prots gross of innovation expenses and xed production costs, which mimic the barriers to entry and the egalitarian forces that characterize these regimes, and idiosyncratic distortions.

The idiosyncratic distortion prole is parameterized by the productivity-elasticity _υt_ and the scaling parameter _ZI,t_ . We calibrate the productivity-elasticity estimating the regression coecient between the logarithm of _TFPR_ and the logarithm of _TFPQ_ between 1998 and 2005. The data stems from the Annual Surveys of Industrial Production for the years 1998 through 2005. These surveys are conducted by the National Bureau of Statistics covering the universe of industrial rms (both

> 15Recall that _ZI_ determines the average value of the idiosyncratic distortion in the economy, which exerts a direct eect on the marginal return to capital.

24
privately-owned and state-owned) with sales above 5 million RMB (equivalent to roughly $600,000). We take the estimate for 1998 as the one characterizing the initial stationary allocation. We dene _TFPR_ and _TFPQ_ exactly as in Hsieh and Klenow (2009). The scaling parameter _ZI_ , which shapes the average distortion in the economy, has a direct mapping on the capital-output ratio in the stationary equilibrium. Hence, we calibrate its values in 1998 and 2011 to replicate China's capital-output ratio in these years. The parameter values governing the idiosyncratic distortions in the initial and terminal steady states are reported in table 3 The prot tax and the xed production cost are calibrated to match statistics of the rm size and earnings distribution. As said earlier in the text, these reducedform instruments are intended to tractably capture the various elements that hinder private entrepreneurial activity and compress the earnings distribution in a communist regime such as China's in 1998. Our strategy for their calibration is to appeal to observable outcomes on which these instruments exert a rst-order eect. To this end, we set the average rm size and the earnings share accounted for by the richest 1% of households in 1998 as empirical moments. We target an average rm size of 3.1 times the average rm size in the U.S. manufacturing sector and a top earnings share of 8% which we draw from the World Inequality Database (Piketty et al. 2019). The strategy results in a xed production cost of _fc_ = 48 _._ 1 , equivalent to 57% of the average prots gross of innovation expenses and xed costs in the initial steady state, and a prot tax _τ_ 0<sup>_π_= 0</sup><sup>_._4.Theseparametervaluesarealsoreportedintable3</sup> The pace of reversal of the distortions during the reform is disciplined as follows. For idiosyncratic distortions, we t a linear trend to the time series of regression coefcients of _log_ ( _TFPR_ ) and _log_ ( _TFPQ_ ) estimated from the rm-level data between 1998 and 2005. The linear trend allows us to project the evolution of idiosyncratic distortions beyond the estimating period into 2011, which is the last year in our aggregate data. We assume that in the terminal steady-state, idiosyncratic distortions stabilize at the level projected for 2011. The evolution of the scaling parameter _ZI,t_ is set to converge linearly between 1998 and 2011 from the initial an the terminal values. In terms of the prot taxes, we also feed a linear path of reversal disciplined to match the pace reduction of the average rm size in China during the acceleration. In this way, while the average rm size dynamics will be replicated by construction, the implied dynamics of inequality will be untargeted, and hence can be used as validation for the model's mechanisms. In terms of the xed production cost, we assume they remain at the initial steady state's level, in reection of the 25
Table 3: Calibration of Distortions in China's Initial and Terminal Stationary Equilibrium.

|||China's C|ase Study||
|---|---|---|---|---|
||Value in<br>1998|Source/Target|Value in<br>2011|Source/Target|
|Productivity-<br>Elasticity of<br>Distortions, _ν_|0.578|Regression coecient<br>_log_(_TFPR_) on<br>_log_(_TFPQ_), Annual<br>Surveys of Industrial<br>Production 1998|0.36|Projected regression<br>coecient of<br>log (_TFPR_) on<br>log (_TFPQ_) for 2011|
|Scale-Parameter<br>of Distortions, _ZI_|10.05|Capital-output ratio<br>1998|32.07|Capital-output ratio<br>2011|
|_τ _<sup>_π_</sup>|0.4|Earnings Share top 1%<br>richest Households,<br>World Inequality<br>Database|0|Assumption|
|||Average rm size in||Assumption based on|
|_fc_|48.1|China relative to the<br>U.S. in 1998, equal to<br>3.1|48.1|persisting entry<br>Barriers Brandt et al.<br>(2020)|

Note: The data for the estimation of regression coecients between _log_ ( _TFPR_ ) and _log_ ( _TFPQ_ ) stems from the Annual Survey of Industrial producers for the years 1998-2005. The capital-output ratios are drawn from the Penn World Table Database, version 10.0 Zeileis 2021, Feenstra et al. 2015. The earnings data for China in the World Inequality Database draws from Piketty et al. 2019.

pervasive entry distortions that still characterize China's economy (Brandt et al. 2020). The resulting paths of the productivity-elasticity of idiosyncratic distortions and the prot taxes are plotted in gure 5.1.

# 5.3 Benchmark Reforms: Idiosyncratic Distortions vs Entry Distortions

We begin the quantitative analysis by exploring the transition dynamics implied by reforms that either dismantle entry or idiosyncratic distortions. The objective of this exercise is to more clearly illustrate the mechanisms driving the transition depending on the type of reforms. Figure 5.2 illustrates the dynamics of _TFP,_ average size, the 26
Figure 5.1: Calibration of Distortions and Reforms <!-- Start of picture text --> 0.6 0.6<br>G<br>G GGG<br>G<br>GG<br>0.4 0.4 G<br>0.2 0.2<br>G Estimated Value<br>G Linear Fit<br>0.0 0.0<br>2000 2005 2010 2015 2020 2000 2005 2010 2015 2020<br>Year Year<br>Profit Tax<br>TFPR−TFPQ elasticity<br><!-- End of picture text --> NOTE: The left panel illustrates the regression coecient between _log_ ( _TFPR_ ) and _log_ ( _TFPQ_ ) for the period 1998-2011. The dots correspond to the point estimates from China's Annual Survey of Industrial Production for 1998 through 2005. We dene _log_ ( _TFPR_ ) and _log_ ( _TFPQ_ ) as in Hsieh and Klenow 2009. The solid line illustrates a linear t on the estimated values projected on to 2011. We assume that reforms stabilize in 2011, and the productivity-elasticity of idiosyncratic distortions remain constant a the 2011 level. The initial steady state is represented by the elasticity estimate for 1998. The right panel illustrates the calibration of the prot tax. The solid dot corresponds to our calibration for 1998, while the solid line corresponds to the reform. The initial value is calibrated, jointly with the xed production cost, targeting the earnings share of the richest top 1% of households and the average rm size. The solid line is calibrated to replicate the average rm size dynamics during the transition.

investment rate, and the innovation expenditure rate for each reform.

Figure 5.2 shows that the model can capture the qualitative features of growth accelerations in the data. In particular, the model delivers a protracted path for measured _TFP_ and a hump-shaped behavior of the investment rate. In reforms lifting idiosyncratic distortions, the main driver of these two features is the innovation decisions of rms. Absent any reallocation friction, the allocative eciency gains accrue immediately. Moreover, the removal of distortions encourages the most productive rms to innovate, accelerating the convergence. However, the enhanced incentives to innovate by the most productive rms coexist with the disincentive to innovate among the least productive ones, who beneted from the distorted environment. Given the stochastic nature of entrepreneurial ability, it takes time for these rms to exit the market, a force that protracts the transition. When lifting entry distortions, on the other hand, the most relevant force protracting the transition is given by the dierence in the distribution of entrepreneurial talent between entering rms and in27
Figure 5.2: Transition Dynamics: Idiosyncratic Distortions vs Entry Distortions <!-- Start of picture text --> TFP Average Size<br>Idiosyncratic Dist<br>Profit Tax (right axis)<br>Idiosyncratic Dist<br>Profit Tax<br>0 10 20 30 40 50 0 10 20 30 40 50<br>Periods Periods<br>Investment Rate Innovation Rate<br>0 10 20 30 40 50 0 10 20 30 40 50<br>Periods Periods<br>1.20 6 0.8<br>5<br>1.10 4 0.6<br>1.00 32 0.4<br>0.90 1 0.2<br>0.02 0.12<br>−0.02 0.08<br>−0.06 0.04<br><!-- End of picture text --> _TFP_ and _Average Size_ are measured as ratio with respect to the initial steady state values . The Investment rates and innovation expenditure rates are measured as absolute deviations from the distorted steady state ratios.

cumbents. The distribution of entrepreneurial ability at entry is calibrated to match the life-cycle growth of rms in the U.S. which requires a substantial gap between the average productivity of entrants and incumbents. When entry distortions are lifted, a burst of new entrepreneurs enters the market, increasing the density on the left tail of the productivity distribution. As these entrepreneurs innovate and their abilities follow their stochastic course, the distribution converges sluggishly to the stationary one, protracting the dynamics of productivity in the aggregate<sup>16</sup> . The properties of the innovation proles along the transition dynamics as well as the evolution of the productivity distribution of rms in both reforms are discussed in greater detail in 16The stochastic component of the evolution of idiosyncratic productivity is a feature that distinguishes our model from a neoclassical model of capital accumulation with adjustment costs. Even in a model with exogenous innovation, which dispenses from the protractedness induced by convex innovation costs, the transition may be protracted and feature a hump-shaped investment. One example of this case is when we remove entry barriers in a context of exogenous innovation, discussed in appendix B.1 and illustrated in gure B.2. There, the transition is driven purely by the stochastic shocks to idiosyncratic productivity, which drive the convergence of the productivity distribution at entry to the stationary one. Because the shock process induces a sluggish convergence of the productivity distribution, it leads to a hump-shaped dynamics of the investment rate. This case would be akin to a neoclassical growth model with exogenous productivity growth and frictionless capital accumulation, as in Imrohoroglu et al. (2006), the dierence being that _TFP_ growth would not be entirely exogenous, but resulting from an endogenous burst of entry.

28
# appendix B.1

The divergent dynamics of average size provide validation to the choice of idiosyncratic distortions and prot taxes as instruments to capture the divergent dynamics of average size in the data. Subsidies to low productivity rms at the expense of taxes to the highly productive ones promote the entry of new rms in models that, like ours, features a distribution of entrants' productivity with lower average productivity than incumbents (e.g., Fattal-Jaef, 2018). The entry of new rms translates into a reduction in average rm size in the distorted allocation. When idiosyncratic distortions are removed, the average size increases, as in the experience of the average growth acceleration. Entry distortions exert the opposite eect. By discouraging entrepreneurship, prot taxes concentrate production into fewer rms, and increases average size. When the distortions are lifted, the average size declines, as observed in the post-communist transitions.

Figure 5.2 also reveals notable dierences in the speed of transition depending on the nature of the reform. While measured _TFP_ declines abruptly following a reversal of entry distortions, it recovers faster, achieving a half-life that is 4 years lower than in the case of idiosyncratic distortions. This dierential response can also be understood by exploring the changes in the distribution of innovation eorts across rms and the evolution of the productivity distribution. When entry distortions are lifted, there is a burst of entry and all rms' innovation proles are shifted upwards. As a result, the economy reallocates labor towards innovation and rm creation, both of which are not capitalized in national income and product accounts<sup>17</sup> , dragging on aggregate productivity on impact. Thereafter, however, the burst in innovation materializes and aggregate productivity accelerates. When the productivity-dependent idiosyncratic distortions are lifted, it is only the most productive rms that increase innovation. However, there are few productive rms in the initial productivity distribution, leading to a minimal impulse on aggregate productivity. Moreover, the least productive rms, which enjoyed subsidies under the distorted regime and cut down on innovation after the reform, drift slowly towards exit due to the stochastic nature of the productivity process, holding down the growth in aggregate produc17The Bureau of Economic Analysis in the US has started to incorporate some forms of intangible investment, such as software and entertainment, into the National Income and Product Accounts. However, as argued by Corrado et al. (2006) the majority of intangible investment still goes unmeasured in national accounts. Thus, we take the approach of treating payments to labor that go into intangible capital accumulation, which in the model corresponds to payments to labor devoted to innovation, as an expense rather than an investment. Furthermore, these adjustments are not done in the national accounts of the countries and periods under study.

29
tivity. Combined, these two forces explain the more sluggish convergence relative to the case of entry distortions. The appendix B.1 develops these intuitions in greater detail.

A nal noteworthy property of both transitions is the hump-shaped dynamics of investment. As in Imrohoroglu et al. (2006)'s analysis of the post-war Japanese economy, accounting for _TFP_ growth turned to be essential in generating the humpshaped dynamics of the investment rate. In our model, the _TFP_ dynamics are generated endogenously, through the innovation incentives triggered by the implementation of reforms. Unlike Imrohoroglu et al. (2006), however, the investment rate rst drops on impact prior to engaging in sustained growth. This is an implication of the endogenous nature of _TFP_ and consumption smoothing, which requires the investment of resources for innovation purposes and induces households to preserve consumption by reducing the investment rate<sup>18</sup> .

# 5.4 Case Study

Equipped with an understanding of how idiosyncratic distortions and prot taxes contribute to shaping transitional dynamics in the model and with a calibration strategy for the path of reversal of distortions, we proceed to evaluate the extent to which the reform can account for the observed growth in _TFP_ in China between 1998 and 2011. We begin discussing the long-run implications of the mix of distortions at the initial and the terminal allocations and then characterize the transitional dynamics.

## 5.4.1 Long-Run Implications

Consider rst the long-run implications of the calibrated reforms in the model. Table 4 reports the values of _GDP, TFP,_ the number of entrepreneurs, and the average rm size in the steady-state with 2011 distortions relative to the steady-state with distortions calibrated to 1998. The table also reports the earnings share of the top 1% richest individuals in the population as absolute dierences between the initial 18One way to mitigate or reverse the initial investment decline is through capital adjustment costs. This friction would precipitate the accumulation of physical capital albeit at the expense of slowing down innovation. The fall in the investment rate, however, does not occur in our consideration of China's case study. There, we allow the scaling parameter of the idiosyncratic distortion prole to target the capital-output ratio observed in 2011. Since this is notably higher than the starting capital-output ratio of 1998, it implies an investment subsidy that makes households willing to increase both innovation and physical capital accumulation, at the expense of lower consumption.

30
and terminal values. The rst column shows the long run eects of the baseline reform, where both idiosyncratic distortions and prot taxes are removed, and the second column reports the results from a partial reform where only the productivityelasticity of distortions is alleviated.

Table 4: Steady State Analysis: Terminal vs Initial Allocations

||Baseline Reform|Misallocation Only Reform|
|---|---|---|
|GDP|1.42|1.09|
|TFP|1.19|1.10|
|Entrepreneurs|2.06|0.62|
|Av. Size|0.48|1.61|
|Top 1% (dierence|0.08|0.03|
|between steady<br>states)|||

NOTE: Table 4 shows the values of _GDP, TFP,_ the number of entrepreneurs, and the average rm size in the steady-state with 2011 distortions relative to the steady-state with distortions calibrated to 1998. In the rst column, both idiosyncratic distortion and prot taxes are reversed according to their calibrated values in table3. In the second column, only the productivity-elasticity of distortions is reduced to its 2011 value, leaving the other components of the mix of distortions in 1998 unchanged.

The reversal of distortions in the baseline reform generates a long-run _TFP_ growth of 19%. The average rm size declines by almost 50%, largely explained by a doubling of the rate of entrepreneurship in the economy. The second column in table 4 allows disentangling the contribution of each distortion. Aggregate _TFP_ increases by half as much under the partial reform, dictating that idiosyncratic distortions and prot taxes each contribute in almost equal shares to the total _TFP_ gains. At the micro-level however, the implications of each distortion are notably dierent. As shown in the benchmark reforms, the alleviation of idiosyncratic distortions in isolation generates a decline in the rate of entrepreneurship and an increase in the average rm size, a result that is counter to the evidence and that emphasizes the importance of withdrawing barriers to entrepreneurship in accounting for China's growth. Moreover, the comparison between the full and partial reforms yields signicant dierences in the growth of income inequality. In the full reform, the rise in inequality is on par with the one observed in the data, whereas abstracting from the prot-tax reform accounts for less than half of the observed increase.

31
# 5.5 Development Dynamics

Here we conduct the quantitative evaluation of the model's development dynamics for China's growth acceleration. The construction of the reforms involved feeding a linear t of the observed path of reversal of the productivity-elasticity of idiosyncratic distortions into the model as well as a protracted reversion of prot taxes. The calibration of the speed of reversion of prot taxes and the value of the average idiosyncratic distortions was determined so that, by construction, the predicted transitional dynamics will be able to match the dynamics of the average rm size and the value of the investment rate in the terminal stationary equilibrium. The evaluation of the model, then, is based on two non-targeted moments: the fraction of the observed _TFP_ growth that the model can account since the inception of the reforms until 2011 and the dynamics of the top earnings inequality relative to the data.

Figure 5.3 illustrates the dynamics of _TFP,_ the investment rate, the top 1% earnings share and the average rm size. The solid black line corresponds to the dynamics in the model, and the light gray line represents the data. We report the _TFP_ and the average rm size relative to their value in the initial steady-state, the top 1% earnings share as percentages, and the investment rate as dierences from the initial steady state.

The model predicts a protracted growth in aggregate productivity that can account for one-third of the _TFP_ growth in the data. As discussed in the benchmark reforms, the protractedness of _TFP_ allows for a hump-shaped behavior of the investment rate during the transition. Unlike Imrohoroglu et al. 2006, who appeal to an exogenous path of _TFP_ growth to attain a hump-shaped behavior of the savings rate in post-war Japan, our model delivers such an outcome through the endogenous response of innovation decisions of rms to the changes in the economy's underlying distortions. The endogenous path of aggregate productivity also translates into a hump-shaped dynamics for the rate of return to capital, which we portray in the right panel of gure 5.4. Quantitatively, the investment rate follows closely the overall dynamics in the data, although as said earlier, the quantitative t is an outcome of the calibration strategy for the terminal value of the scaling component of the idiosyncratic distortion prole, _ZI,_ 2011 , which we set to achieve China's capital-output ratio in 2011.<sup>19</sup>

> 19Along the transition, the investment rate increases too promptly. As discussed in footnote 16, the dynamics could be smoother, and therefore closer to the data, if we were to introduce

32
Figure 5.3: Post-Communist Transition Dynamics: China 1998-2011 <!-- Start of picture text --> TFP Investment Rate<br>Model<br>Data<br>1998 2002 2006 2010 1998 2002 2006 2010<br>Year Year<br>Top 1% Earnings Share Av Size<br>1998 2002 2006 2010 1998 2002 2006 2010<br>Year Year<br>1.3 0.15<br>1.1 0.05<br>Relative to SS 1998 Diff from SS 1998<br>0.9 −0.05<br>25 1.1<br>20<br>15 0.9<br>%<br>10 0.7<br>5 Rel. to SS 1998<br>0 0.5<br><!-- End of picture text --> The data for _TFP_ corresponds Penn World Table's (Zeileis 2021) _rtfnpa_ measure of _TFP_ between 1998 and 2011, linearly detrended by an annual _TFP_ growth of 0.85% in the U.S. The investment rates is the raw data for the period from the same source. The average size data is the same as in section 3. The top income share is drawn from the World Inequality Database, Piketty et al. (2019)). _TFP_ and the average size are expressed as ratios with respect to 1998 values, where, in the case of the model, 1998 stands for the calibration of the economy to the distortions in that year. The investment rate and the ratio of innovation expenditure over _GDP_ are expressed as absolute dierences.

The aggregate behavior of the model is underlaid by dynamics of the average rm size and the earnings in inequality that resembles the data. While we calibrated the pace of reversal of the prot taxes to replicate the observed behavior of the average rm size, the dynamics of inequality were non-targeted. The growth in earnings inequality arises, on one hand, from the reduction of prot taxes, which increases the share of earnings that entrepreneurs can appropriate and, on the other hand, from the higher expenses on innovation, which widens the earnings gap between wage earners and business owners and concentrates income among the most talented entrepreneurs. These properties can be seen in gure 5.4, which depicts the dynamics of the wage rate, the average entrepreneurial prots, and the average earnings among the richest entrepreneurs.

We conclude the case study with an exploration of the relative contribution of each component of China's reforms, the alleviation of idiosyncratic distortions and adjustment cost to investment.

33
Figure 5.4: Prots, Wages, and the Rate of Return to Capital <!-- Start of picture text --> Profits and Wages Rental Rate Capital Stock<br>Average Earnings top 1%<br>Wage Rate<br>Average Profits<br>1998 2002 2006 2010 1998 2002 2006 2010<br>Year Year<br>8<br>4<br>7<br>3 6<br>%<br>5<br>Relative to SS 1998 2<br>4<br>1<br>3<br><!-- End of picture text --> the removal of prot taxes, in explaining the aggregate and micro-level dynamics predicted by the model. To do so, we compute a partial reform where only the productivity-elasticity of distortions follows its calibrated path of reversal, while the prot tax remains at its initial steady state value.

Figure 5.5 shows that the abstracting from the elimination of prot taxes reduces the aggregate productivity growth to half as much as the one yielded by the full reform and is accompanied by micro-level dynamics that are counterfactual. The average rm size increases and stabilizes above the initial steady-state's level, a feature that the benchmark reforms anticipate should happen in response to reductions in the degree of productivity-dependent idiosyncratic distortions, but one that is at odds with China's experience. Moreover, the increase in top income inequality is also substantially lower than the growth generated by the full reform. When prot taxes are kept in place, the incentive to increase innovation expenses is subdued, thereby mitigating the divergence between entrepreneurial prots among the top entrepreneurs, the average entrepreneurial prot, and the wage rate.

34
Figure 5.5: Decomposition of Post-Communist Transitions: Full Reform vs Reducing Idiosyncratic Distortions <!-- Start of picture text --> TFP Investment Rate<br>Full Reform<br>Reform Misalloc<br>1998 2002 2006 2010 1998 2002 2006 2010<br>Year Year<br>Income Share Top 1% Av Size<br>1998 2002 2006 2010 1998 2002 2006 2010<br>Year Year<br>1.10<br>0.15<br>1.00<br>0.05<br>Relative to SS 1998 Diff from SS 1998<br>0.90 −0.05<br>25 2.0<br>20<br>15 1.5<br>10<br>1.0<br>5 Rel. to SS 1998<br>Difference from 1998 0 0.5<br><!-- End of picture text --> Note: The gure reports the transitional dynamics of the _TFP_ , the Investment Rate, the Income Share of the Top 1% earnings, and the average rm size under the baseline reform (Full Reform) and under a partial reform where the productivity elasticity of the idiosyncratic distortions follows its calibrated path, and the capital-output ratio and the prot tax remain xed at their initial values (Reform Misalloc). The _TFP_ and the average rm size are reported relative to their 1998 values, the top earnings share is presented in percentage, and the investment rate is reported as absolute dierence from the initial steady-state.

# 6 Conclusion

In this paper we presented a quantitative model of economic transitions to aid in understanding the macro and micro patterns of development dynamics in post-war acceleration episodes and post-communist transitions.

Our model builds upon recent theories of rm-level innovation, with entry, exit, and a stationary rm size distribution. We innovated upon these theories by interacting the built-in mechanisms of the model with two types of allocative distortions, idiosyncratic distortions and prot taxes, and by characterizing the transition dynamics. Furthermore, our analysis exploits the time-series dimension in existing empirical studies of misallocation in developing countries to come up with a novel strategy to discipline reforms. This allowed us to explore the quantitative behavior of the model in the context of a calibrated path of dismantlement of distortions.

Our ndings suggest that our theory can account for the salient features of development dynamics in acceleration episodes. A property of our ndings is that, 35
despite dispensing from frictions to resource reallocation, e.g., nancial frictions, the model can deliver a protracted path of growth in the rate of investment and in the _TFP_ . A key feature for the sustained growth in these variables is our theory of innovation, and the co-existence of heterogeneous incentives to invest in intangible capital along transition paths. There, the incentives to spur innovation from new and previously taxed entrepreneurs interact with a decline in innovation incentives from older cohorts of rms with relatively low productivity. As a result from this tension, it takes several years for the _TFP_ to attain its new steady state level.

The quantitative evaluation of the model in the context of China's growth acceleration reveals that there is still a large fraction of the observed productivity growth that the model cannot account for. In future research, we shall investigate plausible extensions to the model that may shed light on the missing forces. One potential avenue is the consideration of an open economy and the possibility that, either through the competitive eects of international trade or through the direct diusion from multinational production, the model could account for a closer share of observed productivity growth in the data. Another abstraction in our current analysis that would help the model explain a higher share of the observed growth in _TFP_ in China is the uncorrelated component of the dispersion in marginal revenue products. Accounting for uncorrelated dispersion would induce rank-reversal and magnify the allocative ineciency, forces that would increase the productivity eect of distortions.

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# A Data Description

We rst provide a list of the countries captured as accelerations by the methodology of Hausmann et.al (2005) and the full list of post-communist transitions.

For these countries, we construct the average of _TFP_ and investment rate dynamics relative to the acceleration year, or relative to the liberalization year in the case of a post-communist transition, which we date to be 1990. The underlying 39
Table 5: List of All Sustained Accelerations, Successful Post-Communist Transitions, and All Post-Communist Transition Countries

|Sustaine|d Growt|h Accelerations|S|uccessful Post-Communist|All Post-Communist|
|---|---|---|---|---|---|
|Albania|1994|Morocco|1958|Russia|Russia|
|Armenia|2001|Morocco|2000|Estonia|Georgia|
|Belgium|1960|Mexico|1963|Uzbekistan|Estonia|
|Bulgaria|2001|North Macedonia|2003|Armenia|Moldova|
|Belarus|1998|Mali|1985|Azerbaijan|Kyrgyzstan|
|Botswana|1968|Mali|1993|Turkmenistan|Uzbekistan|
|Canada|1963|Myanmar|1991|Bulgaria|Tajikistan|
|Chile|1975|Mongolia|2002|Belarus|Armenia|
|Chile|1987|Mozambique|1996|Kazakhstan|Azerbaijan|
|China|1961|Mauritius|1971|North Macedonia|Turkmenistan|
|China|1979|Mauritius|1984|Czech Republic|Bulgaria|
|China|1993|Malawi|1965|Hungary|Belarus|
|China|2002|Malaysia|1968|Latvia|Kazakhstan|
|Congo|1968|Namibia|2000|Lithuania|North Macedonia|
|Colombia|2003|Nigeria|1958|Poland|Czech Republic|
|Costa Rica|1965|Pakistan|1961|Romania|Hungary|
|Denmark|1958|Panama|1966|Slovakia|Latvia|
|Dominican Republic|1992|Panama|1989|Albania|Lithuania|
|Dominican Republic|2005|Panama|2004|China|Poland|
|Egypt|1959|Peru|2003|Vietnam|Romania|
|Egypt|1978|Poland|1994|Laos|Slovenia|
|Spain|1960|Portugal|1960||Slovakia|
|Spain|1984|Portugal|1985||Albania|
|Ethiopia|2004|Romania|1971||China|
|Finland|1968|Romania|2002||Vietnam|
|United Kingdom|1983|Rwanda|1996||Laos|
|Ghana|2007|Sudan|1995||Ukraine|
|Equatorial Guinea|1990|Singapore|1968|||
|Greece|1960|Singapore|1989|||
|Hong Kong|2002|Singapore|2002|||
|Indonesia|1968|El Salvador|1992|||
|Indonesia|2003|Slovakia|2002|||
|Ireland|1959|Chad|1999|||
|Ireland|1987|Thailand|1958|||
|Japan|1958|Thailand|1965|||
|Kazakhstan|1998|Thailand|2002|||
|Cambodia|2000|Turkmenistan|2002|||
|Republic of Korea|1964|Trinidad and Tobago|1995|||
|Republic of Korea|1984|Tunisia|1968|||
|Laos|1979|Turkey|1982|||
|Laos|1990|Turkey|2003|||
|Laos|2007|Taiwan|1961|||
|Sri Lanka|1977|Tanzania|1999|||
|Sri Lanka|1991|Uzbekistan|2004|||
|Sri Lanka|2005|Viet Nam|1991|||
|Lithuania|1998|||||

40
data comes from Penn World Tables version 10.1. _TFP_ is taken directly from the variable _rtfpna_ in the database, while the investment rate is given by _cshi_ . The lines in gure 3.1 correspond to simple averages among countries within each group. Average size dynamics for Singapore, Japan, and Korea 3.2 are constructed based on the data in Buera and Shin (2013). The average rm size for Chile and Romania was constructed from the supplementary material accompanying Bartelsman et al. (2009). For Hungary, the data comes from Varela (2017).

In terms of computing the average size dynamics for China, we have two data sources that we use for dierent purposes: the Census Yearbooks for 1995, 2004, and 2008; and the Annual Survey of Industrial Production conducted by the National Bureau of Statistics for the years 1998 through 2007. Since part our calibration of the Chinese economy in 1998 relies on matching the average size ratios with the US, we need to make sure that the dataset covers most rms in the economy in order to avoid biasing the calibration of the underlying distortion. Thus, for calibration purposes, we appeal to data from the Census Yearbooks as reported in Brandt et al. (2014). They report the total number of rms and the employment level from the Census Yearbooks of 1995, 2004, and 2008, allowing us to compute the average size in these years. The average size for 1995, our calibration target in the model, amounts to 166 workers. We plot this number along with the other two available data points in gure 3.2<sup>20</sup> of motivating facts.

We appeal to the alternative dataset, the NBSsurveys, to provide a longer and more continuous point of comparison for the model with respect to predictions about the evolution of average rm size during the reforms. The Annual Survey of Industrial Production conducted by the National Bureau of Statistics covers all non-state rms with 5 million yuan in revenue or more. Even though we nd this data useful for illustrating the evolution of the average rm size for a longer period of time (see gure 5.3), appealing to it for calibration purposes would have delivered a much higher value of the at component of the prot tax distortion. That is because in the surveys, the average size of an industrial rm in China in 1998 was 341 workers, twice as large as the magnitude emerging from the Census. Matching this target would have required a stronger disincentive to entrepreneurship in the model.

> 20The gure also shows a data point for 1993. We thank Gueorgui Kambourov for calculating this number for us. The source is the same as in Brandt et.al (2014), which did not report number of rms and employment data for the year 1993 in their work.

41
# B Complementary Quantitative Exercises

## B.1 Micro-Level Adjustments in Benchmark Reforms

The dierential response of the economy response to reforms that remove entry and idiosyncratic distortions can be understood by exploring the micro-level adjustments, particularly the response in the distribution of innovation eorts across rms over time and the evolution of the productivity distribution. We illustrate these objects in gure B.1. The top two panels depict the response of innovation probabilities as a function of the rms' underlying physical productivity ( _TFPQ_ ) at a number of representative points of the transition: the initial steady-state ( _SS_ 0) _,_ the terminal steady-state ( _SST_ ) , and periods 1 and 10 ( _t_ = 1 _, t_ = 10) . Similarly, the bottom two panels depict the productivity distribution of rms at the same instances of the transition path.

Figure B.1 shows that both entry and idiosyncratic distortions depress innovation incentives, but idiosyncratic distortions have a disproportionate eect among the most productive rms in the economy (lines labeled _SS_ 0 in the top gures). This distinguishing feature of idiosyncratic distortions manifests in the properties of the productivity distribution. The share of rms at the top of the distribution declines sharply under idiosyncratic distortions (line _SS_ 0 of bottom left gure) whereas it shows almost no change under entry distortions (line _SS_ 0 of bottom right gure). As a result, when reforms are implemented and innovation intensities recover, aggregate innovation expenses increases strongly in the case of entry distortions, where there is a high share of highly productive rms to take advantage of the improved incentives to innovation, while it does so by about half as much in the case of idiosyncratic distortions, where there share of such rms is signicantly smaller.

The sharper increase in the rate of innovation helps rationalize the stronger decline and the speedier recovery of _TFP_ when removing entry distortions. As the economy expands innovation eorts and increases entry, it reallocates labor towards to innovation and rm creation, both of which are not capitalized in national income and product accounts<sup>21</sup> . Therefore, aggregate productivity declines on im21The Bureau of Economic Analysis in the US has started to incorporate some forms if intangible investment, such as software and entertainment, into the National Income and Product Accounts. However, as argued by Corrado et al. (2006) the majority of intangible investment still goes unmeasured in national accounts. Thus, we take the approach of treating payments to labor that go into intangible capital accumulation, which in the model corresponds to payments to labor devoted to innovation, as an expense rather than an investment. Furthermore, these adjustments are not done in the national accounts of the countries and periods under study.

42
Figure B.1: Innovation Proles and Productivity Distributions <!-- Start of picture text --> Idiosyncratic Distortions Entry Distortions<br>SST<br>SS0 t=1 t=10 SST SS0 t=1<br>t=10<br>1 2 3 4 1 2 3 4<br>Log Z Log Z<br>Idiosyncratic Distortions Entry Distortions<br>SST SST<br>SS0 SS0<br>t=1 t=1<br>t=10 t=10<br>1 2 3 4 1 2 3 4<br>Log Z Log Z<br>0.5 0.5<br>0.4 0.4<br>0.3 0.3<br>0.2 0.2<br>Innovation Probability 0.1 Innovation Probability 0.1<br>0.0 0.0<br>0.20 0.20<br>0.15 0.15<br>Pdf 0.10 Pdf 0.10<br>0.05 0.05<br>0.00 0.00<br><!-- End of picture text --> The top panel plots the innovation proles in the initial and terminal steady states, and periods 1 and 10 along the transition following reforms that reverse idiosyncratic (top left) and entry (top right) distortions. The bottom panels illustrate the _pdf_ of the distribution of physical productivity ( _TFP_ ) at the same points of the transition.

pact. Thereafter, the properties of the productivity distribution at the onset of the reforms discussed above allows for a quicker recovery than in the event of removing idiosyncratic distortions.

# B.2 Benchmark Reforms: The Role of Innovation and Reallocation

How do endogenous innovation and resource reallocation contribute to shaping the dynamics of development? We address this question in this section.

We evaluate reforms that dismantle idiosyncratic and entry distortions considering separately cases where innovation is endogenous, as in the previous section, or exogenous, in which case resource reallocation is the sole force driving the transition. To represent an economy with exogenous innovation, we endow rms with the same innovation prole as in the undistorted stationary allocation with endogenous innovation. Firms do not have to invest in achieving this innovation prole and hence, do not have a technology to innovate more or less as a result of distortions, so rm dynamics are exogenous. Recall that all experiments calibrate distortions so as to achieve the same _TFP_ growth (see table 2) Consider rst the role of innovation and reallocation for the behavior of macroeconomic variables in gure B.2. There, we plot _TFP_ and the investment rates for 43
each type of reforms overlaying the cases with endogenous and exogenous innovation.

Figure B.2: Transition Dynamics: Idiosyncratic Distortions vs Entry Distortions <!-- Start of picture text --> TFP − Idiosyncratic Distortion TFP − Entry Distortion<br>Endogenous Innov.<br>Exogenous Innov.<br>0 10 20 30 40 50 0 10 20 30 40 50<br>Periods Periods<br>Investment Rate − Idiosyncratic Distortion Investment Rate − Entry Distortion<br>0 10 20 30 40 50 0 10 20 30 40 50<br>Periods Periods<br>1.20 1.20<br>1.10 1.10<br>1.00 1.00<br>0.90 0.90<br>0.02 0.02<br>−0.02 −0.02<br>−0.06 −0.06<br><!-- End of picture text --> _TFP_ is measured as ratio with respect to the initial steady state values . The Investment rates is measured as absolute deviations from the distorted steady state ratios.

The main message of the gure is the dierential contribution of endogenous innovation to the speed of convergence of _TFP_ across reforms. When dismantling idiosyncratic distortions, an active response in the rms' expenses on innovation is essential for adding protractedness to the dynamics. Conversely, in the case of entry distortions, the dynamics of _TFP_ under exogenous innovation experience almost no change on impact but are substantially more protracted throughout the transition than in the baseline with endogenous innovation.

The productivity distributions are, again, illustrative of the mechanisms underlying the contribution of endogenous innovation to the speed of transitions. Consider rst the case of reversing idiosyncratic distortions, which are depicted in the top two panels of gure B.3. The case with exogenous innovation (top right) shows that there is a substantial increase in entrepreneurship in the distorted stationary allocation, manifested in the notable shift to the left of the productivity distribution. However, as soon as distortions are lifted and the selection of entrepreneurs improves, the distribution converges almost immediately to the undistorted stationary one and, hence, so does aggregate _TFP._ With endogenous innovation, the immediate productivity gain upon reversal of the misallocation is more muted, given that the productivity distribution (labeled _t_ = 1 ) is still far from the stationary one. As innovation expenses pay o, the distribution shifts to the right, but 10 periods into the transition 44
the distribution has not yet settled into the stationary one. The protracted pace of convergence in the distribution feeds into the dynamics of aggregate _TFP._ When the reforms lift entry distortions, the drivers of the speed of transition are reversed. With exogenous innovation (bottom right), the immediate eect of the reform is to create a burst in the entry of new entrepreneurs that makes the distribution of rms across productivity be almost entirely dominated by the distribution of entrants (line labeled _t_ = 1 ). Thereafter the distribution converges to the stationary one at a pace dictated by the exogenous stochastic process of rm dynamics. When allowing for endogenous innovation (bottom left), the burst in entry also leads to a contraction in the right tail of the distribution. However, as rms increase their expenses in innovation, the convergence of the distribution is accelerated.

Figure B.3: Innovation Proles and Productivity Distributions <!-- Start of picture text --> Idiosyncratic Distortions Endo. Innov. Idiosyncratic Distortions Exo. Innov.<br>SST SST<br>SS0 SS0<br>t=1 t=1<br>t=10 t=10<br>1 2 3 4 1 2 3 4<br>Log Z Log Z<br>Entry Distortions Endo. Innov. Entry Distortions Exo. Innov.<br>SST SST<br>SS0 SS0<br>t=1 t=1<br>t=10 t=10<br>1 2 3 4 1 2 3 4<br>Log Z Log Z<br>0.20 0.20<br>0.15 0.15<br>Pdf 0.10 Pdf 0.10<br>0.05 0.05<br>0.00 0.00<br>0.20 0.20<br>0.15 0.15<br>Pdf 0.10 Pdf 0.10<br>0.05 0.05<br>0.00 0.00<br><!-- End of picture text --> The top two panels illustrate the _pdf_ of the distribution of physical productivity ( _TFP_ ) at various points of the transition for economies with endogenous (top left) and exogenous (top right) innovation, under a reform eliminating idiosyncratic distortions. The bottom gures illustrate the same objects for the case of reforms reversing entry distortions.

The dierence in the behavior of _TFP_ help rationalize the behavior of investment dynamics. With exogenous innovation and idiosyncratic distortions, the immediate jump in _TFP_ induces a neoclassical-shaped response of investment, increasing on impact and converging to the steady state level from above.<sup>22</sup> In the case of entry

> 22Recall that the idiosyncratic distortions were calibrated so that the capital to output ratio was undistorted. Thus, the behavior of investment dynamics cannot be attributed to an investment specic component of idiosyncratic distortions.

45
distortions, investment dynamics are qualitatively similar, and intricately related to the protracted adjustment in _TFP._ However, when innovation is endogenous, the economy postpones investment so as to invest in innovation at the same time it preserves consumption smoothing.

# C Chile's Growth Acceleration 1985-1996

In earlier versions of the manuscript, we considered Chile's growth acceleration between 1985 and 2011 as a complementary case study to that of China. Considering Chile's acceleration was motivated by the availability of rm-level data covering the acceleration period, a key ingredient for a tight calibration of the pace of reversal of distortions in the model. However, while the Chilean acceleration surpasses the criterion for counting as a sustained growth acceleration, it is one that is very contaminated by cyclical elements, driven by the strong recovery the economy was undergoing after a deep recession in the early 1980s. Moreover, as shown in the growth accounting exercise depicted in gure C.1, it is only in the early years that the acceleration was fueled by rapid and sustained _TFP_ growth, the ingredient of the acceleration that our theory seeks to account for, whereas it was physical and capital accumulation that became the primary driving forces in the second half of the period. For this reason, we decided to focus on China's growth acceleration as case study for the evaluation of our model and to leave the characterization of Chile's less clear-cut acceleration episode for this appendix.

## C.1 Calibration of Chile's Growth Acceleration

We think of Chile's economy prior to its growth take-o as subject to idiosyncratic distortions, and model its acceleration as driven a protracted alleviation of these distortions. Based on Chile's ENIA (Encuesta Nacional Industrial Anual), a yearly industrial survey covering the universe of manufacturing plants with 10 or more workers<sup>23</sup> , we estimate the productivity-elasticity of idiosyncratic distortions. As before, the productivity elasticity is estimated as the regression coecient between the _log_ ( _TFPR_ ) and _log_ ( _TFPQ_ ) , where _TFPR_ and _TFPQ_ are measured exactly as in Hsieh and Klenow (2009). Similarly to how we proceed in China's case study,

> 23We work with the version of the ENIA that is provided in Chen and Irarrazabal (2015)'s replication material, downloadable from https://www.economicdynamics.org/codes/13/1361/pack_nalversion.zip

46
Figure C.1: Growth Accounting: Chile's Growth Acceleration <!-- Start of picture text --> Growth Accounting: Chile 1983−2011<br><!-- End of picture text --> <!-- Start of picture text --> GDP per worker<br>Labor Augmenting TFP<br>K/Y<br>Human Capital Index<br>1985 1990 1995 2000 2005 2010<br>Year<br>0.8<br>0.6<br>0.4<br>0.2<br>Log Difference from 1998 0.0<br>−0.2<br><!-- End of picture text --> Note:(2021).TheWe datadecomposefor therealgrowth _GDP_ accountingper worker,exerciseas<sup>_<u>Y</u>_</sup> _L_<sup>=</sup> stems<sup>_TFP_</sup> from 1 _−_ <u>1</u> _α_ � the _<u>ky</u>_ � 1 Penn _−αα hc_ World, whereTablesreal _GDP_ Databaseis measuredZeileis according to _rgdpna_ in the data, _L_ is the number of employed agents, _k_ is _rkna_ , and _hc_ is the human capital index provided by the data. The labor share, (1 _− α_ ) , is given by the labor share reported in the data, _lbsh,_ for the year 2011.

we t a linear trend to the regression coecients, which we use to extrapolate the elasticities outside the estimation period until 2011, the year in which we assume the reform stalls and distortions stabilize. The result from this calibration strategy is illustrated in gure C.2.

We dispense from prot taxes but continue to rely on xed costs of production to replicate the average rm size in Chile prior to the acceleration. Since we appealed to prot taxes to characterize the egalitarian forces and the barriers to private entrepreneurship that are characteristic of a communist regime, we do not see these taxes as pertinent to think about Chile's acceleration. However, for consistency with a calibration strategy that seeks to start-o the economy at a level of the average rm size that is consistent with the data, we preserve the xed cost specication.

A property of Chile's development dynamics that does not align well with that of the average growth acceleration is the behavior of the investment rate. At the onset of the acceleration, the investment rate declines strongly, constituting a signicant drag on aggregate growth, and then recovers abruptly so that at the point where the _TFP_ impulse stalls, the capital-output ratio starts to increase. This deviation 47
Figure C.2: Productivity-Elasticity of Distortions in Chile <!-- Start of picture text --> 0.6<br>G<br>0.4<br>G G<br>G G G G Estimated Value<br>G G G G Linear Fit<br>G G G<br>G<br>G<br>0.2<br>1990 2000 2010<br>Year<br>TFPR−TFPQ elasticity<br><!-- End of picture text --> Note: The gure illustrates the regression coecient between _log_ ( _TFPR_ ) and _log_ ( _TFPQ_ ) for the period 1984-2011. The dots correspond to the point estimates from Chile's ENIA (Encuesta Nacional Industrial Anual) for 1984 through 1996. We dene _log_ ( _TFPR_ ) and _log_ ( _TFPQ_ ) as in Hsieh and Klenow 2009. The solid line illustrates a linear t on the estimated values projected on to 2011. We assume that reforms stabilize in 2011, and the productivity-elasticity of idiosyncratic distortions remain constant a the 2011 level. The initial steady state is represented by the elasticity estimate for 1984.

in the behavior of the investment rate from the pattern exhibited by the average growth acceleration carries consequences for the calibration of the average idiosyncratic distortion in the economy, controlled by the parameter _ZIt_ in the idiosyncratic distortion prole. This parameter was set to reconcile the growth in the capital output ratio in the model with that of the data. In China's acceleration this could be achieved parsimoniously, due to the somewhat monotonic rise in the capital-output ratio throughout the transition. This is not the case under Chile's cyclical behavior of the investment rate. For this reason, we decided to abstract from seeking to match the behavior of the capital output ratio, and preserve the value of _ZI_ in 1984 and in 2011, the initial and terminal points of the transition, to attain a common capital-output ratio.

# C.2 Development Dynamics

Figure C.3 shows the development dynamics under Chile's calibrated reforms. Although the model can almost fully account for the overall growth in _TFP_ from the 48
beginning until the end of the period, it cannot capture the fast rise in _TFP_ in the rst decade of the acceleration nor it can it explain the decline thereafter. As said, the smooth impulse implied by the calibrated reform, leads to a more protracted growth in aggregate productivity and cannot generate contractions.

Figure C.3: Development Dynamics: Chile's Growth Acceleration 1984-2011 <!-- Start of picture text --> TFP Investment Rate<br>Model<br>Data<br>1985 1995 2005 1985 1995 2005<br>Year Year<br>Employment Share Innovation Av Size<br>0 5 10 15 20 25 30 1985 1995 2005<br>Year Year<br>1.4 0.15<br>0.10<br>1.2<br>0.05<br>Relative to SS 1998 1.0 Diff from SS 1998 0.00<br>0.8 −0.05<br>0.07 2.0<br>1.8<br>0.06<br>1.6<br>0.05 1.4<br>Diff from SS 1998 0.04 Rel. to SS 1998 1.2<br>1.0<br>0.03<br><!-- End of picture text --> Note: The data for _TFP_ is constructed from the Penn World Tables Database (Zeileis 2021). We construct _TFP_ using _rgdpna_ as the measure of real _GDP,_ the product of the population and the human capital index ( _pop∗hc_ ) as the measure of the labor input, and _rkna_ as the measure of the capital stock. We xed the labor share at the value reported by the data for the year 2011, _lsh_ (2011) . Once the series of _TFP_ is construct it, we linearly de-trend it assuming an annual productivity growth in the U.S. of 0.85%. The investment rate is drawn directly from the Penn World Tables. We construct the average rm size from the ENIA (Encuesta Nacional Industrial Anual), extracted from the replication material for Chen and Irarrazabal (2015). The average rm size is dened as the ratio between total employment and the total number of rms.

The atypical behavior of the investment rate during Chile's acceleration cannot be accounted for by the model either. While we could have improved the model's t by adjusting the average idiosyncratic distortion to attain a higher level of the capital to output ratio at the end of the acceleration period, the model would not have been able to capture the cyclical behavior of the investment rate. The model does capture, however, the qualitative property of an increasing pattern of the investment rate, 49
which is a virtue derived from the endogenous response of innovation decisions and the resulting eect on the rate of return to capital.

Lastly, the interaction between occupational choices, innovation expenses, and the reversal of idiosyncratic distortions leads to a rise in the average rm size, as in the data. Quantitatively, however, the rise predicted by the model is more protracted than the one observed in Chile.

# C.3 Life-Cycle of Firms during Acceleration Episodes

In addition to the interest in the literature in documenting cross-country dierences in the rm size distribution, recent studies have shifted the focus towards investigating dierences in the life-cycle growth of rms between developed and developing economies.<sup>24</sup> Because of data limitations, most current empirical investigations of the cross-country dierences in the life-cycle of rms has been carried out inferring the life-cycle from the cross-sectional distributions of employment across ages, instead of tracking the life cycle of a cohort.

In this section we investigate the accuracy of this approximation in the context of an economy undergoing a growth acceleration. For this purpose, we compare the evolution of the cross-sectional distribution of employment across ages at various points of the transition path, alongside the life-cycle growth of the cohort of rms that enters the economy at the onset of the reform. We choose Chile's acceleration as illustrative example, given the simpler nature of the its reform in the model, entailing the withdrawal of a single distortion.

Specically, gure C.4 illustrates the cross-sectional distribution of employment and age at Chile's initial steady state (labeled ss 1980), at the post-reform steady state (ss Chile post-reform), and for the years 1980 (period 1 of reform), 1995, and 2011. The gure also depicts the life-cycle growth of the cohort born in 1980.<sup>25</sup> Figure C.4 shows that the protractedness displayed by the aggregate productivity in gure C.3 is underlaid by a comparable sluggishness in the convergence of the cross-sectional life-cycle of employment. After making a small upward jump in the period of the reform (see line labeled t=1980), by the year 2011 it is still quite far from having converged to the stationary distribution of the terminal stationary allocation (ss Chile post-reform)

> 24Hsieh and Klenow (2014) being the most salient study in this family of papers.

> 25It is a proper life-cycle in the sense that we kept track of the time series evolution of employment for a given cohort, conditional on survival.

50
Figure C.4: Life Cycle of Firms during Acceleration Episodes: Chile 1980-2011 <!-- Start of picture text --> 2<br>ss 1980<br>ss Chile post−reform<br>t=1995<br>1.8 t=2011<br>t=1980 (per 1 of reform)<br>Cohort from 1980<br>1.6<br>1.4<br>1.2<br>1<br>0 10 20 30 40 50 60<br>Age<br>Employment relative to Age 1<br><!-- End of picture text --> In terms of understanding the source of this sluggishness, recall that the shape of the cross-sectional life-cycle is determined by a combination of age and cohort eects. On the one hand, newly created rms are innovating at a pace consistent with the more friendly economic environment and are, therefore, making the life-cycle look steeper. On the other hand, older cohorts comprise low productivity, formerly subsidized entrepreneurs whose protection is being withdrawn by the reform and are consequently cutting down on innovation and headed towards exit. Since these low productivity rms have accumulated investments in productivity, the productivity process implies that it takes time for these rms to drift down towards the exit threshold. Hence, they contribute to making the life-cycle look atter.

The sluggishness in the convergence of the cross-sectional distribution of employment across age raise a word of caution to using it as an input to back out the underlying idiosyncratic distortions in the economy. Suppose a researcher were to observe the cross-sectional distribution of employment over age for Chile in 2011, and one were to use a stationary model of rm dynamics to infer the degree of allocative distortions that are necessary to replicate the cross-sectional life cycle in the data.<sup>26</sup> Since the life cycle of rms in the cross section of the model for 2011 is well below

> 26This is the kind of counterfactual constructed in Hsieh and Klenow (2014) to quantify the aggregate implications of the dierences in the life-cycle of rms between the U.S., India, and Mexico

51
the one at the new steady state, the researcher would back out distortions that are more severe than those that are actually underlying the economy in 2011, point at which the prole of distortion adopts it lowest estimated value and stabilizes. Had the researcher been able to construct the life-cycle of a cohort of rms, the imputed degree of distortions would have been milder, and closer to the actual degree of distortions in 2011, given that the life-cycle of the cohort is closest to the cross-sectional life cycle consistent with the steady state associated with the distortions of 2011.

# D Self-Employment and the Number of Firms: Evidence and the Model's Predictions

The paper stresses the behavior of the average rm size as the relevant empirical counterpart to assess the implications of distortions on the rate of entrepreneurship and the rm-size distribution. However, being an entrepreneurial model of rm entry and exit, it is useful to review evidence that more directly speaks to this margin of adjustment.

To this end, gures D.1 and D.2 report the dynamics of the rate of self-employment and the number of rms along China's and Chile's growth accelerations. Both these metrics have merits and limitations in capturing the notion of a rm in the model. Self-employment, on one hand, better reects entrepreneurial activity from individuals that are on the margin of entrepreneurial activity or seeking for work in the labor market, but is less likely to reect the innovation and growth potential of that entrepreneurial rms exhibit in the model. The number of rms, on the other hand, is subject to the opposite trade-o. Stemming from China's Annual Survey of Industries, which covers rms beyond a certain size, it captures rms with a certain number of employees and stock of capital, but also captures businesses with a more sophisticated ownership structure whose survival is less linked to an occupational choice from the entrepreneur. Since, as we show below, both measures exhibit a similar behavior, we argue they provide empirical validity to the channels in the model.

Turning, then, to the results, let us begin with gure D.1, which illustrates the fraction of entrepreneurs in the model and the fraction of self-employed in the labor force for China and Chile. We see that in both cases the model captures the direction of change in the rate of self-employment, except for the 1995-2005 period in Chile, and the 1999-2001 period in China. Despite these non-monotonicities, we interpret 52
the evidence as supportive of the model.

Figure D.1: Self-Employment in Model and Data <!-- Start of picture text --> Fraction of Entrepreneurs Chile Fraction of Entrepreneurs China: Model vs Data<br>Model<br>Data<br>Model<br>Data Self−Empl<br>1985 1990 1995 2000 2005 2010 1995 2000 2005 2010<br>time Year<br>1.2 2.0<br>1.1 1.8<br>1.0<br>1.6<br>0.9<br>1.4<br>0.8<br>Relative to 1991 Relative to 1998<br>1.2<br>0.7<br>0.6 1.0<br>0.5 0.8<br><!-- End of picture text --> Note: Chile's data on Self-Employment is drawn from the International Labor Organization's ILOstat database. Both the model and the data are normalized to be equal to one in 1991, which is the rst data point. Self-Employment in China is drawn from China's Statistical Yearbooks of 2018, and is dened as the ratio of Self-Employed individuals in urban areas over the total number Urban Employed Persons. The data is measured relative to its value in 1998, and the model is measured relative to the initial steady state, which is calibrated to the distortions measured for 1998.

To complement the above, we turn now to discussing the implications of adopting the number of rms as the empirical counterpart for rms in the model. We can see in gure D.2 that a similar validation for the model's mechanisms emerges under this metric, albeit with dierent quantitative t. In particular, the model falls short of capturing the spike in the number of rms in China between 2003 and 2005, while it over-predicts the decline in the number of rms in the early years of Chile's acceleration, and under predicts it towards the end.

# E Decomposition of TFPR into Capital and Output Distortions

The paper adopts _TFPR_ as the summary of idiosyncratic distortions in the data, and uses the properties of the distribution of _TFPR_ to discipline the distribution of revenue taxes in the model. However, _TFPR_ is dened by a combination of output distortions and capital distortions, as labeled in Hsieh and Klenow (2009). To assess the extent to which each ingredient is contributing to the overall dynamics of _TFPR_ , we provide a decomposition in the gures that follow.

As a quick reminder, _TFPR_ is proportional to capital and output distortions in 53
Figure D.2: Number of Firms in Model and Data <!-- Start of picture text --> Number of Firms Chile: Model vs Data Number of Firms China: Model vs Data<br>Model Model<br>Data Data<br>1984 1986 1988 1990 1992 1994 1996 1998 1999 2000 2001 2002 2003 2004 2005<br>time time<br>1.1 2.5<br>1.0<br>0.9 2.0<br>0.8<br>Relative to 1983 Relative to 1998<br>0.7 1.5<br>0.6<br>0.5 1.0<br><!-- End of picture text --> Note: The number of rms in Chile are aggregated from Chile's Encuenta Nacional Industrial Anual (ENIA) for the period 1983-1996. The number of rms in China is computed from the Annual Survey of Industries for the years 1998-2005.

the following fashion Based on this denition, our approach to addressing the decomposition is to construct two alternative counterfactual measures of _TFPR_ in which one distortion is shut down at a time where _log_ � _TFPRTFPRiK_ � is the log of _TFPR_ assuming the only distortion is the capital one, relative to the industry average _TFPR,_ and where _log_ � _TFPRTFPRiy_ � is the same object assuming the output distortion is the only active distortion.

Equipped with these alternative denition, we separately compute their regres- _TFP_ _<u>Qi</u>_ sion coecients with respect to _log ._ In the context of the model, where � _TFPQ_ � capital distortions create a wedge in the cost of renting capital, a decline in the capital-distortions' elasticity with respect to _TFPQ_ implies that, during acceleration episodes, more productive rms become more able to increase their capital labor ratios. A decline in the output distortion's elasticity, on the other hand, implies that the more productive rms become more able to increase size attracting labor and capital in proportion to their technological shares. With respect to _TFP_ , 54
however, a decline in both types of elasticity is indicative of higher incentives for more productive rms to innovate.

The results for Chile and China are plotted in gure E.1, where the vertical axis measures the evolution of the regression coecients as dierences from their respective values in the rst period of the respective samples.

Figure E.1: Output and Capital Distortions and the Dynamics of TFPR/TFPQ Elasticity <!-- Start of picture text --> CHINA: Regression Coefficient TFPR−TFPQ: Decomposition CHILE: Regression Coefficient TFPR−TFPQ: Decomposition<br>Baseline Baseline<br>TauY only TauY only<br>TauK only TauK only<br>1998 1999 2000 2001 2002 2003 2004 2005 1980 1985 1990 1995<br>Year Year<br>0.10 0.10<br>0.05<br>0.05<br>0.00<br>0.00<br>−0.05<br>−0.05<br>Difference from 1998 Difference from 1980 −0.10<br>−0.10<br>−0.15<br>−0.15 −0.20<br><!-- End of picture text --> In Chile, Figure E.1 shows that the output distortion's elasticity (gray line) tracks the overall elasticity very closely throughout the entire period, whereas the capital distortion (green line) shows a milder and noisier decline starting in 1985. In China, the gure shows that the output distortion's elasticity (gray line) falls the most between 1998 and 2002, with the capital distortion (green line) playing a bigger role since 2003.

Given our primary goal of accounting for _TFP_ dynamics, and that we are seeking to do so though the interaction between endogenous rm dynamics and the productivity-dependent component of distortions (abstracting from reallocation barriers), we nd the evidence to provide support for our approach of loading all of the _TFPR/TFPQ_ elasticity on the output component.

# F Calibration of the Size Distribution of Entrants

Besides calibrating the shape parameter _η_ to match moments of the size distribution of entrants in the data, we can further explore the goodness of t of the Pareto assumption by comparing the entire employment size distribution of entrants with the data. We plot the employment-weighted distribution of entrants in gure F.1.

55
Figure F.1: Employment Weighted Size Distribution of Entrants: Model and Data <!-- Start of picture text --> 1<br>Calib<br>0.9 Data<br>0.8<br>0.7<br>0.6<br>0.5<br>0.4<br>0.3<br>0.2<br>0.1<br>0<br>1−4 5−9 10−19 20−49 50−99 100−249 250−499<br><!-- End of picture text --> Note: The data corresponds to the employment-weighted distribution of rm sizes from the Business Dynamics Statistics database for the manufacturing sector in 2007. The unit of analysis are rms, and entrants are identied as rms with age equal to zero. Data points for rms with employment greater than 499 are undisclosed in the database.

The gure shows that while the Pareto distribution tracks closely the empirical distribution of entrants, it slightly under-predicts the shares towards the right tail of the distribution. There are two features of the equilibrium that are aected by the properties of the size distribution of entrants: the dynamics of employment over the life-cycle and the speed of convergence along transitional dynamics. Since large rms innovate more intensively, a smaller share at the top decreases the speed of employment growth over the life-cycle conditional on survival, and delays the speed of convergence. We experimented with a Log-Normal distribution, and found that aggregate and micro-level implications are largely unaected once parameter values are re-calibrated to satisfy the empirical targets, specially the ones referring to the average size of entrants relative to incumbents and the employment ratio between 21-25 and 1 year old rms.

56