Productivity Volatility and Misallocation

Transcription

1 Productivity Volatility and Misallocation Allan Collard-Wexler NYU and NBER March 3, 2011 Abstract Plant-level data from the World Bank s Enterprise Research Data on 34 countries shows considerable differences in the dispersion of productivity within these countries. I show that countries which have more time-series variation in productivity will also have more dispersed productivity. This volatility mechanism explains between 40% and 60% of the cross-country productivity dispersion in the World Bank Data. Moreover, a calibrated model of investment with adjustment costs shows that increasing the volatility of productivity can quantitatively replicate the observed relationship between misallocation and volatility seen in the data. 1 Introduction It is a well-documented fact that there are large differences in plant productivities. Moreover, the extent of this dispersion varies considerably across countries. A growing literature addresses the welfare effect of this productivity dispersion, most prominently the work of Hsieh and Klenow (2009) on misallocation. They show that if the manufacturing sector in India and China had the same productivity dispersion as the manufacturing sector in the United States, output would increase by between 30% and 60%. Much of the work following this paper has tried to find mechanisms to explain why productivity differences do not get driven out by reallocation, such as the work of Restuccia and Rogerson (2008), Collard-Wexler (2009), Midrigan and Xu (2009), and Moll (2010). Using data from the World Bank s Enterprise Data sets on plants in 34 countries I show that much of the cross-sectional dispersion of productivity is correlated with the time-series volatility of productivity: countries that exhibit the greatest time-series volatility of productivity also have the greatest cross-sectional dispersion in productivity. Productivity dispersion is important from a welfare perspective to the extent that it causes misallocation. For the purposes of this paper, misallocation can be defined as the failure of equalization of the marginal revenue product of capital across plants in the same country. I would like to thank Dave Backus for introducing me to the World Bank Data, and Daniel Xu and Alessandro Gavazza for their comments. 1

2 Greater volatility of productivity gives rise to misallocation through two channels. The first is a purely passive mechanism: more volatility in the productivity process will bounce firms around the productivity distribution. Using estimates of the volatility of productivity process via an AR(1) process with mean-reversion, I find that the volatility of productivity varies from 0.2 to 1.2 across countries, and this volatility would generate the magnitude of productivity dispersion observed in the data which varies from 0.5 for Poland to 1.6 for Bangladesh. If capital cannot be frictionlessly transferred between plants (if there are adjustment costs) then this volatility in productivity will translate into misallocation. The second channel is an active mechanism. If productivity is a mean reverting process, then high levels of productivity volatility will imply a lower information content of current productivity on the expected net present value of the marginal product of capital, which is used by firms in their investment decisions. In countries with more volatility of productivity, there will be less adjustment of investment to differences in current productivity. Again this second channel, which operates through the firms optimal policy decisions, also yields misallocation. What is important to notice is that if one believes that frictions generate productivity dispersion, then policies that make it easier or harder to fire and hire workers or policies that make access to capital market more uniform are essential. However, if the crosssectional differences in the marginal revenue product of capital are caused by different volatilities in productivity, then the welfare effect of different levels of productivity dispersion are ambiguous and may be non-existent. Essentially, misallocation may be inefficient from static perspective, but not necessarily inefficient from a dynamic perspective. The work in this paper shows that if one believes that time series volatility of productivity is exogenous, then cross-country differences in the volatility of productivity are large enough to explain the misallocation observed between different countries. The main caveat of this paper is that I do not provide a model which explains size of adjustment costs necessary to generate the appropriate frictions that prevent reallocation of capital across plants, nor do I provide much insight into what generates cross-country differences in the volatility of productivity in the first place. All I can say is that the model where I assume the same adjustment cost across all countries, but a different productivity processes, quantitatively generates the cross-country differences in misallocation that are observed in World Bank Enterprise level data. 2 Model I use a standard model of investment that follows the work of Bloom (2009), Dixit and Pindyck (1994), and Caballero and Pindyck (1996) quite closely. A firm has a constant returns to scale Cobb-Douglas production function for value-added output Q it (i.e. net 2

3 of materials which enter in a Leontieff like way) given by 1 : Q it = P it à it K α itl 1 α it (2) and the demand curve for the firm s product is given by a constant elasticity of demand curve: Q it = B it P ɛ it (3) Combining these two equations, I obtain the value-added sales generating function: S it = A 1 a b it K a itl b it (4) where A it = Ã1 1 ɛ it B 1 ɛ, a = α(1 1 ɛ ) and b = (1 α)(1 1 ɛ ). Firms can hire labor in each period for a wage w. However, investment decisions are affected by a one period time to build. Thus the static first-order condition with respect to labor yields: and thus π L = ba1 a b it L it = Thus the firm s period profits are given by: which can be written more compactly as: K a itl b 1 it w = 0 (5) ( ) 1 b 1 b 1 a b A 1 b K a 1 b (6) w ( ) 1 [ ] π(a it, K it ) = A 1 a 1 b K 1 b b 1 b b w w w (7) π(a it, K it ) = γk a 1 b (8) where γ = A 1 ( 1 b b ) 1 [ 1 b b w w w]. Denote the demand-efficiency term Y it AR(1) process given by: = A 1 a b it. Suppose that Y it follows an ln(y it ) = µ + ρ ln(y it 1 ) + σ c ν it (9) where ν it N (0, 1) is an i.i.d. standard normal random variable. Notice that I will allow the volatility of productivity, as measured by σ c, to vary from one country to another. Indeed, in the computed model, this volatility parameter is the only difference between countries. Capital depreciates at rate δ so K it+1 = δk it + I it where I it denotes investment. The cost of investment, denoted C(I it, K it, Y it ) follows Bloom (2009) and is composed of 1) a fixed disruption cost of investing, 2) capital irreversabilities captured by a lower 1 One can run the estimates in the paper using productivity generated by a gross production function of the type: Q it = P it à it M αm it K α k it Lα l it (1) where M it denotes material inputs. I find the same effects using this production function. 3

4 sale price than purchase price, and 3) a convex adjustment cost as a function of the percent investment rate: C(I it, K it, Y it ) = C F K1(I it 0)π(Y it, K it ) + I it + (1 CP K)Iit ( ) (10) + C Q K K Iit it K it A firm s value function V is given by the Bellman equation: V (Y it, K it ) = max π(y it, K it ) C(I it, K it, Y it ) I it ( ) Yit+ 1 ρy it µ (11) + β V (Y it+1, δk it + I it )φ dy it+1 Y it+1 σ and thus a firm s policy function I (Y it, K it ) is just the investment level that maximizes the firms continuation value. Note that since there is no entry or exit in this model (which is a consequence of the absence of fixed costs and decreasing returns to scale in the revenue equation) there is no truncation of the productivity distribution. Thus the cross-sectional standard deviation of productivity is given by the ergodic distribution of Y it yielded by the formula: σ Std.y it = (12) 1 ρ 2 where y it = ln(y it ) and in general I follow the convention of labeling variables expressed in logs in lower case. As well, the static marginal revenue product of capital (henceforth MRP K ) is given by: MRP K = π K = γ a 1 b K a 1+b 1 b = a S it (13) 1 b K it Thus the logarithm of the MRP K is log(mrp K ) = log(a) log(1 b) + log(s it ) log(k it ), which implies that the dispersion (measured in standard deviations) of log(mrp K ) is: Std. (log(mrp K )) = Std. (log(s it ) log(k it )) (14) Moreover, the volatility of log(mrp K ) is just Std.(log(S it ) log(s it+1 ) log(k it ) + log(k it+1 )). I use baseline parameters taken from Bloom (2009) presented in Table 1, and estimates of the process for Y it discussed later in the paper in Table 4 on page 9, to compute the model. 2 2 Note that the adjustment cost function proposed by Bloom (2009) is invariant to a rescaling of all variables. Thus if there are different currency units for different countries, this will not affect the predicted cost. 4

5 Bloom (2009) Parameters Estimated AR(1) Parameters α = 1 3 ρ = 0.8 ɛ = 4 µ = 0 δ = 10% σ = 0.7 β = % CK P = 40% CK F = 1.2% C Q K = Calibrated Parameter w = Computational Results Table 1: Baseline Parameters To illustrate the effect of productivity volatility on the characteristics of the industry in terms of investment and capital, I compute the optimal investment policies for the value function in equation (11). I solve this model using a discretized version of the state space (Y it, K it ). Specifically, I use a grid of capital states going from log capital 3 to log capital equal to 20 in increments of 0.1. Moreover I use a grid of productivity y it = log(y it ) with 50 grid points whose transition matrix and grid points are computed using Tauchen (1986) s method. 3 Using the computed optimal policies, I simulate the evolution of the industry for 100 plants over a 1000 periods. Table 2 shows properties of the simulated data for different volatility parameters σ ranging from 0.2 to 1.8, which encompass the range of cross-country volatility found in the data. As the volatility parameter σ increases from 0.2 to 1.8, the dispersion of productivity increases from 0.55 to As well, the dispersion of the ratio of sales to capital increases from 0.59 to Likewise, the volatility of the sales to capital ratio increases from 0.44 to Since the volatility of sales to capital ratio is a combination of the volatility of productivity and the adjustment of capital stock to the firm s productivity, I also compute the volatility of capital and the probability of observing zero investment. The adjustment of capital is a hump shaped function of volatility, where adjustment of capital peaks at a variance σ of 1.0. Likewise, the probability of investing peaks at σ = 1.0. Note that there are two effects which cause this hump shaped response of investment to volatility. First, as productivity shocks increase, there is a greater change in productivity for firms to respond to. Second, as productivity volatility increases, productivity becomes a poorer predictor of future productivity; i.e., there is less signal in a change in productivity. This means that firms are less likely to either invest or disinvest. On net, the main effect of higher productivity volatility is to increase the passive mechanism for generating dispersion of the marginal revenue product of capital. The adjustment of capital stock to productivity also varies with volatility, but it is quantitatively of a lower order of magnitude. As a preview of the results later in the paper, the 3 The model is solved in MATLAB using policy iteration with a sparse transition matrix since there are 8500 states. 5

6 volatility of productivity ranges from 0.2 to 1.2, and the dispersion of the marginal revenue product of capital ranges from 0.5 to about 2.0. Thus the productivity volatility mechanism can by itself generate large cross-country differences in misallocation. Volatility Dispersion (Standard Deviation) of Volatility of Zero σ Productivity Log Sales Capital Ratio Log Sales Capital Ratio Capital Investment y it s it k it s it k it k it Table 2: Computed Statistics for Different Volatility Levels 3 Data I use data from the World Bank s Enterprise Research Data to investigate misallocation. Specifically, I use the comprehensive dataset ( This data is collected by the World Bank across 41 countries and many different industries. 4 The main advantage of this dataset is the comparable collection of data across several countries. Indeed, without this comparability, it would be more difficult to argue that differences in measurement error are not responsible for the differences we observe across countries. Furthermore, information on sales,assets, and employment are collected for a three year period, which allows me to use the panel component of the data, and compute changes in productivity and capital. I calculate productivity in two different ways, which yield very similar results. The first technique computes productivity (y it ) as the gap between value added and labor and capital inputs: y it = s it αitl l it αitk k it (15) where s it denotes the log of sales minus the cost of materials, and αit l and αk it denote the plant specific input cost shares of labor and capital respectively. 5 The second technique computes productivity ((yit OLS ) as the residual of a regression of value added on capital and labor, with country fixed effects: which I will call the OLS measure of productivity. 6 s it = α l l it + α k itk it + δ c + y OLS it (16) 4 The countries and industries that I use are listed in Table 9 and Table 10 in the appendix. 5 In other words, αit l = Lit L it+k it and αit k = Kit L it+k it. 6 While there are many techniques for measuring productivity it turns out that the ranking of a country s productivity dispersion is relatively unaffected when using different estimation techniques. 6

7 I drop observations whose productivity is above 6 in absolute value to reduce the issue of outliers driving the empirics. Dropping plants with more than 2 or 9 in absolute value does not change the pattern of results reported in the paper. Table 3 presents summary statistics of the data, where the first set of statistics are at the establishment level, the second are at the country level (for 34 countries which have data), the third at the industry level (for 23 industries), and the final set are at the country-industry level. While there are over establishments in the data, only about can be used to compute the volatility of productivity, since I need both information on sales, materials, assets, and salaries to compute productivity, and two years of this information to compute the change in productivity. There are considerable differences in establishment size in this data. While the mean establishment has 138 workers, the smallest establishment employs no workers and the largest establishment employs over Log sales are on average 9.4, but there is a striking variance in establishments sales, as the standard deviation of log sales is 3.6. Log value added is substantially lower than log sales, with a mean of 8.7, but with a similar standard deviation. Productivity has a mean of -0.5 when I use the first technique for computing it, and mechanically has a mean of 0 when I use OLS. The standard deviations of both of these measures of productivity are similar: 1.2 for productivity computed using input cost shares and 1.0 for productivity computed using an OLS regression with country fixed effects. The average investment capital ratio is -2.7 in log terms, or about 6%. Again there is large variation in investment intensity across plants as the standard deviation of the log investment capital ratio is 1.3. Furthermore, in about half of all years, firms don t invest at all. Sales change quite a bit from year to year, as the mean change in log sales is 0.1, but the variance of this change is very large, at about 0.7. Likewise, productivity changes substantially from year to year, as the standard deviation of productivity change is 0.7, which is a big number given the standard deviation of productivity itself is 1.2. The bottom panels present aggregate statistics at the country, industry, and countryindustry level. The standard deviation of productivity within a country ranges from 0.49 to 1.66, which are important differences. Moreover, the standard deviation in the change in productivity within a country varies between 0.2 and 1.2. Similar statistics are shown at the industry level of aggregation, and I find a standard deviation of productivity between 0.83 and 1.47, and a standard deviation of the change in productivity between 0.42 and It is interesting to note that there are fewer cross-industry differences in productivity dispersion and volatility than cross-country differences. Finally, the country-industry statistics show greater differences in productivity dispersion and volatility than statistics at either the country or industry level. 4 Results In this section I show that the relationship between misallocation and volatility is similar to the one predicted by the model in section 2. First, I estimate the country specific volatility of productivity. Second, I present regressions of country level productivity 7

8 Variable Mean Std. Dev. Min. Max. N Establishment Level Data Workers Log Sales Log Materials Log Value Added Log Assets Log Salaries Productivity Productivity (OLS) Log Value Added Capital Ratio Log Investment Zero Investment Log Investment Capital Ratio Sales Change Productivity Change Country Level Data Observations per Country Standard Deviation of Productivity Standard Deviation of Productivity (OLS) Interquartile Range Deviation of Productivity Range of Productivity Standard Deviation of Change in Productivity Industry Level Data Observations per Industry Industry Std. of Productivity Industry Std. of Change in Productivity Country-Industry Level Data Observations per Country-Industry Country-Industry Std. of Productivity Country-Industry Std. of Change in Productivity Source: World Bank Enterprise Research Data. Table 3: Summary Statistics 8

9 dispersion and misallocation on country level productivity volatility. Table 4 shows the estimates of the AR(1) process for productivity y it = µ+αy it 1 + ση it by Maximum Likelihood. Column I shows the base estimates, while columns II and III allow the variance term σ to vary by the size of the plant s capital stock, and by the standard deviation of the change in productivity for the plant in that country, or Std.(y it y it 1 i C) where C indexes countries. While plant size, as proxied by capital assets, has no effect on the volatility of productivity at the plant level, the country s average volatility has a large effect on plant level volatility, which is to be expected as σ and the standard deviation of change in productivity in a country are essentially measures of the same process. For this reason I will often interchange σ c for Std.(y it y it 1 i C) in the regressions in this paper since the standard deviation of changes in productivity is more directly measurable. When I add country fixed effects for the variance of productivity in column IV, I find that the standard deviation of the country fixed effect term is 0.19, indicating that there are considerable cross-country differences in the size of the productivity shocks in different countries. Likewise, column V shows that there are also considerable differences in the size of the productivity shocks received by plants in different industries as the standard deviation of the industry fixed effect is Dependent Var: Productivity y it I II III IV V Last Year s Productivity y it *** 0.79*** 0.81*** 0.81*** 0.79*** (0.02) (0.02) (0.02) (0.02) (0.02) Constant 0.09*** 0.09*** 0.09*** -0.12*** -0.15*** (0.01) (0.01) (0.01) (0.01) (0.03) Variance σ Constant 0.69*** 0.59*** *** 0.67*** (0.05) (0.12) (0.01) (0.00) (0.00) Log Assets 0.01 (0.01) Standard Deviation of Change in Productivity 0.92*** (0.02) Country Fixed Effect X Variance of Country Fixed Effect 0.19 Industry Fixed Effect X Variance of Industry Fixed Effect 0.15 Observations Countries Industries 25 Log-Likelihood Standard Errors Clustered by Country in Columns I-IV and by Industry in Column V. Table 4: Time Series Process for Productivity Using the estimates of the AR(1) process in Table 4 in Column VI, the slope of the relationship between Std.y it and σ should be 1.6. Moreover, the country with the lowest volatility has a σ of 0.29 (Poland), while the country with the highest volatility has a σ of 1.11 (Bangladesh). The simple arithmetic of the AR(1) process would then 9

10 predict a standard deviation of productivity of 0.47 for Poland and 1.81 for Bangladesh due to the differences in volatility in these countries. In fact, Bangladesh has a productivity dispersion of 1.65 as measured by the standard deviation of productivity, and Poland has a standard deviation of Figure 1 plots the data on country level productivity dispersion against country level volatility of productivity. The relationship between productivity volatility and crosssectional dispersion predicted by the stationary distribution of the AR(1) process is also plotted on this graph. This prediction fits the data very well. While this relationship is mechanical, in the sense that it is the outcome of a statistical process, it does rely quite heavily on the fact that a country s volatility σ C is stable over time. 2 Standard Deviation of Productivity Standard Deviation of Change in Productivity Note: Circle Size is proportional to the number of plants per country. Line indicates the prediction from the stationary distribution of an AR(1) process: Std.y it = 1 ρ σ. 2 Figure 1: Plot of Productivity Dispersion and Productivity Volatility Figure 2 plots the relationship between the dispersion of the marginal revenue product of capital, or Std.(s it k it ), against country level productivity volatility. I also plot the predicted relationship between MRP K and σ from the computed model in Table 2. At low levels of volatility, the model s prediction does quite well at predicting country level misallocation. However, at high levels of productivity dispersion, the model predicts substantially more misallocation than is observed in the data. 10

11 Standard Deviation of Log Sales-Capital Ratio Standard Deviation of Change in Productivity Note: Circle Size is proportional to the number of plants per country. Line is prediction from Table 2. Figure 2: Misallocation and Productivity Volatility I can think of two justifications for the over-prediction of misallocation at high levels of productivity volatility. The first is a greater difficulty measuring volatility for countries that have larger changes in plant productivity from year to year. This would attenuate the relationship between misallocation and volatility observed in the data. The second justification stems from the fact that the model s adjustment costs are taken from Bloom (2009), who estimates these adjustment costs for firms in Compustat in the United States. These adjustment costs may be inappropriate for establishments in the developing countries surveyed by the World Bank. However, I would need countries to have lower adjustment costs in more volatile countries in order to square the model s prediction with the data. Thus the misallocation puzzle is flipped to why do countries with more misallocation have such low adjustment costs for capital? While the preceding Figures are illustrative of the role of productivity volatility in generating different levels of misallocation, they do not directly tell us about the statistical significance of this mechanism. Table 5 presents regressions of productivity dispersion on productivity volatility. Column I shows regressions at the country level weighted by the number of productivity observations per country. This weighting is used to give more importance to countries whose measurement or productivity dispersion and 11

12 productivity volatility is relatively precise. In other words, it is a simple proxy for weighting by the optimal weighting matrix: the inverse of the covariance matrix of the estimated productivity dispersion and productivity volatility. 7 Column II shows results that are unweighted by the number of observations per country. In Column I and II, I find coefficients on the standard deviation of the change in productivity of 0.8 and 0.7, with standard errors of less than 0.2. Thus there is strong statistical support for the hypothesis that dispersion and volatility are related. Column III adds industry fixed effect and Column IV adds log salaries, log assets, and industry fixed effects. The coefficients are fairly similar to those found without industry fixed effects or information on salaries and assets at 0.8 and 0.7. These coefficients also have comparable standard errors, even though to combine information at the country level (such as volatility) and information at the plant level (such as assets) I run the regression using all plants in the data and cluster the standard errors at the country level. These regressions eliminate the concern that dispersion and volatility are co-generated by a third variable such as a country s industrial composition, or the size of plants within a country. While the regressions in Table 5 have coefficients on the dispersion volatility relationship of 0.8, the stationary distribution of the model would predict a slope of 1 1 ρ = 2.1. Thus the dispersion-volatility relationship is weaker than the forecast from the simple statistical model. A lower estimated coefficient could be interpreted as an issue of error in variables for volatility σ C (see for instance Bound and Krueger (1991)). This could be due to real measurement error in σ C which would induce attenuation bias in the regression of dispersion on volatility. As well, a country s volatility is not stable over time, as the autocorrelation of σ C is about Again, this drift of a country s volatility σ C would also reduce the slope estimated in Table 5. Table 6 presents regressions of the standard deviation of the log of the ratio of value added to capital; i.e. misallocation, on productivity volatility. I use the same controls as in Table 5, and as such the only difference between Table 5 and Table 6 is the dependent variable. The coefficients in each Column are 1.0, 0.8, 1.0 and 1.0. They all have t-statistics above 4, and thus are statistically quite significant. Moreover, the R-squared is 0.4 in Column I when I have no controls, and increases to 0.5 when I include industry fixed-effects. Thus a substantial fraction of cross-country differences in misallocation can be attributed to differences in country specific productivity volatility. Finally I look at the relationship between capital volatility and the volatility of the productivity process. Table?? predicts that higher volatility of productivity will be accompanied by more adjustment of capital stock, up to a volatility of about 1.0. Figure 3 presents a scatterplot of capital volatility on productivity volatility along with the predictions from Table??. Note that the computational results do a good job of matching the observed pattern of adjustment in capital and productivity volatility; at least to the extent that asset volatility does not differ between countries with the same productivity volatility. The regression of the volatility of capital on the volatility of the productivity process yields a coefficient of 0.4 with a T-stat above 3. Thus countries which have a more 7 Since I am running a regression of estimated quantities on estimated quantities, there is a clear twostep issue in computing standard errors as in Murphy and Topel (1985). I have computed standard errors using a two-step cluster bootstrap procedure and find very similar standard errors as what I present in Table 5. 12

13 Dependent Var: Standard Deviation of Productivity I II (unweighted) III IV Standard Deviation of 0.79*** 0.66*** 0.82*** 0.74*** Change in Productivity (0.18) (0.18) (0.18) (0.14) Log Assets 0.02** (0.01) Log Salaries -0.03** (0.01) Industry FE X X Constant 0.55*** 0.63*** 0.61*** 0.69*** (0.15) (0.13) (0.14) (0.12) Observations Countries R-Squared Note: Standard Errors Clustered by Country. Accounting for Sampling Error in the computation of standard deviations using a clustered bootstrap yields very close standard errors. Table 5: Effect of Time-Series Volatility on Productivity Dispersion Dependent Var: Standard Deviation Log Value Added Capital Ratio I II (unweighted) III IV Standard Deviation of Change in Productivity 0.96*** 0.81*** 1.03*** 1.04*** (0.23) (0.22) (0.21) (0.21) Log Assets 0.01 (0.01) Log Salaries (0.01) Industry FE X X Constant 0.61** 0.70*** 0.60*** 0.61*** (0.17) (0.16) (0.13) (0.13) Observations Countries R-Squared Note: Standard Errors Clustered by Country. Table 6: Effect of Time-Series Volatility on Misallocation 13

14 volatile productivity process also have more volatility of capital stock. It is important to note that this relationship is less mechanical than it might at first seem, since a very small component of productivity changes come from changes in capital stock. Instead, the bulk of productivity changes stem from changes in value added itself..8 Standard Deviation of Change in Capital Standard Deviation of Change in Productivity Note: Circle Size is proportional to the number of plants per country. Line is prediction from Table 2. Figure 3: Capital Volatility and Productivity Volatility 4.1 Robustness Checks I perform several different robustness checks to ensure that the volatility-productivity connection is not the outcome of an issue in the data. First I want to make sure that different measures of productivity dispersion also generate a similar relationship between dispersion and volatility. Table 7 in the appendix shows different measures of dispersion, such as the interquartile range, the percentile range, and the standard deviation of productivity using OLS. With each of these measures of productivity dispersion, I find similar results and statistical significance. In particular, using either the interquartile range or the percentile range ensures that outliers are not generating the dispersion-volatility result. Likewise, using alternate measures of productivity verifies that choosing other techniques for computing productivity does not change the results. 14

15 Second, Table 8 in the appendix runs regressions where the units of observation are the 299 country-industry pairs. In Columns III and IV, I can include both industry and country fixed-effects (but not their interactions). This enables me to control for either industry or country specific factors that might artificially generate the volatilitydispersion relationship. For instance, in different countries it may be more or less straightforward to measure productivity. Including country fixed-effects bars these country specific factors from explaining the dispersion-volatility relationship. I find somewhat lower coefficients in this regression, 0.55 without any controls and 0.38 when I add country and industry fixed-effects. However, these effects are fairly precise, with t-stats above 7, in part because there are far more country-industry pairs (299) than countries (34). Putting in country and industry fixed effects eliminates crosscountry and cross-industry variation. This will change the noise to signal ratio in these regressions and change the attenuation bias due to errors in variables. Thus, inserting additional fixed effects could reduce the estimated regression coefficient. 4.2 Alternative Explanations The most direct alternative explanation for the patterns found in this paper is measurement error. Measurement error could simultaneously generate the volatility of productivity and the dispersion of productivity itself. For instance, suppose the data is pure measurement error such as: where η N (0, 1). Then the change in productivity is: y it = δ ct + ση it (17) y it y it 1 = (δ ct + ση it ) (δ ct 1 + ση it 1 ) = (δ ct δ ct 1 ) + σ(η it η it 1 ) (18) This means that the expression for Std.(y it ) = σ and the expression for Std.(y it y it 1 ) = σ 2 1 ρ where ρ is the serial correlation of η. Thus the coefficient in the regression of the regression of productivity dispersion on 1 productivity volatility should be 2 1 ρ. In particular, the ratio of productivity dispersion to productivity volatility is about 1.6, therefore the correlation of measurement error of productivity would need to be approximately 0.6 to replicate the observed relationship. While it is difficult to directly falsify the hypothesis of measurement error, this measurement error must have a very specific serial correlation to rationalize the results in this paper Reverse Causality Another potential explanation for the observed volatility-misallocation relationship is that it is misallocation which causes volatility, not the other way around. To check for this possibility, in Table 11 in the appendix shows the volatility of productivity for 8 It is quite straightforward to refute the hypothesis of pure measurement error, since y it is correlated with firm decisions such as investment. In fact an increase of one standard deviation in productivity raises the investment capital ratio by 40%. However, this does not exclude the hypothesis that productivity is partially measurement error. 15

16 each quantile of the productivity distribution. I find that the first and last quantile of productivity have substantially more volatility than the remaining quantiles. However, when I drop the first and last quantiles and rerun the estimates in Table 5, I find very similar results. Likewise, including the level of productivity in the regressions in Table 5 does not change the results either. 4.4 Caveats There are some important caveats to the role of volatility in misallocation. First, the main driver of misallocation is adjustment costs. I am using adjustment costs estimated off of Compustat data for American firms, and I make no attempt to rationalize the magnitude of these adjustment costs. Thus this paper makes no claim to explain misallocation itself, just the variation of misallocation in different countries. Second, I provide no mechanism to explain why countries differ in their volatility. In fact, it is not an easy task to find stories for differences in volatility of productivity that hold up in the data. For instance, one might expect mining to have greater productivity shocks than retail, but in fact they have very similar volatilities. Third, I cannot exclude the hypothesis that some form of measurement error could be generating the volatility-misallocation pattern seen in the data. This is mainly because it is difficult to convert the hypothesis of unstructured measurement error into a falsifiable hypothesis. 5 Conclusion There are large difference in the dispersion of productivity across countries. These differences translate into differences in the extent of misallocation, defined as the dispersion of the marginal revenue product of capital between firms, in various countries. Over half of these differences can be explained in terms of differences in the volatility of the productivity process itself. Moreover, the relationship between misallocation and volatility can be predicted quantitatively quite accurately by a model of investment with adjustment costs calibrated using the parameters from Bloom (2009). If differences in the volatility of the productivity process are at the root of differences in misallocation between countries, this has stark implications as to the welfare effects of misallocation. The prior literature has tended to focus on factors that yield either differences in the price for capital at different plants, or frictions that would elevate the cost of purchasing and selling capital in different countries. However, if misallocation can be produced by the same prices of capital and the same adjustment costs, but differences in the volatility of productivity process itself, then the welfare costs of misallocation are ambiguous, and may not exist. This paper raises the question, where do differences in volatility come from in the first place? From the perspective of the model, either greater changes in demand or productivity shocks, or a greater elasticity of demand ɛ, would generate greater changes in Y it. Indeed any factor that elevates β in a CAPM model would generate productivity volatility. While this paper is somewhat agnostic as to the source of volatility differences, it is clear than in models of industry dynamics, volatility is an essential difference between countries. 16

17 References Bloom, N. (2009): The Impact of Uncertainty Shocks, Econometrica, 77(3), Bound, J., and A. Krueger (1991): The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right?, Journal of Labor Economics, 9(1), Caballero, R., and R. Pindyck (1996): Uncertainty, investment, and industry evolution, International Economic Review, 37(3), Collard-Wexler, A. (2009): Productivity Dispersion and Plant Selection in the Ready-Mix Concrete Industry, Working Paper, New York University. Dixit, A., and R. Pindyck (1994): Investment Under Uncertainty. Princeton University Press. Hsieh, C.-T., and P. J. Klenow (2009): Misallocation and Manufacturing TFP in China and India, Quarterly Journal of Economics, 124(4), Midrigan, V., and D. Y. Xu (2009): Finance and Misallocation, Discussion paper, NYU. Moll, B. (2010): Productivity Losses from Financial Frictions: Can Self-Financing Undo Capital Misallocation?, Discussion paper, Princeton University. Murphy, K. M., and R. H. Topel (1985): Estimation and Inference in Two-Step Econometric Models, Journal of Business and Economic Statistics, 3(4), Restuccia, D., and R. Rogerson (2008): Policy distortions and aggregate productivity with heterogeneous establishments, Review of Economic Dynamics, 11(4), Tauchen, G. (1986): Finite State Markov-Chain Approximations to Univariate and Vector Autoregressions, Economics Letters, 20(2),

18 6 Appendix Dependent Var Std. y it IQR y it percentile y it Std. yit OLS Standard Deviation of 0.79*** 0.90** 1.93** 0.86** Change in Productivity (0.18) (0.26) (0.54) (0.26) Constant 0.55*** 0.68*** 1.31** 0.40 (0.15) (0.18) (0.38) (0.21) Observations Countries R-Squared F-Stat Table 7: Robustness Checks: Different Measures of Productivity Dispersion Dependent Var: Standard Deviation of Productivity I II III IV Standard Deviation of Change in 0.55*** 0.56*** 0.38*** 0.38*** Productivity Country Sector (0.06) (0.06) (0.05) (0.05) Log Assets ** (0.00) (0.00) Productivity -0.02*** -0.00** (0.00) (0.00) Industry FE X X Country FE X X Constant 0.66*** 0.70*** 0.83*** 0.87*** (0.04) (0.06) (0.04) (0.05) Observations Country-Industry R-Squared Standard Errors Clustered by Industry-Country. Table 8: Industry-Country Productivity Dispersion and Productivity Volatility 18

19 Country Productivity Standard Deviation N Algeria Bangladesh Benin Brazil Chile Costa Rica Ecuador Egypt El Salvador Eritrea Ethiopia Guatemala Guyana Honduras India Indonesia Kyrgyzstan Lithuania Madagascar Malawi Mauritius Moldova Morocco Nicaragua Pakistan Peru Poland South Africa Sri Lanka Tajikistan Thailand Turkey Uzbekistan Vietnam Table 9: List of Country Productivity Dispersion 19

20 Industry Standard Deviation of Productivity N Textiles Leather Garments Agro industry Food Beverages Metals and machines Electronics Chemicals and Pharmaceuticals Construction Wood and furniture Non-metallic Paper Sport goods IT services Other manufacturing Retail and wholesale Transport Mining and quarrying Auto Other transport Other unclassified Table 10: List of Industry Productivity Dispersion Note: Each Quantile has 1298 observations. Quantile of Standard Deviation of Productivity Change in Productivity Total 0.67 Table 11: More Dispersed Productivity Have Greater Volatility only for the top and bottom quantile. 20