Marginal returns to capital

Marginal returns to capital are estimated for each time spell based on the corresponding pooled cross-sectional data. Prots of microenterprise i (πi) are modeled as a function of the production factors capital (K_i) and labor (L_i), a vector of exogenous variables (Z_i) and unobserved factors at the individual level (θ_i). An example of the latter term is entrepreneurial ability, which determines prots and capital stock simultaneously:

π_i =f[K_i(θ_i), L_i, θ_i] (3) The earnings function is modeled with a log-linear transformation where α_i corre-sponds to the intercept andεi to the error term:

lnπ_i(K_i, L_i) =α_i +β_KlnK_i+L⁰_iβ_L+Z_i⁰β_Z+θ_i⁰β_θ+ε_i (4) Prots, capital and labor are introduced in log terms. The dependent variable π_i is measured by the average monthly prots that the entrepreneur reports to earn. For the case of capital stock, the replacement cost of the owned working equipment and premises plus inventories are considered. The vector of labor includes the weekly hours that the entrepreneur and both, paid and unpaid workers, normally destine to operating the microenterprise. The vectorZ_icaptures rm and entrepreneur's characteristics that may aect earnings such as: age, gender and marital status of the entrepreneur, plus age of the rm. The square terms of both age variables are considered to explore the rate of the corresponding eects. Also, ve schooling categories are used, where education lower than primary school serves as a reference. The vector also includes the log of the average wage at a given year, industry and state to capture the opportunity costs of (i) belonging to the wage sector and (ii) making protable investments given short term shocks that vary across locations. Lastly, dummy variables seize year and industry eects. For a more detailed description of the control variables, please refer to the Appendix 1A.

The correlation between capital investment and the unobserved ability of the en-trepreneur may lead to the under- or overestimation of marginal returns to capital.

For instance, ability may lead to an upward bias of the estimate βˆ_K because (i) en-trepreneurs with better skills might generate more capital and prots or (ii) because reversed causality between capital and prots may prevail. On the contrary, a down-ward bias can also emerge because (i) under capital market imperfections, very high ability individuals would be more willing to start a business, even at very low levels of

capital, relative to lower ability individuals and (ii) due to the classical measurement error for prots and capital. To address concerns related with ability, the model spec-ication takes rst into consideration schooling and age; and second, introduces two ability proxies.

The vector θ_i measures the ability of the i th individual rst, with a dummy for book keeping because higher ability individuals are more likely to develop an accounting system that provides them with an objective overview of their rm's performance.

Second, four dummies capture the motivation of the entrepreneur to start the business:

(i) complementing family income and having more exible hours, (ii) family tradition or obtaining a higher income, (iii) not nding a job or being laid o, and (iv) another motivation. Where the rst category serves as reference. The intuition behind is that more capable individuals will be eager to enter self-employment and more likely to put a protable idea into action.

It should be noted that Equation 4 assumes that the unobserved ability can be modeled in an additive manner. The inclusion of ability measures leads to unbiased es-timations provided that they are uncorrelated with optimal capital stock; thus implying that ability increases prots without increasing marginal returns. The cross-sectional nature of the data makes it dicult to deal with ability biases and the considered proxies are imperfect. However, they are available for the whole sample and are good predictors of rm performance. In that sense, a third mechanism to further consider bias concerns is introduced. Specically, the sample is partitioned into dierent levels of capital and three subsamples are considered: (i) very low levels of capital, which comprises rms that operate with an equivalent of up to 250 USD in capital stock, (ii) low capital, ranging between 250 and 1250 USD, and (iii) intermediate levels of capital, ranging between 1250 and 6200 USD. These thresholds were chosen based on two cri-teria. First, the sample distribution is considered to derive subsamples with a similar number of observations. Second, to generate subsets that are roughly comparable with those chosen byMcKenzie and Woodru (2006) once they are adjusted by base year and exchange rate.

The log-log model and marginal returns are estimated separately for the complete sample and for each partitioning by levels of capital. To reduce boundary eects in the parametric estimations, about 20 percent of the subsequent observations are added to each capital partitioning. The marginal returns are next estimated over the relevant capital ranges thus diminishing results' sensitivity. The regression analysis disregards inuential outliers from each subsample by ascertaining them with the DFITS-statistic.

In that sense, the cut-o threshold is|DF IT S|_i = 2 qk

N where k stands for the degrees of freedom plus one and N for the number of observations (Belsley et al., 1980).

The regression results are shown in Table 4. As expected, both input factors (capital and labor) have a positive economic eect over earnings. At very low levels of capital the labor elasticity is higher than the elasticity of capital, thus suggesting that prots are mostly determined by the number of hours that the entrepreneur destines to his/her business. The gap between factor elasticities narrows as capital stocks increase such that, at intermediate levels of capital, the eect reverses and prots are mostly deter-mined by capital. These observations hold across decades. When the elasticities of the

three sources of labor are compared, it can be observed that those from the owner's working hours are the highest, followed by paid workers and then by unpaid workers. It is noticeable that the contribution that unpaid workers make to prots is substantially lower relative to paid workers and to the owner's labor. Furthermore, it decreases as capital stocks increase. Across decades, microenterprises became less dependent on the owner's labor and increased their reliance on capital to generate prots. Regarding paid labor, its elasticity increased across all capital levels and over time.

The sign of the control variables is also aligned with expectations and is consistent across decades. For instance, both, age of the entrepreneur and of the rm, support the existence of a learning eect that is positive at a decreasing rate. When very low capital businesses are compared across decades, it can be observed that it still takes them about 55 years of operation to reach their maximum contribution to prots. The turning point being so high regardless the level of capital stock suggests that rms do increase their earning the longer they stay in the market. This coincides with the observation of rms staying, on average, three years longer in business than what they used to during the 1990s. Regarding other socioeconomic characteristics, there is a negative and signicant gender eect over prots which decreases as capital levels increase and over time. Nonetheless, ceteris paribus, the sole fact of being a woman translates into 36 to 43 percent lower prots relative to entrepreneurs that are men.

Education has positive and nonlinear eect over prots. Having an undergraduate degree is highly signicant in statistical and economic terms. However, the positive inuence of education has decreased across decades regardless the capital level and schooling category. This suggests that, despite the increase in educational attainment that the economy has experienced, the accumulation of human capital is generating lower marginal returns in terms of earnings. Even highly educated individuals are nd-ing increasnd-ing diculties in maknd-ing their business prosper. With respect to marriage, the positive eect is only signicant at intermediate levels of capital.

The opportunity cost captured by the hourly average wage in the industry and state is positive and it has increased across decades regardless the level of capital. Regard-ing the variables used as ability proxies, the signs and signicance levels coincide with expectations. Specically, the eects of (i) following a book keeping method and (ii) having entered the business due to family tradition or to increase income are positive, highly signicant and large in economic terms. The fact that the remaining motivation categories have a positive eect with respect to complementing family income and hav-ing more exible hours shows that the latter survivalist approach to entrepreneurship poses an important limitation for the development of the rm. In other words, seeing the microenterprise as a milking source rather than as a growth opportunity, strays en-trepreneurial possibilities. Despite the imperfection of the discussed dummies as ability proxies, their association with higher earnings does support the idea that they provide some measure of ability.

In what follows, I estimate the marginal returns to capital and analyse their be-haviour to answer the empirical question: (i) Are marginal returns to capital low at low levels of investment? It should be bear in mind that logging the dependent and control variables implies assuming a constant capital elasticity of prots. Also, the marginal returns are the product of the output elasticity of capital

βˆ_K

Table4:Parametricestimationsofmarginalreturnstocapital AlllevelsofcapitalVerylowLowIntermediate R+(0,250](250,1250](1250,6200] Controlvariablelogmonthlyprotslogmonthlyprotslogmonthlyprotslogmonthlyprots 2010s1990s2010s1990s2010s1990s2010s1990s (1a)(1b)(2a)(2b)(3a)(3b)(4a)(4b) Logofcapital0.163***0.122***0.143***0.091***0.188***0.143***0.161***0.183*** (0.004)(0.004)(0.011)(0.004)(0.010)(0.006)(0.008)(0.007) Logofentrepreneur'sstotallaborhours0.138***0.345***0.176***0.410***0.097***0.281***0.061**0.155*** (0.011)(0.015)(0.010)(0.016)(0.011)(0.016)(0.012)(0.011) Logofpaidworkers'totallaborhours0.036***0.036***0.033***0.024***0.035***0.037***0.040***0.039*** (0.002)(0.002)(0.003)(0.002)(0.002)(0.002)(0.002)(0.003) Logofunpaidworkers'totallaborhours0.007***0.006***0.017***0.012***0.006*0.011**-0.0020.001 (0.002)(0.002)(0.001)(0.002)(0.002)(0.003)(0.002)(0.003) Ageofentrepreneur0.017***0.015***0.009***0.015***0.017***0.017***0.022***0.010* (0.001)(0.002)(0.002)(0.002)(0.003)(0.002)(0.004)(0.004) Agesquaredofentrepreneur-2.67e-4***-2.53e-4***-1.96e-4***-2.70e-4***-2.44e-4***-2.75e-4***-3.03e-4***-1.76e-4** (1.77e-5)(1.56e-5)(2.42e-5)(1.93e-5)(2.73e-5)(2.04e-5)(4.10e-5)(4.06e-5) Femaleentrepreneur-0.447***-0.397***-0.514***-0.429***-0.363***-0.378***-0.359***-0.287*** (0.023)(0.018)(0.023)(0.020)(0.016)(0.018)(0.027)(0.030) Married0.0030.038-0.0100.016-0.0100.043*0.027*0.103*** (0.009)(0.018)(0.012)(0.020)(0.015)(0.018)(0.011)(0.016) Primaryschool(entrepreneur)-0.0170.063***-0.0380.037**0.0580.063**0.0510.126** (0.027)(0.010)(0.026)(0.008)(0.041)(0.017)(0.059)(0.028) Secondaryschool(entrepreneur)0.0460.118***0.0030.075**0.121*0.115***0.144*0.216*** (0.021)(0.016)(0.038)(0.018)(0.048)(0.018)(0.054)(0.032) Highschool(entrepreneur)0.094*0.247***0.0660.180**0.159*0.216***0.190**0.328*** (0.028)(0.023)(0.045)(0.034)(0.050)(0.036)(0.050)(0.024) Atleastundergraduatestudies(entrepreneur)0.260***0.492***0.187**0.415***0.327***0.418***0.370***0.520*** (0.030)(0.032)(0.041)(0.034)(0.058)(0.030)(0.055)(0.029)

Table5:....Continuation AlllevelsofcapitalVerylowLowIntermediate R+(0,250](250,1250](1250,6200] Controlvariablelogmonthlyprotslogmonthlyprotslogmonthlyprotslogmonthlyprots 2010s1990s2010s1990s2010s1990s2010s1990s (1a)(1b)(2a)(2b)(3a)(3b)(4a)(4b) Ageofrm0.015***0.015***0.016***0.015***0.011***0.013**0.016***0.015** (0.002)(0.003)(0.003)(0.003)(0.001)(0.004)(0.003)(0.003) Ageofrmsquared-2.72e-4***-2.74e-4**-2.56e-4**-2.52e-4**-1.74e-4***-2.17e-4-2.76e-4**-2.87e-4** (4.49e-5)(6.50e-5)(7.23e-5)(6.94e-05)(3.10e-5)(9.83e-5)(6.43e-5)(6.83e-5) Logofaveragehourlywageintheindustryandstate0.308***0.252**0.302***0.286**0.303***0.245*0.310***0.236* (0.045)(0.071)(0.050)(0.062)(0.047)(0.082)(0.031)(0.083) Enteredbusinessduetofamilytraditionortoincreaseincome0.162***0.232***0.134**0.223***0.185***0.235***0.160***0.237*** (0.021)(0.012)(0.034)(0.024)(0.028)(0.020)(0.021)(0.026) Enteredbusinessbecausecouldnotndajoborwaslaido0.066**0.0050.054*0.0010.0840.0030.0470.032 (0.018)(0.021)(0.022)(0.021)(0.041)(0.033)(0.034)(0.045) Enteredbusinessduetoanotherreason0.117***0.091**0.079**0.076*0.125***0.091*0.120***0.113** (0.015)(0.024)(0.021)(0.030)(0.022)(0.027)(0.016)(0.026) Bookkeeping0.167***0.130**0.226***0.141**0.150***0.135**0.117***0.087 (0.014)(0.031)(0.019)(0.028)(0.014)(0.030)(0.017)(0.044) Intercept3.058***2.371***3.300***2.188***2.929***2.481***3.152***2.637*** (0.0907)(0.230)(0.107)(0.193)(0.141)(0.321)(0.134)(0.245) YeareectsYesYesYesYesYesYesYesYes IndustryeectsYesYesYesYesYesYesYesYes Observations13,78716,8606,9399,2446,9637,3155,5846,828 RobustR-squared0.5340.5850.4520.5360.3580.4240.3780.399 ***p<0.001,**p<0.01,*p<0.05 (1)Estimationsofthedouble-logmodelareparametric.(2)Forestimationpurposes,onlypositivecapitalandprotsareconsideredandinuentialoutliersareascertained theDFITS-statistic.(3)Thegroupingofrmsbylevelofcapitalclassiesthemintoverylow(0,250],low(250,1250],andintermediate(1250,6200].Ateachrangeof anadditional20percentoftheobservationsareconsideredtodiminishboundaryeects.(4)Robuststandarderrorsarecorrectedforclustering.(5)Nominalvalues reportedin2016MXPconvertedintoUSD.(6)Referencecategoriesare:sector(manufactures),motivation(complementingfamilyincomeandhavingmoreexiblehours), (lessthanprimaryschool),men,years(1994and2008).

Table 6: Mean monthly marginal returns by levels of capital (percent)

Sector

Very low Low Intermediate

(0,250] (250,1250] (1250,6200]

1990s 2010s 1990s 2010s 1990s 2010s

Manufactures 44 62 6 10 3 2

Commerce 62 45 7 9 3 3

Services 48 56 7 9 3 3

Construction 49 55 6 8 4 4

All sectors (m) 57 59 8 10 3 3

All sectors (p50) 18 24 5 8 2 2

. Note: The reported values by sector correspond to the mean.

δπ

The marginal returns are computed at the average protability (^¯π¯K) because the estimated elasticity is an average eect; however, the medians are also reported to show skewness and heterogeneity. In Table 6 a detailed and stratied summary of the monthly marginal returns to capital across decades is reported. It shows that the marginal returns are almost 60 percent at very low capital levels⁵⁰. The very high marginal returns hold true across decades. It can also be observed that marginal returns to capital follow a decreasing pattern over capital until they reach an average of about three percent, which roughly corresponds to the market interest rate. It is also noticeable that there is a wider gap between mean and median marginal returns the lower capital is, thus evidencing higher heterogeneity across these microenterprises.

To check whether sector aggregation yields to dierent patterns of capital marginal returns, I run the econometric analysis for each sector as an independent subsample.

The reported marginal returns are thus estimated with the βˆ_K that captures specic sectorial eects. The overall decreasing pattern of M RK is in line with the ndings of previous studies. Specically, across all years and sectors, marginal returns are not initially low as the described model of poverty trap would predict. There is no censored pattern for marginal returns and no capital threshold is observable. It is not true that rms with low levels of capital only have access to low-productivity industries. In fact, poorly capitalized rms are highly protable.

50The study of (Grimm et al., 2011a; McKenzie and Woodru, 2006) reported an approximate of 15 percent for monthly average marginal returns in the Mexican case. However, their sample excludes women and they report median marginal returns. The capital ranges are roughly comparable, but the partitioning is still dierent and more detailed in this case. Also, the log-log model facilitates the interpretation of the capital coecient as elasticity.

A direct comparison of marginal returns across sectors might be inaccurate given their dierences in capital intensity. However, the intertemporal comparison is relevant.

First, it should be noticed that marginal returns at very low and low capital levels have increased in the past decades while those at intermediate levels remained unchanged.

The marginal returns in commerce, which is the sector that increased its share the most during the past years, exhibits a decrease in marginal returns at very low levels of capital. In other words, vendors became more numerous and the protability of their businesses decreased. All other sectors increased their marginal returns in the same capital range.

When the marginal returns are scrutinized based on diverse characteristics of the owner and the rm, the heterogeneity of microenterprises is apparent once again. With respect to socioeconomic characteristics, it can be observed that marginal returns are positively correlated with the owner's education. Also, the marginal returns' gap of rms owned by male and women decreased from nine to four percentage points. Re-garding the relationship between labor and marginal returns to capital, it is interesting to notice that marginal returns are negatively correlated with the size of the rm.

However, the dierence between the marginal returns of one person rms and those that provide employment narrowed across decades. Lastly, marginal returns from rms without premises are substantially higher than those with premises at very low levels of capital. Such discrepancy decreases as capital stock increases and, at intermediate lev-els of capital, the average marginal returns are at similar levlev-els regardless the ownership of an establishment.

In Appendix 1B I include robustness checks and the corresponding estimations of marginal returns to capital. In both cases, the decreasing pattern of marginal returns over capital stock levels holds. Specically, model one (RC1) excludes all ability mea-sures. The results show that the introduced proxies make a downwards correction to the unobservable ability bias. The second model (RC2) replaces the prots measure by the dierence between benets and costs. The pattern holds, but self-reported prots provide a more accurate measure (De Mel et al., 2009).