## Solow

Try to build a simple Excel simulation of our growth model, streamlined. We can embed it in a full production function, but just use the following for simplicity:

1. Y0 = AK0α – output is a function of capital
2. I0 = S0 = sY0 – investment is equal to savings
3. K1 = K0 (1-δ) + I0 – capital grows with investment less depreciation

You can then calculate Y1, and create a bunch of rows. How fast does it converge? It’s clearer if you set (say) A = 10, with (say) K0=1 and depreciation not too much higher than savings so that the capital stock grows rather than shrinks, say s=8% and δ=12%. What you choose for α alpha doesn’t really matter, so say 0.33. [A=10 helps keep initial savings greater than initial depreciation so that the capital stock grows]

Of course you gain the ability to tweak it if you add in L labor with a growth rate (1+gl) relative to the previous period (row!). Ditto letting TFP “A” growth at (1+ga). You can start with these set to zero, but then let labor grow. But if you add L, you want to focus on Y/L not total output Y.

## Mortgage Rates

For many people, mortgage rates are the most important rates they will consider in their entire lives. Because of this, mortgage rates need to be understood and analyzed. This post delves into correlations that mortgage rates share with other interest rates and the maximum percentage of income that people should dedicate to mortgage payments. Looking at the 30 year mortgage rate graph from FRED doesn’t show much. One can see a huge spike in the rates during the early 1980’s, which can be attributed to high levels of inflation during that time. The closest comparable interest rate is the 10 year treasury rate. The rates almost perfectly match. If one compares the 30 year mortgage rate to a 1 year treasury rate, there is a much greater variance, but the general trends still remain. An important question becomes why the mortgage rate so closely follows the 10 year treasury rates. The answer comes from the average time the mortgage owner actually owns the mortgage. In other words, on average the mortgage is paid off in 10 years. For this reason, the 10 year treasury rate serves as a very accurate measure of the mortgage rate.

One of the more important facts homeowners need to know about mortgage rates is that a lower mortgage rate is better than a higher interest rate. This comes from the monthly payment the homeowner would pay. A lower interest rate means there is less interest to pay to the lender, so the monthly payments are lower. Similarly, a higher interest rate means the homeowner has to pay more interest compared to lower interest rates per month. Another important decision to make on a mortgage is whether to have a fixed-rate mortgage or an adjustable mortgage rate. A fixed-rate means the interest rate remains the same throughout the term of the mortgage, while an adjustable interest rate means the interest rate changes occasionally over the term of the mortgage. What are the advantages and disadvantages of both? When should a homeowner decide to use one over the other? Fixed-rate mortgages are most effective when the mortgage rate is low, while adjustable rates may be a better decision at high mortgage rates. After all, there shouldn’t be many people happy with paying 15% interest on a mortgage for 30 years. An adjustable rate would allow that to potentially fall over the 30 years and save the homeowner a boatload of money.

People can find mortgage calculators all over the internet that allow them to quickly determine how much they would pay every month for a given house price and mortgage rate. This allows a homeowner to determine the maximum mortgage a lender would give. The general cut-off for mortgages is a monthly payment no greater than 28& of monthly income. Most lenders would feel uncomfortable lending money to potentially higher risk homeowners, especially after the Great Recession. Overall, mortgage rates play a huge role in economy and should be understood thoroughly.

## The Logic of a Tax Cut

We frequently see claims that a lower tax rate – particularly of corporate or personal income taxes – will work miracles. That is seldom the case.

First, the stated tax rates are not the realized tax rates. While on paper someone with \$500,000 in income is paying a 39.9% rate, the rate on the first \$450,000 in income is lower: even without deductions the average rate drops to 29%. With the normal array of deductions for mortgages and this and that it will be lower. Yes, as economists we look at marginal rates. But is someone in this tax position working for an hourly wage, where they can choose to put in another hour a day and thereby boost their income, but aren’t doing so because they just don’t earn enough? (Working 10-hour days and 6-day weeks gives 3000 hours a year, so they’re earning \$160 an hour before tax, \$100 an hour after income tax. [There are other taxes.] So dropping taxes to 30% so that they earn \$117 an hour will lead them to work 3200 hours??)

The example above is for individuals. If your income is high, though, you’re unlikely to be earning all of this as a wage. Everything else – dividends, gains on shares – are taxed at lower rates. Unfortunately W&L doesn’t pay me with stock options… Anyway, the ability to shield income is far greater for large corporations, many of which pay no tax at all. Cutting taxes from zero to zero provides no incentive effect.

…there’s not much room for a boom…

Second, for companies the incentive is presumably to expand their business. Cutting taxes provides a higher return on investment. So does lowering interest rates. But we’ve already performed the latter experiment many times over, we have a lot of data on how that affects business investment. The answer is that on the margin the impact is almost nil. Most businesses have a hurdle rate of return that they use, one that surveys show is infrequently adjusted. The bottom line, robust across work in different time periods and different countries with several different methodologies, is that expectations affect investment, but that small changes in the cost of capital from shifts in tax rates and interest rates do not.

Exploring the latter is a potential Econ 398 Capstone project.

Now relative to the recent distant past there is room for improvement. As we’ve just read, that distant past was also one of higher real and nominal growth rates. In addition, the US economy is approaching its full potential (full employment, high capacity utilization). There’s not much room for a boom.

There are tax rates that are high, particularly for power workers. Even on minimum wage you need to pay social security and medicare taxes. You may lose benefits if you go back to work, even part-time at a low wage, if you’re on disability or receive certain other benefits. That can result in an effective tax of over 100%. Those in the next administration operate in a world where they never encounter such taxes.

## Treasures vs Corporate Bonds

Treasuries and corporate bonds are two types of investments ruled by interest rates. The interest rate on corporate bonds will always be higher due to the increased risk of default. Treasuries are less likely to default because of the guaranteed safety in investing with a world power like the United States. If the country does end up in a bind, they could also just print out money to guarantee a return, whereas a corporation does not have that same ability. While Treasuries and corporate bonds will not have the same interest rate 99.99% of the time, any movements in the fed funds rate will affect both investments in the same manner.

The interest rate on a Treasury is assigned by the FOMC, and they are usually divided into three categories. Treasury Bills have the shortest maturity of less than a year and do not pay a fixed interest rate. Instead they are issued through a bidding process at a discount from par. Treasury notes have maturity between one and 10 years, and have a fixed-interest rate set by the Federal Reserve. Treasury bonds have a maturity of more than 10 years, and also have a fixed interest rate. As the interest rate rises, the price of treasuries fall consistent with other types of bonds. Because the return on these investments is so low, they’re normally seen as the safest type of investment and one of the best places to store money in order to avoid market risk.

Corporate bond rates have a higher interest rate than Treasuries, but depending on the issuer can still be seen as a safe investment. The interest rate and yield corporate bonds offer is dependent on their rating. Ratings higher than BBB can be considered investment grade and will have relatively low interest rates, with the lowest coming from any issuer with a rating of AAA (equal to that of the U.S government). Ratings lower than BB are seen as sub-investment grade and have high interest rates. Like any other bond, when interest rates fall the price of the bond will rise and vice versa. This means that corporate bonds are still subject to any fluctuation in the interest rates set by the Fed, even though they are not a direct reflection of Treasuries. Corporate bonds are inherently riskier because they do not have the guarantee of the U.S Government and will always have a higher interest rate even if the issuer has a low default risk

## What is the New Normal for U.S. Growth?

In his article, “What Is the New Normal for U.S. Growth,” John Fernald argues that the United States could plausibly see a decline in average GDP growth to a range of 1.5-1.75%, which is well below historic growth rates. He examines trends in demographics, education, and productivity to determine inputs into his calculation of expected GDP growth rate, in which GDP growth = growth in worker hours + GDP per hour. He uses the labor force growth rate, especially in relation to the overall population growth rate, to determine the growth in worker hours. Labor force growth is expected to be low due to a consistently low overall population growth rate as well as the aging of baby boomers so that they retire and leave the work force. The Congressional Budget Office predicted the labor force growth rate to be .5% per year for the next decade, so Fernald translates this to project a .5% per year growth in worker hours. To determine GDP per hour, Fernald examines past fluctuations in productivity growth. He argues that productivity growth cycles between strong and weak, or normal, periods, and thus compares the U.S.’s current low productivity growth rate to that of the last era of low productivity growth (1973-1995). If the U.S. returns to its 1973-95 pace, then GDP growth would be about 1.75%. However, Fernald also argues that it is very possible for productivity growth to be less than that of 1973-95 because educational attainment has plateaued and thus education does not contribute as much to productivity growth as it would have in the past. With this scenario, Fernald calculates GDP growth to be closer to 1.5%.

Fernald then argues that the primary reason for this relatively low expected GDP growth rate is demographics, and that a workers hours growth rate of .5% would have made growth in the 1973-95 period just as slow as the current rate. He then acknowledges that due to uncertainty about future productivity, it is very possible that his predicted rate of GDP growth underestimates actual growth, particularly if there is a new wave of productivity-improving technology as was the case during past productivity booms. Despite this possible inaccuracy, Fernald’s estimated GDP growth rate has strong implications for future economic conditions and possible policy changes. People can expect slower growth in wages, sales, and tax revenue, as well as lower interest rates. However, Fernald also argues that it is possible to improve productivity and thus improve these rates by encouraging innovation, improving infrastructure, and providing better (and possibly cheaper) education.

While this is an interesting argument, it is very oversimplified, especially when examining the role productivity plays in his equation for the GDP growth rate. He fails to discuss the effect of productivity growth, particularly technological innovation, on the growth rate of worker hours, as technology advances that replace workers’ jobs or make them more efficient could lead to a slower rate of worker hours growth. However, this improved technology taking the place of workers does not necessarily lead to slower GDP growth, as the work is still getting done. In this case, he would have underestimated the GDP growth rate. Therefore, I think he should restructure his equation for GDP growth to include a more nuanced interpretation of productivity, as well as change his argument so that demographic is not the sole determinant of the growth in worker hours.

## Long and Short Rates

1. Arbitrage. With perfect foresight and no risk premium the return one-year bond should be equal to the interest rate on a six-month bond bought today, reinvested in a six-month bond bought six months from now. (1+i1)(1+i2)=(1+yr) reflects compounding. Now rates are quoted as one-year rates, so if the six-month rate is quoted as 0.6% then the actual return is (1+x)(1+x)=1.006 so sqrt(1.006)=(1+x)=1.0029955 or 1.003. That is, half the one-year rate is a very close approximation when rates are low. So if the one year rate is 1.0082, then the implied return for the second six months is 1.0083/1.003 = 1.0052. That is, markets expect the 6-month interest rate six months from now to be 1.04%. In other words, the FOMC will continue boosting rates at a steady pace.
2. Here is what has happened since 1990 to long rates. I used the average of 20-year and 30-year bond rates, in part because there are years in which only one or the other was available. Just to check, I downloaded the excel spreadsheet as an .xml file (Excel 2004 format), imported into Stata, and regressed interest rate = constant + a*date + b*date2. That’s the trend line in the graph. (I forgot to convert the date sequence to give the proper x-axis labels. The series starts Jan 2, 1990 and runs to yesterday.)
3. I also calculated the implied yield on long bonds, using the same approach as in (1) above, by comparing the yields on 7 year bonds and 10 year bonds, and 20 year bonds versus 30 year bonds. That graph shows that markets have built in somewhat higher yields.
• Is it sensible that over the next 30 years inflation will never top 2%? In other words, if I were to factor in a risk premium, what would change?
• Back out from that what markets “believe” growth will be 20-odd years from now.
• What questions does that raise? (Many, I trust!)

## Winter 2017 Syllabus

TuTh 11:50am-1:15pm

Early-Fielding 200

under construction (duh!)

## Winter 2017 Capstone TuTh 11:50am-1:15pm

“Long” Treasuries yield a scant 2.6% over 30 years. Basic theory suggests this should should equal expected growth rate plus inflation. If a rise in the CPI of 2% per annum is the Fed’s target, then do investors really expect that to never be attained? or attained but with real growth bouncing around at 1% pa? Now we can – will! – poke around with data using FRED, and refine this query. Then we can link it to a simple growth model. That will lead to a set of topics revolving around productivity, aging, and saving for the future. Out of those can come a wide array of research topics for a capstone project.

This course will have several components. One is to do a research paper on a topic tied to the course theme. (I can consider other topics, if you can present a compelling case.) That will require you to explore the literature on a topic, and present what is known and what we economists would like to know.

A second component is to explore data. How is the US economy doing? Criteria, metrics, evaluation … learning how to locate data and set forth a concise, coherent argument is another part of what we will do. For that I will assign topics for blogs and class presentations.

Third, we will have policy proposals for you to critique. If you but scour the news you should find plenty.

The latter part of the term will evolve to incorporate your paper topics. Early on we will read a couple papers, particularly Robert Gordon and then several on technology; review the basic growth model, and explore the concept of “demographic dividend(s)” in the context of the US economy and countries such as India and China.

draft of Oct 28, 2016

Note: I have left material from previous capstones “up” but this term will be very different in content and approach.

## Monday’s paper

Clements, Benedict, Kamil Dybczak, Victor Gaspar, Sanjeev Gupta, and Mauricio Soto. 2015. “The Fiscal Consequences of Shrinking Populations.” SDN/15/21. International Monetary Fund.

1. What is “fiscal sustainability”? They provide a very specific approach.

2. How do they use “solow”?

3. What is the “demographic dividend”?

## Social Security and Retirement

We will continue our discussion of intergenerational transfers and overlapping generations issues. To make it concrete, we’ll look at the US Social Security programs.

1. FAQs: http://ssa.gov/oact/ProgData/fundFAQ.html#&a0=-1
2. Current SS system stats: http://ssa.gov/pubs/EN-05-10003.pdf
3. Summary of program and issues: http://ssa.gov/OACT/TRSUM/tr15summary.pdf
4. The full Trustees Report: http://ssa.gov/OACT/TR/2015/tr2015.pdf
5. Wikipedia: See in particular for the history of the system: https://en.wikipedia.org/wiki/Social_Security_(United_States)

## Fertility by Educational Attainment

A report by the Census Bureau titled, Fertility of Women in the United States: 2012 describes the characteristics of mothers by variables such as race, location, and age. The factor that this post will focus on is educational attainment.

One measure that the report uses is completed fertility for women aged 40-50. Since most women are done having children by around 40, this table shows how many children a typical woman has had in her lifetime. This data is separated by education cohort. (I can’t figure out how to insert excel graphs into the post. So refer to table 2 on the pdf linked at the bottom) The table shows that as education increases, births per 1,000 women decreases. When you transform the data to births per woman, you can see that women with no high school diploma have on average 0.9 more children than women with professional or graduate degrees.

…fertility affects future growth…

Another interesting chart is figure three. For each five year age range starting at 15, the graph shows how birth rates change with education. For women under 30 years old, those with a high school diploma or less have much higher birth rates than the other levels. However,  once you pass age 30, women with Bachelor’s degrees have the highest fertility rates.

Thus, women with little education tend to have more children and have them earlier in life compared to those with more education.

Census Report

## Youth (Non)employment

As a followup to our class conversation on summer jobs on Friday, here’s a link to an item on “What happened to summer jobs?” on the Forbes Modeled Behavior site.

## A Brief Overview of Bergeaud et al.’s Paper

This paper attempts to:

1. compare GDP per capita level and growth across 17 advanced countries over 1890-2013.
2. compare the level and growth of the main components (TFP, capital intensity, working time, and employment rate) of GDP per capita in order to see how they contribute to the GDP per capita difference.
3. test the convergence hypothesis of GDP per capita and its components over different sub-periods.

The second half of this paper focuses on convergence. This is the hypothesis that economies with lower per capita income will tend to grow faster than the ones with higher per capita income. There are mainly 3 types of convergence: absolute convergence, conditional convergence, and club convergence. One of the two approaches to convergence is sigma-convergence. It refers to the reduction of dispersion of levels of income across economies with time.

Through data presentation and analysis, it yields the following results:

• All countries have at least one huge growth in GDP per capita in the 20th century, but in a staggered manner.
• Almost all countries have faced a huge decline in GDP per capita growth.
• The GDP per capita leadership shifted over years.
• Overall convergence among advanced countries.
• GDP per capita convergence to the leadership position is not always happening.
• Employment rates and hours worked did not contribute to the overall convergence process.

My observation:

The paper claims that its analysis’ originality is that “it is presented over a long period, on a large set of countries, with data reconstituted in purchasing power parity and on the basis of, as much as possible, consistent assumptions.” However, most of the results it yields are simple observations such as “all countries experienced at least one big wave of GDP per capita growth during the 20th Century, but in a staggered manner” and “all most all countries have suffered, during the last decades of the period, from a huge decline in GDP per capita growth.” I think the paper could develop more into the implications of these observations. Also, since this is a time-series analysis, endogeneity and dual causality might present and I think the paper should address a bit more on that. For example, the paper talks about the impact of institutions on the components of GDP per capita. Is it possible that those components shape the institutions as well?

## Dynamic Scoring

I post expanded notes from my weekly radio show at Autos and Economics on blogspot.com. This week I was asked to comment on Trump’s tax proposals. That’s a moving target, so I shifted my focus to another theme of the Republican candidates: tax cuts will pay for themselves.

1. Can you add graphs on what has happened to our structural budget deficit after previous tax cuts? – for example, those under Reagan, Bush Jr and Obama (yes, he passed a big cut as part of the ARRA, the American Recovery and Reinvestment Act of 2009).
2. Similarly, can you set up a spreadsheet of base GDP growth versus a hypothetical tax-accelerated GDP growth rate [pick a non-trivial increment, say a bump from 2.5% to 3.0%, a 20 percent boost, greater in magnitude than the tax cut]. Do a net present value calculation of taxes!
• under the base plan (at say 20%) and
• those under the revised level (say 18%, or a 10 percent cut)?
• Now that faster growth won’t be immediate, if it’s a supply-side effect, right? So put in a delay, maybe a phase-in over 4 years.
3. How long does it take for the combination of faster growth and lower taxes to generate more revenue than under the base case?
4. How robust are those results to modest changes?
• if we add a demand-side effect, 3% growth from the start, how does it change our results?
• what growth is needed for net present value to be equal (at say a 3% discount rate to reflect the low rates anticipated in current long-term bond yields)

So far I’ve not tried doing this, so I suspect what we’ll find, but don’t know the result.

## Consumer Price Index

An index is used to compare economic data, typically price or quantity against a base value. Specifically, the Consumer Price Index is used to measure changes in prices of a bundle of goods and services over different periods of time for consumers. It covers a variety of goods and services that the BLS consolidated into 8 groups. These groups are food and beverages, housing, apparel, transportation, medical care, recreation, education and communication, and other goods and services. It can be used to measure inflation through change in consumption. The CPI can somewhat be used to measure cost-of-living but does not include governmental or environmental factors and so cannot be viewed as a complete cost-of-living index.

## Capstone Topic

My topic of interest is import-substitution. Governments in developing economies sometimes try to protect developing industries by taxing or disallowing importation of the good or service produced by this industry. Most literature says that open trade policies are most beneficial to helping an economy grow. But, I would ideally like to try and find two countries with similar economies and social climates just with different protectionist policies.

Papers of interest:

A Reconsideration of Import Substitution
By: Henry J. Bruton
Import Substitution and Export-led Growth: A study of Taiwan’s Petrochemical Industry
By: Wan-Wen Chu
Comparing technical efficiency between import-substitution-oriented and export-oriented foreign firms in a developing economy
By: Tain-jy Chen and De-piao Tang

## Capstone paper topics

My paper topic idea is to look at the intersection of Stolper-Samuelson and the benefits of international trade for US workers. Essentially if unskilled workers are the scare factor in Stolper-Samuelson then their wages should have gone down and they would be worse off. Evidence from the past few decades confirms that in labor markets composed mainly of manufacturing industries that compete with China wages have gone down (Autor, Dorn, and Hanson). However, there’s also evidence that trade, mainly with China, has reduced the prices of goods that comprise the majority of lower class’ budget, and that this decrease in prices has actually made them better off than before (Broda and Romalis) . It’s unclear if the effect of lower wages or lower prices is larger. Essentially I am interested in looking at the effects of Chinese trade (and international trade) on inequality in the US.

For alternate ideas, Professor Anderson says I can use his Indian data for a project, but I am still unfamiliar with it and don’t have any ideas for what I would do with it. It would make doing 399 much more feasible. I am open to other ideas on macro policies and international development.

Autor, Dorn, and Hanson-http://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.103.6.2121

Broda and Romalis-http://www.etsg.org/ETSG2008/Papers/Romalis.pdf

Dani Rodrik blog post on the idea-http://rodrik.typepad.com/dani_rodriks_weblog/2008/06/stolper-samuelson-for-the-real-world.html

## Paper Topics

My idea is to look at the studies of the Great Depression in the 1930s and the U.S. subprime mortgage crisis in 2008 since the decades before both events are similar (both with an increase in liquidity, low inflation rate, etc.). Nordic countries happened to outperformed most other Western countries during the 1930s, I want to investigate the reasons behind it, and try to see if these countries performed differently in 2008. I could also look into the Nordic crisis in 1980s instead of the financial crisis and compare the labor policy to identify the key reason why the Nordic crisis happened.

Related Studies:
Mayes, “Did Recent Experience of a Financial Crisis Help in Coping with the Current Financial Turmoil?”
Peicuti, “The Great Depression and the Great Recession.”
Grytten, “Why Was the Great Depression Not So Great in the Nordic Countries?”

As an alternative choice, I could look into the relationship between export diversification and monetary policies. To be more specific, how do Brazil and Finland (or China) differ in monetary policies in a specific era and how does that contribute to the export diversification and economic performance?

Related Studies:
Whalley and Medianu, “The Deepening China-Brazil Economic Relationship.”
Jawadi, Mallick, and Sousa, “Nonlinear Monetary Policy Reaction Functions in Large Emerging Economies.”
Naude and Rossouw, “Export Diversification and Economic Performance.”

## Possible Paper Topics

My first choice for a paper topic is the relationship between FDI and trade. I want to see if increases in FDI will lead to an increase in trade between the countries involved, a reduction in trade, or no change.  It will be interesting to see how FDI and trade respond to each other since they are two of the most important ways that nations can interact with each other in the global economy. If one reduces the other, it may cause policy makers to reevaluate their economic policies. Also, since many developing nations aggressively court FDI, the relationship between FDI and trade could have a large impact on how they grow.

One paper by Joshua Aizenman and Ilan Noy suggests that FDI’s relationship with trade depends on the type of FDI.  Horizontal FDI occurs when foreign companies “jump trade barriers by replicating similar plants in different markets.” This happens when foreign firms feel that it will be more efficient to replicate the entire production process in a foreign nation instead of one part of it. Conversely, vertical FDI is when a firm decides to locate one stage of the production process in a foreign nation. The authors believe that horizontal FDI is a substitute for trade while vertical FDI is a complement. They also note that horizontal trade is more common between developed nations while vertical FDI is more common when one of the nations is developed and the other is developing. Thus, for developing nations, FDI usually leads to trade.

Another paper by Bruce Blonigen states that the relationship between FDI and trade depends on what types of products are exported. His data has product level trade and FDI information for Japanese 10 digit HS products in the United States. Blonigen finds that FDI outflows from Japan to the United States increased exports of related intermediate goods, but decreased exports of related final goods.

One alternate topic that I could research is how a country’s trade behavior differs with their largest trade partners relative to everyone else. In other words, does the top export location of a particular country get a better price than everyone else, a worse price, or no difference?

Paper Sources

Aizenman, Joshua, and Ilan Noy. “FDI and trade—Two-Way Linkages?” The Quarterly Review of Economics and Finance, Real and Financial Aspects of Financial IntegrationPapers drawn from the 3rd INFINITI conference on International Financial Integration, held at the Institute for International Integration Studies, Trinity College, Dublin, June 2005The 3rd INFINITI conference on International Financial Integration, 46, no. 3 (July 2006): 317–37. doi:10.1016/j.qref.2006.02.004.

Blonigen, Bruce A. “In Search of Substitution Between Foreign Production and Exports.” NBER Working Paper. National Bureau of Economic Research, Inc, 1999. https://ideas.repec.org/p/nbr/nberwo/7154.html.

## Shifts and movements along the aggregate production function

Robert Solow’s Paper “Technical Change and the Aggregate Production Function” details a method of distinguishing shifts of the aggregate production function from movements along it. The aggregate production function describes output as a product of labor, capital, natural resources, and other inputs. Solow returns to the function to discuss how to segregate changes in output per head due to technical changes from those caused by variations in the availability of capital per head.

After explaining his method, he uses it to analyze the US from 1909 to 1949. The result is an average increase of 1.5% in output per year over the period, and found that at the end of the forty years output per man hour had approximately doubled. While his analysis was fairly “crude,” he found that on average technical change in this period was average and that the rate at which output increased grew from 1% on average during the first two decades to 2% during the last two. In addition, when the aggregate production function is corrected for these technical changes, diminishing returns are evident.