FINANCIACIÒN DE LOS PROYECTOS

In this section I calibrate/Estimate the model parameters to match the observations in China and the US. Standard parameters are chosen from previous work and are equal across the two economies. However, to disentangle the role of distortions (transitory, permanent, and correlated) on the one hand and frictions to capital adjustment on the other hand, the parameters governing these two channels are chosen jointly to match the corresponding moments from the firm-level data in each country.

A period is assumed to be a year and therefore, the intertemporal discount rate denoted by β is set to 0.95. Capital depreciation rate δ is set to 0.08 and the constant elasticity of substitution between intermediate goods γ is set to 3 following Hsieh and Klenow (2009). The shares of labor and capital αK and αL are set to 1₃ and 2₃ respectively. I also assume that ρz = 0.9 in both countries as the persistence of firm level productivity does not vary substantially across countries.14Having fixed ρ_z, σ_z is chosen separately for US and China such that the dispersion of the stationary distribution resulted from the AR(1) process matches the dispersion in firm level log productivity found in the data.

The rest of the parameters θ = [c_f, ce, ψ, ρ, σλ, σκ] are estimated jointly to minimize the distance between target moments and their corresponding values in the each country. The AR(1) process for firm level productivity shown inEquation 2.7 is approximated with the method introduced inKopecky and Suen(2010) with 50 grid points. Permanent distortions are approximated with an AR(1) process with persistence equal to 0.999 and 10 grid points. Transitory distortions are not discretely approximated as they are not a part of the state space. Also, log capital stock is equally spaced 50 grid points in an interval (k, k) where the upper and lower bounds are chosen to not be binding for investment and disinvestment decisions of active firms. The distribution from which the entrants draw their initial state variables is determined by combining three independent distributions over Z, T , and K. Productivity and distortions are drawn from the stationary distributions resulted from the corresponding AR(1) process and initial capital stock is drawn from a uniform distribution over the grid points in (k, k).

Having discretized the state space, I solve for the unique stationary equilibrium with entry and exit numerically. Endogenous entry and exit of firms together with exogenous parameters determine the evolution of the measure of active firms as follows:

µt+1(B) = Z

s∈S

(1 − χ(s)) Q(s, B) µ_t(ds) + ν(B) M_t+1 (2.17)

In which µt is the measure of active firms in time t, Mt+1 is the mass of entrants in next period, ν(.) is the probability measure associated with the distribution from which

14

new entrants draw i.e. G(z, λ, k). Also, Q(s, B) is the probability transition function of the state vector s = (z, λ, k). The central part of solving for the general equilibrium is convergence of a discretized version of the above mapping to a stationary distribution.15

All cross sectional target moments are computed using a random sampling of size 105 from the resulting stationary distribution. For moments that have a panel dimension (dispersion of investment) the sample is comprised of remaining firms i.e. the exiting firms are dropped from the panel sample.

The following describes the rest of parameters to be estimated and the target moments used to estimate them. c_f and c_eare costs of operation and entry, both measured in units of final output, for which the target moments are exit rate and average employment of firms respectively. The exit rate is computed as the ratio of the mass of exiting firms to all active firms in the stationary equilibrium and average employment is measured by dividing the exogenous mass of workers (L) by the endogenous mass of active firms (N = R

µ ds). ψ

measures the severity of adjustment costs. I follow the adjustment cost literature and use the dispersion of investment (changes in log of capital) as a target moment for adjustment costs.16The target moment to pin down the degree of correlated distortions is ρ_{z,tf pr}which is directly affected by the parameter ρ in the model. The moment chosen to pin down the value of σ_λ is the correlation of tf pr with exit decision conditional on firm level productivity. The moment is computed in the model by regressing χ on tf pr after controlling for z. Finally, σκ is calibrated to match the dispersion of tf pr.Table 2.1summarizes the fixed parameters and their values as well as the estimated parameters and their corresponding target moments:

Table 2.2 shows the corresponding target moments in China and the US. θ is estimated by minimizing the following loss function in which Γ(θ) is the vector of moments in the model, ˆΓ is the vector of moments in the data, and W is a re-scaling matrix assuring equal

weight on all moments.

L(θ) = (Γ(θ) − ˆΓ)0 W (Γ(θ) − ˆΓ) (2.18)

As Table 2.2 shows, the Chinese economy shows more dispersion in tf pr, exhibits a stronger correlation between firm productivity and tf pr, and also a larger dispersion in investment. Moreover, the conditional correlation between exit and the level of tf pr is zero in the US while positive in China neither of which are consistent with the negative correlation predicted by the adjustment cost hypothesis shown inFigure 2.2.

15

When discretized, µ is a vector of length Ns= Nλ× Nz× Nkand convergence is achieved by iteration from a given arbitrary initial vector. The corresponding discrete version of Q(s, B) is an Ns× Nsprobability transition matrix which incorporates the capital policy function as well as the probability transition matrices of z and λ. The criteria for convergence is ||µt− µt+1||∞< 10−6.

16

Table 2.1: Summary of Parameters

Parameter Description Value/Target

Fixed γ Elasticity of Substitution 3 β Discount Rate 0.95 δ Capital Depreciation 0.08 αK Capital Share 0.33 αL Labor Share 0.66

ρz Persistence of Log Productivity 0.90

σz Dispersion of Log Productivity 0.37 (US) / 0.41 (China)

Estimated

cf Fixed Cost of Operation Exit Rate

ce Entry Cost Mean Employment

ψ Adjustment Cost σi

ρ Correlated Distortions ρz,tf pr

σλ Permanent Distortions ρ(χ, tf pr|z)

σκ Transitory Distortions σtf pr

Notes. All fixed parameters except for σz are equal in the US and China while all the estimated parameters are country specific. σiis the standard deviation of ∆k, ρz,tf pr is the coefficient of a linear regression where tf pr is the dependent variable and z independent variable, and ρ(χ, tf pr|z) is the coefficient of a linear re- gression with χ as dependent and tf pr as independent, controlling for z.

Table 2.2: Target Moments: US and China

Moments Exit Rate Mean Emp σi ρz,tf pr ρ(χ, tf pr|z) σtf pr

US 10 22 0.24 0.1 0.00 0.49

China 10 22 0.37 0.5 0.08 0.96

Notes. Exit rate is approximated to be roughly 10% annually for a wide range of economies as reported in

Tybout(2000),Bartelsman et al.(2004). Average employment in manufacturing establishments is reported to be 22 inBento and Restuccia(2017) for the US. Due to lack of information on the Chinese manufactur- ing establishments size, I use the same figure for the case of China.Hsieh and Klenow(2014) report ρz,tf pr to be 0.1 in the US and approximately 0.5 in developing economies such as India and Mexico. σiis taken fromDavid and Venkateswaran(2017) and ρ(χ, tf pr|z) is backed out from the exit regression estimates in

Hsieh and Klenow (2009) as explained in the appendix. σtf pr is also taken from the statistics reported in

Table 2.3: Calibrated Parameters and Moments: US and China

Parameter cf ce ψ ρ σλ σκ

US 51 724 41 0.86 0.00 1.14

China 280 260 4.4 -0.5 0.6 1.9

Moment Exit Rate Mean Emp σi ρz,tf pr ρ(χ, tf pr|z) σtf pr

US 10.5 21.1 0.29 0.13 0.00 0.50

China 10.4 22.6 0.35 0.51 0.09 0.96

Notes. cf, ce, and ψ are rounded to the nearest integer. Parameters governing distortions are rounded to two decimal points. The moment figures result from the model simulations with the calibrated and estimated parameters.

Table 2.3 shows the estimated parameters and moments for both economies. The first panel in Table 2.3 shows that compared to the US, the policy distortions are more severe across the board in China. Both permanent and transitory distortions have a higher dis- persion in China. Furthermore, a more negative ρ estimated for China implies a higher likelihood that more productive firms face more obstacles in China.17 On the other hand, there seems to be a higher adjustment costs of capital in the US as the calibrated parameter for ψ is almost ten times larger in the US. This is partially due to the fact that the reported variance in the firm level productivity is much larger in China while the investment variance is not proportionally higher in China. The second panel reports the calibrated moments in each economy when the estimated parameters are combined with the fixed parameters in Table 2.1.

Having calibrated the model to the manufacturing sectors in the US and China, I now proceed to disentangle the effects that each of the different sources have in generating static misallocation in each country. There are four distinct sources of generating static misallocation. ψ determines the severity of capital adjustment costs while ρ, σλ, and σκ capture the degree of correlated, permanent, and transitory distortions. In order to estimate the effect of each channel separately, I first set each of the above parameters to zero while keeping all other parameters constant at the estimated level inTable 2.3. I then compute the standard deviation of tf pr in the counterfactual economy and compare it to the estimated level. In order to separate the effects of capital frictions from distortionary policies, I also keep ψ at the estimated level while set all parameters governing distortions to zero and re- compute the standard deviation of tf pr. Table 2.4summarizes the counterfactual results.

The first feature whichTable 2.4shows is that in both economies, distortions account for a larger share of observed static misallocation. When shutting down all three types of dis- tortions and keeping the adjustment cost parameter at the estimated level, approximately 45% of the dispersion in tf pr is eliminated in the US. When focusing on the adjustment

Table 2.4: Contribution to Static Misallocation

Frictions Distortions

Adjustment Cost Correlated Permanent Transitory All

Counterfactual ψ = 0 ρ = 0 σλ= 0 σκ= 0 τ = 0

∆σ_{tf pr}%

US 3.53 -10.92 0 59.75 44.66

China 6.53 8.83 5.63 47.37 67.38

Notes. All figures are in percentages. Each figure is computed as X∗= (1 −X_X˜) × 100, where X∗is the figure in the table, X is σtf pr in the fully calibrated model, and ˜X is σtf pr under the counterfactual specified in each column.

cost, this effect is less than 4%. The results are qualitatively similar in China where distor- tions explain more than two thirds of the dispersion in tf pr while adjustment costs explain roughly 7% of it. This has implications for the potential gains in aggregate productivity in both countries. Contrary to the conclusion in Asker et al. (2014), the larger share of mea- sured misallocation explained by policy distortions implies that large gains in productivity can be achieved by changes in distortionary policies in developing economies.18

Furthermore, when decomposing the effects of different types of distortions, it can be seen that the permanent distortions do not explain the variation in tf pr in the US while they play a positive, albeit small role in China. This is due to the fact that the observed selection inefficiency (i.e. ρ(χ, tf pr|z)) is zero for the US as reported inTable 2.2. The two countries qualitatively differ in effects of correlated distortions as well. In the US economy, changing ρ to zero in fact increases the dispersion of tf pr resulting in a negative number for the share of correlated distortions. However, approximately 9% of the dispersion in tf pr is explained by correlated distortions in China. This stems from the fact that the estimates of ρ inTable 2.3 are of opposite sings in the two countries. A positive estimate for the US indicates that more productive firms are supported by distortionary policies at the expense of less productive firms. Conversely, the negative estimate of ρ in China indicates that larger and more productive firms face more obstacles compared to smaller and less productive ones. Furthermore, the strongest source of the dispersion in tf pr is the transitory distortions in both economies which explain nearly half of the measured static misallocation.

18_{The current theoretical framework can be used to compute the gains in measured aggregate productivity} which is left for future work. However, using similar methodologies and data, and assuming the entire measured misallocation is caused by distortions, the misallocation literature (e.g.Hsieh and Klenow(2009) reports numbers as high as 100% gain in aggregate productivity in developing economies.

2.4

Conclusion

This paper studies the relative significance of different frictions and distortionary policies on generating misallocation of inputs measured traditionally by the dispersion of marginal products across firms. Calibrating a general equilibrium model of firm dynamics with en- dogenous entry and exit to the US and Chinese economies, I separate the role that adjust- ment costs as well as distortionary policies play in causing dispersion of marginal products. The results show that adjustment cost of capital explains less than 10% of the measured misallocation in both countries. On the contrary, policy distortions explain more than two thirds of the measured misallocation in China and approximately 45% in the US. The cal- ibrated model also shows that compared to the US, there are more severe permanent and correlated distortions in China. The conclusions of this paper imply that considering the capital formation frictions only slightly reduce the losses in aggregate productivity caused by distortionary policies that the misallocation literature documents in developing countries.

Chapter 3

Cross-Country Differences in

Productivity:

Abstract

This paper uses firm-level data for a wide range of countries and provides estimates of total factor productivity – hereafter TFP – in the manufacturing sector. Aggregate TFP at the country level and its importance in explaining income difference across the world are analyzed. I show that when constructed from firm-level data, the variation in TFP across countries is lower than commonly calculated in the development accounting literature using aggregate variables. I find that less than 55% of income differences across countries can be explained by differences in TFP.

Keywords: Total Factor Productivity, Misallocation, Selection, Policy Distortions, Adjust-

3.1

Introduction

What explains the vast differences in standards of living across countries? The development accounting literature uses cross-country data on output and inputs to assess the relative contribution of differences in input quantities (i.e. physical and human capital) and dif- ferences in the efficiency (i.e. productivity) with which the inputs are used to these vast differences. Traditionally, the share of the observed differences that cannot be accounted for by variation in measured inputs is seen as differences in total factor productivity – hereafter TFP – across poor and rich countries. Different authors report radically different results on the importance of these two channels using very similar methods. The key reason for this controversy is that there are difficulties in measurement of physical and human capital at the country level. In this paper, I suggest a new method that constructs measurements of TFP at the country level using data at the firm level where measuring inputs of production is less prone to the aforementioned inaccuracies.

To keep the results comparable to the previous work, I assume a Cobb–Douglas pro- duction function at the firm level which yields an aggregate production function similar to those widely used in the development accounting literature. However, as opposed to pre- vious work, I do not impose a constant returns to scale assumption and instead, estimate the production function using the firm-level data available. As a benchmark, I estimate the firm-level production function using ordinary least squares – hereafter OLS. Since the OLS estimates of parameters are likely to be inconsistent, I estimate the production function using the method introduced inOlley and Pakes (1996) – hereafter OP – to correct for po- tential biases in the estimation of the capital and labor elasticities. The main two channels that could cause bias in estimation of capital and labor elasticities are as follows: firstly, since the levels of labor and capital a firm hires are potentially positively correlated with the productivity level of the firm which is unobserved by the econometrician, it is possible that the OLS method overestimates the elasticities of labor and capital. Secondly, because firms with higher level of capital can survive negative shocks to their productivity and remain active in the industry and that the data is collected from the population of firms that have not exited, a negative bias in estimating capital elasticity might exists. The OP method ad- dresses both these issues and provides more accurate estimates of the production function parameters.

Having estimated the firm-level production function with both methods described above, I infer the firm-level TFP from the data on sales, employment, and capital levels. The proposed method thus, provides a distribution of the firm-level TFP from which one can approximate TFP at the country level and study its variation in time and across countries.1

1

This approach also provides the possibility of comparing other moments of the TFP distribution across countries. In particular, age-productivity and size-productivity profiles of firms are thought to mirror ineffi- ciencies and policy distortions in the developing world. For an example, seeHsieh and Klenow(2014).

I provide two methods using which the country-level TFP can be backed out from the distribution of firm-level TFP. I then compute what the income differences across poor and rich countries would be if they had access to the same levels of human and physical capital and only differed in TFP levels. Using both measures of the country-level TFP, I conclude that while there are significant differences in total factor productivity across poor and rich countries, these differences in the efficiency explain less than 55% of output per-worker differences across countries.

Related Literature – The first attempt to quantitatively assess how important factors

of production are in explaining income differences was done byMankiw et al.(1992). They augment human capital to the standard Solow growth model and estimate cross-country regressions of production function with aggregate data. In their study TFP is the residual to a production function regression and therefore the success rate of inputs in explaining the differences in output per-worker is measured by the R-Squared of the regression. They report R2 = 0.78 and conclude that the lower levels of human and physical capital are the main driving forces of the income differences across rich and poor countries. Klenow and Rodriguez-Clare(1997) criticize using regression analysis and point out the potential endo- geneity issues arising from running such regressions. They propose an accounting method that is not prone to these errors caused by estimation. In an accounting exercise, one needs to collect measures of aggregate output and inputs, calibrate an aggregate production func- tion to the observed moments in the data (mainly capital and labor share in the output), and compute the variation of the output explained by the variation in inputs. They show that the rival inputs of production (physical and human capital ) explain a third of the variation in per-worker output within their sample. Using a similar strategy and with slight modifications,Hall and Jones (1999b) also conclude that the variation in TFP is the dom- inant force in explaining the differences in the standards of living across countries. Caselli (2005) uses updated data and reports that the “success rates” of the inputs never exceed