Inconsistency and Impossible Problems
Definition of INCONSISTENCY from the American Heritage Dictionary.
1. Displaying or marked by a lack of consistency, especially:
Not regular or predictable; erratic: inconsistent behavior.
Lacking in correct logical relation; contradictory: inconsistent statements.
Not in agreement or harmony; incompatible: an intersection inconsistent with the road map.
2. Mathematics. Not solvable for the unknowns by the same set of values. Used of two or more equations or inequalities.
Inconsistencies in problem solutions seem to be correlated with the social competence of students. Remarkable but apparently true.
Impossible problems also arise from inconsistency. This implies a type of conflict at the systemic level. When we have a system with inconsistent truths within, we are naturally led to impossible problems. This can occur from regulations that are contradictory. These can come from government agencies or industry leaders who exhibit inconsistent behavior. These arise when two different solutions can be based, logically, upon the rules or expected of exchange. They can be variant in time.
Examples: Time inconsistency in monetary or taxation problems. In simple terms, we need to devise a plan for two time periods. There are two options, (1) to make a policy optimal for both periods taken together, and (2) to make a plan optimal for period 2 only. OR... Time inconsistency is present because the optimal choice (about whether the government should have discretion in period two) is one thing (no) in period one and something different (yes) in period two. Thus, the term inconsistent refers to a time chance in the rules of operation.
Time inconsistencies are within the transactions of at least two groups or agencies. They usually refer to two or more time periods where there can be one decision for both periods taken in whole, or there can be a change in decision in a later period toward some optimal goal henceforth. One group or both groups have the power to make a change. Yet, neither of them know which will make the change, when or how. Time inconsistencies create impossible problems because there are at hand two strategies to pursue now regarding the policies to come. The presence of time-inconsistencies lead to the nonexistence of equilibria or non optimal equilbria in the systems involved.
Example. The Fed vs.The Market. During the years from 2011 through 2014, the Federal Reserve bank printed massive amounts of money and plunged it into the economy with the resultant surge in the stock market. Each period, of say one month, saw about $85B added. The market players, most of us, were constantly aware of this and played out investment games accounting for the next period much like the previous. Yet, there were thoughts given to a sudden change in Fed policy. When, in 2013, Ben Bernenke suggested a cessation of the Fed policy, the market went into free fall. Yet, the policy change did not take place, and the market continued to rise to new and record heights. Yet, there is no equilibrium in the market because the government can change the policy at any time. It is a certainty the Fed policy must change. The Market players are betting there will be an advanced warning and surely have exit strategies in place. It the change is sudden it could destabilize the market, with disastrous effect.
Example. The Start-Up vs. The Competition. A new company with a great idea seeks capitalization. Yet, the idea can be replicated by potential competitors. For example, a new virus software based on data mining of known computing malware issues. The new company knows this, but the competitors do not know the long-term potential for success of this idea. The investors understand that by investing they can achieve gains over the first period, say one year, but are unaware of what competitors may do when the idea is exposed. What is unknown and virtually unknowable is their policy during the next or subsequent periods. Their impossible problem is what may happen in the next period when potential competitors may actually compete. They must measure their expected return on investment. Google was once in this situation with their initial search engine. Apple faced this problem with their iPod and iPad. The problem is really impossible, but decisions must be made.
There is a new development in science, and that is the concept of adaptive inconsistent logic. There posits the idea that inconsistencies in science seems to be with us now and always have been. Consider the Ptolemaic theory of astronomy vs. the Copernican theory vs. the Newtonian theory. The first was shown to have inconsistencies as measurements became sharper, and the Copernican theory with sun centered circular orbits also were ultimately not predictive. The Newtonian theory (with Kepler's laws) seem to have established cosmology once and for all. The ultiimate and monotonic theory was achieved. Then came Einstein with relativity and quantum effects which showed how gravity worked, and the classical Newtonian theory was changed forever. Yet all, in their time, were adequate for the tasks at hand. Inconsistencies were fixed. Nowadays, inconsistencies have been more embraced (Neheus, 1999) and arguments made with an inconsistent-tolerant logic are more-or-less accepted. The only stipulation is that conclusions made should sustain after the inconsistencies have been removed. This new theory of inconsistency, which formerly illustrated impossible problems, is now the proving ground for improved or alternative theories.
References.
Barro, R.J. & Gordon, D.B. Rules, Discretion and Reputation in a Model of Monetary Policy, Journal Of Monetary Economics (12), 1983, 101-121
Barro, R.J., Recent Developments in the Theory of Rules versus Discretion, Economic Journal Supplement, 1986
Cukierman, Webb & Neyapti, Measuring the Independence of Central Banks and its Effect on Policy Outcomes, World Bank Economic Review, Volume 6, No. 63, 1993
Evans, M.D.D., Optimal Precommitment in Macroeconomic Policy: A Game Theoretic Analysis of Fiscal Policy Oxford Economic Papers, 42(4) October 1990, 695- 714
Fountas, S., Interactions among Private Investors and Government Policies: Rules versus Discretion, Journal of Economic Studies, 21(2), 1994, 38-56
Friedman, M., The Role of Monetary Policy, American Economic Review, May 1968
Giavazzi & Pagano, The Advantage of Tying Ones' Hands, European Economic Review, March 1988
Kydland & Prescott, Rules rather than Discretion: The Inconsistency of Optimal Plans, Journal of Political Economy, June 1977
Meheus, Joke, Inconsistency in Science, Kluwer, 1999
Minford, P., Time Inconsistency, Democracy and Optimal Contingent Rules, Oxford Economic Papers, April 1995
van der Ploeg, F., Trade Unions, Investment, and Employment: A Non Co-operative Approach European Economic Review, 31(7), October 1987, 1465-92
Rogers, C. A., Expenditure Taxes, Income Taxes, and Time Inconsistency, Journal of Public Economics, 32(2), March, 215-30
Rogoff, The Optimal Degree of Commitment to an Intermediate Monetary Target, Quarterly Journal of Economics, November 1985
Whynes D.K. (1989) The Political Business Cycle, in Current Issues in Macroeconomics, ed. Greenaway, D. MacMillan, Basingstoke
http://astro.temple.edu/~swansonc/606ol/time-con/Time-con.htm
Definition of INCONSISTENCY from the American Heritage Dictionary.
1. Displaying or marked by a lack of consistency, especially:
Not regular or predictable; erratic: inconsistent behavior.
Lacking in correct logical relation; contradictory: inconsistent statements.
Not in agreement or harmony; incompatible: an intersection inconsistent with the road map.
2. Mathematics. Not solvable for the unknowns by the same set of values. Used of two or more equations or inequalities.
Inconsistencies in problem solutions seem to be correlated with the social competence of students. Remarkable but apparently true.
Impossible problems also arise from inconsistency. This implies a type of conflict at the systemic level. When we have a system with inconsistent truths within, we are naturally led to impossible problems. This can occur from regulations that are contradictory. These can come from government agencies or industry leaders who exhibit inconsistent behavior. These arise when two different solutions can be based, logically, upon the rules or expected of exchange. They can be variant in time.
Examples: Time inconsistency in monetary or taxation problems. In simple terms, we need to devise a plan for two time periods. There are two options, (1) to make a policy optimal for both periods taken together, and (2) to make a plan optimal for period 2 only. OR... Time inconsistency is present because the optimal choice (about whether the government should have discretion in period two) is one thing (no) in period one and something different (yes) in period two. Thus, the term inconsistent refers to a time chance in the rules of operation.
Time inconsistencies are within the transactions of at least two groups or agencies. They usually refer to two or more time periods where there can be one decision for both periods taken in whole, or there can be a change in decision in a later period toward some optimal goal henceforth. One group or both groups have the power to make a change. Yet, neither of them know which will make the change, when or how. Time inconsistencies create impossible problems because there are at hand two strategies to pursue now regarding the policies to come. The presence of time-inconsistencies lead to the nonexistence of equilibria or non optimal equilbria in the systems involved.
Example. The Fed vs.The Market. During the years from 2011 through 2014, the Federal Reserve bank printed massive amounts of money and plunged it into the economy with the resultant surge in the stock market. Each period, of say one month, saw about $85B added. The market players, most of us, were constantly aware of this and played out investment games accounting for the next period much like the previous. Yet, there were thoughts given to a sudden change in Fed policy. When, in 2013, Ben Bernenke suggested a cessation of the Fed policy, the market went into free fall. Yet, the policy change did not take place, and the market continued to rise to new and record heights. Yet, there is no equilibrium in the market because the government can change the policy at any time. It is a certainty the Fed policy must change. The Market players are betting there will be an advanced warning and surely have exit strategies in place. It the change is sudden it could destabilize the market, with disastrous effect.
Example. The Start-Up vs. The Competition. A new company with a great idea seeks capitalization. Yet, the idea can be replicated by potential competitors. For example, a new virus software based on data mining of known computing malware issues. The new company knows this, but the competitors do not know the long-term potential for success of this idea. The investors understand that by investing they can achieve gains over the first period, say one year, but are unaware of what competitors may do when the idea is exposed. What is unknown and virtually unknowable is their policy during the next or subsequent periods. Their impossible problem is what may happen in the next period when potential competitors may actually compete. They must measure their expected return on investment. Google was once in this situation with their initial search engine. Apple faced this problem with their iPod and iPad. The problem is really impossible, but decisions must be made.
There is a new development in science, and that is the concept of adaptive inconsistent logic. There posits the idea that inconsistencies in science seems to be with us now and always have been. Consider the Ptolemaic theory of astronomy vs. the Copernican theory vs. the Newtonian theory. The first was shown to have inconsistencies as measurements became sharper, and the Copernican theory with sun centered circular orbits also were ultimately not predictive. The Newtonian theory (with Kepler's laws) seem to have established cosmology once and for all. The ultiimate and monotonic theory was achieved. Then came Einstein with relativity and quantum effects which showed how gravity worked, and the classical Newtonian theory was changed forever. Yet all, in their time, were adequate for the tasks at hand. Inconsistencies were fixed. Nowadays, inconsistencies have been more embraced (Neheus, 1999) and arguments made with an inconsistent-tolerant logic are more-or-less accepted. The only stipulation is that conclusions made should sustain after the inconsistencies have been removed. This new theory of inconsistency, which formerly illustrated impossible problems, is now the proving ground for improved or alternative theories.
References.
Barro, R.J. & Gordon, D.B. Rules, Discretion and Reputation in a Model of Monetary Policy, Journal Of Monetary Economics (12), 1983, 101-121
Barro, R.J., Recent Developments in the Theory of Rules versus Discretion, Economic Journal Supplement, 1986
Cukierman, Webb & Neyapti, Measuring the Independence of Central Banks and its Effect on Policy Outcomes, World Bank Economic Review, Volume 6, No. 63, 1993
Evans, M.D.D., Optimal Precommitment in Macroeconomic Policy: A Game Theoretic Analysis of Fiscal Policy Oxford Economic Papers, 42(4) October 1990, 695- 714
Fountas, S., Interactions among Private Investors and Government Policies: Rules versus Discretion, Journal of Economic Studies, 21(2), 1994, 38-56
Friedman, M., The Role of Monetary Policy, American Economic Review, May 1968
Giavazzi & Pagano, The Advantage of Tying Ones' Hands, European Economic Review, March 1988
Kydland & Prescott, Rules rather than Discretion: The Inconsistency of Optimal Plans, Journal of Political Economy, June 1977
Meheus, Joke, Inconsistency in Science, Kluwer, 1999
Minford, P., Time Inconsistency, Democracy and Optimal Contingent Rules, Oxford Economic Papers, April 1995
van der Ploeg, F., Trade Unions, Investment, and Employment: A Non Co-operative Approach European Economic Review, 31(7), October 1987, 1465-92
Rogers, C. A., Expenditure Taxes, Income Taxes, and Time Inconsistency, Journal of Public Economics, 32(2), March, 215-30
Rogoff, The Optimal Degree of Commitment to an Intermediate Monetary Target, Quarterly Journal of Economics, November 1985
Whynes D.K. (1989) The Political Business Cycle, in Current Issues in Macroeconomics, ed. Greenaway, D. MacMillan, Basingstoke
http://astro.temple.edu/~swansonc/606ol/time-con/Time-con.htm
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