Farm Size and Productivity: A New Look at the Old Debate Revisited Author(s): Graham Dyer Source: Economic and Political Weekly, Vol. 33, No. 26 (Jun. 27 - Jul. 3, 1998), pp. A113- A116 Published by: Economic and Political Weekly Stable URL: https://www.jstor.org/stable/4406934 Accessed: 08-06-2020 05:58 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
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These differences in cropping pattern can be even more pronounced at the village level and across farm size categories themselves. Indeed, the exclusion of the potato crop, in particular, may have biased the analysis against finding an inverse size-productivity relationship in certain districts [Roy 1979: 76-77]. Similarly, it is not beyond the bounds of possibility that the exclusion of important commercial crops like wheat and rapeseed may bias the results in the opposite direction for certain areas. This is not to suggest that the inverse relationship is a crop specific phenomenon, but given that the evidence supporting its existence in certain regions is overwhelmingly related to the gross crop value pernet cropped area, and is not generally associated with the physical yields of individual crops, then differential cropping patterns must be potentially important, along with cropping intensities [Bharadwaj 1974]. The results produced by the village level regression analysis, presented in table 1 of Chattopadhyay and Sengupta's article, provide scant confirmation of the inverse relationship at the village level. Only 12 of the 60 linear regressions at the village level produce statistically significant negative correlation coefficients (and half of these occur in zone V alone). As is to be expected. the log-linear regressions produce slightly better results, with 14 statistically significant negative correlation coefficients.6 As Chattopadhyay and Sengupta themselves admit, out of 60 villages, a significant negative relation is valid for only nine villages where bPth the linear and log-linear regressions give significant results.7 One can go further. If the authors are explicitly employing the log-linear regressions to reinforce and guarantee the linear results, then surely, the supplementary Kendall rank correlation coefficients should be used in the same way (otherwise this latter test is redundant). Applying the same reinforcement criteria to the latter results would suggest that only six out of the 60 village level regressions support a statistically significant inverse relationship between farm size and output per hectare. Only one of the six zones produces a signi- ficant negative relation at the zonal level for the linear regression (perhaps significantly, Zone II, ostensibly a relatively backward zone). None of the log-linear regression and rank correlation coefficients for the zonal levels is statistically significant. This is not an adequately strong statistical basis, therefore, on which to confirm the existence of such a relationship in West Bengal agriculture. The authors claim that Bhattacharya and Saini (1972) achieved similar results. They did not, and this has significant implications for the next stage in the analysis. The preponderance of negative coefficients had suggested to the authors that perhaps overall the relationship was indeed negative. To get an overall view at the zonal level, the authors follow Bhattacharya and Saini in carrying out a joint likelihood test for combining the independent village level regressions.x Bhattacharya and Saini were perhaps justified in implementing such a test given their more robust results for at least one of their two districts. Their results for Muzaffarnagar in UP, for the years 1955-56, 1956-57, 1966- 67 and 1967-68, but not forFerozepur district in Punjab in roughly the same years, provide evidence for a statistically significant negative relationship at the district level for all four years above. They employ thejoint likelihood test for overall significance in order to argue that the inverse relationship at the district level is not being generated by aggregation bias, but reflects the preponderance of negative correlation coefficients in the village level regressions. However, Chattopadhyay and Sengupta have no such results to support. As we have seen, none of their zonal level regressions is statistically significant, i e, there seems to be no evidence for a close negative linear relationship between farm size and output per hectare at the zonal level. Now, of course, aggregation bias can cut both ways: it is possible that statistically significant negative correlation coefficients at the village level might be wiped out by aggregation bias at the zonal level. However, as we have seen, only six villages out of 60 produce strong evidence for such a relationship. Furthermore, the overall chi-squared test itself may not be very robust. The overall chi-squared statistic is computed on the basis of thejoint product of the p-values associated with the independent tests at the village level. With p (the area remaining in the left- hand tail of the t distribution) ranging from 0 to 1, it can be seen that one or two very small p-values will have a disproportionate effect on the joint product. In log terms, as p approaches zero, In p approaches minus infinity exponentially. In other words, one or two highly significant results can generate a high chi-squared statistic. Hence Rudra's warning (1976) that it is necessary to have a proper appreciation of what a pooled test implies: if there are n different independent tests with null hypotheses HI, H2 ... Hn, each of which is found to be non-significant, whereas the result of a pooled test is signi- ficant, the implication is that at least one of the null hypotheses has to be rejected. In other words, a significant overall chi-squared statistic means only that at least some of the negative correlation coefficients are signi- ficant. It does not mean that the negative relationship is significant in all the cases. The misleading conclusions adduced by Chattopadhyay and Sengupta from these tests are made further apparent in their table 3 where they produce the average within-village correlation coefficients for each zone. These are, of course, entirely meaningless, the mean correlation coefficient being inflated by the skewed results. There also seems to be some confusion surrounding the analysis of covariance tests which Bhattacharya and Saini employed to investigate possible aggregation bias in their district level regressions.9 They found that the size-productivity relationship at the district level could not be specified by a simple model y = a + bx. Scatter diagrams suggested that y = a, + bx was a more appropriate model as y intercepts differed between villages due to factors such as soil fertility. However, they noted, correctly, that these standard analysis of covariance tests involve the assumption of equal variance in the village level regressions. As might be expected this seemed to be realistic only for the log-linear regressions. Here we have another example of Chattopadhyay and Sengupta blindly following the methodology employed by Bhattacharya and Saini without perhaps fully understanding the implications noted by the latter. While Chattopadhyay and Sengupta do indeed obtain similar results (presented in their table 4) to Bhattacharya and Saini, the meaning of these results must be open to question. While it is clear in both sets of results that the intercept parameters differ between village regressions, the discussion above might suggest that it is difficult to conclude that the hypothesis of equality of the regression coefficients can be accepted. And even if the latter hypothesis cannot be rejected, the regression results themselves might suggest that while villages show different overall levels of land productivity, there is no statistically discernible negative linear relationship between farm size and output per hectare in any individual village. Note, too, that Bhattacharya and Saini themselves admit that the intercept terms explain more of the variance than the regression coefficients. A further issue that needs to be addressed, and one that was again pointed out by Rudra (1976 and 1977), is the question of the range of farm sizes over which an inverse relation- ship might hold. A negative regression or correlation coefficient (either significant or insignificant) between output per hectare and farm size may be generated even though such a relationship holds over a limited range of farm sizes. Indeed, the rather weak cor- relation coefficients presented by Chatto- padhyay and Sengupta may suggest precisely this. It is unfortunate that the authors do not present any scatter diagrams which might reveal discontinuities in the distribution of observations (as Chattopadhyay and Rudra demonstrate in a 1977 addendum to their original article). If this be the case, then yet again, there seems little solid evidence on which to make such important generalisations concerning the inverse relationship. IV Claims Based on the Results Chattopadhyay and Sengupta make a number of claims based on their results. The first is that the study carried out by Bhattacharya and Saini in 1972 had not ruled out the existence of the inverse relation between farm size and productivity, and that their (Chattopadhyay and Sengupta) study "vindicates their (Bhattacharya and Saini) conclusions and in fact, provides strong A-114 Economic and Political Weekly June 27, 1998 This content downloaded from 47.11.129.203 on Mon, 08 Jun 2020 05:58:42 UTC All use subject to https://about.jstor.org/terms
support to it". This claim may be unfounded. As I have argued in the preceding section, the evidence presented by Bhattacharya and Saini is of a more robust nature than that presented by Chattopadhyay and Sengupta. There is a further difference between the two studies that may be pertinent. Bhattacharya and Saini carry out two sets of regression exercises: one between the value of output per net cropped area and farm size, and the second between output per gross cropped area and the size of gross cropped area. These two sets of regressions provide us with more information concerning the pattern of land productivity and cropping intensity across farm size. The situation with Chattopadhyay and Sengupta is less clear, however. They seem to be employing a single hybrid specification in their regression equations: between "farm size (net cultivated area denoted by A) and value of output per hectare of paddy (V/A)"(emphasis added). This would appear to suggest that the auihors are employing value of output per gross cropped hectare in their land productivity variable (and therefore the second A is not the same as the first A). It is ambiguous, and I stand to be corrected on this, but if, indeed, gross cropped area is being used in the productivity measure then the authors may be introducing a significant bias into their data which would tend to weaken any inverse relationship between farm size and land productivity. If the small farms are cropping land more intensively, and perhaps growing a range of other crops besides padi, then the abstraction from both cropping pattern and cropping intensity implied by the form of the data used may well be militating against finding an inverse relationship, particularly in the so-called "relatively less developed regions" (zones I, II and VI). To say that the study by Bhattacharya and Saini did not rule out the existence of an inverse relationship is a rather weak interpretation of their results. Their results tell us much more about the farm size - land productivity relationship and its evolution over time. Their results with respect to net cropped area do indeed confirm an inverse relation for the Muzaffarnagardistrict for the years 1955-56,1956-57, 1966-67,1967-68, but provide little or no support for an inverse relation in Ferozepur (even in the mid- 1950s prior to the green revolution). Their results with regard to gross cropped area amplify that difference, and further suggest a structural break between the pre- and post-green revolution periods. For Muzaffarnagar, the coefficients switch from being negative in the earlier years to positive (but insignificant) in 1968-69, while the coefficients for Ferozepur switch from being insignificant (both positive and negative in different years) to being positive and significant in 1968-69. As Bhattacharya and Saini state: "the correlation seems to have become positive in both the regions" (their emphasis). The latter authors state explicitly that their investigation throws light on the changes in the size-productivity relationship brought ab6ut by the green revolution. This brings us to the second claim by Chattopadhyay and Sengupta. They make the claim that "the inverse relation between farm size and productivity becomes stronger in the agriculturally developed regions of West Bengal compared to the relatively less developed regions". They add that this is possibly due to the effects of the green revolution on the smaller-sized farms, in particular the improvement of the latter through assured all year round irrigation water during the post-green revolution period. This is a most startling claim that requires very close attention. It is all the more startling given the weight of accumulated evidence from a number of other studies which show a breakdown in the inverse relationship with the introduction of green revolution technology and the development of modem capitalist agriculture more generally. Thus, besides the evidence presented by Bhattacharya and Saini above, we have strong evidence of the disappearance of the inverse relationship'in the Punjab areas of India and Pakistan presented by Chadha and Khan, respectively. Roy (1981), in a careful study of Punjab shows that it is precisely in those areas most affected by the green revolution, where the penetration of the new technology has been deepest, that the inverse relationship weakens and disappears. These findings are also supported by Patnaik's analysis of Bhalla's data for Haryana (1987). Dyer (1997) shows, in the case of Egyptian agriculture, that the introduction of green revolution technologies and the intensification of capitalist agriculture first increase cropping intensity and labour input intensity on the larger farms, thereby weakening the inverse relation by increasing output per hectare on the latter. Later, with capital intensification and mechanisation on the larger farms, significant scale economies result in the reversal of the size-productivity relation, the larger capitalist farms generating higher output per hectare than the smaller peasant farms. The evidence presented by Chattopadhyay and Sengupta, if correct, might suggest that a process of catch-up is taking place in West Bengat agriculture, with small farms even- tually gaining access to the new technologies, particularly tubewell irrigation, HYV seeds and chemical fertilisers, thereby re-establish- ing the inverse relation, as Berry and Cline, Bhalla and Lipton (1978) hoped. Or perhaps some other factors might be at work (see the discussion below). Unfortunately, whatever the case might be, the study presented by Chattopadhyay and Sengupta does not allow us to draw any firm conclusions on this matter. Besides the lack of robustness of the data described above, which must certainly weaken the claims of the authors, the organisation of the data employed actually precludes making such claims. The main problem here is the appendance of rather vague captions to the six agro- climatic zones in which the data is organised. The authors tell us that these are based on cultivation practices, type of soil, irrigation facilities and rainfall. The authors inform us that zones III, IV and V are regarded as "prosperous zones" in terms of "soil fertility, irrigation facilities and other factors". But nowhere are we provided with any evidence to support these assertions. Agricultural development or progressivity cannot be gauged in terms of soil fertility. We are not told what the other factors might be, or their bearing on the level of agricultural development. The extent of irrigation facilities can be seen as one indicator of agricultural progressiveness, one of the sine qua nons of the green revolution, but the authors provide no evidence in terms of irrigation ratios in the sample farms/villages, and no indication of the qualitative nature of such facilities.l' In order to come to any sensible conclusion regarding the progressivity of these zones, or even better the sample villages, we would require data on the degree of technological development: the area sown to high yielding varieties, the use of chemical fertilisers and pesticides, the extent of both owned and rental machine inputs, for example. We would also require data on the extent to which peasant farming has been displaced by capitalist farming: possible indicators include the ratio of purchased inputs, particularly chemical fertilisers and pesticides, to total inputs, the ratio of hired labour to family labour, and marketed output ratios, for example. Indicators such as these, which relate to both the forces and relations of production, as well as exchange relations, can tell us the extent to which any particular village or region is agriculturally developed. Whether a reg on has red lateritic soils or coastal saline conditions tells us very little about differential productivity across farm size, either in the static or dynamic context. The final claimon which I wishto comment is the authors' assertion that their findings suggest that "the small farmers in the agriculturally better-endowed regions are relatively more efficient compared to the larger ones". There is now an extensive literature on the causal factors behind the inverse relationship, some focusing on qualitative factor differences (such as soil quality and irrigation), others on differential factors intensities (especially labour input intensity). None of the contributions which emphasise the greater efficiency of small farmers are convincing. Firstly, the size- productivity debate concerns only land productivity, while labour productivity, and increasingly capital productivity, need to be taken into account to measure efficiency. Secondly, the inverse relation relates to total value of output per hectare of farm size, for which evidence exists for a number of case studies. However, there is little evidence to suggest an inverse relationship between the physical yields of individual crops and farm size, which one might expect if small farmers Economic and Political Weekly June 27, 1998 A-115 This content downloaded from 47.11.129.203 on Mon, 08 Jun 2020 05:58:42 UTC All use subject to https://about.jstor.org/terms
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