The Dynamics of Development: Innovation and Reallocation

This paper proposes a quantitative model of firm dynamics with endogenous innovation to study growth acceleration episodes triggered by reforms. The authors find that reforms removing barriers to firm entry lead to persistent growth in TFP and declining average firm size, as in the experience of successful post-communist transitions. Reforms that reverse resource misallocation result in more protracted paths of TFP and rising average firm size, as in the experience of non-communist growth accelerations. When calibrating the reforms to data from Chile's and China?s growth accelerations, the model can replicate the macro and firm-level features of these episodes.


Introduction
A large literature documents the pervasiveness of allocative distortions (e.g. idiosyncratic taxes and subsidies, entry frictions) in developing countries and establishes the quantitative significance of resource misallocation in terms of accounting for crosscountry differences in the level of T F P (Hsieh and Klenow (2009); Bartelsman et al., 2013;Restuccia and Rogerson, 2008;Brandt et al. (2017)). However, despite the importance of distortions for understanding development differences, their effects on the dynamics of development have been relatively unexplored. 1 Building on and extending studies of sustained growth accelerations that highlight the very protracted dynamics of output and TFP (Hausmann et al. (2005) and Buera and Shin (2013)), we propose a quantitative theory of firm dynamics and innovation to study the transitional dynamics triggered by reforms eliminating allocative distortions.
The paper has a substantial and a methodological contribution.
Our substantial contribution is to quantify the response of the economy following twFw: Paper for Policy Research Paper Serieso type of reforms, for which we find support in the data: reforms that eliminate distortions to firm entry, and reforms that withdraw idiosyncratic distortions among incumbents. We find that reforms dismantling entry distortions exhibit a relatively faster convergence, albeit with a more pronounced initial decline in measured TFP, and are associated with a decline in the average size of firms, consistent with the experience of post-communist transitions. On the contrary, reforms dismantling idiosyncratic distortions are more protracted and result in an increase in the average size of firms, which was the case in the rest of the sustained growth acceleration episodes that we document.
We further investigate the role of alternative reforms by considering two cases studies where the paths of reversal of entry and idiosyncratic distortions are tightly calibrated to the speed of reforms in the data: Chile between 1980 and 1996 and China since 1998. We find that the calibrated reforms can account for 35 and 50% of the productivity growth that materialized since the onset of the reforms in Chile and China respectively. Our model also delivers patterns of transition that resemble, both at the aggregate and firm level data, those of the episodes under study. Interestingly, we find that the elimination of entry distortions are the main driver of TFP in the case of China.
On the methodological side, we evaluate the importance of modeling endogenous innovation in accounting for the effects of distortions on development. That is, we characterize the biased incurred by studies ignoring innovation, a common practice in the literature. 2 In terms of long run performance, we find that endogenous innovation is the main driver of the productivity losses independently of the type of distortion affecting the economy. Turning to development dynamics, we show that when idiosyncratic distortions are the main object of reform, abstracting from innovation yields neoclassical-shaped transitions, with an immediate adjustment in TFP and declining investment rates, which are counterfactual. Conversely, when liberalizing entry distortions, resource reallocation is the main driver of protractedness, with endogenous innovation contributing to speeding up the transition. We reach these conclusions by comparing the implications of the benchmark model against a version of it where the process of firm dynamics is exogenous and calibrated to match the firm dynamics in an undistorted economy.
Our baseline economy builds on Lucas (1978), which we extend to incorporate a theory of innovation along the lines of Atkeson and Burstein (2010). 3 There is a large household populated by a continuum of individuals, who are heterogeneous with respect to the ability to operate a firm. 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 firm. 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: 1) distortions to occupational choices, modeled as taxes to the firm's profits gross of innovation expenses, and 2) distortions to the allocation of resources across firms, modeled as idiosyncratic wedges in the spirit of Restuccia and Rogerson (2008) and ?.
We motivate the importance of alternative type of reforms by documenting divergent dynamics in the evolution of the firm size distribution between countries transitioning from a communist regime and the rest of the growth acceleration episodes.
While the average firm size increases in the latter, it declines in countries disman-tling a centrally planned economy. Entry and idiosyncratic distortions are suitable instruments for replicating these patterns. On one hand, entry distortions discourage entry and increase average firm size, consistent with the data for communist regimes. On the other hand, distortions that correlate positively with the firm's idiosyncratic productivity have the effect of depressing the average firm size, as in the case of the initial allocations of the rest of the accelerations. In addition to this indirect inference, in the case studies we provide evidence of misallocation using firm level data to calibrate the extent of idiosyncratic distortions, and appeal to data on average firm size to discipline the calibration of the entry distortions.
Why are transitions dynamics following the dismantling of idiosyncratic distortions slower? In this case, TFP is depressed in the distorted stationary equilibrium mainly due to a reduction in the fraction of firms at the top of the productivity distribution and, to a lesser extent, due to the misallocation of resources across firms.
When distortions are lifted, productivity rises on impact only as a result of an efficient reallocation of resources. However, the productivity distribution is still far from the one corresponding to the undistorted allocation, so the initial rise is mild.
As innovation expenses among the most productive firms increase, the distribution starts to slowly converge, which in turns translates into a sluggish convergence of TFP. Under entry distortions, the primary driver of the decline in T F P in the stationary allocation is the reduction in the number of firms and the aggregate innovation expenditure. Because the fall in innovation is independent of the firm's productivity, the productivity distribution does not show a significant contraction in the share of firms at the top. When the entry frictions are removed, measured T F P drops on impact in reflection of the re-allocation of labor into the innovation activities, and due to the sharp rise in the entry of new firms, whose productivity distribution features a lower average productivity. Then, as innovation incentives recover, the prevalence of highly productive firms allows for a faster recovery in aggregate innovation expenses and, hence,a speedier recovery of T F P .
What is the contribution of endogenous innovation in shaping transition dynamics? The answer depends on the type of reform. In the case of idiosyncratic distortions, with exogenous innovation, the distribution of physical productivity in the distorted allocation is only affected by selection, an effect that is small in our framework. Thus the decline in TFP is almost entirely accounted for by misallocation. Absent any reallocation barrier T F P jump almost immediately to the 4 undistorted level once the reform is implemented. When reversing entry distortions, the effect of exogenous innovation is to delay the transition. The pace of the transition in this case is primarily driven by the convergence of the productivity distribution of firms upon reform, which is largely determined by the productivity distribution of entrants, to the stationary one. With exogenous innovation, such convergence is slow, as implied by the properties of our calibrated process of firm dynamics. Had we allowed for the innovation channel, as in the baseline model, the improved incentives to innovate would have accelerated the transition.
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 studies are in section 5. Lastly, we conclude.

Related Literature
Our study provides a unified framework for thinking about the long run implications of various types of allocative distortions, and for investigating 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 in isolation.
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), andRestuccia andRogerson (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 take direct summary statistics about the degree of resource misallocation in developing countries from the empirical branch of the literature, and use them to discipline the extent of misallocation in the model at the onset of our transition experiments, and their dynamics afterwards. Secondly, we contribute to the quantitative side of the literature, investigating the extent to which the dynamic responses from firms, such as innovation, entry, and exit, complement the static allocative responses in shaping long run losses in productivity and in explaining the speed of transition to the 5 equilibrium with fewer distortions. 4 The second feature of our work connects us with the literature on neoclassical transition dynamics. Christiano (1989) and King and Rebelo (1993) were the first to emphasize the shortcomings of the frictionless neoclassical model when it comes to reproducing features of transition dynamics in miracle economies. In the data, transition dynamics of fast growing economies are characterized by sustained growth in income per-capita and total factor productivity, delayed but protracted investment surges, and hump-shaped interest rate dynamics. These features cannot be jointly reproduced by the many extensions to the canonical neoclassical growth model, unless one introduces an exogenous path of TFP that accompanies the convergence in capital stocks, as shown for the case of Japan by Imrohoroglu et al. (2006). Our contribution is to develop a model that can account endogenously for the joint dynamics of investment rates and TFP, and at the same time delivers rich firm-level implications that can be validated against firm-level data.
Two papers in the literature stand out for their proximity with ours. Buera and Shin (2013) develops 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 financial frictions that delay capital reallocation, transition paths triggered by the removal of idiosyncratic distortions are characterized by investment and interest rate dynamics that are closer to 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. On one hand, we take the paper's historical accounts of growth accelerations in fast growing economies as providing empirical support for the idea that reforms that remove allocative distortions occurred at the beginning of these growth accelerations. Secondly, our model provides a complementary mechanism through which macroeconomic dynamics can depart from those of the standard neoclassical model. Rather than emphasizing frictions 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 firms' innovation efforts, can generate transition paths for output, investment, and TFP similar to those in the data in a frictionless setup.
Furthermore, because innovation outcomes are risky, the productivity distribution of firms reflects the increased innovation efforts by firms with a lag, which allows the model to generate sustained and protracted increases in TFP, a weakness of the theories based on barriers to factor reallocation.
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 firms 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, life-cycle dynamics of firms in the frictionless steady state of our model are different from those of the distorted equilibrium. In turn, these differences are generated endogenously, from a theory of innovation that connects firm growth to allocative frictions. Secondly, the predictions about entry along the transition path in our model differ from those in Atkeson and Kehoe (2007). In the case with idiosyncratic distortions, entry is inefficiently encouraged by subsidies in the pre-reform steady state of our economy, which implies that our development paths are characterized by reductions in entrepreneurship, and increases in the average firm size. Lastly, because of our focus on growth accelerations, we follow a different strategy for parameterizing the pre-reform stationary equilibrium, appealing to firm-level data in low income countries to discipline the choice of distortions that hinder output and productivity.

Motivating Facts
We set the stage for the quantitative model presenting a number of facts regarding macroeconomic and microeconomic features of transitions around the world. We consider separately two types of convergence episodes: sustained growth accelerations in the post-war period, identified appealing to the methodology of Hausmann et al. (2005), and post-communist transitions. 5 As we shall explain in greater detail below, we proceed in this way because of the fundamental differences in the adjustments occurring at the micro-level between these episodes, differences that we want to carefully account for in the theory that we develop later.

Aggregate and Firm-Level Features of Accelerations and Post-Communist Transitions
Consider first the behavior of aggregate variables. 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 challenge for the standard neoclassical growth model, the workhorse model to study transitions, since that model is silent about TFP dynamics and predicts a decreasing path in the investment rate when converging towards an equilibrium with a 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. 7 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 fit 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 following a growth acceleration (years t + 7 through t + 16) is above 2 percent. We use the growth acceleration data from Buera and Shin (2017) who apply Hausmann et al. (2005) methodology to an updated sample (Penn World Tables 8.0). The complete list of post-communist countries and the list of acceleration episodes picked up by the methodology is presented in the appendix. 6 Since accelerations occur at different 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.
7 Christiano (1989), King andRebelo (1993), Chen et.al. (2006), and Buera and Shin (2013) are salient examples of papers that have noted the conflict between the neoclassical growth model and macroeconomic data on transitions, and developed extensions of the neoclassical model to bridge The left panel plots T F P dynamics for the simple average of post-communist transitions and acceleration episodes. The right panel illustrates the average of investment rates. The horizontal axes measure 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 specific date which we identify, using the methodology, as the start of the growth take-off. T F P 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 the appendix. The sustained gGowth a While exhibiting similar characteristics in the aggregate, acceleration episodes and post-communist transitions differ notably in the adjustments taking place at the micro level, in particular regarding the size distribution of firms. To see this, figure 3.2 reproduces the dynamics of the average size of manufacturing firms, in 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.  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 first available year with firm level data in the case of post-communist transitions. Given the substantial differences 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.
in China and the economies of former Soviet Union countries. 8 Our contribution is to extend this analysis to a more recent period, and to revisit the previous findings through the lens of newer datasets.
Similarly, the fact that average firm size tends to increase with development has also been noted before in the literature. In fact, our data for average size dynamics during accelerations draws exactly from that in Buera and Shin (2013). What has not been equally emphasized before is the notion that divergences from this average behavior can be determined by the nature of the underlying transformations taking place in the economy and that one such transformation that differs from the average is a post-communist liberalization.

From the Data to a Theory of Transitions
In this paper we focus on economic transitions that are triggered by large scale economic reforms. While growth accelerations tend to be highly unpredictable, it is also the case that economic reforms constitute one of the few significant predictors of a sustained growth take-off. This has been established in the context of reduced form regressions, as in Hausmann et al. (2005), as well as through narrative historical accounts of the wave of reforms that preceded the growth accelerations of the so called miracle economies, provided by Buera and Shin (2013). Therefore, we think of economic transitions in the model as emerging from reforms that eliminate allocative and entry distortions in the economy.
The patterns of development that we described above, in particular the divergent dynamics in the average firm size, guide us in the identification of the family of distortions that are adequate for thinking about the allocations prior to 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. 9 The evidence shows that allocative distortions, identified as reduced form idiosyncratic wedges, tend to tax productive firms more heavily than unproductive ones, a feature that facilitates the survival of low productivity firms, discourages innovation and, ultimately, reduces the scale of operations of the firms. 10 When dismantled, these type of distortions deliver dynamics of average firm size that are consistent with what we observed for the average acceleration. The dynamics of post-communist transitions, on the other hand, suggest that the inherent barriers to the creation and operation of firms constitute a more prevalent source of distortion. 11 Barriers to entry concentrate production in fewer and larger firms. Thus, their dismantlement is consistent with a spreading of production 9 Throughout 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.
10 The correlated nature of idiosyncratic distortions with respect to the distribution of firms' productivity is a pervasive property of resource misallocation around the world. Hsieh and Klenow (2007) first 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, 2009for Uruguay, Camacho and Conover, 2010for 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.
11 More direct evidence is provided by Brandt et al. (2017), who show that entry barriers are the salient friction for explaining cross-regional growth disparities in China. into more and smaller firms, 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 fit 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.

Model
We sutdy 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 profit, or make her participate in the labor force, in exchange for a fixed wage. Each individual commits to participate in a risk-sharing agreement that insulates individual consumption from fluctuations in idiosyncratic income. In addition to occupational choices, the head of household chooses aggregate consumption and investment in order to maximize lifetime utility.
There are endogenous and exogenous forces for firm dynamics and resource reallocation. The endogenous component stems from entrepreneur's 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 firms with policies and distortions to factor allocation.
We first 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 firms 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.

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: Aggregate labor supply and aggregate profits, L s t and Π t respectively, are defined as follows: where o t (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 M t (z) denotes the endogenous distribution of agents over productivity levels.
All these objects will be characterized in detail below.

Occupational Choice
We assume that the head of 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 final good combining their own idiosyncratic productivity, z, together with capital and labor into a Cobb-13 Douglas production function with decreasing returns to scale: 12 We assume that there are perfectly flexible 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: which yields the following expressions for optimal capital and labor demands: The indirect profit 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). Specifically, 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 firm's investments in innovation, and an exogenous standard deviation.
Let ∆ denote the change in the logarithm of productivity that a firm 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 down-grade) 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 firms 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 of properties of the size distribution and firm life-cycle dynamics in the U.S. 13 Taking capital and labor demands from the static profit maximization problem, entrepreneurs' innovation decision solves the following optimization problem: with v E 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 allow 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 firm's life-cycle dynamics, and for shaping the responses to reforms.
It follows from the above that the value of a worker is simply defined by the wage rate in the period, plus the discounted expected value of resetting occupations in the following period: with the value of an agent before making an occupational choice given by

Aggregation and Definition 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 M t (z) . We need to characterize the evolution of this distribution in order to be able to aggregate individual decisions and compute equilibrium prices.
Say we start with a given distribution M t (z) at the beginning of period t. Entrepreneurs move across productivity levels in accordance to their innovation decisions, 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 16 of agents across productivity levels: The second 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 ∆ downgrade to xe −∆ < z with probability 1 − p t (x), and those with productivity level x ∈ ze −∆ , z upgrade to xe ∆ > z with probability p t (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 , p t (z)} ; sequences of interest rates and wage rates {r t , w t }; and a distribution of agents over productivity {M t (z)}; such that given an initial capital stock K 0 and a given distribution of talent draws for workers F (z), household's and firm's decision solve their dynamic optimization problems and capital and labor markets clear and the distribution of entrepreneurial productivity evolves according to (4.2).
Similarly, a long run equilibrium of this economy is one where individual decisions, aggregate quantities, and prices are constant, and the distribution of productivity is stationary.

Output and Productivity
A well known property of our model with decreasing returns to scale and frictionless factor markets is that the production side of the economy aggregates into the following aggregate production function: where L p,t stands for aggregate labor demand for the production of the final good only: Measured TFP, in turn, can be computed from the following expression: Notice that we have made an adjustment to our measure of T F P t so as to make it comparable with that in income accounting studies. The expression reflects the fact that output is deflated using the entire labor force, which has a unit measure, regardless of occupation, while in the model only a subset of the agents are involved in the production of goods. The other fraction, workers in innovation, make intangible contributions that we assume go unmeasured in GDP.

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 firms, and entry barriers that distort occupational choices and increase the average firm size.
Idiosyncratic distortions are modeled as productivity-dependent taxes to the firms' revenues, while entry distortions are implemented through taxes to the prof-its of the firms gross of innovation expenses. 14 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. The profit taxes, on the other hand, are less standard. We appeal to taxes to the profits of firms, 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 firms. In addition, a profit tax is a natural instrument to capture the nature of a communist regime, where profits are ultimately collectivized, or captured by the party elite.
In terms of accounting for differences in average firm size at the onset of growth accelerations, we appeal to fixed costs of production, rather than appealing to profit taxes as we do in the case of communist regimes. While profit taxes indeed constitute an entry barrier, they also comprise a strong disincentive to innovation. 15 When calibrated to replicate average size differences at the beginning of Chile's acceleration, we find that the required profit tax would imply a collapse of all firm growth in the economy. While slower life-cycle growth is indeed a feature of developing countries, we see the implications of profit taxes on firm dynamics to be too extreme unless we are thinking about a communist allocation. Thus, when considering Chile's case study, we will assume that firms confront a fixed cost of operation f c , in units of the final good in the economy. The fixed costs reduce profits and, hence, discourages entrepreneurship, but has no implications for the decisions to innovate for firms that are sufficiently far from the exit point.
Formally, let τ t (z) and τ π t denote the revenue and profit tax rates corresponding to a firm with productivity z in period t. Notice that the profit tax is identical across firms, while revenue taxes are idiosyncratic to the firm's productivity, according to the following function: . (4. 3) The slope parameter in the misallocation schedule υ t controls the degree of linear relationship between the logarithm of the marginal revenue product of the firm (T F P R) and the logarithm of physical productivity (T F P Q). As explained in greater detail in the calibration section, we appeal to Chile's and China's firm-level data to estimate the regression coefficient between these variables to discipline its parameterization. The productivity index z separates firms into those that get a revenue subsidy from those that get a revenue tax. We exploit this degree of freedom to set z I so that idiosyncratic distortions are neutral with respect to the investment rate in the economy.
In terms of the profit tax, it can be shown that unlike a flat revenue tax, a flat profit tax has a direct effect on occupational choices, innovation, and, thereby, the average size of a firm. We appeal to data on the latter for former communist countries to determine its value in the quantitative analysis.
We now turn to incorporating the profit and revenue taxes into the optimization problems of the agents. Consider first the value of an entrepreneur with productivity z and associated revenue and profit taxes τ t (z) and τ π t . This is given by the following expression: which in addition to the tax distortions, also reflects the fixed cost of production f c Profit taxes have a direct effect on the firm'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 profitability, as reflected in the firm's static profit maximization problem: A feature of the value of entrepreneurship worth highlighting is that profit taxes affect the operating profits of the entrepreneur gross of the expenditure on innovation. In the context of the theory, this assumption is necessary in order to ensure that the profit tax indeed distorts the innovation decision of the entrepreneur. To the extent that the profit taxes are intended to capture the distortions to managers' incentives to invest in technology under a communist regime, it is necessary that these taxes have a non-neutral effect over the rate of return to innovation relative to the marginal cost of innovation expenses. It is to accomplish this goal that we set the tax to affect operating profits gross of innovation expenses.
We conclude the section by presenting the definitions of aggregate output and productivity in the version of the economy with distortions: and The misallocation effect of revenue taxes is manifested in the aggregation of individual productivity, which now reflects the inefficiency in the distribution of capital and labor across producers. The dynamic effects of revenue and profit taxes, which operate through distortions to innovation, are captured in the distribution of firms across productivity levels M t (z).

Quantitative Exploration
We organize the presentation the quantitative analysis as follows. We first characterize the response of the economy in response to reforms that dismantle idiosyncratic distortions or entry distortions in isolation. We refer to these reforms as benchmark.
The distinguishing features of these reforms is that they are implemented abruptly and their magnitude is not calibrated to match any one specific episode but, rather,

Calibration
Parameters related to technology, shocks, and preferences will be calibrated to match features of the US, a relatively undistorted economy, while distortions will be disciplined appealing to firm-level data for Chile and China.

Parameters Common Across Economies
There are 7 parameters that remain invariant across the types of economies that we consider: the coefficient 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, and the capital depreciation rate δ. In addition, we must specify and parameterize the distribution of entrepreneurial ability types among workers.
For the coefficient 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.
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 firm size distribution, the average employment ratio between firms aged 21-25 to 1 year old, and the log dispersion of the distribution of employment growth rates for large firms. 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. 16 The parameter values resulting from this strategy are reported in

Reforms
We now turn to discussing the strategy for calibrating the parameter values governing the distortions in the model, and their paths of reversal in the reforms that lead to development dynamics. These are given by a sequence of slopes of the revenue tax profile, υ t , a sequence of profit taxes, τ π t , and a sequence of fixed costs of production f c,t . We first 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 studies.

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 profits of the firms, with which we characterize the barriers to firm entry of communist regimes. In order to quantify the contribution of the innovation and reallocation channels in shaping the macro and micro properties of transitions, we investigate each type of reform in the context of two versions of the model, one where we shut down endogenous innovation, so that resource reallocation is the sole driving force, and one were all forces are at play. Thus, the analysis requires that we apply our calibration strategy to parameterize distortion in each of these reform cases.
The idiosyncratic distortions and the profit tax rate are calibrated so as to match the observed growth in T F P that occurs between the starting and the ending point  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 T F P from achieving the undistorted steady state allocation matches the 20\% detrended $TFP$ growth observed in the data for an average acceleration.
profit tax rate that is required across the endogenous and exogenous innovation models, which contrasts with the similarity of the calibrated values of the slope of the idiosyncratic distortion profile. In the case of profit taxes, the discouragement to entry is reinforced by the disincentives to innovation. This compounding of forces calls for a lower flat profit tax in the endogenous innovation model to generate the same T F P gap as in the exogenous innovation one. In the case of idiosyncratic distortions, the disincentives to innovation have a dampening effect over the productivity losses from resource misallocation. This occurs because a lower pace of innovation compresses the distribution of physical productivity across which resources are misallocated, hence mitigating the losses from misallocation. 17 When innovation is exogenous, the economy does not feature a reduction in T F P by means of lower physical productivity but, by misallocating across an exogenously dispersed distribution, it generates larger losses from misallocation. What the table indicates is that despite their different composition, a roughly identical degree of distortion is capable of generating the same contraction in aggregate productivity.

Case Studies
For the case studies, we pursue a richer calibration strategy that enables us to pin down parameter values for the combination of distortions that affect Chile and China in their initial steady states, and that also allows us to discipline the rate of reversal of these distortions along the transition path. As a reminder, we are interpreting Chile's level of (under) development prior to its growth acceleration as an outcome of a combination of idiosyncratic distortions and fixed costs of production. On the other hand, we are modeling China's communist regime as a result of the combination of taxes to the profits gross of innovation expenses, which mimic the barriers to entry that characterize these regimes, and idiosyncratic distortions.
We calibrate the slope of the idiosyncratic distortion profile appealing to estimates of the regression coefficient between the logarithm of T F P R and the logarithm of T F P Q computed from firm-level manufacturing data. For Chile, we read these values for the period 1980-1996 from Chen and Irarrazabal (2015). This work studies the decade of recovery in Chile following the 1982 financial crises applying the methodology of Hsieh and Klenow (2009)  Regarding entry barriers, we lack an empirical counterpart from which to back out profit taxes and fixed costs directly from the data. It is known, however, that these frictions have a direct effect over the economy's average firm size. Thus, we calibrate the fixed cost in Chile and the profit tax in China to match the ratio between the average firm size between these economies and the US.
The Chilean database is a census of manufacturing firms with at least 10 workers. We take this into account when computing the average firm size in the US, conditioning also on 10 workers or more. We find that the ratio of average sizes between plants in Chile in 1998 and the US in 2007 is equal to 0.44. Conditional With respect to the time path of entry distortions, we again lack a direct way of inferring the evolution of these frictions from the data. Our procedure here is as follows. For China, we assume that the profit tax is withdrawn once and for all upon reform, and let the time series of misallocation frictions summarize the inefficiencies in the progressive adoption of a market economy. That is, we set τ π t>1998 = 0 immediately after the reform. We do not interpret our choice as a denial that entry distortions still exist in China. In fact, Brandt et al. (2017) show that entry barriers are key in accounting for cross-regional growth disparities in China. An alternative would have been to identify a sequence of progressive reductions in the profit taxes using the observed dynamics of the average firm size in China as disciplining device.
We explored experiments with such flavor and found that, while indeed successful at tracking more closely the average size, they did not carry significant changes to the aggregate performance of the model. This is because the data itself shows a strong decline in the average firm size, suggesting that entry distortions, albeit persistent, must have decreased rapidly and substantially in China after 1998. For this reason, we chose to minimize the degree of protractedness in the transitions that is infused from protractedness in reforms, and load it all on the time-path of misallocation.
For Chile, on the other hand, we assume that the fixed cost of operation, which drives the average size ratio with the US in the steady state, is held constant at the initial level throughout the entire transition path. We find reassurance for this assumption in the observed dynamics of average size in Chile. Had fixed costs indeed gone down markedly in Chile, we would have expected a decline, or at least a slowdown, in the growth of the average size. To the contrary, what we observe is a fast increase from an already high starting point. For this reason, we decided to assume that Chile's transition is entirely attributable to the reduction of allocative frictions. 18 A last feature regarding the parameterization of the path of allocative distortions refers to the scaling parameter Z I,t . We have a clear disciplining target for its value in the initial and terminal steady states, since we are introducing this degree of freedom to neutralize any effect of distortions on the capital to output ratio in the long run. However, we have no clear target for its parameterization along the transition. Absent a clear best practice, we proceed as with the parameterization of the slope parameter. That is, we fit a linear trend between the initial and terminal values and use it to predict values for every period in between.

Benchmark Reforms: Idiosyncratic Distortions vs Entry Distortions
We begin the quantitative analysis with an exploration of the properties of transition dynamics implied by each type of reform. Figure 5.2 illustrates the dynamics of T F P, average size, the investment rate, and the innovation expenditure rate for reforms removing entry and idiosyncratic distortions. T F P 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.
The figure reveals notable differences in the patterns of transition depending on the nature of the reform. Dismantling idiosyncratic distortions yields a protracted growth in T F P , accompanied by increasing average firm size, an increasing rate of innovation, and investment rates that decline on impact but increase thereafter.
In contrast, T F P declines abruptly following a reversal of entry distortions but recovers at a faster pace, featuring a half-life that is 4 years lower than in the case of idiosyncratic distortions. Similarly, the investment rate shows a stronger decline upon reform, but catches up rapidly. More notorious are the differences in the dynamic of average firm size and the dynamics of the innovation rate. The average firm size decreases over time in the case of entry distortions, while the share of expenses in innovation relative to GDP increases by twice as much.
The divergent dynamics of average size provide validation to the choice of idiosyncratic distortions and profit taxes as instruments to capture the divergent dynamics of average size in the data. Subsidies to low productivity firms at the expense of highly productive ones promote the entry of new firms in models that, like ours, features a distribution of entrants' productivity with a lower average productivity than incumbents. The entry of new firms translates in a reduction in average firm size in the distorted allocation. Entry distortions exert the opposite effect. By discouraging entrepreneurship, profit taxes concentrate production into fewer firms and increases average size.
The differential response of the economy at the macro level can be understood by exploring the micro-level adjustments, particularly the response in the distribution of innovation efforts across firms over time, and the evolution of the productivity distribution. We illustrate these objects in figure  The sharper increase in the rate of innovation helps rationalize the stronger decline and speedier subsequent recovery in the T F P and in the rate of investment when removing entry distortions. As the economy expands innovation efforts, it reallocates labor towards these activities, which are not capitalized as measured capital in national accounts. 19 Hence, aggregate productivity declines on impact and it does so by a higher amount in the case of entry distortions, where the rise in innovation expenses are higher. This is reinforced by the rise in the entry of new entrepreneurs that takes place upon reforming entry distortions. Since entrants draw 19 The 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.

Entry Distortions
The top panel plots the innovation profiles 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 (T F P ) at the same points of the transition. entrepreneurial ability from a distribution with lower average productivity (bottom right panel of figure 5.3, lines labeled t = 1 vs SS0), the rise in entry further reduces T F P . In terms of the dynamics of investment, these can be rationalized as a result of consumption smoothing together with a desire to postpone investment until the returns to innovation have raised the rate of return to capital.

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 firms with the same innovation profile as in the undistorted stationary allocation with endogenous innovation. Firms do not have to invest in achieving this innovation profile and hence, do not have a technology to innovate more or less as a result of distortions, so firm dynamics are exogenous.
Consider first the role of innovation and reallocation for the behavior of macroeconomic variables in figure 5.4. There, we plot T F P and the investment rates for each type of reforms overlaying the cases with endogenous and exogenous innovation. 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 T F P. With endogenous innovation, the immedi-ate 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 off, the distribution shifts to the right, but 10 periods into the transition the distribution has not yet settled into the stationary one. The protracted pace of convergence in the distribution feeds into the dynamics of aggregate T F P.
When the reforms lift entry distortions, the drivers of the speed of transition are reversed. With exogenous innovation (bottom right), the immediate effect of the reform is to create a burst in the entry of new entrepreneurs that makes the distribution of firms 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 firm 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 firms increase their expenses in innovation, the convergence of the distribution is accelerated. The difference in the behavior of T F P help rationalize the behavior of investment dynamics. With exogenous innovation and idiosyncratic distortions, the immediate jump in T F P induces a neoclassical-shaped response of investment, increasing on impact and converging to the steady state level from above. 20 In the case of entry distortions, investment dynamics are qualitatively similar, and intricately related to the protracted adjustment in T F P. However, when innovation is endogenous, the economy postpones investment so as to invest in innovation at the same time it preserves consumption smoothing.

Case Studies
We proceed now to evaluating the ability of our theory to replicate the transition properties of two case studies: 1) Chile between 1980 and 2011, which we adopt as representative of an average acceleration, and 2) China between 1998 and 2011, which we adopt as representative of a successful post-communist transition.

Long-Run Implications
Consider first the long run implications of the calibrated distortions in the model. 21 Table 3 reproduces salient steady state outcomes for the pre-acceleration allocation of Chile in 1980 and the communist allocation of China in 1998. Since the latter features multiple distortions, we provide a decomposition of the long run outcomes considering each type of distortion in isolation. The table shows the value of each variable in the respective distorted stationary equilibrium, expressed relative to its value in the undistorted one or, as is the case with the share of entrepreneurs in the population, as an absolute deviation between the shares across allocations.
Allocative distortions in Chile generate a 19% decline in T F P and a 24% decline in output relative to the levels in the undistorted stationary equilibrium. The average firm size conditional on ten or more workers is only 44% of the one in the US, which is exactly the target that we were seeking to match with the fixed cost of production. In China, the combination of misallocation and profit taxes drag aggregate productivity by 50%, and output by 60%. The average size in this case becomes tree times as high as in the US which, again, is an outcome of our calibration strategy for the flat component of profit taxation.
The table also shows a decomposition of the total losses in T F P into those that 20 Recall 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 specific component of idiosyncratic distortions. 21 The full detail of the calibration of these episodes is in section 5.2 stem from the endogenous innovation channel and those coming from the allocative channel. We construct this case computing the counterfactual aggregate productivity that would result from resolving misallocation, but preserving the distribution of physical productivity from the distorted stationary equilibrium, and then measuring it relative to the undistorted level of T F P . In doing so, we are capturing the costs for the economy of the distorted innovation profiles only, but liberalizing it from misallocation. Results are in the row labeled T F P dynamics. We find that the dynamic component of T F P accounts for the bulk of the total gains, both in Chile's and China's benchmark experiments. In the former, after resolving misallocation, T F P is still 11% below the undistorted value, while in China aggregate productivity is still 40% below the efficient level. Looking ahead into the transition dynamics, this finding is indicative of the importance of the response of firms' innovation decisions in shaping the speed of the transition dynamics, for the bulk of the growth in T F P will end up coming from this source.
In terms of disentangling the disruptive effects of allocative distortions from those of profit taxes in China, the last two columns in table 3 show the long run outcomes for steady states with different combination of active distortions: the benchmark, and a case with idiosyncratic distortions only. The communist forces that we subsume into the profit taxes are essential for replicating the features of the size distribution of firms in China. Had misallocation been the only distortion, firms would have tended to be smaller, not larger, than in the US (last column in the table). Furthermore, in addition to helping replicate the properties of the firm size distribution, the calibrated value of profit taxes prove to be a powerful source of productivity losses, as shown by the milder 25% loss in T F P that would occur had there been no such taxes.
The steady state analysis gives us an idea of the type of adjustment that would have to take place along a full transition path to development. The economies have to close significant development gaps, especially for communist regimes, and are expected to exhibit substantial reorganizations at the micro-level, in light of the differences in innovation, entrepreneurship rates, and the firm size distribution.

Development Dynamics
Here we turn to the main goal of the paper, to investigate the macro and firm- The figure shows that the calibrated reform is able to capture the qualitative features of the dynamics of TFP, investment, and average firm size in the data. The investment rate is, by construction, starting and finishing at the same level between the two steady states. However, along the transition, it declines in the onset of the reform and increases smoothly until it reverses back to the steady state, a reversal that materializes beyond 2011. Physical capital investment declines in response to the economy's allocation of resources towards the financing of innovation expenses. As innovation pays off and productivity starts to increase, the rate of return to capital goes up and so does the rate of tangible capital investment in the economy. The sudden reform precipitates the changes, but preserves the qualitative conclusions.
The model also captures the adjustments in the size distribution of firms, as manifested by the dynamics of the average firm size. Although less abruptly than in the data, the average size of firms increases by 30% between 1980 and 2011. In the last period with available firm-level data, the average firm size had increased by 50% in Chile. As argued in the context of steady state analysis, the increase in the average firm size depends, on the one hand, to the progressive dismantlement of distortions, which eliminates subsidies at the bottom of the productivity distribution and discourages low-productivity entrepreneurship, and on the other hand on the increase in innovation investment by productive firms, which concentrates employment and production into fewer and more productive entrepreneurs.
Overall, while the model is quantitatively successful at capturing some of the patterns of transitions that we observe in the data, it also exhibits some weaknesses that warn us about the need to thinking about other forces underlying a growth acceleration, or other growth triggers than the particular type of reform that we consider here. The model can account for half of the total gains in productivity at the end of the period and it can replicate the hump-shaped dynamics of investment in the data although, again, at magnitudes that fall short from the empirical counterparts. 23 The figures also show that the dynamics predicted by the model are excessively protracted relatively to what we see in the data. Even in the case of a sudden implementation of the reform, it takes longer in the model than in the data to converge to the equilibrium consistent with the reformed business climate. This can be inferred not only from the dynamics of T F P, but also from the average firm 23 Recall that we calibrated distortions so that they were neutral with respect to capital to output ratios. Thus, part of the divergence between theory and data in terms of the dynamics of investment could stem from our abstraction from investment wedges. Consideration of adjustment costs to the investment in physical capital could also contribute to improving the behavior of the investment rate in the model, particularly in the first years post-reform. However, these would delay the dynamics of T F P even further by crowding out intangible capital accumulation.

Innovation Rate
The data for T F P corresponds to the trend component of HP filtered (smoothing parameter of 100) Chinese data between 1998 and 2011. The investment rates is the raw data for the period. The average size data is the same as in section 3. T F P 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 differences.
The model is also able to replicate the similarity between acceleration episodes and post-communist transitions from an aggregate point of view, at the same time that it accounts for the differential behavior of firms at the micro level. This can be noted in that, contrary to Chile, the average firm size declines for a number of periods along the transitions, while TFP and investment rate display the same increasing pattern. Of course, the two experiments differ in the magnitudes, which is not surprising in light of the different development gaps to be bridged by the 39 reforms that we propose for each country.
The protractedness of the adjustment in T F P is also a feature of the model's response to a more sudden reform, like the one implied by our implementation of a communist liberalization. In this case the half-life of the transition for T F P and The model also predicts a significantly weaker increase in the investment rate relative to what we observe in the data. As in the case of acceleration episodes, investment in physical capital declines upon reform, and does so more abruptly in light of the larger productivity gaps that need to be closed by investing in technology.
The flip-side of the deeper contraction in investment is the greater increase in the innovation expenditure rate, which is twice as large as in the acceleration episode upon reform, and almost three times as large by 2011. Relative to the data, however, the extent of decrease and increase in the investment rate in the model is notably The dynamics of average firm size warrant a closer inspection. The steady state analysis anticipates that the calibrated reform for China generates a contraction in average firm size. However, there are opposing forces shaping the path of the average firm size that manifest with different strength at different stages along the transition, generating a non-monotone trajectory of convergence. One the other hand, 24 The remarks in footnote 23 apply to the Chinese case as well.
removing idiosyncratic distortions increases the average firm size, on the other hand eliminating profit taxes reduces it. Because the calibrated reform withdraws profit taxes more abruptly than idiosyncratic distortions, the average firm size declines strongly during the early years of the transition, to just about 9% of the initial steady state value. Thereafter, the entry into entrepreneurship and the decline in average size persists for a few periods, until the expansionary effect from undoing misallocation starts to prevail. The average size flattens out and eventually increases gradually towards the new steady state value. The increasing part does not materialize until later than 2011 so, in a sense, it constitutes a forecast from the model about what we should expect to happen with the dynamics of the average firm size in China in the near future.
We conclude the analysis of post-communist transitions by performing an experiment that allows us to disentangle the relative contribution of each ingredient of a post-communist reform in shaping the development dynamics. Concretely, we compute a counterfactual reform in which only the communist features, embedded in the profit taxes, are dismantled, while resource misallocation persists at the same level as in the initial allocation. We overlay the results form this experiment, which we label partial, with those of the benchmark, which we label full in figure 5.8 below. 25 It follows from the figure that the fundamental force driving the dynamics of China during the liberalization years is the withdrawal of the profit distortions.
Removing this friction allows China to reap almost all of the productivity gains from the more comprehensive reform. The figure also reinforces the intuition that the contribution of improvements in allocative efficiency for average firm size manifest later in the transition process, pushing average size upwards. As shown in the lower-left panel of the figure, average size is below the benchmark level throughout the partial transition. Lastly, the bottom right figure shows that even though the productivity gains from the partial reform are, by 2011, very similar to the complete reform, they require a slower investment in innovation to achieve them. 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 effects.
On the one hand, newly created firms 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 firms have accumulated investments in productivity, the productivity process implies that it takes time for these firms to drift down towards the exit threshold. Hence, they contribute to making the life-cycle look flatter.
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 firm dynamics to infer the degree of allocative distortions that are necessary to replicate the cross-sectional life cycle in the data.

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 firm-level innovation, with entry and exit and a stationary firm size distribution. We innovated upon these theories by interacting the built-in mechanisms of the model with two types of allocative distortions, misallocation wedges and progressive profit taxes, and characterizing 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 findings suggest that our theory can account for the salient features of development dynamics in acceleration episodes and post-communist transitions. A property of our findings is that, despite dispensing from frictions to resource reallocation, e.g., financial frictions, the model can deliver a protracted path of growth in the rate of investment and in TFP in the economy. 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 firms with relatively low productivity. As a result from this tension, it takes several years for TFP to attain its new steady state level.
Our work also provides results that feedback into the empirical literature. In

A Data Description
We first provide a list of the countries captured by the methodology of Hausmann et.al (2005) as accelerations, and the full list of post-communist transitions.
For these countries, we construct3.1 the average of T F P 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 data comes from Penn World Tables version 8.1. T F P is taken directly from the variable rtf pna in the database, while the investment rate is given by csh i . The lines 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 we need to make sure that the dataset covers most firms in the economy in order to avoid biasing the calibration of the underlying distortion. Thus, for calibration 48 purposes, we appeal to data from the Census Yearbooks as reported in Brandt, Van Biesebroeck, and Zhang (2014) . They report the total number of firms and the employment level from the Census Yearbooks of 1995Yearbooks of , 2004Yearbooks of , and 2008 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 figure 3.2 29 of motivating facts.
We appeal to the alternative dataset, the NBSsurveys, to provide a longer and When we contrast the model's predictions about transitions with data, we make them comparable by making the following adjustments to the latter. First, for T F P, we extract the trend component of the time series of Chile and China applying the Hoddrick-Prescott filter, with a smoothing parameter λ = 100. Then, since we work with a model that features no growth in the stationary equilibrium, we extract a balanced growth path rate of improvement in aggregate productivity of 0.8% per year to the HP filtered trends. We estimate this growth rate to be 0.8%, which is the average post-war T F P growth rate in the USA implied by the PWT database 8.1.

B 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 fit of the Pareto 29 The figure 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 firms and employment data for the year 1993 in their work.
49 assumption by comparing the entire employment size distribution of entrants with the data. We plot the employment-weighted distribution of entrants in figure B.1.