Senior Economic Seminar - Villanova University by chenmeixiu

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									Senior Economic
    Seminar
                 Ken Taylor
                 Spring 2010

 Prerequisites:
       1. Econ. 2101 & 2102
       2. Completion of the Statistics
       course requirement.
       3. Senior standing


           Econ. 4132
Course Goals:
   Integrate knowledge and skills
   Enhance research skills
   Enhance writing skills
   Enhance presentation skills
   Enhance teamwork skills
   Understand economic growth



            Econ. 4132
    Course tasks & topics
       for discussion:
   Your first job
   The Internet as a research tool
   The writing of economics
    (professional writing)
   The presentation of professional
    writing
   The power and limits of economics
   Transactions costs and market
    structure
   Methodology and research
    methods
            Econ. 4132
    Course tasks & topics
       for discussion:
   Computer lab…using SPSS
   Why is there economic
    growth?
   Economic growth…facts,
    figures & productivity
   Economic Growth Theory


          Econ. 4132
     Graded Elements of
          Course
   Senior Thesis…300 points
   Growth theory exams…200 points
   Current event report/presentation…100
    points
   In-class Assignments, Quizzes and
    Participation…100 points
   Senior Thesis Presentation at
    Conference - extra credit - 5 extra credit
    points added to final grade
   Discussant at Ursinus Conference
    extra credit - 2.5 points added to final
    grade
              Econ. 4132
Syllabus … and other
important information
   http://www.homepage.villanova.ed
    u/kenneth.taylor
   The syllabus is a contract between
    the student and the professor
   Posted lecture notes
   Specific assignments, updates and
    date changes will be posted on the
    website … so check it often

            Econ. 4132
        Your first job
“Think of yourself as an undervalued
   asset that is about to go public.”
           Congratulations!
      You are now an official…
               Gopher




          Econ. 4132
          Your first job
   Average time spent in first job is
    2.2 years.
   The typical professional will have
    three major career changes during
    their working years.




            Econ. 4132
        Internet tools &
           resources
   Searching for what you need
    online.
   Starts with a most basic question:
    Which search engine do I use?
   Depends on what you’re searching
    for.
   Search engines come in all sizes
    and search in different ways.

            Econ. 4132
         Internet tools &
            resources
   Most common…specially designed
    software called “spiders” that crawl
    all over the Internet looking for
    texts where the search keywords
    appear.
   This is true for “open text” search
    engines.
   There are also “subject tree”
    search engines.
            Econ. 4132
         Internet tools &
            resources
   Premier subject tree index is…
                   Yahoo!
   The human method of compiling a
    directory takes more time and
    therefore doesn’t provide the
    breath of results that a true engine
    does.
   But…it is more intuitive.
   Note: Google Directory
            Econ. 4132
         Internet tools &
            resources
   Open text searches…
   To make sure you get relevant matches,
    it helps to think of multiple words to
    search for.
   A recent survey showed that 60% of all
    searchers never type in anything else
    than one word in a search.
   Use quotation marks around multiple
    words.


             Econ. 4132
         Internet tools &
            resources
   Add a “+” sign to focus your search still
    more since some search engines ignore
    the word “and.”
   People who avoid advance search
    techniques are using some of the least
    qualified tools.
   Some of the best data sources are not
    found on the World Wide Web but rather
    in proprietary data bases accessible only
    from within an organization.
   Ours: http://www.library.villanova.edu/

             Econ. 4132
         Internet tools &
            resources
   Let’s go explore and experiment…
   http://www.homepage.villanova.edu/kenn
    eth.taylor
   Yahoo! Search - Directory Search
   Google
   Vivisimo
   AlltheWeb
   Northern Light
   Ask
   Resource shelf

             Econ. 4132
                        Professional Writing
1. Writing is the Economist’s Trade…

•   Big secret in economics is that good writing pays well and bad
    writing pays badly.
2. Writing is thinking…
•   You do not learn the details of an argument until writing it in
    detail, and in the details you uncover the flaws in the
    fundamentals.
3. Rules can help, but bad rules hurt…
•   Like mathematics, writing can be learned.
•   Classic forms of rhetoric…
•   Invention...the framing of arguments worth listening to.
                                    Econ. 4132
• Arrangement... A good deal of economic prose implies that the only
proper arrangement of an empirical study is: Introduction, outline of
the rest of the paper, the literature review, the theory, the model, the
results, suggestions for future study.
• Style... begins with mere fluency, getting the stuff down on paper.
And it ends up with revising, again and again, until you have taken
out every snare and ugliness. Style guide (e.g. MLA)…up to you.
4. Teachable tricks to get the first draft...
• Write too early rather than too late.
• Research is writing.
• Read through your notes or file of notes (which is Invention) trying
to see an outline in it (which is Arrangement).
• Now set aside the broad outline, keeping it steadily in mind. You
need it as a goal to give the writing direction. You can change it, and
                                      Econ. 4132
should do so, as the essay takes shape.
5. Keep your spirits up, forge ahead
• If you have a block and can’t think of anything to say, you might read
more, calculate more, in general research more (educate yourself) or at
least take a break.
• Regard your outline as an aid, not a master.
• At the end of a session, or at any substantial break, always write
down your thoughts, however vague, on what will come next.
• After a break you may have trouble getting back into “the spirit” of
writing... reread a big chunk of the draft to get back in the mood ... and
insert, amend, revise, correct, cancel, delete and improve your way to
where you next need to begin writing.
6. Speak to an audience of human beings
• If people wrote more like the way they spoke their writing would
have more vigor.
                                     Econ. 4132
• Control your tone: The tone of the writing and much of its clarity
depends on choosing and then keeping an appropriate implied reader.
• Avoid boilerplate: boilerplate in prose is all that is prefabricated and
predictable.
• Writing must be interesting.
• Get to the point that skeptical but serious readers care about and
stick to it (reports…executive summary, detailed report, appendices).
• The art of the hook.
• Make tables, graphs, and displayed equations readable.
        [1] Try to be clear and brief.
        [2] Titles and headings in tables should be as close to self-
        explanatory as possible... use words not acronyms.
        [3] The same thing can be said of displayed equations.
                                     Econ. 4132
7. Above all, look at your words...
• Flee the cliché when a more original word or expression is more
precise and vivid.
• Word-smithing is part of thinking.
8. Conclusion…
• To improve in writing style at all you must become your own
harshest editor and critic.
• Good writing is difficult … but remember:
• Good writing pays well…
                      … and bad writing doesn’t pay at all.



                                   Econ. 4132
               Making a Professional Presentation
Rule #1: Nothing is more deadly than a presentation delivered as it
   was written.
1. The Structure of a Presentation…
•   The Rule of Tell'em:
    [1] Tell'em what you are going to tell'em,
    [2] Tell it to them, and then…
    [3] Tell'em what you told them.
•   Translation: Start with an introduction; including an "agenda" or
    set of goals for the presentation, provide the content;
    information and summarize the presentation.


                                     Econ. 4132
• Where do you start?...Last is First – The Summary/Conclusion Slide
       [1] One researched "fact" of presenting that has been around
       for a while is that most people attending a presentation will
       "remember" no more than five key points.
       [2] What you have to determine is what are the key points.
• How do you get your audience to remember what you want them to?
       [1] Start preparing with the last slide.
       [2] When you are ready to create your presentation, forget the
       details for a minute, forget the presentation's organization,
       instead:
       [3] Write out your conclusion or summary slide first! It should
       emphasize the most important points you plan to make.
       [4] Once you have visualized those points, it's relatively easy
       build your presentation around them.
                                   Econ. 4132
2. The Basic Rules of Good Presentations…

                 KISS - Keep It Simple Stupid!
• There are numerous ways to apply this ancient adage. The bottom
line is that the more complicated you let things get, the more trouble
you can expect.
• Rehearse the presentation…
       [1] To present the most professional image, you need to know
       your presentation.
       [2] Rehearsing the presentation includes more than just going
       over what you will be saying. Rehearsing includes the entire
       presentation. Use the same tools too.
       [3] It's okay to occasionally leave the main "script" but,
       wandering presentations that lack focus, or those too
                                     notes,
       dependent on working fromEcon. 4132 or long pauses to compose
       your thoughts are never acceptable.
• Don't memorize: Rehearsing is one thing, committing the
presentation to memory and performing it by heart, is not the way to
go. You need to present, not to recite.
• Use your notes very sparingly. Too much time spent reading notes
may convince your audience that you are unprepared.
• Dress for success.
• Pace yourself - don't go too fast, or too slow.
       [1] A general rule, every "slide" deserves at least 10 seconds,
       and none rate more than 100.
• Determine your communication needs, the presentation
environment, and select the right group of tools to get your message
across.
• Creating support materials: Don't assume that your message will
stick. Provide your audience with the right support materials.
                                   Econ. 4132
3. It is Time to Speak Out -- Giving an Effective Presentation
• On Fear and Death...It's been said that most people, including a
great many executives, fear presenting to large groups even more than
they fear death. You are not alone.
• The naked audience … the friendly faces …. deep breathing (calm
and center yourself).
• Your place as a presenter ... controlling your audience. Face your
audience. Observe them. Make eye contact … don't wander around
the room, don't look down.
• Lose the computer … that is … don't hide behind it. Get a remote
mouse and get back up in front of the group, where you belong, as
presenter, leader, moderator, and communicator.
• Retain control of the flow of the presentation. Where appropriate
defer questions to later in the presentation or afterwards.
                                    Econ. 4132
• If you do defer any questions: Follow through as promised. Nothing
will damage your credibility in the long run, more than not keeping
your word.
4. Now what will make it even better? …
• Enthusiasm … Absolutely nothing will help your presentation more
than communicating with passion and confidence.
• The power of language … The words you select will dramatically
impact your audiences reaction – to both your ideas and your
effectiveness as a presenter (tone of voice again).
• Humor -- The right amount of humor - used judiciously, can go a
long way to build rapport with your audience, and keep your
audience interested and attentive. As a rule, don't tell jokes for their
own sake, drop in your humor where it fits, relating to a point, or a
break between sections.
                                     Econ. 4132
• Quotations … Appropriate quotations can make a noticeable impact
on your audience. Make them relevant … and interesting.
• Have a backup plan: What if your projector dies, computer crashes,
slide tray still on the table at home, power goes out. What is plan B.
(And did you practice it?)
• Five things to do when you are done…
       [1] Thank them!
       [2] Make materials available.
       [3] Make yourself available.
       [4] Provide them with a method of reaching you.
       [5] Get feedback.


                                   Econ. 4132
               The Power and Limits of Economics
A. Model: A theoretical construct composed of a number of
   assumptions from which conclusions or predictions are deduced.
   1. Assumptions - often simpler than reality.
   2. Purpose of model is to make predictions … Test: how well it
   predicts.
   3. Models => continual collection of data for verification and
   prediction.
   4. Related concepts:
       a. Ceteris Paribus
       b. Positive vs. normative analysis
       c. Marginal analysis
       d. Deterministic versus stochastic relationships
                                 Econ. 4132
       e. Accounting cost, opportunity cost and transaction cost
The Firm as Coordinator of Economic Activity…
1. Market vs. Managerial Coordination
   a. Despite the diversity of firms they all have one thing in
   common: the function of coordinating economic activity -
   of helping to decide what goods are to be produced, how to
   produce and what quantities to produce.
   b. To understand how firms carry out this function, it is
   useful to distinguish between two kinds of coordination.
A. Market coordination - Coordination of economy activity
   using the price system to transmit information and provide
   incentives (invisible hand).
B. Managerial coordination - Coordination of economic
   activity by means of directives from managers to
   subordinates (visible hand). 4132
                              Econ.
C. Coordination within the firm…
      a. In a famous essay on the nature of the firm, Ronald
      Coase posed a question about these two ways of
      coordinating economic activity.
      1. If the market works as well as economists say it does
      why is managerial coordination ever used at all?
      2. Answer: The market is not used for every situation
      where coordination is required because there are
      transaction costs to using it.
               a. There are costs in finding out what prices are, in
               negotiating contracts, assembling components,
               writing bills and receipts, and straightening things
               out when contracts are not carried through.
               b. Car example…
      3. But, in answering one question Coase found himself
      presented with another:
                               Econ. 4132
       a. If managerial coordination works so well, why use the
       market at all? (Run economy as one big firm…this is
       what was attempted under communism)
       b. Answer: Managerial coordination turns out to have
       transaction costs of its own, as well as savings in
       transactions costs.

- Under managerial coordination, the person actually doing the
job does not need to know all the reasons behind the decision to
do it, and that is a savings (specialization & division of labor).

- Sometimes the costs of supplying information to a manager or
other central decision maker are greater than the costs of
supplying that same information to people close to the job. When
that is the case, managerial coordination loses it advantage over
market coordination…
                               Econ. 4132
                       … remember diseconomies to scale?
D. The Limits of the Firm…
a. Coase concluded that the firm is an organization that uses
managerial coordination internally and uses the market to
coordinate its activities with those of other firms and individuals
(consumers)…but where are the boundaries?
b. Each firm tends to expand the scope of its operations until the
transaction costs of organizing one additional task within the
firm become equal to the costs of organizing the same task
outside the firm through the market (competition: seek & find).
c. This point varies from industry to industry. By allowing each
firm to expand to its optimal scope of operation and by leaving
coordination among firms to the market, total transactions costs
for the economy are minimized.
                                over
d. The limit of the firm variesEcon. 4132time: technological change.
               Team Research Techniques & Questions
•   Teamwork: Teams & Projects...
•   Empirical/business research method:
    1. What do you want to investigate?
    2. Form clear hypotheses or research questions… Modeling.
    3. Information and data collection…Verification.
    4. Analysis, synthesis and reporting.
• Mathematical economics: An approach to economic analysis in which
the economist makes use of symbols in the statement of the problem and
also draws upon known mathematical theorems to aid in reasoning.
• The major difference between quantitative economics and
literary/heuristic economics lies principally in the fact that in the former,
the assumptions and conclusions are stated in mathematical symbols
rather than words and in equations rather than sentences.
                                   Econ. 4132
• Why is it necessary to go beyond geometric methods?
       - While geometric analysis has the important advantage of
       being visual, it also suffers from a serious dimensional
       limitation.
• Mathematical approach has following advantages…
1. The “language” used is more concise, precise and objective.

2. There exists a wealth of mathematical theorems at our service.
3. Forces us to state explicitly all our assumptions => keeps us from
the pitfall of unintentional adoption of unwanted implicit
assumptions.
• Economic Models - any economic theory is necessarily an
abstraction from the real world… so how does one “model” some
economic phenomenon?
                                Econ. 4132
•   Sensible procedure: pick out what appeals to our reason to be the
    primary factors and relationships relevant to our problem and to
    focus our attention on these alone.
•   Ingredients of a mathematical model:
1. Consists of a set of equations designed to describe the structure
   of the model.
2. By relating a number of variables to one another in certain ways,
   these equations give mathematical form to the set of analytical
   assumptions adopted.
3. Through application of the relevant mathematical operations to
   these equations, we seek to derive a set of conclusions which
   logically follow from those assumptions.
4. Variable: something whose magnitude can change (take on
   different values).
                                Econ. 4132
•   Properly constructed, an economic model can be solved to
    give us the solution values of a certain set of variables.
    … number of equations needed for a unique solution?
1. Such variables, who’s solution values we seek, are known as
   endogenous variables (originating from within).
2. An economic model may also include variables which are
   assumed to be determined by forces external to the model -
   magnitudes are accepted as given data only called exogenous
   variables (originating from without).
3. Variables often appear in combination with fixed numbers
   (e.g. 7P or .5TR)
    - A constant is a magnitude that does not change and is the
    antithesis to a variable.
                                 to a variable, it is often referred to
    - When a constant is joinedEcon. 4132
    as the coefficient of that variable.
•    However, a coefficient may be symbolic rather than numerical
    (e.g. instead of 7P we may write aP in order to obtain a higher
    level of generality)
    - To identify its special status, we give it the distinctive name
    parametric constant or simply parameter.
•    Convention... parametric constants are normally represented by
    the symbols a, b, c or their Greek counterparts α, β, γ although
    other symbols are permissible.
•   Equations and Identities: In economic applications we may
    distinguish between three types of equations:
1. Definitional equations…sets up an identity between two
   alternate expressions that have exactly the same meaning.
2. Behavioral equations... specifies the manner in which a variable
   behaves in response to changes in other variables.
                                  Econ. 4132
Note: It is primarily through the specification of the form of the
   behavioral equations that we give mathematical expression to the
   assumptions adopted for a model.
3. Equilibrium conditions… An equation that describes the
   prerequisite for the attainment of equilibrium.
                  
                  Statistical Methods in Research
•   The world of the business economist is most often stochastic and
    rarely deterministic.
•   Statistical theory and the tools of the trade (SPSS, SAS &
    Excel).



                                Econ. 4132
                  Regression and Correlation Analysis
Economists and business researchers frequently must estimate how
one variable is related to, or affected by, another variable (estimation
of the parametric constants plus the intercept point).
To estimate quantitative relationships, economists use regression
techniques; and to determine how strong such relationships are, they
use correlation techniques.
Relationship among variables and scatter diagrams.
• Inverse versus direct relationship?
• Linear or nonlinear?
• Strength of relationship? (Relative … yet often seen by the
"tightness" of points around trend line).
• Correlation Analysis ... Whereas regression analysis describes the
                                   variables, correlation analysis
type of relationship between twoEcon. 4132
describes the strength of the relationship between two variables.
Four principal goals of regression/correlation analysis…
1. RA provides estimates of the dependent variable for given values of
the independent variable....the regression line.
2. RA provides measures of the errors that are likely to be involved in
using the regression line to estimate the dependent variable....construct
confidence intervals.
3. RA provides an estimate of the effect on the mean value of Y on a
one-unit change in X.
4. CA provides estimates of how strong the relationship is between the
two variables... the coefficient of correlation and the coefficient of
determination.
Linear Regression Model... OLS (Ordinary Least Squares)
       Assumptions…
                                 Econ. 4132
a. The mean value of Y, given the value of X, is a linear function of
X....the population or true regression line.
b. The standard deviation of the conditional distribution of Y is the
same regardless of the specified value of the independent
variable....homoscedasticity.
c. The values of Y are independent of one another....non-
autoregression.
d. The conditional distribution of Y is normal.
e. Non-stochastic or fixed X.
The five assumptions underlying RA can be stated somewhat
differently. Together they imply that:
Yi =a + bx1 + bx2 + … + bxn + 
  = A normally distributed random variable with a mean of zero and
                                Econ. 4132
a constant standard deviation. An error term or the residual.
Characteristics of Least-Squares Estimates...
1. a and b are unbiased estimators of A and B.
2. Of all unbiased estimators, a and b have the smallest standard
deviations of their sampling distributions => most efficient
estimators.
3. a and b are consistent estimators of A and B (the population coefs.)
Standard Error of Estimate…
Estimating the Conditional Mean…
       … Estimating the vertical coordinate of the point on the
       population regression line corresponding to a given value of
       the independent variable: the average of the dependent
       variable over many occurrences.
Predicting an Individual Value of "y"…
                                Econ. 4132
       … Create a confidence interval for a unique event => the next
       value of x* which occurs.
Coefficient of Determination...
- Uses the concept of variation: which refers to a sum of squared
deviations.
- R2 = RSS/ TSS
- R2c = Corrected or Adjusted Coefficient of Determination: Corrected
for lost degrees of freedom.
The Correlation Coefficient (Pearson)...
- Measures the strength of the relationship between "x" and "y“... And
between “xi” and xj”
- The sign of "r" must equal the sign of the slope of the relationship =>
the value of "r" ranges from -1 to +1.
                                  Econ. 4132
Confidence interval of "B" (the slope of the population regression
line…or coefficient on an independent variable)
2. May conduct hypothesis testing...H0: B = 0; Ha: B  0
- If H0: B = 0 is true, there is no relationship between the designated
dependent and independent variables.
- Test statistics: t = (b - B)/Sb
- Decision rules ... Note: "t" statistics are typically produced on
computer output (t-stat = b/Sb). There is a useful rule of thumb if "n"
minus the lost degrees of freedom (k) is greater than or equal to 15.
"k" = the number of estimated parameters in the regression.
- If t-stat  2 => reject H0 at the = .05 level
- If t-stat  3 => reject H0 at the = .01 level

                                    Econ. 4132
Analysis of Variance…
1. Often used to test the overall significance of a regression model =>
it is used to test whether all of the true regression coefficients in the
equation equal zero: H0: B1 = B2 = .... = Bn = 0
Ha: at least one Bi  0
- Decision rule: Reject the null hypothesis if the ratio of the explained
mean square to the unexplained mean square exceeds F with v1 = k - 1
and v2 = n - k degrees of freedom.
- Because of computer use, it is seldom necessary to calculate the
numbers in the table by hand (reported “critical value”).
Dummy Variable Technique…
- Multiple regression can be used to analyze the effects of qualitative
variables.
                               Econ. 4132
- Dummy variable = a qualitative variable which can equal "0" or "1".
Hazards and Problems in Regression and Correlation Analysis…
1. A high coefficient of correlation does not necessarily imply
causality between the dependent and independent variables.
2. Even if an observed correlation is due to a causal relationship, the
direction of causation may be the reverse of that implied by the
regression.
3. Extrapolation - dangerous for there is no data to support the
assumption that the relationship is linear beyond the range of the
sample data.
4. Important to recognize that a regression is based on past data. The
environment is dynamic so underlying forces may have altered
relationship between the variables in such a way that prediction from
a regression may be inaccurate
5. When carrying out a regression, it is important to try to make sure
that the assumptions are met. Econ. 4132
6. Multicollinearity ... A situation in which two or more of the
independent variables are very highly correlated.
- If present in sufficient magnitude, it is impossible to estimate the
regression coefficients of both independent variables because the data
provides no information concerning the effect of one independent
variable, holding the other independent variable constant (i.e. all that
can be observed is the effect of both independent variables together).
- Commonly encountered with time-series data sets.
- How does one detect multicollinearity? … By estimating the
correlation coefficients among the independent variables.
- If some of these correlation coefficients are close to +1 or -1,
multicollinearity is likely to be a problem.


                                 Econ. 4132
7. Serial Correlation and the Durbin-Watson Test…
- Another potential problem: the error terms may not be independent
(they are "serially correlated").
- Most often encountered in time-series data.
8. Analyzing the Residuals…
- If the assumptions underlying regression are violated, this is likely
to show up in a plot of the residuals.
1. Specification error: missing an important variable(s).
2. Besides being useful in detecting specification errors, the
residuals can also be plotted to detect departures from the
assumptions: normality, non-autoregression, homoscedasitity and
linearity.

                                 Econ. 4132
H. Coping with departures from the assumptions.
1. Nonlinearlity - logarithmic transformation or fit a quadratic
equation (or any other higher-order polynomial) to the data.
2. Serial correlation - transformation of the data.
3. Heterscedasticiy (More common with cross-sectional data sets) –
transformation of the data.
Both too complicated to present yet important to know there are
techniques to help cope with these problems.
4. This does not imply that it is possible to deal with any or all
departures from the assumptions.
Choosing the best form of a multiple regression equation...
- Stepwise Multiple Regression: specifies which independent
variables seem to provide the best explanation of the behavior of the
dependent variable.             Econ. 4132
   … The computer selects from a list of potential independent
   variables the one that results in the greatest reduction in the
   variation unexplained by the regression of Y on X.
                    SPSS exercise: employee.sav
1. Log into www.citrixweb.villanova.edu. Sign in with your standard
   login, open “academic applications”, then “math” click on the
   SPSS icon
2. Open “employee.sav” file. Check out the variable names and
   descriptions. (may need to download from my website)
3. Have to transform “gender”. Transform  recode  into same
   variable  old and new values, m = 0, f = 1 (add each time) 
   continue  okay.
4. Have to redefine gender from “string” to “numeric”. Click on
   “Variable View” tab on bottom. Find “gender” on list  “type”
   next to gender…button appears  “numeric”.
                               Econ. 4132
                       SPSS exercise: employee.sav
Assignment: Regress SALARY against these five explanatory variables, run tests
    of significance on these variables, interpret the meaning of the coefficients
    for those you find significant as well as the R2, and test for the overall
    significance of the regression model.
- Dependent variable = salary => current salary
- Independent variables:
1.   educ = educational level (years)
2.   gender = gender of employee
         0 = male; 1 = female
3.   jobtime = months since hire
4.   prevexp = previous experience (months)
5.   race = minority classification
          0 = white; 1 = minority
                                        Econ. 4132
                         SPSS exercise: World95.sav
-    Dependent variable = infant mortality (deaths per 1000 live births) =
     babymort. Independent variables … you have to decide.
Suggestions:
1.   I would not suggest constructing dummy variables for this
     assignment…although it might be tempting.
2.   This is a cross sectional data set so be on the lookout for heteroscadasticity.
3.   Build a correlation table for your explanatory variables: Check for
     multicolinearity. Develop a logical approach if you find variables with
     correlations in excess of  .75
Team Assignment:
1.   Keep a handwritten record of everything you decide and do. Include the
     results from #2 & #3 below…this record is to be handed in.
2.   Write down your model specification and test the overall model (ANOVA)
     and the significance of each explanatory variable.
3.   Interpret your significant  coefficients and suggest a policy response.
                                        Econ. 4132
                Introduction to Economic Growth
•   Survey of the current thinking and controversy on economic
    growth...
A. Economist disagree on how best to foster it.
B. Some economist argue that they can answer questions by making
   their growth models more complex. Others, however, believe
   that simplicity is the key.
C. One of the leaders of the back to basics school is Gregory
   Mankiw (Harvard).
•   He argues that “neoclassical” growth models such as those first
    developed in the 1950's by Robert Solow can teach policy makers
    almost everything that they need to know about growth.
•   The neoclassical approach focuses on capital accumulation.
                               Econ. 4132
• By saving and investing more, a country can increase the
amount of capital that it leaves to its future workers, thereby
raising their productivity and hence their income. Eventually, a
country reaches a point at which each generation saves just
enough to replace the capital that it has depleted. At this point,
income per head can grow only as fast as the technology it has
access to improves.
• Many say this is too simple of a model. It provides some
powerful insights into the link between savings and growth, but it
has two drawbacks.
   [1] It predicts specific relationships among some basic
   economic statistics. Yet some of these predictions fail to fit
   the facts. For example, income disparities between countries
   are greater than the differences in their savings rates would
   suggest (even when adjusted for stage of development).
                             Econ. 4132
       [2] Although the model says that economic growth ultimately
       depends on the rate of technological change, it fails to explain
       exactly what determines this rate.
D. Despite these limitations Dr. Mankiw believes that the neoclassical
model is the best way to understand growth. Reasons...
[1] He argues that the goal of growth theory should be to explain why
some countries grow faster than others, not why they grow in the first
place. He asserts that ideas flow freely, and that all countries
therefore have access to the same technologies…or ways to convert
capital and labor into outputs.
[2] Poor countries do things differently, he says, because they have
less capital with which to work. If this is true, learning more about
technological change would not help to explain differences in
countries’ growth rates.
[3] He also believes that the neoclassical model’s empirical problems
                                 Econ. 4132

stem from a simple failure to adjust for human capital.
[4] Just as economies devote some of their current resources to new
plant and equipment, they also spend some of these resources on
improving their workers’ skills.

[5] Dr. Mankiw estimates that, in a typical country, about 2/3 of all
labor income derives from such investments. The typical country
therefore derives about 4/5 of its total income from capital…human
and physical…as opposed to raw labor. That is far higher than the 1/3
share that economists typically assume.
[6] Once this difference is accounted for, many of the neoclassical
model’s empirical anomalies disappear.

E. Many economists disagree for several reasons...
[1] Accounting for human capital raises as many questions as it
answers. Paul Romer (Stanford) estimates that if differences in
income across countries stem from disparate levels of human capital,
                                  countries should be about 100 times
then returns to education in poorEcon. 4132
larger than in rich ones (implausible).
[2] Many economists do not believe that technologies can be ignored.
Whereas Dr. Mankiw believes that technologies are universally
available, his critics argue that implementing them often requires
subtle know-how, market/institutional synergies and integrated
networks that are expensive to transmit across borders…not to
mention the impact of corporate secrecy and intellectual property
rights.
F. Complications…
• This is why critics of the neoclassical approach prefer “endogenous
growth” models which deal with technological change explicitly.

• These models focus on the incentives to create new knowledge and
the ways in which this knowledge spreads.
       [1] They do so by incorporating microeconomic decision-
       making and by explicitly examining the interaction between
       researchers and producers. 4132
                               Econ.
• Dr. Mankiw points out that it is difficult to make international
comparisons using this approach: Because concepts such as
“knowledge” are so difficult to measure, it is impossible to compare
them across different countries. The ease with which the neoclassical
approach can integrate available statistics is another of its big
advantages.
G. Despite their differences, both the neoclassical and endogenous
growth models suffer from other shortcomings:
• They both ignore other important factors which affect growth: Extent
to which a country embraces free trade, free enterprise, democracy,
rule of law in general (protection of private property rights in
particular) and the role of natural resources.
• The precise relationship between these traits and growth is hard to
pin down yet they may matter as much or even more than savings
rates, schooling and basic research.
                                 Econ. 4132
…So, what historical factors have propelled the invention of new
  technologies?
•   Fourteen factors proposed as historical causes of technological
    change (most of these not testable).
1. Long life expectancy: gives prospective inventors the years
   necessary to accumulate technical knowledge, as well as the
   patience and security to embark on long development programs
   yielding delayed rewards.
2. The availability of cheap slave labor in classical times
   discouraged innovation. Once slavery outlawed high wages or
   labor scarcity stimulated search for technological solutions.
3. Patents and other property laws protected ownership rights of
   inventors and reward innovation.
4. Modern industrial societies provide extensive opportunities for
                               Econ. 4132
   technical training.
5. Strong individualism (such as in the US) allows successful
   inventors to keep earnings for themselves. There are cultures (e.g.
   New Guinea) where any money earned is shared among
   relatives…make more money, more relatives move in and expect to
   be fed and supported…creates disincentive.
6. Modern capitalism is, and the ancient Roman economy was not,
   organized in a way that made it potentially rewarding to invest
   capital in technological development.
7. Risk-taking behavior (the entrepreneurial spirit), necessary for
   efforts at innovation, are more prevalent in some societies than in
   others.
8. The scientific outlook is a unique feature of post-Renaissance
   European society and has contributed heavily to its modern
   technological preeminence (decision making driven by rationality).
9. Tolerance of diverse views and of heretics fosters innovation,
                                  outlook
   whereas a strongly traditionalEcon. 4132 (e.g. China) emphasizes
   conformity and tradition.
10. Religions vary greatly in their compatibility with technological
    innovation…some branches of Judaism and Christianity claim to
    be especially compatible with it, while some branches of Islam,
    Hinduism and Brahmanism may be especially incompatible.
   The next factors have an inconsistent influence on technological
   development…but are important in certain cases.
11. War…stimulates innovation and invention; but destroys as well.
12. Centralized government…boosted in post-WWII Germany and
    Japan but crushed it in China after A.D. 1500 or in the USSR.
13. Climate…rigorous climate induces technological change to
    enhance survival…but benign climate creates freedom to invent.
14. Resource abundance…relative abundance might stimulate
    development of inventions (e.g. water mill technology in rainy
    Europe). But scarcity might induce search for new ways of doing
    things (Britain deforestationEcon. 4132 of coal)
                                  => use
                        Technological Waves
1. Over the past two centuries, real GDP per head in the rich
industrial economies has grown by an average of around 1.6% a year,
a rate at which real income per head doubles every 44 years.
2. However, historically such growth has been the exception, not the
rule.
3. Clearly it is difficult to be precise about the figures, but crude
estimates suggest that in the 13 centuries up to 1800, real output per
head in Western Europe crept up by an average of no more than
0.1%-0.2% a year.
   • At that pace living standards do not improve noticeably during
   an individual lifetime, and real incomes double only every 500
   years.
4. What has changed in modern times is the pace of technological
                              Econ. 4132
innovation.
Econ. 4132
• The Middle Ages did come up with a few inventions, such as
windmills and horseshoes, but technological progress was
imperceptible compared with what is happening now.
• Since Adam Smith, economists have recognized that technological
change is important for long-term growth, but only in the past two
decades have they been studying the subject in earnest.
5. Until Paul Romer’s path-breaking work in the late 1980s – early
1990s, Joseph Schumpeter was one of the few economist who had
tried to explain growth mainly in terms of technological innovation.
• In the 1930s he presented a model that postulated growth through the
interaction of bursts of technological development and intense
competition between firms.
• Schumpeter saw capitalism as moving in long waves: every 50 years
or so, technological revolutions would cause “gales of creative
                                       would be swept away and replaced
destruction” in which old industries 4132
                                 Econ.

by new ones.
• Each wave of technology would fuel an upsurge in investment and
provide a swathe of jobs in new industries.
• Evidence... first long wave from the 1780s to the 1840 brought the
steam power that drove the early industrial revolution (spinning jenny,
cotton gin, factory, etc.).
       [1] The second from the 1840s to the 1890s introduced the
       railways, steamer and the telegraph.
       [2] The third from the 1890s to the 1930s produced electric
       power, the automobile, the airplane and the telephone.
       [3] The forth, from 1945 to the early 1970s was fueled by
       cheap oil and the integration of the car/truck/airplane into
       economic activity (commercial applications) on a massive
       scale (in many ways and extension of the third) - television &
       inventions of two world wars (autobahn, atomic energy, jet
       engine, plastics, mainframe computer, etc.). => Supporting
                                 Econ. 4132

       infrastructure fully developed.
       [4] The fifth, beginning in the early 1970s, is being powered by
       information technology (the computer chip).
6. “The Dynamo and the Computer: An Historical Perspective on the
Modern Productivity Paradox.” Paul David, American Economic
Review, May 1990.
• Added an important insight: There is often a delay of several decades
before technological breakthroughs deliver economy wide
productivity gains.
• Firms take time to identify the most efficient way to use new
technology and to make organizational changes. It is the wide
diffusion of a technology rather than its invention that brings the
biggest benefits (tipping point & network effects).
• David’s study => the introduction of the electric dynamo in the early
1880s (which opened up the way for the commercial use of electricity)
                                   productivity gains.
took 40 years to yield significantEcon. 4132
• Growth in productivity in industrial economies actually slowed
down after 1890 and did not revive until the 1920s.
       - This partly reflected the slow adoption of electricity: In
       1899 electricity accounted for less than 5% of power used
       in American manufacturing; only in 1919 did its share
       reach 50%.
       - And even when firms had installed electricity, it still took
       them a long time to learn how to organize their factories
       around electric power and to take advantage of its
       flexibility.
       - Previously, machines had to be put next to water wheels
       or steam engines … electricity allowed them to be placed
       along aproduction line to maximize the efficiency of the
       work flow.

                                Econ. 4132
• Another important fact uncovered by recent studies is that each new
technological wave is taking less time than the last to funnel through
to productivity gains.



                                Econ. 4132
Econ. 4132
Productivity change in the nonfarm business sector, 1947-2008




 • Definitions: Non-farm business productivity…3 parts: labor,
 capital, TFP or MFP.
 • Difference between “Employment Cost Index” and “Unit Labor
 Cost”?
 • Average productivity gains slowed down in America from early
 1970s to early 1990s:1870 – 1979 … 2.3%; 1947 – 1973 … 2.8%;
 1973 – 1998 … 1.1%.            Econ. 4132
• Led many to fear that the big, rapid gains in the American
standard of living were ending.
• Between 1996 and 2006, productivity reaccelerated to about
2.4% per year: This is well above the average rate of the
previous 20 years (1.4%).
• Many believe that this is due to the diffusion of information
technology (i.e. the computer and its application in all its
myriad forms). Most major inventions/innovations emerging
from computer chip now well past their respective “tipping
points.”
• This is a big improvement over the 1.4% average growth in
the two decades to 1995 and is equivalent of real incomes
doubling every 35 years instead of every 50 years.
                              Econ. 4132
• But … will it last: 2002 = 4.8%, 2003 = 4.4%, 2004 = 4.1%;
2005 = 2.3% , 2006 = 1.6%, 2007 =1.8%. 2008 = 2.8%, 2009 =
5.1%.
                            Econ. 4132
Econ. 4132
                  Introduction to Economic Growth
                           By: Charles Jones
Ch. #1 Why are we so rich and they so poor?
• A prerequisite to better policies is a better understanding of
economic growth.
• Economic growth (development is highly correlated with other
measures of quality of life).
• Fact #1: There is enormous variation in per capita income across
economies.
       - How measured? … market exchange rates (disequilibrium
       rates) … purchasing power parity-adjusted exchange rates
       (equilibrium or real exchange rates).

                                  Econ. 4132
    - The actual value of a currency in terms of its ability to purchase
    similar products …. Big Mac Index.
•   Fact #2: Rates of growth vary substantially across countries.
       - Robert Lucas: A country growing at g percent per year will
       double its per capita income every 70/g years.
       - US: double every 50 years (30 if early 2000s rates continue).
       - China: double every 8 years (9% growth rate).
       - Over spans of time, a small difference in growth rates can
       lead to enormous differences in per capita incomes (table
       below).
•   Fact #3: In the US over the past century:
1. The real rate of return to capital, r, shows no trend upward or
   downward.
                                  Econ. 4132
The Big Mac Index
(7/2009)

The Big Mac index is
based on the theory of
“purchasing-power
parity”. Under PPP,
exchange rates should
adjust to equalize the
price of a common
basket of goods and
services across
countries. Our basket
is the Big Mac.

Video Clip


                         Econ. 4132
     The Variety of Growth Experiences
                             Real GDP per        Real GDP per
                             Person at           Person at End   Growth Rate
Country          Period      Beginning of Period of Period       (per year)
Japan            1890-1997        $1,196             $23,400        2.82%
Brazil           1900-1990          619               6,240          2.41
Mexico           1900-1997          922               8,120          2.27
Germany          1870-1997         1,738             21,300          1.99
Canada           1870-1997         1,890             21,860          1,95
China            1900-1997          570               3,570          1.91
Argentina        1900-1997         1,824              9,950          1.76
United States    1870-1997         3,188             28,740          1.75
Indonesia        1900-1997          708               3,450          1.65
United Kingdom   1870-1997         3,826             20,520          1.33
India            1900-1997          537               1,950          1.34
Pakistan         1900-1997          587               1,590          1.03
Bangladesh       1900-1997          495               1,050          0.78
1. The share of income devoted to capital rK/Y, and labor, wL/Y,
   show no trend.
•   wL/Y = .7
•   rK/Y = .3
Note: Returns to entrepreneurs and land (natural resources) ignored
   (two factor model). Although it’s important to note that as a
   percent of national income, profits recently hit an all time high
   (mid-2007 = 8.9%)
3. The average growth rate of output per person has been positive
   and relatively constant over time.
•   Per capita GDP = 1.8% per year.
Fact #4: Growth in output and growth in the volume of international
       trade are closely related.
                                Econ. 4132
•   Trade intensity ratio?
… the sum of exports and imports divided by GDP.
-   NICs … can exceed 150%! (Singapore was 480% in 2006)
                      #2 The Solow Model
Assumptions:
1. Nation produces and consumes only a single, homogeneous
   good (output). Firms are price takers.
2. Closed economy.
3. Technology is exogenous.
4. Individuals save a constant fraction of their income (s) and
   spend a constant fraction of their time accumulating skills (u).
5. Population growth rate is given by n and that the labor force
                              Econ. 4132
   participation rate is constant.
1. Y = F(K,L) = KL1-
2. Ķ = sY – dK
“d” = rate of capital depreciation (.05)
The capital accumulation equation in per worker terms:
3. ķ = sy – (n + d)k
Implies that the change in capital per worker each period is
   determined by three things:
•   Investment per worker , sy, increases k.
•   Depreciation per worker, dk, reduces k.
•   Population growth, nk, reduces k.
4. The Solow diagram: shows how output per worker evolves over
    time.
                                  Econ. 4132
                           ķ = sy – (n + d)k
•   Remember: (n + d)k maps the amount of investment per person
    required to keep the amount of capital per worker constant. “sy”
    maps the amount of investment per person in the current period.
•   Importance of difference between curves:
1. When positive: sy > (n + d)k => capital deepening occurs.
2. “k*” = steady state point => amount of capital per worker remains
   constant (Figure 2.2, p. 28). => capital widening occurs. The
   actual capital stock, K, continues to grow but is matched by an
   increase in population.
3. Fact: Growth slows down along the transition path. The farther an
   economy is below its “steady state” the faster it will grow. As a
   nation approaches its “steady state”, its rate of economic growth
   slows down.
                                Econ. 4132

-   Figure 2.3 => steady-state value of output per worker.
5. How do we get sustained growth?: Technology…
Y = F(K,AL) = K(AL)1-
•   A is “labor-augmenting” and grows at a constant rate:
•   A = A0egt
•   Å/A = g
6. Balanced growth path = outcome in which capital, output,
    consumption and population grow at constant rates.
•   The Solow model with technology reveals that technological
    progress is the source of sustained per capita growth.
    note: gy = gk = g
•   Output per worker and capital per worker both grow at the rate of
    exogenous technological change (g).
•   “k” and “y” are no longer constant in the long run (at the steady
                                Econ. 4132

    state).
• The new state variable becomes:
k (tilde) = K/AL … represents the ratio of capital per worker to
technology.
• Output per worker along the “balanced growth path” is
determined by technology, the investment rate, and the population
growth rate.
• Changes in the investment rate or the population growth rate
affect the level of long-run output per worker but do not affect the
long-run growth rate of output per worker.
• Policy changes increase growth rates but only temporarily along
the transition to the new steady state. => policy changes have no
long-run growth effect.
• Policy changes have “level effects”; that is, a permanent policy
change can permanently raise (or lower) the level of per capita
                             Econ. 4132
output.
6. Some conclusions …
• Sustained growth occurs only in the presence of technological
progress.
• Without technological progress capital accumulation runs into
diminishing returns.
• With technological progress present, improvements in technology
offset diminishing returns (coincidental…nothing objective here).
• Labor productivity grows as a result.
• Therefore, studying productivity (sources of growth in output) is a
means to validate the Solow model.
• Total factor productivity growth or multifactor productivity growth.
7. Growth accounting for the US … table on pg. 46:
Y = BKL1- where “B” is a Hicks-neutral productivity parameter
                               Econ. 4132

(Solow again: led to modern productivity accounting).
•   1.4% of growth rate of GDP per worker unexplained (residual)!
•   One interpretation: this TFP residual due to technological change
    and innovation (synergies and network effects).
•   Table reveals infamous slowdown in productivity growth from
    1960-1990 (cause: substantial decline in growth rate of TFP).
•   Note: this happened in all developed countries, not just the US.
•   Explanations of slowdown:
1. Rise in energy prices during 1970s.
2. Slowdown in R&D spending in late 1960s.
3. Shift in structure of economy away from manufacturing (high
   productivity) to services (lower productivity).
4. Growth of productivity in 50’s and early 60’s may have been
                                (application of new ideas).
   artificially high after WWII Econ. 4132
5. The information technology revolution: temporary slowdown as
economy switches over to new modes of production (David study).
• This would imply a subsequent boom in productivity after #5 runs
its course (witness the late 1990’s early 2000’s).
6. No definitive answer … probably a mixture of all ideas cited.
    #3 Empirical Applications of Neoclassical Growth Models
• Solow model works best if extended to include human capital.
Y = K(AH)1-
H = skilled labor = euL
 = positive constant = .1 … Based on empirical evidence that one
more year of schooling increases wages by 10%.
u = fraction of an individual’s time spent learning skills.
                                 Econ. 4132
L = total amount of raw labor used in economy.
Econ. 4132
Equation used to solve model:
    y = kAh1- … where
•   lower case denotes variable divided by L.
•   h = eu
Conclusions:
•   In the steady state, per capita output grows at the rate of
    technological progress … “g” (same as in Solow model).
•   Assuming  = 1/3,  = .1, g + d = .075, model “fit” not great in
    comparing across countries (graph page 59).
•   Yet, by incorporating actual technology levels of various
    countries into the calculations, the “fit” of the neoclassical model
    is strikingly improved (yet not perfect).
    - Uses the production function to compute the level of “A” for
                                Econ. 4132
    each country.
• Model suggests that countries are poor because they have low
investment rates, low levels of educational attainment, and low levels
of installed technologies (and possibly too high of population growth
rates).
• Estimates of “A” are not controlled for differences in the quality of
educational systems across countries, therefore the estimates should
be thought of as total factor productivity levels rather than technology
levels relative to base country (USA).
• Solow model doesn’t help us to understand why some countries
invest more than others, or why some countries attain higher levels of
technology or productivity or education (tied closely to government
policies and social institutions …Ch. #7)
Convergence hypothesis: under certain circumstances, less developed
nations should grow faster than more developed countries.
• Implication is that over time, the differences in per capita income
                                   Econ. 4132

around the world should narrow.
• Hypothesis supported by technology transfer and our growth theory
discussion (transition path toward steady state).
• Empirical studies indicate that it is true for some counties (a sample
of industrialized countries), yet it fails to explain differences in growth
rates across the world as a whole.
• The Neoclassical growth model suggests that this discrepancy occurs
because countries do not have the same steady state.
       - Those that do converge, the sample of industrialized
       countries, have the same steady state.
       - Because all countries do not have the same investment rates,
       population growth rates, or technology levels, they are not
       generally expected to grow toward the same steady-state target.
       - From this theoretical and empirical growth theory work
       comes an important principle:
                                  Econ. 4132
               The principle of transition dynamics:
• The further an economy is below its steady state, the faster the
economy should grow. The further an economy is above its steady
state, the slower the economy should grow.
• Principle can be used to explain differences in growth rates across
countries of the world.
                       Global income distribution:
   Fact: For the world as a whole, the enormous gaps in income
   across countries have generally not narrowed over time.
   - The neoclassical model allows us to consider how the income
   distribution is likely to evolve in the future.
   - Figure 3.10, pg. 74.

                                 Econ. 4132
                            Predictions:
1. At the top of the income distributions, a number of economies will
   have relative incomes exceeding that of the US (Singapore,
   France, Spain and Italy).
   - Why? … in the neoclassical model, relative incomes are
   determined by capital investment, population growth and human
   investment rates. The US rates are not the highest in the world.
   - In 1990’s this fact was mitigated by relatively higher US
   productivity, educational attainment and capital deepening.
   - Any technological lead the US currently has is likely to get
   smaller in the future.
2. Given that the lower-income countries are near their steady states,
    there will be no tendency for their relative income to increase in
    the future => low incomes appear to be permanent (the steady state
                                 Econ. 4132
    outcome).
                    #4 The Economics of Ideas
• Neoclassical model highlights its own shortcoming: technology is
critical … but is left unmodeled.
• Ideas => improve the technology or means of production, allowing a
given bundle of inputs to produce more or better output. Ultimately,
through the application of new ideas to production, these ideas
generate a higher level of utility.
• Ideas  Nonrivalry  Increasing Returns  Imperfect competition
       - Most goods are “rivalrous”  my use or consumption of a
       good precludes your use or consumption.
       - Ideas are nonrivalrous  once created, anyone can use it.
       - Important characteristic of ideas: excludability…
       - It affects the degree to which the owner of the good can
       charge a fee for its use. Econ. 4132
       - Ideas are nonrivalrous goods that vary substantially in their
       degree of excludability (figure 4.1, p. 81).
       - Nonrivalrous goods need to be produced only once.
       - This means that for such goods all costs are “up front” 
Additional units can be produced for a miniscule marginal cost. The
only reason we observe a positive marginal cost is since the idea is
embodied in a rivalrous good (e.g. a CD, DVD, a book).
       - Major fact: The economics of ideas is tied to the presence of
       increasing returns to scale and imperfect competition.
• Increasing returns: all costs are fixed, therefore each additional unit
produced pulls average cost down.
• Imperfect competition: with increasing returns to scale, average cost
is always greater than marginal cost  marginal cost pricing always
results in negative profits  this is 4132 a case of perfect competition.
                                 Econ.
                                       not
• We have already noted that economic growth is, in the context of
the history of humankind, a very recent development.
• Why then did it begin when it did (1720 - 1760)?
• Douglass North: the development of intellectual property rights, a
cumulative process that occurred over centuries, is responsible for
modern economic growth (patents, copyrights and an effective legal
system to enforce those rights).  large potential monetary returns
encourages individuals to innovate and invent.
       - Therefore, the Industrial Revolution began when it did
because the social institutions protecting intellectual property rights
and market incentives were sufficiently well developed.
• How do we measure the presence of “ideas”: Proxy variables for
ideas: (1) patent counts (2) R&D spending [level and share relative to
GDP] (3) number of scientists and engineers.
                                Econ. 4132
• Interesting fact: the increase in award of patents to foreigners 
The US system has increasingly attracted innovations and
inventions from around the world. This has enhanced our economic
growth in the post WWII era.
Theory implies that the size or scale of the economy important in
the economics of ideas.
The “New” Economic Growth Theory is based upon this
understanding of the nature and importance of ideas.
               #5 The Engine of Economic Growth
• Endogenous growth theory or new growth theory: an attempt to
develop an explicit theory of technological progress.
• Paul Romer (1990)… basic premise: Technological progress is
driven by research and development.
• Aggregate production function and accumulation equations for
capital and labor are identical to those in the Solow model.
                               Econ. 4132

• A = “stock of ideas” and Å = LA where…
A(t) = the stock of knowledge or the number of ideas that have been
    invented over the course of history up until time “t”.
Å = the number of new ideas produced at any given point in time.
 = rate at which they discover new ideas (productivity of research).
LA = the number of people attempting to discover new ideas.
•   Next equation … LA + LY = L
LY = portion of labor involved in producing output.
•   What affects the rate at which new ideas are discovered ()?
1. Could be constant.
2. Could depend on the stock of ideas that have already been
   invented.
    a. The invention of ideas in the past may raise the productivity of
                                  Econ. 4132
    researchers today (standing on the shoulders) 
“” is an increasing function of A.

3. On the other hand, perhaps the most obvious (or valuable) ideas
are discovered first and subsequent ideas are increasingly difficult to
discover (fishing out effect).
“” is a decreasing function of A.

• Model of the rate at which new ideas are produced:
   (bar) = A … where “” denotes returns to scale in research or
   a knowledge spillover parameter.

If  > 0  increasing returns (standing on the shoulders) dominates.
If  < 0  decreasing returns (fishing out) dominates.
If  = 0  constant returns to research or stock of knowledge has no
effect on the discovery of new ideas.
• It is also possible that the average productivity of research ()
depends upon the number of people searching for new ideas at any
                                    Econ. 4132
point in time:
Å = LA A where…
“” is a parameter representing the rate of growth of researchers and
the productivity of those researchers.
If  < 1  an externality associated with duplication … some ideas
that are produced are not really new (simultaneous research efforts or
“stepping on toes effect”).
If  > 0  standing on the shoulders effect present.
• Growth in the Romer model:
gA = n/(1 - )
Given that gA = gk = gy along a balanced growth path.
States that the long-run rate of growth of the economy is determined
by the parameters of the production function for ideas () and the rate
of growth of researchers which is ultimately given by the population
                                  Econ. 4132
growth rate (n).
Some important insights:
•   Effect of population growth is two-fold:
    a. More people reduces the amount of capital per person reducing
    the level of income along a balanced growth path.
    b. More people mean more researchers who are the key input into
    the creative process. Therefore, a larger population generates more
    ideas, and because ideas are nonrivalrous, everyone in the
    economy benefits. This then increases the level of income along a
    balanced growth path.
    - Important insight: If the population or the number of researchers
    stops growing, long-run growth ceases.
2. Even after we endogenize technology, the long-run growth rate of
   income cannot be manipulated by policy makers using such
   conventional policies such as subsidies to R&D.
                                 Econ. 4132

    - such policies will have “level” effects…
•   Government policy resulting in a permanent increase in the share
    of the population devoted to research raises the rate of
    technological progress temporarily, but not in the long-run (typical
    level effect). Also note that the level of technology is permanently
    higher. Transition dynamics similar to those generated by an
    increase in the investment rate in the Solow model.
3. Model also predicts that a larger world economy will be a richer
   world economy (positive feature of globalization). Fact arises
   from the nonrivalrous nature of ideas: a larger economy provides
   a larger market for an idea, raising the return to research (a
   demand side effect). In addition, a more populous world economy
   simply has more potential creators of ideas (a supply side effect).
4. Note that solving the Romer model requires the presence of
   increasing returns and imperfect competition (basic essence of
   ideas in the economy). Note: reason for intermediate sector in
                                 good,
   discussion in the book (final Econ. 4132 intermediate & research).
Microfoundations of the Romer model: Imperfect competition in a
   general equilibrium environment…
•   3 sector model: final-goods sector an intermediate goods
    sector…firms that produce output…and the research sector that
    produces ideas (take the form of new types or forms of capital
    goods)
A. The Final-Goods Sector: characterized by perfect competition
   producing good “Y”.
                             Y = LY1-α∑xα
…as “j” goes from 1 to “A”, where “A” measures the number of
  capital goods that are available to the final-goods sector.
•   Note: in this model invention coming from the research sector
    result in the creation of new or improved capital for use in the
    final-goods sector to produce more output (Y).
                                 Econ. 4132
• This sector displays constant returns to scale (double input =>
double output)
• Firms have to decide how much labor and capital to use in
producing output by the standard maximization process deployed in
economics.
• Standard outcome on first order conditions:
w = (1-α) Y/LY (firms hire labor until the MPPL = w) and…
pj = αLY1-αxjα-1 (firms rent capital good until the MPPj equals the
rental price pj)
B. The Intermediate-Goods Sector…monopolies who produce the
capital to sell to the final-goods producers.
• Monopoly status gained by purchasing the rights to a new idea
from the research sector (treated as a fixed cost).
                                Econ. 4132
• The intermediate sector is characterized by a simple production
function…one unit of raw capital translates into one new unit of
capital.
• So the intermediate sector firm seeks to maximize the following:
                       Max π = pj(xj)xj – rxj


…where pj(xj) = the demand function for the capital good found
in the equation on the previous slide and r = MCj or interest rate.
• The first order conditions leads the following definition for the
price:
                    p = 1/{1/[1 + {p’(x)x}/p]}r
…with the elasticity of demand, p’(x)x}/p = α – 1
• These firms charge a price that is a markup over marginal cost
“r”…or p = [1/ α]r (solution for each monopolist in sector)
                               Econ. 4132
…this gives us the result that all capital goods sell for the same
price and each monopolist earns the same profit:
                          Π = α(1 – α)Y/A
C. The Research Sector
• Ideas => designs for new capital goods. Once an idea is
“discovered” a patent is awarded.
• New designs are discovered according to the previously
discussed equation: Å = LA A
• The inventor then sells the idea to an intermediate-goods firm.
• Bidders for a patent will pay the present discounted value of the
profits to be earned by the firm (PA).
• PA can change over time but any deviation from the opportunity
cost of capital (r) will be “arbitraged” away.
                                  Econ. 4132
…another way of saying this is:
                          rPA = π + PA(dot)
…the left hand side is the interest earned from investing PA in the
bank while the right hand side is the profits plus capital gains/loss
from a change in the price of the patent.
• Along a balanced growth path r and π/PA must be constant so the
above equation implies that:
                            PA = π/[r – n]
…This is the price of a patent along a balanced growth path.
D. Given the market structure just described we can then solve the
Romer model…but some notes before we go on:
• The model displays constant returns to K and L…but increasing
returns to A (ideas).
                                Econ. 4132
• Given that all the firms in this sector are monopolists, prices of the
capital goods they produce are set above MCs.
• Monopoly rents, though, end up being extracted by the inventors
in the research sector…so there really are no economic profits in the
model: all rents go to pay for some factor input.
We solved for the growth rate in the steady state prior to this section
on the microfoundations of the model, so we don’t need to do again.
• This means that the only things which still must be solved for is
the allocation of labor between the final goods and research sectors.
First, the wage rate in the final-goods sector equals its marginal
product:
                         WY = (1 – α)[Y/LY]
… while labor in the research sector is compensated based on the
value of the designs they create: 4132
                                Econ.
                           WR = δ[bar]PA
Due to free entry into both sectors both these wages will equalize:
   WY = WR
•   While he doesn’t show how to derive this in the chapter (it can
    be found in the appendix) the share of the population working in
    the research sector is:
                        sR = 1/[1 +{r-n}/αgA]
Two interesting implications of this expression are:
1. The faster the economy grows, the higher gA will be, and the
   higher the fraction of the share of the work force working in the
   research sector (sR).
2. The higher the discount rate (r) applied to current profits to
   calculate the net present discounted value, the lower this share
                                a higher
   will be (sR lowered through Econ. 4132 {r-n})
With some additional algebra (not shown in chapter) it can be
shown that the interest rate in the Romer model is given by:
                              r = α2Y/K
• Comparing this to the former expression given for the marginal
product of capital, one will note that this is smaller value.
• This is signification, for in the Solow model…with perfect
competition and constant returns to scale…all factors were paid
their marginal products.
• This is not true in the Romer model…due to the presence of
increasing returns to scale => all factors can not be paid their
marginal products.
• So what happens to the difference?...it gets paid to inventors in
the research sector to compensate them for their work on their
ideas.
                                Econ. 4132
5. Is the share of the population that works in research optimal?
-   Romer model answer is “no”.
-   There are three distortions to research in the model that cause sR
    (share of the population engaged in R&D) to differ from its
    optimal level.
    [1] Markets value research based on the derived stream of profits
    by any new idea. What the market does not value is the fact that
    new inventions may affect the productivity of future research ( >
    0). This results in an under-investment in R&D.
    [2] “Stepping on toes” effect … a classic externality. Too many
    researchers working on the same idea at different firms creates
    wasteful duplication. Implies and over-investment in R&D.
    [3] “Consumer surplus” effect. An inventor of a new design
    captures a monopoly profit yet only a portion of total consumer
    surplus => too little R&D. Econ. 4132
- In practice, Romer concludes, these distortions can be very large.
- Empirical studies strongly suggest that  > 0 and that the positive
externalities of research outweigh the negative externalities. The
market, therefore, even in the presence of the modern patent system,
tends to provide too little research.
- One final insight … Neoclassical economics strongly condemns
monopoly. The economy of ideas suggest that if firms are not allowed
to price above MC, economic growth will stagnate. Therefore,
imperfect competition and monopoly pricing power is increasingly
critical for future economic growth (a final irony).
         #6 A Simple Model of Growth and Development
• How do technologies diffuse across countries?
• Model of this chapter adds onto Romer’s model with the inclusion
of an avenue for technology transfer.
                                 Econ. 4132
- Chapter starts assuming we are dealing with an undeveloped country.
- Model then assumes the following link between physical and human
   capital in that country: A worker with a high skill level can use
   more capital than a worker with a low skill level. Skill, therefore,
   is now viewed as the range of intermediate goods that an
   individual can learn to use.
1. Accumulation of skill (h)…
   ĥ = euAh1- 
Where…
   u = the amount of time an individual spends accumulating skill
   instead of working.
   A = the world technology frontier (given exogenously)
    > 0 (a scaling parameter: ignored until last paragraph of chapter)
                                 Econ. 4132

   0<1
• Interpretation…
       - first term we saw before … suggests an exponential structure
       of skill accumulation.
       - “” term represents is a scaling factor: reflects efficacy of
       educational system & effects from culture.
       - the last two terms suggest that the change in skill is a
       geometrically weighted average of the frontier skill level, A,
       and the individual’s skill level “h”. Skills are viewed here as
       progressive intermediate inputs.
• Other assumptions…
   - the technological frontier is assumed to evolve because of
   investment in R&D by the advanced economies of the world.
   - there is a world pool of ideas that are freely available to any
   country…but to take advantage of these ideas a country must first
                                 Econ. 4132

   learn to use them.
• Conclusions…
1. The growth rate of the economy is given by the growth rate of
human capital while this growth rate in turn is determined by the
growth rate of the world technological frontier.
2. For any country, the more time individuals spend accumulating
skills, the closer the economy is to the technological frontier.
3. Output per worker along the balanced growth path given by:
               y*(t) = (sk/[n+g+d])/1-([/g][eu]1/)A*(t)
Terms…
sk/[n+g+d])/1- says that countries that invest more in physical capital
will be richer, and countries that have rapidly growing populations
will be poorer.
[/g][eu]1/ states that countries that spend more time accumulating
                                   Econ. 4132
skills will be closer to the technological frontier and will be richer.
A*(t) is the technological frontier and generates the growth in output
per worker over time (along the balance growth path):
                          gy = gk = gh = gA =g
4. Model encapsulates the “new growth theory” … economies grow
because they learn to use new ideas invented throughout the world.
       - Implicit assumption: technologies are available worldwide for
       anyone to use.
5. Even armed with this advanced model of economic growth,
empirical studies show that TFP levels vary considerably across
countries (not explained by the “new growth theory” model)…this
issue addressed in next chapter.
6. Technology transfer…more complicated than assumed in “new
growth theory” model…for at least this reason:
       - international patent protection (intellectual property rights)
                                 Econ. 4132
       and increasing global enforcement.
     #7 Infrastructure and Long-run Economic Performance
•   Why is it that some countries invest more than others, and why
    do individuals in some countries spend more time learning to use
    new technologies?
•    So far we have assumed that investment rates (sk) and the time
    individuals spend accumulating skill (u) are given exogenously.
1. Decision as to whether to start up a business in a foreign country
   or not…based on benefit-cost analysis.
    - Involves a one-time setup cost F.
    - Let  = the expected present value of the profit stream from this
    subsidiary.
    - Decision criterion straightforward:
      F  invest …  < F  do not invest.
                                 Econ. 4132
• This basic framework can be used to evaluate other decisions such as
the decision of whether or not an individual should invest the time and
money to accumulate skills.
• In any decision one must attempt to understand what determines the
magnitudes of F and .
• Chapter explores the hypothesis that there is a great deal of variation
in the costs of setting up a business and the ability of investors to reap
returns from their investments between countries.
• In many countries there is a powerful bureaucrat that stands in the
middle of decisions. They are the ones who approve domestic
economic activities, grant licenses, write permits and inspect facilities.
Without a strong set of laws disallowing such activity, they may seek a
bribe (a “fee”).
   - There may be many of these bribes that must be paid in order to
   set up a business collectivelyEcon. 4132 a sunk cost  corruption.
                                  forming
Each year, Transparency International
draws on surveys of businessmen and
country experts to gauge perceptions of
corruption in 179 countries around the
world. It defines corruption as the abuse
of public office for private gain. This
year, Chad shared the bottom slot with
Bangladesh. Corruption has declined
significantly over the past year in a
number of countries, including France,
Hong Kong, Taiwan and Nigeria.


       Transparency International


                                Econ. 4132
Determinants of : the expected profitability of an investment…
1. The size of the market…need not be limited by national borders.
2. The extent to which the economy favors production instead of
   diversion (takes the form of the theft or expropriation of
   resources from productive units and individuals).
   - Acts like a tax and encourages investment by the entrepreneur in
   finding ways to avoid the diversion.
   - Balance between production or diversion in a country’s social
   infrastructure primarily determined by the culture, government
   and the institutions of society.
3. The stability of the economic environment.
   - A country where the rules and institutions are changing
   frequently may be a risky place in which to invest.
                               Econ. 4132
•   Conclusions: Countries in which there are small markets, have
    social infrastructure encouraging diversion and having an
    unstable economic environment will have less domestic
    investment in capital (sk), less foreign direct investment and less
    investment by individuals in accumulating productive skills (h).
•   The reason why people from such a nation will not invest in
    accumulating skills:
    - Skilled individuals are not allowed to earn the full return on
    their skills: Much of their potential return from their skills is
    wasted by diversion. The higher their skill set, the greater the
    potential gain from bribing them and the greater the time such
    individuals will spend trying to avoid being a target of
    corruption.
    - Also, if the environment is too prone to diversion, skilled
    individuals will emigrate, depriving the country of their potential
                                  Econ. 4132
    contribution to economic growth.
•   Also, the social infrastructure of an economy may influence the
    type of investments that are undertaken.
    - e.g. In a risky environment a company may invest heavily in
    security personnel, fences, alarms and other security apparatus
    (closed circuit cameras, metal detectors, other surveillance and
    identification devices). All reduce productivity.
•   In contrast, the empirical evidence suggests that a country will
    attract financial capital, secure technology transfer from abroad
    and see its people invest in accumulating skills when…
1. Its institutions and laws favor production over diversion.
2. The nation is open to international trade and global competition.
3. Its political, social and economic institutions are stable (democracy).
•   Translates into such countries having higher total factor
    productivity and therefore economic growth and standard of living
                                  Econ. 4132

    (higher sk, u, sR,  and A) .
With this reasoning we can rewrite the aggregate production function
   of an economy as…
                            Y = IK(hL)1-
Where I = the influence of a nation’s social infrastructure on the
  productivity of its inputs.
•   Implications:
1. Two countries with the same K, h and L may still produce different
   amounts of output because the economic environments in which
   these inputs are used to produce output differ (shows up in
   differing “A”s or “TFP”s that will be reflected in differing “I”s).
2. Fundamental changes in social infrastructure can then generate
   growth miracles and growth disasters (e.g. Asian Tigers, Nigeria or
   Zimbabwe)
    - Why do such changes in infrastructure occur?
                                Econ. 4132
• Answer lies in culture, political economy and economic history
…unique in every case.
• Quote from Douglass North: “From the redistribute societies of
ancient Egyptian dynasties through the slavery systems of the Greek
and Roman world to the medieval manor, there was a persistent
tension between the ownership structure which maximized the rents to
the ruler (and his group) and an efficient system that reduced
transaction costs and encouraged economic growth. This fundamental
dichotomy is the root cause of the failure of societies to experience
sustained economic growth.”
• An examination of the very long-run distribution of world income
suggests there has been some “convergence” toward the U.S. at the top
of the income distribution.
       - There are more countries moving up than moving down in the
       distribution. Why?
                                Econ. 4132
•   One theory: Societies are gradually discovering the kind of
    institutions and policies that are conducive to successful economic
    performance.
•   Institutions and policies are nothing other than “ideas”. From our
    earlier discussion this means that there are better ideas out there
    waiting to be found.
•   Over the broad course of history, better institutions have been
    discovered, gradually implemented and diffused around the world.
•   Modern telecommunications, global education and the Internet all
    serve to spread new and better ideas more quickly than in the past.
•   Another contributing factor is likely globalization: discipline of
    the market and the need to adjust domestic rule of law and
    government policies and public institutions to facilitate national
    business success in the global marketplace.
                                 Econ. 4132
          #8 Alternative Theories of Endogenous Growth
• All the models we’ve presented imply that changes in government
policies only have level effects but no long-run growth effects. This
result has bothered those who feel that policy can make a long-run
difference in economic growth.
• This chapter gives a brief survey of some of the alternative growth
models that have been developed in the past decade. These models
permit policies to impact the long-run growth rate.
The “AK” Model of endogenous growth…
• Using the original Solow model we can modify the production
function such that α = 1:
                                Y = AK
…where A equals some positive constant.
• Recall that capital accumulation is4132
                                 Econ. given by the following equation:
                              Ķ = sY – dK
• Assume that there is no population growth => we can interpret the
upper-case letters as per capita variables.
Now go back to the Solow diagram:
• Assumption: in figure 8.1… total investment is larger than total
depreciation.
• dK line reflects the amount of investment that has to occur just to
replace the deprecation of the capital stock.
• The sY curve is total investment as a function of the capital stock.
• Note: because Y is linear in K, this curve is actually a straight line, a
critical property of the AK model.
• Implication: the capital stock is always growing => growth in the
model never stops (because there are no diminishing returns to the
relative accumulation of capital).Econ. 4132
• So here there are constant returns to the accumulation of capital (the
marginal product of capital always equals “A”).
• After some mathematical manipulation it can be shown that the
growth rate of output is equal to the growth rate of capital:
                        gY = Y[dot]/Y = sA – d
 Key result: the growth rate of the economy is an increasing
function of the investment rate.
 Government policies that increase the investment rate
permanently increase the growth rate of the economy.
 Result can be interpreted in the context of the Solow model with α
< 1. Recall that when this is true, the sY line is a curve and the steady
state occurs when sY = dK. “α” measures the curvature of the sY
curve: if α is low, then the curvature is rapid; if high, then the
curvature is flatter => K* is farther out so the transition to the steady
                                  Econ. 4132
state is longer.
• α = 1 is the limiting case in which transition dynamics never end.
• Therefore, in the AK model growth is generated endogenously =>
never have to assume an exogenous growth rate.
• Given the linear differential equation in the model, a permanent
change in g permanently increases the growth rate of the economy.
                             A [dot] = gA
• Other endogenous growth models exploit this intuition…
Robert Lucas’ model on human capital:
Production function… Y = Kα(hL)1-α
Human capital assumed to evolve according to: h[dot] = (1-u)h
… where u = time working and (1 – u) = time accumulating skills
• We can see that an increase in the time accumulating skills will
                                 Econ. 4132
increase the growth rate of human capital.
• Therefore, a policy that leads to a permanent increase in the time
individuals spend obtaining skills generates permanent increases in the
growth of output per worker: g = (1 – u).
Externalities and AK models…
• We saw that the presence of ideas or technology in the production
function means that production is characterized by increasing returns
to scale => imperfect competition.
• There is a way to deal with the increasing returns so that we can
maintain perfect competition in the model.
• We saw earlier that the nature of the process means that individuals
can not be adequately compensated for accumulating knowledge.
• If the accumulation of knowledge is itself an accidental by-product
of other activity in the economy it may occur despite inadequate
compensation (it may be an externality).
                                 Econ. 4132
                 Production function… Y = BKαL1-α
Suppose that the accumulation of capital generates new knowledge
about production in the economy as a whole:
                             B = AK1-α
An accidental by-product of the accumulation of capital by firms in
the economy is the improvement of the technology that firms use to
produce (B).
 In this way one can maintain perfect competition and assume that
the accumulation of knowledge is an externality of some other
activity in the economy (e.g. capital formation)
 Combining the two equations above gives us:
                            Y = AKL1- α
…. Assuming the population normalized to 1 this yields the same
“AK” equation we saw at the beginning of this lecture.
                              Econ. 4132
Conclusion: two ways to deal with increasing returns to scale if we
   want to endogenize the accumulation of knowledge into our
   model:
1. Imperfect competition (done earlier… and Jones thinks is the
   appropriate assumption)
2. Treat it as an externality of endogenous variables... This way one
   can keep the assumption of perfect competition.
Another conclusion is that it is relatively easy to formulate models in
   which policy decisions can have a permanent impact on the rate
   of economic growth.
… is this true?
•   On the “yes” side: we have learned that private property and
    patent protection in conjunction with enforcement of intellectual
    property rights… actions of government… are crucial to
    activating economic growth.Econ. 4132
• While this argues for a role of government in the economic growth
process, it leaves open the question of ongoing policy actions and
their consequences… e.g. if the government makes a permanent
increase in subsidies in R&D, how long will the growth enhancing
effects last? That is the important question.
• The answer to this question is crucial in evaluating the potential
impact of policy.
• First, empirical research suggests that there is no evidence to
support the hypothesis that the differential equation presented
earlier is linear. For example, the first model forces us to assume
that α = 1 while studies have shown that the share of output
attributable to capital is 1/3.
• Also, if the differential equation governing the evolution of
technology is linear then it follows that as an economy grows
bigger, per capita growth rates should increase.
                                Econ. 4132
•   You can get this outcome by assuming that λ = 1 and φ =
    1…which leads to the rate of change of ideas being defined by:
                      Å/A = δLA
... Again there is a lot of empirical evidence that the numbers of
     scientist and engineers engaged in R&D have grown enormously
     over the years yet Å/A has grown at a relatively constant 1.8%
     for 40 years!
… Therefore, the evidence greatly favors a model which is
  curvilinear (φ < 1).
•   Other facts…
1. Over the past 100 years the investment in education has grown
   enormously.
2. Also during this time the fraction of the labor force representing
   scientists and engineers has increased (by a factor of 3!).
                                Econ. 4132
3. Finally, investment rates in advanced capital (e.g. computers) has
increased as well.
… in other words, there have been large increases in many of the
variables which endogenous growth theory indicates are important.
… and despite these developments, average growth rates in the US
(the country most studied) are no higher today than they were from
1870 to 1929!
4. These alternative endogenous growth models help us to
understand the overall growth by giving us new thinking on the
process. This leads us to the general observation that…
“… economic growth <is> the endogenous outcome of an economy
in which profit-seeking individuals who are allowed to earn rents on
the fruits of their labors search for newer and better ideas.”
… clearly then economic growth is endogenous.
                               Econ. 4132
     #9 Natural Resources and Economic Growth

Chapter explores the consequences for economic growth once we
incorporate earth’s finite supply of nonrenewable resources.

Solow model revisited:

                         Y = BKαTβL1-α-β

Where T = fixed amount of land.

As in the Solow model, this economy exhibits exogenous
technological progress (B) & population growth the capital
accumulates in the standard fashion.


                              Econ. 4132
•   After some mathematical manipulation it can be shown that along
    a balanced growth path, the growth rate of total output is defined
    by:
                         gY = g + (1- β[bar])n
Where (to simplify notation):
g ≡ gB/(1 – α) … gB = growth rate of exogenous technology
β[bar] ≡ β/(1 – α)
•   Growth rate of output per worker is then:
                           gy = g - β[bar]n
Notes:
1. If β = 0  land plays no role in model and results collapse to
   Solow results.
                                Econ. 4132
2. The long run growth rate of the economy with land depends on
   more than just the rate of technological change.
3. Equation suggests there is a classic race between technological
   progress and the diminishing returns introduced by land as a
   fixed factor.
4. Increases in the level of technology, B, make labor, land, and
   capital all more productive. If these increases are sufficiently
   large, they can offset the population pressure on the fixed
   resource and lead to sustained growth in per capita income.
5. Finally, the more important land is in production (the higher the
   value for β), the lower the long-run growth rate will be.
The above assumes that land is in fixed supply, but it could be used
   every period without suffering depletion!  the model is
   relevant for the discussion of renewable resources.
                                 Econ. 4132
To include nonrenewable resources in our growth model we need to
consider:
                           Y = BKαEγL1-α- γ
Where …
E = the energy input into production
• The resource stock is defined by a differential equation similar to
the capital accumulation equation, only it dissipates rather than
accumulates:
R[dot] = -E  in the long run, a constant fraction of the remaining
stock of energy is used in production each period.
• The amount of energy used in production each period is given by:
                             E = sER0e-sEt
Where …                          Econ. 4132
sE = E/R … the constant fraction of the remaining energy stock that
is used in production each period.
R0 = the initial stock of nonrenewable energy resources.
• With some mathematical manipulation of this model, along with
the observation that along the balanced growth path the capital-
output ratio is constant, the growth rate of total output becomes:
                     gY = g - γ[bar]sE + (1 - γ[bar])n
Where …
g ≡ gB/(1 – α)
γ[bar] ≡ γ/(1 – α)
Now, the growth rate of output per worker along the balanced
growth path becomes:
                          gy = g - γ[bar](sE +n)
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Notes…
1. An increase in the depletion rate sE reduces the long run growth
   rate of the economy.  We can raise the economy’s long run
   growth rate by reducing the depletion rate permanently and
   accepting a lower income today.
2. Important question: How much of the growth drag is present due
   to our use of nonrenewable resources?
Empirical investigation …
The growth rate of output per worker along a balanced growth path
   in a composite model with both land and energy is given by:
                gy = g - (β[bar] + γ[bar])n - γ[bar]sE
Where …
Everything after g creates “growth drag” due to the presence of
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   natural resources.
Given empirical research, it is shown that:
                (β[bar] + γ[bar])n - γ[bar]SE = .0031
… which means the annual per capita growth in the US economy is
  lower by about 0.3% due to the presence of renewable and
  nonrenewable resources.
1. Compare this to the observed US growth rate of 1.8% per year
    0.3% represents a 15% reduction in the growth rate.
2. Remember the compound effect of the growth rate  for the
   period stretching from 1776 to today, per capita incomes would
   be twice as high had we grown 0.3% faster.
3. An alternative way to interpret this number it to convert it to a
   constant proportion of income every year. Assuming a discount
   rate of 6%, the reduction in growth resulting from the presence
   of nonrenewable resources is equivalent to a permanent
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   reduction in annual income of 7.1%.
• In all the above, we have been using a Cobb-Douglas production
function  factor income shares are equal to the exponents on the
factors in the production function.  factor income shares are
constant over time.
• While the share of income going to capital and labor over time does
indeed seem to be constant, empirical evidence suggests that the
shares of income paid to renewable and nonrenewable resources are
in fact falling over time.
• To the extent that this is true, the growth drag calculations given
above are inaccurate.
                      The power of market prices:
The price of resources relative to the price of labor is given by:
                          PE/w = (vE/vL)/(E/L)
Where…                            Econ. 4132
vE = factor share paid to nonrenewable resources (γ)
vL = factor share paid to labor = 1 – α – γ
PE = price index of nonrenewable resources
w = wage rate
• From this expression we can conclude that as natural resources are
depleted over time and as population grows, E/L will fall  the
population pressure on natural resources tends to raise the relative
price of resources (look at equation).
• Further, if the factor shares are constant this would mean that we
should see a rising share of income going to natural resources … we
don’t.
• Empirical data on the price of fossil fuels relative to the average US
wage shows a consistent decline between 1949 to the early 1970s; an
abrupt spike from 1974-1979 and a continuation of the pre-1974
decline since then (at least until 2004) 
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• Suggests that, in an economic sense, fossil fuels are increasingly less
scarce than labor, rather than more scarce!
• Further examination of the factor share of energy in the US
economy from 1949-99 (figure 9.3) shows that the fossil fuel share of
GDP has fallen from just over 3% in 1949 to about 1.7% in 2004
(probably nearer to 2% today).  the factor share of energy vE is not
constant but rather declining.
• This has been occurring while the use of energy per person in
America has been increasing (figure 9.4)! US consumes 25% of all oil
consumed globally each year.
The Cobb-Douglas production function is the inappropriate one to
use.
Adjustment of model to the use of CES production function (constant
elasticity of substitution) …
                     Y = F(K,E) = (Kρ + (BE) ρ)1/ ρ
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Where … ρ = the curvature parameter of the production function.
• The elasticity of substitution between capital and energy is:
σ ≡ 1/(1- ρ)
Where …
ρ<1
• The energy share of output in the context of a CES production
function becomes:
                       vE ≡ PEE/Y ≡ (BE/Y)ρ
• Theoretically, we would expect the ratio E/Y to be declining 
nonrenewable resources are being depleted and GDP is growing
(empirically correct).

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How the energy share (vE) can decline:
1. If ρ is greater than zero and if B is constant (or not growing too
   rapidly), then the energy share will decline over time.
   •   If ρ is greater than zero, then the elasticity of substitution
       between capital and energy is greater than one  as the price
       of energy rises, it is relatively easy to substitute capital for
       energy in production.
2. If ρ is negative, then the elasticity of substitution between capital
   and energy is less than one  it is not easy to substitute capital for
   energy… as E/Y declines, the energy share of income would rises.
   This is what we would expect if nothing else changes. But energy-
   specific technological change (B) can reverse this outcome
   •   Even though energy is a necessary input into production, the
       rise in the price of nonrenewable resources has induced
       energy-specific technological change of about 1.4% per year
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       (amount needed to explain decline in energy share of GDP).
Important points to consider:
• Resource-augmenting technological progress in energy-saving
   may run into diminishing returns  the energy share could rise
   at some point in the future (e.g. info-tech wave peaking).

•   Martin Weitzman has shown that the welfare loss associated with
    natural resource depletion is equal to the factor share of those
    nonrenewable resources in production.  between 1% and 2%
    for the world as a whole (a relatively small number).

•   He further concludes that resource market prices reflect the
    belief that there are sufficient possibilities for both substitution
    and innovation in regards to nonrenewable resources.  finite
    nonrenewable resources have not been a large impediment to
    growth (technofix solution).

•   Remember that all of this was based on pre-2000 data. Could the
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    world be changing?
              #10 Understanding Economic Growth

               Why are we so rich and they so poor?

1. Output, and income per worker determined by…
    - Rate of investment in private inputs such as physical capital
        and skills (human capital).
    - High rates of productivity of factor inputs (plus TFP).
        Note: productivity and efficiency go hand-in-hand.
    - Growth rate of the labor force.
    - The generation of new ideas that add to the stock of
        technology.
2. An economy’s laws, government policies, and institutions
   combine to define a nation’s “social infrastructure” in which
   individuals and firms produce and transact. Plays a very
                                    nation’s relative per capita GDP
   important role in determining a4132
                              Econ.

   and prospects for growth.
              What is the engine of economic growth?
1. Solow model states that growth will cease unless the technology
   of production improves exponentially.
   - Therefore, the engine of economic growth is invention and
   innovation (which we measure in the aggregate as productivity).
   - Romer model examines this “engine” and places “ideas” and the
   products they spawn in a unique light.
   - The nonrivalrous nature of ideas and the increasingly important
   role they are playing in the economy suggest that the dominance
   of increasing returns to scale and imperfect competition are
   crucial to the economic growth process
   - P > MC in the long run provides the “fuel” for the engine of
   growth (huge profits that are partially reinvested in R&D).
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                  How do we understand growth miracles?
• Growth miracles are reflected in the movement of an economy within the
world income distribution.
• Something happens to shift a nation’s steady-state relative income from
values that were very low relative to the US to values that are relatively high
(typically led by a change in social infrastructure).
• Once the steady-state shifts up, the principles of transition dynamics kick
in resulting in the observed “growth miracle”.
• Eventually, growth rates in these countries must slow to the rate given by
the rate the world technology frontier expands.
Chapter ends by stating that in the world’s poorest regions the potential for
robust economic growth lies dormant.
… Ignores the carrying capacity of earth (unknown but finite), the role of
non-renewable resources in the future and the cultural complexities within
non-globalizing nations.
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                                   The End
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