Abstract:
This is an invention implying a system and method to construct synthetic data of said financial variables i.e., prices and quantities and to construct sophisticated econometric models that achieve convergence with related estimations already published. These system and method is abled to run under different risk scenarios and input settings; they also allow lower costs by simulating time frequencies, variables and factors of economic activity, through the use of random number machines and Monte Carlo simulations. This invention furnishes risk sensitivities based on sophisticated econometric models and mathematical not lineal models and a set of behavioral and statistic assumptions by using the synthetic data herein constructed. Great results in providing criteria for risk management and decision making with 99% of statistical significance. Modifications of this invention can generate a multiplicity of applications by those skilled in the art. Thus, the input problem treated should be taken as illustrative and not restrictive.

Description:
FIELD OF THE INVENTION 
       [0001]    There is a wide tradition in the field of applied economics in relation with diminishing the risk on your entrepreneurial activity. For the present case, the invention targets the farm economic activity. This invention consists on a computerized work, which is manifested in appearance in a system and method for compute synthetic data. It uses sophisticate econometric techniques and models, besides the intrinsic statistic information conveyed on the variables in a research study. 
       BACKGROUND 
       [0002]    There is a considerable literature delving into risk and uncertainty, which are present in farm economic activity including an analysis for diminishing cost and losses and increasing profits, by using similar econometric techniques as this invention does. However, those techniques do not achieve the same precision grade and statistic significance as this invention does, while they neither use effectively simulation scenarios. This invention is not only important to assess the current situation for the farmer entrepreneur, but also provides tools in decision-making in the food-crop production, with a low cost. For example, food sovereignty is important since it is a milestone for supporting the economic growth of a nation. If there is no food sovereignty, the country might end not relying on its own decisions with respect to food production. As a result, a chain of undesirable economic consequences might follow. 
         [0003]    Unique features of the invention: The author have knowledge of codes and/or system and methods that try to solve the same sample problem input that this invention uses. However, none of them are successful in solving the problem that this invention does. 
         [0004]    List of competing inventors or labs or works that keeps a resemblance with the present invention: Compass Lexecon. Atanu Saha, Ph.D. Executive Vice President and Head of New York Office, 156 West 56 th  Street, 19 th  Floor, New York, N.Y. 10019. Regarding Saha similar work: Scripps Nob Hill versus Presley Companies, expert analysis regarding the timing and incidence of product failure; expert analysis on behalf of investment banks and financial institutions in several mutual fund ‘market timing’ and ‘A versus B’ shares matters. The analyses involved quantification of damages, if any, suffered by investors, using sophisticated econometric models and statistical tools; Sanchez versus Certified Grocers et al., expert analysis for defendant Certified Grocers regarding lost wages, lost future earnings and other economic damages. 
         [0005]    List all of the features that distinguish the invention over the related technologies: It is well known that the use of farm data is very expensive, since there is a need to design and pay for the experiment, the survey, the data collection, etcetera. Also it is expensive, because it takes a long time for obtaining the crop production information i.e., some crops have one or two cycles per year; another crops, per example coffee, even can take three-to-four years to produce the seed. Thus, this invention is relevant because it makes possible to perform crop risk analysis and input-output prices studies from a computer desk. This invention provides a system and method that allows an analysis based on simulations. Thus, it allows testing for different uncertainty conditions or risk scenarios, providing information and criteria to determine the best decisions under these conditions. Very little data input is necessary. As a result, the experiment costs drops dramatically. This invention allows replicating the natural phenomena through a series of cycles or simulations based on the statistic information which has the intrinsic probabilistic distribution properties of the variables. In addition, this system and method is abled to replicate related published results. In this way this invention allows calibration and at the same time a high grade of precision based on its results as well as a 99% of statistic significance. 
         [0006]    Best mode of making the invention: The best mode is using Matlab language. However, the implementation in other languages can be done using equivalent instructions in chosen programing languages i.e., Fortram, C, R, etcetera. 
         [0007]    Possible alternative versions of the invention: Possible alternatives involve the use of this system and method to different crops. In part references it is mentioned the use of similar systems for raspberry. In fact, the author believes, any crop could be subjected to this type of analysis. In the sample problem input a sample of 60; 45 and 15 farms were used. The factor among them is a multiple of 15. An alternative version could involve using a different factor for a simulation in order to represent states or even a country i.e., 1,000; 1,000; 1,000,000; etcetera. Other option is using real data with this invention, in order to obtain results without involving random numbers. This could bring peace of mind for those parties that are interested in this analysis but do not fully understand the possibilities of synthetic data. One advantage of having this invention is that its user can calibrate it with those econometric models which use real data or vice versa, whatever it works better for the user. Finally, other type of alternative version is to modify this invention slightly such as it better matches specific products. Example of this products are found in references i.e., mutual funds; economic damages valuation; financial decisions; stock returns; futures markets; hedge funds; stock prices; adoption of emerging technologies under uncertainty; optimal response under uncertainty; cell phone companies; households decisions; etcetera. 
         [0008]    Probable uses of the invention: This invention could be use by: Farm associations; state governments; consulting firms; Wall Street; commercial banks; Federal Reserve; national governments; classroom teaching; etcetera. 
       SUMMARY OF THE INVENTION 
       [0009]    In summary, this system and method helps individual farmers and/or economic agents and also different aggregations of them; state government and nations to analyze their current situation by giving them statistic tools and econometric models that allows them to take grounded i.e., food-crop decisions. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0010]    For what follows and for the understanding of the present invention, it will be more readily apparent from the following detailed description of drawings with respect to the invention embodiments: 
           [0011]      FIG. 1  is a flow chart of a method for an embodiment to assign initial number of observations and values for the random variables in accordance with the present invention; 
           [0012]      FIG. 2  is a flow chart of a method for an embodiment to generate synthetic data based on descriptive statistics and the uniform distribution in accordance with the present invention; 
           [0013]      FIG. 3  is an illustration of a Weibull distribution function drawing for the error term with shape 3.8 and scale 1.3. The center of the boxplot displays the median; 
           [0014]      FIG. 4  is a flow chart of a method for an embodiment to compute standard errors in accordance with the present invention; 
           [0015]      FIG. 5  is Table 4: ML Estimates of Weibull Parameters; 
           [0016]      FIG. 6  is equation 11 in Saha; 
           [0017]      FIG. 7  is Table 3. Summary Statistics; 
           [0018]      FIG. 8  is a flow chart of a method for an embodiment for the first stage on Saha CDE non random part estimation method in accordance with the present invention; 
           [0019]      FIG. 9  is the output of the first stage on Saha estimation CDE non random part method. A stands for technology; a 1  stands for the elasticity coefficient of capital; a 2  stands for the elasticity coefficient of materials and h stands for hat; 
           [0020]      FIG. 10  is a flow chart of a method for an embodiment for the second stage on Saha CDE random part estimation method: G stands for the log of the square error term in accordance with the present invention; 
           [0021]      FIG. 11  is the output of the second stage on Saha CDE random part estimation method: m 1  stands for the elasticity coefficient for input not risk reducing; m 2  stands for the elasticity coefficient for inputs risk reducing and h stands for hat in accordance with the present invention; 
           [0022]      FIG. 12  is a flow chart of a method for an embodiment for the wealth function computation in accordance with the present invention; 
           [0023]      FIG. 13  is the wealth function computation output: alpha is the expo-power utility parameter; beta is the expo-power utility parameter and h stands for hat; 
           [0024]      FIG. 14  is the partial production elasticities output: mmiu 1  stands for the partial production elasticity of ×1; mmiu 5  stands for the partial production elasticity of ×2 and h stands for hat; 
           [0025]      FIG. 15  is a flow chart of a method for an embodiment to compute Only CDE in accordance with the present invention; 
           [0026]      FIG. 16  is the output for Only CDE: A stands for technology; a 1  stands for the elasticity coefficient of capital; a 2  stands for the elasticity coefficient of materials; m 1  stands for the elasticity coefficient for input not risk reducing; m 2  stands for the elasticity coefficient for inputs risk reducing; mmiu 1  stands for the partial production elasticity of ×1; mmiu 5  stands for the partial production elasticity of ×2; m and b stands for only CDE and h stands for hat; 
           [0027]      FIG. 17  is a flow chart of a method for an embodiment to compute the second estimation method under CARA in Table (5) in accordance with the present invention; 
           [0028]      FIG. 18  is the output part of the second estimation method under CARA in Table (5): A stands for technology; a 1  stands for the elasticity coefficient of capital; a 2  stands for the elasticity coefficient of materials; m 1  is stands for the elasticity coefficient for input not risk reducing; m 2  stands for the elasticity coefficient for inputs risk reducing; mmiu 1  stands for the partial production elasticity of ×1; mmiu 2  stands for the partial production elasticity of ×2; 
           [0029]      FIG. 19  Table 5. Parameter estimates of EP Utility and CDE Production Function; 
           [0030]      FIG. 20  is a flow chart of a method for an embodiment to compute Table 6 in accordance with the present invention; 
           [0031]      FIG. 21  is Table 6. Arrow-Pratt Risk Aversion Measures. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Manual 
       [0032]    In the following manual, it is used a sample problem input based on Saha, A., R. Shumway and H. Talpaz. 1994. “Joint Estimation of Risk Preference and Production Technology Using the Expo-Power Utility Function” American Journal of Agricultural Economics 76, 173-184, during the rest of the manual this paper would be referring as Saha or authors indistinctly. 
         [0033]    1. Generate the random data for the experiment using a Monte Carlo simulation, emulating the variables use in Saha. To simplify things you can use the Matlab integrated modules that provide already random number generators. From the sample problem input, take the mean and standard deviation to generate the input variables as follows: 
         [0034]    1.a. Assign initial values for the random variables. Please note that in this system and method sample problem input, the names, values, and functions match with those in Saha. Take into consideration the number of observations i.e., all farms are 15 and the number of years are four, so it gives back 60 observations, 15 times four (Step  10 ). To assign the started values pick the ones already published in Table 5 in Saha (Step  12 ). See  FIG. 1 . 
         [0035]    1.b. Once you completed the above step, proceed to generate the input variables. Be careful not to hit negative values. Remember than in economics negative prices and quantities do not have meaning. 
         [0036]    To generate the synthetic data reported in Table 3, see  FIG. 2 , it was used the random number generator with a uniform distribution (Step  22 ), taking into account the mean and standard deviation in Saha (Step  20 ). Although, it seems that the correct way to proceed is by using a random Weibull distribution. This characteristic seems to come from the fact that given the mean and standard deviation from the raw data, a symmetrical distribution around the mean reaches negative numbers. Therefore, the standard deviations have to be adjusted accordingly. That is to say, instead of allowing the data dispersion to be within two standard deviation range away from the mean and reach negative values, take different factors among one and two standard deviations. In consequence, it is generated the independent variables using a random number generator (Step  24 ). 
         [0037]    2. Error term generation. Follow Saha to generate the Weibull error term, with b scale parameter and c shape. Take initial values those coming from Table 4 of the paper, and call it (ε_). The graph of this distribution is presented in  FIG. 3 . 
         [0038]    In  FIG. 3 , you can see that the Weibull distribution for the error term only takes positive values and it is skewed to the left. This made economics sense as described above. 
         [0039]    The standard errors were calculated with based on the Marquardt-Lavenberg gradient expansion algorithm (Step  42 ), where the diagonal terms of the curvature matrix are increased by a factor that is optimized in each search step for optimum values (see Bevington and D. K. Robinson (1992), also see Patel, J. K., C. H. Kapadia, and D. B. Owen (1976)). The asymptotic variance-covariance matrix of the parameter estimates for maximum likelihood is the matrix computed as the inverse of the Fisher&#39;s information matrix (Step  40 ), which is obtained after running max. likelihood regression. The corresponding system and method are reported in  FIG. 4 . 
         [0040]    The tables in Saha are referred by their numbers, herein reproduced along with the report of the synthetic variables and estimates values. The standard errors for the maximization of the log-likelihood Weibull are reported in Table 4, in here reproduced along with the corresponding simulation estimates b and c. Besides, the estimated mean and standard deviation of Weibull e (error) are reported. The sample standard for epsilon es (error from the sample) was simulated, along with its mean and standard deviation. See  FIG. 5 . 
         [0041]    The variance of the estimated epsilon (e_) is 1.1322 and for (es) is 0.3284 (i.e. every time you hit the run button it changes, because a new random number is generated). However, the variance coming from these trials keeps a close resemblance to the one herein mention. Also, the variable Q 1  is generated with the corresponding formula taken from Saha, see  FIG. 6 . 
         [0042]    In what follows, it is presented the summary statistics reported in Table 3, along with those generated from this simulation, see  FIG. 7 . 
         [0043]    3. According to Saha, the complexity of the estimation of equation (14) can be substantially reduced if prior parameters b and c estimates of the Weibull p.d.f in equation (15) are used in the estimation of equation (14). 
         [0044]    3.1. Estimate b and c for equation (15) and call them bh and ch i.e., bh=1.2976 and ch=3.7357, see the above estimation description in the first part for a refresher on how these parameters are estimated. 
         [0045]    For the parameter starting values, according with Saha, they can be provided through prior estimation using a Just-Pope method with some modifications to address the fact that ε, the stochastic yield variable has a Weibull distribution. Saha mentions that the starting values for the production function parameters proceed in two stages. 
         [0046]    Thus, implement the first stage following Saha estimation method description as: “In the first stage, the production function is estimated through nonlinear least squares on (16) . . .”. Having this purpose in mind, use the Levenberg-Marquardt algorithm for non-linear least squares (see Seber, G. A. F., and C. J. Wild (2003)) (Step  80 ). This algorithm does not compute robust fits. For robust fits, you need to use an algorithm (see DuMouchel, W. H., and F. L. O&#39;Brien (1989)) that iteratively refits a weighted nonlinear regression, where the weights at each iteration are based on each observation&#39;s residual from the previous iteration. For the estimation of the nonrandom part, equation (16) through non-linear least squares gives, take starting values from the published ones (Step  82 ), see  FIG. 8 . Not traces of endogeneity are detected. The corresponding system and method are reported in  FIG. 8  (Prajnesgu (2008), retrieved from http://ageconsearch.umn.edu/bitstream/47684/2/16-Prajneshu.pdf): 
         [0047]    Thus, the corresponding output for the above defined variables is reported in  FIG. 9 . 
         [0048]    where the h stands for hat; se stands for standard error. These results are also reported in their corresponding tables. 
         [0049]    3.2 The second stage corresponds with the estimation of the random part of equation (16), see  FIG. 10 . A specific structure in the random part is to be imposed, in the same manner mention by Saha (Step  100 ). The corresponding parameters for this stage are the conditional mean of G or log of the square error term: (According with Just, R, and J. David (2011, p. 10) E(ε)=0, the expected value of the error is zero or the expected mean value for the error term is zero. Although, for this case this assumption is not quite correct). 
         [0050]    So, the output values corresponding with the variables of interest from the above system and method embodiment of  FIG. 10  are reported in  FIG. 11 . 
         [0051]    4. According to Saha after estimating M=[m 1 h m 2 h], the starting values for EP utility parameters alpha and beta can be found through a suitable grid search. 
         [0052]    In the above respect, the grid search would be faster if you optimize and found the maximum value, see  FIG. 12 . Thus, since the parameters and independent random variables needed for computing wealth are already estimated (called W), proceed through the optimization path (Step  120 ). Performing this evaluation on a complete grid, as required by the max function, will be much less efficient since it samples a small subset of grid discrete points. Optimization algorithms could be used for continuous grid search. 
         [0053]    Note that the profit function does not include the output price, because Saha has normalized with respect to it. Thus it becomes the unit. Also, with this procedure the joint estimation is integrated in W computation. Moreover, this computation integrates the Cobb Douglas and exponential forms previously obtained through equation (16) in its two stages. To be more explicit about computing W, use the independent random variables generated and the parameters already determined in previous optimizations (Step  122 ), plus the published alpha value as an initial starting value. 
         [0054]    Therefore, the above simulated output parameters of interest are presented in  FIG. 13 . 
         [0055]    The partial production elasticities at the sample mean are reported in Table 5, see  FIG. 14 . 
         [0056]    5. In here Saha Empirical Model section finishes. Is in this section where it is described the estimation procedure, which corresponds to this manual with the estimation part. In addition, there is a system and method to simulate all the parameters reported in Table 5 for the method corresponding to joint estimation. Remember that there is not needed for computing r 1  (capital input prices) and r 2  (material input price), since they are given as independent variables since the beginning (their mean and standard deviation are reported in Table 3). In other words, there is no need to solve equation (14) to obtain the input prices. 
         [0057]    Thus, the (2n+5)×1 φ vector is computed with all the above mentioned system and method. The interpretation on the number of parameter in the φ vector is (2 for alpha and beta, n for 15 farms);  5  (for A, a 1 , a 2 , m 1  and m 2 ), which are reported already as output from the non-linear least squares implementation. In this way all the estimations needed in equation (14) are already simulated, thanks to the implemented models embodiments presented in this invention. 
         [0058]    Moreover, in the identity expressed in equation (6) on Saha, which could be worded as follows: optimal input levels are identical to maximize expected utility. In other words, this invention works in the left hand side of identity (6) in order to find the optimal input levels. Therefore, the simulated procedure implemented for obtaining the vector φ is by finding the optimal input levels. This procedure is endorsed by Saha equation (6) identity. Therefore, by taking the optimization procedure that is used and the identity in (6) altogether, it is also maximizing the expected utility. 
         [0059]    In this final part the sensitivity estimates are simulated and compared with those reported in Saha. To implement this analysis, follow Saha: “Comparison of the three sets of estimation results underscores the sensitivity of estimates to alternative assumptions” p. 182. 
         [0060]    Later on, the authors mention that efficiency gain can be assessed by comparing standard errors of the three sets of estimations reported in Table 5. Also, comparisons are considered for m coefficients and SSE. 
         [0061]    5.1 In order to carry over this task, it is required to proceed in a similar way as explained in Part 2 to estimate the third method of Table 5: Only CDE, see  FIG. 15 . Thus, construct the risk scenario only CDE, change ×1; ×2 and the error distribution parameter b (Step  150 ). Take starting values from the published ones and repeat the process of  FIGS. 8 and 10  (Step  152 ). 
         [0062]    So, after changing ×1, ×2; error distribution parameter: b. The corresponding estimates are reported in  FIG. 16 . 
         [0063]    5.2. For the second method estimation in Table (5), see  FIG. 17 . Thus construct the risk scenario under CARA, change alpha; beta and the error distribution parameter b (Step  170 ). 
         [0064]    Take the starting values from the published ones and rename them A=AA; risk aversion parameters: alpha, beta; risk distribution parameters: m 1 =n 1 , m 2 =n 2 ; and error distribution parameter: b. and repeat the process of  FIG. 8  and  FIG. 10  (Step  172 ). The corresponding estimates are reported in  FIG. 18 . 
         [0065]    In Table 5 the published and simulation estimates are provided, see  FIG. 19 . 
         [0066]    As it can be seen the convergence between A; a 1  and a 2  for the simulation model and the authors publish estimates is achieved. Nonetheless, the standard errors for the simulation are very small with respect to the ones reported. A similar pattern is emulated for the methods Under CARA and Only CDE. When looking only at the standard errors for the corresponding simulation, they present the same pattern as the reported ones. Please note that the smallest simulation standard errors belong to Joint estimation, follow by Under CARA and Only CDE. These characteristics in Saha words are expressed as follows: “. . . a prominent feature of these results is that the standard errors of estimates under the joint estimation procedure are consistently and considerable lower than those under alternative settings. This suggests that there is indeed a substantial efficiency gain in joint estimation, corroborating similar findings by Love and Buccola.” 
         [0067]    For m 1  and m 2  coefficients convergence are also achieved. The standard errors for the simulation are small when compared to those from the reported estimation. Input  2  materials, is risk reducing, in joint estimation and Under CARA. For the column. Only CDE convergence is not achieved between reported and simulated estimates, however, they keep the same positive sign with respect to its publish analog. Overall, regarding m 1  and m 2  simulation behavior it is concluded as Saha does: “. . . when jointly estimated, coefficient m 2  is negative and significant, suggesting that ×2 is a risk reducing input: the same parameter is positive and significant when non-jointly estimated. This suggests that estimation from the utility functions—as is prevalent in a considerable body of applied research—may lead to serious errors in inference.” 
         [0068]    Regarding the SSE, taking into account its different qualifications, are smaller for the joint estimation, than for Under CARA and Only CDE. Therefore, globally, this statistic indicates that the best model is the joint estimation (although SSE for Only CDE cannot be compared with the rest of columns or methods. This happens because this method considers different variables). 
         [0069]    The partial production elasticities, keep similar values across methods. The partial production elasticity for materials takes values in the interval [0.52 0.70]. This behavior is consistent with empirical observation, according with Saha. In other words: “. . . it should be recalled that the materials category include a large array of inputs such as fertilizer, seed, machinery operating inputs, and miscellaneous purchased inputs.” This mention material input diversity could explain, interalia, why they find ×2 as risk reducing. 
         [0070]    5.3 Next, system and method for computing Table 6 and Table 6 are presented. In  FIG. 20 , Step  200  it is constructed the risk sensitivities for the mean wealth; absolute risk aversion and relative risk aversion by using linear least squares regression. For Step  202  take the starting values from the published ones or construct their numeric values by running linear least squares for each corresponding optimization i.e., mean wealth. In  FIG. 21  the corresponding output is reported as the Arrow-Pratt Risk Aversion Measures. 
         [0071]    The first row of Table 6 belongs to the a parameter, which is already reported in Table 5 for all farmers. Convergence between the model and the reported estimates are achieved for all farmers and large farmers, with the exception of small farms. An analog case is presented in the estimation of the mean wealth, where all and large farmers achieved convergence, while small farmers do not. The absolute risk aversion estimates maintain consistency regarding a positive sign. The coefficient convergence is achieved with the second decimal. 
         [0072]    The reported behavior for small and large farmers with respect to A( W ) and R( W ) are mimicked by the simulation. Also, in the preceding paragraph was explained why small farmers have a somehow different trend. For instance, the bigger dispersion between simulation and reported estimates is found for small farms. Perhaps, this is due to its relative smaller size in the overall sample and thus to its implicitly diminishing representativeness in the whole sample. Thus, it could be concluded as the authors do: “Arrow-Pratt estimates for both groups are consistent with DARA and IRRA. The small farmers do show a higher level of A( W ) and a lower level of R( W ) than do the larger farmers.” 
         [0073]    The simulation of the null hypothesis of risk neutrality has achieved convergence in all three cases. Then, they also present a similar pattern as the published null hypothesis values. Therefore, it could be used the author&#39;s explanation for this case: “. . . the hypothesis of risk neutrality is clearly rejected in favor of risk averse preference structure. Further EP utility parameter estimates provide evidence of decreasing absolute risk aversion (DARA) because {circumflex over (α)}&lt;1, and increasing relative risk aversion (IRRA) because {circumflex over (β)}&gt;0.” This last quote is taken from the conclusions presented by Saha: “The empirical findings clearly rejected the null hypothesis of risk neutrality in favor of risk aversion among Kansas farmers. We also found evidence of decreasing absolute and increasing relative risk aversion.” 
         [0074]    It is used Saha&#39;s conclusion and explanations to present a panoramic view about what the reported simulation estimates imply, in terms of methodology and risk assessment, thanks to their close resemblance with the published paper&#39;s results. 
         [0075]    In general, the implemented models and their simulated parameters have achieved convergence with the results reported in the selected paper Saha et al. (1994). All the data use in this simulation is synthetic and the inventor does create all the econometric models. 
         [0076]    End of the Manual.